Online fractional order parameter identification method based on neural network and secondary ripple suppression

Abstract

The invention discloses an online fractional order parameter identification method based on a neural network and secondary ripple suppression, and the method comprises the steps: taking a single-phase two-stage inverter system as an object, carrying out the modal analysis of a fractional order model of a front-stage buck circuit, and obtaining a fractional order state equation representing the dynamic characteristics of a capacitor / inductor; establishing a fractional order discretization recursion model of the single-phase two-stage inverter based on GL fractional order calculus definition; constructing a neural network structure according to a recursive relationship between capacitor voltage and current in the discrete model, and constructing a mean square error loss function by taking actual sampling voltage and current values as reference values and taking neural network output as an estimated value in the process of normal operation of the inverter and synchronous suppression of second harmonics; solving a partial derivative of the loss function to obtain a gradient expression corresponding to each weight, and updating the weight of the neural network by adopting a gradient descent algorithm; and calculating and outputting parameters of the fractional order capacitor and the inductor in real time according to the fractional order discrete model and the weight.

Description

Technical Field

[0001] This invention relates to the field of power electronics technology, and specifically to a non-invasive online fractional-order parameter identification method for power electronic converters that integrates neural networks and secondary current ripple suppression. Background Technology

[0002] With the increasing demand for renewable energy, two-stage inverters have received growing attention, finding wide application in grid-connected photovoltaic systems, electric vehicles, and electrified aircraft. The DC bus capacitor is a critical component in most two-stage inverters, helping to suppress DC bus voltage ripple, absorb current ripple, and balance the instantaneous power difference between the converter's front and back ends. Capacitors are among the most prone to aging. As they age, their equivalent series resistance increases while their capacitance decreases, leading to increased voltage ripple, increased power loss, and even catastrophic inverter failure. Therefore, real-time monitoring of their health is crucial.

[0003] Although second-harmonic suppression methods are relatively mature, most studies have not considered the impact of parameter offset. Parameter offset can affect the normal operation of two-stage inverters in practice, causing the reference voltage to deviate from the theoretical value, reducing the harmonic suppression effect, and introducing additional harmonics that further degrade power quality. Therefore, adaptive control of ripple suppression capability can be achieved through online parameter identification.

[0004] Currently, parameter identification technology has been widely studied in power electronic systems such as motors, batteries, and converters. The methods can be broadly categorized into offline and online identification. Offline identification methods primarily target parameters such as inductance and capacitance in motor systems. Their advantage lies in the fact that they do not require embedding a real-time control system, making them relatively simple to operate. However, this method typically requires repeated experiments to obtain accurate results and cannot track changes in system parameters in real time, exhibiting weak adaptability. Online identification methods, on the other hand, usually utilize signals from within the system for parameter estimation. This not only allows for more accurate acquisition of actual parameter values ​​but also suppresses errors caused by external interference, resulting in higher accuracy. Furthermore, online methods can update parameters such as capacitance and inductance in real time during system operation, facilitating dynamic system optimization and demonstrating stronger adaptability. However, conventional online methods often rely on series equivalent models of capacitors, and their identification accuracy is largely limited by the accuracy of the model.

[0005] In recent years, with the rapid development of artificial intelligence technology and the continuous improvement of computing hardware performance, the application of neural network algorithms in parameter identification has been increasing. This type of method constructs a loss function and trains the model with the goal of minimizing the loss value, gradually bringing the model output closer to the actual parameters. Since the gradient of the function indicates the direction of the fastest loss descent, iteratively updating the parameters using the gradient descent algorithm can achieve fast and accurate identification.

