LCL type inverter control method based on step-by-step decoupling

Abstract

The application relates to the technical field of automatic control, in particular to an LCL type inverter control method based on step-by-step decoupling, which comprises the following steps: collecting inductance current and grid-connected point voltage signals and converting to generate rotating field state sampling data, analyzing a phase angle to generate a voltage vector geometric correction factor, calculating a tracking error and combining inductance parameters to generate a variable structure damping adjustment gain, superimposing an active damping component and a corrected voltage component to generate an inverter switch driving signal.In the application, a sliding mode variable structure observer is used to reconstruct the capacitor current in real time, noise interference caused by direct measurement is avoided, and parameter robustness is enhanced; the voltage vector geometric correction factor is used to accurately compensate the coupling component in the rotating coordinate system, decoupling mismatch caused by phase deviation is eliminated, the active damping gain is adjusted according to the energy level of the tracking error, the adaptive balance of dynamic response and resonance suppression is realized, and the grid-connected current quality and stability are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology, and in particular to a control method for LCL inverters based on step-by-step decoupling. Background Technology

[0002] The field of automatic control technology encompasses the theoretical and technical systems that utilize control devices to enable controlled objects or processes to operate automatically according to predetermined rules. It covers a complete closed-loop process from sensor signal acquisition, system modeling, controller design to actuator action. It mainly includes frequency domain analysis from classical control theory and state-space methods from modern control theory, aiming to solve problems related to system stability, accuracy, and speed. It is widely used in the automated regulation of industrial production processes, aerospace, and power electronic devices. Among these, the traditional LCL inverter control method refers to the technical means of regulating the current or voltage of inverter circuits with LCL filters. It employs an active damping control strategy with capacitor current feedback to suppress the resonance spikes of the LCL filter. By acquiring grid current and capacitor current signals, it converts the AC quantities in the three-phase stationary coordinate system into DC quantities in the two-phase rotating coordinate system through coordinate transformation. A proportional-integral controller is used to adjust the current error, and a pulse-width modulation signal is generated to drive the inverter power switches in conjunction with a grid voltage feedforward strategy.

[0003] Existing technologies rely on capacitor current feedback for active damping control. When filter parameters are perturbed or grid impedance changes, the fixed control parameters reduce the system stability margin. Furthermore, using traditional proportional-integral controllers to adjust AC quantities in a rotating coordinate system cannot balance dynamic response speed and steady-state tracking accuracy when dealing with high-order LCL resonant objects. In addition, the grid voltage feedforward strategy is limited by sampling noise and measurement deviation, causing grid connection point voltage distortion to be directly coupled to the current loop, resulting in increased grid current waveform distortion rate and decreased system robustness. Summary of the Invention

[0004] To address the technical problems existing in the prior art, embodiments of the present invention provide a control method for LCL-type inverters based on step-by-step decoupling.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a step-decoupling LCL inverter control method, comprising the following steps: S1: Collect the inductor current and grid connection point voltage signals of the LCL inverter, convert them into a sampling sequence, use the transformation matrix to project the sampling sequence to extract the orthogonal axis data, and generate rotating domain state sampling data; S2: Combining the rotating domain state sampling data and the inductor current estimate, construct the current observation deviation and the sliding surface function of the current observation deviation, determine the switching gain and filter according to the polarity of the sliding surface function, and generate the capacitor current sliding mode reconstruction data. S3: Analyze the inverter and grid connection point phase angles of the rotating domain state sampling data, obtain the voltage phase difference and the sine and cosine components of the voltage phase difference, and generate the voltage vector geometric correction factor; S4: Calculate the tracking error of the rotating domain state sampling data, combine the inductance parameter and the square of the tracking error to obtain the error energy level scalar, compare the error energy level scalar with the energy boundary standard, and generate the variable structure damping adjustment gain. S5: Multiply the variable structure damping adjustment gain and the capacitor current sliding mode reconstruction data to generate an active damping component, and superimpose the voltage feedforward, the adjustment output and the component corrected by the voltage vector geometric correction factor to generate the inverter switching drive signal.

[0006] As a further embodiment of the present invention, the rotating domain state sampling data includes direct-axis voltage sampling values, quadrature-axis voltage sampling values, direct-axis current sampling values, and quadrature-axis current sampling values ​​in the rotating coordinate system; the capacitor current sliding mode reconstruction data includes the filtered switching gain value and the capacitor current estimate output by the sliding mode observer; the voltage vector geometric correction factor includes the sine component of the voltage phase difference, the cosine component of the voltage phase difference, and the rotating correction matrix for compensating for decoupling model mismatch; the variable structure damping adjustment gain includes the linear damping coefficient based on scalar matching of error energy level and the dynamically adjusted variable structure control gain value; and the inverter switching drive signal includes the switching pulse sequence generated by space vector modulation and the turn-on and turn-off control commands of the inverter power devices.

[0007] As a further aspect of the present invention, the specific steps of S1 are as follows: S101: Acquires inductor current and grid connection point voltage signals of LCL inverter, starts analog-to-digital conversion channel to perform synchronous sampling and holding operation on inductor current and grid connection point voltage analog signals, discretizes analog amplitude in continuous time domain into digital code according to clock frequency, and performs time-sequence alignment and integration of three-phase current data and three-phase voltage data according to time step order to generate discretized sampling sequence. S102: Call the three-phase voltage values ​​in the discretized sampling sequence, use a second-order generalized integrator to extract the fundamental positive sequence component and calculate the real-time phase angle of the grid connection point voltage vector, calculate the corresponding sine function value and cosine function value based on the real-time phase angle value, fill the sine function value and the cosine function value into the mapping determinant from the three-phase stationary coordinate system to the two-phase rotating coordinate system, and establish the coordinate projection transformation matrix; S103: Based on the coordinate projection transformation matrix, perform matrix multiplication on the three-phase current and voltage data included in the discretized sampling sequence, convert the time-varying sinusoidal AC quantity into a linear DC quantity through coordinate axis rotation transformation, separate and extract the direct axis component values ​​that are consistent with the magnetic flux orientation and the quadrature axis component values ​​that are orthogonal to the magnetic flux orientation in the rotating coordinate system, and perform vector synthesis on the direct axis component values ​​and the quadrature axis component values ​​to generate rotating domain state sampling data.

