Quantitative analysis method based on VSG control system dynamic interaction model

Abstract

The invention discloses a quantitative analysis method based on a VSG control system dynamic interaction model. The method comprises the following steps: establishing a multi-VSG grid-connected system dynamic interaction analysis model, and obtaining apparent power matrix expressions of all grid-connected VSGs; on the basis of a relative gain analysis theory, according to the apparent power matrix expression of each VSG, constructing a corresponding relative gain array matrix, obtaining a power coupling degree coefficient in a single machine, and performing power coupling analysis; and according to the apparent power matrix of each VSG, focusing on an active power or reactive power analysis model, obtaining an interaction influence coefficient between the VSG and other VSGs in the system, and carrying out interaction influence analysis. According to the method, a relative gain array matrix and a multi-VSG grid-connected model are utilized to reveal the influence of key control parameters and power grid impedance in the system on the power coupling characteristic of the converter and the interaction mechanism among a plurality of converter units.

Description

Technical Field

[0001] This invention relates to a dynamic interaction analysis method for a VSG control system, specifically a quantitative analysis method based on a dynamic interaction model of a VSG control system, belonging to the field of power control technology. Background Technology

[0002] Recently, inverter-interface distributed generation, including wind and solar power, has been developing rapidly. However, the continuous increase in its penetration rate has exacerbated problems such as insufficient system inertia and weak grid voltage / frequency support capabilities, which severely limits the grid-connected capacity of distributed generation. To address this, the concept of Virtual Synchronous Generators (VSGs) has emerged. By simulating the external characteristics of traditional synchronous generators, VSGs provide a promising technical approach for the grid-friendly integration of large-scale renewable energy sources, becoming a current research hotspot in grid-connected power generation technology.

[0003] However, interactions between power control loops and among multiple VSGs can degrade control performance and even pose a risk to the stable operation of the system. Therefore, establishing an accurate and convenient model of a multi-VSG grid-connected system is crucial for analyzing dynamic interaction characteristics and identifying influencing factors. Researchers in the field of power systems focus on variables such as active power (P), reactive power (Q), voltage (V), and frequency (f). This has led to the development of a generalized P / ω “admittance” or “impedance” model that incorporates these variables. However, these models typically assume constant voltage and neglect power coupling effects. Therefore, these models are only highly accurate when system voltage fluctuations are ignored and line impedance is primarily inductive, and they lack quantitative analysis of the interaction effects between power control loops and among multiple VSGs. Summary of the Invention

[0004] To address the problems existing in the prior art, the present invention aims to provide a quantitative analysis method based on a dynamic interaction model of a VSG control system. This method establishes a [PQ]-[ωV] model with power, frequency, and voltage amplitude as variables, which can directly describe power coupling characteristics and is easily extended to multi-converter systems. Furthermore, based on relative gain matrix theory, a quantitative analysis method is proposed to quantify the degree of power coupling and the interaction between multiple converters. In addition, the influence of key control parameters and grid impedance on the power coupling characteristics of the converter, as well as the interaction mechanism between multiple converter units, are investigated. The frequency range in which interaction is likely to occur is determined, and the interaction strength in different frequency bands is compared.

[0005] To achieve the above technical objectives, this invention provides a quantitative analysis method based on a dynamic interaction model of a VSG control system, comprising:

[0006] Step S1: Establish a dynamic interaction analysis model for a multi-VSG grid-connected system and obtain the apparent power matrix of all grid-connected VSGs;

[0007] Step S2: Based on the relative gain analysis theory, construct the corresponding relative gain array matrix according to the apparent power matrix of each VSG, obtain the power coupling coefficient inside each unit, and perform power coupling analysis.

[0008] Step S3: Based on the apparent power matrix of each VSG, construct its active power or reactive power analysis model respectively, obtain the interaction influence coefficient between it and the remaining VSGs in the system, and perform interaction influence analysis.

[0009] The technical solution provided by this invention reveals the influence of key control parameters and grid impedance on the power coupling characteristics of converters in multi-VSG grid-connected systems through a dynamic interaction analysis model of multi-VSG grid-connected systems, using relative gain array matrix and active or reactive power models, as well as the interaction mechanism between multiple converter units, and determines the frequency range in which interaction is likely to occur, and compares the interaction intensity of different frequency bands.

