Grid-connected inverter stability judgment method based on voltage stability and small signal stability

Abstract

The application discloses a grid-connected inverter stability judging method based on voltage stability and small signal stability, and belongs to the field of stability analysis of the grid-connected inverter. The judging method comprises the following steps: analyzing the grid-connected inverter port voltage level containing the grid impedance to obtain the voltage stability domain of the normal working mode of the inverter; maintaining the inverter working point voltage in the stability domain through the reactive power compensation measure, measuring the sequence impedance of the gray-box inverter under different grid strengths; training the neural network model by using the sequence impedance measurement data, obtaining the sequence impedance surface of the grid-connected inverter with the grid strength change according to the proxy model; and judging the stability of the grid-connected inverter to obtain the small signal stability domain of the inverter. The stability judging method simultaneously considers the voltage stability and the small signal stability, and does not need to repeatedly measure the inverter impedance on line in the case that the internal control of the inverter is unknown.

Description

Technical Field

[0001] This invention belongs to the field of stability analysis of grid-connected inverters, and specifically relates to a method for determining the stability of grid-connected inverters based on voltage stability and small-signal stability. Background Technology

[0002] When different types of faults and disturbances occur in the power system, the voltage at the inverter's grid connection point will experience corresponding drops or rises, and there are certain requirements regarding the voltage range of the grid connection point. Therefore, it is necessary to analyze the output voltage of the grid-connected inverter. If this voltage exceeds the required range, measures need to be taken to maintain the grid connection point voltage, such as on-load tap-changing transformers and reactive power compensation. Due to the confidentiality of core technologies by manufacturers, the control structure of grid-connected inverters on the market cannot be obtained through theoretical analysis. In weak grid environments, the stability of gray-box model inverters cannot be theoretically verified.

[0003] Reference 1, "Yu L, Sun H, Xu S, Zhao B, et al. A Critical System Strength Evaluation of a Power System with High Penetration of Renewable Energy Generations[J]. CSEE Journal of Power and Energy Systems, 2022, 8(3): 710-720," quantifies the short-circuit ratio and grid impedance ratio to measure the strength of a power system. Through static voltage stability analysis, a mathematical expression for the critical short-circuit ratio considering the influence of grid impedance ratio is derived. However, the static voltage stability boundary may exceed the actual operating boundary of the grid-connected inverter. In practical applications, the inverter may enter a fault mode before reaching the static voltage stability boundary.

[0004] Reference 2, "Zhang M, Wang X, Yang D, et al. Artificial Neural Network Based Identification of Multi-Operating-Point Impedance Model[J].IEEE Transactions on Power Electronics, 2020: 1-1," proposes using a neural network to train inverter dq impedance data collected at multiple system steady-state operating points to establish an inverter impedance model considering changes in operating point. However, in practical applications, various measures are taken to ensure that the steady-state operating point of the inverter does not change significantly.

[0005] In summary, existing stability analyses of grid-connected inverters have the following problems:

[0006] 1) In practical applications, the output voltage range of grid-connected inverters is limited. Exceeding this range will cause the inverter to enter an abnormal working mode and shut down.

[0007] 2) After measures are taken to maintain the steady-state operating point of the inverter, the impedance of the grid-connected inverter will change. Summary of the Invention

[0008] This invention provides a method for judging the stability of grid-connected inverters based on voltage stability and small-signal stability, which is used to solve the problem of judging the stability of gray-box grid-connected inverters under different grid strengths.

[0009] To address the technical challenges of this invention, a stability assessment method for grid-connected inverters based on voltage stability and small-signal stability is proposed. The topology involved in the stability assessment method includes a power grid, a grid-connected inverter, and an impedance measurement and calculation unit. The impedance measurement and calculation unit includes a sampling unit, an impedance calculation unit, and a neural network unit. The sampling unit is connected to the common coupling point (PCC) connecting the power grid and the grid-connected inverter, and its output is connected to the input of the impedance calculation unit. The neural network unit is connected to the output of the impedance calculation unit.

