Stability Detection Method and System for Grid-Based and Network-Based Converters Based on Impedance Modeling

Abstract

A stability detection method and system for grid-connected and grid-connected converters based on impedance modeling is proposed. This method determines the impedance matrix of the voltage source inverter based on a small-signal model of the voltage source inverter, and establishes a first impedance ratio, a second impedance ratio, and a third impedance ratio with the equivalent impedance matrix of the power grid. If the first impedance ratio does not satisfy the Nyquist stability criterion, the converter is determined to be in a negatively damped state; if the first impedance ratio satisfies the Nyquist stability criterion, the converter is determined to be in a positively damped or underdamped state. The product of the second and third impedance ratios is used as the oscillation damping coefficient. If the oscillation damping coefficient is less than zero, the converter is determined to be in a negatively damped 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 positively damped stable state. This method accurately describes the dynamic characteristics of the converter under nonlinear and large disturbance conditions.

Description

Technical Field

[0001] This invention belongs to the field of power system stability control technology, specifically, it relates to a stability detection method and system for grid-connected and grid-connected converters based on impedance modeling. Background Technology

[0002] Currently, with the widespread application of renewable energy, a large number of distributed power sources and energy storage devices have emerged in power systems. To improve the stability and flexibility of power systems, effective control and management of these distributed power sources and energy storage devices are necessary. A common solution is to use converters to connect distributed power sources and energy storage devices to the grid. Traditional grid-connected converters are increasingly widely used in power systems, enabling energy conversion and transmission between different voltage levels.

[0003] In existing technologies, converter stability analysis is one of the key issues in the design and operation of power systems. Currently, traditional converter stability analysis methods are mainly based on linear models and frequency domain analysis. While these methods can provide useful results in some cases, they are not effective enough for handling the stability analysis of large-scale, complex power systems. Traditional stability analysis methods, such as eigenvalue analysis and Nyquist plot analysis, often require system simplification, neglecting some nonlinear and coupling effects, leading to inaccurate results. Most traditional methods focus primarily on time-domain analysis, insufficiently considering interactions and stability effects in the frequency domain. However, in practical applications, frequency-domain analysis is crucial for understanding the system's response and stability at different frequencies. Grid-connected and network-connected converters encounter various dynamic changes in actual operation, such as load variations and grid disturbances. Traditional methods struggle to predict the impact of these changes on system stability in real time and accurately. In summary, traditional stability analysis methods typically require precise linearized models, making it difficult to accurately describe the dynamic behavior of nonlinear systems and under large disturbance conditions. Traditional methods are mainly applicable to the stability analysis of single-type converters, lacking comprehensive analysis of multi-converter systems and failing to handle the interactions within such 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] To address the shortcomings of existing technologies, this invention provides a stability detection method and system for grid-connected and grid-connected converters based on impedance modeling. By employing impedance modeling, 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] This invention proposes a stability detection method for grid-connected and grid-connected converters based on impedance modeling. The grid-connected and grid-connected converters employ voltage source inverters. The control system of the voltage source inverter includes multiple components, characterized by including:

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

[0008] When the control system operates in open-loop mode, the grid connection point voltage disturbance is used as the input signal of the small-signal model of the voltage source inverter, and the grid connection point current disturbance is used as the output signal of the small-signal model of the voltage source inverter. The equivalent open-loop admittance matrix of the voltage source inverter is determined using the transfer functions of the small-signal models of each link in the path from the input signal to the output signal. When the control system operates in closed-loop mode, the grid connection point voltage disturbance is used as the first input signal of the small-signal model of the voltage source inverter, the change in the current reference value is used as the second input signal of the small-signal model of the voltage source inverter, and the grid connection point current disturbance is used as the output signal of the small-signal model of the voltage source inverter. The equivalent admittance matrix of the current feedback branch is determined using the transfer functions of the small-signal models of each link in the path from the first input signal to the second input signal to the output signal. 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.

[0009] 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. It is then determined 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 negatively damped state. If the first impedance ratio satisfies the Nyquist stability criterion, the converter is determined to be in a positively damped or underdamped state. The product of the second and third impedance ratios is used as the oscillation damping coefficient. If the oscillation damping coefficient is less than zero, the converter is determined to be in a negatively damped 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 positively damped stable state.

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

[0011] The transfer functions of the small-signal models of each component in the control system include:

[0012] The transfer functions of the small-signal model of the filter stage and the admittance matrix of the filter inductor; the transfer function of the grid voltage feedforward branch affected by the error of the phase-locked loop (PLL); the transfer function of the positive PARK transform of the current control signal affected by the error of the PLL; the transfer function of the inverse PARK transform of the voltage control signal affected by the PLL error; 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 stage; 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 stage; the transfer function of the small-signal model of the current feedback branch when it is not working under open-loop control; the transfer function of the small-signal model of the modulation stage; the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the PLL 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 and negative-sequence components.

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

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

[0015] Based on the structure of the phase-locked loop (PLL), the transfer function of the PLL small-signal model is established, and the voltage sampling coefficients are used to correct the transfer function of the PLL small-signal model. Based on the corrected transfer function of the PLL small-signal model, the transfer functions of the PLL error affecting the grid voltage feedforward branch, the PLL error affecting the positive PARK transform of the current control signal, and the PLL error affecting the inverse PARK transform of the voltage control signal are determined respectively.

[0016] A dual-orthogonal signal generator is used to separate the fundamental voltage and fundamental current of the signal branch of the phase-locked loop (PLL) in a stationary two-dimensional coordinate system. When the fundamental voltage of the signal branch of the PLL contains only a positive-sequence component, the equivalent filter transfer function in the dq coordinate system is determined. When the fundamental voltage of the signal branch of the grid voltage feedforward branch contains both positive-sequence 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 grid includes a filter inductor, a filter capacitor, a transformer equivalent inductance, a transformer equivalent resistance, an equivalent inductance of the grid connection line, and an equivalent resistance of the grid connection line connected in series.

[0018] When a voltage source inverter is connected to the grid via a filter inductor, the grid connection point is located between the filter inductor and the filter capacitor. The voltage source inverter is connected to an 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] In the formula, Y L1 G is the admittance matrix of the filter inductor in an L-type filter. L1 Z is the transfer function of the small-signal model of the L-type filter. Lf Let L be the filter inductor impedance matrix. f ω0 is the filter inductance, ω0 is the angular frequency of the synchronous rotating coordinate system, and s is the Laplace operator;

[0021] When a voltage source inverter is connected to the grid via a filter inductor and a filter capacitor, the grid connection point is located between the filter capacitor and the equivalent inductance of the transformer. The voltage source inverter is connected to an 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] In the formula, Y L2 G is the admittance matrix of the filter inductor in an LC filter. L2 Y is the transfer function of the small-signal model of an LC filter. Cf C is the admittance matrix of the filter capacitor. f This is the equivalent value of the filter capacitor;

[0024] When a voltage source inverter is connected to the grid via a filter inductor, filter capacitor, and transformer, the grid connection point is located between the equivalent resistance of the transformer and the equivalent inductance of the grid connection line. The voltage source inverter is connected to an 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] In the formula, Y L3 G is the admittance matrix of the filter inductor in an LCL filter. L3 Z is the transfer function of the small-signal model of an LCL filter. LRT Let L be the equivalent inductive branch impedance matrix of the transformer. T R is the equivalent reactance on the low-voltage side of the transformer. T This is the equivalent resistance on the low-voltage side of the transformer.

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

[0028]

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

[0030] Based on the transfer function of the modified phase-locked loop (PLL) small-signal model, and using the voltage sampling coefficients and the steady-state operating point voltage in the ideal rotating coordinate system, the transfer function of the error in the PLL affecting the grid voltage feedforward branch is determined, satisfying the following relationship:

[0031]

[0032] In the formula, The transfer function of the grid voltage feedforward branch is used to explain how the error in the phase-locked loop affects the grid voltage feedforward branch. This refers to the stable operating point voltage in an ideal rotating coordinate system.

[0033] Based on the transfer function of the modified phase-locked loop (PLL) small-signal model, and using the current sampling coefficients and the steady-state operating current in an ideal rotating coordinate system, the transfer function of the positive PARK transform of the current control signal influenced by the error of the PLL is determined, satisfying the following relationship:

[0034]

[0035] In the formula, The transfer function of the positive PARK transform of the current control signal is given by the error of the phase-locked loop (PLL) circuit. ig For current sampling coefficients, This refers to the stable operating point current in an ideal rotating coordinate system.

[0036] Based on the transfer function of the modified phase-locked loop small-signal model, using the voltage sampling coefficients and the voltage setpoint before the inverse PARK transformation, the transfer function of the phase-locked error affecting the inverse PARK transformation of the voltage control signal is determined, satisfying the following relationship:

[0037]

[0038] In the formula, The transfer function of the inverse PARK transform of the voltage control signal is given by the effect of phase-locked loop error. This is the voltage setpoint before the inverse PARK transformation.