[0010] As a preferred embodiment, in the dynamic interaction analysis model of the multi-VSG grid-connected system, the dynamic behavior of the main circuit of the i-th VSG is described as follows:

[0011] Formula 1: ;

[0012] In Equation 1, i id and i iq The output currents L and L are the d-axis and q-axis output currents, respectively. fi and R fi These represent the filter inductance and resistance on the mains side, respectively. ω n The rated angular frequency, , , , The subscript "0" and the superscript "˜" represent steady-state value and small-signal change, respectively. , Indicates the output phase angle of the converter. This indicates the phase angle of the PCC point in the grid connection.

[0013] As a preferred embodiment, the process for obtaining the dynamic interaction analysis model of the multi-VSG grid-connected system is as follows:

[0014] Step S1-1: Obtain the current, i id and i iq The steady-state value and small perturbation are given by the following formula:

[0015] Formula 2: ;

[0016] Formula 3: ;

[0017] Step S1-2: Obtain the active and reactive power on the inverter side, substitute them into step S1-1, and obtain the matrix form of the output power, the formula of which is:

[0018] Formula 4: ;

[0019] Formula 5: ;

[0020] Step S1-3: Using the same method as step S1-2, obtain the matrix form of the power transmitted to the power grid, the formula of which is:

[0021] Formula 6: ;

[0022] Formula 7: ;

[0023] Step S1-4: Since the control bandwidth of the power loop is much smaller than that of the dual closed-loop system, the expression for VSG control is:

[0024] Formula 8: ;

[0025] In equations 2-8, X fi =ω n L fi δ ip =δ i -δ p , , , , The subscript "0" and the superscript "˜" represent the steady-state value and the small-signal change, respectively. , ; , .

[0026] Further optimization, in formula 5 and They are respectively:

[0027] Equation 5-1:

[0028] ;

[0029] Equation 5-2:

[0030] .

[0031] Further optimization, in Equation 7 and They are respectively:

[0032] Equation 7-1:

[0033] ;

[0034] Equation 7-2:

[0035] .

[0036] As a preferred embodiment, the process of obtaining the apparent power matrix is ​​as follows:

[0037] Steps S1-5: Based on the matrix form of the obtained output power, the matrix form of the power transmitted to the grid, and the expression for VSG control, reconstruct the inverter-side output power, the expression of which is:

[0038] Formula 9: ;

[0039] Step S1-6: Obtain the relationship between the grid-side feed-in power and the grid voltage / frequency, expressed as follows:

[0040] Formula 10: ;

[0041] Steps S1-7: According to the law of conservation of energy, obtain the output power of the i-th VSG and derive the apparent power matrix of all grid-connected VSGs. The process is as follows:

[0042] Formula 11: ;

[0043] Formula 12: ;

[0044] Formula 13: ;

[0045] Formula 14: ;

[0046] Formula 15: ;

[0047] Formula 16: ;

[0048] Formula 17: ;

[0049] In equations 11-17, I represents 2 2 identity matrices. Further optimization, in Equation 9... and They are respectively:

[0050] Equation 9-1: ;

[0051] Equation 9-2: .

[0052] Further optimization, in Equation 10 and They are respectively:

[0053] Equation 10-1:

[0054] ;

[0055] Equation 10-2:

[0056] .

[0057] As a preferred embodiment, the construction process of the relative gain array matrix is ​​as follows: Based on the relative gain analysis theory, the relative gain array matrix is ​​obtained through the apparent power matrix, and its expression is:

[0058] Formula 18: ;

[0059] Formula 19: ;

[0060] In equations 18 and 19, t ij and r ij These are the first amplification factor and the second amplification factor, which correspond to the apparent power matrix in the following order according to the table below. and ; For operation variables, Let be the controlled variable; H is a frequency domain matrix, whose elements are t. ij , This represents the Hadama product.

[0061] Relative Gain Array (RGA) analysis is an effective method for analyzing the interaction effects in multi-input multi-output (MIMO) control systems. Its advantage lies in its computational simplicity, as the strength of the interaction between control loops can be determined solely from the diagonal elements of the RGA matrix; where the diagonal elements t... 11 and t 22 These represent the closed-loop dynamic responses of active and reactive power to changes in their respective reference values, respectively. Conversely, the elements outside the diagonal characterize the cross-coupling strength between power loops; the frequency domain matrix H provides a quantitative measure of power coupling between different frequency bands.