[0010] The stability determination method includes the following steps:

[0011] Step 1: Let the fundamental frequency of the grid-connected inverter be the fundamental frequency f0, and the rated output voltage of the grid-connected inverter be the rated output voltage U. N The minimum output voltage of a grid-connected inverter in normal operating mode is the minimum output voltage U. min ;

[0012] Step 2, let the relationship between the output voltage of the grid-connected inverter and the grid impedance be:

[0013]

[0014] in:

[0015]

[0016] In the formula, U is the actual output voltage of the grid-connected inverter, λ1 is the first variable of voltage sensitivity, λ2 is the second variable of voltage sensitivity, P is the output active power of the grid-connected inverter, Q is the output reactive power of the grid-connected inverter, S is the apparent power of the grid-connected inverter, X is the inductive reactance value in the grid impedance, R is the impedance value in the grid impedance, and SCR is the short-circuit ratio.

[0017] Step 3: Set the grid impedance ratio GIR = X / R to a constant value, the active power P and reactive power Q of the grid-connected inverter to constant values, and the actual output voltage U of the grid-connected inverter to the minimum output voltage U.min Substituting into the formula in step 2, the voltage stability critical short-circuit ratio (SCR) is calculated. V The voltage stability region of the grid-connected inverter under normal operating conditions is denoted as the voltage stability region Ω. V Ω V =[SCR V ,+∞];

[0018] Step 4: Set the short-circuit ratio range for impedance measurement, collect the sequence impedance data of the grid-connected inverter, and train a neural network model using the sequence impedance measurement data. Based on the surrogate model, obtain the sequence impedance surface of the grid-connected inverter under varying grid intensity. The specific steps are as follows:

[0019] Step 4.1, Setting the measurement parameters:

[0020] Set the short-circuit ratio range for impedance measurement to [SCR]. min SCR max ], frequency range [f min f max ], of which SCR min SCR is the lower limit of the short-circuit ratio for impedance measurement. max f is the upper limit of the short-circuit ratio for impedance measurement. min As the lower limit of frequency, f max This is the upper limit of the frequency.

[0021] In the short-circuit ratio measurement range [SCR] min SCR max Within a given interval of ε0, the measured short-circuit ratio is set, and the measured short-circuit ratios are recorded sequentially from smallest to largest as SCR. m Where m = 1, 2, ..., M, M is the number of short-circuit ratio measurements; in the frequency range [f min f max Within a given interval τ0, disturbance frequencies are set at equal intervals, and these frequencies are recorded as f in ascending order. n , where n = 1, 2, ..., N, and N is the number of perturbation frequencies;

[0022] Step 4.2, if the short-circuit ratio (SCR) is measured... m Not within the voltage stability range Ω V If the grid-connected inverter is determined to be operating in an abnormal working mode, proceed to step 4.3; otherwise, proceed directly to step 4.4.

[0023] Step 4.3: Add a reactive power compensation device to maintain the output port voltage of the grid-connected inverter;

[0024] Set reactive power compensation standard γ = U C / U N U cThe output voltage of the grid-connected inverter after power compensation;

[0025] Calculate the reactive power compensation capacity Q Em And let Q be... Em For positive values, the formula is:

[0026] (1+GIR 2 )Q Em 2 -2γ 2 μGIRQ Em =-(1+GIR) 2 )P 2 +2γ 2 μP+γ 2 μ 2 -γ 4 μ 2

[0027] Where μ is an intermediate variable.

[0028] Step 4.4, in a measurement of the short-circuit ratio (SCR) m Below, a disturbance frequency of f is injected into the common coupling point PCC. n The voltage disturbance is measured and the short-circuit ratio (SCR) is acquired by the sampling unit. m The lower perturbation frequency is f n The voltage and current responses;

[0029] Step 4.5, following the method in Step 4.4, for each measured short-circuit ratio (SCR) m The frequency f of each disturbance is measured below. n The voltage and current responses under different conditions are analyzed to obtain M×N sets of voltage and current response data;

[0030] Input the voltage and current response data of M×N groups into the impedance calculation unit, and output the measured impedance Z of M×N grid-connected inverters. mn Record each measured impedance Z mn Amplitude |Z| mn and measuring impedance Z mn phase θ mn ;

[0031] Step 4.6, measure the short-circuit ratio (SCR) m Disturbance frequency f n Amplitude |Z| mn and phase θ mn The input neural network unit trains the RBF neural network, and the output impedance proxy model of the grid-connected inverter is used to obtain the measurement short-circuit ratio range [SCR]. min SCR max Any short-circuit ratio SCR within [the range]t Frequency range [f] min f max Any frequency f within ] t The magnitude and phase of the sequence impedance are denoted as the magnitude of the sequence impedance |Z|. t And sequence impedance phase θ t ;

[0032] Step 4.7, with frequency f t The horizontal axis represents the short-circuit ratio (SCR). t The vertical axis represents the sequence impedance magnitude |Z|. t And sequence impedance phase θ t Using the vertical axis as the plotting axis, plot the sequence impedance magnitude surface and the phase surface of the grid-connected inverter; and plot the grid impedance magnitude surface and the grid impedance phase surface in the same coordinate system based on the data provided by the grid.