[0008] As a further aspect of the present invention, the specific steps of S2 are as follows: S201: Call the direct axis and quadrature axis current sampling values ​​in the rotating domain state sampling data, read the direct axis and quadrature axis inductor current prediction values ​​output by the sliding mode observer state equation in the previous calculation step, perform vector subtraction operation on the current sampling value and the inductor current prediction value, calculate the vector difference magnitude of the two in the rotating coordinate system, and establish the current observation deviation state quantity. S202: Based on the current observation deviation state quantity, construct a sliding surface function describing the state convergence trajectory, call symbolic operation logic to extract the algebraic symbol of the sliding surface function, compare the relative polarity of the algebraic symbol with the zero-level reference, output a positive feedback coefficient when the polarity is positive, output a negative feedback coefficient when the polarity is negative, and generate a nonlinear switching gain signal. S203: Feed the nonlinear switching gain signal into a digital low-pass filter, set the cutoff bandwidth parameter of the filter according to the inverter switching frequency, perform frequency domain attenuation operation on the signal to suppress high-frequency jitter harmonics, extract the smoothed component after filtering and map it into the observer feedback compensation term, correct the state estimate, and generate capacitor current sliding mode reconstruction data.

[0009] As a further aspect of the present invention, the specific steps of S3 are as follows: S301: Call the rotating domain state sampling data, extract the inverter-side output voltage quadrature axis component and the grid connection point voltage quadrature axis component, perform four-quadrant arctangent operation on the quadrature axis component respectively, analyze the real-time angular position of the voltage vector in the rotating coordinate system, and linearize the calculation results to eliminate jump points, obtain the inverter output voltage phase value and the grid connection point voltage phase value, and establish inverter and grid connection point phase angle data; S302: Based on the inverter and grid connection point phase angle data, extract the inverter output voltage phase value and the grid connection point voltage phase value, perform angle difference operation, calculate the relative offset between the two, and constrain the relative offset within a preset angle period range through modulo operation processing, quantify the degree of lag or lead of the inverter output side relative to the grid side, and generate voltage phase deviation variable. S303: For the voltage phase deviation variable, perform sine trigonometric function operations and cosine trigonometric function operations to obtain the sine component value and cosine component value of the phase difference. According to the rotation coordinate transformation rule, fill the sine component value and cosine component value into the diagonal and off-diagonal element positions of the correction matrix to construct a second-order rotation matrix for compensating for the mismatch of the decoupling model and generate the voltage vector geometric correction factor.

[0010] As a further aspect of the present invention, the step of constraining the relative offset within a preset angular period range through modulo operation specifically involves: using twice the value of pi as the period reference, performing a modulo operation on the relative offset, and mapping the result of the modulo operation to a numerical range with a negative value of pi as the lower limit and a positive value of pi as the upper limit.

[0011] As a further aspect of the present invention, the specific steps of S4 are as follows: S401: Call the grid-connected current direct-axis component and quadrature-axis component in the rotating domain state sampling data, read the controller's preset direct-axis current command value and quadrature-axis current command value, perform subtraction operations on the direct-axis current command value and the grid-connected current direct-axis component, and the quadrature-axis current command value and the grid-connected current quadrature-axis component respectively, obtain the real-time deviation values ​​in the direct-axis and quadrature-axis directions, and generate the grid-connected current tracking error vector; S402: Based on the grid-connected current tracking error vector, analyze the direct-axis error component and the quadrature-axis error component, perform a square operation on the direct-axis error component and the quadrature-axis error component and accumulate to obtain the squared error magnitude value, call the inductance parameter of the inverter-side filter inductor, perform a multiplication operation on the squared error magnitude value and the inductance parameter and introduce a proportional coefficient to establish an error energy level scalar; S403: For the error energy level scalar, a preset energy boundary reference value is used to distinguish the operating modes. The error energy level scalar is compared with the energy boundary reference value. Based on the comparison logic, it is determined whether it is in the steady-state region or the transient region. If it is in the steady-state region, the damping coefficient is calculated by mapping a linear function relationship. If it is in the transient region, the calculation of the damping coefficient is switched to a nonlinear function relationship. Based on the calculation result, the dynamically changing control parameters are output to generate the variable structure damping adjustment gain.

[0012] As a further aspect of the present invention, the step of performing a multiplication operation on the squared error magnitude and the inductance parameter and introducing a proportional coefficient to establish an error energy level scalar specifically involves: setting the value of the proportional coefficient to 0.5, performing a product operation on the squared error magnitude and the inductance parameter of the inverter-side filter inductor, multiplying the result by the proportional coefficient, and quantifying the real-time virtual potential energy value as the error energy level scalar.

[0013] As a further aspect of the present invention, the specific steps of S5 are as follows: S501: Call the direct axis and quadrature axis values ​​in the variable structure damping adjustment gain and capacitor current sliding mode reconstruction data, perform numerical multiplication to map the current dimension state quantity to the voltage dimension feedback control quantity, construct a virtual damping voltage term to suppress the resonance spike of the LCL filter, and generate an active damping control component. S502: Call the voltage vector geometric correction factor to obtain the preset inter-axis cross-coupling voltage parameters in the rotating coordinate system, use the voltage vector geometric correction factor to perform matrix multiplication correction operation on the cross-coupling voltage parameters to avoid the decoupling model mismatch caused by coordinate transformation phase deviation, extract the geometrically corrected inter-axis coupling compensation voltage value, and generate the geometrically corrected decoupling voltage vector. S503: Based on the active damping control component and the geometrically corrected decoupled voltage vector, the output voltage value of the grid-connected current PI regulator and the grid-connected point voltage feedforward value are collected. According to the inverter voltage equation, algebraic addition, subtraction and superposition operations are performed on the output voltage value, grid-connected point voltage feedforward value, damping component and decoupled vector to synthesize the reference voltage command in the rotating coordinate system and generate the comprehensive modulation voltage command. S504: For the comprehensive modulation voltage command, execute space vector pulse width modulation logic operation, determine the sector position of the reference voltage vector and calculate the duration of the basic voltage vector, generate the corresponding PWM pulse sequence based on the duration, control the on and off states of the inverter bridge arm power switch, and generate inverter switching drive signal.