[0062] As a preferred embodiment, the power coupling coefficient is an element W in the relative gain array matrix W. 11 The power coupling analysis process is as follows: when 0 W 11 When W is 1, the closer it is to 1, the weaker the interaction between channels and the lower the power coupling; when W 11 >1 indicates that the power control channels are interconnected, and as W... 11 With the increase of , P and Q cannot be controlled independently.

[0063] As a preferred embodiment, the interaction influence coefficient is the transfer function P1 / P1* or Q1 / Q1*; the interaction influence analysis process is as follows: the closer the transfer function is to 1, the smaller the influence from other VSGs.

[0064] Compared with the prior art, the beneficial technical effects provided by the present invention are as follows:

[0065] The method provided in this invention establishes a [PQ]-[ωV] model with power, frequency, and voltage amplitude as variables, which can directly describe power coupling characteristics and is easily extended to multi-converter systems. Furthermore, based on relative gain matrix theory, a quantitative analysis method is proposed to quantify the degree of power coupling and the interaction between multiple converters. In addition, the influence of key control parameters and grid impedance on the power coupling characteristics of the converter, as well as the interaction mechanism between multiple converter units, are studied. The frequency range in which interaction is likely to occur is determined, and the interaction intensity in different frequency bands is compared. Attached Figure Description

[0066] Figure 1 This is a schematic diagram of the interaction of the power control loop under different J values ​​in Embodiment 2 of the present invention;

[0067] in, Figure 1 (a) is H i_12 Bode plot of (s), Figure 1 (b) is W 11 Bode plot;

[0068] Figure 2 This is a schematic diagram of the interaction of the power control loop under different Lg values ​​in Embodiment 1 of the present invention;

[0069] in, Figure 2 (a) is H i_12 Bode plot of (s), Figure 2 (b) is W 11 Bode plot;

[0070] Figure 3 This refers to the amplitude of P1 / P1* under different grid-connected VSG numbers in Embodiment 2 of the present invention;

[0071] Figure 4 This is a waveform diagram of the active power response under a step disturbance of the reactive power reference value in Embodiment 2 of the present invention.

[0072] Figure 5 This is the active power response waveform diagram under the superposition of sinusoidal disturbance and reactive power reference value in Embodiment 2 of the present invention;

[0073] in, Figure 5 (a) shows the active power response waveforms under different J values. Figure 5 (b) is the active power response waveform when J=80;

[0074] Figure 6 The active power response waveform under sinusoidal disturbance superimposed on the reactive power reference values ​​under different Lg values ​​in Embodiment 2 of the present invention;

[0075] Figure 7 This is the active power response waveform of a single VSG in a multi-VSG grid-connected system in Embodiment 2 of the present invention;

[0076] in, Figure 7 (a) The active power response waveforms of VSG-1 in two VSG grid-connected systems (green lines) and three VSG grid-connected systems (blue lines). Figure 7 (b) is the active power response waveform of VSG-1 after a sinusoidal disturbance is superimposed on the active power reference of VSG-2. Detailed Implementation

[0077] To make the objectives, technical solutions, and advantages of the present invention more apparent, exemplary embodiments according to the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are merely a part of the embodiments of the present invention, and not all of the embodiments of the present invention. It should be understood that the present invention is not limited to the exemplary embodiments described herein. Based on the embodiments of the present invention described herein, all other embodiments obtained by those skilled in the art without inventive effort should fall within the protection scope of the present invention.

[0078] Example 1

[0079] This embodiment provides a quantitative analysis method based on the dynamic interaction model of the VSG control system, including:

[0080] Step S1: Establish a dynamic interaction analysis model for a multi-VSG grid-connected system and obtain the apparent power matrix of all grid-connected VSGs;

[0081] Step S2: Based on the relative gain analysis theory, construct the corresponding relative gain array matrix according to the apparent power matrix of each VSG, obtain the power coupling coefficient inside each unit, and perform power coupling analysis.

[0082] Step S3: Based on the apparent power matrix of each VSG, construct its active power or reactive power analysis model respectively, obtain the interaction influence coefficient between it and the remaining VSGs in the system, and perform interaction influence analysis.

