Low leakage current modulation and common mode voltage suppression method for micro-inverters

Abstract

The application discloses a low-leakage-current modulation and common-mode voltage suppression method for a micro inverter, belongs to the technical field of electricity, and solves the problem that the control parameters of a conventional method are constant and the suppression effect is insufficient under working condition changes by realizing real-time sensing of the working condition of the micro inverter and dynamically adjusting key parameters of a fractional order sliding mode controller. Thus, adaptive matching of the control strategy and the real-time working condition is realized, the common-mode voltage suppression capability of the micro inverter in the whole working condition range is improved, the leakage current is reduced, and the stability of system operation and the power quality are ensured.

Description

Technical Field

[0001] This application relates to the field of electrical technology, and in particular to a method for low leakage current modulation and common-mode voltage suppression for micro-inverters. Background Technology

[0002] As a key interface device in distributed photovoltaic power generation systems, the leakage current caused by common-mode voltage in microinverters directly affects system safety and power quality. Traditional common-mode voltage suppression methods typically employ sliding mode control technology, using sliding surface functions and reaching laws to suppress common-mode voltage fluctuations. However, the control parameters of traditional sliding mode controllers are tuned based on fixed operating conditions. When microinverters face complex operating conditions such as sudden load changes or reactive power injection, the fixed control parameters struggle to adapt to these changes, leading to a decrease in common-mode voltage suppression effectiveness.

[0003] To address these issues, related technologies have attempted to introduce information entropy to monitor system operating status, employ fractional-order sliding mode control to improve control robustness, or utilize optimization algorithms to tune control parameters. However, information entropy is typically only used for offline analysis such as fault diagnosis and fails to effectively interact with the real-time control process; the order and reaching law parameters in fractional-order sliding mode control remain fixed values, lacking the ability to adaptively adjust to changes in operating conditions; and optimization algorithms are often used as offline tools for one-time parameter optimization, making it difficult to cope with the dynamic evolution of operating conditions.

[0004] Therefore, how to achieve adaptive matching between control parameters and real-time operating conditions during the operation of a micro-inverter, so that the control system can dynamically adjust the control strategy according to changes in operating conditions, and thus effectively suppress common-mode voltage across the entire operating range, has become a pressing technical problem that needs to be solved. Summary of the Invention

[0005] This application provides a method for low leakage current modulation and common-mode voltage suppression in micro-inverters, the technical solution of which is as follows: On one hand, a low leakage current modulation and common-mode voltage suppression method for microinverters is provided, executed by the digital signal processor of the microinverter, the method comprising: The real-time electrical quantities of the microinverter are collected, including output current and common-mode voltage. The real-time electrical quantities and the output error of the fractional-order sliding mode controller are dynamically weighted and fused to obtain the entropy calculation dynamic weight; based on the entropy calculation dynamic weight and the real-time electrical quantities, the information entropy is calculated to obtain the dynamic operating condition entropy value; The dynamic working condition entropy value and sliding mode parameter benchmark are subjected to parameter adaptive mapping to obtain fractional order adjustment amount and reaching law coefficient adjustment amount; Based on the fractional order adjustment, the approach law coefficient adjustment, and the current common-mode voltage tracking error, the sliding mode control law is calculated to generate a duty cycle correction. The duty cycle correction is then superimposed with the basic duty cycle to generate a PWM drive signal to control the power switching of the micro-inverter.

[0006] On one hand, a computer device is provided, the computer device including one or more processors and one or more memories, the one or more memories storing at least one computer program, the computer program being loaded and executed by the one or more processors to implement the low leakage current modulation and common-mode voltage suppression method for microinverters.

[0007] On one hand, a computer-readable storage medium is provided, wherein at least one computer program is stored in the computer-readable storage medium, the computer program being loaded and executed by a processor to implement the low leakage current modulation and common-mode voltage suppression method for microinverters.

[0008] On one hand, a computer program product or computer program is provided, which includes program code stored in a computer-readable storage medium. A processor of a computer device reads the program code from the computer-readable storage medium and executes the program code, causing the computer device to perform the aforementioned low leakage current modulation and common-mode voltage suppression method for microinverters. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a flowchart of a low leakage current modulation and common-mode voltage suppression method for a micro-inverter provided in an embodiment of this application; Figure 2 This is a flowchart of another low leakage current modulation and common-mode voltage suppression method for micro-inverters provided in the embodiments of this application; Figure 3 This is a flowchart of another low leakage current modulation and common-mode voltage suppression method for micro-inverters provided in the embodiments of this application; Figure 4 This is a flowchart of another low leakage current modulation and common-mode voltage suppression method for microinverters provided in the embodiments of this application; Figure 5This is a flowchart of another low leakage current modulation and common-mode voltage suppression method for micro-inverters provided in the embodiments of this application. Detailed Implementation

[0011] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0012] In this application, the terms "first," "second," etc., are used to distinguish identical or similar items with essentially the same function. It should be understood that there is no logical or temporal dependency between "first," "second," and "nth," nor are there any restrictions on quantity or execution order.

[0013] It should be noted that the information (including but not limited to user device information, user personal information, etc.), data (including but not limited to data used for analysis, data stored, data displayed, etc.) and signals involved in this application are all authorized by the user or fully authorized by all parties, and the collection, use and processing of related data must comply with the relevant laws, regulations and standards of the relevant countries and regions.

[0014] In microinverters, conventional common-mode voltage suppression methods use constant sliding mode control parameters, which are difficult to adapt to changes in operating conditions such as sudden load changes or reactive power injection, resulting in insufficient common-mode voltage suppression. Existing technologies attempt to introduce information entropy, fractional-order sliding mode control, or optimization algorithms, but information entropy fails to fully interact with real-time control, fractional-order parameters lack adaptability, and optimization algorithms are mostly non-real-time optimizations, all of which cannot achieve real-time matching between control parameters and real-time operating conditions.

[0015] To address this, this application proposes a low leakage current modulation and common-mode voltage suppression method for microinverters, executed by the microinverter's digital signal processor. See [link to relevant documentation] Figure 1 The method includes: 101. Collect the real-time electrical quantities of the microinverter, including output current and common-mode voltage.

[0016] 102. Dynamically weight the real-time electrical quantities and the output error of the fractional-order sliding mode controller to obtain the dynamic weight for entropy calculation.

[0017] 103. Based on the entropy calculation of dynamic weights and real-time electrical quantities, information entropy is calculated to obtain the dynamic operating condition entropy value.

[0018] 104. Perform adaptive parameter mapping on the dynamic working condition entropy value and sliding mode parameter benchmark to obtain the fractional order adjustment amount and the approach law coefficient adjustment amount.

[0019] 105. Based on the fractional order adjustment, the approach law coefficient adjustment, and the current common-mode voltage tracking error, the sliding mode control law is calculated to generate the duty cycle correction. The duty cycle correction is then superimposed with the basic duty cycle to generate a PWM drive signal to control the power switching of the micro-inverter.

[0020] For ease of understanding, the following explains some key terms in this embodiment: A microinverter is a power electronic device that converts direct current (DC) to alternating current (AC). It is commonly used in distributed photovoltaic (PV) power generation systems, and its operating status directly affects the power quality of the power grid.

[0021] A digital signal processor is a microprocessor dedicated to digital signal processing, which in this method is responsible for executing control algorithms and data processing tasks.

[0022] Real-time electrical quantities refer to electrical parameters acquired in real time by sensors during the operation of a microinverter, such as output current and common-mode voltage. These parameters reflect the instantaneous operating status of the system.

[0023] Common-mode voltage refers to the voltage between the output terminal of a micro-inverter and ground. Fluctuations in common-mode voltage can lead to leakage current, affecting system safety and electromagnetic compatibility.

[0024] Fractional sliding mode controllers are nonlinear controllers based on fractional calculus theory. They are characterized by the introduction of fractional order, which provides control characteristics and robustness.

[0025] Dynamic operating condition entropy is a quantitative indicator that measures the complexity or uncertainty of the current operating conditions of a micro-inverter. Its value reflects the degree of change in operating conditions.

[0026] Sliding mode parameter references refer to the preset control parameter reference values ​​of fractional-order sliding mode controllers under standard or ideal operating conditions, including fractional-order order reference values ​​and reaching law coefficient reference values.

[0027] The fractional order adjustment and the approach law coefficient adjustment are parameter increments or decrements obtained by adaptively correcting the sliding mode parameter reference based on the dynamic operating condition entropy value, and are used to dynamically adjust the performance of the controller.

[0028] Sliding mode control law calculation refers to the process of calculating the controller's output command based on sliding mode control theory, combined with the current system state and adjusted control parameters, in order to control the system state.

[0029] A PWM drive signal is a signal that controls the on-time of a power switch by adjusting the pulse width, and is used to control the output power and waveform of a micro inverter.

[0030] This embodiment provides a method for low leakage current modulation and common-mode voltage suppression in microinverters. Specifically, the method includes the following steps: Real-time electrical quantities of the microinverter are acquired, including output current and common-mode voltage. For example, analog signals can be directly input to a digital signal processor for sampling by connecting a conventional current transformer and a conventional voltage transformer to the output of the microinverter to obtain initial current and voltage data. This initial data is considered as the real-time electrical quantities, including output current and common-mode voltage.

[0031] Dynamic weighting is applied to real-time electrical quantities and the output error of the fractional-mode sliding mode controller to obtain the dynamic weights for entropy calculation. For example, real-time electrical quantities (such as the instantaneous values ​​of output current and common-mode voltage) can be linearly weighted and summed with the current common-mode voltage tracking error of the fractional-mode sliding mode controller. The weighting coefficients can be preset to constant values; for example, the weight of real-time electrical quantities is 0.7, and the weight of output error is 0.3. This yields an initial fusion result, which serves as the dynamic weight for entropy calculation.

[0032] Furthermore, information entropy is calculated based on the dynamic weights calculated from entropy and real-time electrical quantities to obtain the dynamic operating condition entropy value. For example, the output current and common-mode voltage in real-time electrical quantities can be divided into amplitude intervals, and their frequency of occurrence in each interval can be statistically analyzed. Then, based on these frequency distributions, their respective entropy values ​​are calculated using the Shannon entropy formula. The dynamic weights for entropy calculation can be used as a multiplication factor, directly applied to these calculated entropy values, and then the corrected entropy values ​​are summed to obtain the dynamic operating condition entropy value.

[0033] Furthermore, an adaptive mapping is performed on the dynamic operating condition entropy value and the sliding mode parameter reference to obtain the fractional-order adjustment and the reaching law coefficient adjustment. For example, a mapping table can be pre-established, which divides the dynamic operating condition entropy value into several levels, each level corresponding to a set of constant fractional-order adjustment and reaching law coefficient adjustment. After calculating the dynamic operating condition entropy value, its corresponding level is found, and the adjustment value corresponding to that level is directly obtained. The sliding mode parameter reference is then added to or subtracted from these adjustment values ​​to obtain the final adjustment.

[0034] The sliding mode control law is calculated based on the fractional-order adjustment, the reaching law coefficient adjustment, and the current common-mode voltage tracking error to generate a duty cycle correction. This correction is then superimposed on the base duty cycle to generate a PWM drive signal, which controls the power switch of the microinverter. For example, the fractional-order adjustment and the reaching law coefficient adjustment can be directly substituted into a pre-defined sliding mode control law equation. This equation can be a linear combination; for instance, the duty cycle correction equals a constant multiplied by the current common-mode voltage tracking error, plus another constant multiplied by the sign function of the sliding surface function, where the constant term is influenced by the adjustment. The calculated duty cycle correction is algebraically superimposed on the base duty cycle to form the PWM drive signal, which is sent to the power switch of the microinverter to adjust its on / off state.

[0035] This method addresses the limitations of conventional methods, such as constant control parameters and insufficient suppression performance under varying operating conditions, by real-time sensing of the microinverter's operating conditions and dynamic adjustment of key parameters of the fractional-mode sliding controller. This achieves adaptive matching between the control strategy and real-time operating conditions, improving the microinverter's common-mode voltage suppression capability across the entire operating range, reducing leakage current, and ensuring system stability and power quality.

[0036] In some embodiments described above in this application, real-time electrical quantities are collected to provide control input. However, during implementation, the directly collected waveforms may contain high-frequency noise and interference, affecting the accuracy of subsequent dynamic weight fusion and information entropy calculation. Furthermore, the lack of extraction of common-mode voltage spectrum characteristics results in the inability to fully capture the dynamic changes in system operating conditions, thereby reducing the effectiveness of fractional-order sliding mode control in suppressing leakage current and common-mode voltage.

[0037] To address this, this application further proposes a method for acquiring real-time electrical quantities of the microinverter. The method includes: synchronously acquiring the three-phase current at the output terminal of the microinverter and the DC bus positive and negative terminal voltages to ground using voltage and current sensors to obtain initial current waveforms and initial common-mode voltage waveforms. The initial current waveform and the initial common-mode voltage waveform are then subjected to low-pass filtering to obtain the output current and the pre-processed common-mode voltage. The pre-processed common-mode voltage is then subjected to spectral analysis to obtain common-mode spectral characteristics. The output current, the pre-processed common-mode voltage, and the common-mode spectral characteristics are collectively used as the real-time electrical quantity.

[0038] Specifically, the three-phase current at the output of the microinverter and the DC bus positive and negative voltages to ground are synchronously acquired using voltage and current sensors to obtain initial current waveforms and initial common-mode voltage waveforms. This aims to acquire raw electrical information about the microinverter's operating status, providing foundational data for subsequent control algorithms. Synchronous acquisition ensures the time correspondence between different electrical quantities, avoiding phase errors or data inconsistencies caused by asynchronous sampling. For example, high-precision, high-sampling-rate Hall current sensors and isolated voltage sensors can be used, with a unified sampling clock or hardware triggering mechanism to ensure simultaneous data capture of the three-phase current and DC bus positive and negative voltages to ground. Alternatively, a multi-channel synchronous data acquisition card can be used, simultaneously inputting the analog output signals of the voltage and current sensors to different channels of the acquisition card, and then performing unified analog-to-digital conversion by the card's internal synchronous sampling module to obtain synchronized digital sampling data.

[0039] The initial current waveform and the initial common-mode voltage waveform are low-pass filtered to obtain the output current and the pre-processed common-mode voltage. The purpose is to eliminate potential high-frequency noise and transient interference in the original acquired signal, extract the effective components of the signal, and improve the accuracy and robustness of subsequent data processing and control algorithms. For example, IIR (Infinite Impulse Response) filters such as digital Butterworth filters or Chebyshev filters can be used. By selecting appropriate cutoff frequencies and orders, the acquired initial current waveform and initial common-mode voltage waveform can be filtered in real time within a digital signal processor. Alternatively, FIR (Finite Impulse Response) filters, such as moving average filters or FIR filters designed using the window function method, can be used to perform weighted averaging of the data through a sliding window to smooth the signal and suppress high-frequency noise.

[0040] Spectral analysis of the preprocessed common-mode voltage is performed to obtain its common-mode spectral characteristics. This aims to reveal the frequency components and distribution of the common-mode voltage, thereby gaining a deeper understanding of its generation mechanism and fluctuation patterns, and providing a basis for more refined operating condition identification and control strategy adjustment. For example, the Fast Fourier Transform (FFT) algorithm can be used to decompose the preprocessed common-mode voltage signal within a certain time window, obtaining the amplitude and phase information of different frequency components, and extracting the main frequency components, harmonic content, or energy distribution of specific frequency bands as common-mode spectral characteristics. Alternatively, time-frequency analysis methods such as wavelet transform or short-time Fourier transform (STFT) can be used to analyze the common-mode voltage signal simultaneously in the time and frequency domains to capture its dynamic spectral characteristics, such as the changing trends of specific frequency components over time, and use these as common-mode spectral characteristics.

[0041] The output current, the preprocessed common-mode voltage, and the common-mode spectral characteristics are collectively used as the real-time electrical quantity. The aim is to integrate multi-dimensional and multi-level electrical information to form a comprehensive set of real-time electrical quantities reflecting the operating status of the micro-inverter. This provides richer and more accurate inputs for subsequent dynamic weight fusion and information entropy calculation, thereby improving the adaptive capability and suppression effect of the control system. For example, in a digital signal processor, the filtered output current data, the preprocessed common-mode voltage data, and the common-mode spectral characteristics obtained through spectral analysis are encapsulated into a unified data structure or vector and periodically updated and passed to subsequent control modules. Alternatively, a multi-dimensional feature space can be established, using the instantaneous value of the output current, the instantaneous value of the preprocessed common-mode voltage, and common-mode spectral characteristics (such as the main frequency amplitude and harmonic distortion rate) as different dimensions of this feature space to collectively constitute the real-time electrical quantity, facilitating subsequent identification of complex operating conditions and adaptive parameter mapping.

[0042] The above technical solution utilizes voltage and current sensors to synchronously acquire the three-phase current at the output of the micro-inverter and the DC bus positive and negative voltages to ground. This ensures precise temporal alignment of the original electrical quantities, avoiding errors caused by asynchronous sampling and laying a reliable foundation for subsequent data processing. Low-pass filtering of the initial current and common-mode voltage waveforms effectively removes high-frequency noise and transient interference, resulting in purer and more accurate output current and pre-processed common-mode voltage. This improves the input data quality for subsequent dynamic weight fusion and information entropy calculation. Furthermore, spectral analysis of the pre-processed common-mode voltage allows for in-depth analysis of its frequency components and fluctuation patterns, revealing its common-mode spectral characteristics. This enables the system to not only perceive the instantaneous amplitude of the common-mode voltage but also understand its inherent dynamic changes, significantly enriching the understanding of the micro-inverter's operating conditions. By combining the output current, pre-processed common-mode voltage, and common-mode spectral characteristics as real-time electrical quantities, multi-dimensional information from both the time and frequency domains is integrated, providing the fractional sliding mode controller with comprehensive, accurate, and insightful operating condition inputs. This enhances the controller's adaptability to complex operating conditions, enabling it to more effectively suppress leakage current and common-mode voltage.

[0043] In some of the solutions described above in this application, a dynamic weight fusion of real-time electrical quantities and the output error of a fractional-order sliding mode controller is proposed to obtain dynamic weights for entropy calculation, which are used to adapt to changes in operating conditions and improve control accuracy. However, in this process, due to the lack of fine extraction of current and common-mode voltage characteristics and a real-time feedback mechanism for control effectiveness, the dynamic weight fusion may not accurately capture the dynamic evolution of the system state, resulting in insufficiently adaptive and robust fused weights, which in turn affects the accuracy of subsequent information entropy calculation and parameter adjustment.

[0044] To address this, this application further proposes a method for dynamically weighting and fusing real-time electrical quantities and the output error of a fractional-order sliding mode controller to obtain dynamic weights for entropy calculation. (See [link to relevant documentation]). Figure 2 The specific steps include: 201. Perform time-frequency domain transformation on the output current in real-time electrical quantities to extract the current waveform complexity features, and perform fluctuation amplitude statistics on the common-mode voltage in real-time electrical quantities to extract the common-mode voltage fluctuation severity features.

[0045] 202. Construct current operating condition entropy components based on current waveform complexity characteristics, and construct common mode operating condition entropy components based on common mode voltage fluctuation severity characteristics.

[0046] 203. Obtain the output error of the fractional sliding mode controller, which includes the current common-mode voltage tracking error and the sliding mode chattering intensity. Then, comprehensively evaluate the current common-mode voltage tracking error and the sliding mode chattering intensity to obtain the control performance degradation degree.

[0047] 204. Generate a first modulation coefficient for the current entropy component and a second modulation coefficient for the common-mode entropy component based on the control performance degradation degree. Couple the first modulation coefficient with the current entropy component and the second modulation coefficient with the common-mode entropy component to obtain the current entropy and common-mode entropy corrected by control performance feedback.

[0048] 205. Input the current operating condition entropy and common mode operating condition entropy corrected by control performance feedback into the nonlinear fusion network. The nonlinear fusion network dynamically adjusts the fusion weights based on the degree of control performance degradation and outputs the entropy to calculate the dynamic weights.

[0049] This study involves performing a time-frequency domain transformation on the output current in real-time electrical quantities to extract current waveform complexity features. The aim is to extract deeper information reflecting the complexity of the micro-inverter's operating conditions from the original output current signal, such as harmonic content, transient impacts, and noise levels. This information is crucial for accurately assessing the system state. This time-frequency domain transformation can employ wavelet transform. By selecting different wavelet basis functions and decomposition levels, the current signal is decomposed into different frequency scales, and then the energy distribution or entropy value at each scale is analyzed to characterize the complexity. Alternatively, the Hilbert-Huang transform can be used. Empirical mode decomposition (EMD) decomposes the signal into a series of intrinsic mode functions (IMFs), and then a Hilbert transform is performed on these IMFs to obtain the instantaneous frequency and amplitude of the signal, thereby calculating the complexity features.

[0050] This study statistically analyzes the fluctuation amplitude of common-mode voltage in real-time electrical quantities to extract the characteristics of common-mode voltage fluctuation severity. The aim is to capture transient changes and disturbance intensity of common-mode voltage, which may indicate internal system anomalies or external interference. This analysis is directly significant for evaluating common-mode voltage suppression effectiveness and potential leakage current risks. The fluctuation amplitude statistics can calculate the peak-to-peak value of the common-mode voltage within a preset time window, i.e., the difference between the maximum and minimum values, directly reflecting the fluctuation range. Alternatively, it can calculate the variance or standard deviation of the common-mode voltage within a preset time window, quantifying its dispersion relative to the mean and reflecting the severity of the fluctuation.

[0051] The purpose of constructing current condition entropy components based on current waveform complexity features is to unify complex current characteristic information into a physically meaningful metric, facilitating subsequent fusion and decision-making, and providing an indicator to quantify the degree of "chaos" in the current operating condition. This construction process can directly use current waveform complexity features (such as wavelet packet energy entropy, spectral entropy, etc.) as current condition entropy components. Alternatively, multiple extracted current complexity sub-features (such as harmonic distortion rate, transient impact number, noise power, etc.) can be fused through nonlinear mapping functions (such as the Sigmoid function, Gaussian radial basis function, etc.) or fuzzy logic systems to generate a comprehensive current condition entropy component.

[0052] This study constructs common-mode operating condition entropy components based on the severity characteristics of common-mode voltage fluctuations. The aim is to unify common-mode voltage fluctuation information into a physically meaningful metric, facilitating subsequent fusion and decision-making, and providing an indicator to quantify the current degree of common-mode voltage "disturbance." This construction process maps common-mode voltage fluctuation severity characteristics (such as peak-to-peak value and variance) to entropy values ​​between 0 and 1 using a pre-defined nonlinear function (such as an exponential or logarithmic function), serving as the common-mode operating condition entropy components. Alternatively, the common-mode voltage fluctuation severity characteristics can be divided into intervals, their distribution frequency at different fluctuation levels can be statistically analyzed, and then the common-mode operating condition entropy components can be calculated based on the Shannon entropy formula.

[0053] The output error of the fractional-mode sliding mode controller, including the current common-mode voltage tracking error and the sliding mode chattering intensity, is obtained to monitor the controller's operating status and performance in real time. By acquiring these key error indicators, the effectiveness of the current control strategy can be evaluated, providing a basis for subsequent adaptive adjustments. The current common-mode voltage tracking error can be obtained by directly measuring the actual common-mode voltage and comparing it with a set reference value. The sliding mode chattering intensity can be quantified by analyzing the high-frequency components of the sign function term in the sliding mode control law or by calculating the spectral energy distribution of the control output signal.

[0054] A comprehensive evaluation of the current common-mode voltage tracking error and sliding mode chattering intensity is conducted to obtain the control performance degradation degree, aiming to provide a unified and quantitative indicator to reflect the overall health of the control system. This indicator can guide subsequent parameter adjustments and ensure timely intervention when control performance deteriorates. This comprehensive evaluation can be performed using a weighted summation method, multiplying the absolute value of the current common-mode voltage tracking error and the sliding mode chattering intensity by preset weights and then summing the results to obtain the control performance degradation degree. Alternatively, a fuzzy logic inference system can be used, taking the tracking error and chattering intensity as inputs, and inferring using fuzzy rules and membership functions to output a fuzzy control performance degradation degree level, which is then defuzzified into a specific numerical value.

[0055] The system generates a first modulation coefficient for the current-mode entropy component and a second modulation coefficient for the common-mode entropy component based on the control performance degradation. This aims to dynamically adjust the importance of different entropy components in subsequent fusion based on the current performance of the control system. When control performance deteriorates, the modulation coefficients can enhance or weaken the influence of specific entropy components, thereby guiding the system to make more effective parameter adjustments. This generation process can be achieved by designing a nonlinear mapping function (such as a sigmoid function or exponential function), taking the control performance degradation as input, and outputting the first and second modulation coefficients. Alternatively, a lookup table method can be used, retrieving the corresponding modulation coefficient from a pre-defined lookup table based on the interval in which the control performance degradation occurs.

[0056] By coupling the first modulation coefficient with the current-mode entropy component and the second modulation coefficient with the common-mode entropy component, we obtain the current-mode entropy and common-mode entropy corrected by control performance feedback. This aims to integrate the real-time performance feedback of the control system into the characterization of the entropy. Through this coupling, the entropy not only reflects the complexity of the original electrical quantities but also the effectiveness of the current control strategy in handling these complexities, making the entropy value more instructive. The most direct coupling method is multiplication, where the corrected entropy component equals the modulation coefficient multiplied by the original entropy component. Alternatively, a weighted average method can be used; for example, the corrected entropy component equals (1 minus the modulation coefficient) multiplied by the original entropy component plus the modulation coefficient multiplied by the desired entropy component.

[0057] The current operating condition entropy and common-mode operating condition entropy, corrected by control performance feedback, are input into a nonlinear fusion network. This network dynamically adjusts the fusion weights based on the control performance degradation and outputs a dynamic weight calculated from the entropy. The aim is to intelligently fuse the two corrected operating condition entropy components to generate a unified, dynamically adaptive entropy weight. This process considers the current performance status of the control system, ensuring that the fused weight accurately guides subsequent adaptive parameter mapping. This nonlinear fusion network can employ a feedforward neural network, using the corrected current operating condition entropy, common-mode operating condition entropy, and control performance degradation as inputs. It then performs nonlinear mapping through a multilayer perceptron and activation functions, outputting the dynamic weight calculated from the entropy. Alternatively, a fuzzy neural network or an adaptive neurofuzzy inference system can be used. The input variables are fuzzified, inference is performed using fuzzy rules, and the self-learning capability of the neural network is utilized to adjust the fuzzy rules and membership functions, thereby achieving dynamic weight fusion.

