Impedance modeling-based network tracking and network constructing type converter stability detection method and system

Abstract

According to the method and the system, an impedance matrix of a voltage source type inverter is determined based on a small signal model of the voltage source type inverter, and a first impedance ratio, a second impedance ratio and a third impedance ratio are established with an equivalent impedance matrix of a power grid; if the first impedance ratio does not meet the Nyquist stability criterion, determining that the converter is in a negative damping state; if the first impedance ratio meets the Nyquist stability criterion, it is judged that the converter is in a positive damping state or an under-damping state; and taking the product of the second impedance ratio and the third impedance ratio as an oscillation damping coefficient, if the oscillation damping coefficient is less than zero, judging that the converter is in a negative damping stable state, and if the oscillation damping coefficient is greater than or equal to zero and less than a critical damping coefficient, judging that the converter is in an under-damping stable state. If the oscillation damping coefficient is larger than or equal to the critical damping coefficient, it is judged that the converter is in a positive damping stable state, and the dynamic characteristics of the converter under the nonlinear and large-disturbance conditions are accurately described.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system stability control, and in particular, relates to a stability detection method and system for grid-following and grid-forming converters based on impedance modeling. Background Art

[0002] At present, with the widespread application of renewable energy, a large number of distributed power sources and energy storage devices have appeared in the power system. In order to improve the stability and flexibility of the power system, these distributed power sources and energy storage devices need to be effectively controlled and managed. A common solution is to use converters to connect distributed power sources and energy storage devices to the power grid. Traditional grid-following and grid-building converters are increasingly used in power systems. These converters can realize energy conversion and transmission between different voltage levels in the power system.

[0003] In the existing technology, the stability analysis of converters is one of the key issues in the design and operation of power systems. At present, the traditional converter stability analysis methods are mainly based on linear models and frequency domain analysis methods. These methods can provide useful results in some cases, but they are not effective enough to deal with the stability analysis of large-scale and complex power systems. Traditional stability analysis methods, such as characteristic root analysis and Nyquist plot analysis, usually require the system to be simplified and ignore some nonlinear and coupling effects, resulting in inaccurate analysis results. Most traditional methods focus on time domain analysis, and insufficient consideration is given to the interaction and stability effects in the frequency domain. In practical applications, frequency domain analysis is crucial to understanding the response and stability of the system at different frequencies. Grid-following and grid-forming converters will encounter various dynamic changes in actual operation, such as load changes, grid disturbances, etc. Traditional methods are difficult to predict the impact of these changes on system stability in real time and accurately. In summary, traditional stability analysis methods usually require accurate linearization models, which are difficult to accurately describe the dynamic behavior of nonlinear systems and large disturbance conditions. Traditional methods are mainly applicable to the stability analysis of a single type of converter, lack comprehensive analysis of multi-converter systems, and are difficult to deal with the interaction of multi-converter systems. Traditional analysis methods are computationally intensive and inefficient when dealing with high-dimensional and complex systems, making it difficult to achieve real-time monitoring and online analysis. Summary of the invention

[0004] In order to solve the deficiencies in the prior art, the present invention provides a stability detection method and system for grid-following and grid-forming type converters based on impedance modeling. The impedance modeling method is adopted, and the dynamic characteristics of the converter under nonlinear and large disturbance conditions can be accurately described through input and output impedance modeling.

[0005] The present invention adopts the following technical solution.

[0006] The present invention proposes a stability detection method for grid-following and grid-forming type converters based on impedance modeling. The grid-following and grid-forming type converters use voltage source inverters. The control system of the voltage source inverter includes multiple links, which are characterized by including:

[0007] Obtain the transfer function of the small signal model of each link in the control system, and construct the small signal model of the voltage source inverter according to the connection relationship of each link in the control system;

[0008] When the control system operates in an open-loop mode, the grid-connected point voltage disturbance is used as the input signal of the small signal model of the voltage source inverter, the grid-connected point current disturbance is used as the output signal of the small signal model of the voltage source inverter, and the transfer function of the small signal model of each link on the path from the input signal to the output signal is used to determine the equivalent open-loop admittance matrix of the voltage source inverter; when the control system operates in a closed-loop mode, the grid-connected point voltage disturbance is used as the first input signal of the small signal model of the voltage source inverter, the current reference value change is used as the second input signal of the small signal model of the voltage source inverter, and the grid-connected point current disturbance is used as the output signal of the small signal model of the voltage source inverter, and the transfer function of the small signal model of each link on the path from the first input signal and the second input signal to the output signal is used to determine the equivalent admittance matrix of the current feedback branch; the product of the inverse matrix of the equivalent open-loop admittance of the voltage source inverter and the inverse matrix of the equivalent admittance matrix of the current feedback branch is used as the impedance matrix of the voltage source inverter;

[0009] The first impedance ratio, the second impedance ratio and the third impedance ratio are established by using the equivalent impedance matrix of the power grid and the equivalent impedance matrix of the voltage source inverter; it is judged whether the first impedance ratio satisfies the Nyquist stability criterion, if the first impedance ratio does not satisfy the Nyquist stability criterion, the converter is determined to be in a negative damping state; if the first impedance ratio satisfies the Nyquist stability criterion, the converter is determined to be in a positive damping state or an underdamped state; the product of the second impedance ratio and the third impedance ratio is used as an oscillation damping coefficient, if the oscillation damping coefficient is less than zero, the converter is determined to be in a negative damping stable state, if the oscillation damping coefficient is greater than or equal to zero and less than the critical damping coefficient, the converter is determined to be in an underdamped stable state, and if the oscillation damping coefficient is greater than or equal to the critical damping coefficient, the converter is determined to be in a positive damping stable state.

[0010] Preferably, the control system of the voltage source inverter includes: a filter link, a phase-locked loop link, a grid voltage feedforward branch, a current sampling channel, a voltage sampling channel, a control delay link, a current control loop, a cross-coupling compensation link, a current feedback branch, and a modulation link;

[0011] The transfer function of the small signal model of each link in the control system includes:

[0012] The transfer function of the small signal model of the filter link and the admittance matrix of the filter inductor of the filter link, the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, the transfer function of the error of the phase-locked loop link affecting the positive PARK transformation of the current control signal, the transfer function of the phase-locked error affecting the inverse PARK transformation of the voltage control signal, the transfer function of the small signal model of the low-pass filter on the current sampling channel, the transfer function of the small signal model of the low-pass filter on the voltage sampling channel, the transfer function of the small signal model of the control delay link, the transfer function of the small signal model of the PI controller in the current control loop, the transfer function of the small signal model of the cross-coupling compensation link, the transfer function of the small signal model when the current feedback branch is not working under open-loop control, the transfer function of the small signal model of the modulation link, the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the phase-locked loop link contains only positive sequence components, and the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive sequence components and negative sequence components.

[0013] Preferably, obtaining the transfer function of the small signal model of the filter link includes:

[0014] Based on the equivalent circuit of the voltage source inverter connected to the AC power grid, the filter type is determined according to the grid connection point position of the voltage source inverter, and the transfer function of the small signal model of the determined type of filter and the admittance matrix of the filter inductor in the determined type of filter are obtained;

[0015] Based on the structure of the phase-locked loop, the transfer function of the small signal model of the phase-locked loop is established, and the transfer function of the small signal model of the phase-locked loop is corrected using the voltage sampling coefficient; based on the transfer function of the corrected small signal model of the phase-locked loop, the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, the transfer function of the error of the phase-locked loop link affecting the positive PARK transformation of the current control signal, and the transfer function of the phase-locked error affecting the reverse PARK transformation of the voltage control signal are determined respectively;

[0016] A dual orthogonal signal generator is used to separate the positive and negative sequences of the fundamental voltage and fundamental current on the signal branch of the phase-locked loop link in a stationary two-dimensional coordinate system. When the fundamental voltage on the signal branch of the phase-locked loop link contains only positive sequence components, the equivalent filter transfer function in the dq coordinate system is determined. When the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive and negative sequence components, the equivalent filter transfer function in the dq coordinate system is determined.

[0017] Preferably, the equivalent circuit of the voltage source inverter connected to the AC power grid includes a filter inductor, a filter capacitor, a transformer equivalent inductor, a transformer equivalent resistor, an equivalent inductor of the grid-connected line, and an equivalent resistor of the grid-connected line connected in series;

[0018] When the voltage source inverter is connected to the grid connection point through the filter inductor, the grid connection point is located between the filter inductor and the filter capacitor, and the voltage source inverter is connected to the L-type filter; the transfer function of the small signal model of the L-type filter and the admittance matrix of the filter inductor in the L-type filter satisfy the following relationship:

[0019]

[0020] Where Y L1 is the admittance matrix of the filter inductor in the L-type filter, G L1 is the transfer function of the L-type filter small signal model, Z Lf is the filter inductor impedance matrix, L f is the filter inductance, ω0 is the angular frequency of the synchronous rotating coordinate system, and s is the Laplace operator;

[0021] When the voltage source inverter is connected to the grid connection point through the filter inductor and the filter capacitor, the grid connection point is located between the filter capacitor and the equivalent inductance of the transformer, and the voltage source inverter is connected to the LC filter; the transfer function of the small signal model of the LC filter and the admittance matrix of the filter inductor in the LC filter satisfy the following relationship:

[0022]

[0023] Where Y L2 is the admittance matrix of the filter inductor in the LC filter, G L2 is the transfer function of the LC filter small signal model, Y Cf is the filter capacitor admittance matrix, C f is the equivalent value of the filter capacitor;

[0024] When the voltage source inverter is connected to the grid point through the filter inductor, filter capacitor and transformer, the grid point is located between the equivalent resistance of the transformer and the equivalent inductance of the grid-connected line, and the voltage source inverter is connected to the LCL filter; the transfer function of the small signal model of the LCL filter and the admittance matrix of the filter inductor in the LCL filter satisfy the following relationship:

[0025]

[0026] Where Y L3 is the admittance matrix of the filter inductor in the LCL filter, G L3 is the transfer function of the small signal model of the LCL filter, Z LRT is the transformer equivalent inductive branch impedance matrix, L T is the equivalent reactance of the transformer low voltage side, R T is the equivalent resistance of the transformer low voltage side.

[0027] Preferably, the transfer function of the phase-locked loop small signal model corrected by the voltage sampling coefficient satisfies the following relationship:

[0028]

[0029] In the formula, G PLL is the transfer function of the modified phase-locked loop small signal model, G PI-PLL is the transfer function between the voltage disturbance and the dynamic error in the small signal model of the phase-locked loop, s is the Laplace operator, is the d-axis component of the stable operating point voltage in the ideal rotating coordinate system, k vp is the voltage sampling coefficient;

[0030] Based on the transfer function of the modified small signal model of the phase-locked loop, the voltage sampling coefficient and the stable operating point voltage in the ideal rotating coordinate system are used to determine the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, which satisfies the following relationship:

[0031]

[0032] In the formula, The error in the phase-locked loop affects the transfer function of the grid voltage feedforward branch. is the stable operating point voltage in the ideal rotating coordinate system;

[0033] Based on the transfer function of the modified small signal model of the phase-locked loop, the transfer function of the positive PARK transformation of the current control signal affected by the error of the phase-locked loop link is determined by using the current sampling coefficient and the stable operating point current in the ideal rotating coordinate system, which satisfies the following relationship:

[0034]

[0035] In the formula, is the transfer function of the error in the phase-locked loop link affecting the positive PARK transformation of the current control signal, k ig is the current sampling coefficient, is the stable operating point current in the ideal rotating coordinate system;

[0036] Based on the transfer function of the modified small signal model of the phase-locked loop, the voltage sampling coefficient and the voltage given value before the inverse PARK transformation are used to determine the transfer function of the phase-locked error affecting the inverse PARK transformation of the voltage control signal, which satisfies the following relationship:

[0037]

[0038] In the formula, The transfer function of the inverse PARK transformation of the voltage control signal affected by the phase-locked error is: It is the voltage given value before the anti-PARK transformation.

[0039] Preferably, the dq-axis component of the grid-connected point voltage disturbance is used as the first input signal of the small signal model of the voltage source inverter; the current reference value change is used as the second input signal of the small signal model of the voltage source inverter, and the current reference value change is zero during power open-loop control; and the dq-axis component of the grid-connected point current disturbance is used as the output signal of the small signal model of the voltage source inverter.

[0040] Preferably, when the control system operates in an open-loop mode, the equivalent open-loop admittance matrix of the voltage source inverter satisfies the following relationship:

[0041]

[0042] Where Y eq1 is the equivalent open-loop admittance matrix of the voltage source inverter, Y L is the admittance matrix of the filter inductor of the filter link, G L is the transfer function of the small signal model of the filter link, K PWM is the transfer function of the small signal model of the modulation link, G del is the transfer function of the small signal model that controls the delay link, The transfer function of the inverse PARK transformation of the voltage control signal affected by the phase-locked error is: The error in the phase-locked loop affects the transfer function of the grid voltage feedforward branch. is the transfer function of the error in the phase-locked loop link affecting the positive PARK transformation of the current control signal, G f1 is the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the phase-locked loop contains only the positive sequence component, G f2 is the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive sequence components and negative sequence components, G cc1 is the transfer function of the small signal model of the PI controller in the current control loop, G cc2 is the transfer function of the small signal model of the cross-coupling compensation link, k vp is the voltage sampling factor, G sam is the transfer function of the small signal model when the current feedback branch is not working under open-loop control, G lpv is the transfer function of the small signal model of the low-pass filter on the voltage sampling channel.