[0083] As a preferred embodiment, in the dynamic interaction analysis model of the multi-VSG grid-connected system, the dynamic behavior of the main circuit of the i-th VSG is described as follows:

[0084] Formula 1: ;

[0085] In Equation 1, i id and i iq These are the output currents for the d-axis and q-axis, respectively.

[0086] As a preferred embodiment, the process for obtaining the dynamic interaction analysis model of the multi-VSG grid-connected system is as follows:

[0087] Step S1-1: Obtain the current, i id and i iq The steady-state value and small perturbation are given by the following formula:

[0088] Formula 2: ;

[0089] Formula 3: ;

[0090] Step S1-2: Obtain the active and reactive power on the inverter side, substitute them into step S1-1, and obtain the matrix form of the output power, the formula of which is:

[0091] Formula 4: ;

[0092] Formula 5: ;

[0093] Step S1-3: Using the same method as step S1-2, obtain the matrix form of the power transmitted to the power grid, the formula of which is:

[0094] Formula 6: ;

[0095] Formula 7: ;

[0096] Step S1-4: Since the control bandwidth of the power loop is much smaller than that of the dual closed-loop system, the expression for VSG control is:

[0097] Formula 8: ;

[0098] In equations 2-8, X fi =ω n L fi δip =δ i -δ p , , , , The subscript "0" and the superscript "˜" represent the steady-state value and the small-signal change, respectively. , ; , .

[0099] Further optimization, in formula 5 and They are respectively:

[0100] Equation 5-1:

[0101] ;

[0102] Equation 5-2:

[0103] .

[0104] Further optimization, in Equation 7 and They are respectively:

[0105] Equation 7-1:

[0106] ;

[0107] Equation 7-2:

[0108] .

[0109] As a preferred embodiment, the process of obtaining the apparent power matrix is ​​as follows:

[0110] Steps S1-5: Based on the matrix form of the obtained output power, the matrix form of the power transmitted to the grid, and the expression for VSG control, reconstruct the inverter-side output power, the expression of which is:

[0111] Formula 9: ;

[0112] Step S1-6: Obtain the relationship between the grid-side feed-in power and the grid voltage / frequency, expressed as follows:

[0113] Formula 10: (It is suggested to modify the subscript to distinguish them.)

[0114] Steps S1-7: According to the law of conservation of energy, obtain the output power of the i-th VSG and derive the apparent power matrix of all grid-connected VSGs. The process is as follows:

[0115] Formula 11: ;

[0116] Formula 12: ;

[0117] Formula 13: ;

[0118] Formula 14: ;

[0119] Formula 15: ;

[0120] Formula 16: ;

[0121] Formula 17: ;

[0122] In equations 11-17, I represents 2 2 identity matrices. Further optimization, in Equation 9... and They are respectively:

[0123] Equation 9-1: ;

[0124] Equation 9-2: .

[0125] Further optimization, in Equation 10 and They are respectively:

[0126] Equation 10-1:

[0127] ;

[0128] Equation 10-2:

[0129] .

[0130] As a preferred embodiment, the construction process of the relative gain array matrix is ​​as follows: Based on the relative gain analysis theory, the relative gain array matrix is ​​obtained through the apparent power matrix, and its expression is:

[0131] Formula 18: ;

[0132] Formula 19: ;

[0133] In equations 18 and 19, t ij and r ij These are the first amplification factor and the second amplification factor, which correspond to the apparent power matrix in the following order according to the table below. and ; For operation variables, Let be the controlled variable; H is a frequency domain matrix, whose elements are t. ij , This represents the Hadama product.

[0134] As a preferred embodiment, the power coupling coefficient is an element W in the relative gain array matrix W. 11 The power coupling analysis process is as follows: when 0 W 11 When the value is 1, the closer it is to 1, the weaker the interaction between channels and the lower the degree of power coupling.

[0135] As a preferred embodiment, the interaction influence coefficient is a transfer function P1 / P1* or Q1 / Q1*; the process of interaction influence analysis is as follows: the value range of the transfer function is 0~1, and the closer it is to 1, the smaller the influence of other VSGs.