[0058] Through the above technical solutions, this application performs time-frequency domain transformation on the output current in real-time electrical quantities to extract the complexity features of the current waveform, and performs fluctuation amplitude statistics on the common-mode voltage to extract the severity features of the common-mode voltage fluctuation, thus achieving refined perception of the operating conditions of the micro-inverter. Based on these refined features, current operating condition entropy components and common-mode operating condition entropy components are constructed, which can more accurately quantify the uncertainty and complexity of the current and common-mode voltage states, providing high-quality input for subsequent dynamic weight fusion. Simultaneously, by acquiring the output error of the fractional-order sliding mode controller, including the current common-mode voltage tracking error and the sliding mode chattering intensity, and comprehensively evaluating them to obtain the control performance degradation degree, this application introduces a real-time feedback mechanism for the control system performance. Based on this degradation degree, a first modulation coefficient for the current operating condition entropy component and a second modulation coefficient for the common-mode operating condition entropy component are generated, and these are coupled with the corresponding entropy components to obtain the current operating condition entropy and common-mode operating condition entropy corrected by control performance feedback. This feedback correction mechanism ensures that the representation of operating condition entropy not only reflects the characteristics of the original electrical quantities but also incorporates the current performance status of the controller, guaranteeing the sensitivity and guidance of operating condition entropy to the control system state. These feedback-corrected entropy components are input into a nonlinear fusion network, which dynamically adjusts the fusion weights based on the degree of control performance degradation, outputting dynamic weights for entropy calculation. This process enables the fusion weights to adaptively adjust according to the complexity of the actual operating conditions of the micro-inverter and the real-time changes in the control system performance, overcoming the limitations of fixed weights or simple linear fusion in traditional methods. Through this refined feature extraction, real-time performance feedback, and intelligent nonlinear fusion, this application can generate more accurate and adaptive dynamic weights for entropy calculation, thus providing a reliable basis for subsequent information entropy calculation and sliding mode parameter adaptive mapping. This improves the robustness and effectiveness of low leakage current modulation and common-mode voltage suppression of the micro-inverter under complex and variable operating conditions, effectively avoiding the problem of control performance degradation caused by changes in operating conditions.

[0059] In some of the solutions described above in this application, time-frequency domain transformation is used to extract the complexity features of the current waveform, and fluctuation amplitude statistics of the common-mode voltage are used to extract the severity features of the common-mode voltage fluctuation, in order to construct the current operating condition entropy component and the common-mode operating condition entropy component. However, in the implementation process, traditional feature extraction methods may not be able to fully capture the complex dynamic changes of the current waveform and the multidimensional and severe characteristics of the common-mode voltage fluctuation, resulting in insufficient accuracy in the calculation of the entropy component, which in turn affects the accuracy of subsequent dynamic weight fusion and the adaptive capability of the control system.

[0060] To address this, this application further proposes performing time-frequency domain transformation on the output current of real-time electrical quantities to extract current waveform complexity features, and statistically analyzing the fluctuation amplitude of common-mode voltage in real-time electrical quantities to extract common-mode voltage fluctuation severity features. Specifically, this includes: performing wavelet packet decomposition on the output current of the real-time electrical quantity to obtain wavelet packet coefficients for multiple frequency bands; determining the energy value of each frequency band wavelet packet coefficient and normalizing the energy value to obtain an energy distribution vector; calculating the information entropy based on this energy distribution vector to obtain the current waveform complexity feature; performing sliding window sampling on the common-mode voltage of the real-time electrical quantity to obtain the common-mode voltage sequence within the current window; determining the peak-to-peak value and variance of the common-mode voltage sequence to obtain a first fluctuation amplitude sub-feature and a second fluctuation amplitude sub-feature; and weightedly fusing the first and second fluctuation amplitude sub-features to obtain the common-mode voltage fluctuation severity feature.

[0061] The wavelet packet decomposition of the output current in this real-time electrical quantity, yielding wavelet packet coefficients for multiple frequency bands, refers to multi-scale, multi-resolution frequency domain analysis of the output current signal using wavelet packet transform. Wavelet packet decomposition can further decompose both low-frequency and high-frequency components of the signal, providing a finer frequency band division than traditional wavelet decomposition. This allows for comprehensive capture of complex dynamic changes in the current signal, such as harmonics and transient impulses. In practical applications, different wavelet basis functions can be selected, such as Daubechies wavelet, Symlets wavelet, or Coiflets wavelet, and an appropriate number of decomposition levels can be set according to signal characteristics and analysis requirements to obtain wavelet packet coefficients for different frequency bands. For example, a 3-level decomposition using the Daubechies 4 wavelet basis can be used to balance computational efficiency and feature capture capability. Alternatively, a 4-level decomposition using the Symlets 8 wavelet basis can be used to capture more subtle transient changes.

[0062] Determining the energy values ​​of wavelet packet coefficients for each frequency band and normalizing them to obtain an energy distribution vector involves calculating the signal energy within each frequency band after obtaining the wavelet packet coefficients. Energy value is an indicator of signal strength within a specific frequency band, quantifying the contribution of different frequency components to the complexity of the current waveform. Normalizing these energy values ​​aims to eliminate the absolute differences in energy magnitude across different frequency bands, mapping them to a unified scale to form an energy distribution vector with probabilistic distribution characteristics, ensuring comparability in subsequent information entropy calculations. The energy value can be calculated as the square root of the sum of squares of the wavelet packet coefficients for each frequency band, or simply as the sum of squares. Normalization can be performed using L1 norm normalization, dividing the energy value of each frequency band by the sum of all frequency band energy values, so that the sum of the elements of the energy distribution vector is 1. Alternatively, maximum value normalization can be used, scaling all energy values ​​to between 0 and 1.

[0063] The information entropy calculation based on the energy distribution vector yields the complexity characteristics of the current waveform. This involves using information entropy theory to calculate the normalized energy distribution vector. Information entropy is an indicator that measures the uncertainty or randomness of information; here, it is used to quantify the complexity of the current waveform's energy distribution across different frequency bands. A higher entropy value indicates a more uniform energy distribution across frequency bands, resulting in a more complex and uncertain current waveform. Conversely, a lower entropy value indicates that energy is concentrated in a few frequency bands, leading to a relatively simple waveform. This provides a quantitative indicator to characterize the complexity of the current waveform. The calculation method can employ the Shannon entropy formula, H = -Σ(pi × log2(pi)), where pi is each element in the energy distribution vector. Alternatively, generalized entropy forms such as Renyi entropy or Tsallis entropy can be considered to accommodate different complexity measurement needs.

[0064] Sliding window sampling of the common-mode voltage in this real-time electrical quantity to obtain the common-mode voltage sequence within the current window refers to using the sliding window technique to extract local data from the common-mode voltage time-series signal. Sliding window sampling acquires a series of local data segments by moving a fixed-size window across the time series with a fixed step size. This allows for real-time and dynamic capture of the local fluctuation characteristics of the common-mode voltage, avoiding the computational burden of analyzing the entire historical data and promptly reflecting fluctuations under current operating conditions. A fixed-length sampling window can be set, for example, containing 100 sampling points, and sliding across the common-mode voltage time-series signal with a small step size, such as 50 sampling points, acquiring a new common-mode voltage sequence with each slide. Alternatively, an adaptive window size can be used, dynamically adjusting the window length according to the rate of change of the common-mode voltage to better capture fluctuations at different time scales.

[0065] Determining the peak-to-peak value and variance of the common-mode voltage sequence, and obtaining the first and second fluctuation amplitude sub-features, refers to calculating the peak-to-peak value and variance after acquiring the common-mode voltage sequence within the current window. The peak-to-peak value is the difference between the maximum and minimum values ​​of the signal, directly reflecting the extreme degree of common-mode voltage fluctuation, i.e., the maximum fluctuation amplitude. Variance is a statistical measure of data dispersion, reflecting the average strength or stability of signal fluctuations, providing a statistical measure of fluctuation severity. Combining both allows for a comprehensive characterization of the fluctuation severity of common-mode voltage from different dimensions, overcoming the limitations of a single indicator. The peak-to-peak value can be obtained by finding the maximum and minimum values ​​within the sampling window and calculating their difference. The variance can be obtained by averaging the squares of the differences between all sampling points within the window and the average value.

[0066] The common-mode voltage fluctuation severity feature is obtained by weighted fusion of the first and second fluctuation amplitude sub-features. This involves weighting the peak-to-peak value and variance, two complementary sub-features. By weighted fusion of these two sub-features, a more comprehensive and robust common-mode voltage fluctuation severity feature can be generated, avoiding the limitations of a single indicator and allowing adjustment of the contribution of different sub-features according to actual needs. A linear weighted fusion can be used, i.e., severity feature = w1 × peak-to-peak value + w2 × variance, where w1 and w2 are weight coefficients, and w1 + w2 = 1. The weight coefficients can be preset based on expert experience; for example, increasing the weight of the peak-to-peak value when focusing on extreme fluctuations. Alternatively, the optimal weights can be learned from historical data using machine learning methods (such as regression analysis).

[0067] Through the above technical solutions, this application can more accurately capture the complexity of the output current waveform and the severity of common-mode voltage fluctuations of a micro-inverter under complex operating conditions. Specifically, wavelet packet decomposition is used to perform multi-scale time-frequency analysis on the output current, which can comprehensively reveal the complex dynamic components such as harmonics and transients contained in the current signal, and quantify its complexity through energy distribution entropy, avoiding the problem of traditional methods not fully capturing complex waveform features. At the same time, by combining sliding window sampling with weighted fusion of peak-to-peak value and variance, the severity of common-mode voltage fluctuations can be evaluated in real time and in multiple dimensions, making up for the insufficiency of a single index in fully reflecting the fluctuation characteristics. These accurately extracted current waveform complexity features and common-mode voltage fluctuation severity features provide more reliable and refined inputs for the subsequent construction of current operating condition entropy components and common-mode operating condition entropy components, thereby improving the accuracy of entropy calculation. This improvement in accuracy further ensures the effectiveness of dynamic weight fusion, enabling the control system to more accurately perceive and respond to changes in operating conditions, thereby achieving more effective suppression of the common-mode voltage of the micro-inverter and improving the adaptive control performance and operational stability of the system.

[0068] In some embodiments described above, this application proposes constructing current-condition entropy components and common-condition entropy components based on current waveform complexity characteristics and common-mode voltage fluctuation severity characteristics to characterize the operating conditions of a micro-inverter. However, in this process, the current waveform complexity characteristics may not fully decompose its modal characteristics, resulting in an inability to capture the inherent dynamic changes of the current waveform. Simultaneously, the common-mode voltage fluctuation severity characteristics may not effectively quantify its fluctuation distribution, leading to an inability to accurately reflect the real-time evolution pattern of the common-mode voltage. These shortcomings prevent the entropy components from accurately characterizing the dynamic uncertainties of the operating conditions, thereby affecting the accuracy of subsequent dynamic weight fusion and control parameter adjustment.

[0069] To address this, this application further proposes a method for constructing current operating condition entropy components based on current waveform complexity characteristics and common-mode voltage fluctuation severity characteristics. Specifically, this includes: performing modal decomposition on the current waveform complexity characteristics to obtain multiple intrinsic mode function (IMF) components; extracting the instantaneous amplitude and frequency of each IMF component to form an amplitude-frequency feature vector set; matching the amplitude-frequency feature vector set with a typical operating mode library to obtain the mode membership vector of the micro-inverter's current operating condition; calculating the information entropy of the mode membership vector to obtain the current operating condition entropy component; dividing the common-mode voltage fluctuation severity characteristics into amplitude intervals to obtain multiple fluctuation amplitude levels; statistically analyzing the frequency of the common-mode voltage falling into each fluctuation amplitude level within a preset time window to form a fluctuation level distribution vector; and inputting the fluctuation level distribution vector into a preset entropy value mapping function, which, after nonlinear transformation, outputs the common-mode operating condition entropy component.

[0070] This approach involves mode decomposition of the complex characteristics of current waveforms to obtain multiple intrinsic mode function (IMF) components. The aim is to decompose complex current waveform signals into a series of simpler intrinsic oscillation modes with specific physical meanings. This helps reveal the hidden dynamic characteristics and multi-scale structures within the signal. For example, Empirical Mode Decomposition (EMD) or its improved algorithms (such as Ensemble Empirical Mode Decomposition (EEMD)) can be used to adaptively decompose the signal into a series of IMFs, each IMF representing an oscillation component of the signal at different time scales. Alternatively, Variational Mode Decomposition (VMD) can be employed, solving an optimization problem to decompose the signal into several mode components with compact spectra.

[0071] The instantaneous amplitude and frequency of each intrinsic mode function (IMF) component are extracted to form an amplitude-frequency eigenvector set. The purpose is to quantify the energy and frequency changes of each IMF over time. The instantaneous amplitude reflects the energy intensity of the mode, while the instantaneous frequency characterizes the oscillation velocity of the mode. For example, a Hilbert-Huang transform (HHT) can be applied to each IMF to obtain its analytic signal, from which the instantaneous amplitude and frequency can be calculated. Alternatively, time-frequency analysis methods such as short-time Fourier transform (STFT) or wavelet transform can be used to extract the amplitude and frequency information of each modal component at different time points and frequency scales.

[0072] The amplitude-frequency feature vector set is matched with a typical operating mode library to obtain the modal membership vector of the microinverter's current operating condition. This vector serves to assess the similarity or degree of affiliation between the extracted amplitude-frequency features and various predefined typical operating mode patterns. The typical operating mode library can contain amplitude-frequency feature samples collected and processed under different load, illumination, or grid conditions. The matching process can be achieved by calculating the distance (e.g., Euclidean distance, Mahalanobis distance) between the current amplitude-frequency feature vector set and each typical mode in the library, or by training classifiers such as Support Vector Machine (SVM) or K-Nearest Neighbors (KNN), thereby obtaining the membership degree of the current operating condition to each typical mode.

[0073] Information entropy is calculated from the modal membership vector to obtain the current condition entropy component. The purpose is to quantify the distribution uncertainty of the current condition across different typical operating modes. Information entropy is an indicator of the uncertainty of a random variable. The more uniform the distribution of the modal membership vector, meaning the more difficult it is to definitively classify the current condition into a specific typical mode, the larger the information entropy value, indicating higher complexity and uncertainty of the operating condition. For example, the Shannon entropy formula can be used to calculate the normalized modal membership vector to obtain the current condition entropy component.

[0074] The amplitude range of common-mode voltage fluctuation severity characteristics is divided into multiple fluctuation amplitude levels. The purpose is to discretize the continuous common-mode voltage fluctuation severity characteristics to facilitate statistical analysis of their distribution characteristics. This is achieved by dividing the range of fluctuation severity characteristics into several non-overlapping intervals, each interval representing a fluctuation amplitude level. For example, equal-width intervals can be used to divide the entire fluctuation range into several levels on an average basis. Alternatively, equal-frequency intervals can be used to ensure that each level contains approximately the same number of sample points.

[0075] The frequency of common-mode voltage falling into each fluctuation amplitude level within a preset time window is statistically analyzed to form a fluctuation level distribution vector. Its function is to capture the temporal distribution pattern of common-mode voltage fluctuations at different amplitude levels. By monitoring the real-time value of the common-mode voltage within a sliding time window and recording the number of times it falls into each fluctuation amplitude level, a frequency distribution vector reflecting the fluctuation pattern is formed. For example, a fixed-length sliding window can be set, and the frequency statistics for each level are updated whenever a new common-mode voltage data point enters the window.

[0076] The fluctuation level distribution vector is input into a preset entropy mapping function, and after nonlinear transformation, the common-mode operating condition entropy component is output. The purpose is to transform the fluctuation level distribution of common-mode voltage into an entropy value that can quantify its uncertainty and complexity. The preset entropy mapping function can be a nonlinear function, such as the sigmoid function, logarithmic function, or polynomial function, which maps the characteristics of the fluctuation level distribution vector (e.g., uniformity, dispersion, etc.) to a physically meaningful entropy value. For example, this mapping function can calculate the Shannon entropy of the fluctuation level distribution vector and then perform a nonlinear transformation on this entropy value to better reflect the dynamic characteristics of common-mode voltage operation.

[0077] Through the above technical solution, this application can more accurately construct the current operating condition entropy component and the common-mode operating condition entropy component, overcoming the problems of inaccurate and incomplete operating condition characterization in traditional methods. This refined operating condition characterization capability enables the subsequent dynamic weight fusion process to more accurately assess the importance of different operating condition characteristics, thereby providing a more reliable basis for the adaptive adjustment of parameters of the fractional-order sliding mode controller, improving the accuracy and robustness of common-mode voltage suppression of micro-inverters under complex and variable operating conditions, and effectively reducing leakage current.

[0078] In some embodiments described above in this application, a modulation coefficient is generated based on the degree of control performance degradation to provide feedback correction for current operating condition entropy and common-mode operating condition entropy, thereby achieving dynamic weight fusion. However, in its implementation, if the evaluation of the degree of control performance degradation relies solely on the current instantaneous value while ignoring historical trends, it may lead to inaccurate weight allocation, failing to effectively capture long-term deviations and instabilities in the dynamic evolution of operating conditions, thus reducing the accuracy and robustness of adaptive adjustment.

[0079] To address this, this application further proposes a comprehensive evaluation of the current common-mode voltage tracking error and the sliding mode chattering intensity to obtain the control performance degradation degree, comprising the following steps: integrating the absolute value of the current common-mode voltage tracking error to obtain the cumulative error; extracting the high-frequency components of the sliding mode chattering intensity to obtain the chattering high-frequency energy ratio; calculating the first deviation and the second deviation from their respective preset expected thresholds based on the cumulative error and the chattering high-frequency energy ratio; acquiring the first deviation sequence and the second deviation sequence at multiple moments within a historical time window, and generating a first dynamic weight and a second dynamic weight based on the changing trends of the first deviation sequence and the second deviation sequence; multiplying the first deviation by the first dynamic weight and the second deviation by the second dynamic weight, and summing the multiplication results to obtain the control performance degradation degree.

[0080] Specifically, the absolute value of the current common-mode voltage tracking error is integrated to obtain the accumulated error. This step aims to quantify the degree of accumulation of the common-mode voltage tracking error over a period of time, reflecting the long-term deviation of the system's control performance. This can be achieved by performing continuous or discrete absolute value integration on the error signal within a preset time window, such as using trapezoidal integration or rectangular integration to sum the sampled points. Alternatively, an exponentially weighted moving average can be used to smooth the absolute value of the error to reflect the recent trend of error accumulation.

[0081] Simultaneously, high-frequency components of the chattering intensity are extracted to obtain the high-frequency energy proportion of the chattering. This step is used to identify and quantify the inherent high-frequency chattering phenomenon in sliding mode control and evaluate its impact on system performance. One approach is to perform spectral analysis on the sliding mode chattering signal using Fast Fourier Transform (FFT) or Short-Time Fourier Transform (STFT) and then calculate the proportion of energy in a specific high-frequency band to the total energy. Another approach is to use wavelet transform to decompose the chattering signal into different frequency scales and extract the energy of the high-frequency wavelet coefficients to obtain the high-frequency energy proportion of the chattering.

[0082] Based on this, and using the accumulated error and the proportion of high-frequency jitter energy, a first deviation and a second deviation are calculated from their respective preset expected thresholds. This step aims to quantify the degree of deviation by comparing the actually measured performance indicators with ideal or acceptable performance levels. For example, the first deviation can be obtained by calculating the absolute difference or ratio between the accumulated error and the preset error threshold. Similarly, the second deviation can be obtained by calculating the difference or ratio between the proportion of high-frequency jitter energy and the preset jitter threshold. These thresholds can be set according to system design requirements or empirical data.

[0083] To more comprehensively evaluate control effectiveness, a first deviation sequence and a second deviation sequence are obtained at multiple points within a historical time window. Based on the changing trends of these first and second deviation sequences, first and second dynamic weights are generated. This step introduces a time dimension, capturing the dynamic evolution of performance deviation by analyzing historical data. For example, methods such as moving averages, exponential smoothing, or linear regression can be used to analyze the trend of the deviation sequence. When the deviation shows a continuous deterioration trend, the corresponding dynamic weight increases. Conversely, when the deviation shows an improvement trend, the dynamic weight decreases. Furthermore, machine learning algorithms, such as support vector machines or neural networks, can be used to perform pattern recognition on the historical sequences, thereby generating more refined dynamic weights.

[0084] The first deviation is multiplied by the first dynamic weight, and the second deviation is multiplied by the second dynamic weight. The results are then summed to obtain the control performance degradation degree. This step weights and fuses the deviations of the two key performance indicators with their respective dynamic weights to form a comprehensive control performance degradation index. This weighted summation method ensures that when assessing the overall system degradation, both the current deviation and the importance of historical trends to the current assessment are considered, allowing the degradation degree to more accurately and sensitively reflect the true state of system performance.

[0085] Through the above technical solution, this application comprehensively evaluates the current common-mode voltage tracking error and sliding mode chattering intensity, and incorporates historical trends to generate a control performance degradation degree, thus solving the problem of insufficient accuracy caused by ignoring long-term dynamics in weight fusion. The absolute value of the current common-mode voltage tracking error is integrated to obtain the cumulative error, which quantifies the long-term cumulative deviation of the error and avoids the persistence problem that may be ignored by relying solely on instantaneous values. High-frequency components are extracted from the sliding mode chattering intensity to obtain the chattering high-frequency energy ratio. This focuses on high-frequency components to capture control instability and ensures that the evaluation covers the rapid changing characteristics of chattering. Based on the cumulative error and the chattering high-frequency energy ratio, the first deviation and the second deviation from the preset expected threshold are calculated respectively. This quantifies the degree of deviation between the error and chattering by comparing the actual value with the ideal threshold, providing a benchmark for subsequent weight adjustment. Then, the first deviation sequence and the second deviation sequence at multiple moments within the historical time window are obtained, which introduces time-dimensional data to capture the evolution of the deviation. Based on the sequence change trend, a first dynamic weight and a second dynamic weight are generated. These dynamically assign different importance to recent trends, enabling the weights to adapt to gradual changes in operating conditions. Multiplying the first deviation by the first dynamic weight and the second deviation by the second dynamic weight, and then summing the results, yields the control performance degradation degree. This is then used to generate a comprehensive index through weighted fusion, ensuring that the degradation degree assessment reflects both the current state and historical trends, thus improving overall adaptability. This more accurate and comprehensive control performance degradation degree can serve as a control variable for subsequent nonlinear fusion network dynamic adjustment of fusion weights (as described in claim 3 above). This allows the entropy-calculated dynamic weights to more accurately reflect the operating state of the micro-inverter under complex conditions, thereby improving the adaptability and robustness of the entire low leakage current modulation and common-mode voltage suppression method.

[0086] In some of the embodiments described above in this application, modulation coefficients are generated based on the degree of control performance degradation to adjust the current condition entropy and the common mode condition entropy. However, in the implementation process, the generation of modulation coefficients lacks adaptive consideration of transient changes in current condition and long-term trends in common mode condition, which leads to the inability of the degree of control performance degradation to effectively distinguish and respond to the dynamic evolution of real-time condition, affecting the accuracy of subsequent entropy calculation of dynamic weights and the robustness of the control system.

[0087] In response, this application further proposes a method for generating a first modulation coefficient for the current operating condition entropy component and a second modulation coefficient for the common-mode operating condition entropy component, specifically including: Orthogonal decomposition was performed on the control performance degradation to extract a first degradation factor strongly correlated with common-mode voltage tracking error and a second degradation factor strongly correlated with sliding mode chattering intensity. Control performance degradation is a comprehensive indicator measuring the degree of performance decline in a micro-inverter control system, which can be caused by various factors, such as excessive common-mode voltage tracking error or excessive sliding mode chattering intensity. To more accurately identify and respond to these different degradation sources, this application employs orthogonal decomposition technology. Orthogonal decomposition is a mathematical method that aims to transform interrelated variables into a set of independent variables (i.e., orthogonal components), thereby separating the independent contributions of different degradation factors to the control performance degradation. For example, multivariate statistical methods such as principal component analysis (PCA) or independent component analysis (ICA) can be used to process historical data on control performance degradation and its components (such as common-mode voltage tracking error and sliding mode chattering intensity) to extract the first degradation factor mainly reflecting the influence of common-mode voltage tracking error and the second degradation factor mainly reflecting the influence of sliding mode chattering intensity. Another approach is to construct an orthogonal projection matrix based on experience or model knowledge, projecting the degree of control performance degradation onto a predefined orthogonal basis to separate components that are strongly correlated with specific degradation modes.

[0088] The rate of change of the current entropy component at the current moment is determined to obtain the transient fluctuation of the current entropy. The current entropy component characterizes the complexity and uncertainty of the micro-inverter's output current waveform and is an important indicator reflecting the current operating condition. During micro-inverter operation, factors such as load abrupt changes and grid disturbances can cause rapid changes in the current condition. These transient changes place higher demands on the response speed and stability of the control system. Therefore, it is necessary to determine the rate of change of the current entropy component at the current moment to quantify this transient fluctuation. For example, the instantaneous rate of change can be obtained by calculating the difference between the current entropy component at the current moment and the current entropy component at the previous sampling moment, and dividing by the sampling time interval. Alternatively, methods such as Kalman filtering or sliding window linear regression can be used to smooth and differentiate the time series of the current entropy component, thereby more robustly estimating its transient fluctuation.

[0089] The first degradation factor is nonlinearly coupled with the transient fluctuation of the current entropy to generate the first modulation coefficient, which adaptively adjusts according to the transient changes in the current condition. The first modulation coefficient aims to dynamically adjust the current condition entropy component based on the degree of degradation strongly correlated with common-mode voltage tracking error in control effectiveness and the transient changes in the current condition. Nonlinear coupling refers to combining two or more input variables through a nonlinear function to produce an output variable. This combination method can better capture the complex interactions between variables. For example, a nonlinear mapping relationship based on the Sigmoid or Tanh function can be designed, using the first degradation factor and the transient fluctuation of the current entropy as inputs, and outputting the first modulation coefficient. This allows the first modulation coefficient to increase when the first degradation factor is large (i.e., the common-mode voltage tracking error is severe) and the transient fluctuation of the current entropy is intense, thereby enhancing the modulation strength of the current condition entropy component. Another implementation method is to construct a polynomial function or radial basis function network, and achieve nonlinear coupling by learning the relationship between the first degradation factor, the transient fluctuation of the current entropy, and the desired modulation coefficient from historical data.