[0014] As a further aspect of the present invention, the matrix multiplication correction operation of the cross-coupled voltage parameters using the voltage vector geometric correction factor specifically involves: constructing the voltage vector geometric correction factor into a second-order correction matrix; constructing the preset inter-axis cross-coupled voltage parameters in the rotating coordinate system into a two-dimensional state vector; performing a left multiplication operation on the two-dimensional state vector using the second-order correction matrix; calculating the cumulative sum of the multiplications of the matrix row elements and the vector elements respectively; and outputting the corrected direct-axis voltage component and cross-axis voltage component and combining them to generate a geometrically corrected decoupling voltage vector.

[0015] Compared with the prior art, the advantages and positive effects of the present invention are as follows: In this invention, the capacitor current state is reconstructed using sliding mode observation technology. The switching characteristics of the sliding mode surface function ensure that the observed values ​​are invariant to parameter perturbations and external disturbances, eliminating the measurement noise and delay effects introduced by physical sensors. A geometric correction matrix is ​​constructed based on the phase analysis of the rotating domain state data to compensate for the voltage vector deviation between the inverter and the grid connection point in real time, achieving precise decoupling control in a two-phase rotating coordinate system. Combined with the error energy level, the damping gain is adaptively adjusted to improve the dynamic tracking capability of the command signal while ensuring resonance suppression, thus establishing a high-quality grid-connected current waveform. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention, 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 the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a schematic diagram of the steps of the present invention; Figure 2 This is a detailed schematic diagram of S1 of the present invention; Figure 3 This is a detailed schematic diagram of S2 of the present invention; Figure 4 This is a detailed schematic diagram of S3 of the present invention; Figure 5 This is a detailed schematic diagram of S4 of the present invention; Figure 6 This is a detailed schematic diagram of S5 of the present invention. Detailed Implementation

[0018] The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0019] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0020] Please see Figure 1 This invention provides a control method for an LCL inverter based on step-by-step decoupling, comprising the following steps: S1: Collect analog signals of inductor current and grid connection point voltage of LCL inverter, convert the analog signal of grid connection point voltage into a sampling sequence using an analog-to-digital converter, construct the Clark and Park transformation matrix, perform coordinate projection on the sampling sequence, extract the direct axis and quadrature axis data in the rotating coordinate system, and obtain the state sampling data of the rotating domain. S2: Subtract the inductor current estimate from the rotating domain state sampling data to construct a sliding mode surface function with the current observation deviation as input. Select the switching gain value according to the polarity of the sliding mode surface function, perform filtering on the switching gain value, and generate capacitor current sliding mode reconstruction data. S3: Calculate the phase angle between the LCL inverter and the grid connection point voltage in the rotating domain state sampling data, obtain the voltage phase difference using arctangent logic, calculate the sine and cosine components of the voltage phase difference, construct the rotation correction matrix for compensating for the mismatch of the decoupling model, and generate the voltage vector geometric correction factor. S4: Calculate the tracking error between the grid current and the command in the rotating domain state sampling data, square the tracking error and combine it with the inductance parameters to obtain the error energy level scalar, compare the error energy level scalar with the energy boundary standard, match the linear function as the damping adjustment coefficient, and generate the variable structure damping adjustment gain. S5: Perform multiplication on the variable structure damping adjustment gain and the capacitor current sliding mode reconstruction data to obtain the active damping component, superimpose the voltage feedforward, the regulator output and the decoupled voltage component corrected by the voltage vector geometric correction factor, process the superposition result using space vector modulation logic, and generate the inverter switching drive signal. The rotating domain state sampling data includes direct-axis voltage sampling values, quadrature-axis voltage sampling values, direct-axis current sampling values, and quadrature-axis current sampling values ​​in the rotating coordinate system. The capacitor current sliding mode reconstruction data includes the filtered switching gain value and the capacitor current estimate output by the sliding mode observer. The voltage vector geometric correction factor includes the sine component of the voltage phase difference, the cosine component of the voltage phase difference, and the rotating correction matrix for compensating for the mismatch of the decoupling model. The variable structure damping adjustment gain includes the linear damping coefficient based on the scalar matching of the error energy level and the dynamically adjusted variable structure control gain value. The inverter switching drive signal includes the switching pulse sequence generated by space vector modulation and the turn-on and turn-off control commands of the inverter power devices.

[0021] Please see Figure 2 The specific steps of S1 are as follows: S101: Acquires inductor current and grid connection point voltage signals of LCL inverter, starts analog-to-digital conversion channel to perform synchronous sampling and holding operation on inductor current and grid connection point voltage analog signals, discretizes analog amplitude in continuous time domain into digital code according to clock frequency, and performs time-sequence alignment and integration of three-phase current data and three-phase voltage data according to time step order to generate discretized sampling sequence. The Hall current sensor and high-precision voltage transformer connected to the inductors and common grid connection point of the LCL inverter are activated, and the sampling frequency is set to 10000 Hz to capture the three-phase inductor current analog signal and the three-phase grid connection point voltage analog signal in real time. After receiving a unified synchronous trigger pulse, the multi-channel analog-to-digital converter immediately performs a sample-and-hold operation on the above six analog signals, mapping the continuously changing analog voltage amplitude to a 12-bit or 16-bit digital code. For example, when the analog input range is from -10 volts to +10 volts, and the current A-phase current sensor output voltage is 5 volts, the analog-to-digital converter quantizes it into a digital integer value of 24576 (assuming 16-bit resolution and unsigned mapping). Subsequently, the processor reads the conversion results of each channel and checks the timestamp label of each channel's data according to the preset time step parameter. It compensates for the microsecond-level delay caused by differences in transmission line impedance or the converter's multiplexing mechanism, and strictly aligns the three-phase current data and three-phase voltage data on the time axis through an interpolation algorithm. After processing, this set of physical quantity data containing six dimensions at the same time is stored in the first-in-first-out queue of the high-speed cache memory to generate a discretized sampling sequence with temporal consistency.