[0136] Example 2

[0137] This embodiment is based on the quantitative analysis method provided in Embodiment 1, and analyzes both single VSG grid-connected systems and multi-VSG grid-connected systems. The process is as follows:

[0138] First, a quantitative analysis of the coupling between active and reactive power is conducted based on the RGA principle. The interaction effects in the system are closely related to key control parameters and grid impedance. The Bode plot of the transfer function in Equation 17 can determine the oscillation frequency of the system, but it cannot quantitatively analyze the extent of its influence. To demonstrate the advantages of the proposed analysis method, it is compared with traditional frequency domain analysis methods.

[0139] Taking a single VSG grid-connected system as an example, the coupling degree of active and reactive power control loops was quantitatively analyzed based on the RGA method. To clearly demonstrate the advantages of the proposed quantitative analysis method, the influence of key parameters on the power coupling degree was analyzed. Figure 1 (a) and Figure 1 (b) Shows H when J=80, 180, and 280 respectively. i_12 (s) and W 11 The Bode plot. H i_12 The Bode plot of the transfer function of (s) reflects the interaction between the VSG power control loops. Figure 1 (b) illustrates the effect of virtual inertia J on W at different frequencies. 11 The impact. For example... Figure 1 As shown in (a), with the increase of J, the peak amplitude in the low-frequency band increases, while the oscillation frequency decreases. Figure 1(b), there is hard power coupling in the low-frequency band and the mid-frequency band. In the frequency range of 2 Hz < f < 6 Hz, as J increases, the negative interaction between the power control channels gradually strengthens, and the system frequency with the most severe negative interaction effect also gradually decreases. In the frequency range of 30 Hz < f < 60 Hz, changing J has little effect. From Figure 1 (a) and Figure 1 (b), the oscillation frequencies obtained are the same, and the trend of amplitude change is also the same. In addition, as shown in Figure 1 (b), at the peak frequencies in the mid-frequency band and the low-frequency band, the severity of power coupling is clearly visible. This means that the influence degrees of different frequency bands can be quantified more clearly. Figure 2 (a) and Figure 2 (b) respectively show the Bode plots of H i_12 (s) and W 11 when the grid-side inductance values are Lg = 2 mH, 4 mH, and 6 mH respectively. As shown in Figure 2 (a), as Lg increases, the peak amplitude in the low-frequency band decreases, and the oscillation frequency decreases slightly. As shown in Figure 2 (b), in the frequency range of 2 Hz < f < 6 Hz, decreasing Lg will gradually strengthen the negative interaction between the power control channels, and the frequency with the most severe negative interaction effect will increase slightly. In the frequency range of 30 Hz < f < 60 Hz, decreasing Lg will weaken the negative interaction. The oscillation frequencies obtained from Figure 2 (a) and Figure 2 (b) are consistent, and the trend of amplitude change is also the same. In addition, according to Figure 2 (b), the influence degrees of different frequency bands can be quantified more clearly.

[0140] Secondly, quantitatively analyze the dynamic interaction between multiple converters. The parameters of each VSG are designed to be equal. The output power response is affected by the coupling of active power and reactive power and the interaction with other VSGs. To focus on the interaction between VSGs, consider the interference of the reactive power reference value to be zero, and the power coupling has been analyzed in a single VSG grid-connected system. The transfer function P1 / P1* reflects the correlation degree between VSG-1 and itself. The closer its value is to 1, the less affected it is by other VSGs. Figure 3 shows the value of P1 / P1*. It can be observed that under the interference of the active power reference value, the interaction between VSGs mainly occurs in the low-frequency band (denoted as f11 and f12 respectively).

[0141] Based on the above analysis, the conclusion can be drawn that the power coupling degree of the VSG is closely related to the system frequency. In addition, this degree varies significantly at different frequency points, and the peak values appear in the low-frequency and medium-frequency bands. This influence on the power coupling degree mainly occurs within the frequency ranges of 2Hz < f < 6Hz (low frequency) and 30Hz < f < 60Hz (medium frequency). The specific frequency range is affected by key control parameters. The virtual inertia J mainly affects the power coupling degree within the low-frequency range. The grid inductance affects both the low-frequency and medium-frequency ranges. In addition, when ignoring the reactive power reference interference, the interaction between multiple VSGs mainly occurs within the low-frequency range of 0Hz < f < 7Hz.