[0043] Preferably, when the control system operates in a closed-loop mode, the equivalent admittance matrix of the current feedback branch satisfies the following relationship:

[0044] Y eq2 =[E2-GL K PWM G del (G cc2 -G cc1 ) ig G sam G lpi ] -1

[0045] Where Y eq2 is the equivalent admittance matrix of the current feedback branch, E2 is the second-order unit matrix, G L is the transfer function of the small signal model of the filter link, K PWM is the transfer function of the small signal model of the modulation link, G del is the transfer function of the small signal model for controlling the delay link, G cc1 is the transfer function of the small signal model of the PI controller in the current control loop, G cc2 is the transfer function of the small signal model of the cross-coupling compensation link, k ig is the current sampling coefficient, G sam is the transfer function of the small signal model when the current feedback branch is not working under open-loop control, G lpi is the transfer function of the small signal model of the low-pass filter on the current sampling channel.

[0046] Preferably, based on the small signal model of the voltage source inverter, the grid connection point voltage disturbance and the grid connection point current disturbance satisfy the following relationship:

[0047] Δi gdq =Y eq2 (s)Y eq1 (s)Δu pdq

[0048] In the formula, Δu pdq is the dq-axis component of the grid-connected point voltage disturbance, Δi gdq is the dq axis component of the current disturbance at the grid connection point, Y eq1 (s) is the equivalent open-loop admittance matrix of the voltage source inverter in the complex frequency domain, Y eq2 (s) is the equivalent admittance matrix of the current feedback branch in the complex frequency domain.

[0049] Preferably, the equivalent impedance matrix of the voltage source inverter using the L-type filter in the complex frequency domain satisfies the following relationship:

[0050]

[0051] In the formula, Z i-L (s) is the equivalent impedance matrix of the voltage source inverter using an L-type filter in the complex frequency domain; Z eq1(s) is the equivalent open-loop impedance matrix of the voltage source inverter, Z eq2 (s) is the equivalent impedance matrix of the current feedback branch, Z cdd (s) is the self-impedance on the d-axis in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cdq (s) is the cross impedance encountered by the q-axis current caused by the d-axis voltage in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cqd (s) is the cross impedance encountered by the d-axis current caused by the q-axis voltage in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cqq (s) is the self-impedance on the q-axis in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain.

[0052] Preferably, when the voltage source inverter is connected to the grid point via the filter inductor and the filter capacitor, the equivalent impedance Z based on the LC filter is i-LC The equivalent impedance matrix of the voltage source inverter in the complex frequency domain satisfies the following relationship:

[0053]

[0054] In the formula, Z i-LC (s) is the equivalent impedance matrix of the voltage source inverter using LC filter in the complex frequency domain, Y Cf is the filter capacitor admittance matrix;

[0055] When the voltage source inverter is connected to the grid through filter inductor, filter capacitor and transformer, the equivalent impedance Z based on the LCL filter is i-LCL The equivalent impedance matrix of the voltage source inverter in the complex frequency domain satisfies the following relationship:

[0056]

[0057] In the formula, Z i-LCL is the equivalent impedance matrix of the voltage source inverter using LCL filter in the complex frequency domain; Y Cf is the filter capacitor admittance matrix, Z LRT is the transformer equivalent inductive branch impedance matrix.

[0058] Preferably, the equivalent impedance matrix of the power grid satisfies the following relationship:

[0059]

[0060] Z gdd (s) is the self-impedance on the d-axis in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gdq(s) is the cross impedance encountered by the q-axis current caused by the d-axis voltage in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gqd (s) is the cross impedance encountered by the d-axis current caused by the q-axis voltage in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gqq (s) is the self-impedance on the q-axis in the equivalent impedance matrix of the power grid in the complex frequency domain;

[0061] The d-axis component and the q-axis component of the first impedance ratio respectively satisfy the following relationships:

[0062]

[0063] The d-axis component and the q-axis component of the second impedance ratio respectively satisfy the following relationships:

[0064]

[0065] The d-axis component and the q-axis component of the third impedance ratio respectively satisfy the following relationships:

[0066]

[0067] In the formula, R 1d , R 1q are the d-axis component and q-axis component of the first impedance ratio, R 2d , R 2q are the d-axis component and q-axis component of the second impedance ratio, R 3d , R 3q They are the d-axis component and q-axis component of the third impedance ratio respectively.

[0068] Preferably, the critical damping coefficient ξ c Satisfies the following relationship:

[0069]

[0070] In the formula, R s , C s , L s are the equivalent resistance, equivalent capacitance and equivalent inductance of the power grid respectively.

[0071] Preferably, the phase margin is calculated using the oscillation damping coefficient as a stability evaluation index for the grid-following and grid-forming converters, satisfying the following relationship:

[0072]

[0073] Where ξ is the oscillation damping coefficient and PM is the phase margin.

[0074] The present invention also proposes a stability detection system for grid-following and grid-forming type converters based on impedance modeling. The grid-following and grid-forming type converters use voltage source inverters. The control system of the voltage source inverter includes multiple links, including:

[0075] The impedance modeling module is used to obtain the transfer function of the small signal model of each link in the control system, and construct the small signal model of the voltage source inverter according to the connection relationship of each link in the control system; when the control system operates in the open-loop mode, the grid-connected point voltage disturbance is used as the input signal of the small signal model of the voltage source inverter, and the grid-connected point current disturbance is used as the output signal of the small signal model of the voltage source inverter. The transfer function of the small signal model of each link on the path from the input signal to the output signal is used to determine the equivalent open-loop admittance matrix of the voltage source inverter; when the control system operates in the closed-loop mode, the grid-connected point voltage disturbance is used as the input signal of the small signal model of the voltage source inverter, and the grid-connected point current disturbance is used as the output signal of the small signal model of the voltage source inverter. The point voltage disturbance is used as the first input signal of the small signal model of the voltage source inverter, the current reference value change is used as the second input signal of the small signal model of the voltage source inverter, and the grid-connected point current disturbance is used as the output signal of the small signal model of the voltage source inverter. The transfer function of the small signal model of each link on the path from the first input signal and the second input signal to the output signal is used to determine the equivalent admittance matrix of the current feedback branch; the product of the inverse matrix of the equivalent open-loop admittance of the voltage source inverter and the inverse matrix of the equivalent admittance matrix of the current feedback branch is used as the impedance matrix of the voltage source inverter;

[0076] The stability detection module is used to establish a first impedance ratio, a second impedance ratio and a third impedance ratio by using an equivalent impedance matrix of a power grid and an equivalent impedance matrix of a voltage source inverter; determine whether the first impedance ratio satisfies the Nyquist stability criterion, and if the first impedance ratio does not satisfy the Nyquist stability criterion, determine that the converter is in a negative damping state; if the first impedance ratio satisfies the Nyquist stability criterion, determine that the converter is in a positive damping state or an underdamped state; use the product of the second impedance ratio and the third impedance ratio as an oscillation damping coefficient, and if the oscillation damping coefficient is less than zero, determine that the converter is in a negative damping stable state, if the oscillation damping coefficient is greater than or equal to zero and less than a critical damping coefficient, determine that the converter is in an underdamped stable state, and if the oscillation damping coefficient is greater than or equal to the critical damping coefficient, determine that the converter is in a positive damping stable state.

[0077] Preferably, the control system of the voltage source inverter includes: a filter link, a phase-locked loop link, a grid voltage feedforward branch, a current sampling channel, a voltage sampling channel, a control delay link, a current control loop, a cross-coupling compensation link, a current feedback branch, and a modulation link;

[0078] The transfer function of the small signal model of each link in the control system includes:

[0079] The transfer function of the small signal model of the filter link and the admittance matrix of the filter inductor of the filter link, the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, the transfer function of the error of the phase-locked loop link affecting the positive PARK transformation of the current control signal, the transfer function of the phase-locked error affecting the inverse PARK transformation of the voltage control signal, the transfer function of the small signal model of the low-pass filter on the current sampling channel, the transfer function of the small signal model of the low-pass filter on the voltage sampling channel, the transfer function of the small signal model of the control delay link, the transfer function of the small signal model of the PI controller in the current control loop, the transfer function of the small signal model of the cross-coupling compensation link, the transfer function of the small signal model when the current feedback branch is not working under open-loop control, the transfer function of the small signal model of the modulation link, the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the phase-locked loop link contains only positive sequence components, and the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive sequence components and negative sequence components.

[0080] Preferably, obtaining the transfer function of the small signal model of the filter link includes:

[0081] Based on the equivalent circuit of the voltage source inverter connected to the AC power grid, the filter type is determined according to the grid connection point position of the voltage source inverter, and the transfer function of the small signal model of the determined type of filter and the admittance matrix of the filter inductor in the determined type of filter are obtained;

[0082] Based on the structure of the phase-locked loop, the transfer function of the small signal model of the phase-locked loop is established, and the transfer function of the small signal model of the phase-locked loop is corrected using the voltage sampling coefficient; based on the transfer function of the corrected small signal model of the phase-locked loop, the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, the transfer function of the error of the phase-locked loop link affecting the positive PARK transformation of the current control signal, and the transfer function of the phase-locked error affecting the reverse PARK transformation of the voltage control signal are determined respectively;

[0083] A dual orthogonal signal generator is used to separate the positive and negative sequences of the fundamental voltage and fundamental current on the signal branch of the phase-locked loop link in a stationary two-dimensional coordinate system. When the fundamental voltage on the signal branch of the phase-locked loop link contains only positive sequence components, the equivalent filter transfer function in the dq coordinate system is determined. When the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive and negative sequence components, the equivalent filter transfer function in the dq coordinate system is determined.

[0084] Preferably, the equivalent circuit of the voltage source inverter connected to the AC power grid includes a filter inductor, a filter capacitor, a transformer equivalent inductor, a transformer equivalent resistor, an equivalent inductor of the grid-connected line, and an equivalent resistor of the grid-connected line connected in series;

[0085] When the voltage source inverter is connected to the grid connection point through the filter inductor, the grid connection point is located between the filter inductor and the filter capacitor, and the voltage source inverter is connected to the L-type filter; the transfer function of the small signal model of the L-type filter and the admittance matrix of the filter inductor in the L-type filter satisfy the following relationship:

[0086]

[0087] Where Y L1 is the admittance matrix of the filter inductor in the L-type filter, G L1 is the transfer function of the L-type filter small signal model, Z Lf is the filter inductor impedance matrix, L f is the filter inductance, ω0 is the angular frequency of the synchronous rotating coordinate system, and s is the Laplace operator;

[0088] When the voltage source inverter is connected to the grid connection point through the filter inductor and the filter capacitor, the grid connection point is located between the filter capacitor and the equivalent inductance of the transformer, and the voltage source inverter is connected to the LC filter; the transfer function of the small signal model of the LC filter and the admittance matrix of the filter inductor in the LC filter satisfy the following relationship:

[0089]

[0090] Where Y L2 is the admittance matrix of the filter inductor in the LC filter, G L2 is the transfer function of the LC filter small signal model, Y Cf is the filter capacitor admittance matrix, C f is the equivalent value of the filter capacitor;

[0091] When the voltage source inverter is connected to the grid point through the filter inductor, filter capacitor and transformer, the grid point is located between the equivalent resistance of the transformer and the equivalent inductance of the grid-connected line, and the voltage source inverter is connected to the LCL filter; the transfer function of the small signal model of the LCL filter and the admittance matrix of the filter inductor in the LCL filter satisfy the following relationship:

[0092]

[0093] Where Y L3 is the admittance matrix of the filter inductor in the LCL filter, G L3 is the transfer function of the small signal model of the LCL filter, Z LRT is the transformer equivalent inductive branch impedance matrix, L T is the equivalent reactance of the transformer low voltage side, R T is the equivalent resistance of the transformer low voltage side.

[0094] Preferably, the transfer function of the phase-locked loop small signal model corrected by the voltage sampling coefficient satisfies the following relationship:

[0095]

[0096] In the formula, G PLL is the transfer function of the modified phase-locked loop small signal model, G PI-PLL is the transfer function between the voltage disturbance and the dynamic error in the small signal model of the phase-locked loop, s is the Laplace operator, is the d-axis component of the stable operating point voltage in the ideal rotating coordinate system, k vp is the voltage sampling coefficient;

[0097] Based on the transfer function of the modified small signal model of the phase-locked loop, the voltage sampling coefficient and the stable operating point voltage in the ideal rotating coordinate system are used to determine the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, which satisfies the following relationship:

[0098]

[0099] In the formula, The error in the phase-locked loop affects the transfer function of the grid voltage feedforward branch. is the stable operating point voltage in the ideal rotating coordinate system;

[0100] Based on the transfer function of the modified small signal model of the phase-locked loop, the transfer function of the positive PARK transformation of the current control signal affected by the error of the phase-locked loop link is determined by using the current sampling coefficient and the stable operating point current in the ideal rotating coordinate system, which satisfies the following relationship:

[0101]

[0102] In the formula, is the transfer function of the error in the phase-locked loop link affecting the positive PARK transformation of the current control signal, k ig is the current sampling coefficient, is the stable operating point current in the ideal rotating coordinate system;

[0103] Based on the transfer function of the modified small signal model of the phase-locked loop, the voltage sampling coefficient and the voltage given value before the inverse PARK transformation are used to determine the transfer function of the phase-locked error affecting the inverse PARK transformation of the voltage control signal, which satisfies the following relationship:

[0104]

[0105] In the formula, The transfer function of the inverse PARK transformation of the voltage control signal affected by the phase-locked error is: It is the voltage given value before the anti-PARK transformation.

[0106] Preferably, the dq-axis component of the grid-connected point voltage disturbance is used as the first input signal of the small signal model of the voltage source inverter; the current reference value change is used as the second input signal of the small signal model of the voltage source inverter, and the current reference value change is zero during power open-loop control; and the dq-axis component of the grid-connected point current disturbance is used as the output signal of the small signal model of the voltage source inverter.

