Dynamic circuit modeling and analysis method for multi-network VSG parallel system

Abstract

The invention discloses a dynamic circuit modeling and analysis method for a multi-network VSG parallel system, and the method comprises the steps: constructing a mechanical admittance model of the multi-network VSG parallel system based on an electromechanical comparison principle, and carrying out the dynamic circuit modeling of the multi-network VSG parallel system through employing a circuit system element instead of a mechanical element. The dynamic response process of the system under the action of active power instruction change and load disturbance can be clearly reflected, and collaborative modeling and interaction mechanism analysis of the operation characteristics of the multi-network VSG parallel system are realized. According to the method, the power frequency response characteristic analysis of the multi-network VSG parallel system can be realized without depending on a complex system simulation platform, and the method can be conveniently applied to the research on power frequency oscillation characteristic analysis and response performance optimization of the multi-network VSG parallel system.

Description

Technical Field

[0001] The present invention relates to the field of VSG control technology, and in particular to a dynamic circuit modeling and analysis method for a multi-grid VSG parallel system, which is applicable to the multi-grid VSG parallel system in power electronics technology and the microgrid island / off-grid control field containing such a multi-grid VSG parallel system. Background Art

[0002] While meshed virtual synchronous generators (VSGs) possess a certain virtual inertia support capability when operating in parallel, meshed VSG parallel systems can suffer from dynamic power frequency oscillation and overshoot under disturbances such as active power commands and loads. When multiple meshed VSGs are connected in parallel via a common coupling (PCC), interactions occur between the active power-frequency control loops of the multiple meshed VSGs, further complicating the operational characteristics of the multiple meshed VSG parallel system. Therefore, constructing a circuit model or simulation model that can fully describe the power-frequency response characteristics of the multiple meshed VSG parallel system is of great significance for analyzing power-frequency oscillation characteristics and studying related suppression strategies.

[0003] To this end, people have conducted various studies, such as the article entitled "Small-signal modeling and characteristiccomparative analysis for a single grid-connected grid-forming VSG with full-order and second-order", LIANG CF, SHI RL, JU CW, et al., "Engineering Science and Technology, an International Journal", Vol. 59, 2024, p. 101879; this article established small-signal models of full-order and second-order grid-forming VSGs and systematically compared their dynamic response characteristics, providing a theoretical basis for simplifying the modeling and parameter tuning of grid-forming VSG systems. However, its research focuses on single-machine grid connection and does not involve the coordinated dynamic analysis of multi-machine parallel systems.

[0004] An article entitled "Analysis of Active Power Oscillation Characteristics of Energy Storage VSG Parallel Networking System and Its Improvement Strategy" is published in "Electric Power Automation Equipment" Volume 44, Issue 05, 2024, Pages 51-57. Based on the establishment of a state space small signal model of the energy storage VSG parallel networking system, this article gives the reasons for the existence of power frequency oscillation in the system and its suppression method. However, when the system structure and parameters change, the state space equation needs to be re-established, which makes the system modeling process cumbersome and complicated, resulting in poor practicality and scalability, and difficult to efficiently promote to the application of multiple VSG parallel systems.

[0005] An article entitled "Analysis Method for Harmonic Interaction in Multi-Inverter AC Distributed Parallel Systems" is published in Automation of Electric Power Systems, Vol. 49, No. 5, 2025, pp. 164-175. This article constructs an impedance model of a multi-inverter parallel system based on the impedance analysis method and analyzes the interaction between harmonics in the system. It has the advantages of simple modeling, clear physical meaning, and easy expansion. However, it cannot obtain the system's output active power and frequency response. It is usually used in constant frequency systems. When used in a grid-type VSG system with frequency droop characteristics, it is necessary to add port characteristics that characterize the dynamic behavior of the fundamental wave.

[0006] The article entitled "P / Q-ω / V admittance modeling and oscillation analysis for multi-VSG grid-connected system" by FU SQ, SUN Y, LIN JH, et al., "IEEE Transactions on Power Systems", Vol. 38, No. 6, 2023, pp. 5849-5859, uses the P / ω admittance method to construct a P / ω admittance model for a multi-grid VSG grid-connected system, making up for the deficiency of the impedance analysis method that cannot be used to analyze the power stability of the system. On this basis, the low-frequency oscillation mechanism of the multi-VSG grid-connected system is analyzed, but the applicability and feasibility of this method in analyzing multi-VSG parallel systems are not considered.

[0007] As can be seen from the above, existing technologies can provide certain solutions and technical support for the collaborative modeling and interaction mechanism analysis of the operating characteristics of multi-network VSG parallel systems. However, when used for the analysis of the power-frequency response characteristics of multi-network VSG parallel systems and the research on their suppression methods, there are still shortcomings such as the modeling object is limited to a single-machine system, the spatial state equation is complex, it is difficult to fully reflect the system's power-frequency dynamic response characteristics, and the scope of application is limited. Summary of the Invention

[0008] To overcome the limitations of the various technical solutions presented in the background art, the present invention provides a dynamic circuit modeling and analysis method for a multi-grid VSG parallel system. This method constructs a mechanical admittance model of the multi-grid VSG parallel system based on the principle of electromechanical analogy, and uses circuit system components instead of mechanical components to perform dynamic circuit modeling of the multi-grid VSG parallel system. This method can clearly reflect the system's dynamic response process under changes in active power instructions and load disturbances, and achieves collaborative modeling and interactive mechanism analysis of the operating characteristics of the multi-grid VSG parallel system. The present invention has the advantages of accurately analyzing the system's power-frequency response characteristics without the need to establish a complex multi-grid VSG parallel system simulation model, and has a low computational load. It can be conveniently applied to research on power-frequency oscillation characteristic analysis and response performance optimization of multi-grid VSG parallel systems.

[0009] In order to achieve the above object, the technical solution adopted by the present invention is:

[0010] A dynamic circuit modeling and analysis method for a multi-network VSG parallel system includes the following steps:

[0011] Step 1: Using the electromechanical analogy principle, the rotor motion equation of the grid-type VSG is compared with the voltage and current equation of the RLC circuit to obtain the analogy relationship between the mechanical components and the circuit system components;

[0012] Step 2: Based on the analogy relationship obtained in step 1, the power frequency small signal model in the stand-alone VSG mode is equivalent to a mechanical admittance two-terminal network including a current source and a first admittance and a second admittance, and these are connected in sequence to obtain the mechanical admittance model of the multi-network VSG parallel system;

[0013] Step 3: Based on the analogy between mechanical elements and circuit system elements obtained in step 1 and the mechanical admittance model of the multi-network VSG parallel system obtained in step 2, the circuit model of the multi-network VSG parallel system can be obtained by replacing the mechanical elements with circuit system elements.