[0006] In most existing studies, capacitors and inductors are typically modeled and analyzed as integer-order components. However, real-world devices are not ideal integer-order components and often exhibit parasitic resistance. Their common equivalent model consists of an ideal capacitor, inductor, and resistor connected in series. Using integer-order models for circuit analysis introduces significant errors; therefore, fractional-order theory has gained increasing attention in the field of power electronics in recent years. Fractional-order modeling methods can more accurately describe the dynamic behavior of components, helping to improve system control accuracy and overall performance, and better meeting practical application needs. Compared to traditional integer-order models, fractional-order models not only possess memory characteristics and higher accuracy but are also more suitable for parameter identification, especially for achieving high-precision parameter identification online. Summary of the Invention

[0007] The main objective of this invention is to overcome the aforementioned deficiencies in the prior art and propose an online fractional-order parameter identification method based on neural networks and second-order ripple suppression. This method enables simultaneous online identification of parameters of multiple devices, such as DC bus capacitors, in converters such as single-phase two-stage inverters. This method requires no additional test circuits or sensors, does not interrupt system operation, and does not add extra hardware. It utilizes only the voltage, current, and other electrical quantities in the existing harmonic suppression control of the system to achieve high-precision, low-cost, and integrated online parameter identification. This provides an effective technical foundation for assessing the aging status of capacitors and inductors, monitoring the status of inverter systems, optimizing second-order harmonic suppression performance, and self-tuning control loop parameters. It has strong engineering applicability and promotional value.

[0008] The present invention adopts the following technical solution:

[0009] On the one hand, an online fractional-order parameter identification method based on neural networks and quadratic ripple suppression includes:

[0010] Taking a single-phase two-stage inverter system including a front-end Buck circuit and a back-end inverter circuit as the object, a fractional-order equivalent circuit model is established for the front-end Buck circuit, and modal analysis is performed to obtain the fractional-order state equations characterizing the dynamic characteristics of the capacitor / inductor.

[0011] Based on the fractional state equations and the definition of fractional calculus in GL, a fractional discretized state-space equation for the front-end buck circuit in a single-phase two-stage inverter is established.

[0012] Based on the recursive relationship between capacitor voltage and current in the discretized state-space equation, a neural network structure is constructed. During the normal operation of the inverter and the synchronous suppression of second harmonics, the actual voltage and current values ​​collected by the system are used as reference values, and the voltage and current output by the neural network are used as estimated values. A loss function based on the mean square error of the predicted and actual values ​​is constructed. The partial derivative of the loss function is obtained to obtain the gradient expression corresponding to each weight, and the gradient descent algorithm is used to update the neural network weights online. Based on the established fractional-order discretized state-space equation and the identified weights, the capacitance and order of the fractional-order capacitor and the inductance and order of the fractional-order inductor are calculated and output in real time, realizing online parameter identification without interrupting operation, injecting test signals, or affecting the second harmonic suppression performance of the system.

[0013] Preferably, the single-phase two-stage inverter uses dual closed-loop control of voltage and current. To suppress secondary current ripple, a virtual resistor r is introduced in the current feedback loop. s To enhance the system's dynamic response, a bandpass filter with a center frequency of the second harmonic frequency is integrated into the feedback path to selectively amplify the target harmonic components and suppress out-of-band noise, thereby improving the overall performance of the converter. This virtual resistor r... s With bandpass filter G BPF (s) together constitute the second harmonic suppression stage. The voltage and current signals required for parameter identification both come from the voltage and current dual closed-loop control, eliminating the need for additional signal acquisition. This achieves synergistic optimization of the suppression stage and parameter identification. The bandpass filter equation is:

[0014]

[0015] Among them, f b f is the bandwidth of the bandpass filter. o This refers to the output frequency of a single-phase two-stage inverter.

[0016] r s The calculation formula is as follows:

[0017]

[0018] Where h is the second-order ripple current suppression ratio, ω o =2πf o ω is the angular frequency.

[0019] Preferably, in a single-phase two-stage inverter topology, an independent modal analysis is performed on the front-end Buck circuit, using the inductor current i L and bus voltage V bus For the state variables, the fractional-order state equation is:

[0020]

[0021] In the formula, i L and V in These are the inductor current and the input voltage, respectively; C α α and α represent the capacitance and order of the fractional capacitor, respectively; L β β and Z represent the inductance and order of a fractional inductor, respectively; in This represents the input impedance of the subsequent inverter; D is the duty cycle and 0 ≤ D ≤ 1; t is the time variable.

[0022] The input impedance Z of the subsequent inverter in Represented as:

[0023]

[0024] Among them, i inv Indicates the input current; U bus The average voltage of the bus is represented by η1; the efficiency of the downstream inverter is represented by U. m and I m This represents the amplitude of the output voltage and the amplitude of the output current of the subsequent inverter; φ represents the phase angle of the output current; ω o =2πf o It represents angular frequency.