[0107] Preferably, when the control system operates in an open-loop mode, the equivalent open-loop admittance matrix of the voltage source inverter satisfies the following relationship:

[0108]

[0109] Where Y eq1 is the equivalent open-loop admittance matrix of the voltage source inverter, Y L is the admittance matrix of the filter inductor of the filter link, G L is the transfer function of the small signal model of the filter link, K PWM is the transfer function of the small signal model of the modulation link, G del is the transfer function of the small signal model that controls the delay link, The transfer function of the inverse PARK transformation of the voltage control signal affected by the phase-locked error is: The error in the phase-locked loop affects the transfer function of the grid voltage feedforward branch. is the transfer function of the error in the phase-locked loop link affecting the positive PARK transformation of the current control signal, G f1 is the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the phase-locked loop contains only the positive sequence component, G f2 is the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive sequence components and negative sequence components, G cc1 is the transfer function of the small signal model of the PI controller in the current control loop, G cc2 is the transfer function of the small signal model of the cross-coupling compensation link, k vp is the voltage sampling factor, G sam is the transfer function of the small signal model when the current feedback branch is not working under open-loop control, G lpv is the transfer function of the small signal model of the low-pass filter on the voltage sampling channel.

[0110] Preferably, when the control system operates in a closed-loop mode, the equivalent admittance matrix of the current feedback branch satisfies the following relationship:

[0111] Y eq2 =[E2-GL K PWM G del (G cc2 -G cc1 ) ig G sam G lpi ] -1

[0112] Where Y eq2 is the equivalent admittance matrix of the current feedback branch, E2 is the second-order unit matrix, G L is the transfer function of the small signal model of the filter link, K PWM is the transfer function of the small signal model of the modulation link, G del is the transfer function of the small signal model for controlling the delay link, G cc1 is the transfer function of the small signal model of the PI controller in the current control loop, G cc2 is the transfer function of the small signal model of the cross-coupling compensation link, k ig is the current sampling coefficient, G sam is the transfer function of the small signal model when the current feedback branch is not working under open-loop control, G lpi is the transfer function of the small signal model of the low-pass filter on the current sampling channel.

[0113] Preferably, based on the small signal model of the voltage source inverter, the grid connection point voltage disturbance and the grid connection point current disturbance satisfy the following relationship:

[0114] Δi gdq =Y eq2 (s)Y eq1 (s)Δu pdq

[0115] In the formula, Δu pdq is the dq-axis component of the grid-connected point voltage disturbance, Δi gdq is the dq axis component of the current disturbance at the grid connection point, Y eq1 (s) is the equivalent open-loop admittance matrix of the voltage source inverter in the complex frequency domain, Y eq2 (s) is the equivalent admittance matrix of the current feedback branch in the complex frequency domain.

[0116] Preferably, the equivalent impedance matrix of the voltage source inverter using the L-type filter in the complex frequency domain satisfies the following relationship:

[0117]

[0118] In the formula, Z i-L (s) is the equivalent impedance matrix of the voltage source inverter using an L-type filter in the complex frequency domain; Z eq1(s) is the equivalent open-loop impedance matrix of the voltage source inverter, Z eq2 (s) is the equivalent impedance matrix of the current feedback branch, Z cdd (s) is the self-impedance on the d-axis in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cdq (s) is the cross impedance encountered by the q-axis current caused by the d-axis voltage in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cqd (s) is the cross impedance encountered by the d-axis current caused by the q-axis voltage in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cqq (s) is the self-impedance on the q-axis in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain.

[0119] Preferably, when the voltage source inverter is connected to the grid point via the filter inductor and the filter capacitor, the equivalent impedance Z based on the LC filter is i-LC The equivalent impedance matrix of the voltage source inverter in the complex frequency domain satisfies the following relationship:

[0120]

[0121] In the formula, Z i-LC (s) is the equivalent impedance matrix of the voltage source inverter using LC filter in the complex frequency domain, Y Cf is the filter capacitor admittance matrix;

[0122] When the voltage source inverter is connected to the grid through filter inductor, filter capacitor and transformer, the equivalent impedance Z based on the LCL filter is i-LCL The equivalent impedance matrix of the voltage source inverter in the complex frequency domain satisfies the following relationship:

[0123]

[0124] In the formula, Z i-LCL is the equivalent impedance matrix of the voltage source inverter using LCL filter in the complex frequency domain; Y Cf is the filter capacitor admittance matrix, Z LRT is the transformer equivalent inductive branch impedance matrix.

[0125] Preferably, the equivalent impedance matrix of the power grid satisfies the following relationship:

[0126]

[0127] Z gdd (s) is the self-impedance on the d-axis in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gdq(s) is the cross impedance encountered by the q-axis current caused by the d-axis voltage in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gqd (s) is the cross impedance encountered by the d-axis current caused by the q-axis voltage in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gqq (s) is the self-impedance on the q-axis in the equivalent impedance matrix of the power grid in the complex frequency domain;

[0128] The d-axis component and the q-axis component of the first impedance ratio respectively satisfy the following relationships:

[0129]

[0130] The d-axis component and the q-axis component of the second impedance ratio respectively satisfy the following relationships:

[0131]

[0132] The d-axis component and the q-axis component of the third impedance ratio respectively satisfy the following relationships:

[0133]

[0134] In the formula, R 1d , R 1q are the d-axis component and q-axis component of the first impedance ratio, R 2d , R 2q are the d-axis component and q-axis component of the second impedance ratio, R 3d , R 3q They are the d-axis component and q-axis component of the third impedance ratio respectively.

[0135] Preferably, the critical damping coefficient ξ c Satisfies the following relationship:

[0136]

[0137] In the formula, R s , C s , L s are the equivalent resistance, equivalent capacitance and equivalent inductance of the power grid respectively.

[0138] Preferably, the phase margin is calculated using the oscillation damping coefficient as a stability evaluation index for the grid-following and grid-forming converters, satisfying the following relationship:

[0139]

[0140] Where ξ is the oscillation damping coefficient and PM is the phase margin.

[0141] A terminal comprises a processor and a storage medium; the storage medium is used to store instructions; the processor is used to operate according to the instructions to execute the steps of the method.

[0142] A computer-readable storage medium stores a computer program, which implements the steps of the method when executed by a processor.

[0143] The beneficial effects of the present invention are that, compared with the prior art, at least the present invention can comprehensively analyze the interaction between grid-following and grid-forming converters and their influence on system stability through the joint impedance modeling method, and is applicable to multi-converter operation modes and complex systems, with a wider range of applications. In addition, the present invention significantly reduces the computational complexity in the analysis process by introducing efficient calculation algorithms and numerical methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0144] Figure 1 Schematic diagram of the main circuit and control link of the voltage source inverter in the embodiment of the present invention;

[0145] Figure 2 It is a flow chart of the stability detection method of the grid-following type and grid-building type converter based on impedance modeling proposed by the present invention;

[0146] Figure 3 is the grid-connected equivalent circuit of the inverter in the embodiment of the present invention;

[0147] Figure 4 is a block diagram of a small signal model of a filtering link in an embodiment of the present invention;

[0148] Figure 5 A schematic diagram of the dynamic error between the ideal rotating coordinate system and the rotating coordinate system used by the control system in an embodiment of the present invention;

[0149] Figure 6 is a block diagram of a small signal model of a voltage source inverter in an embodiment of the present invention;

[0150] Figure 7 is a schematic diagram of a small signal model based on an admittance model in an embodiment of the present invention;

[0151] Figure 8 This is a schematic diagram of initial stability judgment in an embodiment of the present invention;

[0152] Fig. 9 It is a stable detection flow chart combining impedance ratio and damping characteristics in an embodiment of the present invention. DETAILED DESCRIPTION

[0153] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The embodiments described in this application are only embodiments of a part of the present invention, rather than all embodiments. Based on the spirit of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the protection scope of the present invention.

[0154] In the embodiment, the main circuit and control system of the voltage source type voltage source type inverter are as follows Figure 1 As shown, the inverter side and the load side are equivalent to the form of a voltage source with a load, and the control modes of the voltage source type voltage source inverter include: current control type and voltage control type, among which the control system of the voltage control type voltage source inverter includes droop control and virtual synchronization control.

[0155] Figure 1 In, V dc is the DC voltage of the voltage source inverter, v αβ is the voltage in the α and β coordinate systems, i abc is the current sampling value, u abc is the voltage sampling value, u n is the voltage after positive and negative sequence separation, u p is the grid voltage, u pd 、u pq are the d and q axis voltages at the grid connection point, respectively, Ld 、i Lq are the transformed d-axis and q-axis currents, respectively, and u cq is the voltage after transformation, K p-PLL is the proportional coefficient of the phase-locked loop controller, K i-pll is the integral coefficient of the phase-locked loop controller, ω0 is the angular frequency of the synchronous rotating coordinate system, ω is the angular frequency, P ref , Q ref are active power given value and reactive power given value respectively, i dref 、i qref are the given values ​​of current d and q components respectively, K Pcc is the current loop controller proportional coefficient, K Icc is the integral coefficient of the current loop controller, L f is the filter inductance, θ is the phase angle; L g and R g are the equivalent inductance and equivalent resistance of the grid-connected line, u g is the equivalent voltage of the AC grid.

[0156] SCF-PLL stands for Phase-Locked Loop Block Diagram.

[0157] The present invention proposes a stability detection method for grid-following and grid-forming converters based on impedance modeling. The grid-following and grid-forming converters use voltage source inverters. The control links of the voltage source inverter include but are not limited to: filter link, current sampling channel, voltage sampling channel, control delay link, current control loop, cross-coupling compensation link, current feedback branch, phase-locked loop link, grid voltage feedforward branch, and modulation link. The filter link, phase-locked loop link, and grid voltage feedforward branch are relatively important in the process of impedance modeling and have a great influence. Therefore, in the embodiment, it is necessary to perform impedance modeling on stability according to the impedance models of these three links and perform stability analysis.

[0158] like Figure 2 As shown, the method includes:

[0159] Step 1: Obtain the transfer function of the small signal model of each link in the control system, and construct the small signal model of the voltage source inverter according to the connection relationship of each link in the control system.

[0160] The transfer functions of the small signal models of each link in the control system include: the transfer function G of the small signal model of the filter link L , the admittance matrix Y of the filter inductor of the filter link L , the error of the phase-locked loop affects the transfer function of the grid voltage feedforward branch The error in the phase-locked loop affects the transfer function of the positive PARK transformation of the current control signal Phase-locked error affects the transfer function of the inverse PARK transformation of the voltage control signal The transfer function G of the small signal model of the low-pass filter on the current sampling channel lpi , the transfer function G of the small signal model of the low-pass filter on the voltage sampling channel lpv , the transfer function G of the small signal model of the control delay link del , the transfer function G of the small signal model of the PI controller in the current control loop cc1 , the transfer function G of the small signal model of the cross-coupling compensation link cc2 , the transfer function G of the small signal model when the current feedback branch is not working under open-loop control sam , the transfer function K of the small signal model of the modulation link PWM , the equivalent filter transfer function G in the dq coordinate system when the fundamental voltage on the signal branch of the phase-locked loop contains only the positive sequence component f1 , the equivalent filter transfer function G in the dq coordinate system when the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive sequence components and negative sequence components f2 ;

[0161] Specifically, step 1 includes:

[0162] Step 1.1, based on the equivalent circuit of the voltage source inverter connected to the AC power grid, determine the type of filter according to the grid connection point position of the voltage source inverter; obtain the transfer function of the small signal model of the determined type of filter and the admittance matrix of the filter inductor in the determined type of filter.

[0163] like Figure 3 As shown in the figure, the equivalent circuit of the voltage source inverter connected to the AC grid includes a filter inductor L connected in series. f 、Filter capacitor C f , Transformer equivalent inductance L T , Transformer equivalent resistance R T , the equivalent inductance L of the grid-connected line g , the equivalent resistance R of the grid-connected line g Based on the equivalent circuit, different locations of the selected point of common coupling (PCC) will result in the voltage source inverter being connected to different types of filter links, including:

[0164] When the voltage source inverter is connected to the grid point through the filter inductor, the grid point is located at P1 between the filter inductor and the filter capacitor. The voltage source inverter is connected to an L-type filter, including the filter inductor L f , the equivalent impedance of the L-type filter is Z i-L ;

[0165] The transfer function of the small signal model of the L-type filter and the admittance matrix of the filter inductor in the L-type filter satisfy the following relationship:

[0166]

[0167] Where Y L1 is the admittance matrix of the filter inductor in the L-type filter, G L1 is the transfer function of the L-type filter small signal model, Z Lf is the filter inductor impedance matrix, L f is the filter inductor, ω0 is the angular frequency of the synchronous rotating coordinate system, and s is the Laplace operator.

[0168] When the voltage source inverter is connected to the grid point through the filter inductor and filter capacitor, the grid point is located at P2 between the filter capacitor and the transformer equivalent inductance. The voltage source inverter is connected to the LC filter, including the filter inductor L f And filter capacitor C f , the equivalent impedance of the LC filter is Z i-LC ;

[0169] The transfer function of the small signal model of the LC filter and the admittance matrix of the filter inductor in the LC filter satisfy the following relationship:

[0170]

[0171] Where Y L2 is the admittance matrix of the filter inductor in the LC filter, G L2 is the transfer function of the LC filter small signal model, Y Cf is the filter capacitor admittance matrix, C f is the equivalent value of the filter capacitor.

[0172] In the embodiment, the equivalent capacitance value of the filter capacitor is obtained after the star angle of the star-connected filter capacitor is transformed.