[0039] Preferably, the dq-axis component of the grid connection point voltage disturbance is used as the first input signal of the small-signal model of the voltage source inverter; the change in the current reference value is used as the second input signal of the small-signal model of the voltage source inverter, and the change in the current reference value is zero during power open-loop control; the dq-axis component of the grid connection 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 open-loop mode, the equivalent open-loop admittance matrix of the voltage source inverter satisfies the following relationship:

[0041]

[0042] In the formula, Y eq1 Y is the equivalent open-loop admittance matrix of a voltage source inverter. L G is the admittance matrix of the filter inductor in the filter stage. L K is the transfer function of the small-signal model of the filter stage. PWM G is the transfer function of the small-signal model of the modulation stage. del To control the transfer function of the small-signal model of the delay element, The transfer function of the inverse PARK transform of the voltage control signal is given by the effect of phase-locked loop error. The transfer function of the grid voltage feedforward branch is used to explain how the error in the phase-locked loop affects the grid voltage feedforward branch. To explain the transfer function of the positive PARK transform of the current control signal due to the error in the phase-locked loop, G f1 G 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. f2 G 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 and negative-sequence components. cc1 G is the transfer function of the small-signal model of the PI controller within the current control loop. cc2 Let k be the transfer function of the small-signal model of the cross-coupling compensation stage. vp G is the voltage sampling coefficient. sam G is the transfer function of the small-signal model when the current feedback branch is not working under open-loop control. lpv This 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 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 )k ig G sam G lpi ] -1

[0045] In the formula, Y eq2 Let E2 be the equivalent admittance matrix of the current feedback branch, and G be the second-order identity matrix. L K is the transfer function of the small-signal model of the filter stage. PWM G is the transfer function of the small-signal model of the modulation stage. del To control the transfer function of the small-signal model of the delay element, G cc1 G is the transfer function of the small-signal model of the PI controller within the current control loop. cc2 Let k be the transfer function of the small-signal model of the cross-coupling compensation stage. ig G is the current sampling coefficient. sam G is the transfer function of the small-signal model when the current feedback branch is not working under open-loop control. lpi This 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 voltage disturbance at the grid connection point and the current disturbance at the grid connection point satisfy the following relationship:

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

[0048] In the formula, Δu pdq Let Δi be the dq-axis component of the grid connection point voltage disturbance. gdq Y represents the dq-axis component of the grid connection point current disturbance. 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 a voltage source inverter using an L-type filter in the complex frequency domain satisfies the following relationship:

[0050]

[0051] In the formula, Z i-L (s) represents the equivalent impedance matrix of a 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) represents the self-impedance on the d-axis of the equivalent impedance matrix of a voltage-source inverter in the complex frequency domain, Z cdq (s) represents the cross impedance encountered by the q-axis current caused by the d-axis voltage in the equivalent impedance matrix of a voltage source inverter in the complex frequency domain, Z. cqd (s) represents the cross impedance encountered by the d-axis current caused by the q-axis voltage in the equivalent impedance matrix of a voltage source inverter in the complex frequency domain, Z. cqq (s) represents the self-impedance on the q-axis in the equivalent impedance matrix of a voltage source inverter in the complex frequency domain.

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

[0053]

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

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

[0056]

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

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

[0059]

[0060] Z gdd (s) represents the self-impedance on the d-axis of the equivalent impedance matrix of the power grid in the complex frequency domain, Z gdq(s) represents 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) represents 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) represents 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 and q-axis components of the first impedance ratio satisfy the following relationships:

[0062]

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

[0064]

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

[0066]

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

[0068] Preferably, the critical damping coefficient ξ c The following relationship must be satisfied:

[0069]

[0070] In the formula, R s C s L s These 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 and used as a stability evaluation index for grid-type and grid-type converters, satisfying the following relationship:

[0072]

[0073] In the formula, ξ is the oscillation damping coefficient, and PM is the phase margin.

[0074] This invention also proposes a stability detection system for grid-connected and grid-connected converters based on impedance modeling. The grid-connected and grid-connected converters employ voltage source inverters. The control system of the voltage source inverter includes multiple components, including:

[0075] The impedance modeling module is used to obtain the transfer functions of the small-signal models of each component in the control system. Based on the connection relationships of each component in the control system, it constructs the small-signal model of the voltage source inverter. When the control system operates in open-loop mode, the grid connection point voltage disturbance is used as the input signal of the small-signal model of the voltage source inverter, and the grid connection point current disturbance is used as the output signal. Using the transfer functions of the small-signal models of each component along the path from the input signal to the output signal, the equivalent open-loop admittance matrix of the voltage source inverter is determined. When the control system operates in closed-loop mode, the grid connection... The point voltage disturbance is used as the first input signal of the small-signal model of the voltage source inverter, the change in the current reference value is used as the second input signal of the small-signal model of the voltage source inverter, and the grid connection point current disturbance is used as the output signal of the small-signal model of the voltage source inverter. The equivalent admittance matrix of the current feedback branch is determined by using the transfer function of the small-signal model of each link in the path from the first input signal and the second input signal to the output signal. 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 using the equivalent impedance matrix of the power grid and the equivalent impedance matrix of the voltage source inverter. It then determines 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 negatively damped state. If the first impedance ratio satisfies the Nyquist stability criterion, the converter is determined to be in a positively damped or underdamped state. The product of the second and third impedance ratios is used as the oscillation damping coefficient. If the oscillation damping coefficient is less than zero, the converter is determined to be in a negatively damped 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 positively damped stable state.

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

[0078] The transfer functions of the small-signal models of each component in the control system include:

[0079] The transfer functions of the small-signal model of the filter stage and the admittance matrix of the filter inductor; the transfer function of the grid voltage feedforward branch affected by the error of the phase-locked loop (PLL); the transfer function of the positive PARK transform of the current control signal affected by the error of the PLL; the transfer function of the inverse PARK transform of the voltage control signal affected by the PLL error; 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 stage; 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 stage; the transfer function of the small-signal model of the current feedback branch when it is not working under open-loop control; the transfer function of the small-signal model of the modulation stage; the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the PLL 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 and negative-sequence components.

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

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

[0082] Based on the structure of the phase-locked loop (PLL), the transfer function of the PLL small-signal model is established, and the voltage sampling coefficients are used to correct the transfer function of the PLL small-signal model. Based on the corrected transfer function of the PLL small-signal model, the transfer functions of the PLL error affecting the grid voltage feedforward branch, the PLL error affecting the positive PARK transform of the current control signal, and the PLL error affecting the inverse PARK transform of the voltage control signal are determined respectively.

[0083] A dual-orthogonal signal generator is used to separate the fundamental voltage and fundamental current of the signal branch of the phase-locked loop (PLL) in a stationary two-dimensional coordinate system. When the fundamental voltage of the signal branch of the PLL contains only a positive-sequence component, the equivalent filter transfer function in the dq coordinate system is determined. When the fundamental voltage of the signal branch of the grid voltage feedforward branch contains both positive-sequence 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 grid includes a filter inductor, a filter capacitor, a transformer equivalent inductance, a transformer equivalent resistance, an equivalent inductance of the grid connection line, and an equivalent resistance of the grid connection line connected in series.

[0085] When a voltage source inverter is connected to the grid via a filter inductor, the grid connection point is located between the filter inductor and the filter capacitor. The voltage source inverter is connected to an 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] In the formula, Y L1 G is the admittance matrix of the filter inductor in an L-type filter. L1 Z is the transfer function of the small-signal model of the L-type filter. Lf Let L be the filter inductor impedance matrix. f ω0 is the filter inductance, ω0 is the angular frequency of the synchronous rotating coordinate system, and s is the Laplace operator;

[0088] When a voltage source inverter is connected to the grid via a filter inductor and a filter capacitor, the grid connection point is located between the filter capacitor and the equivalent inductance of the transformer. The voltage source inverter is connected to an 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] In the formula, Y L2 G is the admittance matrix of the filter inductor in an LC filter. L2 Y is the transfer function of the small-signal model of an LC filter. Cf C is the admittance matrix of the filter capacitor. f This is the equivalent value of the filter capacitor;

[0091] When a voltage source inverter is connected to the grid via a filter inductor, filter capacitor, and transformer, the grid connection point is located between the equivalent resistance of the transformer and the equivalent inductance of the grid connection line. The voltage source inverter is connected to an 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] In the formula, Y L3 G is the admittance matrix of the filter inductor in an LCL filter. L3 Z is the transfer function of the small-signal model of an LCL filter. LRT Let L be the equivalent inductive branch impedance matrix of the transformer. T R is the equivalent reactance on the low-voltage side of the transformer. T This is the equivalent resistance on the low-voltage side of the transformer.

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

[0095]

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

[0097] Based on the transfer function of the modified phase-locked loop (PLL) small-signal model, and using the voltage sampling coefficients and the steady-state operating point voltage in the ideal rotating coordinate system, the transfer function of the error in the PLL affecting the grid voltage feedforward branch is determined, satisfying the following relationship:

[0098]

[0099] In the formula, The transfer function of the grid voltage feedforward branch is used to explain how the error in the phase-locked loop affects the grid voltage feedforward branch. This refers to the stable operating point voltage in an ideal rotating coordinate system.