[0025] Preferably, the fractional-order discretized state-space equations of the preceding Buck converter, established using the definition of fractional-order calculus in GL, are as follows:

[0026]

[0027] Among them, i L (k+1) and V bus (k+1) represent the average values ​​of the inductor current and output voltage during the (k+1)th switching cycle, respectively; i L (k) and V bus (k) represents the average value of the inductor current and the output voltage in the k-th switching cycle, respectively; T is the sampling period; j is an integer in the range [0, k]. is the coefficient of Newton's generalized binomial; N is the memory length.

[0028] Preferably, the capacitance value and order C of the fractional capacitor are... α And α, as well as the inductance and order L of the fractional inductor. β The calculation of β involves the following steps: Based on the fractional-order discretized state-space equations of the preceding Buck circuit and the relationship between the input and output of the neural network, the predicted output voltage V is obtained. bus * (k+1) and inductor current i L * The expression for (k+1) is:

[0029]

[0030] Where ω1=T α / C α ω2=α-T α / (Z in C α ), ω N+2 =β,ω N+3 =-T β / L β ω N+4 =DT β / L β ,

[0031] The loss function is constructed using the mean squared error between the predicted and actual values, as follows:

[0032]

[0033] Then, according to the chain rule, J with respect to ω i The partial derivative is expressed as:

[0034]

[0035] For C α For the identification of α, the range of values ​​for i is 1 ≤ i ≤ N+1, therefore:

[0036]

[0037] Combining J with ω i The partial derivatives yield:

[0038]

[0039] For L β For the identification of β, the range of values ​​for i is N+2≤i≤2N+3, therefore:

[0040]

[0041] Let η be the learning rate, then the weights ω i The iterative formula is:

[0042]

[0043] After obtaining the weights, the values ​​of any two ω within the range 1≤i≤N+1 are used. i The expression for C α By inversely solving for α, we obtain estimated values ​​for the capacitance and order of the fractional capacitor:

[0044]

[0045] By any two ω values ​​within the range N+2≤i≤2N+3 i The expression for L β By performing an inverse solution with β, we obtain estimated values ​​for the inductance and order of the fractional inductor:

[0046]

[0047] Preferably, to avoid coincidences, a counter is set. When the iterative descent distance d is less than the set error ε, the counter is incremented by one. Iteration stops only when d < ε for a preset number of consecutive times. The descent distance in each iteration is:

[0048]

[0049] As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following beneficial effects:

[0050] (1) Non-invasive and high precision: The present invention provides a non-invasive online parameter identification method that does not require additional hardware or test signals. It can achieve parameter identification by utilizing the inherent operating characteristics of the system. It is low-cost, easy to implement, and has high identification accuracy.

[0051] (2) Integration of fractional order and neural network: This invention combines a fractional order model that can more accurately describe the characteristics of actual components with a neural network with powerful nonlinear mapping capabilities, which can realize integrated online identification of multiple parameters (capacitance / inductance and their order) and has strong adaptability.

[0052] (3) Harmonic suppression and parameter identification synergy: The parameter identification process of the present invention is carried out synchronously with the inherent second harmonic suppression process of the system, without affecting each other. While improving the overall performance of the system, it provides an effective technical means for condition monitoring, aging assessment and online optimization of control loop.

[0053] (3) Strong engineering applicability: The method of the present invention has a clear structure, is easy to implement in existing control systems (such as DSP), and can be extended to various power electronic converter topologies, with broad engineering application prospects. Attached Figure Description

[0054] Figure 1 This is a topology diagram of a single-phase two-stage inverter with a Buck circuit as the front stage, according to an embodiment of the present invention.

[0055] Figure 2 This is a control and parameter identification structure diagram of a single-phase two-stage inverter with a Buck front-end according to an embodiment of the present invention;

[0056] Figure 3This is a flowchart illustrating the parameter identification process according to an embodiment of the present invention.