[0173] When the voltage source inverter is connected to the grid point through the filter inductor, filter capacitor and transformer, the grid point is located at P3 between the equivalent resistance of the transformer and the equivalent inductance of the grid line. The voltage source inverter is connected to the LCL filter, including the filter inductor L f 、Filter capacitor C f , Transformer equivalent inductance L T And the transformer equivalent resistance R T , the equivalent impedance of the LCL filter is Z i-LCL .

[0174] The transfer function of the small signal model of the LCL filter and the admittance matrix of the filter inductor in the LCL filter satisfy the following relationship:

[0175]

[0176] Where Y L3 is the admittance matrix of the filter inductor in the LCL filter, G L3 is the transfer function of the small signal model of the LCL filter, Z LRT is the transformer equivalent inductive branch impedance matrix, L T is the equivalent reactance of the transformer low voltage side, R T is the equivalent resistance of the transformer low voltage side.

[0177] Regardless of the type of filter, its small signal model is as follows Figure 4 As shown in the dq coordinate system, the dq-axis component Δu of the bridge arm voltage disturbance of the voltage source inverter is bdq The transfer function G of the small signal model after the filter L The value obtained after the grid connection point voltage disturbance dq axis component Δu pdq The admittance matrix Y of the filter inductor in the filter L The sum of the values ​​obtained after the grid connection is taken as the dq axis component Δi of the current disturbance at the grid connection point gdq .

[0178] Step 1.2, based on the structure of the phase-locked loop, establish the transfer function of the small signal model of the phase-locked loop, and use the voltage sampling coefficient to correct the transfer function of the small signal model of the phase-locked loop; based on the transfer function of the corrected small signal model of the phase-locked loop, determine the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, the transfer function of the error of the phase-locked loop link affecting the positive PARK transformation of the current control signal, and the transfer function of the phase-locked error affecting the reverse PARK transformation of the voltage control signal;

[0179] The phase-locked loop is used to detect the voltage and current phase of the grid-connected point to realize the control of the inverter grid-connected power. Since the static frequency offset compensation has no effect on small signal modeling, the small signal equivalent model of SRF-PLL (single synchronous phase-locked loop) in the synchronous rotating coordinate system is as follows: Figure 5 When the grid-connected voltage has rich harmonic components, considering that the internal phase-locked loop is a dynamic adjustment process based on the PI controller, there is a dynamic error Δθ.

[0180] Figure 5 The voltage disturbance dq axis component Δv dq , the manager wants to rotate the coordinate system dq s With the rotating coordinate system dq c The small signal voltage obtained after conversion satisfies the following relationship:

[0181]

[0182] In the formula, is the rotating coordinate system dq c The voltage disturbance at the input of the lower phase-locked loop, is the ideal rotating coordinate system dq s The small signal disturbance at the output of the lower phase-locked loop, Δθ is the dynamic error between the ideal rotating coordinate system and the rotating coordinate system, is the ideal rotating coordinate system dq s The lower stable operating point voltage.

[0183] The ideal rotating coordinate system is strictly synchronized with the grid voltage, so it always contains a certain dynamic error with the rotating coordinate system used by the control system. Considering that the error between the large signal quantities of the two rotating coordinate systems can be ignored, the dynamic error between the ideal rotating coordinate system and the rotating coordinate system satisfies the following relationship:

[0184]

[0185] In the formula, G PI-PLL It is the transfer function between the voltage disturbance and the dynamic error in the small signal model of the phase-locked loop.

[0186] Due to the error of the phase-locked loop, the voltage disturbance in the actual system is not equal to the disturbance of the voltage control signal in the control link. The small error signal of the phase-locked loop and the voltage disturbance satisfy the following relationship:

[0187]

[0188] In the phase-locked loop, the existence of the voltage sampling coefficient and the current sampling coefficient is equivalent to introducing a virtual stable operating point whose value is different from the actual system in the control system. First, the transfer function of the small signal model of the phase-locked loop is corrected using the voltage sampling coefficient to satisfy the following relationship:

[0189]

[0190] In the formula, G PLL is the transfer function of the modified phase-locked loop small signal model, G PI-PLL is the transfer function between the voltage disturbance and the dynamic error in the small signal model of the phase-locked loop, s is the Laplace operator, is the d-axis component of the stable operating point voltage in the ideal rotating coordinate system, k vp is the voltage sampling factor.

[0191] Based on the transfer function of the modified small signal model of the phase-locked loop, the voltage sampling coefficient and the stable operating point voltage in the ideal rotating coordinate system are used to determine the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, which satisfies the following relationship:

[0192]

[0193] In the formula, The error in the phase-locked loop affects the transfer function of the grid voltage feedforward branch. is the stable operating point voltage in the ideal rotating coordinate system.

[0194] Based on the transfer function of the modified small signal model of the phase-locked loop, the transfer function of the positive PARK transformation of the current control signal affected by the error of the phase-locked loop link is determined by using the current sampling coefficient and the stable operating point current in the ideal rotating coordinate system, which satisfies the following relationship:

[0195]

[0196] In the formula, is the transfer function of the error in the phase-locked loop link affecting the positive PARK transformation of the current control signal, k ig is the current sampling coefficient, is the stable operating point current in the ideal rotating coordinate system.

[0197] Based on the transfer function of the modified small signal model of the phase-locked loop, the voltage sampling coefficient and the voltage given value before the inverse PARK transformation are used to determine the transfer function of the phase-locked error affecting the inverse PARK transformation of the voltage control signal, which satisfies the following relationship:

[0198]

[0199] In the formula, The transfer function of the inverse PARK transformation of the voltage control signal affected by the phase-locked error is: It is the voltage given value before the anti-PARK transformation.

[0200] Step 1.3, using a dual orthogonal signal generator, separate the positive and negative sequences of the fundamental voltage and fundamental current on the signal branch of the phase-locked loop in a stationary two-dimensional coordinate system, and determine the equivalent filter transfer function G in the dq coordinate system when the fundamental voltage on the signal branch of the phase-locked loop contains only positive sequence components. f1 , when the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive sequence components and negative sequence components, determine the equivalent filter transfer function G in the dq coordinate system f2 .

[0201] A dual second-order generalized integrator (DSOGI) is a dual second-order generalized integrator that can separate positive and negative sequences.

[0202] In a non-restrictive preferred embodiment, considering that the three-phase system has a DC static operating point in the synchronous rotating coordinate system after coordinate transformation, the essence of the impedance / admittance model of the three-phase voltage source inverter is a small signal linearization model at a stable operating point. In order to ensure the safety of the switching device in actual operation, the current signal fed back to the current controller is the inverter side filter inductor current; at the same time, the reference signal of the current controller is calculated and generated according to the active and reactive power in the dispatch instruction, and the phase difference between the grid current and the filter inductor current can be adjusted by static bias compensation. In order to suppress the influence of the three-phase unbalanced component of the grid voltage on the grid current in the actual system, the signals used for the phase-locked loop link and the grid voltage feedforward branch are all filtered. Therefore, the positive and negative sequence separation of the signal is realized in a static two-dimensional coordinate system based on DSOGI, and the following relationship is satisfied:

[0203]

[0204] Where D(s) is the positive sequence component of the signal, and Q(s) is the negative sequence component of the signal.

[0205] Step 1.4, according to the connection relationship of each link in the control system, we can get Figure 6Small signal model of the voltage source inverter shown.

[0206] Step 2: When the control system operates in an open-loop mode, the grid-connected point voltage disturbance is used as the input signal of the small signal model of the voltage source inverter, and the grid-connected point current disturbance is used as the output signal of the small signal model of the voltage source inverter. The transfer function of the small signal model of each link on the path from the input signal to the output signal is used to determine the equivalent open-loop admittance matrix of the voltage source inverter; when the control system operates in a closed-loop mode, the grid-connected point voltage disturbance is used as the first input signal of the small signal model of the voltage source inverter, and the current reference value change is used as the small signal model of the voltage source inverter. The second input signal of the signal model takes the grid-connected point current disturbance as the output signal of the small signal model of the voltage source inverter, and uses the transfer function of the small signal model of each link on the path from the first input signal and the second input signal to the output signal to determine the equivalent admittance matrix of the current feedback branch, wherein the equivalent admittance matrix of the current feedback branch is connected in series with the equivalent open-loop admittance matrix of the voltage source inverter; and the product of the inverse matrix of the equivalent open-loop admittance of the voltage source inverter and the inverse matrix of the equivalent admittance matrix of the current feedback branch is used as the impedance matrix model of the voltage source inverter.

[0207] The transfer function and connection relationship of the small signal model of each link in the inverter are as follows: Figure 6 shown.

[0208] Δu pdq is the dq-axis component of the grid-connected point voltage disturbance, and is the first input signal of the small signal model of the voltage source inverter; Δi ref is the current reference value variation, which is the second input signal of the small signal model of the voltage source inverter. The current reference value variation is zero during power open-loop control. gdq It is the dq-axis component of the grid-connected point current disturbance and is the output signal of the small signal model of the voltage source inverter.

[0209] When the control system operates in open-loop mode, the role of the current feedback branch is not considered. The grid-connected voltage disturbance is used as the input signal of the small signal model of the voltage source inverter, and the grid-connected current disturbance is used as the output signal of the small signal model of the voltage source inverter. The transfer function of the small signal model of each link on the path from the input signal to the output signal is used to determine the equivalent open-loop admittance matrix of the voltage source inverter, which satisfies the following relationship:

[0210]

[0211] Where Y eq1 is the equivalent open-loop admittance matrix of the voltage source inverter, Y L is the admittance matrix of the filter inductor of the filter link, GL is the transfer function of the small signal model of the filter link, K PWM is the transfer function of the small signal model of the modulation link, G del is the transfer function of the small signal model that controls the delay link, The transfer function of the inverse PARK transformation of the voltage control signal affected by the phase-locked error is: The error in the phase-locked loop affects the transfer function of the grid voltage feedforward branch. is the transfer function of the error in the phase-locked loop link affecting the positive PARK transformation of the current control signal, G f1 is the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the phase-locked loop contains only the positive sequence component, G f2 is the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive sequence components and negative sequence components, G cc1 is the transfer function of the small signal model of the PI controller in the current control loop, G cc2 is the transfer function of the small signal model of the cross-coupling compensation link, k vp is the voltage sampling factor, G sam is the transfer function of the small signal model when the current feedback branch is not working under open-loop control, G lpv is the transfer function of the small signal model of the low-pass filter on the voltage sampling channel.

[0212] The control system operates in a closed-loop mode, taking into account the role of the current feedback branch, the grid-connected point voltage disturbance is used as the first input signal of the small signal model of the voltage source inverter, the current reference value change is used as the second input signal of the small signal model of the voltage source inverter, and the grid-connected point current disturbance is used as the output signal of the small signal model of the voltage source inverter. The transfer function of the small signal model of each link on the path from the first input signal and the second input signal to the output signal is used to determine the equivalent admittance matrix of the current feedback branch, which satisfies the following relationship:

[0213] Y eq2 =[E2-G L K PWM G del (G cc2 -G cc1 ) ig G sam G lpi ] -1

[0214] Where Y eq2 is the equivalent admittance matrix of the current feedback branch, E2 is the second-order unit matrix, G L is the transfer function of the small signal model of the filter link, KPWM is the transfer function of the small signal model of the modulation link, G del is the transfer function of the small signal model for controlling the delay link, G cc1 is the transfer function of the small signal model of the PI controller in the current control loop, G cc2 is the transfer function of the small signal model of the cross-coupling compensation link, k ig is the current sampling coefficient, G sam is the transfer function of the small signal model when the current feedback branch is not working under open-loop control, G lpi is the transfer function of the small signal model of the low-pass filter on the current sampling channel.

[0215] like Figure 7 As shown, the equivalent admittance matrix of the current feedback branch is connected in series with the equivalent open-loop admittance matrix of the voltage source inverter.

[0216] Based on the small signal model of the voltage source inverter, the voltage disturbance at the grid connection point and the current disturbance at the grid connection point satisfy the following relationship:

[0217] Δi gdq =Y eq2 (s)Y eq1 (s)Δu pdq

[0218] In the formula, Δu pdq is the dq-axis component of the grid-connected point voltage disturbance, Δi gdq is the dq axis component of the current disturbance at the grid connection point, Y eq1 (s) is the equivalent open-loop admittance matrix of the voltage source inverter in the complex frequency domain, Y eq2 (s) is the equivalent admittance matrix of the current feedback branch in the complex frequency domain.

[0219] Based on the above formula, after matrix inversion, the equivalent impedance matrix of the voltage source inverter using an L-type filter in the complex frequency domain is obtained, which satisfies the following relationship:

[0220]

[0221] In the formula, Z i-L (s) is the equivalent impedance matrix of the voltage source inverter using an L-type filter in the complex frequency domain; Z eq1 (s) is the equivalent open-loop impedance matrix of the voltage source inverter, Z eq2 (s) is the equivalent impedance matrix of the current feedback branch, Z cdd (s) is the self-impedance on the d-axis in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cdq(s) is the cross impedance encountered by the q-axis current caused by the d-axis voltage in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cqd (s) is the cross impedance encountered by the d-axis current caused by the q-axis voltage in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cqq (s) is the self-impedance on the q-axis in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain.