[0100] Based on the transfer function of the modified phase-locked loop (PLL) small-signal model, and using the current sampling coefficients and the steady-state operating current in an ideal rotating coordinate system, the transfer function of the positive PARK transform of the current control signal influenced by the error of the PLL is determined, satisfying the following relationship:

[0101]

[0102] In the formula, The transfer function of the positive PARK transform of the current control signal is given by the error of the phase-locked loop (PLL) circuit. ig For current sampling coefficients, This refers to the stable operating point current in an ideal rotating coordinate system.

[0103] Based on the transfer function of the modified phase-locked loop small-signal model, using the voltage sampling coefficients and the voltage setpoint before the inverse PARK transformation, the transfer function of the phase-locked error affecting the inverse PARK transformation of the voltage control signal is determined, satisfying the following relationship:

[0104]

[0105] In the formula, The transfer function of the inverse PARK transform of the voltage control signal is given by the effect of phase-locked loop error. This is the voltage setpoint before the inverse PARK transformation.

[0106] Preferably, the dq-axis component of the grid connection point voltage disturbance is used as the first input signal of the small-signal model of the voltage source inverter; the change in the current reference value is used as the second input signal of the small-signal model of the voltage source inverter, and the change in the current reference value is zero during power open-loop control; the dq-axis component of the grid connection 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 open-loop mode, the equivalent open-loop admittance matrix of the voltage source inverter satisfies the following relationship:

[0108]

[0109] In the formula, Y eq1 Y is the equivalent open-loop admittance matrix of a voltage source inverter. L G is the admittance matrix of the filter inductor in the filter stage. L K is the transfer function of the small-signal model of the filter stage. PWM G is the transfer function of the small-signal model of the modulation stage. del To control the transfer function of the small-signal model of the delay element, The transfer function of the inverse PARK transform of the voltage control signal is given by the effect of phase-locked loop error. The transfer function of the grid voltage feedforward branch is used to explain how the error in the phase-locked loop affects the grid voltage feedforward branch. To explain the transfer function of the positive PARK transform of the current control signal due to the error in the phase-locked loop, G f1 G 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. f2 G 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 and negative-sequence components. cc1 G is the transfer function of the small-signal model of the PI controller within the current control loop. cc2 Let k be the transfer function of the small-signal model of the cross-coupling compensation stage. vp G is the voltage sampling coefficient. sam G is the transfer function of the small-signal model when the current feedback branch is not working under open-loop control. lpv This 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 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 )k ig G sam G lpi ] -1

[0112] In the formula, Y eq2 Let E2 be the equivalent admittance matrix of the current feedback branch, and G be the second-order identity matrix. L K is the transfer function of the small-signal model of the filter stage. PWM G is the transfer function of the small-signal model of the modulation stage. del To control the transfer function of the small-signal model of the delay element, G cc1 G is the transfer function of the small-signal model of the PI controller within the current control loop. cc2 Let k be the transfer function of the small-signal model of the cross-coupling compensation stage. ig G is the current sampling coefficient. sam G is the transfer function of the small-signal model when the current feedback branch is not working under open-loop control. lpi This 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 voltage disturbance at the grid connection point and the current disturbance at the grid connection point satisfy the following relationship:

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

[0115] In the formula, Δu pdq Let Δi be the dq-axis component of the grid connection point voltage disturbance. gdq Y represents the dq-axis component of the grid connection point current disturbance. 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 a voltage source inverter using an L-type filter in the complex frequency domain satisfies the following relationship:

[0117]

[0118] In the formula, Z i-L (s) represents the equivalent impedance matrix of a 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) represents the self-impedance on the d-axis of the equivalent impedance matrix of a voltage-source inverter in the complex frequency domain, Z cdq (s) represents the cross impedance encountered by the q-axis current caused by the d-axis voltage in the equivalent impedance matrix of a voltage source inverter in the complex frequency domain, Z. cqd (s) represents the cross impedance encountered by the d-axis current caused by the q-axis voltage in the equivalent impedance matrix of a voltage source inverter in the complex frequency domain, Z. cqq (s) represents the self-impedance on the q-axis in the equivalent impedance matrix of a voltage source inverter in the complex frequency domain.

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

[0120]

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

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

[0123]

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

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

[0126]

[0127] Z gdd (s) represents the self-impedance on the d-axis of the equivalent impedance matrix of the power grid in the complex frequency domain, Z gdq(s) represents 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) represents 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) represents 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 and q-axis components of the first impedance ratio satisfy the following relationships:

[0129]

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

[0131]

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

[0133]

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

[0135] Preferably, the critical damping coefficient ξ c The following relationship must be satisfied:

[0136]

[0137] In the formula, R s C s L s These 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 and used as a stability evaluation index for grid-type and grid-type converters, satisfying the following relationship:

[0139]

[0140] In the formula, ξ is the oscillation damping coefficient, and PM is the phase margin.

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

[0142] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of a method.

[0143] The beneficial effects of this invention are, at least compared with the prior art, that it can comprehensively analyze the interaction between grid-type and mesh-type converters and their impact on system stability through a joint impedance modeling method, making it applicable to multiple converter operating modes and complex systems, thus having a wider range of applications. Furthermore, by introducing efficient calculation algorithms and numerical methods, this invention significantly reduces the computational complexity of the analysis process. Attached Figure Description

[0144] Figure 1 This is a schematic diagram of the main circuit and control loop of the voltage source inverter in an embodiment of the present invention;

[0145] Figure 2 This is a flowchart of the stability detection method for grid-type and grid-type converters based on impedance modeling proposed in this invention;

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

[0147] Figure 4 This is a block diagram of the small-signal model of the filtering stage 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 This is a block diagram of the small-signal model of the voltage source inverter in an embodiment of the present invention;

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

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

[0152] Figure 9 This is a flowchart of a stability detection process combining impedance ratio and damping characteristics in an embodiment of the present invention. Detailed Implementation

[0153] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this invention. The embodiments described in this application are merely some embodiments of this invention, and not all embodiments. Based on the spirit of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of this invention.

[0154] In the embodiment, the main circuit and control system of the voltage source inverter are as follows: Figure 1 As shown, the inverter side and load side are equivalent to a voltage source driving a load. The control methods of voltage source inverters include current control type and voltage control type. Among them, the control system of voltage control type voltage source inverter includes droop control and virtual synchronization control.

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

[0156] SCF-PLL represents a block diagram of a phase-locked loop.

[0157] This invention proposes a stability detection method for grid-connected and grid-connected converters based on impedance modeling. The grid-connected and grid-connected converters employ voltage source inverters. The control components of a voltage source inverter include, but are not limited to: a filter stage, a current sampling channel, a voltage sampling channel, a control delay stage, a current control loop, a cross-coupling compensation stage, a current feedback branch, a phase-locked loop (PLL), a grid voltage feedforward branch, and a modulation stage. The filter stage, PLL, and grid voltage feedforward branch are crucial and have a significant impact on the impedance modeling process. Therefore, in this embodiment, impedance modeling and stability analysis are performed based on the impedance models of these three stages.

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

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

[0160] The transfer functions of the small-signal models of each component in the control system include: the transfer function G of the small-signal model of the filter component. L The admittance matrix Y of the filter inductor in the filter stage L Errors in the phase-locked loop (PLL) circuit affect the transfer function of the grid voltage feedforward branch. Errors in the phase-locked loop (PLL) affect the transfer function of the positive PARK transform of the current control signal. Phase-locked error affects the transfer function of the inverse PARK transform 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 controlling the delay element. del The transfer function G of the small-signal model of the PI controller within the current control loop. cc1 The transfer function G of the small-signal model of the cross-coupling compensation stage 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 stage 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 and negative-sequence components. f2 ;

[0161] Specifically, step 1 includes:

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

[0163] like Figure 3 As shown, the equivalent circuit of a 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) result in voltage source inverters being connected to different types of filter stages, including:

[0164] When a voltage source inverter is connected to the grid via a filter inductor, and the grid connection point is located at point 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] In the formula, Y L1 G is the admittance matrix of the filter inductor in an L-type filter. L1 Z is the transfer function of the small-signal model of the L-type filter. Lf Let L be the filter inductor impedance matrix. f ω is the filter inductance, ω0 is the angular frequency of the synchronous rotating coordinate system, and s is the Laplace operator.

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

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

[0170]

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

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

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

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

[0175]

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

[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 arm voltage disturbance of the voltage source inverter is... bdq The transfer function G of the small-signal model after filtering L The value obtained later is related to the dq-axis component Δu of the grid connection point voltage disturbance. pdq The admittance matrix Y of the filter inductor in the filter L The sum of the values ​​obtained later is used as the dq-axis component Δi of the grid connection point current disturbance. gdq .