[0057] Figure 4 The following is a schematic diagram of the simulation results of an embodiment of the present invention; wherein, (a) bus voltage convergence curve; (b) secondary current ripple ratio; (c) capacitance value identification result; (d) order identification result;

[0058] Where S is the switching transistor of the preceding Buck circuit, D is the diode of the preceding Buck circuit, and L is the switching transistor of the preceding Buck circuit. β - The fractional-order inductor of the preceding Buck circuit, C α - The fractional capacitor of the pre-stage Buck circuit, Z in -Input impedance of the inverter, V in - Input voltage, V bus - Bus voltage, S1 to S4 - Switching transistors of the subsequent inverter circuit. Detailed Implementation

[0059] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0060] In the description of this invention, it should be noted that the terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0061] This embodiment presents an online parameter identification method based on neural networks and fractional-order quadratic ripple suppression, including:

[0062] Taking a single-phase two-stage inverter system including a front-end Buck circuit and a back-end inverter circuit as the object, a fractional-order equivalent circuit model is established for the front-end Buck circuit, and modal analysis is performed to obtain the fractional-order state equations characterizing the dynamic characteristics of the capacitor / inductor.

[0063] Based on the fractional state equations and the GL (Grunwald-Letnikov) definition of fractional calculus, a fractional discretized state-space equation for the front-end buck circuit in a single-phase two-stage inverter is established.

[0064] Based on the recursive relationship between capacitor voltage and current in the discretized state-space equation, a neural network structure is constructed. During the normal operation of the inverter and the synchronous suppression of second harmonics, the actual voltage and current values ​​collected by the system are used as reference values, and the voltage and current output by the neural network are used as estimated values. A loss function based on the mean square error of the predicted and actual values ​​is constructed. The partial derivative of the loss function is obtained to obtain the gradient expression corresponding to each weight, and the gradient descent algorithm is used to update the neural network weights online. Based on the established fractional-order discretized state-space equation and the identified weights, the capacitance and order of the fractional-order capacitor and the inductance and order of the fractional-order inductor are calculated and output in real time, realizing online parameter identification without interrupting operation, injecting test signals, or affecting the second harmonic suppression performance of the system.

[0065] Specifically, such as Figure 1 As shown, the fractional-order model of the single-phase two-stage inverter with Buck as the front stage is based on the input voltage V. in Switch S, diode D, fractional-order inductor L β Fractional capacitance C α It consists of a downstream inverter and a load resistor R. One end of the switching transistor S is connected to the voltage source V. in The positive terminal of one diode; the other end is connected to the negative terminal of diode D and the fractional inductor L. β One end of the fractional inductor is connected to the other end of the fractional capacitor C. α One end is connected to a fractional capacitor C. α The other end is simultaneously connected to the positive terminal of diode D and the voltage source V. in The negative terminal connection; the subsequent inverter and the fractional capacitor C α Parallel connection; wherein, the switching transistor S can be a switching device such as a MOSFET or an IGBT.

[0066] like Figure 2 The control and parameter identification structure diagram of a single-phase two-stage inverter with a Buck front-end is shown below. The single-phase two-stage inverter uses dual closed-loop control for both voltage and current. To suppress secondary current ripple, a virtual resistor r is introduced in the current feedback loop. s To enhance the system's dynamic response, a bandpass filter with a center frequency of the second harmonic frequency is integrated into the feedback path to selectively amplify the target harmonic components and suppress out-of-band noise, thereby improving the overall performance of the converter. This virtual resistor r... s Together with the bandpass filter, it forms the second harmonic suppression stage. The voltage and current signals required for parameter identification are all from the voltage and current dual closed-loop control process, eliminating the need for additional signal acquisition stages and achieving synergistic optimization of the suppression stage and parameter identification.

[0067] The bandpass filter equation is:

[0068]

[0069] Among them, f b f is the bandwidth of the bandpass filter. o This refers to the output frequency of a single-phase two-stage inverter.

[0070] r s The calculation formula is as follows:

[0071]

[0072] Where h is the second-order ripple current suppression ratio, ω o =2πf o ω is the angular frequency.

[0073] like Figure 3 The parameter recognition flowchart shown is as follows.

[0074] S1. System Initialization: In the system initialization phase, the neural network weights ω are first set. i The initial values ​​are then set, followed by the configuration of key algorithm parameters, including memory length N, learning rate η, convergence threshold ε, and consecutive convergence count n. Finally, the iteration counter count is initialized to 0, completing all preparations before the algorithm starts.