[0014] Step 4: Based on the circuit model of the multi-network VSG parallel system obtained in step 3, the transfer function of the multi-network VSG parallel system can be derived according to circuit theory, and the power-frequency response characteristics of the multi-network VSG parallel system can be analyzed using the transfer function.

[0015] Preferably, the rotor motion equation of the grid-type VSG in step 1 is:

[0016]

[0017] The voltage and current equations for the RLC circuit are:

[0018]

[0019] The corresponding relationship between mechanical components and circuit system components is: ΔP ref Corresponding to i S , ΔP e Corresponding to i L , 1 / Dω0 corresponds to R1, 1 / k ω corresponds to R2, Jω0 corresponds to C, Δω corresponds to u, Δω c Corresponding u c , 1 / K corresponds to L; among them, P ref is the active power instruction of the grid-type VSG, P e is the active power of the grid-type VSG, D is the virtual damping parameter of the grid-type VSG, ω0 is the rated angular frequency of the grid-type VSG, k ω is the primary frequency modulation parameter of the meshed VSG, ω is the angular frequency of the meshed VSG, ω c is the angular frequency of the common connection point, J is the virtual inertia parameter of the network-type VSG, K is the synchronous voltage coefficient of the network-type VSG, Δ represents the small perturbation at the equilibrium point, i S is the current source of the RLC circuit, i L is the inductor current of the RLC circuit, R1 and R2 are the parallel resistances of the RLC circuit, C is the parallel capacitance of the RLC circuit, u is the port voltage of the RC parallel branch in the RLC circuit, L is the series inductance of the RLC circuit, u c is the terminal voltage of the RLC circuit.

[0020] Among them, the calculation formula used for the synchronous voltage coefficient K of the grid-type VSG is:

[0021]

[0022] Where U PCC is the voltage amplitude of the common connection point, E is the output voltage amplitude of the meshed VSG, and X is the equivalent inductive reactance of the line.

[0023] Preferably, the admittance in step 2 refers to the inverse of the impedance, and the current source of the mechanical admittance two-terminal network is ΔP after the analogy in step 1 ref The first admittance of the mechanical admittance two-terminal network is Jω0, 1 / Dω0 and 1 / k after the analogy in step 1. ω The inverse of the parallel equivalent impedance Y a The second admittance of the mechanical admittance two-terminal network is the reciprocal Y of the 1 / K equivalent impedance after the analogy in step 1. b , Y a 、Y b The expressions are:

[0024]

[0025] Where J is the virtual inertia parameter of the network-type VSG, D is the virtual damping parameter of the network-type VSG, ω0 is the rated angular frequency of the network-type VSG, k ω is the primary frequency modulation parameter of the meshed VSG, K is the synchronous voltage coefficient of the meshed VSG, and s is the Laplace operator.

[0026] Preferably, the circuit model of the multi-network VSG parallel system in step 3 is S Replacement AP ref ,i L Alternative ΔP e , R1 replaces 1 / Dω0, R2 replaces 1 / k ω , C replaces Jω0, u replaces Δω, u c Replace Δω c , L replaces 1 / K circuit model: where P ref is the active power instruction of the grid-type VSG, P e is the active power of the grid-type VSG, D is the virtual damping parameter of the grid-type VSG, ω0 is the rated angular frequency of the grid-type VSG, k ω is the primary frequency modulation parameter of the meshed VSG, ω is the angular frequency of the meshed VSG, ω c is the angular frequency of the common connection point, J is the virtual inertia parameter of the network-type VSG, K is the synchronous voltage coefficient of the network-type VSG, Δ represents the small perturbation at the equilibrium point, i S is the current source of the RLC circuit, i L is the inductor current of the RLC circuit, R1 and R2 are the parallel resistances of the RLC circuit, C is the parallel capacitance of the RLC circuit, u is the port voltage of the RC parallel branch in the RLC circuit, L is the series inductance of the RLC circuit, u c is the terminal voltage of the RLC circuit.

[0027] Preferably, the transfer function in step 4 is:

[0028]

[0029] Where,

[0030]

[0031]

[0032] Among them, m represents the mth station network type VSG, m∈[1,n], k represents the kth station network type VSG except the mth station, i represents the sum lower limit, n represents the number of network type VSGs in parallel, P em is the active power of the mth grid-type VSG, ω m is the angular frequency of the mth VSG, M Pmis the response coefficient of the mth grid-type VSG active power instruction disturbance to its own active power, F Pm，k is the response coefficient of the kth VSG active power instruction disturbance to the mth VSG active power, S Pm is the response coefficient of load power disturbance to the active power of the mth VSG, M ωm The response coefficient of the active power instruction disturbance of the m-th grid-type VSG to its own angular frequency, F ωm,k is the response coefficient of the kth VSG active power instruction disturbance to the mth VSG angular frequency, S ωm is the response coefficient of load power disturbance to the angular frequency of the mth VSG network, P refm is the active power instruction of the mth grid-type VSG, P refk is the active power instruction of the kth grid-type VSG, P c is the load power, Y am is the first admittance of the mth grid-type VSG, Y ai is the first admittance of the i-th VSG, Y ak is the first admittance of the kth grid-type VSG, Y bm is the second admittance of the mth grid-type VSG, Y bi is the second admittance of the i-th grid-type VSG, Y bk is the second admittance of the kth grid-type VSG, Δ represents the small perturbation at the equilibrium point, || represents series connection, and s is the Laplace operator.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] The present invention discloses a dynamic circuit modeling and analysis method for a multi-network VSG parallel system. This method utilizes the principle of electromechanical analogy to construct a mechanical admittance model for the multi-network VSG parallel system. Furthermore, the method dynamically models the multi-network VSG parallel system by replacing mechanical components with circuit system components. This method can fully and clearly describe the dynamic power-frequency response relationship of the system under active power command input and load disturbance, enabling collaborative modeling and interaction mechanism analysis of the operating characteristics of the multi-network VSG parallel system. This method has the advantage of enabling dynamic characteristic analysis of the multi-network VSG parallel system without relying on a complex system simulation platform. It can be conveniently applied to research on power-frequency oscillation characteristic analysis and response performance optimization of multi-network VSG parallel systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a power frequency small signal model in the meshed VSG parallel mode of an embodiment of the present invention.