[0142] Furthermore, the present invention also verifies the above analysis results through a control hardware-in-the-loop platform. First, the accuracy of the quantitative analysis of power coupling is verified. Figure 4 and Figure 5 respectively show the influence of the inertia coefficient on power coupling. Figure 4 shows the active power response waveforms when J = 80, 180, and 280, and a step disturbance is added to the reactive power reference at 20 seconds. It can be seen that there are serious power coupling phenomena in the low-frequency band (the oscillation frequencies are 4Hz, 2.�Hz, and 2Hz respectively, corresponding to J = 80, 180, and 280) and the medium-frequency band (the oscillation frequency is 55Hz), while changing the inertia coefficient has less influence on power coupling in the medium-frequency band. The amplitude of the low-frequency oscillation increases with the increase of the inertia coefficient. Figure 5 (a) shows the active power response waveforms when J = 80, 180, and 280 under the condition of adding a sinusoidal disturbance to the reactive power reference. The amplitude of the disturbance is 1 kvar, and the frequencies are 2Hz, 2.�Hz, and 3.8Hz respectively (as Figure 1 shown, the frequencies corresponding to the maximum amplitudes within the low-frequency range). It can be seen that in Figure 1 , when J = 280, the oscillation caused by the same amplitude disturbance is more serious and the peak value is larger. Figure 5 (b) shows the active power response waveform when J = 80, and sinusoidal disturbances of 2Hz, 4Hz, and 6Hz are added to the reactive power reference value at 20 seconds. It is observed that the sinusoidal disturbances of 2Hz and 6Hz in the reactive power reference have little influence on the active power. However, the disturbance with a frequency of 4Hz will cause serious oscillation of the active power because as Figure 1 shown, the power coupling degree is the highest near 4Hz. In Figure 1 , since the peak value is far from 1, the disturbance corresponding to the peak frequency will cause more serious oscillation. All the above results are consistent with the Figure 1 analysis results. The accuracy of the quantitative analysis of power coupling in the medium-frequency band can be verified in the same way.

[0143] The effect of line impedance on power coupling is as follows Figure 6 As shown. Figure 6 The active power response waveforms are shown at 20 seconds when a sinusoidal disturbance with a reactive power reference value is applied to the grid side, and Lg is 2mH, 4mH, and 6mH respectively. The amplitude and frequency of the disturbance are 1 kvar, 3.5 Hz, 4 Hz, and 4.5 Hz (e.g., ...). Figure 2 As shown, the frequency corresponding to the maximum amplitude in the low-frequency range), where Lg is 2mH, Figure 2 Power coupling and oscillations caused by disturbances of the same amplitude are more severe in the middle. The CHIL results are consistent with... Figure 2 The quantitative analysis results regarding power coupling are consistent with those in the literature.

[0144] In this case study, the accuracy of the interaction analysis between multiple VSGs was verified. Figure 7 (a) shows the active power response waveforms of VSG-1 in two-VSG grid-connected systems and three-VSG grid-connected systems, with a step disturbance of the active power reference value of VSG-2 introduced at 20 seconds. It can be seen that the interaction of active power among multiple VSGs leads to low-frequency oscillations, and the oscillation frequency is not singular. By applying FFT analysis, the main oscillation frequency bands in the two-VSG grid-connected system are concentrated at 3Hz and 5Hz, while in the three-VSG grid-connected system, the main oscillation frequency bands are concentrated at 2.5Hz and 5Hz. Furthermore, the amplitude of the oscillations decreases as the number of grid-connected systems increases. Figure 7 (b) shows the active power response waveform of VSG-1 in a two-VSG grid-connected system, with sinusoidal disturbances of 1Hz, 3Hz, and 5Hz added to the active power reference value of VSG-2 at 20 seconds. It can be seen that the 1Hz sinusoidal disturbance to the active power reference value of VSG-2 has a small impact on VSG-1. However, disturbances at frequencies of 3Hz and 5Hz cause significant fluctuations in the active power of VSG-1 because the interaction between the two VSGs is concentrated at these two frequencies, such as... Figure 3 As shown. Furthermore, due to Figure 3 The higher the peak value, the more severe the fluctuations caused by interference at the corresponding peak frequency. In summary, the quantitative analysis of power coupling and interaction between multiple VSGs using the technical solution provided by this invention is consistent with the CHIL results, demonstrating the excellent effectiveness of the quantitative analysis method provided by this invention.