[0022] S102: Call the three-phase voltage values ​​in the discretized sampling sequence, use a second-order generalized integrator to extract the fundamental positive sequence component and calculate the real-time phase angle of the voltage vector at the grid connection point, calculate the corresponding sine function value and cosine function value based on the real-time phase angle value, fill the sine function value and cosine function value into the mapping determinant from the three-phase stationary coordinate system to the two-phase rotating coordinate system, and establish the coordinate projection transformation matrix. The three-phase voltage values ​​from the discretized sampling sequence are retrieved from the buffer queue and input into the second-order generalized integrator logic unit. This unit uses two orthogonal integration channels to filter and phase-shift the input signal, separating the fundamental positive-sequence voltage component. It also tracks the zero-crossing position of the grid voltage in real time and analyzes the real-time phase angle of the grid-connected voltage vector using the arctangent function. For example, when the direct-axis component of the fundamental voltage is detected to be 311 volts and the quadrature-axis component to be 0 volts, the calculated real-time phase angle is 0 radians or 23.14 radians (corresponding to an integer number of cycles). Based on this real-time phase angle value, the sine and cosine lookup tables are called to obtain the corresponding high-precision trigonometric function values. Assuming the current phase angle is 0.523 radians (i.e., 30 degrees), the obtained sine function value is 0.5 and the cosine function value is 0.866. Based on the matrix structure requirements of the Park transform, the cosine function value is filled into the first row and first column and the second row and second column of the matrix, the sine function value is filled into the first row and second column, and the negative sine function value is filled into the second row and first column. A dynamic array of 2 rows and 2 columns is constructed in memory to establish the coordinate projection transformation matrix for subsequent coordinate rotation.

[0023] S103: Based on the coordinate projection transformation matrix, matrix multiplication is performed on the three-phase current and voltage data included in the discretized sampling sequence. The time-varying sinusoidal AC quantity is converted into a linear DC quantity through coordinate axis rotation transformation. The direct axis component values ​​that are consistent with the magnetic flux orientation and the quadrature axis component values ​​that are orthogonal to the magnetic flux orientation are separated and extracted in the rotating coordinate system. The direct axis component values ​​and the quadrature axis component values ​​are vector synthesized to generate rotating domain state sampling data. The three-phase current and voltage data from the discretized sampling sequence are first converted from the three-phase stationary coordinate system data (abc) to the two-phase stationary coordinate system data (alpha-beta) using the Clarke transform, followed by a rotational coordinate system transformation. Specifically, the transformation matrix is ​​multiplied by the two-phase stationary coordinate system data vector. Taking the current transformation as an example, the direct-axis current component equals the alpha-axis current multiplied by its cosine value plus the beta-axis current multiplied by its sine value; the quadrature-axis current component equals the beta-axis current multiplied by its cosine value minus the alpha-axis current multiplied by its sine value. Assuming the current alpha-axis current is 10 amps, the beta-axis current is 0 amps, and the rotation angle is 0 radians (i.e., cosine is 1, sine is 0), the calculated direct-axis component value is 10 amps, and the quadrature-axis component value is 0 amps. The direct-axis and quadrature-axis components of the voltage and current calculated at that moment are packaged, the time-varying characteristics of the AC components are removed, and the steady-state components exhibiting DC properties are extracted, generating rotating domain state sampling data containing four key state variables.

[0024] Please see Figure 3 The specific steps of S2 are as follows: S201: Call the direct axis and quadrature axis current sampling values ​​in the rotating domain state sampling data, read the direct axis and quadrature axis inductor current prediction values ​​output by the sliding mode observer state equation in the previous calculation step, perform vector subtraction operation on the current sampling value and the inductor current prediction value, calculate the vector difference magnitude of the two in the rotating coordinate system, and establish the current observation deviation state quantity. The system reads the latest actual current sampling values ​​for the direct and quadrature axes from the rotating domain state sampling data, and simultaneously retrieves the predicted values ​​of the direct and quadrature axis inductor currents calculated in the previous control cycle from the observer's state register. Element-by-element subtraction is performed on these two vectors to quantify the deviation between the model prediction and the actual physical state. Specifically, the direct-axis observation error is obtained by subtracting the predicted direct-axis inductor current from the actual direct-axis current sampling value; the quadrature-axis observation error is obtained by subtracting the predicted quadrature-axis inductor current from the actual quadrature-axis current sampling value. For example, if the current actual direct-axis current sampling value is 15.5 amps, while the sliding mode observer's model-derived direct-axis prediction is 15.2 amps, the calculated vector difference between the two in the rotating coordinate system is positive 0.3 amps. This difference includes not only measurement noise but also implicitly includes unmodeled dynamic information such as capacitor branch shunt current. The calculated direct-axis and quadrature-axis errors are stored in dedicated error state variables, serving as inputs to the sliding mode control law and establishing a current observation deviation state variable characterizing the current observation accuracy.

[0025] S202: Based on the current observation deviation state quantity, construct a sliding surface function describing the state convergence trajectory, call symbolic operation logic to extract the algebraic symbol of the sliding surface function, compare the relative polarity of the algebraic symbol with the zero-level reference, output positive feedback coefficient when the polarity is positive, output negative feedback coefficient when the polarity is negative, and generate a nonlinear switching gain signal. The sliding surface function is defined as equal to the deviation state variable itself, aiming to drive the observation error to converge to 0 along the sliding surface. The sign function logic is invoked to determine the polarity of the deviation values ​​for the direct and quadrature axes. The operation logic is set as follows: if the deviation value is greater than zero, the sign function outputs a positive 1; if the deviation value is less than zero, the sign function outputs a negative 1; if the deviation value is equal to zero, the previous state is maintained or 0 is output. Subsequently, a preset sliding gain coefficient (e.g., 50) is invoked, and this coefficient is multiplied by the output of the sign function. Assuming the current direct axis deviation is positive 0.3 amperes (i.e., sign is positive 1) and the quadrature axis deviation is negative 0.1 amperes (i.e., sign is negative 1), then positive 50 and negative 50 are output as feedback control quantities, respectively. This process transforms the continuously changing error signal into a high-frequency switching signal with an amplitude of 50. This signal, through continuous positive and negative switching, forces the observation state to approximate the true state, generating a high-frequency nonlinear switching gain signal containing disturbance information.