[0090] The statistical mean of the common-mode entropy component within a preset historical window is calculated to obtain the steady-state benchmark value of the common-mode entropy. The common-mode entropy component reflects the complexity and uncertainty of the common-mode voltage of the micro-inverter. Unlike the transient changes in current conditions, the long-term trend and steady-state characteristics of the common-mode voltage are more important for evaluating the overall stability of the system. To avoid excessive influence of short-term disturbances on the common-mode operating condition assessment, this application obtains the steady-state benchmark value of the common-mode entropy by calculating the statistical mean of the common-mode entropy component within a preset historical window. The preset historical window can be a fixed-length time period, such as the past 10 seconds or 100 sampling periods. The statistical mean can be achieved using a simple arithmetic mean method, i.e., summing all common-mode entropy components within the window and dividing by the window length. Alternatively, methods such as exponentially weighted moving average (EWMA) can be used to assign different weights to historical data, making recent data have a greater impact on the mean, thereby better reflecting the recent steady-state trend of the common-mode operating condition.

[0091] The second degradation factor is nonlinearly coupled to the common-mode entropy steady-state reference value to generate the second modulation coefficient, which adaptively adjusts according to the long-term trend of the common-mode operating condition. The second modulation coefficient aims to dynamically adjust the common-mode entropy component based on the degree of degradation strongly correlated with the sliding mode chattering intensity in control effectiveness and the long-term steady-state trend of the common-mode operating condition. Similar to the first modulation coefficient, a nonlinear coupling method is also used to generate the second modulation coefficient to capture the complex relationship between the second degradation factor and the common-mode entropy steady-state reference value. For example, a nonlinear coupler in the form of an exponential or logarithmic function can be designed so that when the second degradation factor is large (i.e., severe sliding mode chattering) and the common-mode entropy steady-state reference value is high (i.e., long-term instability of the common-mode operating condition), the second modulation coefficient can be increased accordingly to enhance the modulation effect on the common-mode entropy component. Another implementation method is to use a fuzzy logic system or lookup table to dynamically look up or infer the corresponding second modulation coefficient based on different combinations of the second degradation factor and the common-mode entropy steady-state reference value.

[0092] Through the above technical solution, this application decomposes the control performance degradation degree orthogonally, decoupling the complex control degradation problem into a first degradation factor strongly correlated with common-mode voltage tracking error and a second degradation factor strongly correlated with sliding mode chattering intensity, thereby achieving accurate identification of different degradation sources. Based on this, for the transient characteristics of current operating conditions, the transient fluctuation of current entropy is obtained by determining the rate of change of the current operating condition entropy component at the current moment, effectively capturing the rapid dynamic changes of current operating conditions. The first degradation factor and the transient fluctuation of current entropy are nonlinearly coupled, and the resulting first modulation coefficient can adaptively adjust according to the transient changes of current operating conditions, ensuring that the modulation of the current operating condition entropy component can respond promptly and be enhanced when the micro-inverter faces transient conditions such as load surges, thereby improving the system's adaptability and robustness in dynamic environments. Simultaneously, for the long-term trend of common-mode operating conditions, this application calculates the statistical mean of the common-mode operating condition entropy component within a preset historical window to obtain the common-mode entropy steady-state benchmark value, effectively filtering out the influence of short-term disturbances and accurately reflecting the long-term stability of common-mode operating conditions. By nonlinearly coupling the second degradation factor with the common-mode entropy steady-state reference value, the generated second modulation coefficient can adaptively adjust according to the long-term trend of common-mode operation. This allows for continuous optimization of the modulation of the common-mode entropy component even under conditions of long-term common-mode voltage fluctuations or persistent chattering, thereby improving the control accuracy and stability of the system under steady-state operation. This refined modulation coefficient generation mechanism enables the subsequent entropy calculation dynamic weights to more accurately reflect the real-time operating conditions of the micro-inverter, thereby optimizing the parameter adaptive mapping and sliding mode control law solution of the fractional-order sliding mode controller, effectively suppressing the common-mode voltage and leakage current of the micro-inverter, and improving the overall performance and reliability of the system.

[0093] In some of the embodiments described above in this application, dynamic weight fusion is proposed to generate entropy and calculate dynamic weights. However, in its implementation, the adjustment of fusion weights may lack an adaptive mechanism and cannot dynamically select and optimize fusion rules based on the degree of control performance degradation, resulting in an unintelligent fusion process that affects control accuracy and stability.

[0094] To address this, this application further proposes inputting the current operating condition entropy corrected by control performance feedback and the common mode operating condition entropy corrected by control performance feedback into a nonlinear fusion network. The nonlinear fusion network dynamically adjusts the fusion weights based on the control performance degradation and outputs the entropy to calculate the dynamic weights. Specifically, this includes: The nonlinear fusion network uses the current operating condition entropy corrected by control performance feedback and the common mode operating condition entropy corrected by control performance feedback as the dual-channel inputs to be fused, and uses the control performance degradation degree as the control variable of the fusion rule.

[0095] The nonlinear fusion network divides the control performance degradation into intervals and dynamically calls the corresponding fusion rules from the fusion rule base according to the interval in which the control performance degradation is located. The fusion rule base includes complementary fusion rules, competitive fusion rules, and enhancement fusion rules.

[0096] Based on the invoked fusion rules, the nonlinear fusion network interactively maps the current condition entropy and the common mode condition entropy to generate the self-suppression coefficient of the current condition entropy and the self-enhancement coefficient of the common mode condition entropy during the fusion process.

[0097] The nonlinear fusion network multiplies the self-suppression coefficient by the current condition entropy and the self-enhancement coefficient by the common mode condition entropy, and aggregates the multiplication results to obtain the dynamic weight of the entropy calculation.

[0098] This nonlinear fusion network is a computational model capable of processing multi-source heterogeneous information and achieving deep information fusion through nonlinear mapping and learning mechanisms. It can capture complex nonlinear relationships between input data and dynamically adjust the fusion strategy according to specific objectives. Its implementation can employ feedforward neural network structures such as multilayer perceptrons (MLPs) or radial basis function (RBF) networks, introducing nonlinearity through activation functions and learning complex mapping relationships between inputs and outputs through training. Alternatively, fuzzy neural networks or adaptive neurofuzzy inference systems (ANFIS) can be used. These systems combine the reasoning capabilities of fuzzy logic with the learning capabilities of neural networks, enabling better handling of uncertainty and fuzzy information and achieving adaptive adjustment of rules.

[0099] The current operating condition entropy and the common-mode operating condition entropy, both corrected by control performance feedback, serve as dual-channel inputs to be fused, representing two pre-processed and corrected key operating condition information streams received by the nonlinear fusion network. These information streams already contain feedback on the control system performance, enabling the fusion process to be based on more accurate and instructive inputs. These two input channels can be independent numerical signals, directly input to the network's input layer, where the network processes the information through different weighted connections. Alternatively, these two input channels can undergo preliminary feature engineering, such as normalization, standardization, or simple combination operations, before being input into the nonlinear fusion network to optimize the network's learning efficiency and fusion effect.

[0100] The control performance degradation degree, as a control variable in the fusion rule, refers to a parameter used to adjust or influence the behavior of other variables during system operation. Here, the control performance degradation degree is an indicator that quantifies the degree of performance degradation of the current control system. Its role is to serve as the basis for adjusting the fusion strategy in the nonlinear fusion network, enabling the fusion process to adaptively adjust according to the actual operating state of the control system. When the control performance degradation degree is high, a more aggressive or conservative fusion strategy may be needed. When the degradation degree is low, a more stable strategy may be adopted. The control performance degradation degree can be directly used as an additional input to the nonlinear fusion network, affecting the network's internal weights or activation function parameters, thereby indirectly controlling the fusion rule. Alternatively, a separate decision module can be used to select or adjust specific subnetworks or parameter sets in the nonlinear fusion network based on the control performance degradation degree, achieving explicit control of the fusion rule.

[0101] Dividing the control performance degradation into intervals aims to discretize continuous degradation values ​​into different intervals, simplifying decision-making logic and allowing for the matching of specific fusion strategies to each interval. This enables the system to take different countermeasures based on the severity of degradation. Equal-width interval division can be used, dividing the degradation range into several equal intervals, for example, dividing 0-100% degradation into "low degradation (0-30%)", "medium degradation (30-70%)", and "high degradation (70-100%)". Alternatively, non-equal-width interval division based on expert experience or data analysis can be used, setting different interval boundaries according to actual system behavior and control requirements. For example, finer divisions can be set near certain key thresholds to capture important state changes.

[0102] This fusion rule base includes complementary, competitive, and reinforcing fusion rules, providing diverse fusion strategies. This allows the nonlinear fusion network to flexibly select the most suitable fusion method for the current operating condition based on different levels of control performance degradation, thereby optimizing the generation of dynamic weights for entropy calculation. Complementary fusion rules are suitable when two input pieces of information provide useful but non-redundant information in different aspects, aiming to combine the advantages of both. Competitive fusion rules are suitable when two input pieces of information may conflict or be redundant, aiming to select the more reliable or more important information. Reinforcing fusion rules are suitable when two input pieces of information can mutually corroborate or amplify each other's effectiveness, aiming to enhance the overall information strength through synergy. Each fusion rule can be composed of a set of predefined mathematical functions or logical judgments. For example, complementary rules can be weighted averages, competitive rules can be taking the maximum or minimum value, and reinforcing rules can be products or nonlinear combinations. Fusion rules can also be pre-trained small neural network modules, each corresponding to a fusion type, with the corresponding module dynamically activated based on the degree of control performance degradation.

[0103] Interactive mapping between the current condition entropy and the common-mode condition entropy means that during the fusion process, the two input information are no longer processed independently, but rather influence and interact with each other. This allows the fusion result to better reflect the intrinsic connection and mutual constraint between the two condition entropies. This can be achieved by setting cross-connections or attention mechanisms within the nonlinear fusion network. For example, a feature of one condition entropy can be used as a modulation signal in the processing of another condition entropy, or information interaction can be achieved through shared weight layers. Alternatively, multiplicative or convolutional operations can be introduced to allow the features of the two condition entropies to generate nonlinear interactions during the fusion process, thus producing more complex fusion features.

[0104] The self-suppression coefficient and the self-enhancing coefficient of the common-mode entropy during the fusion process are generated. These coefficients are the concrete manifestation of dynamically adjusting the fusion weights. The self-suppression coefficient is used to reduce or weaken the contribution of a certain input information to the fusion result, while the self-enhancing coefficient is used to increase or amplify the contribution of a certain input information to the fusion result. By generating the self-suppression and self-enhancing coefficients, the nonlinear fusion network can selectively adjust the proportions of the current condition entropy and the common-mode entropy in the dynamic weights of entropy calculation according to the current operating condition and the degree of control performance degradation, achieving refined adaptive fusion. These coefficients can be dynamically calculated through sub-networks or activation functions within the nonlinear fusion network, with inputs including the degree of control performance degradation and the characteristics of the two condition entropies. They can also be generated through lookup tables or fuzzy logic-based reasoning mechanisms.

[0105] Multiplying the self-suppression coefficient by the current condition entropy and the self-enhancement coefficient by the common-mode condition entropy, and then aggregating the results, is the process of applying the dynamically adjusted fusion weights (self-suppression / self-enhancement coefficients) to the two condition entropies. The multiplication operation directly adjusts the contribution intensity of each condition entropy, and then the aggregation (e.g., summation) yields the dynamic weights for entropy calculation. The most common aggregation operation is a simple addition summation, where the two weighted condition entropies are directly added together. More complex aggregation functions can also be used, such as nonlinear weighted summation, or aggregation can be performed through another small neural network to introduce additional nonlinearity and further optimize the fusion effect.

[0106] The above technical solution addresses the problem that existing dynamic weight fusion methods, when calculating dynamic weights through entropy generation, may lack an adaptive mechanism for adjusting fusion weights. This makes it impossible to dynamically select and optimize fusion rules based on the degree of control performance degradation, resulting in an unintelligent fusion process that affects control accuracy and stability. This application introduces a nonlinear fusion network and uses the degree of control performance degradation as the control variable for the fusion rules, achieving dynamic adaptive adjustment of fusion weights. Specifically, the nonlinear fusion network receives current condition entropy and common-mode condition entropy corrected by control performance feedback as dual-channel inputs. These inputs already contain feedback information about the control system performance. Simultaneously, the degree of control performance degradation is used as a key control variable to guide the fusion process. The nonlinear fusion network divides the degree of control performance degradation into intervals and dynamically calls the most suitable fusion rule (such as complementary, competitive, or reinforcing) from a preset fusion rule library based on the degree of degradation. Based on the called rule, the network interactively maps the current condition entropy and common-mode condition entropy to generate targeted self-suppression and self-reinforcing coefficients. These coefficients precisely reflect the relative proportions of the two operating condition entropies in the dynamic weights under the current control performance. Multiplying these coefficients by the corresponding operating condition entropies and aggregating them yields a highly adaptive dynamic weight for entropy calculation. This dynamic adaptive fusion mechanism, compared to the aforementioned basic scheme of dynamic weight fusion using real-time electrical quantities and fractional-order sliding mode controller output errors, improves the accuracy and real-time performance of the entropy calculation dynamic weights. By deeply integrating control performance degradation into the fusion decision, it ensures that the entropy calculation dynamic weights can more sensitively reflect the actual operating state of the micro-inverter and the performance of the control system under complex operating conditions. For example, when the control system experiences chattering or increased tracking error (high degradation), the fusion network can dynamically adjust its strategy, potentially increasing attention to the entropy of a specific operating condition or suppressing interference from the entropy of another operating condition, thereby generating more instructive dynamic weights. This makes subsequent information entropy calculation and sliding mode parameter adaptive mapping based on these dynamic weights more accurate, improving the common-mode voltage suppression effect and system stability of the micro-inverter across the entire operating range, and effectively reducing leakage current.

[0107] In some of the embodiments described above in this application, it is proposed to calculate information entropy based on entropy calculation of dynamic weights and real-time electrical quantities to obtain dynamic operating condition entropy values ​​for evaluating the uncertainty of system operating conditions. However, in its implementation process, due to the lack of sufficient consideration of the time-domain dynamic characteristics of the output current and the periodic fluctuation characteristics of the common-mode voltage, the calculation of dynamic operating condition entropy values ​​may be inaccurate and unable to accurately reflect the actual operating condition changes, thereby affecting the control effect of subsequent parameter adaptive mapping.

[0108] To address this, this application further proposes a step-by-step approach to calculate the dynamic operating condition entropy value by using entropy to calculate dynamic weights and real-time electrical quantities. See [link to relevant documentation]. Figure 3 ,include: 301. Perform phase space reconstruction on the output current in the real-time electrical quantity to obtain the high-dimensional current trajectory matrix, and perform fluctuation period detection on the common-mode voltage in the real-time electrical quantity to obtain the common-mode period fluctuation sequence.

[0109] 302. Based on the high-dimensional trajectory matrix of the current, the distribution entropy of the neighborhood points is calculated to obtain the current state uncertainty, and based on the common-mode periodic fluctuation sequence, the periodic distribution entropy is calculated to obtain the common-mode periodic uncertainty.

[0110] 303. The entropy is used to calculate the dynamic weight, which is then decomposed into the current weight coefficient and the common-mode weight coefficient. The current weight coefficient is then dynamically corrected based on the current state uncertainty to obtain the corrected current weight.

[0111] 304. Couple the corrected current weight with the current state uncertainty to obtain the current entropy contribution value, and couple the common mode weight coefficient with the common mode period uncertainty to obtain the common mode entropy contribution value. Aggregate the current entropy contribution value and the common mode entropy contribution value to output the dynamic operating condition entropy value.

[0112] Specifically, phase space reconstruction is performed on the output current of this real-time electrical quantity to obtain a high-dimensional current trajectory matrix, aiming to reveal the hidden dynamic characteristics and complex behavior of the system. Phase space reconstruction is a technique that converts one-dimensional time series data into a high-dimensional spatial trajectory. By combining the sampled value at the current moment with the sampled values ​​at several past moments into a high-dimensional vector, the evolution trajectory of the system in phase space can be constructed. One implementation method is to use the delay embedding method. According to Takens' theorem, by selecting an appropriate embedding dimension and delay time, the output current time series signal is mapped to a high-dimensional phase space, forming a series of delay vectors, and then constructing the high-dimensional current trajectory matrix. Another implementation method is to use singular spectral analysis (SSA). By constructing the trajectory matrix and performing singular value decomposition on it, the main components are extracted to reconstruct the phase space, thereby obtaining the high-dimensional current trajectory matrix. This method can effectively separate noise and trend terms in the signal. Simultaneously, the common-mode voltage fluctuation period in this real-time electrical quantity is detected to obtain a common-mode periodic fluctuation sequence, aiming to identify and quantify the periodic or quasi-periodic components present in the common-mode voltage signal. By analyzing the repetition patterns of a signal, periodic information reflecting its fluctuation patterns can be extracted. One approach is to use the autocorrelation function method. By calculating the autocorrelation function of the common-mode voltage time series signal, the peak position can indicate the periodicity of the signal, thus obtaining a common-mode periodic fluctuation sequence. Another approach is to use Fourier transform or wavelet transform. By analyzing the spectral characteristics of the signal, the main frequency components and their corresponding periods can be identified, thereby constructing a common-mode periodic fluctuation sequence.

[0113] Based on this, the entropy of the neighborhood point distribution is calculated using the high-dimensional current trajectory matrix to obtain the current state uncertainty, which aims to measure the complexity and uncertainty of the trajectory point distribution in the high-dimensional phase space. It quantifies the randomness or regularity of the system state by analyzing the distance and distribution patterns between adjacent points in the phase space. One implementation method is to use the approximate entropy (ApEn) or sample entropy (SampEn) algorithm to evaluate the complexity and unpredictability of the high-dimensional current trajectory matrix by calculating the probability of similar patterns occurring in the phase space, thereby obtaining the current state uncertainty. Another implementation method is based on information geometry theory, which constructs a phase space manifold and calculates the geodesic distance distribution of neighboring points on the manifold to solve for the current state uncertainty. Simultaneously, the periodic distribution entropy is calculated based on the common-mode periodic fluctuation sequence to obtain the common-mode periodic uncertainty, aiming to quantify the uniformity and randomness of the periodic value distribution in the common-mode periodic fluctuation sequence, reflecting the stability or disorder of the common-mode voltage periodic fluctuations. One approach is to bin the common-mode periodic fluctuation sequence, count the frequency of each period interval, and then calculate the entropy value of the periodic distribution based on the Shannon entropy formula to obtain the common-mode periodic uncertainty. Another approach is to use generalized entropy theories such as Renyi entropy or Tsallis entropy to nonlinearly weight the probability distribution of the periodic fluctuation sequence to more flexibly characterize its uncertainty.

[0114] Furthermore, the dynamic weight of entropy calculation is decomposed into current weight coefficient and common-mode weight coefficient, aiming to allocate the overall weight to different electrical quantity dimensions for subsequent targeted modulation and fusion. The dynamic weight of entropy calculation is a comprehensive indicator of the overall uncertainty of the system's operating conditions. One implementation method is to proportionally decompose the dynamic weight of entropy calculation into current weight coefficient and common-mode weight coefficient based on a preset scaling factor or a machine learning model trained on historical data. Another implementation method is to use a fuzzy logic inference system to dynamically decompose the dynamic weight of entropy calculation into two components based on real-time operating condition characteristics (such as the relative importance of current and common-mode voltage). The current weight coefficient is dynamically corrected based on the current state uncertainty to obtain the corrected current weight. This aims to adjust the current weight coefficient according to the real-time changes in current state uncertainty to ensure that the contribution of current information in the dynamic operating condition entropy calculation adaptively reflects its reliability and importance. One implementation method is to design a nonlinear correction function that takes the current state uncertainty as input and outputs a correction factor. This correction factor is multiplied or added to the original current weight coefficient to obtain the corrected current weight. Another approach is to establish a lookup table and preset different correction values ​​based on different ranges of current state uncertainty, thereby dynamically adjusting the current weighting coefficient.

[0115] Based on this, the corrected current weight is coupled and modulated with the current state uncertainty to obtain the current entropy contribution value. The aim is to organically combine the corrected current weight and the current state uncertainty to generate a quantity that comprehensively reflects the contribution of the current dimension to the overall operating condition entropy value. One implementation method is to multiply the corrected current weight and the current state uncertainty, and further transform it through a nonlinear function (e.g., an exponential or logarithmic function) to enhance or suppress its contribution. Another implementation method is to use a polynomial function or radial basis function network, taking the corrected current weight and the current state uncertainty as input, and obtaining the current entropy contribution value through nonlinear mapping. Simultaneously, the common-mode weight coefficient is coupled and modulated with the common-mode period uncertainty to obtain the common-mode entropy contribution value. The aim is to combine the common-mode weight coefficient and the common-mode period uncertainty to quantify the contribution of the common-mode voltage dimension to the overall operating condition entropy value. One implementation method is to directly multiply the common-mode weight coefficient and the common-mode period uncertainty, and adjust it by introducing a linear or nonlinear scaling factor as needed. Another approach is to construct a fuzzy inference system, using the common-mode weighting coefficient and common-mode period uncertainty as fuzzy inputs. Through a fuzzy rule base and a defuzzification process, the system outputs the common-mode entropy contribution value. This current entropy contribution value and the common-mode entropy contribution value are then aggregated to output the dynamic operating condition entropy value. The aim is to integrate entropy contributions from different electrical quantity dimensions into a single, comprehensive dynamic operating condition entropy value that comprehensively reflects the overall uncertainty of the micro-inverter's current operating condition. One implementation method is to simply perform a weighted summation of the current entropy contribution value and the common-mode entropy contribution value, where the weights can be preset or dynamically adjusted according to the actual application scenario. Another approach is to use a machine learning model such as a neural network or support vector machine, taking the two entropy contributions as inputs, and training them to obtain a nonlinear aggregation function, outputting the dynamic operating condition entropy value.

[0116] Through the above technical solution, this application can more accurately calculate the entropy value under dynamic operating conditions, solving the problem of inaccurate entropy calculation caused by neglecting the time-domain dynamic characteristics of the output current and the periodic fluctuation characteristics of the common-mode voltage in traditional methods. Specifically, by reconstructing the phase space of the output current, its hidden dynamic characteristics can be deeply explored, transforming the one-dimensional time-series signal into a high-dimensional trajectory matrix, thereby capturing the complex change patterns of the current more comprehensively. At the same time, by detecting the fluctuation period of the common-mode voltage, its periodic fluctuation pattern can be accurately identified, avoiding entropy deviation caused by ignoring periodic characteristics. On this basis, calculating the neighborhood point distribution entropy based on the high-dimensional trajectory matrix of the current can quantify the randomness and complexity of the current state. Calculating the periodic distribution entropy based on the common-mode periodic fluctuation sequence can effectively evaluate the stability of the periodic fluctuation of the common-mode voltage. Furthermore, by dynamically decomposing the entropy calculation weights and dynamically correcting the current weight coefficients according to the uncertainty of the current state, the contribution of different electrical quantity dimensions can be adaptively adjusted according to their own real-time uncertainty, avoiding the limitations of fixed weights. By coupling and modulating the corrected current weight with the current state uncertainty and the common-mode weight coefficient with the common-mode period uncertainty, and then aggregating them to obtain the dynamic operating condition entropy value, it is ensured that this entropy value can accurately and comprehensively characterize the overall uncertainty of the micro-inverter under complex operating conditions. This provides a more accurate and reliable input for subsequent sliding mode parameter adaptive mapping, thereby improving the common-mode voltage suppression effect and system robustness of the micro-inverter across the entire operating range.

[0117] In some of the solutions mentioned above in this application, phase space reconstruction of the output current in real-time electrical quantities and fluctuation period detection of common-mode voltage are proposed to calculate the dynamic operating condition entropy value. However, in this process, improper selection of phase space reconstruction parameters may lead to distortion of the current trajectory, and fluctuation period detection may introduce noise error by relying on a single peak point, resulting in inaccurate entropy value calculation, which cannot accurately reflect the dynamic changes of the micro-inverter operating condition, thereby weakening the effectiveness of subsequent adaptive adjustment of control parameters.

[0118] To address this, this application further proposes a method for reconstructing the phase space of the output current in real-time electrical quantities to obtain a high-dimensional current trajectory matrix, and for detecting the fluctuation period of the common-mode voltage in real-time electrical quantities to obtain a common-mode periodic fluctuation sequence. The specific steps include: Extract the output current timing signal from real-time electrical quantities and determine the embedding dimension and delay time of phase space reconstruction.

[0119] Based on the embedding dimension and delay time, the output current timing signal is mapped by delay coordinates to obtain multiple delay vectors.

[0120] Multiple delay vectors are arranged in time order to construct a high-dimensional current trajectory matrix.

[0121] The common-mode voltage timing signal is extracted from the real-time electrical quantities, and peak detection is performed on the common-mode voltage timing signal to obtain multiple peak positions and multiple trough positions.

[0122] The instantaneous period value is calculated based on the time interval between adjacent peak positions, and the auxiliary period value is calculated based on the time interval between adjacent trough positions.

[0123] The instantaneous periodic value and the auxiliary periodic value are weighted and fused to obtain the common-mode periodic fluctuation sequence.

[0124] Specifically, the output current timing signal is extracted from real-time electrical quantities, and the embedding dimension and delay time of the phase space reconstruction are determined. This aims to provide high-quality raw data for subsequent phase space reconstruction and to identify key reconstruction parameters. The output current timing signal directly reflects the operating state of the microinverter, and its accurate extraction is fundamental to analyzing the system's dynamic behavior. The embedding dimension and delay time are two core parameters of phase space reconstruction, determining the geometry of the reconstructed phase space and its ability to capture the system's dynamic characteristics. For example, the mutual information method or the CC algorithm can be used to determine the optimal embedding dimension and delay time to maximize the independence of trajectory points in the reconstructed phase space and minimize redundant information. Alternatively, the False Nearest Neighbors (FNN) method can be used to determine the embedding dimension, and the autocorrelation function or average displacement method can be used to determine the delay time to ensure that the reconstructed phase space can effectively unfold the dynamic characteristics of the original signal.

[0125] Based on the embedding dimension and the delay time, the output current time-series signal is subjected to delay coordinate mapping to obtain multiple delay vectors. This is the core operation of phase space reconstruction, which transforms one-dimensional time series data into trajectory points in a high-dimensional space, thereby revealing the complex dynamic behavior hidden in the signal. By combining the original signal and its delayed copies into vectors, a phase space that reflects the evolution of the system state can be constructed. For example, delay coordinate mapping can be performed according to Takens' theorem, that is, for a time series x(t), construct a phase space vector Y(t)=[x(t), x(t+τ), ..., x(t+(m-1)τ)], where m is the embedding dimension and τ is the delay time. Alternatively, a more complex non-uniform delay embedding method can be used to dynamically adjust the delay time according to the local characteristics of the signal to better capture the dynamic characteristics of the nonlinear system and generate more representative delay vectors.