[0075] S2. Data Acquisition and Preprocessing: In each switching cycle k, the inductor current i generated by the system during the active suppression of the second harmonic current is acquired in real time. L (k) Bus voltage V bus (k) Input voltage V in (k) and duty cycle D; by performing real-time filtering preprocessing on the above-mentioned operating data derived from the second ripple suppression process, noise interference is effectively suppressed while ensuring that the data used is consistent with the harmonic suppression process, providing high-quality input directly related to the dynamic characteristics of ripple suppression for subsequent parameter identification.

[0076] Specifically, in a single-phase two-stage inverter topology, an independent modal analysis is performed on the front-end Buck circuit, using the inductor current i... L and bus voltage V bus For the state variables, the fractional-order state equation is:

[0077]

[0078] In the formula, i L and V in These are the inductor current and the input voltage, respectively; C α α and α represent the capacitance and order of the fractional capacitor, respectively; L β β and Z represent the inductance and order of a fractional inductor, respectively;in The input impedance of the subsequent inverter is represented by ; D is the duty cycle and 0 ≤ D ≤ 1; t is the time variable.

[0079] To calculate Z in The input current i of the subsequent inverter must be determined first. inv v ac and i ac These represent the output voltage and output current of a single-phase two-stage inverter, respectively. They can be expressed as:

[0080]

[0081] In the formula, U m and I m It refers to the amplitude of the output voltage and the amplitude of the output current of the subsequent inverter. It is the phase angle of the output current. ω o =2πf o It is the angular frequency. The pulsating output power of the subsequent inverter is:

[0082]

[0083] In the formula, P o This represents the effective value of the output power. Ignoring power losses during power conversion, the input current i... inv Represented as:

[0084]

[0085] In the formula, i SHC U represents the secondary current ripple. bus It is the average voltage of the bus.

[0086] The input impedance Z of the subsequent inverter in Represented as:

[0087]

[0088] Where η1 represents the efficiency of the downstream inverter.

[0089] The fractional-order discretized state-space equations of the preceding Buck converter, established using the definition of fractional-order calculus in GL, are as follows:

[0090]

[0091] Among them, i L (k+1) and V bus (k+1) represent the average values ​​of the inductor current and output voltage during the (k+1)th switching cycle, respectively; i L (k) and V bus(k) represents the average value of the inductor current and the output voltage in the k-th switching cycle, respectively; T is the sampling period; j is an integer in the range [0, k]. is the coefficient of Newton's generalized binomial; N is the memory length.

[0092] S3. Neural Network Forward Computation: Based on the fractional-order discretized state-space equation of the preceding Buck circuit and the relationship between the input and output of the neural network, the predicted value V is calculated. bus * (k+1) and i L * The expression for (k+1) is:

[0093]

[0094] Where ω1=T α / C α ω2=α-T α / (Z in C α ), ω N+2 =β,ω N+3 =-T β / L β ω N+4 =DT β / L β ,

[0095] S4. Loss Function Calculation: Using V bus and i L The loss function is constructed from the mean squared errors of the predicted and actual values:

[0096]

[0097] S5. Gradient Calculation and Weight Update: Then, according to the chain rule, J is calculated with respect to ω. i The partial derivative can be expressed as:

[0098]

[0099] For C α For the identification of α, the range of values ​​for i is 1 ≤ i ≤ N+1, therefore:

[0100]

[0101] For neural networks, the output, calculated as the gradient with respect to each weight, is the corresponding input quantity, i.e.:

[0102]

[0103] Where y represents the output of the neural network, such as Vbus * x i Represents the input to the neural network, such as i L Combining J with ω i The partial derivatives yield:

[0104]

[0105] For L β For the identification of β, the range of values ​​for i is N+2≤i≤2N+3, therefore:

[0106]

[0107] Let η be the learning rate, then the weights ω i The iterative formula is:

[0108]

[0109] S6. Parameter Inverse Derivation and Output: After obtaining the weights, use ω1 and ω3 (arbitrarily choose two ω values ​​containing the parameters to be identified) i The expression for C is (that is, the expression for C is) α By performing an inverse solution with α, we can obtain estimates of the capacitance and order:

[0110]

[0111] Through ω N+2 and ω N+3 L can be solved in reverse β The estimated values ​​for β are:

[0112]

[0113] S7. Convergence Check: To avoid coincidences, a counter `count` is set. The counter increments when the iterative descent distance `d` is less than the set error `ε`. Iteration stops only when `d < ε` for `n` consecutive iterations. The descent distance in each iteration is...