[0178] Step 1.2: Based on the structure of the phase-locked loop (PLL), establish the transfer function of the PLL small-signal model, and correct the transfer function of the PLL small-signal model using voltage sampling coefficients; based on the corrected transfer function of the PLL small-signal model, determine the transfer functions of the PLL error affecting the grid voltage feedforward branch, the PLL error affecting the positive PARK transformation of the current control signal, and the PLL error affecting the inverse PARK transformation of the voltage control signal.

[0179] Phase-locked loops (PLLs) are used to detect the voltage and current phase at the grid connection point to control the inverter's grid-connected power. Since static frequency offset compensation has no effect on small-signal modeling, the small-signal equivalent model of an SRF-PLL (single synchronous phase-locked loop) in a synchronous rotating coordinate system is as follows: Figure 5 As shown. When the grid connection point voltage has abundant harmonic components, considering the dynamic adjustment process based on the PI controller inside the phase-locked loop, there is a dynamic error Δθ.

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

[0181]

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

[0183] The ideal rotating coordinate system is strictly synchronized with the mains voltage, therefore it always contains a certain dynamic error compared to the rotating coordinate system used in the control system. Considering that the error between large signal quantities in the two rotating coordinate systems is negligible, 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 This is the transfer function between voltage disturbance and dynamic error in the phase-locked loop small-signal model.

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

[0187]

[0188] In a phase-locked loop (PLL), the existence of voltage and current sampling coefficients is equivalent to introducing a virtual stable operating point in the control system with values ​​different from those of the actual system. First, the transfer function of the PLL small-signal model is corrected using the voltage sampling coefficients, satisfying the following relationship:

[0189]

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

[0191] Based on the transfer function of the modified phase-locked loop (PLL) small-signal model, and using the voltage sampling coefficients and the steady-state operating point voltage in the ideal rotating coordinate system, the transfer function of the error in the PLL affecting the grid voltage feedforward branch is determined, satisfying the following relationship:

[0192]

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

[0194] Based on the transfer function of the modified phase-locked loop (PLL) small-signal model, and using the current sampling coefficients and the steady-state operating current in an ideal rotating coordinate system, the transfer function of the positive PARK transform of the current control signal influenced by the error of the PLL is determined, satisfying the following relationship:

[0195]

[0196] In the formula, The transfer function of the positive PARK transform of the current control signal is given by the error of the phase-locked loop (PLL) circuit. ig For current sampling coefficients, This is the stable operating point current in an ideal rotating coordinate system.

[0197] Based on the transfer function of the modified phase-locked loop small-signal model, using the voltage sampling coefficients and the voltage setpoint before the inverse PARK transformation, the transfer function of the phase-locked error affecting the inverse PARK transformation of the voltage control signal is determined, satisfying the following relationship:

[0198]

[0199] In the formula, The transfer function of the inverse PARK transform of the voltage control signal is given by the effect of phase-locked loop error. This is the voltage setpoint before the inverse PARK transformation.

[0200] Step 1.3: Using a biorthogonal signal generator, the fundamental voltage and fundamental current on the signal branch of the phase-locked loop (PLL) are separated into positive and negative sequences in a stationary two-dimensional coordinate system. When the fundamental voltage on the signal branch of the PLL contains only a positive-sequence component, the equivalent filter transfer function G in the dq coordinate system is determined. f1 When the fundamental voltage on the signal branch of the grid voltage feedforward branch contains both positive-sequence and negative-sequence components, determine the equivalent filter transfer function G in the dq coordinate system. f2 .

[0201] The Dual Second-Order Generalized Integrator (DSOGI) is a dual second-order generalized integrator that achieves positive and negative order separation.

[0202] In a non-limiting preferred embodiment, considering that the three-phase system has a DC static operating point in the synchronous rotating coordinate system after coordinate transformation, the impedance / admittance model of the three-phase voltage source inverter is essentially a small-signal linearized model at the stable operating point. To ensure the safety of switching devices in actual operation, the current signal fed back to the current controller is the inverter-side filter inductor current; simultaneously, the reference signal of the current controller is calculated based on the active and reactive power in the dispatch instructions, and the phase difference between the grid current and the filter inductor current can be adjusted through static bias compensation. To suppress the influence of the three-phase unbalanced components of the grid voltage on the grid current in the actual system, the signals used in the phase-locked loop and the grid voltage feedforward branch are all filtered. Therefore, based on DSOGI, the positive and negative sequence separation of the signal is achieved in the static two-dimensional coordinate system, satisfying the following relationship:

[0203]

[0204] In the formula, 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, obtain as follows: Figure 6The small-signal model of the voltage source inverter is shown.

[0206] Step 2: When the control system operates in open-loop mode, the grid connection point voltage disturbance is used as the input signal of the small-signal model of the voltage source inverter, and the grid connection point current disturbance is used as the output signal of the small-signal model of the voltage source inverter. The equivalent open-loop admittance matrix of the voltage source inverter is determined using the transfer functions of the small-signal models of each stage along the path from the input signal to the output signal. When the control system operates in closed-loop mode, the grid connection point voltage disturbance is used as the first input signal of the small-signal model of the voltage source inverter, and the change in the current reference value is used as the output signal of the small-signal model of the voltage source inverter. The second input signal of the signal model is the grid connection point current disturbance, which is used as the output signal of the small-signal model of the voltage source inverter. The equivalent admittance matrix of the current feedback branch is determined by using the transfer function of the small-signal model of each link in the path from the first input signal and the second input signal to the output signal. 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. 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 functions and connection relationships of the small-signal models of each stage in the inverter are as follows: Figure 6 As shown.

[0208] Δu pdq The dq-axis component of the grid connection point voltage disturbance is the first input signal of the small-signal model of the voltage source inverter; Δi ref The change in the current reference value is the second input signal of the small-signal model of the voltage source inverter. During open-loop power control, the change in the current reference value is zero; Δi gdq The dq-axis component represents the grid connection 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 effect of the current feedback branch is ignored. The grid connection point voltage disturbance is used as the input signal of the small-signal model of the voltage source inverter, and the grid connection point current disturbance is used as the output signal of the small-signal model of the voltage source inverter. Using the transfer functions of the small-signal models of each link in the path from the input signal to the output signal, the equivalent open-loop admittance matrix of the voltage source inverter is determined, satisfying the following relationship:

[0210]

[0211] In the formula, Y eq1 Y is the equivalent open-loop admittance matrix of a voltage source inverter. L G is the admittance matrix of the filter inductor in the filter stage.L K is the transfer function of the small-signal model of the filter stage. PWM G is the transfer function of the small-signal model of the modulation stage. del To control the transfer function of the small-signal model of the delay element, The transfer function of the inverse PARK transform of the voltage control signal is given by the effect of phase-locked loop error. The transfer function of the grid voltage feedforward branch is used to explain how the error in the phase-locked loop affects the grid voltage feedforward branch. To explain the transfer function of the positive PARK transform of the current control signal due to the error in the phase-locked loop, G f1 G 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. f2 G 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 and negative-sequence components. cc1 G is the transfer function of the small-signal model of the PI controller within the current control loop. cc2 Let k be the transfer function of the small-signal model of the cross-coupling compensation stage. vp G is the voltage sampling coefficient. sam G is the transfer function of the small-signal model when the current feedback branch is not working under open-loop control. lpv This 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 closed-loop mode. Considering the role of the current feedback branch, the grid connection point voltage disturbance is used as the first input signal of the small-signal model of the voltage source inverter, the change in the current reference value is used as the second input signal of the small-signal model of the voltage source inverter, and the grid connection point current disturbance is used as the output signal of the small-signal model of the voltage source inverter. Using the transfer functions of the small-signal models of each link on the path from the first and second input signals to the output signal, the equivalent admittance matrix of the current feedback branch is determined, satisfying the following relationship:

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

[0214] In the formula, Y eq2 Let E2 be the equivalent admittance matrix of the current feedback branch, and G be the second-order identity matrix. L K is the transfer function of the small-signal model of the filter stage.PWM G is the transfer function of the small-signal model of the modulation stage. del To control the transfer function of the small-signal model of the delay element, G cc1 G is the transfer function of the small-signal model of the PI controller within the current control loop. cc2 Let k be the transfer function of the small-signal model of the cross-coupling compensation stage. ig G is the current sampling coefficient. sam G is the transfer function of the small-signal model when the current feedback branch is not working under open-loop control. lpi This 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 a 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 Let Δi be the dq-axis component of the grid connection point voltage disturbance. gdq Y represents the dq-axis component of the grid connection point current disturbance. 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 equation, by 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) represents the equivalent impedance matrix of a 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) represents the self-impedance on the d-axis of the equivalent impedance matrix of a voltage-source inverter in the complex frequency domain, Z cdq(s) represents the cross impedance encountered by the q-axis current caused by the d-axis voltage in the equivalent impedance matrix of a voltage source inverter in the complex frequency domain, Z. cqd (s) represents the cross impedance encountered by the d-axis current caused by the q-axis voltage in the equivalent impedance matrix of a voltage source inverter in the complex frequency domain, Z. cqq (s) represents the self-impedance on the q-axis in the equivalent impedance matrix of a voltage source inverter in the complex frequency domain.