[0126] The multiple delay vectors are arranged in chronological order to construct a high-dimensional trajectory matrix for the current. This aims to organize the generated delay vectors according to their corresponding time order into a matrix. This matrix is ​​a product of phase space reconstruction; it represents the trajectory of the micro-inverter output current in a structured form within the multi-dimensional phase space, providing a data foundation for subsequent calculations of neighborhood point distribution entropy. For example, all generated delay vectors can be simply stacked as rows or columns of a matrix to form an m-row N-column (or N-row m-column) matrix, where N is the number of effective delay vectors. Alternatively, during the arrangement process, the trajectory matrix can be preprocessed, such as normalized or centered, to eliminate dimensional differences between different dimensions and improve the numerical stability of subsequent entropy calculations.

[0127] The common-mode voltage time-series signal is extracted from the real-time electrical quantity, and peak detection is performed on this signal to obtain multiple peak and trough positions. The aim is to identify key characteristic points of the periodic fluctuations in the common-mode voltage signal. The peak and trough values ​​of the common-mode voltage are important indicators of its fluctuation period; accurately detecting these positions is a prerequisite for calculating the period value and helps to capture the dynamic changes of the common-mode voltage. For example, a threshold-based method can be used for peak detection, where a peak is identified when the signal value exceeds a certain preset threshold and its derivative changes from positive to negative, and vice versa. Alternatively, a local maximum / minimum detection algorithm can be used, such as finding the maximum and minimum values ​​within a sliding window and combining this with the signal's second derivative information to accurately determine the positions of peaks and troughs.

[0128] The instantaneous period value is calculated based on the time interval between adjacent peak positions, and the auxiliary period value is calculated based on the time interval between adjacent trough positions. The aim is to obtain the periodic information of the common-mode voltage by calculating the time intervals between consecutive peaks or troughs. The instantaneous period value directly reflects the local periodicity of the signal, while the auxiliary period value provides additional periodic information, helping to improve the robustness of period estimation, especially when the signal contains noise or distortion. For example, the instantaneous period value can be directly obtained from the difference in timestamps between adjacent peak positions, and the auxiliary period value is similarly obtained from the difference in timestamps between adjacent trough positions. To improve calculation accuracy, after detecting peaks / troughs, interpolation processing (such as spline interpolation) can be performed on the local region to more accurately determine the time position of the peak / trough points, thereby calculating more accurate instantaneous and auxiliary period values.

[0129] The common-mode periodic fluctuation sequence is obtained by weighted fusion of the instantaneous periodic value and the auxiliary periodic value. This aims to comprehensively utilize the information from both the instantaneous and auxiliary periodic values ​​to obtain a more stable, accurate, and less sensitive common-mode periodic fluctuation sequence to noise and outliers. By assigning different weights to periodic values ​​from different sources, they can be optimally combined based on their reliability or importance. For example, fixed-weight fusion can be used, linearly weighting the instantaneous and auxiliary periodic values ​​at a preset ratio. Alternatively, dynamic weighted fusion can be used, dynamically adjusting the weights of the instantaneous and auxiliary periodic values ​​based on signal quality (such as signal-to-noise ratio and waveform symmetry) or current operating conditions. For instance, a higher weight can be assigned to the instantaneous periodic value when the signal quality is good, while the weight of the auxiliary periodic value can be appropriately increased when signal distortion exists, thus generating a more robust common-mode periodic fluctuation sequence.

[0130] Through the above technical solution, this application solves the problems of inaccurate reconstruction parameters and insufficient robustness of period detection by refining the specific implementation steps of phase space reconstruction and fluctuation period detection, thereby ensuring the accuracy of current trajectory and voltage period sequence and providing a reliable foundation for dynamic operating condition entropy calculation. Specifically, the output current time sequence signal is extracted as the original input for reconstruction, avoiding distortion caused by missing data. The embedding dimension and delay time of phase space reconstruction are determined, and the reconstruction process is optimized through scientific parameter selection to reduce trajectory deviation caused by inappropriate dimension or delay. Delay coordinate mapping is performed based on the embedding dimension and delay time, and multiple delay vectors are generated to capture the nonlinear behavior of the current by utilizing the parameter adaptive mapping signal dynamic characteristics. The multiple delay vectors are arranged in time order to construct a high-dimensional current trajectory matrix, organizing the data into a structured representation, which facilitates neighborhood point analysis in subsequent entropy calculation. At the same time, the common-mode voltage time sequence signal is extracted to provide a complete data source for period detection. Peak detection is performed on the common-mode voltage time sequence signal to obtain multiple peak positions and multiple trough positions, identifying key fluctuation points to cover all characteristics of voltage changes. The instantaneous period value is calculated based on adjacent peak positions, directly reflecting the main period characteristics of voltage fluctuation. Auxiliary periodic values ​​are calculated based on adjacent trough locations to supplement trough information and address noise interference. The instantaneous periodic values ​​and auxiliary periodic values ​​are weighted and fused, combining the complementary advantages of different calculation methods to generate a robust common-mode periodic fluctuation sequence, eliminating the error accumulation of a single detection method. This enables more accurate and reliable entropy values ​​for subsequent calculations of neighborhood point distribution entropy based on the high-dimensional current trajectory matrix to obtain current state uncertainty, and for calculations of periodic distribution entropy based on the common-mode periodic fluctuation sequence to obtain common-mode periodic uncertainty. This more accurately reflects the dynamic operating conditions of the micro-inverter, providing a solid data foundation for subsequent adaptive adjustment of sliding mode control parameters and improving the common-mode voltage suppression effect and system stability of the micro-inverter under complex operating conditions.

[0131] In some of the solutions described above in this application, the current state uncertainty is calculated by performing neighborhood point distribution entropy calculation based on the high-dimensional current trajectory matrix, and the common-mode period uncertainty is calculated by performing period distribution entropy calculation based on the common-mode periodic fluctuation sequence, in order to calculate the dynamic operating condition entropy value. However, in practice, the methods for calculating the current state uncertainty and the common-mode period uncertainty may not be accurate enough to fully capture the complexity of the current state and periodic fluctuations, resulting in inaccurate dynamic operating condition entropy values, which in turn affects the adaptive adjustment of subsequent control parameters.

[0132] To address this, this application further proposes a method for calculating the entropy of neighborhood points based on the high-dimensional current trajectory matrix to obtain the current state uncertainty, and for calculating the periodic distribution entropy based on the common-mode periodic fluctuation sequence to obtain the common-mode periodic uncertainty. The specific steps include: dividing the high-dimensional current trajectory matrix into spatial grids to obtain multiple phase space sub-regions; counting the number of trajectory points falling into each phase space sub-region to obtain the regional point density distribution; calculating the information entropy based on the regional point density distribution to obtain the current state uncertainty; numerically quantizing the common-mode periodic fluctuation sequence to obtain multiple discrete period levels; counting the frequency of the common-mode periodic fluctuation sequence falling into each discrete period level to form a period level frequency distribution; and calculating the information entropy based on the period level frequency distribution to obtain the common-mode periodic uncertainty.

[0133] Specifically, the high-dimensional current trajectory matrix is ​​spatially meshed to obtain multiple phase space sub-regions. The aim is to discretize the high-dimensional phase space into a finite number of non-overlapping sub-regions, facilitating statistical analysis of trajectory points within the phase space and thus capturing local characteristics of the system behavior. For example, a uniform mesh partitioning can be used, dividing the phase space into several equal intervals in each dimension to form regular hypercube sub-regions. Alternatively, an adaptive mesh partitioning can be employed, such as partitioning based on trajectory point density. In regions with high trajectory point density, the mesh can be finer, while in regions with low density, it can be coarser, to better capture local details and improve computational efficiency.

[0134] The purpose of counting the number of trajectory points falling into each sub-region of phase space is to obtain the regional point density distribution. This aims to quantify the frequency or probability of the system state occupying different regions in phase space, directly reflecting the dwell time or likelihood of the system in different states, and is the basis for constructing probability distributions. For example, all trajectory points in the high-dimensional current trajectory matrix can be directly traversed to count the total number of points falling into each sub-region of phase space. Alternatively, the trajectory points can be weighted, for example, by weighting them according to their temporal order or their position within the sub-region, to reflect the different contributions of different trajectory points to the regional density.

[0135] Based on this, information entropy is calculated using the regional point density distribution to obtain the current state uncertainty. Information entropy is an indicator that measures the uncertainty or information content of a random variable; here, it aims to quantify the complexity, randomness, or unpredictability of the current state distribution in phase space. For example, the classic Shannon entropy formula can be used for calculation: H = -Σp(i) × log(p(i)), where p(i) is the trajectory point density (or normalized frequency) of the i-th phase space sub-region. Alternatively, approximate entropy or sample entropy methods can be used. These methods consider the length and similarity of the time series during calculation, are more suitable for time series of finite length, and can better reflect the complexity and uncertainty of system dynamics.

[0136] Simultaneously, the common-mode periodic fluctuation sequence is numerically quantized to obtain multiple discrete periodic levels. This aims to discretize the continuously changing common-mode periodic fluctuation sequence into a finite number of representative periodic levels, which helps simplify complex continuous data into statistically analyzable categories, facilitating subsequent frequency statistics and information entropy calculations. For example, the value range of the common-mode periodic fluctuation sequence can be divided into several intervals of equal width, each interval corresponding to a discrete periodic level. Alternatively, equal-frequency interval division can be used, that is, based on the distribution characteristics of the periodic fluctuation sequence, the data is divided into levels such that each interval contains approximately the same number of data points.

[0137] Furthermore, the frequency of each discrete periodic level falling within the common-mode periodic fluctuation sequence is statistically analyzed to form a periodic level frequency distribution, aiming to reveal the patterns and regularities of common-mode periodic fluctuations. Through the frequency distribution, it is possible to intuitively understand which periodic levels are primary and which are secondary, thus providing a basis for assessing the stability of periodic fluctuations. For example, the number of times each discrete periodic level occurs within a preset time window can be directly counted. Alternatively, the frequency of each discrete periodic level can be counted and divided by the total length of the periodic fluctuation sequence to obtain the probability or relative frequency of each level.

[0138] Information entropy calculations are performed on the frequency distribution of periodic levels to obtain the common-mode periodic uncertainty, aiming to quantify the regularity or stability of common-mode periodic fluctuations. Higher entropy values ​​indicate more complex and irregular periodic fluctuation patterns, potentially containing multiple periodic components or random disturbances. Lower entropy values ​​indicate simpler and more stable periodic fluctuation patterns. For example, the Shannon entropy formula can be used for calculation. Alternatively, considering the potential correlation between periods in periodic fluctuations, methods such as conditional entropy or transition entropy can be used to capture the time dependence in the periodic fluctuation sequence, thereby providing a more comprehensive assessment of its uncertainty.

[0139] Through the aforementioned technical solutions, this application achieves more accurate capture of the complex distribution characteristics of the current state in phase space by performing fine spatial grid division and regional point density statistics on the high-dimensional current trajectory matrix, and then calculating the information entropy based on this. This results in a more precise current state uncertainty. Simultaneously, by performing reasonable numerical quantization and frequency distribution statistics on the common-mode periodic fluctuation sequence, and then calculating the information entropy based on this, this application can more effectively identify the regularity and stability of the common-mode periodic fluctuations, thus obtaining a more reliable common-mode periodic uncertainty. These precise and reliable uncertainty calculation results provide a solid foundation for the accurate generation of subsequent dynamic operating condition entropy values. When these precise current state uncertainties and common-mode periodic uncertainties are used to calculate the dynamic operating condition entropy value, the accuracy of the dynamic operating condition entropy value in representing the actual operating conditions of the micro-inverter can be improved. This high-precision operating condition representation enables the subsequent sliding mode parameter adaptive mapping to respond more sensitively and accurately to changes in operating conditions, thereby generating more reasonable fractional-order adjustment amounts and reaching law coefficient adjustment amounts. This helps to generate more accurate duty cycle correction values ​​in sliding mode control law calculations, effectively suppressing the common-mode voltage of the micro-inverter, reducing leakage current, and improving system stability and safety.

[0140] In some of the solutions mentioned above in this application, information entropy is calculated based on entropy calculation of dynamic weights and real-time electrical quantities to obtain dynamic operating condition entropy values. However, in this process, the method of coupling modulation entropy contribution may lack dynamic adaptability and cannot effectively handle transient changes in current and common-mode voltage, resulting in inaccurate entropy calculation and affecting the adaptive adjustment of subsequent control parameters.

[0141] To address this, this application further proposes coupling and modulating the corrected current weight with the current state uncertainty to obtain a current entropy contribution value, and coupling and modulating the common-mode weight coefficient with the common-mode period uncertainty to obtain a common-mode entropy contribution value. Specifically, this includes: inputting the corrected current weight and the current state uncertainty into a first nonlinear modulation function; multiplying the corrected current weight and the current state uncertainty by the first nonlinear modulation function and taking the natural logarithm to obtain the current entropy base value; obtaining the rate of change of the current state uncertainty within a preset window and dynamically compensating the current entropy base value based on this rate of change to obtain the current entropy contribution value; multiplying the common-mode weight coefficient with the common-mode period uncertainty to obtain the common-mode entropy base value; normalizing the common-mode period uncertainty to obtain a normalized period uncertainty; and attenuating and suppressing the common-mode entropy base value based on the normalized period uncertainty to obtain the common-mode entropy contribution value.

[0142] In this process, the corrected current weight and the current state uncertainty are input into a first nonlinear modulation function. This first nonlinear modulation function multiplies the corrected current weight and the current state uncertainty, and then takes the natural logarithm to obtain the basic value of the current entropy. This step aims to capture the complex relationship between the corrected current weight and the current state uncertainty more accurately through nonlinear mapping, thus laying the foundation for calculating the current entropy contribution. The first nonlinear modulation function can take various forms. For example, besides taking the natural logarithm after multiplication, it can also be an exponential function, a sigmoid function, a Tanh function, or a nonlinear mapping model constructed by combining polynomial fitting, neural networks, etc. These functions can map the linear or nonlinear combination of input variables to a new space to better reflect their inherent correlation.

[0143] The rate of change of the current state uncertainty within a preset window is obtained, and the current entropy baseline value is dynamically compensated based on this rate of change to obtain the current entropy contribution value. The purpose of this step is to introduce dynamic change information of the current state, correct the initially calculated current entropy baseline value, and ensure it reflects the transient characteristics of the current operating condition. The preset window can be a sliding window of fixed time length; for example, the rate of change can be obtained by calculating the difference or percentage change of the current state uncertainty between the current moment and the previous moment or the previous N moments. Dynamic compensation can be implemented using weighted summation, multiplicative correction, or lookup tables. For example, when the rate of change is large, the compensation amount can be increased to amplify the current entropy contribution value, and vice versa.

[0144] Multiplying the common-mode weighting coefficient by the common-mode periodic uncertainty yields the basic value of the common-mode entropy. This step is a preliminary calculation of the common-mode entropy contribution, reflecting the direct correlation between the common-mode weighting coefficient and the common-mode periodic uncertainty through a simple linear product. Besides simple multiplication, other linear or nonlinear combinations can be used, such as weighted averages or dot products, to adapt to different application scenarios and data characteristics.

[0145] The common-mode periodic uncertainty is normalized to obtain the normalized periodic uncertainty. Based on this normalized periodic uncertainty, the common-mode entropy base value is then attenuated to obtain the common-mode entropy contribution value. The purpose of normalization is to map the common-mode periodic uncertainty to a uniform numerical range, eliminating the influence of dimensions and facilitating subsequent comparisons and processing. Common normalization methods include min-max normalization or Z-score standardization. Attenuation suppression adjusts the common-mode entropy base value based on the magnitude of the normalized uncertainty to prevent the common-mode entropy contribution value from being too large or too small in certain extreme cases, thereby improving its robustness and accuracy. Attenuation suppression can be implemented using piecewise functions, exponential decay functions, or sigmoid functions. For example, when the normalized periodic uncertainty is high, a larger attenuation factor can be applied to avoid overestimating the entropy value of the common-mode operating condition.

[0146] Through the above technical solution, this application uses a dynamic coupling modulation method to accurately calculate the current entropy contribution value and the common-mode entropy contribution value, solving the problem of inaccurate entropy contribution value calculation in the information entropy solution process, thereby improving the accuracy of the dynamic operating condition entropy value. Specifically, the corrected current weight and the current state uncertainty are input into a first nonlinear modulation function. This function multiplies the two and takes the natural logarithm to obtain the current entropy base value. This step uses a nonlinear function to process the weight and uncertainty, capturing the complex nonlinear relationship between them, avoiding errors caused by simple linear combinations, and ensuring that the entropy base value can reflect the true uncertainty of the current state. The rate of change of the current state uncertainty within a preset window is obtained, and the current entropy base value is dynamically compensated according to the rate of change to obtain the current entropy contribution value. By introducing the rate of change as a dynamic factor, the entropy base value is compensated, enabling it to adapt to transient fluctuations in the current state and improving the response capability of the entropy contribution value to rapid changes. Then, the common-mode weight coefficient is multiplied by the common-mode period uncertainty to obtain the common-mode entropy base value. This basic multiplication operation provides a preliminary estimate of the common-mode entropy. The common-mode periodic uncertainty is normalized to obtain the normalized periodic uncertainty. Based on its magnitude, the common-mode entropy base value is attenuated and suppressed to obtain the common-mode entropy contribution value. Normalization standardizes the uncertainty for easier comparison, and the suppression of the entropy base value based on its magnitude prevents excessive entropy contribution when uncertainty is high, thus maintaining the stability and reliability of the entropy contribution value and avoiding overestimation or underestimation. This refined entropy contribution calculation method allows the aggregated dynamic operating condition entropy value to more accurately and sensitively reflect the true operating state of the micro-inverter under complex operating conditions, providing a more reliable basis for subsequent adaptive adjustment of sliding mode parameters, thereby improving the common-mode voltage suppression effect and system stability of the micro-inverter across the entire operating range.

[0147] In some of the solutions described above in this application, parameter adaptive mapping is proposed to generate fractional order adjustment amounts and reaching law coefficient adjustment amounts. However, in this process, the mapping process fails to fully capture the transient change characteristics and amplitude intensity characteristics of the dynamic operating condition entropy value, resulting in the generated adjustment amount being unable to accurately respond to the dynamic evolution of the operating condition, thus affecting the adaptive capability of the sliding mode controller.

[0148] To address this, this application proposes a parameter adaptive mapping method to adaptively map the dynamic operating condition entropy value and the sliding mode parameter benchmark, thereby obtaining the fractional-order adjustment amount and the reaching law coefficient adjustment amount. See [link to relevant documentation]. Figure 4 The method specifically includes the following steps: 401. Extract the rate of change of the entropy value under the dynamic operating condition to obtain the transient rate of change of the entropy value, and quantize the amplitude of the entropy value under the dynamic operating condition to obtain the entropy value amplitude level.

[0149] Extracting the rate of change of dynamic operating condition entropy values ​​aims to capture their instantaneous dynamic characteristics and reflect the rapid evolution trend of the operating conditions. This can be achieved in several ways. For example, the difference method can be used, calculating the ratio of the difference between dynamic operating condition entropy values ​​at consecutive sampling times to the time interval. Alternatively, a Kalman filter can be used to estimate the state of the dynamic operating condition entropy values, and the rate of change can be extracted from the estimated state. Simultaneously, amplitude quantization of the dynamic operating condition entropy values ​​aims to discretize their intensity level to characterize the severity of the disturbance. This can be achieved through preset threshold division, i.e., setting a series of thresholds based on experience or simulation results to place the dynamic operating condition entropy values ​​into different intervals, each interval corresponding to an amplitude level (e.g., low, medium, high). Alternatively, fuzzy logic quantization can be used, designing fuzzy membership functions to map the dynamic operating condition entropy values ​​to different fuzzy sets, each set representing an amplitude level.

[0150] 402. Input the transient rate of change of the entropy value and the magnitude level of the entropy value into the coupled mapping network. The coupled mapping network interactively fuses the transient rate of change of the entropy value and the magnitude level of the entropy value to generate the comprehensive operating condition disturbance degree.

[0151] The coupled mapping network is a specially designed computational network whose core function is to deeply process and organically combine information from two different dimensions—the transient rate of change of entropy and the magnitude of entropy—to form a unified and comprehensive evaluation index for operating condition disturbances. This interactive fusion process can be implemented through various network structures. For example, a multilayer perceptron (MLP) can be constructed, using the transient rate of change of entropy and the magnitude of entropy as input layers, and generating a comprehensive operating condition disturbance degree through nonlinear transformations in the hidden layers and the output layer. Alternatively, a fuzzy inference system can be designed, using both as fuzzy inputs and fusing them through a fuzzy rule base and inference mechanism. The purpose of interactive fusion is to ensure that the comprehensive operating condition disturbance degree can simultaneously reflect both the rate and intensity of operating condition changes, providing a more comprehensive and accurate disturbance assessment.

[0152] 403. Based on the comprehensive working condition disturbance degree, the fractional order reference value in the sliding mode parameter reference is nonlinearly stretched to obtain the order stretching amount.

[0153] The purpose of nonlinear stretching is to dynamically adjust the baseline value of the fractional order based on the overall intensity of the operating condition disturbance, thereby enhancing the robustness of the controller. This nonlinear stretching can be achieved through power function stretching, for example, using a power function of the form: Stretch Amount = Fractional Order Baseline Value × (1 + k × Overall Operating Condition Disturbance Degree^p), where k and p are adjustable parameters. Alternatively, it can be achieved through a Sigmoid function mapping, mapping the overall operating condition disturbance degree to a factor via the Sigmoid function, and then using this factor to stretch the fractional order baseline value.

[0154] 404. Based on the transient rate of change of the entropy value, the order stretching amount is directionally modulated to generate the fractional order adjustment amount.

[0155] Directional modulation aims to finely adjust the stretched order based on the trend of changing operating conditions (whether it is worsening or improving), so that the fractional-order adjustment not only reflects the amplitude of the disturbance but also its direction of evolution. This can be achieved through sign function modulation, i.e., gaining or attenuating the order stretching amount based on the sign of the transient rate of change of entropy. Alternatively, an asymmetric modulation function can be designed, with stronger modulation when operating conditions worsen and weaker modulation when operating conditions improve.

[0156] 405. Based on the comprehensive working condition disturbance degree, the reference value of the reaching law coefficient in the sliding mode parameter reference is exponentially scaled to obtain the coefficient scaling amount.

[0157] The purpose of exponential scaling is to dynamically adjust the reaching law coefficient based on the overall strength of the operating condition disturbance, thereby changing the speed and aggressiveness of the control system's response to the disturbance. This can be achieved through exponential decay or growth functions, such as using an exponential function of the form: scaling factor = reaching law coefficient reference value × exp(-k × comprehensive operating condition disturbance degree). Alternatively, it can be achieved through a logarithmic function inverse mapping, mapping the comprehensive operating condition disturbance degree inversely to a scaling factor via a logarithmic function, and then multiplying it by the reaching law coefficient reference value.

[0158] 406. Based on the entropy value amplitude level, the scaling amount of the coefficient is saturated and suppressed to obtain the adjustment amount of the reaching law coefficient.

[0159] The purpose of saturation suppression is to limit the adjusted reaching law coefficients according to the severity of the operating disturbance, preventing them from becoming too large or too small, thereby ensuring the stability and practical feasibility of the control system. This can be achieved through hard limiting, i.e., setting different upper and lower limits based on the entropy value amplitude level, and clamping the coefficient scaling to the nearest limit when it exceeds these limits. Alternatively, soft saturation functions, such as the Sigmoid or Tanh function, can be used to smooth the coefficient scaling and avoid abrupt changes.

[0160] Through the above technical solution, this application overcomes the limitations of traditional sliding mode controllers, which have fixed parameters and are difficult to adapt to complex operating conditions. By extracting the transient rate of change and quantizing the amplitude of the entropy value under dynamic operating conditions, and using a coupled mapping network for interactive fusion, this application can comprehensively and accurately evaluate the comprehensive operating condition disturbance faced by the micro-inverter during operation. Based on this comprehensive disturbance, the fractional-order reference value is nonlinearly stretched and directionally modulated in conjunction with the transient rate of change of the entropy value, enabling the fractional-order adjustment to accurately respond to the dynamic evolution of the operating conditions and enhancing the robustness of the controller. At the same time, the reaching law coefficient reference value is exponentially scaled and saturated by combining the entropy value amplitude level, ensuring that the reaching law coefficient adjustment maintains the response speed while avoiding system instability caused by over-adjustment. This refined and adaptive parameter mapping mechanism enables the sliding mode controller to dynamically adjust the control strategy according to real-time operating condition changes, thereby effectively suppressing common-mode voltage across the entire operating condition range and improving the operational stability and power quality of the micro-inverter.

[0161] In some of the above-mentioned schemes in this application, a coupled mapping network is proposed to interactively fuse the transient rate of change of entropy and the magnitude level of entropy to generate a comprehensive operating condition disturbance degree. However, in this process, simple fusion may not be able to fully capture the dynamic directionality and intensity differences of the operating condition changes, resulting in the generated comprehensive operating condition disturbance degree being insufficiently accurate in representing the operating condition disturbance, affecting the accuracy of subsequent sliding mode parameter adaptive mapping, and thus reducing the robustness of common mode voltage suppression of micro-inverters.

[0162] To address this, this application further proposes a coupled mapping network to interactively fuse the transient rate of change of entropy and the magnitude level of entropy to generate a comprehensive operating condition disturbance degree. Specifically, the coupled mapping network performs sign separation on the transient rate of change of entropy to obtain positive and negative components representing the direction of operating condition change, and classifies the magnitude level of entropy to obtain high-magnitude and low-magnitude labels. The coupled mapping network then associates the positive component with the high-magnitude label to generate a first disturbance contribution factor, and associates the negative component with the low-magnitude label to generate a second disturbance contribution factor. The coupled mapping network then performs adversarial aggregation on the first and second disturbance contribution factors to obtain a game equilibrium value between them. Based on the absolute value of the transient rate of change of entropy, the coupled mapping network dynamically selects a corresponding mapping curve from a preset family of disturbance degree mapping curves, inputs the game equilibrium value into the selected mapping curve, and outputs the comprehensive operating condition disturbance degree after nonlinear mapping.

[0163] The coupled mapping network is a computational entity used to process and integrate multi-source information and realize complex nonlinear mappings. Its function is to deeply fuse the transient rate of change and magnitude of the input entropy value to accurately reflect the current comprehensive operating condition disturbance level of the micro-inverter. In practical implementation, this coupled mapping network can be a structure based on an artificial neural network, such as a feedforward neural network. Its input layer receives the transient rate of change and magnitude of the entropy value, performs nonlinear feature extraction and fusion through multiple hidden layers, and generates the comprehensive operating condition disturbance level at the output layer. Alternatively, the coupled mapping network can also be a system based on fuzzy logic reasoning. By defining a fuzzy rule base and membership function, the input quantities are fuzzified and then fuzzy reasoning is performed to obtain the fusion result.