[0036] Figure 21 is a topological diagram of an RLC circuit according to an embodiment of the present invention.

[0037] Figure 3 It is a power-frequency equivalent two-terminal network of the meshed VSG system of an embodiment of the present invention.

[0038] Figure 4 This is a circuit model of a multi-network VSG parallel system according to an embodiment of the present invention.

[0039] Figure 5 is the response coefficient S of the load power disturbance of the multi-grid VSG parallel system to the active power of the m-th grid VSG Pm (s) Bode plots under different parameters.

[0040] Figure 6 is the response coefficient S of the load power disturbance of the multi-grid VSG parallel system to the angular frequency of the m-th grid VSG ωm (s) Bode plots under different parameters.

[0041] Figure 7 This is the circuit model simulation result diagram of the multi-network VSG parallel system.

[0042] Figure 8 This is a comparison chart of the simulation waveforms of the circuit model of the multi-grid VSG parallel system and the traditional power electronics model. DETAILED DESCRIPTION

[0043] The following specific implementation will be further described in conjunction with the above drawings, specifically as follows:

[0044] See also Figure 1 The present invention proposes a dynamic circuit modeling and analysis method for a multi-network VSG parallel system, comprising the following steps:

[0045] Step 1: Using the electromechanical analogy principle, the rotor motion equation of the grid-type virtual synchronous machine (VSG) and Figure 2 By comparing the voltage and current equations of the RLC circuit shown, we can obtain the analogy between mechanical components and circuit system components;

[0046] Among them, the rotor motion equation of the grid-type VSG is:

[0047]

[0048] The voltage and current equations for the RLC circuit are:

[0049]

[0050] The corresponding relationship between mechanical components and circuit system components is: ΔP ref Corresponding to i S , ΔPe Corresponding to i L , 1 / Dω0 corresponds to R1, 1 / k ω corresponds to R2, Jω0 corresponds to C, Δω corresponds to u, Δω c Corresponding u c , 1 / K corresponds to L; among them, P ref is the active power instruction of the grid-type VSG, P e is the active power of the grid-type VSG, D is the virtual damping parameter of the grid-type VSG, ω0 is the rated angular frequency of the grid-type VSG, k ω is the primary frequency modulation parameter of the meshed VSG, ω is the angular frequency of the meshed VSG, ω c is the angular frequency of the common connection point, J is the virtual inertia parameter of the network-type VSG, K is the synchronous voltage coefficient of the network-type VSG, Δ represents the small perturbation at the equilibrium point, i S is the current source of the RLC circuit, i L is the inductor current of the RLC circuit, R is the parallel resistance of the RLC circuit, C is the parallel capacitance of the RLC circuit, u is the port voltage of the RC parallel branch in the RLC circuit, L is the series inductance of the RLC circuit, u c is the terminal voltage of the RLC circuit.

[0051] Among them, the calculation formula used for the synchronous voltage coefficient K of the grid-type VSG is:

[0052]

[0053] Where U PCC is the voltage amplitude of the common connection point, E is the output voltage amplitude of the meshed VSG, and X is the equivalent inductive reactance of the line.

[0054] Step 2: Based on the analogy relationship obtained in step 1, the power frequency small signal model in the grid-type VSG stand-alone mode is equivalent to Figure 3 The mechanical admittance two-terminal network including the current source and the first admittance and the second admittance is connected in sequence to obtain the mechanical admittance model of the multi-network VSG parallel system;

[0055] Wherein, admittance is the inverse of impedance. The current source of the mechanical admittance two-terminal network is ΔP after the analogy in step 1. ref , Δ represents the small perturbation at the equilibrium point, and the first admittance of the mechanical admittance two-terminal network is Jω0, 1 / Dω0 and 1 / k after the analogy in step 1 ω The inverse of the parallel equivalent impedance Y a The second admittance of the mechanical admittance two-terminal network is the reciprocal Y of the 1 / K equivalent impedance after the analogy in step 1. b , Y a 、Y b The expressions are:

[0056]

[0057] Where J is the virtual inertia parameter of the network-type VSG, D is the virtual damping parameter of the network-type VSG, ω0 is the rated angular frequency of the network-type VSG, k ω is the primary frequency modulation parameter of the meshed VSG, K is the synchronous voltage coefficient of the meshed VSG, and s is the Laplace operator.

[0058] Step 3: Based on the analogy between mechanical elements and circuit system elements obtained in step 1 and the mechanical admittance model of the multi-network VSG parallel system obtained in step 2, the circuit system elements are used to replace the mechanical elements to obtain Figure 4 The circuit model of the multi-network VSG parallel system shown;

[0059] Among them, the circuit model of the multi-network VSG parallel system is as follows: S Alternative ΔP ref ,i L Alternative ΔP e , R1 replaces 1 / Dω0, R2 replaces 1 / k ω , C replaces Jω0, u replaces Δω, u c Replace Δω c , L replaces 1 / K circuit model; where P ref is the active power instruction of the grid-type VSG, P e is the active power of the grid-type VSG, D is the virtual damping parameter of the grid-type VSG, ω0 is the rated angular frequency of the grid-type VSG, k ω is the primary frequency modulation parameter of the meshed VSG, ω is the angular frequency of the meshed VSG, ω c is the angular frequency of the common connection point, J is the virtual inertia parameter of the meshed VSG, K is the synchronous voltage coefficient of the meshed VSG, P c is the load power of the grid-type VSG, Δ represents the small disturbance at the equilibrium point, i S is the current source of the RLC circuit, i L is the inductor current of the RLC circuit, R1 and R2 are the parallel resistances of the RLC circuit, C is the parallel capacitance of the RLC circuit, u is the port voltage of the RC parallel branch in the RLC circuit, L is the series inductance of the RLC circuit, u c is the terminal voltage of the RLC circuit.

[0060] Step 4: Based on the circuit model of the multi-network VSG parallel system obtained in step 3, the transfer function of the multi-network VSG parallel system can be derived according to circuit theory, and the power-frequency response characteristics of the multi-network VSG parallel system can be analyzed using the transfer function.