[0033] Step 5: If the sequence impedance amplitude surface of the grid-connected inverter and the grid impedance amplitude surface do not intersect, or there is no intersection with a corresponding phase difference greater than 180°, the small-signal inverter is determined to be stable. Otherwise, the small-signal inverter is unstable, and the maximum short-circuit ratio at which small-signal instability occurs is recorded as SCR. S The grid impedance range Ω considering the small-signal stability of the grid-connected inverter is obtained. S Ω S =[SCR S (+∞).

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0035] 1) Based on the parameters of the gray box grid-connected inverter provided by the vendor, calculate the grid strength range that meets the voltage operation requirements under normal operating mode.

[0036] 2) Considering the impact of grid impedance changes on the sequence impedance of the grid-connected inverter, the trained surrogate model can be used to obtain impedance information under any grid strength within the training range, without the need to repeatedly measure the grid-connected inverter impedance. Attached Figure Description

[0037] Figure 1 This is the topology diagram involved in the stability determination method of the present invention.

[0038] Figure 2 The SCR stability region considering voltage stability.

[0039] Figure 3 This is a surface plot of the impedance sequence impedance magnitude of a grid-connected inverter.

[0040] Figure 4 This is the impedance sequence phase surface diagram of a grid-connected inverter.

[0041] Figure 5 This is a schematic diagram showing the impedance sequence amplitude of the grid-connected inverter and the impedance amplitude of the grid.

[0042] Figure 6 This is a schematic diagram showing the impedance sequence phase of the grid-connected inverter and the impedance phase of the grid. Detailed Implementation

[0043] The present invention will now be described in conjunction with the accompanying drawings and specific embodiments.

[0044] Figure 1 This is a topology diagram related to the grid-connected inverter stability determination method based on voltage stability and small-signal stability proposed in this invention. Figure 1 As can be seen, the topology involved in the stability determination method includes a power grid, a grid-connected inverter, and an impedance measurement and calculation unit. The impedance measurement and calculation unit includes a sampling unit, an impedance calculation unit, and a neural network unit. The sampling unit is connected to the common coupling point PCC connecting the power grid and the grid-connected inverter, and its output terminal is connected to the input terminal of the impedance calculation unit. The neural network unit is connected to the output terminal of the impedance calculation unit.

[0045] exist Figure 1 In the diagram, 10 represents the power grid, 20 represents the impedance measurement and calculation unit, 30 represents the grid-connected inverter, 201 represents the sampling unit, 202 represents the impedance calculation unit, and 203 represents the neural network unit.

[0046] In this invention, the voltage level of the grid-connected inverter port containing grid impedance is analyzed to obtain the voltage stability domain of the inverter's normal operating mode. The inverter's operating point voltage is maintained within the stability domain through reactive power compensation measures. The sequence impedance of the gray box inverter under different grid intensities is measured. The sequence impedance measurement data is used to train a neural network model. The sequence impedance surface of the grid-connected inverter under grid intensity changes is obtained based on the surrogate model. The stability of the grid-connected inverter is judged, and the small-signal stability domain of the inverter is obtained.

[0047] The stability determination method includes the following steps:

[0048] Step 1: Let the fundamental frequency of the grid-connected inverter be the fundamental frequency f0, and the rated output voltage of the grid-connected inverter be the rated output voltage U. N The minimum output voltage of a grid-connected inverter in normal operating mode is the minimum output voltage U. min ;

[0049] Step 2, let the relationship between the output voltage of the grid-connected inverter and the grid impedance be:

[0050]

[0051] in:

[0052]

[0053] In the formula, U is the actual output voltage of the grid-connected inverter, λ1 is the first variable of voltage sensitivity, λ2 is the second variable of voltage sensitivity, P is the output active power of the grid-connected inverter, Q is the output reactive power of the grid-connected inverter, S is the apparent power of the grid-connected inverter, X is the inductive reactance value in the grid impedance, R is the impedance value in the grid impedance, and SCR is the short-circuit ratio.