[0164] The transient rate of change of entropy is sign-separated to obtain positive and negative components representing the direction of change in operating conditions, aiming to clearly distinguish whether the operating conditions are deteriorating or improving. For example, when the transient rate of change of entropy is greater than zero, it indicates that the operating condition disturbance is intensifying; in this case, the rate of change is taken as the positive component, and the negative component is set to zero. Conversely, when the transient rate of change of entropy is less than zero, it indicates that the operating condition disturbance is slowing down or recovering; in this case, the absolute value of the rate of change is taken as the negative component, and the positive component is set to zero. This separation can be achieved through simple conditional statements or through methods such as half-wave rectifiers in signal processing.

[0165] The entropy value amplitude level is graded by intensity to obtain high-amplitude and low-amplitude level labels, the purpose of which is to quantify the severity of the current operating condition disturbance. For example, multiple thresholds can be preset, and the entropy value amplitude level is compared with these thresholds. If the value exceeds a certain high threshold, a high-amplitude level label is generated; if the value is below a certain low threshold, a low-amplitude level label is generated. This grading can be implemented using piecewise functions or fuzzy clustering algorithms. For example, the historical entropy value amplitude level data can be divided into different clusters using the K-means clustering algorithm, and a corresponding level label can be defined for each cluster.

[0166] The system associates the positive change component with the high-amplitude level indicator to generate a first disturbance contribution factor, and associates the negative change component with the low-amplitude level indicator to generate a second disturbance contribution factor. The core principle is to differentiate the processing based on the direction and intensity of the operating condition change. When the operating condition disturbance intensifies (positive change component exists) and the disturbance intensity is high (high-amplitude level indicator exists), its contribution to the total disturbance degree is strengthened through multiplicative coupling or logic gating mechanisms, forming the first disturbance contribution factor. For example, the positive change component can be multiplied by a weighting coefficient associated with the high-amplitude level indicator. Conversely, when the operating condition disturbance decreases (negative change component exists) and the disturbance intensity is low (low-amplitude level indicator exists), its contribution to the total disturbance degree is weakened through a similar mechanism, forming the second disturbance contribution factor. For example, the negative change component (taking its absolute value) can be multiplied by a decay coefficient associated with the low-amplitude level indicator.

[0167] The adversarial aggregation of the first and second disturbance contribution factors yields a game equilibrium value between them, aiming to simulate the dynamic balance between positive and negative disturbance factors and thus obtain a more robust comprehensive evaluation. This can be achieved by calculating the difference between the two contribution factors and incorporating a saturation function to ensure the equilibrium value remains within a reasonable range. For example, a nonlinear function can be designed, taking the first and second disturbance contribution factors as input and outputting the game equilibrium value. This function can reflect which side dominates and its degree of influence when both exist simultaneously.

[0168] Based on the absolute value of the transient rate of change of the entropy value, a corresponding mapping curve is dynamically selected from a preset family of disturbance degree mapping curves. The game equilibrium value is then input into the selected mapping curve, and the comprehensive operating condition disturbance degree is output after nonlinear mapping. The purpose is to adaptively adjust the nonlinear mapping relationship of the disturbance degree according to the rate of change of the operating condition. The preset family of disturbance degree mapping curves can include various nonlinear functions, such as exponential functions, logarithmic functions, sigmoid functions, or polynomial functions. When the absolute value of the transient rate of change of the entropy value is large, it indicates that the operating condition is changing drastically, and a more sensitive mapping curve may be selected. When the absolute value is small, it indicates that the operating condition is changing slowly, and a more stable mapping curve may be selected. This dynamic selection can be achieved through piecewise functions or fuzzy decision logic to ensure that the output comprehensive operating condition disturbance degree can accurately reflect the dynamic characteristics and severity of the current operating condition.

[0169] Through the above technical solution, this application solves the problem of insufficient fusion of directional and intensity information in the generation of comprehensive operating condition disturbance degree by introducing a multi-level interactive fusion mechanism, thereby improving the accuracy of disturbance degree characterization and providing a reliable basis for sliding mode parameter adaptation. Specifically, sign separation of the transient rate of change of entropy value can clearly distinguish the direction of operating condition change, avoid the ignoring of directional information in the fusion, and ensure the pertinence of disturbance assessment. Intensity classification of entropy value amplitude level quantifies the intensity level of operating condition disturbance, providing a differentiated basis for subsequent correlation constraints and preventing the intensity information from being averaged. Then, the positive change component is correlated with the high amplitude level identifier to generate the first disturbance contribution factor, which ensures that when the operating condition change intensifies and the intensity is high, the disturbance contribution is strengthened, highlighting the response requirements of high disturbance scenarios. At the same time, the negative change component is correlated with the low amplitude level identifier to generate the second disturbance contribution factor, which ensures that when the operating condition change slows down and the intensity is low, the disturbance contribution is weakened, avoiding unnecessary adjustment deviations in low disturbance scenarios. Subsequently, the first and second disturbance contribution factors are adversarially aggregated to obtain a game equilibrium value. This simulates the dynamic balance process of positive and negative disturbances, generating a comprehensive disturbance assessment value and eliminating the risk of misjudgment caused by a single dominant direction. The mapping curve is dynamically selected based on the absolute value of the transient rate of change of entropy. This allows for adaptive matching of the most suitable nonlinear mapping function according to the rate of change. The game equilibrium value is input into the selected curve for nonlinear mapping, outputting a comprehensive operating condition disturbance degree. This curve adaptive optimization of the disturbance degree representation makes it more closely reflect the dynamic characteristics of actual operating conditions. This refined disturbance degree characterization enables subsequent sliding mode parameter adaptive mapping to respond more accurately to changes in operating conditions. Therefore, when the micro-inverter faces complex operating conditions such as load surges or reactive power injection, it effectively suppresses common-mode voltage and improves the robustness and stability of the system.

[0170] In some of the solutions mentioned above in this application, a nonlinear stretching of the fractional order benchmark value based on the comprehensive operating condition disturbance degree is proposed to dynamically adjust the fractional order of the sliding mode controller. However, in its implementation, since the comprehensive operating condition disturbance degree is a comprehensive index, direct nonlinear stretching may not accurately adapt to different disturbance ranges and changing trends, resulting in insufficient adjustment and affecting control performance.

[0171] To address this, this application further proposes a method for nonlinearly stretching the fractional-order benchmark value in the sliding mode parameter reference based on the comprehensive operating condition disturbance degree to obtain the order stretching amount. Specifically, this involves: performing interval mapping on the comprehensive operating condition disturbance degree to obtain a normalized disturbance factor, and extracting the rate of change of the comprehensive operating condition disturbance degree to obtain the disturbance change trend. Based on the numerical range of the normalized disturbance factor, the corresponding nonlinear stretching function is dynamically called from the stretching function library. Based on the positive or negative polarity of the disturbance change trend, the output of the nonlinear stretching function is directionally biased to obtain a dynamic stretching coefficient. The fractional-order benchmark value is multiplied by the dynamic stretching coefficient, and the product result is subjected to amplitude limiting processing to obtain the order stretching amount.

[0172] Specifically, interval mapping is performed on the comprehensive operating condition disturbance degree to obtain a normalized disturbance factor. This aims to transform the comprehensive operating condition disturbance degree, which reflects the complexity and uncertainty of the micro-inverter's operating state, into a preset, finite numerical range, such as [0, 1] or [-1, 1], thereby making it comparable under different operating conditions and facilitating subsequent processing. This interval mapping can employ a linear mapping method, for example, by subtracting the minimum value of the comprehensive operating condition disturbance degree and dividing by the difference between its maximum and minimum values ​​to achieve normalization within the [0, 1] range. Alternatively, a nonlinear mapping method can be used, such as the Sigmoid function or the Tanh function, to highlight the differences in certain disturbance intervals. Piecewise linear mapping or a lookup table method can also be used, mapping based on preset disturbance degree intervals and corresponding normalized values.

[0173] Simultaneously, the rate of change of the comprehensive operating condition disturbance is extracted to obtain the disturbance change trend. The purpose is to capture the speed and direction of change of the comprehensive operating condition disturbance over time. This helps determine whether the current operating condition is stabilizing, deteriorating, or improving, providing dynamic directional information for subsequent parameter adjustments. The rate of change can be extracted using the difference method, i.e., calculating the difference between the comprehensive operating condition disturbance at the current moment and the disturbance at the previous moment. Alternatively, the disturbance degree sequence can be smoothed using methods such as the moving average method or Kalman filtering before calculating its derivative or approximate derivative to reduce the influence of noise. Alternatively, the trend can be characterized by fitting a disturbance degree change curve over a period of time and calculating the slope of the fitted curve.

[0174] Based on this, and according to the numerical range of the normalized perturbation factor, the corresponding nonlinear stretching function is dynamically called from the stretching function library. The nonlinear stretching function is used to adjust the fractional-order baseline value according to the degree of perturbation. Since the order adjustment requirements may differ for different perturbation ranges—for example, slight perturbations require fine-tuning, while severe perturbations require large adjustments—the most suitable nonlinear stretching function needs to be dynamically selected based on the numerical range of the normalized perturbation factor. The stretching function library can pre-store various nonlinear functions with different characteristics (such as slope and saturation point), such as polynomial functions, exponential functions, logarithmic functions, or sigmoid functions. Different functions are selected based on the preset range in which the normalized perturbation factor falls. Alternatively, piecewise defined nonlinear functions can be used, with each piece corresponding to a perturbation range, ensuring the continuity and differentiability of the function at the segment points. Mapping functions can also be obtained based on fuzzy logic or neural network training.

[0175] Furthermore, based on the positive or negative polarity of the perturbation trend, the output of the nonlinear stretching function is directionally biased to obtain dynamic stretching coefficients. These dynamic stretching coefficients are multiplicative factors used to adjust the fractional-order baseline value. By combining the positive or negative polarity of the perturbation trend (i.e., whether the perturbation is strengthening or weakening) with the output of the nonlinear stretching function, directional biasing of the output can make order adjustment more forward-looking and adaptive. For example, when the perturbation trend worsens, a positive bias can be added to the output of the nonlinear stretching function. When the perturbation trend improves, a negative bias can be added or a positive bias can be decreased. The magnitude of the bias can be related to the absolute value of the perturbation trend. Alternatively, directional bias can be achieved by multiplying the output of the nonlinear stretching function by a modulation factor based on the perturbation trend, which is greater than 1 when the trend is positive and less than 1 when the trend is negative. A lookup table or decision logic can also be designed to directly select a value from a preset set of dynamic stretching coefficients based on the positive or negative polarity of the perturbation trend.

[0176] The fractional-order reference value is multiplied by a dynamic stretching coefficient, and the product is then subjected to a limiting process to obtain the order stretching amount. The fractional-order reference value is a preset fractional-order parameter under ideal operating conditions. By multiplying it by the dynamic stretching coefficient, the reference value can be dynamically adjusted to obtain an order stretching amount adapted to the current operating conditions. The limiting process ensures that the adjusted order stretching amount is physically reasonable and conducive to the stability of the control system, avoiding instability or performance degradation caused by excessively large or small orders. Limiting can be achieved by setting upper and lower limits. For example, if the product result exceeds a preset maximum order, it is clamped to the maximum order; if it is below a preset minimum order, it is clamped to the minimum order. Alternatively, a soft limiting function can be used, causing the adjustment amount to gradually saturate as it approaches the limit, rather than abruptly truncate, to avoid introducing additional nonlinear shocks.

[0177] Through the above technical solution, this application can solve the problem that direct nonlinear stretching of the comprehensive operating condition disturbance degree cannot accurately adapt to different disturbance ranges and trends. Specifically, by mapping the comprehensive operating condition disturbance degree to a range and standardizing it into a normalized disturbance factor, the disturbance degree under different operating conditions becomes comparable, laying the foundation for subsequent fine-tuning. Simultaneously, extracting the disturbance change trend allows for real-time perception of the dynamic evolution direction of the operating condition, providing forward-looking information for order adjustment. Dynamically calling the nonlinear stretching function based on the numerical range of the normalized disturbance factor ensures that the most suitable adjustment strategy is adopted under different disturbance intensities, avoiding the insufficient adaptability caused by a fixed function. Furthermore, by combining the positive and negative polarities of the disturbance change trend to directionally bias the output of the nonlinear stretching function, the dynamic stretching coefficient not only reflects the disturbance intensity but also incorporates the disturbance trend, thereby achieving more accurate and responsive dynamic adjustment of the fractional-order benchmark value. By multiplying the fractional order reference value with the dynamic stretching coefficient and performing amplitude limiting, while ensuring a reasonable range of adjustment, an order stretching amount that adapts to the current complex working conditions is effectively generated, thereby improving the common-mode voltage suppression effect and system robustness of the sliding mode controller across the entire working range.

[0178] In some of the solutions described above in this application, a nonlinear stretching of the fractional-order benchmark value based on the comprehensive operating condition disturbance degree is proposed to obtain the order stretching amount. However, the order stretching amount only reflects the amplitude influence of the comprehensive operating condition disturbance degree on the fractional-order value, failing to consider the differentiated requirements of the operating condition change direction characterized by the transient rate of change of entropy value for order adjustment. When the operating condition change intensifies, a more aggressive order response is needed to enhance control robustness. When the operating condition change slows down, a more conservative order adjustment is needed to avoid overshoot. Directly processing the order stretching amount uniformly cannot achieve differentiated modulation according to the change direction, resulting in insufficient matching between the order adjustment and the dynamic characteristics of the operating condition.

[0179] In response, this application further proposes to directionally modulate the order stretching amount based on the transient rate of change of entropy, generating the fractional-order adjustment amount, specifically including: By performing sign discrimination on the transient rate of change of the entropy value, a positive modulation sign indicating an aggravation of the change in operating conditions and a negative modulation sign indicating a slowdown of the change in operating conditions are obtained.

[0180] Based on this positive modulation flag, the first modulation depth coefficient corresponding to the current entropy amplitude level is retrieved from the modulation depth library.

[0181] Based on the negative modulation flag, a second modulation depth coefficient corresponding to the current entropy amplitude level is retrieved from the modulation depth library. This second modulation depth coefficient is less than the first modulation depth coefficient.

[0182] The order stretching amount is conditionally fused with the first modulation depth coefficient and the second modulation depth coefficient to obtain the positive adjustment component corresponding to the positive modulation flag and the negative adjustment component corresponding to the negative modulation flag.

[0183] The positive adjustment component and the negative adjustment component are switched smoothly in a time series to obtain the fractional order adjustment amount.

[0184] Specifically, the sign determination of the transient rate of change of entropy aims to identify the changing trend of the current operating condition of the microinverter. For example, by setting a very small positive threshold and a very small negative threshold, when the transient rate of change of entropy is greater than the positive threshold, it is determined that the operating condition change is intensifying, and a positive modulation flag is generated. When the transient rate of change of entropy is less than the negative threshold, it is determined that the operating condition change is slowing down, and a negative modulation flag is generated. Alternatively, a digital filter can be used to smooth the transient rate of change of entropy, and then the sign can be directly determined by the sign function (sgn) to obtain the corresponding modulation flag. This step provides a directional basis for subsequent differentiated modulation.

[0185] Upon receiving the positive modulation flag, the system retrieves the first modulation depth coefficient corresponding to the current entropy amplitude level from a pre-defined modulation depth library. The modulation depth library can be a multi-dimensional lookup table, indexed by the entropy amplitude level and modulation direction. When an aggravation of the operating condition is detected, the system retrieves a larger first modulation depth coefficient from the lookup table based on the current entropy amplitude level. Alternatively, the modulation depth library can consist of a series of parameterized nonlinear functions. When the positive modulation flag is activated, a function is selected that outputs the first modulation depth coefficient based on the entropy amplitude level, and this function is designed to provide stronger modulation intensity when the operating condition deteriorates. This ensures a more proactive response from order adjustments when the operating condition worsens.

[0186] Similarly, upon receiving the negative modulation flag, the system retrieves a second modulation depth coefficient from the modulation depth library corresponding to the current entropy amplitude level. Unlike the first modulation depth coefficient, the second modulation depth coefficient is preset to be smaller than the first. This means that when operating conditions tend to stabilize or improve, the system will select a relatively smaller modulation depth coefficient. For example, in the lookup table, the coefficient corresponding to the negative modulation direction will be smaller than the coefficient corresponding to the positive modulation direction. Alternatively, the selected nonlinear function provides a more moderate modulation intensity when operating conditions improve. This step aims to avoid excessive order adjustments when operating conditions improve, thereby preventing unnecessary chattering or system oscillations.

[0187] The order stretching amount is conditionally fused with the first modulation depth coefficient and the second modulation depth coefficient, respectively. This means that when the positive modulation flag is activated, the order stretching amount is multiplied by the first modulation depth coefficient to obtain the positive adjustment component. When the negative modulation flag is activated, the order stretching amount is multiplied by the second modulation depth coefficient to obtain the negative adjustment component. At any given time, usually only one modulation flag is active, so only one non-zero adjustment component is generated. This conditional fusion mechanism allows the same order stretching amount to produce differentiated adjustment effects depending on the direction of the operating condition change.

[0188] A time-series smoothing switch is performed on the positive and negative adjustment components to obtain the fractional-order adjustment. To avoid abrupt changes in the fractional-order adjustment during changes in operating conditions, a low-pass filter or moving average filter can be used to smooth the selected adjustment components. For example, when switching from positive to negative modulation, the filter will gradually transition the output value from the positive adjustment component to the negative adjustment component, rather than abruptly jumping. Another approach is to use a weighted average or interpolation algorithm, dynamically adjusting the weights during the switching period to ensure a smooth transition between the two components. This step ensures the continuity and stability of the fractional-order adjustment, thereby maintaining the stability of the control system.

[0189] Through the above technical solution, this application introduces a directional modulation mechanism, solving the problem that order adjustment cannot respond differently according to the direction of operating condition changes, thereby improving the matching accuracy between order adjustment and the dynamic characteristics of the operating condition. Specifically, by performing sign discrimination on the transient rate of change of entropy, the direction of operating condition change is quantified into a positive modulation flag (intensified operating condition) and a negative modulation flag (deteriorated operating condition), providing a directional basis for subsequent differentiated modulation. Based on the positive modulation flag, a first modulation depth coefficient corresponding to the current entropy amplitude level is invoked. This coefficient has a larger value to ensure that a stronger modulation intensity is applied to the order stretch when the operating condition intensifies, enabling the controller to respond quickly to the deterioration of the operating condition. Based on the negative modulation flag, a second modulation depth coefficient corresponding to the current entropy amplitude level is invoked. This coefficient has a smaller value to ensure that a weaker modulation intensity is applied to the order stretch when the operating condition deteriorates, avoiding unnecessary chattering caused by order over-adjustment. The order stretch is conditionally fused with different modulation depth coefficients to generate positive and negative adjustment components corresponding to the direction of operating condition change, realizing differentiated output of the same order stretch under different directions of change. The positive and negative adjustment components are smoothly switched in a timely manner to avoid order jumps caused by abrupt changes in sign discrimination, ensuring the continuity and stability of the adjustment process. Overall, these steps enable the order adjustment to consider not only the amplitude of the operating condition disturbance (reflected by the order stretching) but also the direction of the operating condition change (reflected by directional modulation), achieving dual adaptiveness in amplitude and direction. This allows for more precise and stable suppression of common-mode voltage and effective reduction of leakage current when the micro-inverter faces complex dynamic operating conditions.

[0190] In some of the solutions mentioned above in this application, the benchmark value of the reaching law coefficient is adjusted based on the comprehensive operating condition disturbance degree. However, in this process, the traditional linear or fixed scaling method may not be able to accurately capture the nonlinear characteristics of the disturbance, resulting in the adjusted reaching law coefficient not being able to effectively adapt to dynamic operating condition changes, thereby affecting the robustness of sliding mode control and the common mode voltage suppression effect.

[0191] To address this, this application further proposes an exponential scaling method for the reaching law coefficient benchmark value in the sliding mode parameter reference based on the comprehensive operating condition disturbance degree, yielding a coefficient scaling amount. This method includes: normalizing the comprehensive operating condition disturbance degree to obtain a normalized disturbance factor ranging from 0 to 1; dynamically selecting a corresponding exponent base from an exponent base library based on the magnitude of the normalized disturbance factor, where the exponent base is negatively correlated with the normalized disturbance factor; performing a power operation with the normalized disturbance factor as the exponent and the selected exponent base as the base to obtain a dynamic scaling coefficient; multiplying the reaching law coefficient benchmark value by the dynamic scaling coefficient and clamping the amplitude of the product to obtain the coefficient scaling amount.

[0192] The process involves normalizing the overall operating condition disturbance degree to obtain a normalized disturbance factor ranging from 0 to 1. This step aims to map the overall operating condition disturbance degree with different dimensions or ranges to a standardized interval, typically 0 to 1. This process eliminates the influence of the original disturbance degree's numerical value, allowing subsequent parameter selection and calculation to be performed within a unified, dimensionless framework, thereby improving the algorithm's stability and generalization ability. For example, linear normalization methods, such as minimum-maximum normalization, can be used, which involves subtracting a preset minimum value from the current disturbance degree and then dividing by the difference between the maximum and minimum values ​​to obtain the normalized result. Alternatively, nonlinear normalization functions, such as the Sigmoid or Tanh functions, can be used to map the disturbance degree to the range of 0 to 1, introducing nonlinear characteristics to better adapt to certain specific disturbance distributions.

[0193] Based on the magnitude of the normalized disturbance factor, a corresponding exponent base is dynamically selected from the exponent base library. This exponent base is negatively correlated with the normalized disturbance factor. This step intelligently selects a suitable exponent base from the pre-established exponent base library based on the real-time magnitude of the normalized disturbance factor. The negative correlation between the exponent base and the normalized disturbance factor means that the more severe the operating condition disturbance (the larger the normalized disturbance factor), the smaller the selected exponent base. Conversely, the more gradual the operating condition disturbance, the larger the selected exponent base. This dynamic selection mechanism allows subsequent exponentiation operations to produce different degrees of scaling effects according to the severity of the actual operating condition, thereby achieving refined and adaptive adjustment of the reaching law coefficients. For example, this can be implemented using a lookup table method, i.e., a mapping table is pre-built, storing the exponent bases corresponding to different normalized disturbance factor intervals. When the normalized disturbance factor falls within a certain interval, the corresponding exponent base is directly queried and retrieved. Alternatively, this can be achieved by defining a negative correlation function, such as base = f(1 - normalized perturbation factor), where f is a monotonically increasing function, ensuring that the larger the normalized perturbation factor, the smaller the base.

[0194] Taking the normalized perturbation factor as the exponent and the selected exponential base as the base for power operation, a dynamic scaling coefficient is obtained. This step utilizes the dynamically selected exponential base and the normalized perturbation factor obtained in the previous step to generate a dynamic scaling coefficient through power operation. The non-linear characteristic of the power operation enables the scaling coefficient to exhibit a high sensitivity to the change in the working condition perturbation degree. Especially when the perturbation degree changes significantly, a more significant scaling effect can be produced. This non-linear mapping ability is the key to realizing the adaptive adjustment of the reaching law coefficient, and it can capture and reflect the dynamic characteristics under complex working conditions more accurately. For example, the power function calculation can be directly executed through the floating-point operation unit in a digital signal processor (DSP) or a microcontroller. In the case of limited computing resources, the power operation can also be approximately calculated by means of Taylor series expansion, lookup table combined with interpolation method or CORDIC algorithm, etc., to balance the requirements of calculation accuracy and real-time performance.

[0195] Multiply the reaching law coefficient reference value by the dynamic scaling coefficient and perform amplitude clamping on the product result to obtain the coefficient scaling amount. This step multiplies the preset reaching law coefficient reference value by the dynamic scaling coefficient calculated previously, thereby obtaining a preliminarily adjusted reaching law coefficient. Perform amplitude clamping on the product result, that is, limit it within a preset valid range. For example, between the minimum allowable value and the maximum allowable value. The purpose of amplitude clamping is to prevent the reaching law coefficient from becoming too large or too small due to excessive scaling, thus avoiding problems such as intensified chattering, sluggish response or instability of the system, and ensuring the stability and robustness of the control system. For example, after the multiplication operation, the clamping can be directly realized using conditional judgment statements, such as if(result>max_val)result=max_val; if(result<min_val)result=min_val;. In addition, a saturation function can also be used to realize amplitude clamping. When the input value exceeds the preset range, the output of this function is limited to the boundary value, and the original value is maintained within the range.

[0196] The above technical solution normalizes the overall operating condition disturbance, ensuring the consistency and stability of input for subsequent scaling operations. Based on the normalized disturbance factor, an innovative design dynamically selects an exponent base negatively correlated with the disturbance factor from the exponent base library. This allows for a smaller selected base when the operating condition disturbance is severe. Combined with exponentiation, this generates a more dynamic scaling factor, enabling nonlinear and adaptive adjustment of the reaching law coefficient. This exponential scaling mechanism can more accurately capture and respond to the nonlinear disturbance characteristics of the micro-inverter under complex operating conditions, avoiding the limitations of traditional linear or fixed scaling methods. Multiplying the reaching law coefficient base value with the dynamic scaling coefficient and applying amplitude clamping effectively prevents system chattering or slow response caused by excessively large or small reaching law coefficients, ensuring the stability and robustness of the control system. Overall, this solution enables the sliding mode controller to intelligently adjust its reaching speed and intensity according to the severity of real-time operating conditions, thereby effectively suppressing common-mode voltage, reducing leakage current, and improving the operating performance and safety of the micro-inverter across the entire operating range.

[0197] In some of the embodiments described above in this application, a saturation suppression method based on the entropy magnitude level is proposed to adjust the reaching law coefficient. However, in its implementation, since the entropy magnitude level represents different intensities of operating condition disturbances, using a single suppression method may not be able to accurately distinguish between high, medium, and low disturbance intensity levels, resulting in a lack of specificity in the suppression process. This can easily lead to over-suppression or under-suppression, thereby affecting the dynamic adaptability of the reaching law coefficient and causing a decrease or instability in control performance.

[0198] To address this issue, this application proposes a method for saturating and suppressing coefficient scaling based on entropy amplitude levels to obtain the adjustment amount of the reaching law coefficient. The method includes: classifying the entropy amplitude levels to obtain high-level, medium-level, and low-level indicators characterizing the intensity of the disturbance under the operating condition; based on the high-level indicator, calling a first nonlinear suppression function corresponding to the high-level indicator from a suppression intensity library; based on the medium-level indicator, calling a second nonlinear suppression function corresponding to the medium-level indicator from the suppression intensity library; based on the low-level indicator, calling a third nonlinear suppression function corresponding to the low-level indicator from the suppression intensity library; inputting the coefficient scaling amount into the first, second, and third nonlinear suppression functions respectively to obtain a first suppression component, a second suppression component, and a third suppression component; and weighting and fusing the first, second, and third suppression components to obtain the adjustment amount of the reaching law coefficient.