[0061] The transfer function is:

[0062]

[0063] Where,

[0064]

[0065]

[0066] Among them, m represents the mth station network type VSG, m∈[1,n], k represents the kth station network type VSG except the mth station, i represents the sum lower limit, n represents the number of network type VSGs in parallel, P em is the active power of the mth grid-type VSG, ω m is the angular frequency of the mth VSG, M Pm is the response coefficient of the mth grid-type VSG active power instruction disturbance to its own active power, F Pm，k is the response coefficient of the kth VSG active power instruction disturbance to the mth VSG active power, S Pm is the response coefficient of load power disturbance to the active power of the mth VSG, M ωm The response coefficient of the active power instruction disturbance of the m-th grid-type VSG to its own angular frequency, F ωm，k is the response coefficient of the kth VSG active power instruction disturbance to the mth VSG angular frequency, S ωm is the response coefficient of load power disturbance to the angular frequency of the mth VSG network, P refm is the active power instruction of the mth grid-type VSG, P refk is the active power instruction of the kth grid-type VSG, P c is the load power, Y am is the first admittance of the mth grid-type VSG, Y ai is the first admittance of the i-th VSG, Y ak is the first admittance of the kth grid-type VSG, Y bm is the second admittance of the mth grid-type VSG, Y bi is the second admittance of the i-th grid-type VSG, Y bk is the second admittance of the kth grid-type VSG, Δ represents the small perturbation at the equilibrium point, || represents series connection, and s is the Laplace operator.

[0067] Example

[0068] In order to verify the correctness of the dynamic circuit modeling and analysis method of a multi-network type VSG parallel system proposed in the present invention, a transfer function for carrying out system dynamic characteristics analysis is derived based on the circuit model of the multi-network type virtual synchronous machine (VSG) parallel system to carry out frequency domain analysis, and time domain simulation is carried out in combination with the circuit model. The frequency domain analysis results of the transfer function are compared with the time domain simulation results of the circuit model to obtain the power frequency oscillation characteristics and their changing laws of the multi-network type VSG parallel system under different parameter changes, thereby realizing the coordinated analysis of the frequency domain and time domain. Furthermore, the simulation results of the circuit model of a multi-network type VSG parallel system proposed in the present invention are compared and verified with the simulation results of the power electronic model of the traditional multi-network type VSG parallel system. The details are as follows:

[0069] In this embodiment, the differences between the meshing VSGs are ignored. It is assumed that the meshing VSGs have the same parameters and the system lines are set to inductive. The relevant parameters are set as follows:

[0070] The rated capacity of the grid-type VSG is 100kVA, the rated angular frequency ω0 is 314.16rad / s, and the initial value of the virtual inertia parameter J is 6kg·m 2 , the voltage amplitude of the common connection point U PCC The output voltage amplitude E of the grid-type VSG is 311V, and the equivalent inductance L of the transmission line is line The initial value is 0.05mH, and the line equivalent inductive reactance X≈L line The initial value of ω0 is 0.016Ω, the virtual damping parameter D is 50.66J / rad, and the primary frequency modulation parameter k ω It is 15915.5J / rad.

[0071] In this embodiment, the transfer function used to perform system dynamic characteristics analysis is:

[0072]

[0073] Where,

[0074]

[0075] In this embodiment, in order to verify the correctness of the proposed dynamic circuit modeling and analysis method of a multi-network VSG parallel system, the response coefficient S of the transfer function load power disturbance to the active power of the m-th network VSG is plotted according to the frequency domain analysis method. Pm (s) and the response coefficient S of the load power disturbance to the angular frequency of the m-th station network type VSG ωm (s) Bode plots under different parameters, four cases are set, as follows:

[0076] Set verification condition 1 as: Let J = 6kg / m 2 、Lline =0.05mH, and then merged into 2, 4, and 6-station network type VSG.

[0077] Set verification condition 2 as: Let J = 6kg / m 2 、L line =0.5mH, and then merged into 2, 4, and 6-station network type VSG.

[0078] Set verification condition 3 as: Let J = 30kg / m 2 、L line =0.05mH, and then merged into 2, 4, and 6-station network type VSG.

[0079] Set verification condition 4 as: Let J = 30kg / m 2 、L line =0.5mH, and then merged into 2, 4, and 6-station network type VSG.

[0080] In this embodiment, in order to verify the correctness of the proposed dynamic circuit modeling and analysis method of a multi-network type VSG parallel system, a circuit model of the multi-network type VSG parallel system after adopting the present invention is built. At the initial moment, each network type VSG is connected in parallel to stably drag a 90kW resistive load. An additional 30kW load is added. After the system runs stably again, the additional 30kW load is removed. Considering the effects of different parameter changes on the active power P of each network type VSG, the following equation is used to calculate the effect of the dynamic circuit modeling and analysis method of the proposed multi-network type VSG parallel system. em and angular frequency ω m In order to understand the influence of time domain simulation, four time domain simulation conditions are set up, as follows:

[0081] Set simulation condition 1 as: Let J = 6kg / m 2 、L line =0.05mH, and then merged into 2, 4, and 6-station network type VSG.

[0082] Set simulation condition 2 as: Let J = 6kg / m 2 、L line =0.5mH, and then merged into 2, 4, and 6-station network type VSG.

[0083] Set simulation condition 3 as: Let J = 30kg / m 2 、L line =0.05mH, and then merged into 2, 4, and 6-station network type VSG.

[0084] Set simulation condition 4 as: Let J = 30kg / m 2 、L line =0.5mH, and then merged into 2, 4, and 6-station network type VSG.

[0085] In this embodiment, in order to further verify the correctness of the proposed dynamic circuit modeling and analysis method of a multi-grid type VSG parallel system, a circuit model of a multi-grid type VSG parallel system and a power electronic model of a traditional multi-grid type VSG parallel system are constructed for simulation comparison and verification. At the initial moment, each grid type VSG is connected in parallel to stably drag a 90kW resistive load. An additional 30kW load is added. After the system is running stably again, the additional 30kW load is removed. Considering the changes in different parameters, the active power response P of each grid type VSG is calculated. em and angular frequency ω m In order to investigate the impact of time domain simulation, four time domain simulation comparison conditions are set up, as follows:

[0086] Set the simulation comparison condition 1 as: Let J = 6kg / m 2 、L line =0.05mH, and then merged into 2, 4, and 6-station network type VSG.

[0087] Set the simulation comparison condition 2 as: Let J = 6kg / m 2 、L Iine =0.5mH, and then merged into 2, 4, and 6-station network type VSG.

[0088] Set the simulation comparison condition 3 as: Let J = 30kg / m 2 、L 1ine =0.05mH, and then merged into 2, 4, and 6-station network type VSG.

[0089] Set the simulation comparison condition 4 as: Let J = 30kg / m 2 、L line =0.5mH, and then merged into 2, 4, and 6-station network type VSG.