[0026] S203: Feed the nonlinear switching gain signal into the digital low-pass filter, set the cutoff bandwidth parameter of the filter according to the inverter switching frequency, perform frequency domain attenuation operation on the signal, suppress high-frequency jitter harmonics, extract the smoothed component after filtering and map it into the observer feedback compensation term, correct the state estimate, and generate capacitor current sliding mode reconstruction data. Based on the inverter's switching frequency (e.g., 10000 Hz), the filter's cutoff bandwidth is designed to be 2000 Hz to effectively filter out high-frequency jitter noise introduced by sliding mode control, while retaining low-frequency components reflecting the dynamics of the capacitor current. The filter performs discretized first- or second-order filtering operations on the input switching signal sequence. For example, if the current input value is +50, the filter output value at the previous moment is 5, and the filter coefficient is set to 0.1, then the current output value is equal to 0.9 × 5 + 0.1 × 50, resulting in 9.5. After several iterations, the filter output value will stabilize near a value proportional to the actual capacitor current. Subsequently, the inductance parameter of the LCL filter is introduced for scaling, mapping the filtered value to a physical current value, and injecting it as a feedback compensation term into the observer's state equation to correct the predicted state value for the next moment, thereby completing the reconstruction of the capacitor current, which cannot be directly measured, and generating capacitor current sliding mode reconstruction data.

[0027] Please see Figure 4 The specific steps of S3 are as follows: S301: Call the rotating domain state sampling data, extract the inverter-side output voltage quadrature axis components and grid connection point voltage quadrature axis components, perform four-quadrant arctangent operation on the quadrature axis components respectively, analyze the real-time angular position of the voltage vector in the rotating coordinate system, and linearize the calculation results to eliminate jump points, obtain the inverter output voltage phase value and grid connection point voltage phase value, and establish inverter and grid connection point phase angle data; The direct-axis and quadrature-axis components of the inverter-side output voltage and the grid-connected voltage are extracted separately. Using a four-quadrant arctangent algorithm, the absolute phase angle of each voltage vector in the rotating coordinate system is calculated based on the values ​​of its direct-axis and quadrature-axis components. This algorithm automatically determines the quadrant of the vector based on the sign of the components, outputting angle values ​​ranging from negative to positive pi. Subsequently, linearization processing is performed on the calculated angle values, detecting and eliminating 2Pi jump points caused by periodic rotation to ensure the continuity of the phase data. For example, if the direct-axis component of the inverter voltage vector is 300 volts and the quadrature-axis component is 10 volts, the calculated phase angle is approximately 0.033 radians; if the calculated phase angle of the grid-connected voltage vector is 0.030 radians, these two continuous angle values ​​are stored separately as a benchmark for analyzing internal phase angle relationships, establishing inverter and grid-connected phase angle data.

[0028] S302: Based on the inverter and grid connection point phase angle data, extract the inverter output voltage phase value and the grid connection point voltage phase value, perform angle difference operation, calculate the relative offset between the two, and constrain the relative offset within the preset angle period range through modulo operation processing, quantify the degree of lag or lead of the inverter output side relative to the grid side, and generate voltage phase deviation variable. An angle differential operation is performed by subtracting the grid connection point voltage phase value from the inverter output voltage phase value to obtain the initial phase difference between the two. Since the grid voltage is not constant, this phase difference contains accumulated errors over integer multiples of a cycle. Therefore, a modulo operation is performed on the initial phase difference, strictly constraining the result to the range of negative to positive pi. For example, if the inverter phase is 6.30 radians and the grid connection point phase is 0.01 radians (actually spanning one cycle), the direct subtraction yields 6.29 radians. After modulo operation (subtracting 2Pi, approximately 6.283), the relative offset is approximately 0.007 radians. This value precisely quantifies the degree of lag or lead of the inverter output voltage vector relative to the grid voltage vector, reflecting the phase drift caused by the inductor-capacitor branch of the LCL filter. This quantified difference is defined as the voltage phase deviation variable.

[0029] S303: For the voltage phase deviation variable, perform sine trigonometric function operations and cosine trigonometric function operations to obtain the sine component value and cosine component value of the phase difference. According to the rotation coordinate transformation law, fill the sine component value and cosine component value into the diagonal and off-diagonal element positions of the correction matrix to construct a second-order rotation matrix for compensating for the mismatch of the decoupling model and generate the voltage vector geometric correction factor. The trigonometric function unit is invoked to calculate the sine and cosine values ​​of the deviation variable. Assuming the phase deviation variable is 0.1 radians, the calculated sine component value is approximately 0.0998, and the cosine component value is approximately 0.9950. Based on the geometric rules of coordinate transformation, these two values ​​are used to construct a second-order rotation correction matrix. Specifically, the cosine component value is assigned to the diagonal elements of the matrix, the sine component value is assigned to the off-diagonal elements in the first row and second column, and the negative sine component value is assigned to the off-diagonal elements in the second row and first column. Mathematically, this matrix represents a rotation operator that rotates the controller's reference coordinate system to coincide with the coordinate system of the actual physical quantity. This constructed matrix is ​​stored in memory as the geometric reference for correcting decoupling terms in subsequent control algorithms, generating a voltage vector geometric correction factor.

[0030] Please see Figure 5 The specific steps of S4 are as follows: S401: Call the grid-connected current direct-axis component and quadrature-axis component in the rotating domain state sampling data, read the controller's preset direct-axis current command value and quadrature-axis current command value, perform subtraction operations on the direct-axis current command value and the grid-connected current direct-axis component, and the quadrature-axis current command value and the grid-connected current quadrature-axis component respectively, obtain the real-time deviation values ​​in the direct-axis and quadrature-axis directions, and generate the grid-connected current tracking error vector; The system acquires the preset direct-axis current command value and quadrature-axis current command value at the current moment. Subtraction is then performed on these two sets of data to obtain the real-time tracking error. Specifically, the direct-axis current command value is subtracted from the direct-axis component of the grid-connected current to obtain the real-time deviation value in the direct-axis direction; the quadrature-axis current command value is subtracted from the quadrature-axis component of the grid-connected current to obtain the real-time deviation value in the quadrature-axis direction. For example, if the direct-axis current command is set to 20 amps, and the actual acquired direct-axis component of the grid-connected current is 19.5 amps, then the direct-axis deviation is 0.5 amps; if the quadrature-axis command is 0 amps, and the actual component is 0.2 amps, then the quadrature-axis deviation is -0.2 amps. These two scalar values ​​are combined into a two-dimensional vector, which comprehensively reflects the accuracy and response status of the current control loop at the current moment, generating the grid-connected current tracking error vector.