[0199] Specifically, the entropy amplitude levels are graded to obtain high-level, medium-level, and low-level indicators characterizing the intensity of disturbances under operating conditions. This aims to discretize the continuous or quasi-continuous entropy amplitude levels into several distinct, physically meaningful disturbance intensity levels, thus providing a basis for subsequent differentiated suppression strategies. The high-level, medium-level, and low-level indicators represent severe, moderate, and slight disturbance states faced by the system, respectively. This grading can be implemented in various ways. For example, multiple thresholds can be preset, and the entropy amplitude level can be compared with these thresholds. If the entropy amplitude level is higher than a certain upper threshold, it is graded as a high-level indicator. If it is between the upper and lower thresholds, it is graded as a medium-level indicator. If it is lower than the lower threshold, it is graded as a low-level indicator. These thresholds can be determined through offline simulation, expert experience, or historical data analysis. Another approach is to construct a fuzzy logic system, taking the entropy magnitude level as input, and using fuzzy sets (such as "low", "medium", and "high") and fuzzy rules for reasoning. The system outputs the membership degrees of high-level, medium-level, and low-level labels, and then determines the label based on the membership degree.

[0200] Based on the high-level flag, the first nonlinear suppression function corresponding to the high-level flag is called from the suppression strength library. The suppression strength library is a collection of pre-stored nonlinear suppression functions. When the system is identified as experiencing a high-level disturbance, a strong suppression function needs to be called to significantly limit the coefficient scaling, preventing overshoot or instability in the control system under severe disturbances. The role of the first nonlinear suppression function is to provide a strong, nonlinear suppression effect against high-intensity disturbances. For example, the suppression strength library can store multiple piecewise functions. When the high-level flag is activated, a piecewise function with a large slope or strong saturation characteristics within a specific interval is called, whose output value rapidly saturates after reaching a certain threshold. Alternatively, the Sigmoid function or its variants can be used as the nonlinear suppression function. For the high-level flag, a Sigmoid function with a small gain and an early saturation point can be called, causing its response curve to the input (coefficient scaling) to flatten at lower input values, thus achieving strong suppression.

[0201] Based on the medium-level indicator, a second nonlinear suppression function corresponding to the medium-level indicator is called from the suppression strength library. When the system is under medium-level disturbance, moderate suppression is required to avoid overshoot while maintaining a certain response speed. The second nonlinear suppression function aims to provide a nonlinear suppression effect between strong and weak suppression to balance the stability and dynamic performance of the control system. For example, the suppression strength library can store a piecewise function with a moderate slope or moderate saturation characteristics within a specific interval. Its suppression effect is weaker than the first nonlinear suppression function but stronger than the third nonlinear suppression function. Alternatively, a sigmoid function with moderate gain and a moderate saturation point can be called, so that its response curve to the input maintains good linearity within a certain range, but gradually tends to saturate beyond a certain range.

[0202] Based on the low-level flag, the third nonlinear suppression function corresponding to the low-level flag is called from the suppression strength library. When the system is under low-level disturbance, the disturbance is small, and the impact of suppression on control accuracy should be minimized to avoid unnecessary suppression leading to control hysteresis or decreased accuracy. The third nonlinear suppression function provides a weaker nonlinear suppression effect, mainly used for fine-tuning or slightly limiting the coefficient scaling. For example, the suppression strength library can store a piecewise function with a small slope or late saturation characteristic in a specific interval, which has a weaker suppression effect and allows for a larger range of coefficient scaling. Alternatively, a Sigmoid function with a large gain and a late saturation point can be called, so that its response curve to the input remains close to linear over a wide range, with saturation suppression only performed in extreme cases.

[0203] The coefficient scaling is input into the first, second, and third nonlinear suppression functions, respectively, to obtain the first, second, and third suppression components. This step is parallel processing, where the original coefficient scaling (generated from previous steps, reflecting the initial adjustment requirements of the approach law coefficients due to the operating condition disturbance) is simultaneously input into the three nonlinear suppression functions invoked according to different disturbance levels. The purpose of this is to generate a "candidate" suppression result for each disturbance level, namely the first, second, and third suppression components. These components represent the possible values ​​of the coefficient scaling after suppression under different disturbance strength assumptions. In a digital signal processor, the corresponding suppression function can be called directly through function pointers or conditional statements, with the coefficient scaling passed as a parameter, to obtain the corresponding suppression components.

[0204] The first, second, and third suppression components are weighted and fused to obtain the adjustment amount of the reaching law coefficient. Weighted fusion comprehensively considers the three previously generated suppression components based on the current actual operating condition disturbance level to obtain the adjustment amount of the reaching law coefficient. This fusion method allows the system to smoothly transition between different disturbance levels, avoiding abrupt changes caused by level switching, and ensuring that the adjustment amount accurately reflects the current operating condition disturbance intensity. For example, the membership degrees obtained in the level discrimination step (if fuzzy logic discrimination is used, high, medium, and low membership degrees will be obtained) can be used as weights to perform a weighted average of the three suppression components.

[0205] Through the above technical solution, this application can perform refined level discrimination of entropy amplitude, thereby accurately identifying the intensity of the current operating condition disturbance and classifying it into high, medium, and low levels. This hierarchical processing provides a precise basis for subsequent suppression strategies, overcoming the limitation of traditional single suppression methods that cannot distinguish between different disturbance intensities. For different disturbance intensities, this application dynamically calls matching first, second, or third nonlinear suppression functions from a suppression intensity library. For example, when the system faces a high-intensity disturbance, a strong suppression function is called to significantly limit the coefficient scaling, effectively preventing overshoot or chattering in the control system under drastic operating condition changes. When facing a medium-intensity disturbance, a moderate suppression function is called to balance the stability and dynamic response of the control system. When facing a low-intensity disturbance, a weak suppression function is called to minimize the impact on control accuracy and avoid unnecessary hysteresis caused by suppression. By inputting the coefficient scaling into these differentiated nonlinear suppression functions, corresponding suppression components are generated, ensuring that the adjustment of the coefficient scaling is highly targeted. By weighted and fused these suppression components, a smooth transition of the approach law coefficient adjustment between different disturbance levels is achieved, avoiding abrupt changes caused by level switching. Furthermore, this ensures that the approach law coefficient adjustment accurately and robustly reflects the current operating condition disturbance intensity. This hierarchical, differentiated, and fused suppression strategy enhances the dynamic adaptability of the approach law coefficient, enabling the micro-inverter to maintain excellent common-mode voltage suppression performance and system stability even under complex and variable operating conditions. It effectively avoids over-suppression or under-suppression issues, thereby improving the overall performance and reliability of the control system.

[0206] In some of the above-mentioned solutions in this application, a sliding mode control law is proposed to generate a duty cycle correction amount by calculating the fractional order adjustment amount, the approach law coefficient adjustment amount, and the current common-mode voltage tracking error. However, in this process, using fixed preset fractional calculus operators and exponential approach law parameters may lead to insufficient control accuracy and increased chattering when the operating conditions change dynamically, and may fail to adaptively capture the dynamic characteristics of the error or optimize the approach speed, thereby weakening the common-mode voltage suppression effect.

[0207] To address this, this application proposes a method for solving the sliding mode control law, see [link to relevant documentation]. Figure 5 Specifically, it includes: 501. Based on the fractional order adjustment, the order of the preset fractional calculus operator is reconstructed to obtain the dynamic fractional operator. Based on the dynamic fractional operator, the current common-mode voltage tracking error is subjected to fractional calculus to obtain the dynamic characteristics of the fractional error.

[0208] 502. Based on the adjustment amount of the reaching law coefficient, the coefficients of the preset exponential reaching law are reset to obtain the dynamic exponential reaching law. Based on the dynamic exponential reaching law, the sign value of the sliding surface function is modulated to obtain the dynamic compensation amount of the reaching law.

[0209] 503. The fractional-order error dynamic characteristics are fused with the preset equivalent control components to obtain the equivalent control correction.

[0210] 504. The equivalent control correction amount and the dynamic compensation amount of the reaching law are superimposed, and the amplitude of the superposition result is normalized to generate the duty cycle correction amount.

[0211] The fractional-order adjustment is a dynamic parameter that adjusts the order of the fractional-order calculus operator in real time based on the current operating conditions and control performance requirements of the microinverter. This adjustment reflects the system's adaptive requirements for dynamic error characteristics, enabling the fractional-order operator to better capture the complex dynamic behavior of common-mode voltage tracking errors under different operating conditions. In practical implementation, the fractional-order adjustment can be obtained in several ways. For example, a lookup table based on operating condition characteristics (such as load change rate and common-mode voltage fluctuation severity) can be pre-established, and the corresponding order adjustment can be obtained through table lookup. Alternatively, a fuzzy logic inference system can be designed, taking multiple real-time operating condition characteristics as input and outputting the fractional-order adjustment through fuzzy rule inference. Another approach is to utilize a neural network model to learn the mapping relationship between operating conditions and the optimal order adjustment in historical data, thereby predicting and outputting the order adjustment.

[0212] The predefined fractional-order calculus operator is a fundamental operator determined during system design and used to perform fractional-order calculus operations. This operator is typically based on the mathematical definition of fractional calculus, such as the Grünwald-Letnikov definition, the Riemann-Liouville definition, or the Caputo definition. In digital systems, the predefined fractional-order calculus operator can be approximated using the Grünwald-Letnikov difference approximation method, by summing a finite number of terms. Alternatively, frequency domain approximation methods, such as Oustaloup filters or CRONE controllers, can be used to convert the fractional-order operator into an integer-order transfer function for implementation.

[0213] Order reconstruction refers to the process of dynamically modifying or updating the order of a preset fractional-order calculus operator based on the fractional-order order adjustment. This process makes the fractional-order operator no longer fixed but adaptively adjustable according to real-time operating conditions. Specifically, order reconstruction can be achieved by directly modifying the order parameters in the preset operator definition. Alternatively, the system can maintain an operator library containing different order parameters and select the operator model that best matches the current operating conditions based on the fractional-order order adjustment.

[0214] A dynamic fractional operator is a calculus operator whose order parameters can dynamically change with the operating conditions after order reconstruction. This operator can more flexibly adapt to the non-integer order dynamic characteristics of errors, avoiding the inability of fixed operators to capture error evolution under complex operating conditions.

[0215] Fractional calculus involves using dynamic fractional operators to perform fractional differentiation or integration on the current common-mode voltage tracking error. In digital controllers, this operation is typically performed using discretized difference equations. Alternatively, the error signal can be transformed to the frequency domain, fractional operations performed, and then inversely transformed back to the time domain.

[0216] Fractional error dynamic characteristics are error signals obtained after fractional calculus operations. They can more precisely reflect the long-term memory and nonlocality of errors, capture dynamic behaviors that are difficult to describe by traditional integer calculus, and provide richer and more accurate input information for subsequent control law solutions.

[0217] The reaching law coefficient adjustment is a dynamic parameter used to adjust the coefficients in the exponential reaching law, thereby changing the speed and manner in which the system state approaches the sliding surface. This adjustment allows the reaching law to adaptively optimize based on real-time operating conditions and control objectives (such as suppressing chattering and accelerating convergence). In practical applications, the reaching law coefficient adjustment can be generated by a fuzzy rule-based inference system, which judges and outputs the adjustment based on factors such as system chattering intensity and tracking error magnitude. Alternatively, it can be updated online based on system performance indicators (such as chattering suppression effect and convergence speed) using an adaptive law.

[0218] The pre-defined exponential reaching law is a commonly used reaching law in sliding mode control. It typically includes an exponential term and a sign function term, and is used to guide the system state to rapidly approach the sliding surface. Common forms of exponential reaching laws include k×sgn(s)+eta×s or k×sgn(s)+eta×s^alpha, etc.

[0219] Coefficient resetting refers to the process of dynamically modifying or updating the relevant coefficients (such as the reaching velocity coefficient and boundary layer thickness coefficient) in a preset exponential reaching law based on the adjustment amount of the reaching law coefficients. This process makes the parameters of the reaching law no longer fixed values, but can be adaptively adjusted according to real-time operating conditions. Specifically, coefficient resetting can be achieved by directly modifying the coefficient parameters in the reaching law equation. Alternatively, the system can maintain a lookup table containing different coefficient parameters and select appropriate coefficients through interpolation based on the reaching law coefficient adjustment amount.

[0220] The dynamic exponential reaching law is an exponential reaching law whose coefficient parameters can dynamically change with the operating conditions after the coefficients are reset. This reaching law can dynamically adjust the reaching speed and chattering suppression capability according to the real-time operating conditions, thereby effectively suppressing chattering while ensuring rapid system convergence.

[0221] The sign of the sliding surface function is the sign of the sliding surface function s, usually denoted as sgn(s). It indicates the position of the system state relative to the sliding surface and is a key term in the sliding mode control law. In digital systems, a digital comparator can be used to determine the sign of the sliding surface function s, outputting +1, -1, or 0.

[0222] Approach velocity modulation refers to dynamically adjusting the system state's approach velocity to the sliding surface using a dynamic exponential approach law, based on the sign value of the sliding surface function. This process ensures that the system approaches the sliding surface at the optimal speed and in the optimal manner under different operating conditions. Specifically, this can be achieved by substituting the sign value into the dynamic exponential approach law equation. Alternatively, the modulation amount can be determined by finding a preset modulation curve or function and using the sign value and dynamic approach law parameters.

[0223] The dynamic compensation amount of the approaching law is the compensation amount obtained after approaching speed modulation. It reflects the control action required to make the system state approach the sliding surface and takes into account the demand of the approaching speed due to changes in operating conditions.

[0224] In sliding mode control, the pre-defined equivalent control component is the control quantity required to maintain the system state on the sliding surface. It is typically calculated by setting the sliding surface derivative to zero. This component can be obtained by solving for s_dot=0 based on the system's mathematical model. Alternatively, it can be estimated online using an adaptive law or neural network.

[0225] Fusion refers to combining the fractional-order error dynamic characteristics with preset equivalent control components to generate a more accurate equivalent control correction. This fusion method can employ weighted summation: equivalent control correction = w1 × fractional-order error dynamic characteristics + w2 × preset equivalent control components, where w1 and w2 are weighting coefficients. Alternatively, fusion can be achieved through nonlinear mapping methods such as lookup tables, fuzzy logic, or neural networks to better capture the complex relationship between the two.

[0226] The equivalent control correction is an equivalent control component that incorporates the dynamic characteristics of fractional-order errors. It can more accurately reflect the control action required by the system on the sliding surface and takes into account the complex dynamics of the error, thereby improving control accuracy.

[0227] Superposition refers to the linear addition of the equivalent control correction and the dynamic compensation of the reaching law to form the total control quantity. This superposition is a typical configuration of sliding mode control law, in which the equivalent control component is responsible for keeping the system on the sliding surface, while the reaching law component is responsible for guiding the system to approach the sliding surface.

[0228] Amplitude normalization refers to adjusting the superimposed total control value to a preset amplitude range (e.g., -1 to 1 or 0 to 1) to adapt to the physical limitations of the PWM duty cycle. Normalization can be achieved using linear normalization, i.e., normalized value = (x - min_val) / (max_val - min_val). Alternatively, a saturation function can be used to clamp values ​​outside the range to their maximum or minimum values. Another option is to use a non-linear mapping such as the Sigmoid function to map the value to the range of 0 to 1.

[0229] The duty cycle correction is a control quantity obtained after normalization. It is used to correct the basic duty cycle, thereby generating a PWM drive signal to control the power switching of the micro-inverter.

[0230] Through the above technical solution, this application achieves adaptive adjustment of the sliding mode control law by dynamically reconstructing the fractional-order calculus operator and resetting the exponential reaching law coefficients, thus solving the problem of insufficient control accuracy and stability of traditional fixed-parameter sliding mode control under complex operating conditions of micro-inverters. Specifically, based on the fractional-order order adjustment, the preset fractional-order calculus operator is reconstructed to obtain a dynamic fractional-order operator. This allows the control system to flexibly adapt to the non-integer order dynamic characteristics of the common-mode voltage tracking error according to the real-time adjusted order, avoiding the problem that fixed operators cannot capture the error evolution under complex operating conditions. Based on the dynamic fractional-order operator, fractional-order calculus is performed on the current common-mode voltage tracking error to obtain the fractional-order error dynamic characteristics. The dynamic nature of the reconstructed operator is used to accurately extract the time-varying behavior of the error, providing richer and more accurate input information for control. At the same time, based on the reaching law coefficient adjustment, the preset exponential reaching law coefficients are reset to obtain a dynamic exponential reaching law. The reaching law parameters are optimized according to the adjustment, thereby effectively reducing system chattering and improving response speed. Based on the dynamic exponential reaching law, the sign value of the sliding mode surface function is modulated with a reaching speed to obtain a dynamic compensation amount for the reaching law. By dynamically adjusting the reaching behavior through the modulation of the sign value, the robustness of the control is further enhanced. The dynamic characteristics of the fractional-order error are fused with the preset equivalent control components to obtain an equivalent control correction amount. This fusion method allows the equivalent control strategy to better fit the complex dynamic changes of the error. The equivalent control correction amount and the dynamic compensation amount of the reaching law are superimposed, and the amplitude of the superposition result is normalized to generate a duty cycle correction amount. By combining the two compensation amounts and normalizing them, the stability and effectiveness of the output duty cycle are ensured, preventing overshoot or distortion. Overall, the scheme of this application enables the micro-inverter to adaptively adjust the control strategy when facing complex operating conditions such as load changes and reactive power injection, thereby achieving effective suppression of common-mode voltage, reducing leakage current, and improving the safety and power quality of system operation across the entire operating range.

[0231] In some embodiments described above in this application, a method is proposed to reconstruct the order of a preset fractional-order calculus operator based on a fractional-order order adjustment, and then use the reconstructed dynamic operator to calculate the common-mode voltage tracking error to obtain the fractional-order error dynamic characteristics. However, directly reconstructing the operator based on the fractional-order order adjustment may result in an unsmooth dynamic response due to abrupt changes in order or improper selection of the approximation method, affecting the stability and accuracy of fractional-order calculus calculations. Furthermore, simply extracting the amplitude of the calculation results without considering the instantaneous change trend of the error itself to dynamically correct the extracted results means that the obtained fractional-order error dynamic characteristics cannot fully reflect the time-varying behavior of the error, thereby weakening the adaptive capability of sliding mode control.

[0232] To address this, this application further proposes a method to reconstruct the order of a preset fractional-order calculus operator based on a fractional-order order adjustment, obtaining a dynamic fractional-order operator. Then, based on this dynamic fractional-order operator, fractional-order calculus is performed on the current common-mode voltage tracking error to obtain the dynamic characteristics of the fractional-order error. This process includes: superimposing the fractional-order order adjustment with a reference order value to obtain the target fractional-order order at the current moment; matching the corresponding filter parameter set from a fractional-order approximation filter library based on the target fractional-order order; resetting the coefficients of the fractional-order calculus operator based on the matched filter parameter set to obtain the dynamic fractional-order operator; inputting the current common-mode voltage tracking error into the dynamic fractional-order operator for convolution, outputting an initial fractional-order calculus result; extracting the amplitude of the initial fractional-order calculus result, and dynamically correcting the amplitude extraction result based on the instantaneous rate of change of the current common-mode voltage tracking error to obtain the dynamic characteristics of the fractional-order error.

[0233] Specifically, the fractional-order adjustment is superimposed on the order baseline value to achieve smooth and continuous updates of the fractional-order. The fractional-order adjustment is a dynamically generated quantity based on real-time system conditions, reflecting the current demand for the fractional-order. The order baseline value is a preset, stable reference value representing the fractional-order under normal or ideal operating conditions. Through superposition, the order can be dynamically corrected based on real-time changes in operating conditions, avoiding abrupt changes in order. For example, superposition can use simple arithmetic addition, where the target fractional-order equals the order baseline value plus the fractional-order adjustment. Alternatively, a weighted average can be used, where the order baseline value is given a larger weight, while the fractional-order adjustment is given a smaller weight, ensuring the stability of the order adjustment and avoiding operator instability caused by drastic fluctuations in the adjustment amount.

[0234] Based on the target fractional order, the corresponding filter parameter set is matched from the fractional-order approximation filter library. The target fractional order is the dynamic order obtained in the previous step, indicating the specific order of the fractional-order calculus operator required by the current system. The fractional-order approximation filter library is a pre-built database that stores discretized filter parameter sets corresponding to different fractional orders. These parameter sets are usually obtained through offline calculation or optimization and are used to approximate fractional-order calculus operations in digital systems. The matching process aims to select the filter parameter set that best approximates the calculus operation of that order from the library based on the current target fractional order. For example, a lookup table method can be used to directly find the pre-stored parameter set that is closest to the target order. Alternatively, an interpolation method can be used; when the target order does not exist precisely in the library, a more refined parameter set can be obtained by linearly or nonlinearly interpolating the parameters of adjacent orders in the library.

[0235] The coefficients of the fractional-order calculus operator are reset based on the matched filter parameter set to obtain a dynamic fractional-order operator. The matched filter parameter set is selected in the previous step according to the target fractional order. Fractional-order calculus operators usually exist in a discretized form, and their internal coefficients determine the order and characteristics of their fractional calculus. Coefficient resetting refers to updating or reconfiguring the internal coefficients of the fractional-order calculus operator based on the matched parameter set, enabling it to perform calculus operations at the current target fractional order. For example, the matched parameter set can be directly assigned to the operator's coefficients for rapid updating. Alternatively, based on the original coefficients, the new parameter set can be gradually approximated through small-step iterations to achieve a smooth transition of the operator coefficients and reduce system impact.

[0236] The current common-mode voltage tracking error is input into a dynamic fractional operator for convolution, outputting the initial fractional calculus result. The current common-mode voltage tracking error is the deviation between the actual and expected values ​​of the common-mode voltage during the real-time operation of the micro-inverter. The dynamic fractional operator is the operator dynamically reconstructed based on real-time operating conditions in the previous step. Convolution is a common method in digital signal processing for realizing the response of linear time-invariant systems; here, it is used to process the error signal through fractional calculus using a fractional operator. For example, convolution can be performed directly in the time domain, multiplying and accumulating the error sequence with the operator's impulse response point by point. Alternatively, in the frequency domain, the error signal and the operator's transfer function can be Fourier transformed, multiplied, and then subjected to an inverse Fourier transform to improve computational efficiency.

[0237] The initial fractional-order calculus result is used to extract the amplitude, and the extracted amplitude is dynamically corrected based on the instantaneous rate of change of the current common-mode voltage tracking error to obtain the fractional-order error dynamic characteristics. The initial fractional-order calculus result is the direct output of the convolution operation, containing information about the error signal after fractional-order calculus processing. Amplitude extraction aims to obtain the main intensity information of the result, such as its absolute value, root mean square value, or peak value. The instantaneous rate of change of the current common-mode voltage tracking error reflects the rapid changing trend of the error signal. The purpose of dynamic correction is to incorporate the transient changing trend of the error itself into the amplitude extraction result, so that the obtained fractional-order error dynamic characteristics not only contain the intensity information of the error but also reflect its instantaneous evolution characteristics. For example, a weighted average method can be used to fuse the extracted amplitude and the instantaneous rate of change with a certain weight. Alternatively, a nonlinear correction function can be designed to gain or attenuate the amplitude extraction result according to the magnitude of the instantaneous rate of change, thereby more sensitively reflecting the dynamic behavior of the error.

[0238] Through the above technical solution, this application solves the accuracy and stability problems in the generation of dynamic fractional-order operators and the extraction of fractional-order error characteristics by using a smooth order reconstruction mechanism and error-aware dynamic correction, thereby improving the adaptive capability of sliding mode control. Specifically, the fractional-order adjustment amount is superimposed with the order reference value to achieve continuous and smooth order updates, avoiding operator abrupt changes caused by direct jumps in the adjustment amount. Based on the target fractional-order, the corresponding filter parameter set is matched from the fractional-order approximation filter library. The most suitable filter approximation structure is selected according to different order requirements to ensure the accuracy of calculus operations at different orders. Based on the matched filter parameter set, the coefficients of the fractional-order calculus operator are reset to obtain a dynamic fractional-order operator, enabling the internal coefficients of the operator to track changes in the target order in real time and maintain the accuracy of the operation. The current common-mode voltage tracking error is input into the dynamic fractional-order operator for convolution operation, and the initial fractional-order calculus result is output. The dynamic characteristics of the reconstruction operator are used to accurately calculate the fractional-order calculus value of the error. The initial fractional-order calculus results are used to extract amplitude, obtaining key intensity information of the error dynamic characteristics. The amplitude extraction results are then dynamically corrected based on the instantaneous rate of change of the current common-mode voltage tracking error, incorporating the transient trend of the error itself into the correction process. This ensures that the fractional-order error dynamic characteristics not only include amplitude information but also reflect the instantaneous evolution of the error, enhancing the ability to characterize the dynamic behavior of the error. Overall, these steps work synergistically to achieve end-to-end optimization from order adjustment to operator reconstruction to characteristic extraction. This provides more accurate and dynamically responsive fractional-order error information for subsequent sliding mode control law calculations, improving the robustness and adaptability of the micro-inverter's common-mode voltage suppression under complex operating conditions.

[0239] In some of the embodiments described above in this application, a method is proposed to reset the approach law based on the adjustment of the approach law coefficient and generate a compensation amount to suppress common-mode voltage fluctuations and reduce sliding mode chattering. However, in its implementation, the current output state of the sliding surface function and the dynamic rate of change of the common-mode voltage tracking error are not fully considered when resetting the approach law, which may result in the initial compensation amount not being able to accurately adapt to the transient fluctuations of the operating conditions, thereby affecting the modulation accuracy of the approach speed and the stability of the boundary layer, weakening the chattering suppression effect and voltage tracking performance.

[0240] To address this, this application further proposes resetting the coefficients of a preset exponential reaching law based on the reaching law coefficient adjustment to obtain a dynamic exponential reaching law. Then, based on the dynamic exponential reaching law, the sign value of the sliding surface function is modulated with a reaching velocity to obtain a dynamic compensation amount for the reaching law. This method includes the following steps: The dynamic approach coefficient is obtained by superimposing the adjustment amount of the approach law coefficient with the approach law benchmark coefficient.

[0241] Based on the dynamic reaching coefficient, the coefficients of the exponential term and the constant term in the exponential reaching law are updated synchronously to obtain the dynamic exponential reaching law.