[0090] According to the above frequency domain analysis, we can get Figure 5 The response coefficient S of the load power disturbance of the multi-grid VSG parallel system to the active power of the m-th grid VSG is shown as Pm (s) Bode diagrams under different parameters and Figure 6 The response coefficient S of the load power disturbance of the multi-grid VSG parallel system to the angular frequency of the m-th grid VSG is shown as ωm (s) Bode diagram under different parameters. Where m represents the mth grid-type VSG, m∈[1,n], n represents the number of grid-type VSGs in parallel, J represents the virtual inertia parameter of the grid-type VSG, L line The equivalent inductance of the transmission line, Figure 5 (a) is the S of the multi-network VSG parallel system Pm (s) at J = 6 kg / m 2 、L line=0.05mH, and the Bode diagram when 2, 4, and 6 VSGs are incorporated in sequence, namely Figure 5 In (a), the solid line, dashed line and dotted line represent S Pm (s) at J = 6 kg / m 2 、L line =0.05mH, the Bode plots of n=2, n=4 and n=6, Figure 5 (b) is the S of the multi-network VSG parallel system Pm (s) at J = 6 kg / m 2 、L line = 0.5mH, and the Bode diagram when 2, 4, and 6 VSGs are incorporated in sequence, that is, Figure 5 In (b), the solid line, dashed line, and dotted line represent S Pm (s) at J = 6 kg / m 2 、L line =0.5mH, Bode plots of n=2, n=4 and n=6, Figure 5 (c) is the S of the multi-network VSG parallel system Pm (s) at J = 30 kg / m 2 、L line =0.05mH, and the Bode diagram when 2, 4, and 6 VSGs are incorporated in sequence, namely Figure 5 In (c), the solid line, dashed line and dotted line represent S Pm (s) at J = 30 kg / m 2 、L line =0.05mH, the Bode plots of n=2, n=4 and n=6, Figure 5 (d) is the S of the multi-network VSG parallel system Pm (s) When J = 30 kg / m 2 、L line = 0.5mH, and the Bode diagram when 2, 4, and 6 VSGs are incorporated in sequence, that is, Figure 5 In (d), the solid line, dashed line and dotted line represent S Pm (s) at J = 30 kg / m 2 、L line =0.5mH, Bode plots of n=2, n=4 and n=6, Figure 6 (a) is the S of the multi-network VSG parallel system ωm (s) at J = 6 kg / m 2 、L line =0.05mH, and the Bode diagram when 2, 4, and 6 VSGs are incorporated in sequence, namely Figure 6 In (a), the solid line, dashed line and dotted line represent S ωm (s) at J = 6 kg / m 2 、L line=0.05mH, the Bode plots of n=2, n=4 and n=6, Figure 6 (b) is the S of the multi-network VSG parallel system ωm (s) at J = 6 kg / m 2 、L line = 0.5mH, and the Bode diagram when 2, 4, and 6 VSGs are incorporated in sequence, that is, Figure 6 In (b), the solid line, dashed line, and dotted line represent S ωm (s) at J = 6 kg / m 2 、L line =0.05mH, the Bode plots of n=2, n=4 and n=6, Figure 6 (c) is the S of the multi-network VSG parallel system ωm (s) at J = 30 kg / m 2 、L line =0.05mH, and the Bode diagram when 2, 4, and 6 VSGs are incorporated in sequence, namely Figure 6 In (c), the solid line, dashed line and dotted line represent S ωm (s) at J = 30 kg / m 2 、L line =0.05mH, the Bode plots of n=2, n=4 and n=6, Figure 6 (d) is the S of the multi-network VSG parallel system ωm (s) When J = 30 kg / m 2 、L line = 0.5mH, and the Bode diagram when 2, 4, and 6 VSGs are incorporated in sequence, that is, Figure 6 In (d), the solid line, dashed line and dotted line represent S ωm (s) at J = 30 kg / m 2 、L line =0.5mH, Bode plots of n=2, n=4 and n=6.

[0091] According to the above simulation conditions, we can get Figure 7 The circuit model simulation results of the multi-network VSG parallel system are shown in the figure. em represents the active power of the mth VSG, f m represents the frequency of the mth VSG, m∈[1,n], f m =ω m / (2π),ω m represents the angular frequency of the mth grid-type VSG, n represents the number of grid-type VSGs in parallel, J represents the virtual inertia parameter of the grid-type VSG, L line represents the equivalent inductance of the transmission line, Figure 7 (a) The circuit model of the multi-network VSG parallel system at J = 6 kg / m2 、L line =0.05mH, when 2, 4, and 6 VSGs are connected in sequence, P em With f m The simulation waveform is Figure 7 In (a), the solid line, dashed line, and dotted line represent the circuit model of the multi-network VSG parallel system at J = 6 kg / m 2 、L line =0.05mH, when 2, 4, and 6 VSGs are connected in sequence, P e1 ,P e2 With f1, f2, P e1 ,...,P e4 with f1, ..., f4, P e1 ,...,P e6 With the simulation waveform of f1, ..., f6, Figure 7 (b) The circuit model of the multi-network VSG parallel system at J = 6 kg / m 2 、L line =0.5mH, when 2, 4, and 6 VSGs are connected in sequence, P em With f m The simulation waveform is Figure 7 In (b), the solid line, dashed line, and dotted line represent the circuit model of the multi-network VSG parallel system at J = 6 kg / m 2 、L line =0.5mH, when 2, 4, and 6-station network VSG are connected in sequence, P e1 ,P e2 With f1, f2, P e1 ,...,P e4 with f1, ..., f4, P e1 ,...,P e6 With the simulation waveform of f1, ..., f6, Figure 7 (c) The circuit model of the multi-network VSG parallel system at J = 30 kg / m 2 、L line =0.05mH, when 2, 4, and 6 VSGs are connected in sequence, P em With f m The simulation waveform is Figure 7 In (c), the solid line, dashed line, and dotted line represent the circuit model of the multi-network VSG parallel system at J = 30 kg / m 2 、L 1ine =0.05mH, when 2, 4, and 6 VSGs are connected in sequence, P e1 ,P e2 With f1, f2, P e1 ,...,P e4with f1, ..., f4, P e1 ,...,P e6 With the simulation waveform of f1, ..., f6, Figure 7 (d) The circuit model of the multi-network VSG parallel system at J = 30 kg / m 2 、L line =0.5mH, when 2, 4, and 6 VSGs are connected in sequence, P em With f m The simulation waveform is Figure 7 In (d), the solid line, dashed line, and dotted line represent the circuit model of the multi-network VSG parallel system at J = 30 kg / m 2 、L line =0.5mH, when 2, 4, and 6-station network VSG are connected in sequence, P e1 ,P c2 With f1, f2, P e1 ,...,P e4 with f1, ..., f4, P e1 ,...,P e6 Simulation waveforms of f1, ..., f6.