[0054] Step 3: Set the grid impedance ratio GIR = X / R to a constant value, the active power P and reactive power Q of the grid-connected inverter to constant values, and the actual output voltage U of the grid-connected inverter to the minimum output voltage U. min Substituting into the formula in step 2, the voltage stability critical short-circuit ratio (SCR) is calculated. V The voltage stability region of the grid-connected inverter under normal operating conditions is denoted as the voltage stability region Ω. V Ω V =[SCR V ,+∞];

[0055] Step 4: Set the short-circuit ratio range for impedance measurement, collect the sequence impedance data of the grid-connected inverter, and train a neural network model using the sequence impedance measurement data. Based on the surrogate model, obtain the sequence impedance surface of the grid-connected inverter under varying grid intensity. The specific steps are as follows:

[0056] Step 4.1, Setting the measurement parameters:

[0057] Set the short-circuit ratio range for impedance measurement to [SCR]. min SCR max ], frequency range [f min f max ], of which SCR min SCR is the lower limit of the short-circuit ratio for impedance measurement. max f is the upper limit of the short-circuit ratio for impedance measurement. min As the lower limit of frequency, f max This is the upper limit of the frequency.

[0058] In the short-circuit ratio measurement range [SCR] min SCR max |Within the range ε0, the measured short-circuit ratio is set at equal intervals, and the measured short-circuit ratios are recorded in ascending order as SCR. m Where m = 1, 2, ..., M, M is the number of short-circuit ratio measurements; in the frequency range [f min f max Within a given interval τ0, disturbance frequencies are set at equal intervals, and these frequencies are recorded as f in ascending order. n , where n = 1, 2, ..., N, and N is the number of perturbation frequencies;

[0059] Step 4.2, if the short-circuit ratio (SCR) is measured... m Not within the voltage stability range Ω V If the grid-connected inverter is determined to be operating in an abnormal working mode, proceed to step 4.3; otherwise, proceed directly to step 4.4.

[0060] Step 4.3: Add a reactive power compensation device to maintain the output port voltage of the grid-connected inverter;

[0061] Set reactive power compensation standard γ = U C / U N U C The output voltage of the grid-connected inverter after power compensation;

[0062] Calculate the reactive power compensation capacity Q Em And let Q be... Em For positive values, the formula is:

[0063] (1+GIR 2 )Q Em 2 -2γ 2 μGIRQ Em =-(1+GIR) 2 )P 2 +2γ 2 μP+γ 2 μ 2 -γ 4 μ 2

[0064] Where μ is an intermediate variable.

[0065] Step 4.4, in a measurement of the short-circuit ratio (SCR) m Below, a disturbance frequency of f is injected into the common coupling point PCC. n The voltage disturbance is measured and the short-circuit ratio (SCR) is acquired by the sampling unit. m The lower perturbation frequency is f n The voltage and current responses;

[0066] Step 4.5, following the method in Step 4.4, for each measured short-circuit ratio (SCR) m The frequency f of each disturbance is measured below. n The voltage and current responses under different conditions are analyzed to obtain MxN sets of voltage and current response data;

[0067] Input the voltage and current response data of M×N groups into the impedance calculation unit, and output the measured impedance Z of M×N grid-connected inverters. mn Record each measured impedance Z mn Amplitude |Z| mnand measuring impedance Z mn phase θ mn ;

[0068] Step 4.6, measure the short-circuit ratio (SCR) m Disturbance frequency f n Amplitude |Z| mn and phase θ mn The input neural network unit trains the RBF neural network, and the output impedance proxy model of the grid-connected inverter is used to obtain the measurement short-circuit ratio range [SCR]. min SCR max Any short-circuit ratio SCR within [the range] t Frequency range [f] max f max Any frequency f within ] t The magnitude and phase of the sequence impedance are denoted as the magnitude of the sequence impedance |Z|. t And sequence impedance phase θ t ;

[0069] Step 4.7, with frequency f t The horizontal axis represents the short-circuit ratio (SCR). t The vertical axis represents the sequence impedance magnitude |Z|. t And sequence impedance phase θ t Using the vertical axis as the plotting axis, plot the sequence impedance magnitude surface and the phase surface of the grid-connected inverter; and plot the grid impedance magnitude surface and the grid impedance phase surface in the same coordinate system based on the data provided by the grid.