[0242] Obtain the current output value of the sliding surface function, and extract the sign of the current output value to obtain the sign value of the sliding surface function.

[0243] Input the sign value into the dynamic exponential reaching law, and the dynamic exponential reaching law calculates the initial reaching law compensation amount based on the sign value and the dynamic reaching coefficient.

[0244] The rate of change of the current common-mode voltage tracking error is obtained, and the initial reaching law compensation amount is adaptively adjusted at the boundary layer based on the rate of change to obtain the dynamic compensation amount of the reaching law.

[0245] The adjustment amount of the reaching law coefficient originates from the aforementioned steps and is adaptively generated based on the real-time operating conditions of the microinverter. It is used to correct the reaching law parameters. It reflects the specific requirements of the system for the reaching law parameters under the current operating state. The reaching law reference coefficient is a pre-set initial parameter of the reaching law determined under the system design or nominal operating conditions. It provides a stable reference starting point for the dynamic adjustment of the reaching law. The superposition operation aims to effectively integrate the adjustment amount with the reference coefficient to generate a comprehensive reaching law coefficient that reflects the current operating condition requirements. This integration can be a simple arithmetic addition, such as dynamic reaching law coefficient = reaching law reference coefficient + reaching law coefficient adjustment amount. It can also be a weighted average, such as dynamic reaching law coefficient = w1 × reaching law reference coefficient + w2 × reaching law coefficient adjustment amount, where w1 and w2 are preset weight coefficients. The dynamic reaching law coefficient is a coefficient that changes in real time, combining the preset reference value and the adjustment amount adaptively generated based on the current operating conditions. This coefficient will be used to subsequently dynamically adjust the specific parameters of the exponential reaching law to ensure that the reaching law can flexibly respond to changes in operating conditions.

[0246] The exponential reaching law is a commonly used reaching law in sliding mode control. Its general form includes an exponential term and a constant term, used to guide the system state to quickly approach the sliding surface and suppress chattering. For example, it can be expressed as u_sm = -k × s - epsilon × sgn(s), where k is the exponential coefficient and epsilon is the constant coefficient. The exponential and constant coefficients together determine the dynamic characteristics of the reaching law. The exponential coefficient mainly affects the speed at which the system approaches the sliding surface, while the constant coefficient mainly affects chattering suppression capability and steady-state accuracy. Synchronous updating refers to adjusting both the exponential and constant coefficients simultaneously based on the dynamic reaching coefficient. This can be achieved through a preset mapping function or lookup table. For example, two independent mapping functions can be designed: k = f_k (dynamic reaching coefficient) and epsilon = f_epsilon (dynamic reaching coefficient). Alternatively, it can be achieved through proportional relationships, such as k = alpha × dynamic reaching coefficient and epsilon = beta × dynamic reaching coefficient, where alpha and beta are preset scaling factors. The dynamic exponential reaching law is an exponential reaching law with parameters that change in real time. Both the exponential and constant coefficients are adjusted based on the dynamic reaching coefficient. It can dynamically adjust the reaching speed and chattering suppression intensity according to changes in system operating conditions, thereby improving the adaptability and robustness of the control system.

[0247] The current output value of the sliding surface function is the core of sliding mode control; its output value *s* reflects the deviation between the system state and the desired sliding surface. When *s* is close to zero, it indicates that the system state is close to the sliding surface. The sign extraction operation typically refers to obtaining the sign of the sliding surface function's output value. For example, the *sgn(s)* function can be used, outputting 1 when *s* > 0, -1 when *s* < 0, and 0 when *s* = 0. Alternatively, a piecewise function can be used, such as outputting 1 when *s* > delta, -1 when *s* < -delta, and s / delta when |s| <= delta (where delta is a small positive number). The sign value of the sliding surface function indicates which side of the sliding surface the system state is on, and in which direction the system needs to move to approach the sliding surface. It is crucial information for determining the direction of the approaching law. The sign value of the previously obtained sliding surface function is used as one of the inputs to the dynamic exponential approaching law to determine its direction. The dynamic exponential reaching law combines the sign value of the sliding surface function with the previously obtained dynamic reaching coefficients to calculate an initial compensation amount. For example, if the dynamic exponential reaching law is u_sm = -k×s - epsilon×sgn(s), then the initial reaching law compensation amount might be epsilon×sgn(s), or more generally, the part of the reaching law related to the sign function, used to provide control force for rapid approach to the sliding surface. The initial reaching law compensation amount is a preliminary control amount calculated based on the current sliding surface state and the dynamically adjusted reaching law parameters, aiming to guide the system state towards the sliding surface.

[0248] The rate of change of the current common-mode voltage tracking error refers to the speed at which the error between the actual and expected values ​​of the common-mode voltage changes over time. It can reflect the severity and trend of common-mode voltage fluctuations. For example, it can be obtained by performing first-order difference on the error signal or by using a Kalman filter for state estimation. Boundary layer adaptive adjustment refers to dynamically adjusting the thickness or smoothness of the compensation amount based on the rate of change of the common-mode voltage tracking error. For example, when the rate of change is large, the boundary layer thickness can be appropriately increased to reduce chattering. When the rate of change is small, the boundary layer thickness can be decreased to improve tracking accuracy. This can be achieved through a nonlinear function mapping, such as compensation amount _adj = initial compensation amount × f (rate of change), or through fuzzy logic controllers, neural networks, etc., mapping the error rate of change to the adjustment of boundary layer parameters. The dynamic compensation amount of the reaching law is the reaching law compensation amount after boundary layer adaptive adjustment. It not only considers the current state of the sliding surface and the dynamic reaching parameters, but also performs fine-tuning based on the rate of change of the common-mode voltage tracking error to achieve a better balance between suppressing chattering and ensuring tracking accuracy.

[0249] Through the above technical solution, this application can solve the problem caused by the failure to fully consider the current output state of the sliding surface function and the dynamic rate of change of the common-mode voltage tracking error when resetting the reaching law. Specifically, by superimposing the reaching law coefficient adjustment amount with the reaching law reference coefficient, a dynamic reaching coefficient is obtained, which enables the reaching law parameters to integrate the adjustment requirements brought about by changes in operating conditions in real time, avoiding the response lag caused by fixed parameters. On this basis, the exponential term coefficient and constant term coefficient in the exponential reaching law are updated synchronously based on the dynamic reaching coefficient, ensuring that the reaching law maintains the optimal reaching speed and chattering suppression capability under different operating conditions. Furthermore, by obtaining the current output value of the sliding surface function and extracting its sign value, the calculation of the initial reaching law compensation amount can accurately reflect the current deviation of the system from the sliding surface, ensuring the timeliness and accuracy of the control action. More importantly, this application further obtains the current rate of change of the common-mode voltage tracking error and performs boundary layer adaptive adjustment of the initial reaching law compensation amount based on this rate of change, thereby enabling the dynamic compensation amount of the reaching law to be finely corrected according to the severity and trend of common-mode voltage fluctuations. This adaptive adjustment mechanism effectively avoids the contradiction between chattering and tracking accuracy caused by traditional fixed boundary layers, improves the modulation accuracy of approach velocity and boundary layer stability, effectively suppresses sliding mode chattering across the entire operating range, and improves the tracking performance of common mode voltage.

[0250] In some of the above-mentioned schemes in this application, a sliding mode control law is proposed to generate duty cycle correction by calculating the fractional order adjustment amount and the reaching law coefficient adjustment amount. However, in this process, due to the lack of dynamic differential configuration of the sliding mode surface function and the reaching law component, it is difficult to adaptively adjust the control strategy according to the real-time operating condition changes. As a result, the sliding mode control accuracy is insufficient and the common mode voltage suppression effect decreases under complex operating conditions such as load sudden change or reactive power injection.

[0251] To address this, this application proposes a sliding mode control law solution method, comprising: reconstructing the order of a fractional-order calculus operator based on a fractional-order adjustment to obtain a dynamic fractional-order operator; performing fractional-order differentiation on the current common-mode voltage tracking error using this dynamic fractional-order operator to obtain a fractional-order error trajectory; differentially configuring the constant-rate reaching term coefficient and the exponential reaching term coefficient in the exponential reaching law based on the reaching law coefficient adjustment to obtain a first reaching law component with dynamic reaching intensity and a second reaching law component with dynamic boundary layer thickness; nonlinearly coupling the fractional-order error trajectory with the current common-mode voltage tracking error to construct a sliding mode surface function with adaptive error trajectory capability; solving the sliding mode surface function to obtain the sliding mode surface output value; selecting a corresponding reaching law component from the first reaching law component and the second reaching law component based on the amplitude range of the sliding mode surface output value for activation; and superimposing the activated reaching law component with the equivalent control component to obtain the duty cycle correction amount.

[0252] Specifically, the fractional-order calculus operator is reconstructed based on the fractional-order adjustment, resulting in a dynamic fractional-order operator. This dynamic fractional-order operator is then used to perform fractional-order differentiation on the current common-mode voltage tracking error, yielding the fractional-order error trajectory. This step aims to flexibly adjust the order of the fractional-order calculus operator according to the dynamic changes in system operating conditions, thereby more accurately capturing the dynamic characteristics of the common-mode voltage tracking error. The fractional-order calculus operator is a generalized calculus operator, whose order can be any real number, rather than the traditional integer order. By dynamically adjusting its order, the controller can perform more refined analysis and response to error signals across different frequency ranges and time scales. In one implementation, order reconstruction can be achieved using a lookup table method. A mapping relationship between the fractional-order adjustment and the fractional-order calculus operator parameters is pre-established, and the operator parameters are directly queried and updated based on the real-time fractional-order adjustment. In another implementation, an online optimization algorithm, such as a genetic algorithm or a particle swarm optimization algorithm, can be used to optimize the approximation parameters of the fractional-order calculus operator in real time based on the fractional-order adjustment amount and preset performance indicators, thereby achieving dynamic reconstruction of the order.

[0253] Furthermore, based on the adjustment amount of the reaching law coefficients, the coefficients of the constant-velocity reaching term and the exponential reaching term in the exponential reaching law are differentiated to obtain a first reaching law component with dynamic reaching intensity and a second reaching law component with dynamic boundary layer thickness. This step aims to finely configure the reaching law parameters in sliding mode control according to the adjustment amount of the reaching law coefficients to achieve rapid and smooth reaching of the system state. The exponential reaching law typically includes a constant-velocity reaching term (for fast convergence) and an exponential reaching term (for reducing chattering). Differentiated configuration means that the coefficients of these two terms can be adjusted independently, thereby controlling the reaching speed and chattering suppression effect separately. In one implementation, the reaching law coefficient adjustment amount can be mapped to the constant-velocity reaching term coefficients and the exponential reaching term coefficients through a piecewise linear function or a nonlinear function. For example, when the adjustment amount is large, the constant-velocity reaching term coefficient is increased to improve the reaching speed. When the adjustment amount is small, the exponential reaching term coefficient is decreased to reduce chattering. In another implementation, a fuzzy logic controller can be used, taking the adjustment amount of the reaching law coefficient as input, and obtaining the output values ​​of the constant-rate reaching term coefficient and the exponential reaching term coefficient through fuzzy rule reasoning, thereby achieving intelligent differentiated configuration.

[0254] Based on this, the fractional-order error trajectory is nonlinearly coupled with the current common-mode voltage tracking error to construct a sliding surface function with adaptive error trajectory capabilities. This sliding surface function is then solved to obtain the sliding surface output value. This step aims to construct a sliding surface function that can adapt to changing operating conditions by fusing the fractional-order error trajectory and the current common-mode voltage tracking error. Traditional sliding surface functions are usually linear or fixed nonlinear functions constructed based on the current error and its derivative, making them difficult to adapt to complex operating conditions. Nonlinear coupling can more flexibly combine two types of error information, enabling the sliding surface to reflect both the long-term trend and instantaneous changes of the error, thereby enhancing its ability to capture system dynamics. In one implementation, a nonlinear function such as a polynomial function or a sigmoid function can be used to weight and combine the fractional-order error trajectory and the current common-mode voltage tracking error. In another implementation, a neural network can be used, taking the fractional-order error trajectory and the current common-mode voltage tracking error as input, and using the nonlinear mapping capability of the neural network to output the value of the sliding surface function.

[0255] Based on the amplitude range of the sliding surface output value, a corresponding reaching law component is selected from the first reaching law component and the second reaching law component for activation. The activated reaching law component is then superimposed with the equivalent control component to obtain the duty cycle correction. This step aims to intelligently select the most suitable reaching law component for the current operating condition based on the real-time state of the sliding surface output value, thereby optimizing control performance. The amplitude of the sliding surface output value typically reflects the degree to which the system state deviates from the sliding surface. When the deviation is large, a stronger reaching intensity may be required. When the deviation is small, a smoother reaching intensity is needed to reduce chattering. In one implementation, multiple amplitude range thresholds can be set. When the sliding surface output value falls into a certain range, the corresponding reaching law component is activated. For example, when the amplitude is large, the first reaching law component (dynamic reaching intensity) is activated. When the amplitude is small, the second reaching law component (dynamic boundary layer thickness) is activated. In another implementation, a fuzzy decision system can be used, where the amplitude of the sliding surface output value is used as a fuzzy input. The activation weights of the two convergence law components are obtained through fuzzy rule reasoning, and then they are weighted and superimposed.

[0256] Through the above technical solutions, this application solves the problem of insufficient adaptability of sliding mode control laws under complex operating conditions by dynamically reconstructing fractional-order operators, differentially configuring reaching law components, constructing adaptive sliding mode surface functions, and intelligently selecting reaching law components. Specifically, by reconstructing the order of fractional-order calculus operators based on fractional-order order adjustment, the fractional-order operators can dynamically adjust their order according to changes in the real-time operating conditions of the micro-inverter, thereby more accurately capturing the dynamic characteristics of common-mode voltage tracking error and avoiding control deviations that may occur under complex operating conditions with traditional fixed-order operators. By using this dynamic fractional-order operator to perform fractional-order differential operations on the current common-mode voltage tracking error, deep dynamic information of the error signal can be obtained in real time, generating a more refined fractional-order error trajectory, providing richer and more accurate system state information for subsequent sliding mode surface design. At the same time, by differentially configuring the constant-rate reaching term coefficients and exponential reaching term coefficients in the exponential reaching law based on reaching law coefficient adjustment, the reaching law can independently adjust the reaching speed and chattering suppression effect according to operating conditions. This yields a first approach law component with dynamic approach strength and a second approach law component with dynamic boundary layer thickness, providing two approach strategies with different focuses for sliding mode control, enhancing the system's flexibility in responding to different disturbance levels and control objectives. Furthermore, the fractional-order error trajectory is nonlinearly coupled with the current common-mode voltage tracking error to construct a sliding surface function with adaptive error trajectory capabilities. This nonlinear coupling method fully integrates the instantaneous value of the error and its historical dynamic trend, making the sliding surface function no longer fixed but dynamically adjusting its structure and parameters according to the characteristics of the error trajectory, improving the robustness and adaptability of sliding mode control to complex operating conditions. Solving this adaptive sliding surface function yields an accurate sliding surface output value reflecting the current system state, providing a reliable basis for subsequent control decisions. Based on the amplitude range of the sliding surface output value, the most suitable approach law component for the current system deviation is intelligently selected from the dynamically configured first and second approach law components for activation. For example, when the system deviates significantly from the sliding surface, the component with stronger approach capability is activated for rapid convergence. As the system approaches the sliding mode surface, components with smoother characteristics are activated to effectively suppress chattering. The activated reaching law component is superimposed with the equivalent control component to generate a precise and adaptive duty cycle correction. Through this series of dynamic and adaptive control strategies, this application can improve the common-mode voltage suppression effect of micro-inverters under complex operating conditions such as load abrupt changes or reactive power injection, reduce leakage current, and ensure stable system operation.

[0257] In some embodiments described above in this application, a method is proposed to reconstruct the order of a fractional-order calculus operator based on a fractional-order order adjustment, and then use the reconstructed dynamic operator to perform fractional-order differential operations on the current common-mode voltage tracking error to obtain a fractional-order error trajectory. However, when directly reconstructing the operator based on the fractional-order order adjustment, if only the current order value is considered and the historical evolution trend of the order is ignored, unnecessary jumps in the dynamic response of the operator may occur, affecting the continuity and stability of the differential operation. Furthermore, simply outputting the differential operation result without extracting morphological features means that the obtained fractional-order error trajectory cannot fully reflect the evolution of the error over time, thus weakening the value of utilizing the error trajectory morphology in the subsequent sliding surface construction process.

[0258] To address this, this application further proposes reconstructing the order of the fractional-order calculus operator based on the fractional-order order adjustment to obtain a dynamic fractional-order operator. This dynamic fractional-order operator is then used to perform fractional-order differentiation on the current common-mode voltage tracking error to obtain the fractional-order error trajectory, including: The fractional order adjustment is weighted and fused with the fractional order value of the previous time step to obtain the target fractional order at the current time step.

[0259] Based on the deviation between the target fractional order and the current fractional order, the corresponding approximator structure parameters are matched from the fractional approximator library.

[0260] The coefficients of the transfer function of the fractional-order calculus operator are reset based on the approximator structure parameters to obtain the dynamic fractional-order operator.

[0261] The current common-mode voltage tracking error is input into the dynamic fractional operator for convolution operation, and the output is a fractional differential sequence.

[0262] The envelope of the fractional differential sequence is extracted to obtain the fractional error trajectory.

[0263] The fractional order adjustment is a value generated dynamically based on the operating conditions of the microinverter. It is used to adjust the order of the fractional calculus operator and can be a direct order increment or decrement, or an order scaling factor. The previous fractional order value refers to the order of the fractional calculus operator used by the system before the current control cycle. It can be the order value of the previous sampling cycle stored in the controller memory, or a smoothed historical order average. Weighted fusion is a mathematical operation that combines two or more values ​​according to preset weights, aiming to balance the influence of different inputs on the result. For example, it can use a linear weighted average, where the current order adjustment is multiplied by a weight α, and the previous order value is multiplied by a weight (1-α), or a nonlinear weighted fusion based on fuzzy logic or neural networks. The target fractional order is the ideal order of the fractional calculus operator used in the current control cycle, determined after weighted fusion. It can be a specific value, such as 0.85, or a floating-point number within a preset range. The current fractional order refers to the order of the fractional calculus operator currently used by the system. This may differ from the target order. It can be the baseline order set during system initialization or the order that actually took effect after the previous control cycle. This fractional approximator library stores various discretized approximation models for implementing fractional calculus operators and their corresponding structural parameters. For example, it can include parameter sets of approximators of different orders defined based on Oustaloup, Grünwald-Letnikov, or Caputo, or sets of transfer function coefficients optimized for different frequency ranges. The approximator structural parameters describe the numerical set of the specific implementation of the fractional calculus operator approximator, such as the numerator and denominator coefficients of the transfer function, the filter order, etc. These can be coefficients of digital filters (such as FIR or IIR filters) or matrix parameters based on a state-space model. The transfer function of this fractional-order calculus operator describes the input-output relationship of the fractional-order calculus operator in the frequency domain or Z-domain, usually expressed as a polynomial ratio. It can be a discretized transfer function, such as G(z) in the Z-transform form, or the result of discretizing G(s) in the continuous domain S-transform form. The coefficient reset involves updating or reconfiguring the coefficients in the fractional-order calculus operator's transfer function based on the matched approximator structure parameters. For example, the coefficient matrix in the transfer function can be directly replaced, or new coefficients can be dynamically generated based on the approximator parameters using an interpolation algorithm. The dynamic fractional-order operator, after order reconstruction and coefficient reset, is a calculus operator that can dynamically adjust its fractional order according to the current operating conditions. It can be a software module whose internal parameters (such as filter coefficients) can be updated in real time, or it can be a configurable digital signal processor (DSP) instruction set.The current common-mode voltage tracking error refers to the instantaneous difference between the actual value of the common-mode voltage output by the micro-inverter and the expected target value. It can be a sampled and quantized digital signal, or an error signal after low-pass filtering. Convolution is a commonly used mathematical operation in signal processing, used to calculate the integral of the superposition of two functions (or sequences). It is often used in filter signal processing and can be implemented directly using discrete convolution algorithms or through frequency domain multiplication (FFT-IFFT). The fractional derivative sequence is a series of discrete values ​​obtained after performing fractional derivative operations on the current common-mode voltage tracking error using a dynamic fractional operator. It can be a numerical sequence representing the rate of change of the error signal in the sense of fractional derivatives, or a sequence reflecting the memory characteristics of the error signal. Envelope extraction is a method for extracting the amplitude profile or trend line from a signal. It can remove high-frequency noise or details and highlight the overall variation law of the signal. For example, it can be based on the Hilbert Transform, or on methods based on moving average, low-pass filtering, or local maxima connection. The fractional error trajectory is a smooth curve or trend line of the fractional differential sequence obtained after envelope extraction. It can intuitively reflect the dynamic evolution of the common-mode voltage tracking error in the fractional sense. It can be a continuous curve, representing the long-term trend and short-term fluctuations of the error, or it can be a discrete but smooth numerical sequence.

[0264] Through the above technical solution, this application solves the problems of continuity maintenance and morphological feature extraction in the construction process of fractional-order error trajectories by introducing a weighted fusion mechanism of order history information and envelope extraction technology of differential sequences, thereby providing richer error evolution information for subsequent sliding mode surface functions. Specifically, the fractional-order adjustment amount is weighted and fused with the fractional-order order value of the previous moment to obtain the target fractional-order order at the current moment. By introducing historical order information, a smooth transition of order change is achieved, avoiding operator order jumps caused by abrupt changes in the order adjustment amount, and ensuring the continuity of differential operations. Based on the deviation between the target fractional-order order and the current fractional-order order, the corresponding approximator structure parameters are matched from the fractional-order approximator library. The most suitable approximator structure is selected according to the magnitude and direction of the order deviation to ensure the accuracy of differential operations under different order change amplitudes. Based on the approximator structure parameters, the transfer function of the fractional-order calculus operator is reset to obtain a dynamic fractional-order operator, enabling the frequency domain characteristics of the operator to track the change of the target order in real time and maintain the accuracy of the operation. The current common-mode voltage tracking error is input into a dynamic fractional-order operator for convolution, outputting a fractional-order differential sequence. The dynamic characteristics of the reconstruction operator are then used to obtain the fractional-order differential value sequence of the error at continuous time points. Envelope extraction is performed on the fractional-order differential sequence to obtain the fractional-order error trajectory. Envelope extraction technology is used to extract the overall trend and morphological characteristics of the error evolution from the differential sequence, ensuring that the fractional-order error trajectory not only contains differential value information but also reflects the evolution of the error over time, providing morphologically aware input features for subsequent sliding mode surface construction. Overall, these steps work synergistically to achieve end-to-end optimization from smooth order update to precise operator reconstruction and error trajectory morphological extraction, improving the adaptability and robustness of fractional-order sliding mode control under complex operating conditions, effectively suppressing the common-mode voltage of the micro-inverter, and reducing leakage current.

[0265] In some of the above-mentioned schemes of this application, a differential configuration of the constant-rate reaching term coefficient and the exponential reaching term coefficient in the exponential reaching law is proposed based on the reaching law coefficient adjustment amount, in order to generate a first reaching law component with dynamic reaching intensity and a second reaching law component with dynamic boundary layer thickness. However, in this process, the configuration process lacks a detailed analysis of the amplitude and rate of change of the reaching law coefficient adjustment amount, resulting in insufficient dynamic performance of the reaching law component, and it is unable to adaptively optimize according to the real-time intensity change and trend evolution of the working condition, thereby affecting the response accuracy and stability of sliding mode control.

[0266] To address this, this application further proposes a differentiated configuration of the constant-rate reaching term coefficients and exponential reaching term coefficients in the exponential reaching law based on the reaching law coefficient adjustment amount, resulting in a first reaching law component with dynamic reaching intensity and a second reaching law component with dynamic boundary layer thickness. Specifically, this includes: extracting the amplitude of the reaching law coefficient adjustment amount to obtain an adjustment amplitude factor, and extracting the rate of change of the reaching law coefficient adjustment amount to obtain an adjustment trend factor. Based on the numerical range of the adjustment amplitude factor, a corresponding first mapping curve is selected from the reaching intensity mapping curve family, and the adjustment amplitude factor is input into the first mapping curve for nonlinear transformation to obtain the dynamic configuration value of the constant-rate reaching term coefficients. The dynamic configuration value of the constant-rate reaching term coefficients is coupled with the current output value of the sliding surface function to obtain the first reaching law component. Based on the positive or negative polarity of the adjustment trend factor, a corresponding second mapping curve is selected from the boundary layer thickness mapping curve family, and the absolute value of the adjustment trend factor is input into the second mapping curve for nonlinear transformation to obtain the dynamic configuration value of the exponential reaching term coefficients. The dynamic configuration value of the exponential reaching term coefficient is coupled with the absolute value of the current common-mode voltage tracking error to obtain the second reaching law component.

[0267] The adjustment amount of the reaching law coefficient is obtained by adaptively mapping parameters based on the dynamic operating condition entropy value and the sliding mode parameter benchmark. It reflects the need to adjust the reaching law coefficient under the current operating condition. The amplitude of this adjustment amount is extracted to obtain the adjustment amplitude factor. This refers to quantifying the strength of the adjustment amount by calculating its absolute value or its root mean square value within a certain time window. For example, the amplitude can be extracted using the moving average absolute value method or the root mean square value method to characterize the severity of the current operating condition disturbance. This adjustment amplitude factor is a quantitative indicator characterizing the strength of the reaching law coefficient adjustment amount; its value directly reflects the severity of the current operating condition disturbance or the degree to which the control system deviates from the ideal state.

[0268] Extracting the rate of change of the adjustment amount of the reaching law coefficient yields the trend factor, which refers to obtaining the speed and direction of its change by calculating the difference between consecutive sampling times or its slope within a certain time window. For example, the rate of change can be extracted by fitting the slope using the first-order difference method or the least squares method to characterize whether the operating condition disturbance is intensifying or deteriorating. This trend factor is an indicator characterizing the direction and speed of change of the reaching law coefficient adjustment amount; its positive or negative sign indicates whether the operating condition disturbance is increasing or decreasing, and its absolute value reflects the speed of change.