[0092] According to the above simulation comparison conditions, we can get Figure 8 The circuit model of the multi-grid VSG parallel system and the simulation waveform comparison of the traditional power electronic model are shown in the figure. em represents the active power of the mth VSG, f m represents the frequency of the mth VSG, m∈[1,n], f m =ω m / (2π),ω m represents the angular frequency of the mth grid-type VSG, n represents the number of grid-type VSGs in parallel, J represents the virtual inertia parameter of the grid-type VSG, L line represents the equivalent inductance of the transmission line, the solid line represents the traditional power electronic model simulation waveform of the multi-grid VSG parallel system, and the dotted line represents the circuit model simulation waveform of the multi-grid VSG parallel system. Figure 8 (a) The circuit model of the multi-grid VSG parallel system and the traditional power electronics model at J = 6 kg / m 2 、L line =0.05mH, when 2, 4, and 6 VSGs are connected in sequence, P em With f m The simulation waveform comparison is Figure 8 In (a), P e1 ,P e2 With f1, f2, P e1 ,...,P e4 with f1, ..., f4, Pe1 ,...,P e6 The curves pointed to by f1, ..., f6 represent the circuit model of the multi-grid VSG parallel system and the traditional power electronic model at J = 6 kg / m 2 、L line =0.05mH, when 2, 4, and 6 VSGs are connected in sequence, P em With f m The simulation waveform comparison, Figure 8 (b) The circuit model of the multi-grid VSG parallel system and the traditional power electronics model at J = 6 kg / m 2 、L line =0.5mH, when 2, 4, and 6 VSGs are connected in sequence, P em With f m The simulation waveform comparison is Figure 8 In (b), P e1 , P e2 With f1, f2, P e1 ,…,P e4 with f1,…,f4,P e1 ,...,P e6 The curves pointed to by f1, ..., f6 represent the circuit model of the multi-grid VSG parallel system and the traditional power electronic model at J = 6 kg / m 2 、L line =0.5mH, when 2, 4, and 6 VSGs are connected in sequence, P em With f m The simulation waveform comparison, Figure 8 (c) The circuit model of the multi-grid VSG parallel system and the traditional power electronics model at J = 30 kg / m 2 、L line =0.05mH, when 2, 4, and 6 VSGs are connected in sequence, P em With f m The simulation waveform comparison is Figure 8 In (c), P e1 ,P e2 With f1, f2, P e1 ,...,P e4 with f1, ..., f4, P e1 ,...,P e6 The curves pointed to by f1, ..., f6 represent the circuit model of the multi-grid VSG parallel system and the traditional power electronic model at J = 30 kg / m 2 、L line =0.05mH, when 2, 4, and 6 VSGs are connected in sequence, P em With f m The simulation waveform comparison, Figure 8 (d) The circuit model of the multi-grid VSG parallel system and the traditional power electronics model at J = 30 kg / m 2 、L line =0.5mH, when 2, 4, and 6 VSGs are connected in sequence, P em With f m The simulation waveform comparison is Figure 8 In (d), P e1 , P e2 With f1, f2, P e1 ,...,P e4 With f1,…,f4,P el ,...,P e6 The curves pointed to by f1, ..., f6 represent the circuit model of the multi-grid VSG parallel system and the traditional power electronic model at J = 30 kg / m 2 、L lime =0.5mH, when 2, 4, and 6 VSGs are connected in sequence, P em With f m Comparison of simulation waveforms.

[0093] according to Figure 5 (a) It can be seen that when J = 6 kg / m 2 、L line =0.05mH, when 2, 4, and 6-station network VSG are successively incorporated, the coefficient S Pm The Bode plot of (s) shows a horizontal trend, indicating that there will be no oscillation and overshoot in the system step response.

[0094] according to Figure 5 (b) It can be seen that when J = 6 kg / m 2 、L line =0.5mH, when 2, 4, and 6-station grid-type VSGs are sequentially incorporated, the coefficient S Pm The Bode plot of (s) shows a horizontal trend, indicating that there will be no oscillation and overshoot in the system step response.

[0095] according to Figure 5 (c) It can be seen that when J = 30 kg / m 2 、L line =0.05mH, when 2, 4, and 6-station network VSG are successively incorporated, the coefficient S Pm The Bode plot of (s) shows a horizontal trend, indicating that there will be no oscillation and overshoot in the system step response.

[0096] according to Figure 5 (d) It can be seen that when J = 30 kg / m 2 、L line=0.5mH, when 2, 4, and 6-station grid-type VSGs are sequentially incorporated, the coefficient S Pm The Bode plot of (s) shows a horizontal trend, indicating that there will be no oscillation and overshoot in the system step response.

[0097] according to Figure 5 It can be seen that as the number n of grid-connected VSG increases, the system phase-frequency curve remains unchanged, and the amplitude-frequency curve shifts downward, indicating that the system step response output is affected by the gain. line When the value of the system inertia parameter J increases, the Bode diagram of the system basically does not change, indicating that the virtual inertia parameter J and the equivalent inductance L of the transmission line are 1ine When becomes larger, the system step response remains basically unchanged.

[0098] according to Figure 6 (a) It can be seen that when J = 6 kg / m 2 、L line =0.05mH, when 2, 4, and 6-station network VSG are successively incorporated, the coefficient S ωm The Bode plot of (s) has no resonance peak, indicating that there will be no oscillation and overshoot in the system step response.

[0099] according to Figure 6 (b) It can be seen that when J = 6 kg / m 2 、L line =0.5mH, when 2, 4, and 6-station grid-type VSGs are sequentially incorporated, the coefficient S ωm The Bode plot of (s) has no resonance peak, indicating that there will be no oscillation and overshoot in the system step response.

[0100] according to Figure 6 (c) It can be seen that when J = 30 kg / m 2 、L Iine =0.05mH, when 2, 4, and 6-station network VSG are successively incorporated, the coefficient S ωm The Bode plot of (s) has no resonance peak, indicating that there will be no oscillation and overshoot in the system step response.

[0101] according to Figure 6 (d) It can be seen that when J = 30 kg / m 2 、L line =0.5mH, when 2, 4, and 6-station grid-type VSGs are sequentially incorporated, the coefficient S ωm The Bode plot of (s) has no resonance peak, indicating that there will be no oscillation and overshoot in the system step response.