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

[0223]

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

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

[0226]

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

[0228] Step 3: Using the equivalent impedance matrix of the power grid and the equivalent impedance matrix of the voltage source inverter, establish the first impedance ratio, the second impedance ratio, and the 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, 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; 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, 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.

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

[0230]

[0231] Z gdd (s) represents the self-impedance on the d-axis of the equivalent impedance matrix of the power grid in the complex frequency domain, Z gdq (s) represents 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) represents 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) represents 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 R of the first impedance ratio 1d and q-axis component R 1q They respectively satisfy the following relations:

[0233]

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

[0235]

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

[0237]

[0238] First impedance ratio R 1d R 1q Characterizing an equivalent open-loop transfer function, a necessary condition for system stability is that the amplitude-phase frequency response curves of the first impedance ratio on both the d and q channels simultaneously satisfy the Nyquist stability criterion. The second impedance ratio R... 2d R 2q The second impedance ratio characterizes the relationship between harmonic voltages on the grid side and the inverter side, and harmonics of the grid-connected current. Under the combined effect of inverter impedance and grid impedance, the amplitude of the second impedance ratio is the harmonic voltage amplification rate. The third impedance ratio R 3d R 3q The third impedance ratio represents the harmonic current coupling relationship between the two channels d and q. The amplitude of the third impedance ratio is the harmonic current amplification rate of the coupled channel. Therefore, the harmonic current amplification rate of the coupled channel depends on both the main diagonal term and the secondary diagonal term in the impedance matrix.

[0239] In this embodiment, taking the q-channel as an example, the self-impedance Z on the q-axis of the equivalent impedance matrix of the power grid in the complex frequency domain at the intersection frequency is...gqq (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) Equal magnitudes, vector relationship as follows Figure 8 As shown, at the intersection frequency Z gqq (s) When in the "stable region", it exhibits positive resistive-inductive properties. At this time, the self-impedance on the q-axis of the equivalent impedance matrix of the voltage source inverter in the complex frequency domain exhibits negative resistive-capacitive properties, such as... Figure 8 Z in cqq1 In the complex frequency domain, the self-impedance on the q-axis of the equivalent impedance matrix of a voltage source inverter exhibits positive resistivity-capacitance, such as... Figure 8 Z in cqq2 However, as Figure 8 Z in cqq2 As shown, even if the vector is in the "stable region" under this condition, and the first impedance ratio satisfies the Nyquist stability criterion, harmonic resonance instability may still occur under non-unity power factor conditions due to the amplification effect of the second and third impedance ratios on harmonics. Based on the above analysis of the small-signal equivalent circuit and the physical meaning of the impedance ratio, the first impedance ratio satisfying the Nyquist stability criterion is a necessary but not sufficient condition for system stability. It can only be used for rapid initial stability assessment. In harmonic stability analysis, the influence of harmonic amplification represented by the second and third impedance ratios on stability must also be considered. Therefore, as... Figure 9 As shown, the stability test includes:

[0240] The converter is determined to be in a negatively damped state if the first impedance ratio does not meet the Nyquist stability criterion, and in a positively damped or underdamped state if the first impedance ratio meets the Nyquist stability criterion. The product of the second and third impedance ratios is used as the oscillation damping coefficient. If the oscillation damping coefficient is less than zero, the converter is in a negatively damped stable state. If the oscillation damping coefficient is greater than or equal to zero and less than the critical damping coefficient, the converter is in an underdamped stable state. If the oscillation damping coefficient is greater than or equal to the critical damping coefficient, the converter is in a positively damped stable state.

[0241] Critical damping coefficient ξ c The following relationship must be satisfied:

[0242]

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

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

[0245]

[0246] In the formula, ξ is the oscillation damping coefficient, and PM is the phase margin.

[0247] By establishing a detailed impedance model, the behavior of grid-connected and multi-connected converters in complex multi-converter systems can be accurately described, thereby improving the accuracy of system stability analysis. Utilizing impedance modeling methods for stability analysis in the frequency domain allows for comprehensive consideration of the system's response characteristics at different frequencies, providing crucial information for design and optimization. Impedance modeling methods enable real-time and accurate analysis of system stability under dynamic conditions, providing reliable stability assurance for system operation. The impedance modeling stability analysis method of this invention can significantly improve the stability of grid-connected and multi-connected converters in practical applications, promoting the safe and efficient operation of power electronic systems and providing strong technical support for smart grids, renewable energy generation, and electric vehicles.

[0248] Existing converters can utilize impedance-based modeling methods. This approach involves measuring the converter's input and output voltages and currents, and establishing an impedance model based on the relationship between these voltages and currents. Then, by analyzing the converter's impedance model, its stability and performance can be obtained.

[0249] This invention overcomes the shortcomings of existing technologies in terms of model description, applicability, and computational complexity by introducing a stability detection method for grid-type and mesh-type converters based on impedance modeling. It 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, demonstrating significant technical advantages and broad application value.

[0250] This invention also proposes a stability detection system for grid-connected and grid-connected converters based on impedance modeling. The grid-connected and grid-connected converters employ voltage source inverters. The control system of the voltage source inverter includes multiple components, including:

[0251] The impedance modeling module is used to obtain the transfer functions of the small-signal models of each component in the control system. Based on the connection relationships of each component in the control system, it constructs the small-signal model of the voltage source inverter. When the control system operates in open-loop mode, the grid connection point voltage disturbance is used as the input signal of the small-signal model of the voltage source inverter, and the grid connection point current disturbance is used as the output signal. Using the transfer functions of the small-signal models of each component along the path from the input signal to the output signal, the equivalent open-loop admittance matrix of the voltage source inverter is determined. When the control system operates in closed-loop mode, the grid connection... The point voltage disturbance is used as the first input signal of the small-signal model of the voltage source inverter, the change in the current reference value is used as the second input signal of the small-signal model of the voltage source inverter, and the grid connection point current disturbance is used as the output signal of the small-signal model of the voltage source inverter. The equivalent admittance matrix of the current feedback branch is determined by using the transfer function of the small-signal model of each link in the path from the first input signal and the second input signal to the output signal. 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 using the equivalent impedance matrix of the power grid and the equivalent impedance matrix of the voltage source inverter. It then determines 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 negatively damped state. If the first impedance ratio satisfies the Nyquist stability criterion, the converter is determined to be in a positively damped or underdamped state. The product of the second and third impedance ratios is used as the oscillation damping coefficient. If the oscillation damping coefficient is less than zero, the converter is determined to be in a negatively damped 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 positively damped stable state.

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

[0254] The transfer functions of the small-signal models of each component in the control system include:

[0255] The transfer functions of the small-signal model of the filter stage and the admittance matrix of the filter inductor; the transfer function of the grid voltage feedforward branch affected by the error of the phase-locked loop (PLL); the transfer function of the positive PARK transform of the current control signal affected by the error of the PLL; the transfer function of the inverse PARK transform of the voltage control signal affected by the PLL error; 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 stage; 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 stage; the transfer function of the small-signal model of the current feedback branch when it is not working under open-loop control; the transfer function of the small-signal model of the modulation stage; the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the PLL 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 and negative-sequence components.

[0256] Specifically, the transfer function of the small-signal model for obtaining the filter stage includes:

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

[0258] Based on the structure of the phase-locked loop (PLL), the transfer function of the PLL small-signal model is established, and the voltage sampling coefficients are used to correct the transfer function of the PLL small-signal model. Based on the corrected transfer function of the PLL small-signal model, the transfer functions of the PLL error affecting the grid voltage feedforward branch, the PLL error affecting the positive PARK transform of the current control signal, and the PLL error affecting the inverse PARK transform of the voltage control signal are determined respectively.

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

[0260] Specifically, the equivalent circuit of a voltage source inverter connected to the AC grid includes a filter inductor, a filter capacitor, a transformer equivalent inductance, a transformer equivalent resistance, an equivalent inductance of the grid connection line, and an equivalent resistance of the grid connection line, all connected in series.

[0261] When a voltage source inverter is connected to the grid via a filter inductor, the grid connection point is located between the filter inductor and the filter capacitor. The voltage source inverter is connected to an 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] In the formula, Y L1 G is the admittance matrix of the filter inductor in an L-type filter. L1 Z is the transfer function of the small-signal model of the L-type filter. Lf Let L be the filter inductor impedance matrix. f ω0 is the filter inductance, ω0 is the angular frequency of the synchronous rotating coordinate system, and s is the Laplace operator;

[0264] When a voltage source inverter is connected to the grid via a filter inductor and a filter capacitor, the grid connection point is located between the filter capacitor and the equivalent inductance of the transformer. The voltage source inverter is connected to an 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] In the formula, Y L2 G is the admittance matrix of the filter inductor in an LC filter. L2 Y is the transfer function of the small-signal model of an LC filter. Cf C is the admittance matrix of the filter capacitor. f This is the equivalent value of the filter capacitor;

[0267] When a voltage source inverter is connected to the grid via a filter inductor, filter capacitor, and transformer, the grid connection point is located between the equivalent resistance of the transformer and the equivalent inductance of the grid connection line. The voltage source inverter is connected to an 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] In the formula, Y L3 G is the admittance matrix of the filter inductor in an LCL filter. L3 Z is the transfer function of the small-signal model of an LCL filter. LRT Let L be the equivalent inductive branch impedance matrix of the transformer. T R is the equivalent reactance on the low-voltage side of the transformer. T This is the equivalent resistance on the low-voltage side of the transformer.