[0070] Step 5: If the sequence impedance amplitude surface of the grid-connected inverter does not intersect with the grid impedance amplitude surface, or if there is no corresponding phase difference greater than 180°... ° The intersection point is used to determine if the small-signal signal of the grid-connected inverter is stable; otherwise, the small-signal signal of the grid-connected inverter is unstable. The maximum short-circuit ratio at which small-signal instability occurs is recorded as the SCR value. s The grid impedance range Ω considering the small-signal stability of the grid-connected inverter is obtained. s Ω s =[SCR S ,+oo).

[0071] To demonstrate the beneficial effects of the present invention, a simulation was performed.

[0072] Figure 2 This invention considers the SCR stability region for voltage stability and provides the output reactive power and voltage stability critical short-circuit ratio (SCR) of the grid-connected inverter under normal operating conditions. VThe relationship is as follows: The horizontal axis represents the short-circuit ratio (SCR) of the inverter-connected grid system, and the vertical axis represents the reactive power output Q of the grid-connected inverter. Specifically, the grid impedance ratio of the grid-connected inverter is GIR = 14, the active power output P of the grid-connected inverter is 0.9 times the rated power, and the minimum output voltage U of the grid-connected inverter is... min =0.9U N .

[0073] The short-circuit ratio was measured at equal intervals of 0.02 within the short-circuit ratio range [1.08, 1.2]. The perturbation frequency was set at equal intervals of 1 Hz within the frequency range [1, 100]. The impedance scan results were trained using an RBF neural network, which output... Figure 3 The sequence impedance amplitude surface of the grid-connected inverter shown is... Figure 4 The phase surface of the sequence impedance of the grid-connected inverter is shown. Figure 3 In the diagram, the horizontal axis represents the frequency f. t The vertical axis represents the short-circuit ratio (SCR). t The vertical axis represents the order impedance magnitude |Z| t .exist Figure 4 In the diagram, the horizontal axis represents the frequency f. t The vertical axis represents the short-circuit ratio (SCR). t The vertical axis represents the sequence impedance phase θ. t .

[0074] Figure 5 The graph represents the amplitude surface of the sequence impedance of the grid-connected inverter versus the grid impedance within the short-circuit ratio range [1.08, 1.2]. The horizontal axis represents the frequency f. t The vertical axis represents the short-circuit ratio (SCR). t The vertical axis represents the impedance amplitude. Figure 6 This is the phase surface of the grid-connected inverter sequence impedance and the grid impedance, with the horizontal axis representing the frequency f. t The vertical axis represents the short-circuit ratio (SCR). t The vertical axis represents the impedance phase. Figure 5 There is an intersection point A on the intersection line of the two curved surfaces, with coordinates [32.75, 1.1, -23.2]. Figure 6 The phase difference between two points at the same horizontal and vertical coordinates is 238°, indicating that small signal instability occurs. Figure 5 Among all intersections that satisfy the small-signal instability criterion, point A has the largest ordinate, therefore the maximum short-circuit ratio (SCR) for small-signal instability is the largest. S Given a value of 1.1, the grid impedance range Ω considering the small-signal stability of the grid-connected inverter is obtained. S = [1.1, +∞).