[0102] according to Figure 6It can be seen that as the number n of grid-connected VSG increases, the system phase-frequency curve remains unchanged, and the amplitude-frequency curve shifts downward, indicating that the system step response output is affected by the gain. When the virtual inertia parameter J increases, the system Bode diagram corner frequency shifts forward and the bandwidth becomes smaller, indicating that when the virtual inertia parameter J increases, the system step response speed slows down. line When the inductance L of the transmission line increases, the system Bode diagram basically does not change, indicating that the equivalent inductance L of the transmission line line When becomes larger, the system step response remains basically unchanged.

[0103] according to Figure 7 (a) It can be seen that when J = 6 kg / m 2 、L line =0.05mH, when 2, 4, and 6 grid-forming VSGs are connected in sequence and an additional 30kW load is added and removed, the active power of the grid-forming VSG is P em With frequency f m There is neither oscillation nor overshoot.

[0104] according to Figure 7 (b) It can be seen that when J = 6 kg / m 2 、L line =0.5mH, when 2, 4, and 6 grid-forming VSGs are connected in sequence and an additional 30kW load is switched on and off, the active power of the grid-forming VSG is P em With frequency f m There is neither oscillation nor overshoot.

[0105] according to Figure 7 (c) It can be seen that when J = 30 kg / m 2 、L line =0.05mH, when 2, 4, and 6 grid-forming VSGs are connected in sequence and an additional 30kW load is added and removed, the active power of the grid-forming VSG is P em With frequency f m There is neither oscillation nor overshoot.

[0106] according to Figure 7 (d) It can be seen that when J = 30 kg / m 2 、L line =0.5mH, when 2, 4, and 6 grid-forming VSGs are connected in sequence and an additional 30kW load is switched on and off, the active power of the grid-forming VSG is P em With frequency f m There is neither oscillation nor overshoot.

[0107] according to Figure 7 It can be seen that the active power P of the grid-type VSG em As the number of grid-connected VSGs n increases, the frequency of grid-connected VSGs f decreases. mAs the number of grid-connected VSGs n increases, the equivalent inductance L of the transmission line increases. line When it becomes larger, the active power P of the grid-type VSG em With frequency f m There is basically no change, but when the virtual inertia parameter J becomes larger, the network type VSG frequency f m The response speed slows down, and the active power P of the network-type VSG em There is basically no change.

[0108] Will Figure 7 (a) and Figure 5 (a) Figure 6 After comparing the results of (a), it is not difficult to see that this embodiment Figure 7 The circuit model simulation results of the multi-network VSG parallel system in (a) can be compared with Figure 5 (a) Figure 6 The transfer function Bode diagram analysis results in (a) maintain a one-to-one correspondence, which fully reflects the correctness of the dynamic circuit modeling and analysis method of the multi-network VSG parallel system proposed in the present invention.

[0109] Will Figure 7 (b) and Figure 5 (b) Figure 6 After comparing the results of (b), it is not difficult to see that this embodiment Figure 7 The circuit model simulation results of the multi-network VSG parallel system in (b) can be compared with Figure 5 (b) Figure 6 The transfer function Bode diagram analysis results in (b) maintain a one-to-one correspondence, which fully reflects the correctness of the dynamic circuit modeling and analysis method of the multi-network VSG parallel system proposed in the present invention.

[0110] Will Figure 7 (c) and Figure 5 (c) Figure 6 After comparing the results of (c), it is not difficult to see that this embodiment Figure 7 The circuit model simulation results of the multi-network VSG parallel system in (c) can be compared with Figure 5 (c) Figure 6 The transfer function Bode diagram analysis results in (c) maintain a one-to-one correspondence, which fully reflects the correctness of the dynamic circuit modeling and analysis method of the multi-network VSG parallel system proposed in the present invention.

[0111] Will Figure 7 (d) and Figure 5 (d) Figure 6 After comparing the results of (d), it is not difficult to see that this embodiment Figure 7 The circuit model simulation results of the multi-network VSG parallel system in (d) can be compared with Figure 5(d) Figure 6 The transfer function Bode diagram analysis results in (d) maintain a one-to-one correspondence, which fully reflects the correctness of the dynamic circuit modeling and analysis method of the multi-network VSG parallel system proposed in the present invention.

[0112] Will Figure 7 and Figure 5 、 Figure 6 After comparing the results of Figure 7 The circuit model simulation results of the multi-network VSG parallel system can be compared with Figure 5 、 Figure 6 The transfer function Bode diagram analysis results in the embodiment maintain a one-to-one correspondence, which fully reflects the correctness of the dynamic circuit modeling and analysis method of the multi-network VSG parallel system proposed in the present invention.

[0113] according to Figure 8 (a) It can be seen that when J = 6 kg / m 2 、L line =0.05mH, and 2, 4, and 6 grid-type VSGs are sequentially connected, and an additional 30kW load is added and removed, the simulation results of the two models are consistent, which once again demonstrates the correctness of the dynamic circuit modeling and analysis method of the multi-grid-type VSG parallel system proposed in the present invention.

[0114] according to Figure 8 (b) It can be seen that when J = 6 kg / m 2 、L line =0.5mH, and 2, 4, and 6 grid-type VSGs are sequentially connected, and an additional 30kW load is added and removed, the simulation results of the two models are consistent, which once again demonstrates the correctness of the dynamic circuit modeling and analysis method of the multi-grid-type VSG parallel system proposed in the present invention.

[0115] according to Figure 8 (c) It can be seen that when J = 30 kg / m 2 、L line =0.05mH, and 2, 4, and 6 grid-type VSGs are sequentially connected, and an additional 30kW load is added and removed, the simulation results of the two models are consistent, which once again demonstrates the correctness of the dynamic circuit modeling and analysis method of the multi-grid-type VSG parallel system proposed in the present invention.

[0116] according to Figure 8 (d) It can be seen that when J = 30 kg / m 2 、L line =0.5mH, and 2, 4, and 6 grid-type VSGs are sequentially connected, and an additional 30kW load is added and removed, the simulation results of the two models are consistent, which once again demonstrates the correctness of the dynamic circuit modeling and analysis method of the multi-grid-type VSG parallel system proposed in the present invention.

[0117] The above description is a detailed description of the preferred embodiments of the present invention, but the embodiments are not intended to limit the scope of the patent application of the present invention. Any equivalent changes or modifications completed under the technical spirit suggested by the present invention should fall within the patent scope covered by the present invention.