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

[0271]

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

[0273] Based on the transfer function of the modified phase-locked loop (PLL) small-signal model, and using the voltage sampling coefficients and the steady-state operating point voltage in the ideal rotating coordinate system, the transfer function of the error in the PLL affecting the grid voltage feedforward branch is determined, satisfying the following relationship:

[0274]

[0275] In the formula, The transfer function of the grid voltage feedforward branch is used to explain how the error in the phase-locked loop affects the grid voltage feedforward branch. This refers to the stable operating point voltage in an ideal rotating coordinate system.

[0276] Based on the transfer function of the modified phase-locked loop (PLL) small-signal model, and using the current sampling coefficients and the steady-state operating current in an ideal rotating coordinate system, the transfer function of the positive PARK transform of the current control signal influenced by the error of the PLL is determined, satisfying the following relationship:

[0277]

[0278] In the formula, The transfer function of the positive PARK transform of the current control signal is given by the error of the phase-locked loop (PLL) circuit. ig For current sampling coefficients, This refers to the stable operating point current in an ideal rotating coordinate system.

[0279] Based on the transfer function of the modified phase-locked loop small-signal model, using the voltage sampling coefficients and the voltage setpoint before the inverse PARK transformation, the transfer function of the phase-locked error affecting the inverse PARK transformation of the voltage control signal is determined, satisfying the following relationship:

[0280]

[0281] In the formula, The transfer function of the inverse PARK transform of the voltage control signal is given by the effect of phase-locked loop error. This is the voltage setpoint before the inverse PARK transformation.

[0282] Specifically, the dq-axis component of the grid connection point voltage disturbance is used as the first input signal of the small-signal model of the voltage source inverter; the change in the current reference value is used as the second input signal of the small-signal model of the voltage source inverter, and the change in the current reference value is zero during power open-loop control; the dq-axis component of the grid connection 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] In the formula, Y eq1 Y is the equivalent open-loop admittance matrix of a voltage source inverter. L G is the admittance matrix of the filter inductor in the filter stage. L K is the transfer function of the small-signal model of the filter stage. PWM G is the transfer function of the small-signal model of the modulation stage. del To control the transfer function of the small-signal model of the delay element, The transfer function of the inverse PARK transform of the voltage control signal is given by the effect of phase-locked loop error. The transfer function of the grid voltage feedforward branch is used to explain how the error in the phase-locked loop affects the grid voltage feedforward branch. To explain the transfer function of the positive PARK transform of the current control signal due to the error in the phase-locked loop, G f1 G 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. f2 G 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 and negative-sequence components. cc1 G is the transfer function of the small-signal model of the PI controller within the current control loop. cc2 Let k be the transfer function of the small-signal model of the cross-coupling compensation stage. vp G is the voltage sampling coefficient. sam G is the transfer function of the small-signal model when the current feedback branch is not working under open-loop control. lpv This 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 )k ig G sam G lpi ] -1

[0288] In the formula, Y eq2 Let E2 be the equivalent admittance matrix of the current feedback branch, and G be the second-order identity matrix. L K is the transfer function of the small-signal model of the filter stage. PWM G is the transfer function of the small-signal model of the modulation stage. del To control the transfer function of the small-signal model of the delay element, G cc1 G is the transfer function of the small-signal model of the PI controller within the current control loop. cc2 Let k be the transfer function of the small-signal model of the cross-coupling compensation stage. ig G is the current sampling coefficient. sam G is the transfer function of the small-signal model when the current feedback branch is not working under open-loop control. lpi This 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 a 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 Let Δi be the dq-axis component of the grid connection point voltage disturbance. gdq Y represents the dq-axis component of the grid connection point current disturbance. 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 a 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) represents the equivalent impedance matrix of a 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) represents the self-impedance on the d-axis of the equivalent impedance matrix of a voltage-source inverter in the complex frequency domain, Z cdq (s) represents the cross impedance encountered by the q-axis current caused by the d-axis voltage in the equivalent impedance matrix of a voltage source inverter in the complex frequency domain, Z. cqd (s) represents the cross impedance encountered by the d-axis current caused by the q-axis voltage in the equivalent impedance matrix of a voltage source inverter in the complex frequency domain, Z. cqq (s) represents the self-impedance on the q-axis in the equivalent impedance matrix of a voltage source inverter in the complex frequency domain.

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

[0296]

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

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

[0299]

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

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

[0302]

[0303] Z gdd (s) represents the self-impedance on the d-axis of the equivalent impedance matrix of the power grid in the complex frequency domain, Z gdq(s) represents 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) represents 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) represents 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 and q-axis components of the first impedance ratio satisfy the following relationships:

[0305]

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

[0307]

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

[0309]

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

[0311] Specifically, the critical damping coefficient ξ c The following relationship must be satisfied:

[0312]

[0313] In the formula, R s C s L s These 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 and used as a stability evaluation index for grid-type and mesh-type converters, satisfying the following relationship:

[0315]

[0316] In the formula, ξ is the oscillation damping coefficient, and PM is the phase margin.

[0317] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0318] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination of the foregoing. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

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

[0320] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status 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 the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving 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., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0321] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A method for detecting stability of a grid-following and grid-forming converter based on impedance modeling, the grid-following and grid-forming converter employing a voltage source inverter, a control system of the voltage source inverter including a plurality of loops, characterized in that, The method comprises the following steps: obtaining the transfer functions of the small signal models of each link in the control system, and constructing a 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, taking the grid point voltage disturbance as the input signal of the small signal model of the voltage source inverter, taking the grid point current disturbance as the output signal of the small signal model of the voltage source inverter, and determining the equivalent open loop admittance matrix of the voltage source inverter by using the transfer functions of the small signal models of each link on the path from the input signal to the output signal; when the control system operates in a closed loop mode, taking the grid point voltage disturbance as the first input signal of the small signal model of the voltage source inverter, taking the current reference value change as the second input signal of the small signal model of the voltage source inverter, taking the grid point current disturbance as the output signal of the small signal model of the voltage source inverter, and determining the equivalent admittance matrix of the current feedback branch by using the transfer functions of the small signal models of each link on the path from the first input signal and the second input signal to the output signal; taking 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 as the impedance matrix of the voltage source inverter; establishing the first impedance ratio, the second impedance ratio and the third impedance ratio by using the equivalent impedance matrix of the grid and the equivalent impedance matrix of the voltage source inverter; determining whether the first impedance ratio satisfies the Nyquist stability criterion, if the first impedance ratio does not satisfy the Nyquist stability criterion, it is determined that the converter is in a negative damping state; if the first impedance ratio satisfies the Nyquist stability criterion, it is determined that the converter is in a positive damping state or an under-damped state; taking 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, it is determined 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, it is determined that the converter is in an under-damped stable state, and if the oscillation damping coefficient is greater than or equal to the critical damping coefficient, it is determined that the converter is in a positive damping stable state.

2. The impedance modeling-based grid-connected and grid-forming converter stability detection method according to claim 1, wherein the control system of the voltage source inverter comprises: 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. The transfer functions of the small signal models of each link in the control system comprise: ​ The transfer function of the small signal model of the filter link and the admittance matrix of the filter inductance 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 error of the phase-locked loop 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 of the current feedback branch when 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 only contains the positive sequence component, 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 the positive sequence component and the negative sequence component.

3. The impedance modeling-based grid-connected and grid-forming converter stability detection method according to claim 2, characterized in that, the transfer function of the small signal model of the filter link comprises: based on the equivalent circuit of the voltage source inverter connected to the AC power grid, determining the filter type according to the grid connection point position of the voltage source inverter, obtaining the transfer function of the small signal model of the determined type of filter and the admittance matrix of the filter inductance in the determined type of filter; based on the structure of the phase-locked loop, establishing the transfer function of the small signal model of the phase-locked loop, and correcting the transfer function of the small signal model of the phase-locked loop using the voltage sampling coefficient; based on the corrected transfer function of the small signal model of the phase-locked loop, determining 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 error of the phase-locked loop affecting the inverse PARK transformation of the voltage control signal; using a biorthogonal signal generator, separating the positive and negative sequences of the fundamental voltage and the fundamental current on the signal branch of the phase-locked loop link in the stationary two-dimensional coordinate system, determining the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the phase-locked loop link only contains the positive sequence component, and determining 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 the positive sequence component and the negative sequence component.