[0114]

[0115] The simulation experiment will be explained below.

[0116] The fractional-order simulation parameters of the Buck circuit are shown in Table 1, with the input voltage V... in =50V, fractional inductance L β =0.001H β fractional capacitance C α =0.3899F 1-α Switching frequency f sThe frequency is 10kHz, the sampling period is T = 0.00001s, and the bus voltage is V. bus =30V. When the inverter is running normally, the circuit is controlled by the second harmonic suppression method based on virtual resistance. At a certain moment, the inductor and capacitor parameters are identified online according to the above steps while the inverter's operating state remains unchanged.

[0117] Table 1

[0118]

[0119] like Figure 4 As shown, Figure 4 Figure (a) illustrates the convergence characteristics between the actual bus voltage and its predicted value. Waveform analysis shows that the bus voltage exhibits dynamic fluctuation characteristics during normal system operation. The proposed parameter identification method possesses robust and accurate initialization capabilities, achieving rapid and accurate parameter identification at any steady-state operating point of the inverter without manual intervention or preset test signals. The system collects data during the dynamic process to analyze V... bus Prediction and parameter identification are performed, while the second harmonic suppression loop continues to operate to maintain harmonic control. During parameter identification, the inherent second harmonic-induced bus voltage ripples are simultaneously used as excitation for the identification algorithm without affecting harmonic suppression performance. Figure 4 As can be seen from (b), the secondary current ripple accounts for only 0.6% of the DC component. Figure 4 (c) and Figure 4 (d) in the figure shows C respectively α Simulation curves for the identification of α. When the parameter identification algorithm is not started, the identification program is inactive, and the corresponding parameters remain at their initial values. Once the identification program is started, C... α And α converge to approximately 0.3852F. 1-α The values ​​were 0.345, with relative errors of 1.2% and 0.7%, respectively. In the initial stage of identification, the error between the actual bus voltage and its predicted value was relatively large, but as the number of iterations increased, the error gradually decreased, and the two curves eventually converged. After stabilization, the voltage error remained within 50mV for most of the time.

[0120] The above description is merely a preferred embodiment of the present invention; however, the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and its improved concept, should be covered within the scope of protection of the present invention.

Claims

1. An online fractional-order parameter identification method based on neural networks and quadratic ripple suppression, characterized in that, include: Taking a single-phase two-stage inverter system including a front-end Buck circuit and a back-end inverter circuit as the object, a fractional-order equivalent circuit model is established for the front-end Buck circuit, and modal analysis is performed to obtain the fractional-order state equations characterizing the dynamic characteristics of the capacitor / inductor. Based on the fractional state equations and the definition of fractional calculus in GL, a fractional discretized state-space equation for the front-end buck circuit in a single-phase two-stage inverter is established. Based on the recursive relationship between capacitor voltage and current in the discretized state-space equation, a neural network structure is constructed. During the normal operation of the inverter and the synchronous suppression of second harmonics, the actual voltage and current values ​​collected by the system are used as reference values, and the voltage and current output by the neural network are used as estimated values. A loss function based on the mean square error of the predicted and actual values ​​is constructed. The partial derivative of the loss function is obtained to obtain the gradient expression corresponding to each weight, and the gradient descent algorithm is used to update the neural network weights online. Based on the established fractional-order discretized state-space equation and the identified weights, the capacitance and order of the fractional-order capacitor and the inductance and order of the fractional-order inductor are calculated and output in real time, realizing online parameter identification without interrupting operation, injecting test signals, or affecting the second harmonic suppression performance of the system.