[0222] When the voltage source inverter is connected to the grid through the filter inductor and filter capacitor, the equivalent impedance Z based on the LC filter is i-LC The equivalent impedance matrix of the voltage source inverter in the complex frequency domain satisfies the following relationship:

[0223]

[0224] In the formula, Z i-LC (s) is the equivalent impedance matrix of the voltage source inverter using LC filter in the complex frequency domain, Y Cf is the filter capacitor admittance matrix;

[0225] When the voltage source inverter is connected to the grid through filter inductor, filter capacitor and transformer, the equivalent impedance Z based on the LCL filter is i-LCL The equivalent impedance matrix of the voltage source inverter in the complex frequency domain satisfies the following relationship:

[0226]

[0227] In the formula, Z i-LCL is the equivalent impedance matrix of the voltage source inverter using LCL filter in the complex frequency domain; Y Cf is the filter capacitor admittance matrix, Z LRT is the transformer equivalent inductive branch impedance matrix.

[0228] Step 3, using the equivalent impedance matrix of the power grid and the equivalent impedance matrix of the voltage source inverter, establish a first impedance ratio, a second impedance ratio and a third impedance ratio; determine whether the first impedance ratio satisfies the Nyquist stability criterion, if the first impedance ratio does not satisfy the Nyquist stability criterion, determine that the converter is in a negative damping state; if the first impedance ratio satisfies the Nyquist stability criterion, determine that the converter is in a positive damping state or an underdamped state; use the product of the second impedance ratio and the third impedance ratio as the oscillation damping coefficient, if the oscillation damping coefficient is less than zero, determine that the converter is in a negative damping stable state, if the oscillation damping coefficient is greater than or equal to zero and less than the critical damping coefficient, determine that the converter is in an underdamped stable state, if the oscillation damping coefficient is greater than or equal to the critical damping coefficient, determine that the converter is in a positive damping stable state.

[0229] Specifically, the equivalent impedance matrix of the power grid is obtained to satisfy the following relationship:

[0230]

[0231] Z gdd (s) is the self-impedance on the d-axis in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gdq (s) is the cross impedance encountered by the q-axis current caused by the d-axis voltage in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gqd (s) is the cross impedance encountered by the d-axis current caused by the q-axis voltage in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gqq (s) is the self-impedance on the q-axis in the equivalent impedance matrix of the power grid in the complex frequency domain.

[0232] The d-axis component of the first impedance ratio R 1d and the q-axis component R 1q , respectively satisfying the following relations:

[0233]

[0234] The d-axis component of the second impedance ratio R 2d and the q-axis component R 2q , respectively satisfying the following relations:

[0235]

[0236] The d-axis component of the third impedance ratio R 3d and the q-axis component R 3q , respectively satisfying the following relations:

[0237]

[0238] The first impedance ratio R 1d , R 1q Characterize an equivalent open-loop transfer function. The necessary condition for system stability is that the amplitude-phase-frequency characteristic curves of the first impedance ratio on the two channels dq simultaneously meet the Nyquist stability criterion. 2d , R 2q Characterizes the relationship between the harmonic voltage on the grid side and the inverter side and the harmonic current on the grid. Under the combined effect of the inverter impedance and the grid impedance, the amplitude of the second impedance ratio is the harmonic voltage amplification factor. 3d , R 3q Characterizing the harmonic current coupling relationship between the dq channels, the amplitude of the third impedance ratio is the harmonic current amplification factor on the coupled channel. Therefore, the harmonic current amplification factor of the coupled channel depends on both the main diagonal terms and the sub-diagonal terms in the impedance matrix.

[0239] In the embodiment, taking the q channel as an example, the self-impedance Z on the q axis in the equivalent impedance matrix of the power grid in the complex frequency domain at the cutoff frequency isgqq (s) and the self-impedance Z on the q-axis in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain cqq (s) have equal amplitudes, and the vector relationship is as follows Figure 8 As shown, when the cutoff frequency is Z gqq When (s) is in the "stable region", it exhibits positive resistance and inductance. At this time, the self-impedance on the q-axis in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain exhibits negative resistance and capacitance, such as Figure 8 Z cqq1 , the self-impedance on the q-axis in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain shows positive resistance and capacitance, such as Figure 8 Z cqq2 However, if Figure 8 Z cqq2 As shown, even if the vector is in the "stable zone" in this case and the first impedance ratio satisfies the Nyquist stability criterion, the harmonic resonance instability may occur under non-unit power factor conditions due to the amplification effect of the second and third impedance ratios on the harmonics. Based on the above analysis of the physical meaning of the small signal equivalent circuit and the impedance ratio, the first impedance ratio satisfying the Nyquist stability criterion is a necessary but insufficient condition for system stability and can only be used for a quick initial judgment of stability. In the harmonic stability analysis, the influence of the harmonic amplification represented by the second and third impedance ratios on stability must also be considered. Therefore, Fig. 9 As shown, stability testing includes:

[0240] Determine whether the first impedance ratio satisfies the Nyquist stability criterion. If the first impedance ratio does not satisfy the Nyquist stability criterion, determine that the converter is in a negative damping state; if the first impedance ratio satisfies the Nyquist stability criterion, determine that the converter is in a positive damping state or an underdamped state; use the product of the second impedance ratio and the third impedance ratio as the oscillation damping coefficient, if the oscillation damping coefficient is less than zero, determine that the converter is in a negative damping stable state, if the oscillation damping coefficient is greater than or equal to zero and less than the critical damping coefficient, determine that the converter is in an underdamped stable state, and if the oscillation damping coefficient is greater than or equal to the critical damping coefficient, determine that the converter is in a positive damping stable state.

[0241] Critical damping coefficient ξ c Satisfies the following relationship:

[0242]

[0243] In the formula, R s , C s , L s are the equivalent resistance, equivalent capacitance and equivalent inductance of the power grid respectively.

[0244] The phase margin is calculated using the oscillation damping coefficient as a stability evaluation index for grid-following and grid-forming converters, satisfying the following relationship:

[0245]

[0246] Where ξ is the oscillation damping coefficient and PM is the phase margin.

[0247] By establishing a detailed impedance model, the behavior of grid-following and grid-forming converters in complex multi-converter systems can be accurately described, thereby improving the accuracy of system stability analysis. Using impedance modeling methods to perform stability analysis in the frequency domain can fully consider the response characteristics of the system at different frequencies, providing an important basis for design and optimization. Through the impedance modeling method, the stability of the system under dynamically changing conditions can be analyzed in real time and accurately, providing reliable stability guarantees for system operation. Through the impedance modeling stability analysis method of the present invention, the stability of grid-following and grid-forming converters in practical applications can be significantly improved, promoting the safe and efficient operation of power electronic systems, and providing strong technical support for the fields of smart grids, renewable energy generation, and electric vehicles.

[0248] Existing converters can use an impedance modeling method, which measures the input and output voltage and current of the converter and establishes the converter's impedance model based on the relationship between the voltage and current. Then, by analyzing the converter's impedance model, the converter's stability and performance can be obtained.

[0249] The present invention introduces a stability detection method for grid-following and grid-forming converters based on impedance modeling, overcomes the shortcomings of the prior art in terms of model description, scope of application and computational complexity, and provides an efficient, accurate and practical stability analysis tool. This method not only improves the stability and robustness of the system, but is also suitable for real-time monitoring and online analysis, and has significant technical advantages and wide application value.

[0250] The present invention also proposes a stability detection system for grid-following and grid-forming type converters based on impedance modeling. The grid-following and grid-forming type converters use voltage source inverters. The control system of the voltage source inverter includes multiple links, including:

[0251] The impedance modeling module is used to obtain the transfer function of the small signal model of each link in the control system, and construct the small signal model of the voltage source inverter according to the connection relationship of each link in the control system; when the control system operates in the open-loop mode, the grid-connected point voltage disturbance is used as the input signal of the small signal model of the voltage source inverter, and the grid-connected point current disturbance is used as the output signal of the small signal model of the voltage source inverter. The transfer function of the small signal model of each link on the path from the input signal to the output signal is used to determine the equivalent open-loop admittance matrix of the voltage source inverter; when the control system operates in the closed-loop mode, the grid-connected point voltage disturbance is used as the input signal of the small signal model of the voltage source inverter, and the grid-connected point current disturbance is used as the output signal of the small signal model of the voltage source inverter. The point voltage disturbance is used as the first input signal of the small signal model of the voltage source inverter, the current reference value change is used as the second input signal of the small signal model of the voltage source inverter, and the grid-connected point current disturbance is used as the output signal of the small signal model of the voltage source inverter. The transfer function of the small signal model of each link on the path from the first input signal and the second input signal to the output signal is used to determine the equivalent admittance matrix of the current feedback branch; the product of the inverse matrix of the equivalent open-loop admittance of the voltage source inverter and the inverse matrix of the equivalent admittance matrix of the current feedback branch is used as the impedance matrix of the voltage source inverter;

[0252] The stability detection module is used to establish a first impedance ratio, a second impedance ratio and a third impedance ratio by using an equivalent impedance matrix of a power grid and an equivalent impedance matrix of a voltage source inverter; determine whether the first impedance ratio satisfies the Nyquist stability criterion, and if the first impedance ratio does not satisfy the Nyquist stability criterion, determine that the converter is in a negative damping state; if the first impedance ratio satisfies the Nyquist stability criterion, determine that the converter is in a positive damping state or an underdamped state; use the product of the second impedance ratio and the third impedance ratio as an oscillation damping coefficient, and if the oscillation damping coefficient is less than zero, determine that the converter is in a negative damping stable state, if the oscillation damping coefficient is greater than or equal to zero and less than a critical damping coefficient, determine that the converter is in an underdamped stable state, and if the oscillation damping coefficient is greater than or equal to the critical damping coefficient, determine that the converter is in a positive damping stable state.

[0253] Specifically, the control system of the voltage source inverter includes: a filter link, a phase-locked loop link, a grid voltage feedforward branch, a current sampling channel, a voltage sampling channel, a control delay link, a current control loop, a cross-coupling compensation link, a current feedback branch, and a modulation link;

[0254] The transfer function of the small signal model of each link in the control system includes:

[0255] The transfer function of the small signal model of the filter link and the admittance matrix of the filter inductor of the filter link, the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, the transfer function of the error of the phase-locked loop link affecting the positive PARK transformation of the current control signal, the transfer function of the phase-locked error affecting the inverse PARK transformation of the voltage control signal, the transfer function of the small signal model of the low-pass filter on the current sampling channel, the transfer function of the small signal model of the low-pass filter on the voltage sampling channel, the transfer function of the small signal model of the control delay link, the transfer function of the small signal model of the PI controller in the current control loop, the transfer function of the small signal model of the cross-coupling compensation link, the transfer function of the small signal model when the current feedback branch is not working under open-loop control, the transfer function of the small signal model of the modulation link, the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the phase-locked loop link contains only positive sequence components, and the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive sequence components and negative sequence components.

[0256] Specifically, the transfer function of the small signal model of the filter link is obtained including:

[0257] Based on the equivalent circuit of the voltage source inverter connected to the AC power grid, the filter type is determined according to the grid connection point position of the voltage source inverter, and the transfer function of the small signal model of the determined type of filter and the admittance matrix of the filter inductor in the determined type of filter are obtained;

[0258] Based on the structure of the phase-locked loop, the transfer function of the small signal model of the phase-locked loop is established, and the transfer function of the small signal model of the phase-locked loop is corrected using the voltage sampling coefficient; based on the transfer function of the corrected small signal model of the phase-locked loop, the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, the transfer function of the error of the phase-locked loop link affecting the positive PARK transformation of the current control signal, and the transfer function of the phase-locked error affecting the reverse PARK transformation of the voltage control signal are determined respectively;

[0259] A dual orthogonal signal generator is used to separate the positive and negative sequences of the fundamental voltage and fundamental current on the signal branch of the phase-locked loop link in a stationary two-dimensional coordinate system. When the fundamental voltage on the signal branch of the phase-locked loop link contains only positive sequence components, the equivalent filter transfer function in the dq coordinate system is determined. When the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive and negative sequence components, the equivalent filter transfer function in the dq coordinate system is determined.

[0260] Specifically, the equivalent circuit of the voltage source inverter connected to the AC power grid includes a filter inductor, a filter capacitor, a transformer equivalent inductor, a transformer equivalent resistor, an equivalent inductor of the grid-connected line, and an equivalent resistor of the grid-connected line connected in series;

[0261] When the voltage source inverter is connected to the grid connection point through the filter inductor, the grid connection point is located between the filter inductor and the filter capacitor, and the voltage source inverter is connected to the L-type filter; the transfer function of the small signal model of the L-type filter and the admittance matrix of the filter inductor in the L-type filter satisfy the following relationship:

[0262]

[0263] Where Y L1 is the admittance matrix of the filter inductor in the L-type filter, G L1 is the transfer function of the L-type filter small signal model, Z Lf is the filter inductor impedance matrix, L f is the filter inductance, ω0 is the angular frequency of the synchronous rotating coordinate system, and s is the Laplace operator;

[0264] When the voltage source inverter is connected to the grid connection point through the filter inductor and the filter capacitor, the grid connection point is located between the filter capacitor and the equivalent inductance of the transformer, and the voltage source inverter is connected to the LC filter; the transfer function of the small signal model of the LC filter and the admittance matrix of the filter inductor in the LC filter satisfy the following relationship:

[0265]

[0266] Where Y L2 is the admittance matrix of the filter inductor in the LC filter, G L2 is the transfer function of the LC filter small signal model, Y Cf is the filter capacitor admittance matrix, C f is the equivalent value of the filter capacitor;

[0267] When the voltage source inverter is connected to the grid point through the filter inductor, filter capacitor and transformer, the grid point is located between the equivalent resistance of the transformer and the equivalent inductance of the grid-connected line, and the voltage source inverter is connected to the LCL filter; the transfer function of the small signal model of the LCL filter and the admittance matrix of the filter inductor in the LCL filter satisfy the following relationship:

[0268]

[0269] Where Y L3 is the admittance matrix of the filter inductor in the LCL filter, G L3 is the transfer function of the small signal model of the LCL filter, Z LRT is the transformer equivalent inductive branch impedance matrix, L T is the equivalent reactance of the transformer low voltage side, R T is the equivalent resistance of the transformer low voltage side.