4. The impedance modeling-based grid-connected and grid-forming converter stability detection method according to claim 3, characterized in that, the equivalent circuit of the voltage source inverter connected to the AC power grid comprises a series-connected filter inductance, filter capacitance, transformer equivalent inductance, transformer equivalent resistance, equivalent inductance of the grid connection line, and equivalent resistance of the grid connection line. The voltage source inverter is connected to the grid point through a filter inductor, and the grid point is located between the filter inductor and a filter capacitor, and the voltage source inverter is connected to an L-type filter; the transfer function of a small signal model of the L-type filter and a conductance matrix of the filter inductor in the L-type filter satisfy the following relationship: where Y L1 is the admittance matrix of the filter inductors, G L1 is the transfer function of the small-signal model of the L-type filter, Z Lf is the impedance matrix of the filter inductors, L f is the filter inductors, and ω0is the angular frequency of the synchronous rotating coordinate system, and s is the Laplace operator. The voltage source inverter is connected to the grid point through a filter inductor and a filter capacitor, and the grid point is located between the filter capacitor and an equivalent inductor of a transformer, and the voltage source inverter is connected to an LC-type filter; the transfer function of a small signal model of the LC-type filter and a conductance matrix of the filter inductor in the LC-type filter satisfy the following relationship: where Y L2 is the admittance matrix of the filter inductances, G L2 is the transfer function of the small-signal model of the LC filter, Y Cf is the admittance matrix of the filter capacitances, C f is the equivalent value of the filter capacitances; The voltage source inverter is connected to the grid point through a filter inductor, a filter capacitor and a transformer, and the grid point is located between an equivalent resistance of the transformer and an equivalent inductor of a grid line, and the voltage source inverter is connected to an LCL-type filter; the transfer function of a small signal model of the LCL-type filter and a conductance matrix of the filter inductor in the LCL-type filter satisfy the following relationship: In the formula, Y L3 is the admittance matrix of the filter inductance in the LCL type filter, G L3 is the transfer function of the small signal model of the LCL type filter, Z LRT is the equivalent inductive branch impedance matrix of the transformer, L T is the equivalent reactance on the low voltage side of the transformer, R T is the equivalent resistance on the low voltage side of the transformer.

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

6. The impedance modeling-based grid-connected and grid-forming converter stability detection method according to claim 2, characterized in that, The dq-axis components of the grid point voltage disturbance are 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 when the power is open-loop controlled; The dq-axis components of the grid point current disturbance are used as the output signal of the small signal model of the voltage source inverter.

7. The impedance modeling-based grid-connected and grid-forming converter stability detection method according to claim 6, characterized in that, When the control system operates in an open-loop mode, the equivalent open-loop conductance 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 section, G L is the transfer function of the small-signal model of the filter section, K PWM is the transfer function of the small-signal model of the modulation section, G del is the transfer function of the small-signal model of the control delay section, is the transfer function of the phase-locked error influence on the voltage control signal reverse PARK transformation, is the transfer function of the phase-locked loop section error influence on the grid voltage feedforward branch, is the transfer function of the phase-locked loop section error influence on the current control signal positive PARK transformation, 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 section only contains positive sequence components, 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 section, k vp is the voltage sampling coefficient, G sam is the transfer function of the small-signal model when the current feedback branch does not work 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 impedance modeling-based grid-connected and grid-forming converter stability detection method according to claim 7, characterized in that, When the control system operates in a closed-loop mode, the equivalent conductance 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, E2is the second order identity matrix, G L is the transfer function of the small signal model of the filter section, K PWM is the transfer function of the small signal model of the modulation section, G del is the transfer function of the small signal model of the control delay section, G cc1 is the transfer function of the small signal model of the PI controller within the current control loop, G cc2 is the transfer function of the small signal model of the cross-coupling compensation section, k ig is the current sampling coefficient, G sam is the transfer function of the small signal model of the current feedback branch when not active 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 impedance modeling-based grid-connected and grid-forming converter stability detection method according to claim 8, characterized in that, Based on the small signal model of voltage source inverter, the grid voltage disturbance and the grid current disturbance satisfy the following relationship: Δi gdq = Y eq2 (s) Y eq1 (s) Δu pdq where Δu pdq is the dq-axis component of the grid point voltage disturbance, Δi gdq is the dq-axis component of the grid point current disturbance, 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 impedance modeling based grid-following and grid-forming converter stability detection method of claim 9, wherein, The equivalent impedance matrix of the voltage source inverter using L-type filter in complex frequency domain satisfies the following relationship: wherein Z i-L (s) is the equivalent impedance matrix of the voltage source inverter with L-type filter in 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 d-axis in the equivalent impedance matrix of the voltage source inverter in 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 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 complex frequency domain, Z cqq (s) is the self-impedance on q-axis in the equivalent impedance matrix of the voltage source inverter in complex frequency domain.

11. The impedance modeling based grid-following and grid-forming converter stability detection method of claim 10, wherein, When the voltage source inverter is connected to the grid point through a filter inductor and a filter capacitor, the equivalent impedance matrix of the voltage source inverter in the complex frequency domain based on the LC filter satisfies the following relationship: i-LC Z = -jωL + 1 / jωC wherein Z i-LC (s) is the equivalent impedance matrix of the voltage source inverter with LC filter in the complex frequency domain, Y Cf is the filter capacitance admittance matrix; When the voltage source inverter is connected to the grid point through a filter inductor, a filter capacitor and a transformer, the equivalent impedance matrix of the voltage source inverter in the complex frequency domain based on the LCL filter satisfies the following relationship: i-LCL ​ In the formula, Z i-LCL is the equivalent impedance matrix of the voltage source inverter with 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 impedance modeling based grid-following and grid-forming converter stability detection method of claim 11, wherein, The equivalent impedance matrix of the 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 satisfy the following relationship respectively: The d-axis component and the q-axis component of the second impedance ratio satisfy the following relationship respectively: The d-axis component and the q-axis component of the third impedance ratio satisfy the following relationship respectively: wherein R 1d , R 1q are the d-axis and q-axis components of the first impedance ratio, respectively, R 2d , R 2q are the d-axis and q-axis components of the second impedance ratio, respectively, and R 3d , R 3q are the d-axis and q-axis components of the third impedance ratio, respectively.

13. The impedance modeling based grid-following and grid-forming converter stability detection method of claim 1, wherein, Critical damping coefficient ξ c satisfies the following relationship: where R s , C s , and L s are the equivalent resistance, equivalent capacitance, and equivalent inductance of the power grid, respectively.

14. The impedance modeling based grid-following and grid-forming converter stability detection method of claim 1, wherein, The phase margin calculated by the oscillation damping coefficient is used as the grid-following and grid-forming converter stability evaluation index, and the following relationship is satisfied: In the formula, ξ is the oscillation damping coefficient, and PM is the phase margin.

15. An impedance modeling-based grid-connected and grid-forming converter stability detection system, the grid-connected and grid-forming converter employing a voltage source inverter, the control system of the voltage source inverter including a plurality of loops, characterized by, The impedance modeling module is configured to obtain the transfer functions of the small signal models of the links in the control system, and construct the small signal model of the voltage source inverter according to the connection relationship of the links in the control system; when the control system operates in the open loop mode, the grid voltage disturbance is used as the input signal of the small signal model of the voltage source inverter, the grid current disturbance is used as the output signal of the small signal model of the voltage source inverter, and the transfer functions of the small signal models of the links on the path from the input signal to the output signal are 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 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 grid current disturbance is used as the output signal of the small signal model of the voltage source inverter; the transfer functions of the small signal models of the links on the path from the first input signal and the second input signal to the output signal are 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; ​ The stability detection module is configured 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; 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 under-damping state; The product of the second impedance ratio and the third impedance ratio is taken as an oscillation damping coefficient; if the oscillation damping coefficient is less than zero, it is determined 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, it is determined that the converter is in an under-damping stable state; if the oscillation damping coefficient is greater than or equal to the critical damping coefficient, it is determined that the converter is in a positive damping stable state.

16. The impedance modeling-based grid-following and grid-forming converter stability detection system according to claim 15, wherein The control system of the voltage source inverter comprises a filter link, a phase-locked loop link, a power 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; The transfer functions of the small-signal models of the links in the control system include: the transfer function of the small-signal model of the filter link and the admittance matrix of the filter inductance of the filter link, the transfer function of the error influence of the phase-locked loop link on the power grid voltage feedforward branch, the transfer function of the error influence of the phase-locked loop link on the positive PARK transformation of the current control signal, the transfer function of the error influence of the phase-locked loop on the inverse PARK transformation of the voltage control signal, the transfer function of the low-pass filter in the current sampling channel, the transfer function of the low-pass filter in 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 of the current feedback branch 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 only contains positive sequence components, and the equivalent filter transfer function in the dq coordinate system when the fundamental voltage on the signal branch of the power grid voltage feedforward branch contains both positive sequence components and negative sequence components.