2. The online fractional-order parameter identification method based on neural networks and quadratic ripple suppression according to claim 1, characterized in that, A single-phase two-stage inverter uses dual closed-loop control of voltage and current. To suppress secondary current ripple, a virtual resistor r is introduced in the current feedback loop. s To enhance the system's dynamic response, a bandpass filter with a center frequency of the second harmonic frequency is integrated into the feedback path to selectively amplify the target harmonic components and suppress out-of-band noise, thereby improving the overall performance of the converter. This virtual resistor r... s With bandpass filter G BPF (s) together constitute the second harmonic suppression stage. The voltage and current signals required for parameter identification both come from the voltage and current dual closed-loop control, eliminating the need for additional signal acquisition. This achieves synergistic optimization of the suppression stage and parameter identification. The bandpass filter equation is: Among them, f b f is the bandwidth of the bandpass filter. o This refers to the output frequency of a single-phase two-stage inverter. r s The calculation formula is as follows: Where h is the second-order ripple current suppression ratio, ω o =2πf o ω is the angular frequency.

3. The online fractional-order parameter identification method based on neural networks and quadratic ripple suppression according to claim 1, characterized in that, In a single-phase two-stage inverter topology, an independent modal analysis is performed on the front-end Buck circuit, taking the inductor current i as an example. L and bus voltage V bus For the state variables, the fractional-order state equation is: In the formula, i L and V in These are the inductor current and the input voltage, respectively; C α α and α represent the capacitance and order of the fractional capacitor, respectively; L β β and Z represent the inductance and order of a fractional inductor, respectively; in This represents the input impedance of the subsequent inverter; D is the duty cycle and 0 ≤ D ≤ 1; t is the time variable. The input impedance Z of the subsequent inverter in Represented as: Among them, i inv Indicates the input current; U bus The average voltage of the bus is represented by η1; the efficiency of the downstream inverter is represented by U. m and I m This represents the amplitude of the output voltage and the amplitude of the output current of the subsequent inverter; φ represents the phase angle of the output current; ω o =2πf o It represents angular frequency.

4. The online fractional-order parameter identification method based on neural networks and quadratic ripple suppression according to claim 3, characterized in that, The fractional-order discretized state-space equations of the preceding Buck converter, established using the definition of fractional-order calculus in GL, are as follows: Among them, i L (k+1) and V bus (k+1) represent the average values ​​of the inductor current and output voltage during the (k+1)th switching cycle, respectively; i L (k) and V bus (k) represents the average value of the inductor current and the output voltage in the k-th switching cycle, respectively; T is the sampling period; j is an integer in the range [0, k]. is the coefficient of Newton's generalized binomial; N is the memory length.

5. The online fractional-order parameter identification method based on neural networks and quadratic ripple suppression according to claim 1, characterized in that, The capacitance and order C of a fractional capacitor α And α, as well as the inductance and order L of the fractional inductor. β The calculation of β includes the following steps: Based on the fractional-order discretized state-space equations of the preceding Buck circuit and the relationship between the input and output of the neural network, the predicted output voltage V is obtained. bus * (k+1) and inductor current i L * The expression for (k+1) is: where, ω1 = T α / C α , ω2 = α - T α / (Z in C α ), ω N+2 = β, ω N+3 = -T β / L β , ω N+4 = DT β / L β , The loss function is constructed using the mean squared error between the predicted and actual values, as follows: Then, according to the chain rule, J with respect to ω i The partial derivative is expressed as: For C α For the identification of α, the range of values ​​for i is 1 ≤ i ≤ N+1, therefore: Combining J with ω i The partial derivatives yield: For L β For the identification of β, the range of values ​​for i is N+2≤i≤2N+3, therefore: Let η be the learning rate, then the weights ω i The iterative formula is: After obtaining the weights, the values ​​of any two ω within the range 1≤i≤N+1 are used. i The expression for C α By inversely solving for α, we obtain estimated values ​​for the capacitance and order of the fractional capacitor: By any two ω values ​​within the range N+2≤i≤2N+3 i The expression for L β By performing an inverse solution with β, we obtain estimated values ​​for the inductance and order of the fractional inductor:

6. The online fractional-order parameter identification method based on neural networks and quadratic ripple suppression according to claim 5, characterized in that, To avoid coincidences, a counter `count` is set. The counter increments by one when the iterative descent distance `d` is less than the set error `ε`. Iteration stops only when `d` is less than `ε` for a preset number of consecutive iterations. The descent distance in each iteration is:

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