[0270] Specifically, the transfer function of the phase-locked loop small signal model corrected by the voltage sampling coefficient satisfies the following relationship:

[0271]

[0272] In the formula, G PLL is the transfer function of the modified phase-locked loop small signal model, G PI-PLL is the transfer function between the voltage disturbance and the dynamic error in the small signal model of the phase-locked loop, s is the Laplace operator, is the d-axis component of the stable operating point voltage in the ideal rotating coordinate system, k vp is the voltage sampling coefficient;

[0273] Based on the transfer function of the modified small signal model of the phase-locked loop, the voltage sampling coefficient and the stable operating point voltage in the ideal rotating coordinate system are used to determine the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, which satisfies the following relationship:

[0274]

[0275] In the formula, The error in the phase-locked loop affects the transfer function of the grid voltage feedforward branch. is the stable operating point voltage in the ideal rotating coordinate system;

[0276] Based on the transfer function of the modified small signal model of the phase-locked loop, the transfer function of the positive PARK transformation of the current control signal affected by the error of the phase-locked loop link is determined by using the current sampling coefficient and the stable operating point current in the ideal rotating coordinate system, which satisfies the following relationship:

[0277]

[0278] In the formula, is the transfer function of the error in the phase-locked loop link affecting the positive PARK transformation of the current control signal, k ig is the current sampling coefficient, is the stable operating point current in the ideal rotating coordinate system;

[0279] Based on the transfer function of the modified small signal model of the phase-locked loop, the voltage sampling coefficient and the voltage given value before the inverse PARK transformation are used to determine the transfer function of the phase-locked error affecting the inverse PARK transformation of the voltage control signal, which satisfies the following relationship:

[0280]

[0281] In the formula, The transfer function of the inverse PARK transformation of the voltage control signal affected by the phase-locked error is: It is the voltage given value before the anti-PARK transformation.

[0282] Specifically, the dq-axis component of the grid-connected point voltage disturbance is used as the first input signal of the small signal model of the voltage source inverter; the current reference value change is used as the second input signal of the small signal model of the voltage source inverter, and the current reference value change is zero during power open-loop control; the dq-axis component of the grid-connected point current disturbance is used as the output signal of the small signal model of the voltage source inverter.

[0283] Specifically, when the control system operates in open-loop mode, the equivalent open-loop admittance matrix of the voltage source inverter satisfies the following relationship:

[0284]

[0285] Where Y eq1 is the equivalent open-loop admittance matrix of the voltage source inverter, Y L is the admittance matrix of the filter inductor of the filter link, G L is the transfer function of the small signal model of the filter link, K PWM is the transfer function of the small signal model of the modulation link, G del is the transfer function of the small signal model that controls the delay link, The transfer function of the inverse PARK transformation of the voltage control signal affected by the phase-locked error is: The error in the phase-locked loop affects the transfer function of the grid voltage feedforward branch. is the transfer function of the error in the phase-locked loop link affecting the positive PARK transformation of the current control signal, G f1 is the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the phase-locked loop contains only the positive sequence component, G f2 is the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive sequence components and negative sequence components, G cc1 is the transfer function of the small signal model of the PI controller in the current control loop, G cc2 is the transfer function of the small signal model of the cross-coupling compensation link, k vp is the voltage sampling factor, G sam is the transfer function of the small signal model when the current feedback branch is not working under open-loop control, G lpv is the transfer function of the small signal model of the low-pass filter on the voltage sampling channel.

[0286] Specifically, when the control system operates in closed-loop mode, the equivalent admittance matrix of the current feedback branch satisfies the following relationship:

[0287] Y eq2 =[E2-GL K PWM G del (G cc2 -G cc1 ) ig G sam G lpi ] -1

[0288] Where Y eq2 is the equivalent admittance matrix of the current feedback branch, E2 is the second-order unit matrix, G L is the transfer function of the small signal model of the filter link, K PWM is the transfer function of the small signal model of the modulation link, G del is the transfer function of the small signal model for controlling the delay link, G cc1 is the transfer function of the small signal model of the PI controller in the current control loop, G cc2 is the transfer function of the small signal model of the cross-coupling compensation link, k ig is the current sampling coefficient, G sam is the transfer function of the small signal model when the current feedback branch is not working under open-loop control, G lpi is the transfer function of the small signal model of the low-pass filter on the current sampling channel.

[0289] Specifically, based on the small signal model of the voltage source inverter, the voltage disturbance at the grid connection point and the current disturbance at the grid connection point satisfy the following relationship:

[0290] Δi gdq =Y eq2 (s)Y eq1 (s)Δu pdq

[0291] In the formula, Δu pdq is the dq-axis component of the grid-connected point voltage disturbance, Δi gdq is the dq axis component of the current disturbance at the grid connection point, Y eq1 (s) is the equivalent open-loop admittance matrix of the voltage source inverter in the complex frequency domain, Y eq2 (s) is the equivalent admittance matrix of the current feedback branch in the complex frequency domain.

[0292] Specifically, the equivalent impedance matrix of the voltage source inverter using an L-type filter in the complex frequency domain satisfies the following relationship:

[0293]

[0294] In the formula, Z i-L (s) is the equivalent impedance matrix of the voltage source inverter using an L-type filter in the complex frequency domain; Z eq1(s) is the equivalent open-loop impedance matrix of the voltage source inverter, Z eq2 (s) is the equivalent impedance matrix of the current feedback branch, Z cdd (s) is the self-impedance on the d-axis in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cdq (s) is the cross impedance encountered by the q-axis current caused by the d-axis voltage in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cqd (s) is the cross impedance encountered by the d-axis current caused by the q-axis voltage in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cqq (s) is the self-impedance on the q-axis in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain.

[0295] Specifically, when the voltage source inverter is connected to the grid through the filter inductor and filter capacitor, the equivalent impedance Z based on the LC filter is i-LC The equivalent impedance matrix of the voltage source inverter in the complex frequency domain satisfies the following relationship:

[0296]

[0297] In the formula, Z i-LC (s) is the equivalent impedance matrix of the voltage source inverter using LC filter in the complex frequency domain, Y Cf is the filter capacitor admittance matrix;

[0298] When the voltage source inverter is connected to the grid through filter inductor, filter capacitor and transformer, the equivalent impedance Z based on the LCL filter is i-LCL The equivalent impedance matrix of the voltage source inverter in the complex frequency domain satisfies the following relationship:

[0299]

[0300] In the formula, Z i-LCL is the equivalent impedance matrix of the voltage source inverter using LCL filter in the complex frequency domain; Y Cf is the filter capacitor admittance matrix, Z LRT is the transformer equivalent inductive branch impedance matrix.

[0301] Specifically, the equivalent impedance matrix of the power grid satisfies the following relationship:

[0302]

[0303] Z gdd (s) is the self-impedance on the d-axis in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gdq(s) is the cross impedance encountered by the q-axis current caused by the d-axis voltage in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gqd (s) is the cross impedance encountered by the d-axis current caused by the q-axis voltage in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gqq (s) is the self-impedance on the q-axis in the equivalent impedance matrix of the power grid in the complex frequency domain;

[0304] The d-axis component and the q-axis component of the first impedance ratio respectively satisfy the following relationships:

[0305]

[0306] The d-axis component and the q-axis component of the second impedance ratio respectively satisfy the following relationships:

[0307]

[0308] The d-axis component and the q-axis component of the third impedance ratio respectively satisfy the following relationships:

[0309]

[0310] In the formula, R 1d , R 1q are the d-axis component and q-axis component of the first impedance ratio, R 2d , R 2q are the d-axis component and q-axis component of the second impedance ratio, R 3d , R 3q They are the d-axis component and q-axis component of the third impedance ratio respectively.

[0311] Specifically, the critical damping coefficient ξ c Satisfies the following relationship:

[0312]

[0313] In the formula, R s , C s , L s are the equivalent resistance, equivalent capacitance and equivalent inductance of the power grid respectively.

[0314] Specifically, the phase margin is calculated using the oscillation damping coefficient as a stability evaluation index for the grid-following and grid-forming converters, satisfying the following relationship:

[0315]

[0316] Where ξ is the oscillation damping coefficient and PM is the phase margin.

[0317] The present disclosure may be a system, a method and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for causing a processor to implement various aspects of the present disclosure.

[0318] A computer-readable storage medium may be a tangible device that can hold and store instructions used by an instruction execution device. A computer-readable storage medium may be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. More specific examples of computer-readable storage media (a non-exhaustive list) include: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disk read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device, such as a punch card or a raised structure in a groove on which instructions are stored, and any suitable combination of the foregoing. As used herein, a computer-readable storage medium is not to be interpreted as a transient signal per se, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagating through a waveguide or other transmission medium (e.g., a light pulse through a fiber optic cable), or an electrical signal transmitted through a wire.

[0319] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to each computing / processing device, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, optical fiber transmissions, wireless transmissions, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in the computer-readable storage medium in each computing / processing device.

[0320] The computer program instructions for performing the operation of the present disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-related instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages, such as Smalltalk, C++, etc., and conventional procedural programming languages, such as "C" language or similar programming languages. Computer-readable program instructions may be executed completely on a user's computer, partially on a user's computer, as an independent software package, partially on a user's computer, partially on a remote computer, or completely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., using an Internet service provider to connect via the Internet). In some embodiments, an electronic circuit, such as a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA), may be customized by utilizing the state information of the computer-readable program instructions, and the electronic circuit may execute the computer-readable program instructions, thereby realizing various aspects of the present disclosure.

[0321] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents, and any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A stability detection method for grid-following and grid-building type converters based on impedance modeling, the grid-following and grid-building type converters use voltage source inverters, and the control system of the voltage source inverter includes multiple links, characterized in that: include: Obtain the transfer function of the small signal model of each link in the control system, and construct the small signal model of the voltage source inverter according to the connection relationship of each link in the control system; When the control system operates in an open-loop mode, the grid-connected point voltage disturbance is used as the input signal of the small signal model of the voltage source inverter, and the grid-connected point current disturbance is used as the output signal of the small signal model of the voltage source inverter. The transfer function of the small signal model of each link on the path from the input signal to the output signal is used to determine the equivalent open-loop admittance matrix of the voltage source inverter. The control system operates in a closed-loop mode, with the grid-connected point voltage disturbance as the first input signal of the small signal model of the voltage source inverter, the current reference value variation as the second input signal of the small signal model of the voltage source inverter, and the grid-connected point current disturbance as the output signal of the small signal model of the voltage source inverter, and the transfer function of the small signal model of each link on the path from the first input signal and the second input signal to the output signal is used to determine the equivalent admittance matrix of the current feedback branch; The impedance matrix of the voltage source inverter is obtained by multiplying the inverse matrix of the equivalent open-loop admittance of the voltage source inverter and the inverse matrix of the equivalent admittance matrix of the current feedback branch. Using the equivalent impedance matrix of the power grid and the equivalent impedance matrix of the voltage source inverter, a first impedance ratio, a second impedance ratio and a third impedance ratio are established; judging whether the first impedance ratio satisfies the Nyquist stability criterion, if the first impedance ratio does not satisfy the Nyquist stability criterion, judging that the converter is in a negative damping state; if the first impedance ratio satisfies the Nyquist stability criterion, judging that the converter is in a positive damping state or an underdamped state; The product of the second impedance ratio and the third impedance ratio is used as the oscillation damping coefficient. If the oscillation damping coefficient is less than zero, the converter is determined to be in a negative damping stable state. If the oscillation damping coefficient is greater than or equal to zero and less than the critical damping coefficient, the converter is determined to be in an underdamped stable state. If the oscillation damping coefficient is greater than or equal to the critical damping coefficient, the converter is determined to be in a positive damping stable state.

2. The method for detecting stability of grid-following and grid-forming converters based on impedance modeling according to claim 1, characterized in that: The control system of the voltage source inverter includes: filter link, phase-locked loop link, grid voltage feedforward branch, current sampling channel, voltage sampling channel, control delay link, current control loop, cross-coupling compensation link, current feedback branch, modulation link; The transfer function of the small signal model of each link in the control system, including: The transfer function of the small signal model of the filter link and the admittance matrix of the filter inductor of the filter link, the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, the transfer function of the error of the phase-locked loop link affecting the positive PARK transformation of the current control signal, the transfer function of the phase-locked error affecting the inverse PARK transformation of the voltage control signal, the transfer function of the small signal model of the low-pass filter on the current sampling channel, the transfer function of the small signal model of the low-pass filter on the voltage sampling channel, the transfer function of the small signal model of the control delay link, the transfer function of the small signal model of the PI controller in the current control loop, the transfer function of the small signal model of the cross-coupling compensation link, the transfer function of the small signal model when the current feedback branch is not working under open-loop control, the transfer function of the small signal model of the modulation link, the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the phase-locked loop link contains only positive sequence components, and the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive sequence components and negative sequence components.