Claims

1. A quantitative analysis method based on a dynamic interaction model of a VSG control system, characterized in that, include: Step S1: Establish a dynamic interaction analysis model for a multi-VSG grid-connected system and obtain the apparent power matrix of all grid-connected VSGs; Step S2: Based on the relative gain analysis theory, construct the corresponding relative gain array matrix according to the apparent power matrix of each VSG, obtain the power coupling coefficient inside each unit, and perform power coupling analysis. Step S3: Based on the apparent power matrix of each VSG, construct its active power or reactive power analysis model respectively, obtain the interaction influence coefficient between it and the remaining VSGs in the system, and perform interaction influence analysis.

2. The quantitative analysis method based on the dynamic interaction model of the VSG control system according to claim 1, characterized in that: In the dynamic interaction analysis model of the multi-VSG grid-connected system, the dynamic behavior of the main circuit of the i-th VSG is described as follows: Formula 1: ; In Equation 1, i id and i iq The output currents L and L are the d-axis and q-axis output currents, respectively. fi and R fi These represent the filter inductance and resistance on the mains side, respectively. ω n The rated angular frequency, , , , The subscript "0" and the superscript "˜" represent steady-state value and small-signal change, respectively. , Indicates the output phase angle of the converter. This indicates the phase angle of the PCC point in the grid connection.

3. The quantitative analysis method based on the dynamic interaction model of the VSG control system according to claim 2, characterized in that: The process of obtaining the dynamic interaction analysis model of the multi-VSG grid-connected system is as follows: Step S1-1: Obtain the current, i id and i iq The steady-state value and small perturbation are given by the following formula: Formula 2: Formula 3: ; Step S1-2: Obtain the active and reactive power on the inverter side, substitute them into step S1-1, and obtain the matrix form of the output power, the formula of which is: Formula 4: ; Formula 5: ; Step S1-3: Using the same method as step S1-2, obtain the matrix form of the power transmitted to the power grid, the formula of which is: Formula 6: ; Formula 7: ; Step S1-4: Since the control bandwidth of the power loop is much smaller than that of the dual closed-loop system, the expression for VSG control is: Formula 8: ; In equations 2-8, X fi =ω n L fi , , ; , .

4. The quantitative analysis method based on the dynamic interaction model of the VSG control system according to claim 3, characterized in that: The process of obtaining the apparent power matrix is ​​as follows: Steps S1-5: Based on the matrix form of the obtained output power, the matrix form of the power transmitted to the grid, and the expression for VSG control, reconstruct the inverter-side output power, the expression of which is: Formula 9: ; Step S1-6: Obtain the relationship between the grid-side feed-in power and the grid voltage / frequency, expressed as follows: Formula 10: ; Steps S1-7: According to the law of conservation of energy, obtain the output power of the i-th VSG and derive the apparent power matrix of all grid-connected VSGs. The process is as follows: Formula 11: ; Formula 12: ; Formula 13: ; Formula 14: ; Formula 15: ; Formula 16: ; Equation 17: ; In equations 11-17, I represents 2 2. Identity matrix.

5. The quantitative analysis method based on the dynamic interaction model of the VSG control system according to claim 4, characterized in that: The construction process of the relative gain array matrix is ​​as follows: Based on the relative gain analysis theory, the relative gain array matrix is ​​obtained through the apparent power matrix, and its expression is: Formula 18: ; Formula 19: ; In equations 18 and 19, t ij and r ij These are the first amplification factor and the second amplification factor, which correspond to the apparent power matrix in the following order according to the table below. and ; For operation variables, H is the controlled variable; H is a frequency domain matrix with elements t. ij , This represents the Hadama product.

6. The quantitative analysis method based on the dynamic interaction model of the VSG control system according to claim 5, characterized in that: The power coupling coefficient is an element W in the relative gain array matrix W. 11 The power coupling analysis process is as follows: when 0 W 11 When W is 1, the closer it is to 1, the weaker the interaction between channels and the lower the power coupling; when W 11 >1 indicates that the control channels are interconnected, and with W 11 With the increase of , P and Q cannot be controlled independently.

7. The quantitative analysis method based on the dynamic interaction model of the VSG control system according to claim 5, characterized in that: The interaction influence coefficient is the transfer function P1 / P1 or Q1 / Q1 The process of interaction influence analysis is as follows: the closer the transfer function is to 1, the less it is affected by other VSGs.

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