Claims

1. A stability assessment method for a grid-connected inverter based on voltage stability and small-signal stability, wherein the topology involved in the stability assessment method includes a power grid, a grid-connected inverter, and an impedance measurement and calculation unit, wherein the impedance measurement and calculation unit includes a sampling unit, an impedance calculation unit, and a neural network unit, wherein the sampling unit is connected to the common coupling point PCC connecting the power grid and the grid-connected inverter, its output terminal is connected to the input terminal of the impedance calculation unit, and the neural network unit is connected to the output terminal of the impedance calculation unit; Its features are, The stability determination method includes the following steps: Step 1: Let the fundamental frequency of the grid-connected inverter be the fundamental frequency f0, and the rated output voltage of the grid-connected inverter be the rated output voltage U. N The minimum output voltage of a grid-connected inverter in normal operating mode is the minimum output voltage U. min ; Step 2, let the relationship between the output voltage of the grid-connected inverter and the grid impedance be: in: In the formula, U is the actual output voltage of the grid-connected inverter, λ1 is the first variable of voltage sensitivity, λ2 is the second variable of voltage sensitivity, P is the output active power of the grid-connected inverter, Q is the output reactive power of the grid-connected inverter, S is the apparent power of the grid-connected inverter, X is the inductive reactance value in the grid impedance, R is the impedance value in the grid impedance, and SCR is the short-circuit ratio. Step 3: Set the grid impedance ratio GIR = X / R to a constant value, the active power P and reactive power Q of the grid-connected inverter to constant values, and the actual output voltage U of the grid-connected inverter to the minimum output voltage U. min Substituting into the formula in step 2, the voltage stability critical short-circuit ratio (SCR) is calculated. V The voltage stability region of the grid-connected inverter under normal operating conditions is denoted as the voltage stability region Ω. V Ω V =[SCR V ,+∞]; Step 4: Set the short-circuit ratio range for impedance measurement, collect the sequence impedance data of the grid-connected inverter, and train a neural network model using the sequence impedance measurement data. Based on the surrogate model, obtain the sequence impedance surface of the grid-connected inverter under varying grid intensity. The specific steps are as follows: Step 4.1, setting the measurement parameters; Set the short-circuit ratio range for impedance measurement to [SCR]. min SCR max ], frequency range [f min f max ], of which SCR min SCR is the lower limit of the short-circuit ratio for impedance measurement. max f is the upper limit of the short-circuit ratio for impedance measurement. min f is the lower limit of frequency. max This is the upper limit of the frequency. In the short-circuit ratio measurement range [SCR] min SCR max Within a given interval of ε0, the measured short-circuit ratio is set, and the measured short-circuit ratios are recorded sequentially from smallest to largest as SCR. m Where m = 1, 2, ..., M, M is the number of short-circuit ratio measurements; in the frequency range [f min f max Within a given interval τ0, disturbance frequencies are set at equal intervals, and these frequencies are recorded as f in ascending order. n , where n = 1, 2, ..., N, and N is the number of perturbation frequencies; Step 4.2, if the short-circuit ratio (SCR) is measured... m Not within the voltage stability range Ω V If the grid-connected inverter is determined to be operating in an abnormal working mode, proceed to step 4.3; otherwise, proceed directly to step 4.

4. Step 4.3: Add a reactive power compensation device to maintain the output port voltage of the grid-connected inverter; Set reactive power compensation standard γ = U C / U N U C The output voltage of the grid-connected inverter after power compensation; Calculate the reactive power compensation capacity Q Em And let Q be... Em For positive values, the formula is: (1+GIR 2 )Q Em 2 -2c 2 μGIRQ Em =-(1+GIR 2 )P 2 +2c 2 μP+γ 2 m 2 -c 4 m 2 Where μ is an intermediate variable. Step 4.4, in a measurement of the short-circuit ratio (SCR) m Below, a disturbance frequency of f is injected into the common coupling point PCC. n The voltage disturbance is measured and the short-circuit ratio (SCR) is acquired by the sampling unit. m The lower perturbation frequency is f n The voltage and current responses; Step 4.5, following the method in Step 4.4, for each measured short-circuit ratio (SCR) m The frequency f of each disturbance is measured below. n The voltage and current responses under different conditions are analyzed to obtain M×N sets of voltage and current response data; Input the voltage and current response data of M×N groups into the impedance calculation unit, and output the measured impedance Z of M×N grid-connected inverters. mn Record each measured impedance Z mn Amplitude |Z| mn and measuring impedance Z mn phase θ mn ; Step 4.6, measure the short-circuit ratio (SCR) m Disturbance frequency f n Amplitude |Z| mn and phase θ mn The input neural network unit trains the RBF neural network, and the output impedance proxy model of the grid-connected inverter is used to obtain the measurement short-circuit ratio range [SCR]. min SCR max Any short-circuit ratio SCR within [the range] t Frequency range [f] min f max Any frequency f within ] t The magnitude and phase of the sequence impedance are denoted as the magnitude of the sequence impedance |Z|. t And sequence impedance phase θ t ; Step 4.7, with frequency f t The horizontal axis represents the short-circuit ratio (SCR). t The vertical axis represents the sequence impedance magnitude |Z|. t And sequence impedance phase θ t Using the vertical axis as the plotting axis, plot the sequence impedance magnitude surface and the phase surface of the grid-connected inverter; and plot the grid impedance magnitude surface and the grid impedance phase surface in the same coordinate system based on the data provided by the grid. Step 5: If the sequence impedance amplitude surface of the grid-connected inverter and the grid impedance amplitude surface do not intersect, or there is no intersection with a corresponding phase difference greater than 180°, the small-signal inverter is determined to be stable. Otherwise, the small-signal inverter is unstable, and the maximum short-circuit ratio at which small-signal instability occurs is recorded as SCR. s The grid impedance range Ω considering the small-signal stability of the grid-connected inverter is obtained. s Ω S =[SCR s (+∞).

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