3. The method for detecting the stability of grid-following and grid-forming converters based on impedance modeling according to claim 2 is characterized in that: The transfer function of the small signal model of the filter stage is obtained by: Based on the equivalent circuit of the voltage source inverter connected to the AC power grid, the filter type is determined according to the grid connection point position of the voltage source inverter, and the transfer function of the small signal model of the determined type of filter and the admittance matrix of the filter inductor in the determined type of filter are obtained; Based on the structure of the phase-locked loop, the transfer function of the small signal model of the phase-locked loop is established, and the transfer function of the small signal model of the phase-locked loop is corrected using the voltage sampling coefficient; based on the transfer function of the corrected small signal model of the phase-locked loop, the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, the transfer function of the error of the phase-locked loop link affecting the positive PARK transformation of the current control signal, and the transfer function of the phase-locked error affecting the reverse PARK transformation of the voltage control signal are determined respectively; A dual orthogonal signal generator is used to separate the positive and negative sequences of the fundamental voltage and fundamental current on the signal branch of the phase-locked loop link in a stationary two-dimensional coordinate system. When the fundamental voltage on the signal branch of the phase-locked loop link contains only positive sequence components, the equivalent filter transfer function in the dq coordinate system is determined. When the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive and negative sequence components, the equivalent filter transfer function in the dq coordinate system is determined.

4. The method for detecting stability of grid-following and grid-forming converters based on impedance modeling according to claim 3 is characterized in that: The equivalent circuit of the voltage source inverter connected to the AC power grid includes a filter inductor, a filter capacitor, an equivalent inductor of the transformer, an equivalent resistance of the transformer, an equivalent inductor of the grid-connected line, and an equivalent resistance of the grid-connected line connected in series; When the voltage source inverter is connected to the grid connection point through the filter inductor, the grid connection point is located between the filter inductor and the filter capacitor, and the voltage source inverter is connected to the L-type filter; the transfer function of the small signal model of the L-type filter and the admittance matrix of the filter inductor in the L-type filter satisfy the following relationship: Where Y L1 is the admittance matrix of the filter inductor in the L-type filter, G L1 is the transfer function of the L-type filter small signal model, Z Lf is the filter inductor impedance matrix, L f is the filter inductance, ω0 is the angular frequency of the synchronous rotating coordinate system, and s is the Laplace operator; When the voltage source inverter is connected to the grid connection point through the filter inductor and the filter capacitor, the grid connection point is located between the filter capacitor and the equivalent inductance of the transformer, and the voltage source inverter is connected to the LC filter; the transfer function of the small signal model of the LC filter and the admittance matrix of the filter inductor in the LC filter satisfy the following relationship: Where Y L2 is the admittance matrix of the filter inductor in the LC filter, G L2 is the transfer function of the LC filter small signal model, Y Cf is the filter capacitor admittance matrix, C f is the equivalent value of the filter capacitor; When the voltage source inverter is connected to the grid point through the filter inductor, filter capacitor and transformer, the grid point is located between the equivalent resistance of the transformer and the equivalent inductance of the grid-connected line, and the voltage source inverter is connected to the LCL filter; the transfer function of the small signal model of the LCL filter and the admittance matrix of the filter inductor in the LCL filter satisfy the following relationship: Where Y L3 is the admittance matrix of the filter inductor in the LCL filter, G L3 is the transfer function of the small signal model of the LCL filter, Z LRT is the transformer equivalent inductive branch impedance matrix, L T is the equivalent reactance of the transformer low voltage side, R T is the equivalent resistance of the transformer low voltage side.

5. The method for detecting stability of grid-following and grid-forming converters based on impedance modeling according to claim 3 is characterized in that: The transfer function of the small signal model of the phase-locked loop corrected by the voltage sampling coefficient satisfies the following relationship: In the formula, G PLL is the transfer function of the modified phase-locked loop small signal model, G PI-PLL is the transfer function between the voltage disturbance and the dynamic error in the small signal model of the phase-locked loop, s is the Laplace operator, is the d-axis component of the stable operating point voltage in the ideal rotating coordinate system, k vp is the voltage sampling coefficient; Based on the transfer function of the modified small signal model of the phase-locked loop, the voltage sampling coefficient and the stable operating point voltage in the ideal rotating coordinate system are used to determine the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, which satisfies the following relationship: In the formula, is the transfer function of the grid voltage feedforward branch affected by the error of the phase-locked loop. is the stable operating point voltage in the ideal rotating coordinate system; Based on the transfer function of the modified small signal model of the phase-locked loop, the transfer function of the positive PARK transformation of the current control signal affected by the error of the phase-locked loop link is determined by using the current sampling coefficient and the stable operating point current in the ideal rotating coordinate system, which satisfies the following relationship: In the formula, is the transfer function of the error in the phase-locked loop link affecting the positive PARK transformation of the current control signal, k ig is the current sampling coefficient, is the stable operating point current in the ideal rotating coordinate system; Based on the transfer function of the modified small signal model of the phase-locked loop, the voltage sampling coefficient and the voltage given value before the inverse PARK transformation are used to determine the transfer function of the phase-locked error affecting the inverse PARK transformation of the voltage control signal, which satisfies the following relationship: In the formula, The transfer function of the inverse PARK transformation of the voltage control signal affected by the phase-locked error is: It is the voltage given value before the anti-PARK transformation.

6. The method for detecting stability of grid-following and grid-forming converters based on impedance modeling according to claim 2, characterized in that: The dq-axis component of the grid-connected point voltage disturbance is used as the first input signal of the small signal model of the voltage source inverter; The current reference value variation is used as the second input signal of the small signal model of the voltage source inverter, and the current reference value variation is zero during power open-loop control; The dq-axis components of the grid-connected point current disturbance are used as the output signals of the small signal model of the voltage source inverter.

7. The method for detecting stability of grid-following and grid-forming converters based on impedance modeling according to claim 6 is characterized in that: When the control system operates in open-loop mode, the equivalent open-loop admittance matrix of the voltage source inverter satisfies the following relationship: Where Y eq1 is the equivalent open-loop admittance matrix of the voltage source inverter, Y L is the admittance matrix of the filter inductor of the filter link, G L is the transfer function of the small signal model of the filter link, K PWM is the transfer function of the small signal model of the modulation link, G del is the transfer function of the small signal model that controls the delay link, The transfer function of the inverse PARK transformation of the voltage control signal affected by the phase-locked error is: is the transfer function of the grid voltage feedforward branch affected by the error of the phase-locked loop. is the transfer function of the error in the phase-locked loop link affecting the positive PARK transformation of the current control signal, G f1 is the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the phase-locked loop contains only the positive sequence component, G f2 is the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive sequence components and negative sequence components, G cc1 is the transfer function of the small signal model of the PI controller in the current control loop, G cc2 is the transfer function of the small signal model of the cross-coupling compensation link, k vp is the voltage sampling factor, G sam is the transfer function of the small signal model when the current feedback branch is not working under open-loop control, G lpv is the transfer function of the small signal model of the low-pass filter on the voltage sampling channel.

8. The method for detecting stability of grid-following and grid-forming converters based on impedance modeling according to claim 7, characterized in that: When the control system operates in closed-loop mode, the equivalent admittance matrix of the current feedback branch satisfies the following relationship: Y eq2 =[E2-G L K PWM G del (G cc2 -G cc1 )k ig G sam G lpi ] -1 Where Y eq2 is the equivalent admittance matrix of the current feedback branch, E2 is the second-order unit matrix, G L is the transfer function of the small signal model of the filter link, K PWM is the transfer function of the small signal model of the modulation link, G del is the transfer function of the small signal model for controlling the delay link, G cc1 is the transfer function of the small signal model of the PI controller in the current control loop, G cc2 is the transfer function of the small signal model of the cross-coupling compensation link, k ig is the current sampling factor, G sam is the transfer function of the small signal model when the current feedback branch is not working under open-loop control, G lpi is the transfer function of the small signal model of the low-pass filter on the current sampling channel.

9. The method for detecting stability of grid-following and grid-forming converters based on impedance modeling according to claim 8, characterized in that: Based on the small signal model of the voltage source inverter, the voltage disturbance at the grid connection point and the current disturbance at the grid connection point satisfy the following relationship: Δi gdq =Y eq2 (s)Y eq1 (s)Δu pdq In the formula, Δu pdq is the dq-axis component of the grid-connected point voltage disturbance, Δi gdq is the dq axis component of the current disturbance at the grid connection point, Y eq1 (s) is the equivalent open-loop admittance matrix of the voltage source inverter in the complex frequency domain, Y eq2 (s) is the equivalent admittance matrix of the current feedback branch in the complex frequency domain.

10. The method for detecting stability of grid-following and grid-forming converters based on impedance modeling according to claim 9, characterized in that: The equivalent impedance matrix of the voltage source inverter using an L-type filter in the complex frequency domain satisfies the following relationship: In the formula, Z i-L (s) is the equivalent impedance matrix of the voltage source inverter using an L-type filter in the complex frequency domain; Z eq1 (s) is the equivalent open-loop impedance matrix of the voltage source inverter, Z eq2 (s) is the equivalent impedance matrix of the current feedback branch, Z cdd (s) is the self-impedance on the d-axis in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cdq (s) is the cross impedance encountered by the q-axis current caused by the d-axis voltage in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cqd (s) is the cross impedance encountered by the d-axis current caused by the q-axis voltage in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cqq (s) is the self-impedance on the q-axis in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain.

11. The method for detecting stability of grid-following and grid-forming converters based on impedance modeling according to claim 10, characterized in that: When the voltage source inverter is connected to the grid through the filter inductor and filter capacitor, the equivalent impedance Z based on the LC filter is i-LC The equivalent impedance matrix of the voltage source inverter in the complex frequency domain satisfies the following relationship: In the formula, Z i-LC (s) is the equivalent impedance matrix of the voltage source inverter using LC filter in the complex frequency domain, Y Cf is the filter capacitor admittance matrix; When the voltage source inverter is connected to the grid through filter inductor, filter capacitor and transformer, the equivalent impedance Z based on the LCL filter is i-LCL The equivalent impedance matrix of the voltage source inverter in the complex frequency domain satisfies the following relationship: In the formula, Z i-LCL is the equivalent impedance matrix of the voltage source inverter using LCL filter in the complex frequency domain; Y Cf is the filter capacitor admittance matrix, Z LRT is the transformer equivalent inductive branch impedance matrix.

12. The method for detecting stability of grid-following and grid-forming converters based on impedance modeling according to claim 11, characterized in that: The equivalent impedance matrix of the power grid satisfies the following relationship: Z gdd (s) is the self-impedance on the d-axis in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gdq (s) is the cross impedance encountered by the q-axis current caused by the d-axis voltage in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gqd (s) is the cross impedance encountered by the d-axis current caused by the q-axis voltage in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gqq (s) is the self-impedance on the q-axis in the equivalent impedance matrix of the power grid in the complex frequency domain; The d-axis component and the q-axis component of the first impedance ratio respectively satisfy the following relationships: The d-axis component and the q-axis component of the second impedance ratio respectively satisfy the following relationships: The d-axis component and the q-axis component of the third impedance ratio respectively satisfy the following relationships: In the formula, R 1d , R 1q are the d-axis component and q-axis component of the first impedance ratio, R 2d , R 2q are the d-axis component and q-axis component of the second impedance ratio, R 3d , R 3q They are the d-axis component and q-axis component of the third impedance ratio respectively.

13. The method for detecting stability of grid-following and grid-forming converters based on impedance modeling according to claim 1, characterized in that: Critical damping coefficient ξ c Satisfies the following relationship: In the formula, R s , C s , L s are the equivalent resistance, equivalent capacitance and equivalent inductance of the power grid respectively.

14. The method for detecting stability of grid-following and grid-forming converters based on impedance modeling according to claim 1, characterized in that: The phase margin is calculated using the oscillation damping coefficient as a stability evaluation index for grid-following and grid-forming converters, satisfying the following relationship: Where ξ is the oscillation damping coefficient and PM is the phase margin.

15. A stability detection system for grid-following and grid-building type converters based on impedance modeling, the grid-following and grid-building type converters adopt voltage source inverters, and the control system of the voltage source inverter includes multiple links, characterized in that: include: The impedance modeling module is used to obtain the transfer function of the small signal model of each link in the control system, and construct the small signal model of the voltage source inverter according to the connection relationship of each link in the control system; when the control system operates in the open-loop mode, the grid-connected point voltage disturbance is used as the input signal of the small signal model of the voltage source inverter, and the grid-connected point current disturbance is used as the output signal of the small signal model of the voltage source inverter. The transfer function of the small signal model of each link on the path from the input signal to the output signal is used to determine the equivalent open-loop admittance matrix of the voltage source inverter; The control system operates in a closed-loop mode, with the grid-connected point voltage disturbance as the first input signal of the small signal model of the voltage source inverter, the current reference value variation as the second input signal of the small signal model of the voltage source inverter, and the grid-connected point current disturbance as the output signal of the small signal model of the voltage source inverter, and the transfer function of the small signal model of each link on the path from the first input signal and the second input signal to the output signal is used to determine the equivalent admittance matrix of the current feedback branch; The impedance matrix of the voltage source inverter is obtained by multiplying the inverse matrix of the equivalent open-loop admittance of the voltage source inverter and the inverse matrix of the equivalent admittance matrix of the current feedback branch. A stability detection module is used to establish a first impedance ratio, a second impedance ratio and a third impedance ratio by using an equivalent impedance matrix of the power grid and an equivalent impedance matrix of the voltage source inverter; determine whether the first impedance ratio satisfies the Nyquist stability criterion, and if the first impedance ratio does not satisfy the Nyquist stability criterion, determine that the converter is in a negative damping state; if the first impedance ratio satisfies the Nyquist stability criterion, determine that the converter is in a positive damping state or an underdamped state; The product of the second impedance ratio and the third impedance ratio is used as the oscillation damping coefficient. If the oscillation damping coefficient is less than zero, the converter is determined to be in a negative damping stable state. If the oscillation damping coefficient is greater than or equal to zero and less than the critical damping coefficient, the converter is determined to be in an underdamped stable state. If the oscillation damping coefficient is greater than or equal to the critical damping coefficient, the converter is determined to be in a positive damping stable state.