[0269] The family of reaching intensity mapping curves is a predefined set of nonlinear functions. Each curve corresponds to a different reaching intensity configuration strategy, used to map the adjustment magnitude factor to a dynamic configuration value of the constant-rate reaching term coefficient. These curves can be designed based on empirical data, simulation optimization, or expert knowledge; for example, they can include logarithmic curves, exponential curves, S-curves, etc., to adapt to the nonlinear mapping requirements under different magnitude factors. The first mapping curve is a specific curve dynamically selected from the family of reaching intensity mapping curves according to the numerical range of the adjustment magnitude factor. Its function is to transform the quantized magnitude factor into a specific constant-rate reaching term coefficient configuration value. This nonlinear transformation refers to performing mathematical operations on the adjustment magnitude factor through the first mapping curve, so that its output value presents a nonlinear relationship with the input value. For example, the Sigmoid function, ReLU function, or polynomial function can be used for transformation to achieve a more refined and flexible parameter configuration. The dynamic configuration value of the constant-rate reaching term coefficient is a parameter obtained after nonlinear transformation, used to adjust the strength of the constant-rate reaching law, and its value changes dynamically according to the intensity of the operating condition disturbance.

[0270] The current output value of the sliding surface function is a real-time quantity used in sliding mode control to measure the degree to which the system state deviates from the sliding surface. Its magnitude and sign reflect the current control state of the system. Coupling the dynamic configuration value of the constant-velocity reaching term coefficient with the current output value of the sliding surface function yields the first reaching law component. This involves multiplying, weighting, or performing other nonlinear combination operations on the dynamic configuration value and the output value of the sliding surface function to ensure that the strength of the constant-velocity reaching term is correlated in real-time with the degree to which the system deviates from the sliding surface. For example, a simple multiplicative coupling can be used: First reaching law component = Dynamic configuration value × Current output value of the sliding surface function. This first reaching law component is the constant-velocity reaching term in the exponential reaching law, and its strength is dynamically adjusted according to the intensity of the operating disturbance and the degree to which the system deviates from the sliding surface to provide a rapid reaching speed.

[0271] The boundary layer thickness mapping curve family is a predefined set of nonlinear functions. Each curve corresponds to a different boundary layer thickness configuration strategy, used to map the absolute value of the adjustment trend factor to a dynamic configuration value of the exponential approach term coefficient. These curves can be designed based on a trade-off between chattering suppression and control precision; for example, they can include arctangent functions, Gaussian functions, or piecewise linear functions to achieve appropriate boundary layer thicknesses under different trends. The second mapping curve is a specific curve dynamically selected from the boundary layer thickness mapping curve family based on the positive or negative polarity of the adjustment trend factor. Its function is to transform the quantified trend into a specific exponential approach term coefficient configuration value. This nonlinear transformation refers to performing mathematical operations on the absolute value of the adjustment trend factor through the second mapping curve, making the output value exhibit a nonlinear relationship with the input value. For example, exponential functions, logarithmic functions, or sigmoid functions can be used for transformation to achieve fine adjustment of the boundary layer thickness. The dynamic configuration value of the exponential reaching term coefficient is a parameter obtained after nonlinear transformation and used to adjust the strength of the exponential term in the exponential reaching law. Its value will change dynamically according to the changing trend of the operating condition disturbance.

[0272] The absolute value of the current common-mode voltage tracking error is the absolute value of the deviation between the actual and expected common-mode voltage values, reflecting the real-time effect of common-mode voltage suppression. The second reaching law component is obtained by coupling the dynamic configuration value of the exponential reaching term coefficient with the absolute value of the current common-mode voltage tracking error. This involves multiplying, weighting, or performing other nonlinear combinations of the dynamic configuration value and the absolute value of the current common-mode voltage tracking error to ensure that the strength of the exponential reaching term is correlated with the magnitude of the common-mode voltage tracking error in real time. For example, a simple multiplicative coupling can be used: Second reaching law component = Dynamic configuration value × Absolute value of current common-mode voltage tracking error. This second reaching law component is the exponential reaching term in the exponential reaching law, and its strength is dynamically adjusted according to the changing trend of the operating condition disturbance and the magnitude of the common-mode voltage tracking error to effectively suppress chattering while ensuring the reaching speed.

[0273] Through the above technical solution, this application can perform a detailed analysis of the amplitude and rate of change of the approach law coefficient adjustment, thereby realizing the dynamic differentiated configuration of the approach law components. Specifically, the amplitude of the approach law coefficient adjustment is extracted to obtain the adjustment amplitude factor, which quantifies the strength of the adjustment and provides basic data for subsequent configuration, ensuring that the configuration process can reflect the actual strength of the operating condition disturbance. At the same time, the rate of change of the approach law coefficient adjustment is extracted to obtain the adjustment trend factor, which captures the dynamic evolution trend of the adjustment and provides a basis for distinguishing the direction of operating condition change (such as intensification or deceleration), effectively avoiding the lag of fixed configuration. Based on the numerical range of the adjustment amplitude factor, the corresponding first mapping curve is selected from the family of approach intensity mapping curves, and its input is subjected to nonlinear transformation to obtain the dynamic configuration value of the constant velocity approach term coefficient. This method dynamically calls the matching mapping rules according to different intensity ranges, solving the problem that a single mapping cannot adapt to multiple intensity disturbances, making the strength of the constant velocity approach term more accurately match the actual needs and improving the adaptability of the approach intensity. The dynamic configuration value is coupled with the current output value of the sliding surface function to obtain the first reaching law component. This coupling ensures that the reaching law strength is correlated with the control state in real time, guaranteeing that the first reaching law component can quickly respond to changes in the sliding surface and enhancing the dynamic reaching effect. Furthermore, based on the positive or negative polarity of the adjustment trend factor, a corresponding second mapping curve is selected from the family of boundary layer thickness mapping curves, and its absolute value is input for nonlinear transformation to obtain the dynamic configuration value of the exponential reaching term coefficient. This processing method optimizes the mapping selection based on the directionality of the changing trend, solving the defect of ignoring directional differences in boundary layer adjustment, and enhances the robustness of the configuration through nonlinear transformation, enabling the boundary layer thickness to adapt to different rates of change. The dynamic configuration value of the exponential reaching term coefficient is coupled with the absolute value of the current common-mode voltage tracking error to obtain the second reaching law component. This coupling correlates the boundary layer thickness with the real-time error level, ensuring that the second reaching law component can effectively suppress chattering while maintaining the stability of the control system. Overall, this application enables the sliding mode control system of a micro-inverter to adaptively adjust the approach law parameters according to the real-time intensity changes and trend evolution of the operating conditions through multi-dimensional analysis of the adjustment amount of the approach law coefficient and nonlinear dynamic configuration based on the family of mapping curves. This effectively suppresses common-mode voltage across the entire operating range and improves the response accuracy and stability of the control system.

[0274] In some of the solutions mentioned above in this application, a sliding surface function is proposed to generate a sliding control signal. However, in this process, the sliding surface function lacks the ability to adapt to the shape of the error trajectory, which leads to a decrease in control accuracy under complex working conditions.

[0275] To address this, this application proposes a method that nonlinearly couples the fractional-order error trajectory with the current common-mode voltage tracking error to construct a sliding surface function with adaptive error trajectory capabilities, and then solves this sliding surface function to obtain the sliding surface output value. The method specifically includes the following steps: The fractional-order error trajectory is subjected to trajectory morphology recognition to obtain trajectory curvature and energy characteristics. Trajectory morphology recognition aims to deeply analyze the geometry and dynamic characteristics of the fractional-order error trajectory, thereby extracting its inherent patterns and trends. Its core function is to provide a quantitative and refined basis for subsequent nonlinear modulation and weight adjustment, enabling the sliding mode surface function to sense and respond to subtle changes in the error trajectory. The trajectory curvature characteristic describes the degree of curvature of the error trajectory at a certain point or segment. For example, curvature can be quantified by calculating the second derivative or radius of curvature at the trajectory point, specifically by using the three-point circle method or differentiating the spline interpolated data. Alternatively, signal processing methods such as Fourier descriptors or wavelet transforms can be used to extract feature parameters related to the degree of trajectory curvature in the frequency or time-frequency domain. The trajectory energy characteristic describes the intensity or activity of the error trajectory fluctuations over a period of time. For example, the root mean square value, variance, or power spectral density of the trajectory signal can be calculated to reflect its overall energy level. Alternatively, the trajectory signal can be decomposed into different frequency bands using methods such as wavelet packet decomposition or empirical mode decomposition, and the energy proportion of each frequency band can be calculated to characterize the energy distribution at different frequencies.

[0276] Based on the trajectory curvature characteristics, the current common-mode voltage tracking error is nonlinearly modulated to obtain an error modulation component. Nonlinear modulation refers to using the trajectory curvature characteristics as a modulation signal to perform a nonlinear transformation on the current common-mode voltage tracking error, thereby generating a modulation component that reflects the dynamic characteristics of the error trajectory. Its function is to dynamically adjust the weights or shape of the error signal according to the curvature of the error trajectory, making the sliding surface function's response to the error more refined and flexible. For example, the trajectory curvature characteristics can be used as input to a nonlinear function, which takes the current common-mode voltage tracking error as its independent variable and outputs the error modulation component. The nonlinear function can be a sigmoid function, tanh function, or polynomial function, mapping the curvature characteristics to the gain or offset of the error. Alternatively, a lookup table or fuzzy logic system can be constructed to dynamically select different modulation coefficients or modulation functions based on different trajectory curvature characteristic ranges, performing multiplicative or additive modulation on the current common-mode voltage tracking error.

[0277] Simultaneously, based on the trajectory energy characteristics, the error weight coefficients in the sliding surface are dynamically adjusted to obtain adaptive weight coefficients. Dynamic adjustment refers to changing the weight coefficients related to the error term in the sliding surface function in real time according to the magnitude of the trajectory energy characteristics. Its function is to enable the sliding surface function to adaptively adjust its sensitivity to errors according to the severity of the error trajectory, thereby maintaining good control performance under different operating conditions. For example, a gain scheduler can be designed, taking the trajectory energy characteristics as input and outputting adaptive weight coefficients through a preset mapping function (such as a linear function, exponential function, or piecewise function). When the energy characteristics are large, the weight coefficients increase to enhance the response to errors. When the energy characteristics are small, the weight coefficients decrease to avoid over-response. Alternatively, a neural network or fuzzy inference system can be used to learn the nonlinear relationship between the trajectory energy characteristics and the optimal error weight coefficients, thereby achieving intelligent adjustment of the weights.

[0278] The error modulation component is multiplied by the adaptive weighting coefficient to obtain the first sliding surface component. The multiplication operation aims to organically combine the error component, which has been nonlinearly modulated by the trajectory curvature characteristics, with the adaptive weighting coefficient, which is dynamically adjusted according to the trajectory energy characteristics. Its function is to organically combine the morphological information and fluctuation intensity information of the error trajectory to form a sliding surface component that comprehensively reflects the dynamic characteristics of the error, providing a fundamental term for the sliding surface function that can both sense the error morphology and respond to the error intensity. For example, a direct numerical multiplication operation can be performed, i.e., the first sliding surface component equals the error modulation component multiplied by the adaptive weighting coefficient. Alternatively, based on the multiplication operation, an additional nonlinear function, such as the square root or logarithm of the product, can be introduced to further adjust its contribution to the sliding surface.

[0279] Furthermore, the fractional-order error trajectory is input into a preset trajectory shaping function for nonlinear transformation to obtain the second sliding surface component. The trajectory shaping function is a pre-designed nonlinear function used to transform the fractional-order error trajectory to change its shape or characteristics. Its role is to smooth, enhance, or filter the original fractional-order error trajectory to extract or highlight certain specific properties, thereby providing the sliding surface function with an optimized component possessing specific dynamic response characteristics. For example, saturation functions such as the Sigmoid function, tanh function, or arctangent function can be used to nonlinearly compress or stretch the fractional-order error trajectory to limit its amplitude or enhance its sensitivity to small errors. Alternatively, nonlinear mappings such as Gaussian functions, polynomial functions, or radial basis functions can be used to extract features or perform pattern matching on the fractional-order error trajectory to generate a component with a specific shape or dynamic response.

[0280] The first and second sliding surface components are superimposed to construct the sliding surface function, which is then solved to obtain the output value. The superposition operation aims to add the first and second sliding surface components to form the sliding surface function. Its function is to fuse components from two different sources and with different processing methods, thereby constructing a sliding surface function that integrates error trajectory morphology, energy, and shaped error information, giving it stronger adaptability and robustness. For example, a direct numerical addition operation can be performed, meaning the sliding surface function equals the sum of the first and second sliding surface components. Alternatively, an additional weighting coefficient can be introduced to perform a weighted sum of the two components. Solving refers to calculating the value of the constructed sliding surface function at the current moment. Its function is to transform the sliding surface function into a specific numerical output, which serves as the input to the sliding mode control law to generate the duty cycle correction, thereby controlling the power switch of the micro-inverter. For example, the input variables at the current moment (such as error modulation components, adaptive weighting coefficients, fractional error trajectories, etc.) can be directly substituted into the constructed sliding surface function expression for calculation. Alternatively, if the sliding surface function involves complex integral or differential operations, numerical integration or numerical differentiation methods can be used for approximate solutions.

[0281] Through the above technical solution, this application solves the problem of insufficient adaptability of traditional sliding surface functions under dynamic conditions. Specifically, by identifying the trajectory shape of the fractional-order error trajectory, the trajectory curvature and energy characteristics can be accurately obtained, providing a refined basis for subsequent error modulation and weight adjustment, enabling the sliding surface function to deeply perceive the dynamic changes of the error trajectory. Based on the trajectory curvature characteristics, the current common-mode voltage tracking error is nonlinearly modulated to generate an error modulation component. This allows the response intensity and direction of the error signal to be optimized according to the curvature of the error trajectory, thus making the sliding surface more closely conform to the actual error trajectory. Simultaneously, based on the trajectory energy characteristics, the error weight coefficients in the sliding surface are dynamically adjusted to obtain adaptive weight coefficients. This allows the sliding surface to flexibly adjust its sensitivity to errors according to the severity of error fluctuations, avoiding overshoot during severe fluctuations or sluggish response during stable conditions. Multiplying the error modulation component with the adaptive weight coefficients forms the first sliding surface component, realizing the synergistic effect of error shape information and fluctuation intensity information, enhancing the adaptability and stability of the sliding surface. Furthermore, the fractional-order error trajectory is input into a preset trajectory shaping function for nonlinear transformation to obtain the second sliding surface component. By optimizing the error trajectory, the anti-interference capability and robustness of the sliding surface are further improved. By superimposing these two component components to construct the sliding surface function and solving it, this application can generate a sliding surface output value that integrates error trajectory adaptive capability, shape perception capability, and fluctuation response capability. Thus, even when the micro-inverter faces complex operating conditions such as load sudden changes or reactive power injection, it can still effectively suppress common-mode voltage, improving control accuracy and system stability.

[0282] All of the above-mentioned optional technical solutions can be combined in any way to form the optional embodiments of this application, and will not be described in detail here.

[0283] In an exemplary embodiment, a computer-readable storage medium is also provided, such as a memory including a computer program that can be executed by a processor to perform the low leakage current modulation and common-mode voltage suppression method for a microinverter described in the above embodiments. For example, the computer-readable storage medium may be a read-only memory (ROM), a random access memory (RAM), a compact disc read-only memory (CD-ROM), magnetic tape, floppy disk, or optical data storage device, etc.

[0284] In an exemplary embodiment, a computer program product or computer program is also provided, which includes program code stored in a computer-readable storage medium. A processor of a computer device reads the program code from the computer-readable storage medium and executes the program code, causing the computer device to perform the aforementioned low leakage current modulation and common-mode voltage suppression method for microinverters.

[0285] In some embodiments, the computer program involved in the present application embodiments may be deployed and executed on a computer device, or executed on multiple computer devices located in one location, or executed on multiple computer devices distributed in multiple locations and interconnected through a communication network. Multiple computer devices distributed in multiple locations and interconnected through a communication network may constitute a blockchain system.

[0286] Those skilled in the art will understand that all or part of the steps of the above embodiments can be implemented by hardware or by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as a read-only memory, a disk, or an optical disk.

[0287] The above are merely optional embodiments of this application and are not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for low leakage current modulation and common-mode voltage suppression in microinverters, characterized in that, The method, executed by the digital signal processor of the microinverter, includes: The real-time electrical quantities of the microinverter are collected, including output current and common-mode voltage. The real-time electrical quantities and the output error of the fractional-order sliding mode controller are dynamically weighted and fused to obtain the entropy calculation dynamic weight; based on the entropy calculation dynamic weight and the real-time electrical quantities, the information entropy is calculated to obtain the dynamic operating condition entropy value; The dynamic working condition entropy value and sliding mode parameter benchmark are subjected to parameter adaptive mapping to obtain fractional order adjustment amount and reaching law coefficient adjustment amount; Based on the fractional order adjustment, the approach law coefficient adjustment, and the current common-mode voltage tracking error, the sliding mode control law is calculated to generate a duty cycle correction. The duty cycle correction is then superimposed with the basic duty cycle to generate a PWM drive signal to control the power switching of the micro-inverter.

2. The method according to claim 1, characterized in that, The dynamic weight fusion of the real-time electrical quantity and the output error of the fractional-order sliding mode controller to obtain the entropy calculation dynamic weight includes: The output current in the real-time electrical quantities is transformed in the time-frequency domain to extract the current waveform complexity features, and the common-mode voltage in the real-time electrical quantities is statistically analyzed to extract the common-mode voltage fluctuation severity features. The current operating condition entropy component is constructed based on the current waveform complexity characteristics, and the common mode operating condition entropy component is constructed based on the common mode voltage fluctuation severity characteristics. The output error of the fractional sliding mode controller is obtained, which includes the current common-mode voltage tracking error and the sliding mode chattering intensity. The current common-mode voltage tracking error and the sliding mode chattering intensity are comprehensively evaluated to obtain the control performance degradation degree. Based on the control performance degradation, a first modulation coefficient for the current operating condition entropy component and a second modulation coefficient for the common mode operating condition entropy component are generated. The first modulation coefficient is coupled with the current operating condition entropy component, and the second modulation coefficient is coupled with the common mode operating condition entropy component to obtain the current operating condition entropy and common mode operating condition entropy corrected by control performance feedback. The current operating condition entropy and common mode operating condition entropy corrected by control performance feedback are input into the nonlinear fusion network. The nonlinear fusion network dynamically adjusts the fusion weights based on the control performance degradation and outputs the entropy to calculate the dynamic weights.

3. The method according to claim 2, characterized in that, The process involves performing time-frequency domain transformation on the output current in the real-time electrical quantities to extract current waveform complexity features, and statistically analyzing the fluctuation amplitude of the common-mode voltage in the real-time electrical quantities to extract common-mode voltage fluctuation severity features, including: Wavelet packet decomposition is performed on the output current in the real-time electrical quantity to obtain wavelet packet coefficients in multiple frequency bands; The energy values ​​of wavelet packet coefficients in each frequency band are determined, and the energy values ​​of wavelet packet coefficients in each frequency band are normalized to obtain the energy distribution vector; Based on the energy distribution vector, the information entropy is calculated to obtain the current waveform complexity characteristics; The common-mode voltage in the real-time electrical quantities is sampled using a sliding window to obtain the common-mode voltage sequence within the current window; Determine the peak-to-peak value and variance of the common-mode voltage sequence to obtain the first fluctuation amplitude sub-feature and the second fluctuation amplitude sub-feature; The first fluctuation amplitude sub-feature and the second fluctuation amplitude sub-feature are weighted and fused to obtain the common-mode voltage fluctuation severity feature.

4. The method according to claim 1, characterized in that, The step of calculating the dynamic weight based on the entropy and performing information entropy calculation on the real-time electrical quantities to obtain the dynamic operating condition entropy value includes: The output current in the real-time electrical quantities is reconstructed in phase space to obtain a high-dimensional current trajectory matrix, and the common-mode voltage in the real-time electrical quantities is subjected to fluctuation period detection to obtain a common-mode period fluctuation sequence. The current state uncertainty is obtained by calculating the neighborhood point distribution entropy based on the high-dimensional current trajectory matrix, and the common-mode periodic uncertainty is obtained by calculating the periodic distribution entropy based on the common-mode periodic fluctuation sequence. The entropy calculation dynamic weight is decomposed into current weight coefficient and common mode weight coefficient, and the current weight coefficient is dynamically corrected according to the current state uncertainty to obtain the corrected current weight. The corrected current weight is coupled and modulated with the current state uncertainty to obtain the current entropy contribution value. The common mode weight coefficient is coupled and modulated with the common mode period uncertainty to obtain the common mode entropy contribution value. The current entropy contribution value and the common mode entropy contribution value are aggregated to output the dynamic operating condition entropy value.

5. The method according to claim 4, characterized in that, The process of reconstructing the phase space of the output current in the real-time electrical quantities to obtain a high-dimensional current trajectory matrix, and detecting the fluctuation period of the common-mode voltage in the real-time electrical quantities to obtain a common-mode periodic fluctuation sequence, includes: Extract the output current timing signal from the real-time electrical quantities and determine the embedding dimension and delay time of the phase space reconstruction; Based on the embedding dimension and the delay time, the output current timing signal is subjected to delay coordinate mapping to obtain multiple delay vectors; The multiple delay vectors are arranged in chronological order to construct the high-dimensional current trajectory matrix; The common-mode voltage timing signal is extracted from the real-time electrical quantities, and peak detection is performed on the common-mode voltage timing signal to obtain multiple peak positions and multiple trough positions; The instantaneous period value is calculated based on the time interval between adjacent peak positions, and the auxiliary period value is calculated based on the time interval between adjacent trough positions. The instantaneous periodic value and the auxiliary periodic value are weighted and fused to obtain the common-mode periodic fluctuation sequence.

6. The method according to claim 1, characterized in that, The step of adaptively mapping the dynamic working condition entropy value and the sliding mode parameter benchmark to obtain the fractional order adjustment amount and the reaching law coefficient adjustment amount includes: The rate of change of the dynamic operating condition entropy value is extracted to obtain the transient rate of change of the entropy value, and the amplitude of the dynamic operating condition entropy value is quantized to obtain the entropy value amplitude level; The transient rate of change of entropy and the magnitude of entropy are input into a coupled mapping network, which interactively fuses the transient rate of change of entropy and the magnitude of entropy to generate a comprehensive operating condition disturbance degree. Based on the comprehensive working condition disturbance degree, the fractional order reference value in the sliding mode parameter reference is nonlinearly stretched to obtain the order stretching amount. The order stretching amount is directionally modulated based on the transient rate of change of the entropy value to generate the fractional order adjustment amount; Based on the comprehensive operating condition disturbance degree, the reference value of the reaching law coefficient in the sliding mode parameter reference is exponentially scaled to obtain the coefficient scaling amount; Based on the entropy magnitude level, the scaling amount of the coefficient is saturated and suppressed to obtain the adjustment amount of the reaching law coefficient.

7. The method according to claim 6, characterized in that, The coupled mapping network interactively fuses the transient rate of change of the entropy value and the magnitude level of the entropy value to generate a comprehensive operating condition disturbance degree, including: The coupled mapping network performs sign separation on the transient rate of change of the entropy value to obtain positive and negative change components that characterize the direction of change of the working condition, and performs intensity classification on the magnitude level of the entropy value to obtain high magnitude level identifiers and low magnitude level identifiers. The coupled mapping network associates the positive change component with the high amplitude level identifier to generate a first disturbance contribution factor, and associates the negative change component with the low amplitude level identifier to generate a second disturbance contribution factor. The coupled mapping network performs adversarial aggregation on the first perturbation contribution factor and the second perturbation contribution factor to obtain the game equilibrium value between the first perturbation contribution factor and the second perturbation contribution factor. The coupled mapping network dynamically selects the corresponding mapping curve from the preset perturbation degree mapping curve family according to the absolute value of the transient change rate of the entropy value, and inputs the game equilibrium value into the selected mapping curve, and outputs the comprehensive operating condition perturbation degree after nonlinear mapping.

8. The method according to claim 1, characterized in that, The step of calculating the sliding mode control law based on the fractional order adjustment, the approach law coefficient adjustment, and the current common-mode voltage tracking error to generate the duty cycle correction includes: Based on the fractional order adjustment amount, the order of the preset fractional calculus operator is reconstructed to obtain a dynamic fractional operator. Based on the dynamic fractional operator, the current common-mode voltage tracking error is subjected to fractional calculus to obtain the dynamic characteristics of the fractional error. The coefficients of the preset exponential reaching law are reset based on the reaching law coefficient adjustment amount to obtain the dynamic exponential reaching law, and the reaching speed of the sign value of the sliding surface function is modulated based on the dynamic exponential reaching law to obtain the reaching law dynamic compensation amount. The fractional-order error dynamic characteristics are fused with the preset equivalent control components to obtain the equivalent control correction amount; The equivalent control correction amount is superimposed with the approach law dynamic compensation amount, and the superposition result is normalized to generate the duty cycle correction amount.

9. The method according to claim 1, characterized in that, The step of calculating the sliding mode control law based on the fractional order adjustment, the approach law coefficient adjustment, and the current common-mode voltage tracking error to generate the duty cycle correction includes: Based on the fractional order adjustment, the fractional calculus operator is reconstructed to obtain a dynamic fractional operator. The dynamic fractional operator is then used to perform fractional differentiation on the current common-mode voltage tracking error to obtain the fractional error trajectory. Based on the adjustment amount of the reaching law coefficient, the coefficients of the constant-rate reaching term and the coefficients of the exponential reaching term in the exponential reaching law are configured differently to obtain a first reaching law component with dynamic reaching strength and a second reaching law component with dynamic boundary layer thickness. The fractional-order error trajectory is nonlinearly coupled with the current common-mode voltage tracking error to construct a sliding surface function with adaptive error trajectory capability, and the sliding surface function is solved to obtain the sliding surface output value; Based on the amplitude range of the sliding surface output value, the corresponding reaching law component is selected from the first reaching law component and the second reaching law component for activation. The activated reaching law component is superimposed with the equivalent control component to obtain the duty cycle correction amount.

10. The method according to claim 9, characterized in that, The step of nonlinearly coupling the fractional-order error trajectory with the current common-mode voltage tracking error to construct a sliding surface function with adaptive error trajectory, and solving the sliding surface function to obtain the sliding surface output value, includes: The fractional-order error trajectory is subjected to trajectory morphology recognition to obtain trajectory curvature features and trajectory energy features; Based on the trajectory curvature characteristics, the current common-mode voltage tracking error is nonlinearly modulated to obtain the error modulation component; Based on the trajectory energy characteristics, the error weighting coefficients in the sliding surface are dynamically adjusted to obtain adaptive weighting coefficients. Multiply the error modulation component by the adaptive weighting coefficient to obtain the first sliding surface component; The fractional error trajectory is input into a preset trajectory shaping function for nonlinear transformation to obtain the components constituting the second sliding surface; The components of the first sliding surface and the components of the second sliding surface are superimposed to construct the sliding surface function, and the sliding surface function is solved to obtain the output value of the sliding surface.

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