[0031] S402: Based on the grid-connected current tracking error vector, analyze the direct-axis error component and the quadrature-axis error component, perform squaring operation on the direct-axis error component and the quadrature-axis error component and accumulate to obtain the squared error magnitude value, call the inductance parameter of the inverter-side filter inductor, perform multiplication operation on the squared error magnitude value and the inductance parameter and introduce a proportional coefficient to establish an error energy level scalar; The squares of the direct-axis and quadrature-axis error components are performed separately, and the two squared results are added together to obtain the squared value of the error magnitude. Next, the inductance parameter of the inverter-side filter inductor (e.g., 3 millihenries) is retrieved from the memory, and the squared value of the error magnitude is multiplied by this inductance parameter, then multiplied by a constant coefficient of 0.5 to calculate the virtual magnetic field energy stored in the error field. Using the previous example, the square of a direct-axis error of 0.5 amperes is 0.25, and the square of a quadrature-axis error of -0.2 amperes is 0.04, with a sum of 0.29. Substituting this into the calculation logic: 0.5 multiplied by 0.003 (inductance) multiplied by 0.29, the result is 0.000435 joules. This value is a scalar, physically representing the energy level corresponding to the current control deviation. This scalar is used to evaluate the dynamic operating state and establish an error energy level scalar.

[0032] As shown in Table 1, Table 1 presents the energy scalar calculation results under different error states.

[0033] Table 4: Examples of Error Energy Calculation Table 1 clearly shows that as the error increases, the calculated energy scalar exhibits a significant nonlinear growth, providing a highly sensitive criterion for subsequent variable structure control.

[0034] S403: For the error energy level scalar, a preset energy boundary reference value is used to distinguish the operating modes. The error energy level scalar is compared with the energy boundary reference value. Based on the comparison logic, it is determined whether it is in the steady-state region or the transient region. If it is in the steady-state region, the damping coefficient is calculated by mapping a linear function relationship. If it is in the transient region, the calculation of the damping coefficient is switched to a nonlinear function relationship. Based on the calculation results, the dynamically changing control parameters are output to generate the variable structure damping adjustment gain. The system invokes a preset energy threshold value (e.g., set to 0.001 joules), which distinguishes between the steady-state operating region and the transient large disturbance region. The real-time calculated error energy level scalar is compared with the energy threshold value. If the error energy level scalar is less than the threshold value, the system is determined to be in the steady-state region. In this case, a linear function is used to calculate the damping coefficient, outputting a small damping gain (e.g., 10) to ensure steady-state accuracy and bandwidth. If the error energy level scalar is greater than or equal to the threshold value, the system is determined to be in the transient region. The system immediately switches to a nonlinear function, outputting a significantly increased damping coefficient (e.g., 80) to provide strong damping and suppress overshoot and oscillation. For example, when the calculated energy is 0.000435 joules (less than 0.001), the output damping gain is 10; when the energy suddenly increases to 0.039 joules (greater than 0.001), the output damping gain is 80. Based on this logic, the control parameters are refreshed in real time to generate a variable structure damping adjustment gain that can adaptively adjust dynamic characteristics.

[0035] Please see Figure 6 The specific steps of S5 are as follows: S501: Call the direct and quadrature axis values ​​in the variable structure damping adjustment gain and capacitor current sliding mode reconstruction data, perform numerical multiplication to map the current dimension state quantity to the voltage dimension feedback control quantity, construct a virtual damping voltage term to suppress the resonance spike of the LCL filter, and generate active damping control components. The variable structure damping adjustment gain value generated in step S403 and the direct-axis and quadrature-axis components of the capacitor current sliding mode reconstruction data generated in step S203 are read. A numerical multiplication operation is performed, multiplying the damping gain by the direct-axis and quadrature-axis components of the capacitor current, respectively, thereby mapping the current-dimensional state variable to a voltage-dimensional control signal. If the damping adjustment gain is 80 at the current moment, and the reconstructed capacitor current direct-axis component is 0.5 amps and the quadrature-axis component is 0.1 amps, then the calculated direct-axis damping voltage term is 40 volts, and the quadrature-axis damping voltage term is 8 volts. This calculation process is physically equivalent to connecting a controlled virtual resistor in series in the capacitor branch. This resistor only functions at the algorithm level, effectively consuming the resonant energy of the LCL filter without generating actual power loss. These two calculated voltage values ​​are used as active damping control terms to generate active damping control components.

[0036] S502: Call the voltage vector geometric correction factor to obtain the preset inter-axis cross-coupling voltage parameters in the rotating coordinate system. Use the voltage vector geometric correction factor to perform matrix multiplication correction on the cross-coupling voltage parameters to avoid the decoupling model mismatch caused by the phase deviation of coordinate transformation. Extract the geometrically corrected inter-axis coupling compensation voltage value and generate the geometrically corrected decoupling voltage vector. The voltage vector geometric correction factor (i.e., the second-order rotation matrix) generated in step S303 is invoked, and the pre-set inter-axis cross-coupling voltage parameters under the ideal decoupling model are read from memory. These coupling parameters consist of the rotation angular frequency, the filter inductance value, and the corresponding product of the direct and quadrature axis currents. A matrix multiplication correction operation is performed between the voltage vector geometric correction factor and the vector containing the cross-coupling voltage parameters. This operation rotates the decoupling voltage terms, originally based on the ideal coordinate system, to the physical coordinate system where phase shifts actually exist, thereby eliminating decoupling errors caused by asynchronous coordinate transformations. Assuming the ideal direct-axis coupling voltage is -10 volts and the quadrature-axis coupling voltage is 300 volts, after correction using the geometric correction matrix (assuming a minimal rotation angle, approximately a diagonal matrix), the corrected direct-axis coupling compensation value is -9.8 volts, and the quadrature-axis coupling compensation value is 299.5 volts (values ​​are for illustrative purposes only). These corrected voltage values ​​are extracted to generate the geometrically corrected decoupling voltage vector.

[0037] S503: Based on the active damping control component and the geometrically corrected decoupled voltage vector, the output voltage value of the grid-connected current PI regulator and the grid-connected point voltage feedforward value are collected. According to the inverter voltage equation, algebraic addition and subtraction superposition operations are performed on the output voltage value, grid-connected point voltage feedforward value, damping component and decoupling vector to synthesize the reference voltage command in the rotating coordinate system and generate the comprehensive modulation voltage command. Simultaneously, the main control voltage value output by the grid-connected current PI regulator and the feedforward sampling value of the grid-connected point voltage are acquired. Based on the inverter voltage balance equation, an algebraic superposition operation is performed on the above four voltage components. The specific operation logic is as follows: For the direct-axis reference voltage, the PI regulator output value is added to the grid voltage feedforward value, then the active damping control component is subtracted, and finally the geometrically corrected direct-axis decoupled voltage vector is subtracted; the same operation is performed for the quadrature-axis reference voltage. If the direct-axis PI output is 20 volts, the grid feedforward is 311 volts, the damping component is 40 volts, and the decoupling component is -9.8 volts, then the final direct-axis reference voltage command is equal to 20 + 311 - 40 - (-9.8), resulting in 300.8 volts. This operation synthesizes a comprehensive control quantity including fundamental frequency control, feedforward compensation, damping suppression, and decoupling correction, generating a comprehensive modulation voltage command in a rotating coordinate system.