Claims

1. A dynamic circuit modeling and analysis method for a multi-network VSG parallel system, characterized by: The steps include: Step 1: Using the electromechanical analogy principle, the rotor motion equation of the grid-type VSG is compared with the voltage and current equation of the RLC circuit to obtain the analogy relationship between the mechanical components and the circuit system components; Step 2: Based on the analogy relationship obtained in step 1, the power frequency small signal model in the stand-alone VSG mode is equivalent to a mechanical admittance two-terminal network including a current source and a first admittance and a second admittance, and these are connected in sequence to obtain the mechanical admittance model of the multi-network VSG parallel system; Step 3: Based on the analogy between mechanical elements and circuit system elements obtained in step 1 and the mechanical admittance model of the multi-network VSG parallel system obtained in step 2, the circuit model of the multi-network VSG parallel system can be obtained by replacing the mechanical elements with circuit system elements. Step 4: Based on the circuit model of the multi-network VSG parallel system obtained in step 3, the transfer function of the multi-network VSG parallel system can be derived according to circuit theory, and the power-frequency response characteristics of the multi-network VSG parallel system can be analyzed using the transfer function.

2. The dynamic circuit modeling and analysis method of a multi-network VSG parallel system according to claim 1 is characterized in that: The rotor motion equation of the grid-type VSG in step 1 is: The voltage and current equations for the RLC circuit are: The corresponding relationship between mechanical components and circuit system components is: ΔP ref Corresponding to i S , ΔP e Corresponding to i L , 1 / Dω0 corresponds to R1, 1 / k ω corresponds to R2, Jω0 corresponds to C, Δω corresponds to u, Δω c Corresponding u c , 1 / K corresponds to L; Among them, P ref is the active power instruction of the grid-type VSG, P e is the active power of the grid-type VSG, D is the virtual damping parameter of the grid-type VSG, ω0 is the rated angular frequency of the grid-type VSG, k ω is the primary frequency modulation parameter of the meshed VSG, ω is the angular frequency of the meshed VSG, ω c is the angular frequency of the common connection point, J is the virtual inertia parameter of the network-type VSG, K is the synchronous voltage coefficient of the network-type VSG, Δ represents the small perturbation at the equilibrium point, i S is the current source of the RLC circuit, i L is the inductor current of the RLC circuit, R1 and R2 are the parallel resistances of the RLC circuit, C is the parallel capacitance of the RLC circuit, u is the port voltage of the RC parallel branch in the RLC circuit, L is the series inductance of the RLC circuit, u c is the terminal voltage of the RLC circuit. Among them, the calculation formula used for the synchronous voltage coefficient K of the grid-type VSG is: Where U P cC is the voltage amplitude of the common connection point, E is the output voltage amplitude of the meshed VSG, and X is the equivalent inductive reactance of the line.

3. The dynamic circuit modeling and analysis method of a multi-network VSG parallel system according to claim 1 is characterized in that: The admittance in step 2 refers to the inverse of the impedance. The current source of the mechanical admittance two-terminal network is ΔP after the analogy in step 1. ref The first admittance of the mechanical admittance two-terminal network is Jω0, 1 / Dω0 and 1 / k after the analogy in step 1. ω The inverse of the parallel equivalent impedance Y a The second admittance of the mechanical admittance two-terminal network is the reciprocal Y of the 1 / K equivalent impedance after the analogy in step 1. b , Y a 、Y b The expressions are: Where J is the virtual inertia parameter of the network-type VSG, D is the virtual damping parameter of the network-type VSG, ω0 is the rated angular frequency of the network-type VSG, k ω is the primary frequency modulation parameter of the meshed VSG, K is the synchronous voltage coefficient of the meshed VSG, and s is the Laplace operator.

4. The dynamic circuit modeling and analysis method of a multi-network VSG parallel system according to claim 1 is characterized in that: The circuit model of the multi-network VSG parallel system in step 3 is S Alternative ΔP ref ,i L Alternative ΔP e , R1 replaces 1 / Dω0, R2 replaces 1 / k ω , C replaces dω0, u replaces Δω, u c Replace Δω c , circuit model where L replaces 1 / K; Among them, P ref is the active power instruction of the grid-type VSG, P e is the active power of the grid-type VSG, D is the virtual damping parameter of the grid-type VSG, ω0 is the rated angular frequency of the grid-type VSG, k ω is the primary frequency modulation parameter of the meshed VSG, ω is the angular frequency of the meshed VSG, ω c is the angular frequency of the common connection point, J is the virtual inertia parameter of the network-type VSG, K is the synchronous voltage coefficient of the network-type VSG, Δ represents the small perturbation at the equilibrium point, i S is the current source of the RLC circuit, i L is the inductor current of the RLC circuit, R1 and R2 are the parallel resistances of the RLC circuit, C is the parallel capacitance of the RLC circuit, u is the port voltage of the RC parallel branch in the RLC circuit, L is the series inductance of the RLC circuit, u c is the terminal voltage of the RLC circuit.

5. The dynamic circuit modeling and analysis method of a multi-network VSG parallel system according to claim 1 is characterized in that: The transfer function in step 4 is: Where, Among them, m represents the mth station network type VSG, m∈[1,n], k represents the kth station network type VSG except the mth station, i represents the sum lower limit, n represents the number of network type VSGs in parallel, P em is the active power of the mth grid-type VSG, ω m is the angular frequency of the mth VSG, M Pm is the response coefficient of the mth grid-type VSG active power instruction disturbance to its own active power, F Pm,k is the response coefficient of the kth VSG active power instruction disturbance to the mth VSG active power, S Pm is the response coefficient of load power disturbance to the active power of the mth VSG, M ωm The response coefficient of the active power instruction disturbance of the m-th grid-type VSG to its own angular frequency, F ωm,k is the response coefficient of the kth VSG active power instruction disturbance to the mth VSG angular frequency, S ωm is the response coefficient of load power disturbance to the angular frequency of the mth VSG network, P refm is the active power instruction of the mth grid-type VSG, P refk is the active power instruction of the kth grid-type VSG, P c is the load power, Y am is the first admittance of the mth grid-type VSG, Y ai is the first admittance of the i-th VSG, Y ak is the first admittance of the kth grid-type VSG, Y bm is the second admittance of the mth grid-type VSG, Y bi is the second admittance of the i-th grid-type VSG, Y bk is the second admittance of the kth grid-type VSG, Δ represents the small perturbation at the equilibrium point, || represents series connection, and s is the Laplace operator.

Images