17. The impedance modeling-based grid-following and grid-forming converter stability detection system according to claim 16, wherein The acquisition of the transfer function of the small-signal model of the filter link comprises: based on the equivalent circuit of the voltage source inverter connected to the AC power grid, determining the type of the filter according to the grid-connected point position of the voltage source inverter, and acquiring the transfer function of the small-signal model of the filter of the determined type and the admittance matrix of the filter inductance of the determined type of filter; 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 by 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 affecting the voltage feedforward branch of the power grid, the transfer function of the error of the phase-locked loop affecting the positive PARK transformation of the current control signal, and the transfer function of the error of the phase-locked loop affecting the inverse PARK transformation of the voltage control signal are determined respectively; Adopting a dual-orthogonal signal generator, the fundamental voltage and the fundamental current on the signal branch of the phase-locked loop are separated into positive and negative sequences in a stationary two-dimensional coordinate system. When the fundamental voltage on the signal branch of the phase-locked loop only contains a positive sequence component, the equivalent filtering transfer function in the dq coordinate system is determined. When the fundamental voltage on the signal branch of the power grid voltage feedforward branch contains both positive and negative sequence components, the equivalent filtering transfer function in the dq coordinate system is determined.

18. The impedance modeling-based grid-connected and grid-forming converter stability detection system of claim 17, wherein, The equivalent circuit of the voltage source inverter connected to the AC power grid includes a filter inductor, a filter capacitor, a transformer equivalent inductance, a transformer equivalent resistance, an equivalent inductance 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 point through the filter inductor, the grid point is located between the filter inductor and the filter capacitor, and the voltage source inverter is connected to an 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 inductances, G L1 is the transfer function of the small-signal model of the L-type filter, Z Lf is the impedance matrix of the filter inductances, L f is the filter inductance, ω0is 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 point through the filter inductor and the filter capacitor, the grid point is located between the filter capacitor and the transformer equivalent inductance, and the voltage source inverter is connected to an LC-type filter; the transfer function of the small signal model of the LC-type filter and the admittance matrix of the filter inductor in the LC-type filter satisfy the following relationship: where Y L2 is the admittance matrix of the filter inductances, G L2 is the transfer function of the small-signal model of the LC filter, Y Cf is the admittance matrix of the filter capacitances, C f is the equivalent value of the filter capacitances; When the voltage source inverter is connected to the grid point through the filter inductor, the filter capacitor, and the transformer, the grid point is located between the transformer equivalent resistance and the equivalent inductance of the grid-connected line, and the voltage source inverter is connected to an LCL-type filter; the transfer function of the small signal model of the LCL-type filter and the admittance matrix of the filter inductor in the LCL-type filter satisfy the following relationship: wherein Y L3 is the admittance matrix of the filter inductances in the LCL filter, G L3 is the transfer function of the small-signal model of the LCL filter, Z LRT is the equivalent inductive branch impedance matrix of the transformer, L T is the equivalent reactance at the low-voltage side of the transformer, R T is the equivalent resistance at the low-voltage side of the transformer.

19. The impedance modeling-based grid-connected and grid-forming converter stability detection system of claim 17, wherein, 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 G is a transfer function of the modified phase-locked loop small signal model, PI-PLL G is a transfer function between the voltage disturbance and the dynamic error in the phase-locked loop small signal model, s is a Laplace operator, k is a d-axis component of the stable working point voltage in the ideal rotating coordinate system, vp is a 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 affecting the voltage feedforward branch of the power grid is determined by using the voltage sampling coefficient and the stable operating point voltage in the ideal rotating coordinate system, and satisfies the following relationship: In the formula, is the transfer function of the error influence branch of the grid voltage feedforward of the phase-locked loop, is the voltage of the stable working point in the ideal rotating coordinate system. 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 affecting the positive PARK transformation of the current control signal is determined by using the current sampling coefficient and the stable operating point current in the ideal rotating coordinate system, and satisfies the following relationship: In the formula, is the transfer function of the error influence current control signal positive PARK transformation for the phase-locked loop link, k ig is the current sampling coefficient, is the stable working 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 transfer function of the phase-locked error affecting the inverse PARK transformation of the voltage control signal is determined by using the voltage sampling coefficient and the given value of the voltage before the inverse PARK transformation, and the following relationship is satisfied: wherein is the transfer function of the voltage control signal influenced by the phase locked error for the inverse PARK transformation, is the voltage reference before the inverse PARK transformation.

20. The impedance modeling based grid-following and grid-forming converter stability detection system of claim 16, wherein, the dq-axis components of the grid point voltage disturbance are taken as the first input signals of the small signal model of the voltage source inverter; the current reference value variation is taken as the second input signal of the small signal model of the voltage source inverter, and the current reference value variation is zero in the power open-loop control; the dq-axis components of the grid point current disturbance are taken as the output signals of the small signal model of the voltage source inverter.

21. The impedance modeling based grid-following and grid-forming converter stability detection system of claim 20, wherein, when the control system operates in the 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 section, G L is the transfer function of the small-signal model of the filter section, K PWM is the transfer function of the small-signal model of the modulation section, G del is the transfer function of the small-signal model of the control delay section, is the transfer function of the phase-locked error influence on the voltage control signal reverse PARK transformation, is the transfer function of the phase-locked loop section error influence on the grid voltage feedforward branch, is the transfer function of the phase-locked loop section error influence on the current control signal positive PARK transformation, 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 section only contains positive sequence components, 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 section, k vp is the voltage sampling coefficient, G sam is the transfer function of the small-signal model when the current feedback branch does not work 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 impedance modeling based grid-following and grid-forming converter stability detection system of claim 21, wherein, when the control system operates in the 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, E2is the second order identity matrix, G L is the transfer function of the small signal model of the filter section, K PWM is the transfer function of the small signal model of the modulation section, G del is the transfer function of the small signal model of the control delay section, G cc1 is the transfer function of the small signal model of the PI controller within the current control loop, G cc2 is the transfer function of the small signal model of the cross-coupling compensation section, k ig is the current sampling coefficient, G sam is the transfer function of the small signal model of the current feedback branch when not active 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 impedance modeling based grid-following and grid-forming converter stability detection system of claim 22, wherein, based on the small signal model of the voltage source inverter, the grid point voltage disturbance and the grid point current disturbance satisfy the following relationship: Δi gdq = Y eq2 (s) Y eq1 (s) Δu pdq where Δu pdq is the dq-axis component of the grid point voltage disturbance, Δi gdq is the dq-axis component of the grid point current disturbance, 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 impedance modeling based grid-following and grid-forming converter stability detection system of claim 23, wherein, the equivalent impedance matrix of the voltage source inverter using the L-type filter in the complex frequency domain satisfies the following relationship: wherein Z i-L (s) is the equivalent impedance matrix of the voltage source inverter with L-type filter in 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 d-axis in the equivalent impedance matrix of the voltage source inverter in 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 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 complex frequency domain, Z cqq (s) is the self-impedance on q-axis in the equivalent impedance matrix of the voltage source inverter in complex frequency domain.

25. The impedance modeling based grid-following and grid-forming converter stability detection system of claim 24, wherein, When the voltage source inverter is connected to the grid point through a filter inductor and a filter capacitor, the equivalent impedance matrix of the voltage source inverter in the complex frequency domain based on the LC filter satisfies the following relationship: i-LC Z = -jωL + 1 / jωC wherein Z i-LC (s) is the equivalent impedance matrix of the voltage source inverter with LC filter in the complex frequency domain, Y Cf is the filter capacitance admittance matrix; When the voltage source inverter is connected to the grid point through a filter inductor, a filter capacitor and a transformer, the equivalent impedance matrix of the voltage source inverter based on the LCL filter in the complex frequency domain satisfies the following relationship: i-LCL Z In the formula, Z i-LCL is the equivalent impedance matrix of the voltage source inverter with 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 impedance modeling based grid-following and grid-forming converter stability detection system of claim 25, wherein, the equivalent impedance matrix of the 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 satisfy the following relationships, respectively: the d-axis component and the q-axis component of the second impedance ratio satisfy the following relationships, respectively: the d-axis component and the q-axis component of the third impedance ratio satisfy the following relationships, respectively: where R 1d , R 1q are the d-axis and q-axis components of the first impedance ratio, respectively, R 2d , R 2q are the d-axis and q-axis components of the second impedance ratio, respectively, and R 3d , R 3q are the d-axis and q-axis components of the third impedance ratio, respectively.

27. The impedance modeling based grid-following and grid-forming converter stability detection system of claim 15, wherein, Critical damping coefficient ξ c satisfies the following relationship: where R s , C s , and L s are the equivalent resistance, equivalent capacitance, and equivalent inductance of the power grid, respectively.

28. The impedance modeling based grid-following and grid-forming converter stability detection system of claim 15, wherein, the phase margin calculated by the oscillation damping coefficient is taken as the stability evaluation index of the grid-following and grid-forming converter, and the following relationship is satisfied: wherein, 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 configured to store instructions; the processor is configured to operate according to the instructions to perform the steps of the method of any one of claims 1-14.

30. A computer readable storage medium having stored thereon a computer program, characterized in that, The program, when executed by the processor, implements the steps of the method of any of claims 1-14.

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