[0038] S504: For the integrated modulation voltage command, it performs space vector pulse width modulation logic operation, determines the sector position of the reference voltage vector and calculates the duration of the basic voltage vector, generates the corresponding PWM pulse sequence based on the duration, controls the on and off states of the inverter bridge arm power switch tubes, and generates inverter switching drive signals. Based on the values ​​of the direct-axis and quadrature-axis voltage commands and the angle of their composite vector, the hexagonal sector position (e.g., the first sector) of the reference voltage vector is determined. Then, using the volt-second balance principle, the duration of action of the two adjacent basic voltage vectors and the zero vector required to synthesize the reference vector is calculated. Assuming it is in the first sector and the DC bus voltage is 600 volts, the duration of action of basic vector V1 is calculated to be 50 microseconds, V2 to be 30 microseconds, and the zero vector to be 20 microseconds. Based on these time parameters, a corresponding six-channel PWM switching pulse sequence is generated to precisely control the turn-on and turn-off timing of the power switches on the inverter bridge arm. In this way, the inverter output will generate a pulse voltage waveform equivalent to the reference voltage command, and the drive current will follow the command changes, generating the inverter switching drive signal.

[0039] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of protection of the described technical solutions.

Claims

1. A control method for LCL-type inverters based on step-by-step decoupling, characterized in that, Includes the following steps: S1: Collect the inductor current and grid connection point voltage signals of the LCL inverter, convert them into a sampling sequence, use the transformation matrix to project the sampling sequence to extract the orthogonal axis data, and generate rotating domain state sampling data; S2: Combining the rotating domain state sampling data and the inductor current estimate, construct the current observation deviation and the sliding surface function of the current observation deviation, determine the switching gain and filter according to the polarity of the sliding surface function, and generate the capacitor current sliding mode reconstruction data. S3: Analyze the inverter and grid connection point phase angles of the rotating domain state sampling data, obtain the voltage phase difference and the sine and cosine components of the voltage phase difference, and generate the voltage vector geometric correction factor; S4: Calculate the tracking error of the rotating domain state sampling data, combine the inductance parameter and the square of the tracking error to obtain the error energy level scalar, compare the error energy level scalar with the energy boundary standard, and generate the variable structure damping adjustment gain. S5: Multiply the variable structure damping adjustment gain and the capacitor current sliding mode reconstruction data to generate an active damping component, and superimpose the voltage feedforward, the adjustment output and the component corrected by the voltage vector geometric correction factor to generate the inverter switching drive signal.

2. The LCL inverter control method based on step-by-step decoupling according to claim 1, characterized in that, The rotating domain state sampling data includes direct-axis voltage sampling values, quadrature-axis voltage sampling values, direct-axis current sampling values, and quadrature-axis current sampling values ​​in the rotating coordinate system. The capacitor current sliding mode reconstruction data includes the filtered switching gain value and the capacitor current estimate output by the sliding mode observer. The voltage vector geometric correction factor includes the sine component of the voltage phase difference, the cosine component of the voltage phase difference, and the rotating correction matrix for compensating for decoupling model mismatch. The variable structure damping adjustment gain includes the linear damping coefficient based on scalar matching of error energy level and the dynamically adjusted variable structure control gain value. The inverter switching drive signal includes the switching pulse sequence generated by space vector modulation and the turn-on and turn-off control commands of the inverter power devices.

3. The LCL inverter control method based on step-by-step decoupling according to claim 1, characterized in that, The specific steps of S1 are as follows: S101: Acquires inductor current and grid connection point voltage signals of LCL inverter, starts analog-to-digital conversion channel to perform synchronous sampling and holding operation on inductor current and grid connection point voltage analog signals, discretizes analog amplitude in continuous time domain into digital code according to clock frequency, and performs time-sequence alignment and integration of three-phase current data and three-phase voltage data according to time step order to generate discretized sampling sequence. S102: Call the three-phase voltage values ​​in the discretized sampling sequence, use a second-order generalized integrator to extract the fundamental positive sequence component and calculate the real-time phase angle of the grid connection point voltage vector, calculate the corresponding sine function value and cosine function value based on the real-time phase angle value, fill the sine function value and the cosine function value into the mapping determinant from the three-phase stationary coordinate system to the two-phase rotating coordinate system, and establish the coordinate projection transformation matrix; S103: Based on the coordinate projection transformation matrix, perform matrix multiplication on the three-phase current and voltage data included in the discretized sampling sequence, convert the time-varying sinusoidal AC quantity into a linear DC quantity through coordinate axis rotation transformation, separate and extract the direct axis component values ​​that are consistent with the magnetic flux orientation and the quadrature axis component values ​​that are orthogonal to the magnetic flux orientation in the rotating coordinate system, and perform vector synthesis on the direct axis component values ​​and the quadrature axis component values ​​to generate rotating domain state sampling data.

4. The LCL inverter control method based on step-by-step decoupling according to claim 3, characterized in that, The specific steps of S2 are as follows: S201: Call the direct axis and quadrature axis current sampling values ​​in the rotating domain state sampling data, read the direct axis and quadrature axis inductor current prediction values ​​output by the sliding mode observer state equation in the previous calculation step, perform vector subtraction operation on the current sampling value and the inductor current prediction value, calculate the vector difference magnitude of the two in the rotating coordinate system, and establish the current observation deviation state quantity. S202: Based on the current observation deviation state quantity, construct a sliding surface function describing the state convergence trajectory, call symbolic operation logic to extract the algebraic symbol of the sliding surface function, compare the relative polarity of the algebraic symbol with the zero-level reference, output a positive feedback coefficient when the polarity is positive, output a negative feedback coefficient when the polarity is negative, and generate a nonlinear switching gain signal. S203: Feed the nonlinear switching gain signal into a digital low-pass filter, set the cutoff bandwidth parameter of the filter according to the inverter switching frequency, perform frequency domain attenuation operation on the signal to suppress high-frequency jitter harmonics, extract the smoothed component after filtering and map it into the observer feedback compensation term, correct the state estimate, and generate capacitor current sliding mode reconstruction data.