16. The grid-following and grid-building type converter stability detection system based on impedance modeling according to claim 15, characterized in that: The control system of the voltage source inverter includes: filter link, phase-locked loop link, grid voltage feedforward branch, current sampling channel, voltage sampling channel, control delay link, current control loop, cross-coupling compensation link, current feedback branch, modulation link; The transfer function of the small signal model of each link in the control system, including: The transfer function of the small signal model of the filter link and the admittance matrix of the filter inductor of the filter link, the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, the transfer function of the error of the phase-locked loop link affecting the positive PARK transformation of the current control signal, the transfer function of the phase-locked error affecting the inverse PARK transformation of the voltage control signal, the transfer function of the small signal model of the low-pass filter on the current sampling channel, the transfer function of the small signal model of the low-pass filter on the voltage sampling channel, the transfer function of the small signal model of the control delay link, the transfer function of the small signal model of the PI controller in the current control loop, the transfer function of the small signal model of the cross-coupling compensation link, the transfer function of the small signal model when the current feedback branch is not working under open-loop control, the transfer function of the small signal model of the modulation link, the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the phase-locked loop link contains only positive sequence components, and the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive sequence components and negative sequence components.

17. The grid-following and grid-building type converter stability detection system based on impedance modeling according to claim 16, characterized in that: The transfer function of the small signal model of the filter stage is obtained by: Based on the equivalent circuit of the voltage source inverter connected to the AC power grid, the filter type is determined according to the grid connection point position of the voltage source inverter, and the transfer function of the small signal model of the determined type of filter and the admittance matrix of the filter inductor in the determined type of filter are obtained; Based on the structure of the phase-locked loop, the transfer function of the small signal model of the phase-locked loop is established, and the transfer function of the small signal model of the phase-locked loop is corrected using the voltage sampling coefficient; based on the transfer function of the corrected small signal model of the phase-locked loop, the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, the transfer function of the error of the phase-locked loop link affecting the positive PARK transformation of the current control signal, and the transfer function of the phase-locked error affecting the reverse PARK transformation of the voltage control signal are determined respectively; A dual orthogonal signal generator is used to separate the positive and negative sequences of the fundamental voltage and fundamental current on the signal branch of the phase-locked loop link in a stationary two-dimensional coordinate system. When the fundamental voltage on the signal branch of the phase-locked loop link contains only positive sequence components, the equivalent filter transfer function in the dq coordinate system is determined. When the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive and negative sequence components, the equivalent filter transfer function in the dq coordinate system is determined.

18. The grid-following and grid-building type converter stability detection system based on impedance modeling according to claim 17, characterized in that: The equivalent circuit of the voltage source inverter connected to the AC power grid includes a filter inductor, a filter capacitor, an equivalent inductor of the transformer, an equivalent resistance of the transformer, an equivalent inductor of the grid-connected line, and an equivalent resistance of the grid-connected line connected in series; When the voltage source inverter is connected to the grid connection point through the filter inductor, the grid connection point is located between the filter inductor and the filter capacitor, and the voltage source inverter is connected to the L-type filter; the transfer function of the small signal model of the L-type filter and the admittance matrix of the filter inductor in the L-type filter satisfy the following relationship: Where Y L1 is the admittance matrix of the filter inductor in the L-type filter, G L1 is the transfer function of the L-type filter small signal model, Z Lf is the filter inductor impedance matrix, L f is the filter inductance, ω0 is the angular frequency of the synchronous rotating coordinate system, and s is the Laplace operator; When the voltage source inverter is connected to the grid connection point through the filter inductor and the filter capacitor, the grid connection point is located between the filter capacitor and the equivalent inductance of the transformer, and the voltage source inverter is connected to the LC filter; the transfer function of the small signal model of the LC filter and the admittance matrix of the filter inductor in the LC filter satisfy the following relationship: Where Y L2 is the admittance matrix of the filter inductor in the LC filter, G L2 is the transfer function of the LC filter small signal model, Y Cf is the filter capacitor admittance matrix, C f is the equivalent value of the filter capacitor; When the voltage source inverter is connected to the grid point through the filter inductor, filter capacitor and transformer, the grid point is located between the equivalent resistance of the transformer and the equivalent inductance of the grid-connected line, and the voltage source inverter is connected to the LCL filter; the transfer function of the small signal model of the LCL filter and the admittance matrix of the filter inductor in the LCL filter satisfy the following relationship: Where Y L3 is the admittance matrix of the filter inductor in the LCL filter, G L3 is the transfer function of the small signal model of the LCL filter, Z LRT is the transformer equivalent inductive branch impedance matrix, L T is the equivalent reactance of the transformer low voltage side, R T is the equivalent resistance of the transformer low voltage side.

19. The grid-following and grid-building type converter stability detection system based on impedance modeling according to claim 17, characterized in that: The transfer function of the small signal model of the phase-locked loop corrected by the voltage sampling coefficient satisfies the following relationship: In the formula, G PLL is the transfer function of the modified phase-locked loop small signal model, G PI-PLL is the transfer function between the voltage disturbance and the dynamic error in the small signal model of the phase-locked loop, s is the Laplace operator, is the d-axis component of the stable operating point voltage in the ideal rotating coordinate system, k vp is the voltage sampling coefficient; Based on the transfer function of the modified small signal model of the phase-locked loop, the voltage sampling coefficient and the stable operating point voltage in the ideal rotating coordinate system are used to determine the transfer function of the error of the phase-locked loop link affecting the grid voltage feedforward branch, which satisfies the following relationship: In the formula, is the transfer function of the grid voltage feedforward branch affected by the error of the phase-locked loop. is the stable operating point voltage in the ideal rotating coordinate system; Based on the transfer function of the modified small signal model of the phase-locked loop, the transfer function of the positive PARK transformation of the current control signal affected by the error of the phase-locked loop link is determined by using the current sampling coefficient and the stable operating point current in the ideal rotating coordinate system, which satisfies the following relationship: In the formula, is the transfer function of the error in the phase-locked loop link affecting the positive PARK transformation of the current control signal, k ig is the current sampling coefficient, is the stable operating point current in the ideal rotating coordinate system; Based on the transfer function of the modified small signal model of the phase-locked loop, the voltage sampling coefficient and the voltage given value before the inverse PARK transformation are used to determine the transfer function of the phase-locked error affecting the inverse PARK transformation of the voltage control signal, which satisfies the following relationship: In the formula, The transfer function of the inverse PARK transformation of the voltage control signal affected by the phase-locked error is: It is the voltage given value before the anti-PARK transformation.

20. The grid-following and grid-building type converter stability detection system based on impedance modeling according to claim 16, characterized in that: The dq-axis component of the grid-connected point voltage disturbance is used as the first input signal of the small signal model of the voltage source inverter; The current reference value variation is used as the second input signal of the small signal model of the voltage source inverter, and the current reference value variation is zero during power open-loop control; The dq-axis components of the grid-connected point current disturbance are used as the output signals of the small signal model of the voltage source inverter.

21. The grid-following and grid-building type converter stability detection system based on impedance modeling according to claim 20, characterized in that: When the control system operates in open-loop mode, the equivalent open-loop admittance matrix of the voltage source inverter satisfies the following relationship: Where Y eq1 is the equivalent open-loop admittance matrix of the voltage source inverter, Y L is the admittance matrix of the filter inductor of the filter link, G L is the transfer function of the small signal model of the filter link, K PWM is the transfer function of the small signal model of the modulation link, G del is the transfer function of the small signal model that controls the delay link, The transfer function of the inverse PARK transformation of the voltage control signal affected by the phase-locked error is: is the transfer function of the grid voltage feedforward branch affected by the error of the phase-locked loop. is the transfer function of the error in the phase-locked loop link affecting the positive PARK transformation of the current control signal, G f1 is the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the phase-locked loop contains only the positive sequence component, G f2 is the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive sequence components and negative sequence components, G cc1 is the transfer function of the small signal model of the PI controller in the current control loop, G cc2 is the transfer function of the small signal model of the cross-coupling compensation link, k vp is the voltage sampling factor, G sam is the transfer function of the small signal model when the current feedback branch is not working under open-loop control, G lpv is the transfer function of the small signal model of the low-pass filter on the voltage sampling channel.

22. The grid-following and grid-building type converter stability detection system based on impedance modeling according to claim 21, characterized in that: When the control system operates in closed-loop mode, the equivalent admittance matrix of the current feedback branch satisfies the following relationship: Y eq2 =[E2-G L K PWM G del (G cc2 -G cc1 )k ig G sam G lpi ] -1 Where Y eq2 is the equivalent admittance matrix of the current feedback branch, E2 is the second-order unit matrix, G L is the transfer function of the small signal model of the filter link, K PWM is the transfer function of the small signal model of the modulation link, G del is the transfer function of the small signal model for controlling the delay link, G cc1 is the transfer function of the small signal model of the PI controller in the current control loop, G cc2 is the transfer function of the small signal model of the cross-coupling compensation link, k ig is the current sampling factor, G sam is the transfer function of the small signal model when the current feedback branch is not working under open-loop control, G lpi is the transfer function of the small signal model of the low-pass filter on the current sampling channel.

23. The grid-following and grid-building type converter stability detection system based on impedance modeling according to claim 22, characterized in that: Based on the small signal model of the voltage source inverter, the voltage disturbance at the grid connection point and the current disturbance at the grid connection point satisfy the following relationship: Δi gdq =Y eq2 (s)Y eq1 (s)Δu pdq In the formula, Δu pdq is the dq-axis component of the grid-connected point voltage disturbance, Δi gdq is the dq axis component of the current disturbance at the grid connection point, Y eq1 (s) is the equivalent open-loop admittance matrix of the voltage source inverter in the complex frequency domain, Y eq2 (s) is the equivalent admittance matrix of the current feedback branch in the complex frequency domain.

24. The grid-following and grid-building type converter stability detection system based on impedance modeling according to claim 23, characterized in that: The equivalent impedance matrix of the voltage source inverter using an L-type filter in the complex frequency domain satisfies the following relationship: In the formula, Z i-L (s) is the equivalent impedance matrix of the voltage source inverter using an L-type filter in the complex frequency domain; Z eq1 (s) is the equivalent open-loop impedance matrix of the voltage source inverter, Z eq2 (s) is the equivalent impedance matrix of the current feedback branch, Z cdd (s) is the self-impedance on the d-axis in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cdq (s) is the cross impedance encountered by the q-axis current caused by the d-axis voltage in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cqd (s) is the cross impedance encountered by the d-axis current caused by the q-axis voltage in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain, Z cqq (s) is the self-impedance on the q-axis in the equivalent impedance matrix of the voltage source inverter in the complex frequency domain.

25. The grid-following and grid-building type converter stability detection system based on impedance modeling according to claim 24, characterized in that: When the voltage source inverter is connected to the grid through the filter inductor and filter capacitor, the equivalent impedance Z based on the LC filter is i-LC The equivalent impedance matrix of the voltage source inverter in the complex frequency domain satisfies the following relationship: In the formula, Z i-LC (s) is the equivalent impedance matrix of the voltage source inverter using LC filter in the complex frequency domain, Y Cf is the filter capacitor admittance matrix; When the voltage source inverter is connected to the grid through filter inductor, filter capacitor and transformer, the equivalent impedance Z based on the LCL filter is i-LCL The equivalent impedance matrix of the voltage source inverter in the complex frequency domain satisfies the following relationship: In the formula, Z i-LCL is the equivalent impedance matrix of the voltage source inverter using LCL filter in the complex frequency domain; Y Cf is the filter capacitor admittance matrix, Z LRT is the transformer equivalent inductive branch impedance matrix.

26. The grid-following and grid-building type converter stability detection system based on impedance modeling according to claim 25, characterized in that: The equivalent impedance matrix of the power grid satisfies the following relationship: Z gdd (s) is the self-impedance on the d-axis in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gdq (s) is the cross impedance encountered by the q-axis current caused by the d-axis voltage in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gqd (s) is the cross impedance encountered by the d-axis current caused by the q-axis voltage in the equivalent impedance matrix of the power grid in the complex frequency domain, Z gqq (s) is the self-impedance on the q-axis in the equivalent impedance matrix of the power grid in the complex frequency domain; The d-axis component and the q-axis component of the first impedance ratio respectively satisfy the following relationships: The d-axis component and the q-axis component of the second impedance ratio respectively satisfy the following relationships: The d-axis component and the q-axis component of the third impedance ratio respectively satisfy the following relationships: In the formula, R 1d , R 1q are the d-axis component and q-axis component of the first impedance ratio, R 2d , R 2q are the d-axis component and q-axis component of the second impedance ratio, R 3d , R 3q They are the d-axis component and q-axis component of the third impedance ratio respectively.

27. The grid-following and grid-building type converter stability detection system based on impedance modeling according to claim 15, characterized in that: Critical damping coefficient ξ c Satisfies the following relationship: In the formula, R s , C s , L s are the equivalent resistance, equivalent capacitance and equivalent inductance of the power grid respectively.

28. The grid-following and grid-building type converter stability detection system based on impedance modeling according to claim 15, characterized in that: The phase margin is calculated using the oscillation damping coefficient as a stability evaluation index for grid-following and grid-forming converters, satisfying the following relationship: Where ξ is the oscillation damping coefficient and PM is the phase margin.

29. A terminal comprising a processor and a storage medium; characterized in that: The storage medium is used to store instructions; The processor is configured to operate according to the instructions to execute the steps of the method according to any one of claims 1 to 14.

30. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 14 are implemented.

Images