5. The LCL inverter control method based on step-by-step decoupling according to claim 4, characterized in that, The specific steps for S3 are as follows: S301: Call the rotating domain state sampling data, extract the inverter-side output voltage quadrature axis component and the grid connection point voltage quadrature axis component, perform four-quadrant arctangent operation on the quadrature axis component respectively, analyze the real-time angular position of the voltage vector in the rotating coordinate system, and linearize the calculation results to eliminate jump points, obtain the inverter output voltage phase value and the grid connection point voltage phase value, and establish inverter and grid connection point phase angle data; S302: Based on the inverter and grid connection point phase angle data, extract the inverter output voltage phase value and the grid connection point voltage phase value, perform angle difference operation, calculate the relative offset between the two, and constrain the relative offset within a preset angle period range through modulo operation processing, quantify the degree of lag or lead of the inverter output side relative to the grid side, and generate voltage phase deviation variable. S303: For the voltage phase deviation variable, perform sine trigonometric function operations and cosine trigonometric function operations to obtain the sine component value and cosine component value of the phase difference. According to the rotation coordinate transformation rule, fill the sine component value and cosine component value into the diagonal and off-diagonal element positions of the correction matrix to construct a second-order rotation matrix for compensating for the mismatch of the decoupling model and generate the voltage vector geometric correction factor.

6. The LCL inverter control method based on step-by-step decoupling according to claim 5, characterized in that, The specific method of constraining the relative offset within a preset angular period range through modulo operation is as follows: using twice the value of pi as the period reference, performing a modulo operation on the relative offset, and mapping the result of the modulo operation to a numerical range with a negative value of pi as the lower limit and a positive value of pi as the upper limit.

7. The LCL inverter control method based on step-by-step decoupling according to claim 5, characterized in that, The specific steps of S4 are as follows: S401: Call the grid-connected current direct-axis component and quadrature-axis component in the rotating domain state sampling data, read the controller's preset direct-axis current command value and quadrature-axis current command value, perform subtraction operations on the direct-axis current command value and the grid-connected current direct-axis component, and the quadrature-axis current command value and the grid-connected current quadrature-axis component respectively, obtain the real-time deviation values ​​in the direct-axis and quadrature-axis directions, and generate the grid-connected current tracking error vector; S402: Based on the grid-connected current tracking error vector, analyze the direct-axis error component and the quadrature-axis error component, perform a square operation on the direct-axis error component and the quadrature-axis error component and accumulate to obtain the squared error magnitude value, call the inductance parameter of the inverter-side filter inductor, perform a multiplication operation on the squared error magnitude value and the inductance parameter and introduce a proportional coefficient to establish an error energy level scalar; S403: For the error energy level scalar, a preset energy boundary reference value is used to distinguish the operating modes. The error energy level scalar is compared with the energy boundary reference value. Based on the comparison logic, it is determined whether it is in the steady-state region or the transient region. If it is in the steady-state region, the damping coefficient is calculated by mapping a linear function relationship. If it is in the transient region, the calculation of the damping coefficient is switched to a nonlinear function relationship. Based on the calculation result, the dynamically changing control parameters are output to generate the variable structure damping adjustment gain.

8. The LCL inverter control method based on step-by-step decoupling according to claim 7, characterized in that, The process of performing a multiplication operation between the squared error magnitude and the inductance parameter and introducing a proportional coefficient to establish an error energy level scalar is as follows: the proportional coefficient is set to 0.5, the squared error magnitude is multiplied by the inductance parameter of the inverter-side filter inductor, the result is multiplied by the proportional coefficient, and the real-time virtual potential energy value is quantified as the error energy level scalar.

9. The LCL inverter control method based on step-by-step decoupling according to claim 7, characterized in that, The specific steps of S5 are as follows: S501: Call the direct axis and quadrature axis values ​​in the variable structure damping adjustment gain and capacitor current sliding mode reconstruction data, perform numerical multiplication to map the current dimension state quantity to the voltage dimension feedback control quantity, construct a virtual damping voltage term to suppress the resonance spike of the LCL filter, and generate an active damping control component. S502: Call the voltage vector geometric correction factor to obtain the preset inter-axis cross-coupling voltage parameters in the rotating coordinate system, use the voltage vector geometric correction factor to perform matrix multiplication correction operation on the cross-coupling voltage parameters to avoid the decoupling model mismatch caused by coordinate transformation phase deviation, extract the geometrically corrected inter-axis coupling compensation voltage value, and generate the geometrically corrected decoupling voltage vector. S503: Based on the active damping control component and the geometrically corrected decoupled voltage vector, the output voltage value of the grid-connected current PI regulator and the grid-connected point voltage feedforward value are collected. According to the inverter voltage equation, algebraic addition, subtraction and superposition operations are performed on the output voltage value, grid-connected point voltage feedforward value, damping component and decoupled vector to synthesize the reference voltage command in the rotating coordinate system and generate the comprehensive modulation voltage command. S504: For the comprehensive modulation voltage command, execute space vector pulse width modulation logic operation, determine the sector position of the reference voltage vector and calculate the duration of the basic voltage vector, generate the corresponding PWM pulse sequence based on the duration, control the on and off states of the inverter bridge arm power switch, and generate inverter switching drive signal.

10. The LCL inverter control method based on step-by-step decoupling according to claim 9, characterized in that, The specific steps of performing matrix multiplication correction on the cross-coupled voltage parameters using the voltage vector geometric correction factor are as follows: the voltage vector geometric correction factor is constructed into a second-order correction matrix, the preset inter-axis cross-coupled voltage parameters in the rotating coordinate system are constructed into a two-dimensional state vector, the two-dimensional state vector is left-multiplied using the second-order correction matrix, the cumulative sum of the multiplication of the matrix row elements and the vector elements is calculated respectively, and the corrected direct-axis voltage component and cross-axis voltage component are output and combined to generate a geometrically corrected decoupling voltage vector.

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