A dynamic phasor-impedance joint modeling method for a network-constructed energy storage system

Abstract

The application discloses a kind of dynamic phasor-impedance joint modeling methods of network type energy storage system, belong to energy storage grid-connected stability analysis field.It includes: constructing system topology and establishing the benchmark mathematical model under each submodule local reference coordinate system;Using dynamic phasor method to each submodule small signal linearization and unified to public reference coordinate system interconnection, constructs whole system dynamic phasor state space model;Using complex vector form establishes the dq domain impedance model considering power synchronization ring dynamic phase difference between control coordinate system and stable coordinate system, deduces equivalent output impedance model;Based on state space model, eigenvalue and participation factor analysis is carried out, and based on impedance model, frequency domain stability is judged with generalized Nyquist criterion, to realize time-frequency domain joint stability analysis.The application solves the problem that existing modeling ignores power synchronization ring dynamic and dynamic phase difference between two coordinate systems, accurately identifies oscillation risk, and improves the stable operation ability of high penetration rate network type energy storage grid-connected system.

Description

Technical Field

[0001] This invention relates to the field of stability analysis technology for grid-type energy storage, and specifically to a dynamic phasor-impedance joint modeling method for grid-type energy storage systems. Background Technology

[0002] The new power system with new energy as the main body has the characteristics of "double high" of high proportion of renewable energy and high proportion of power electronic equipment. The system inertia level is constantly decreasing and the frequency and voltage support capabilities are weakening. Grid-type energy storage can autonomously establish voltage and frequency references through power synchronization control such as droop control and virtual synchronizing machine control. It exhibits voltage source characteristics and has active inertia support and voltage support capabilities, as recorded in reference [1]. Compared with traditional grid-connected energy storage that relies on phase-locked loop to achieve grid synchronization, grid-type energy storage has better adaptability under weak grid conditions and has become a key technical means to improve the frequency stability and voltage support capabilities of the new power system.

[0003] However, with the increasing proportion of power electronic equipment, the oscillation and instability caused by the multi-scale dynamic interaction between power electronic equipment and AC power grid has become increasingly prominent, as recorded in reference [2]. Grid-type energy storage is essentially a power electronic device with multiple control loops and multiple control parameters. There are complex dynamic couplings between its power synchronization loop, reactive power-voltage control loop, filtering loop and line network. When it is connected to the grid through the grid impedance, it will also have a wide range of impedance interaction with the grid. At present, the influence of control parameters on system stability is not clear, and there is a lack of quantitative models to guide parameter optimization design. Moreover, when multiple grid-type energy storage devices are connected in parallel, the coupling mechanism between control parameters and network parameters is also unclear due to the interaction of each device through the line impedance. Therefore, establishing an accurate and efficient small-signal model of the grid-type energy storage system and carrying out stability analysis is the key to ensuring the safe and stable operation of the grid-type energy storage system.

[0004] Existing small-signal modeling and stability analysis methods for grid-connected converters are mainly divided into two categories: time-domain eigenvalue analysis based on state-space models and frequency-domain analysis based on impedance models. However, both have shortcomings. Firstly, the time-domain eigenvalue analysis method based on the state-space model establishes a full-order state-space model covering all control links and the main circuit, and uses eigenvalues ​​and participating factors to identify the oscillation mode and associated state variables of the system, as described in reference [3]. Although this method can fully characterize the dynamic characteristics of the system, the dimension of the state matrix increases significantly with the increase in the number of parallel devices and control links, the computational load for modeling and solving is large, and it is difficult to intuitively reflect the impedance interaction mechanism between the converter and the power grid.

[0005] Secondly, the frequency domain analysis method based on the impedance model equates the converter to the output impedance and the grid to the grid impedance. The stability of the grid-connected system is determined based on the Nyquist stability criterion. The physical meaning is clear and it is easy to verify by frequency sweep measurement. However, most of the existing impedance modeling is for grid-connected converters that achieve synchronization with phase-locked loops, as recorded in reference [4]. The impedance research for grid-connected converters usually only considers the power control loop and does not fully cover the multiple control loops of grid-connected energy storage. In particular, it ignores the dynamic characteristics of the power synchronization loop and the dynamic phase difference between the control coordinate system and the stable coordinate system due to the difference in rotational angular velocity. This results in insufficient accuracy of the impedance model in the low frequency band, making it difficult to accurately characterize the wideband impedance characteristics of grid-connected energy storage, which in turn affects the accuracy of frequency domain stability determination.

[0006] Third, the dynamic phasor method performs Fourier decomposition on the time-domain waveform of the state variables within a sliding time window to extract time-varying dynamic phasors. This can effectively reduce the model order while preserving the high-frequency dynamic characteristics of the system. It has been applied in the averaging modeling of power electronic circuits, as recorded in reference [5]. However, there are few reports on applying the dynamic phasor method to the modeling of multi-control loops in grid-type energy storage and combining the dynamic phasor state-space model with the impedance model to achieve joint stability analysis in the time and frequency domains.

[0007] In summary, there is an urgent need to establish a joint modeling method for grid-type energy storage systems that integrates the dynamic phasor method and the impedance method. Through joint stability analysis combining time-domain eigenvalue analysis and frequency-domain Nyquist criterion, the system can evaluate the impact of multiple control loop parameters and grid conditions on system stability, providing theoretical support for parameter optimization design and stable operation of grid-type energy storage.

[0008] References: [1] Lü Zhipeng, Sheng Wanxing, Zhong Qingchang, et al. Virtual synchronous generator and its application in microgrids [J]. Proceedings of the CSEE, 2014, 34(16): 2591-2603. [2] Yuan Xiaoming, Cheng Shijie, Hu Jiabing. Multi-scale voltage-power angle dynamic stability problem of power electronic power system [J]. Proceedings of the CSEE, 2016, 36(19): 5145-5154. [3] Pogaku N, Prodanovic M, Green T C. Modeling, analysis and testing of autonomous operation of an inverter-based microgrid[J]. IEEE Transactionson Power Electronics, 2007, 22(2): 613-625. [4] Cespedes M, Sun J. Impedance modeling and analysis of grid-connected voltage-source converters[J]. IEEE Transactions on PowerElectronics, 2014, 29(3): 1254-1261. [5] Sanders SR, Noworolski JM, Liu XZ, et al. Generalized averaging method for power conversion circuits[J]. IEEE Transactions on PowerElectronics, 1991, 6(2): 251-259. Summary of the Invention To address the shortcomings of existing grid-based energy storage modeling methods, which neglect the dynamic characteristics of power synchronization and the dynamic phase difference between the control and stable coordinate systems, and lack joint time-domain and frequency-domain analysis methods, this invention provides a dynamic phasor-impedance joint modeling method for grid-based energy storage systems. This method combines a dynamic phasor state-space model with a dq-domain impedance model that considers the dynamic phase difference, and achieves joint stability assessment in the time and frequency domains through joint eigenvalue analysis and the generalized Nyquist criterion. It boasts high modeling accuracy and computational efficiency, and can accurately identify broadband oscillation risks, providing reliable technical support for stability analysis and control parameter optimization of high-penetration grid-connected energy storage systems.

[0009] The technical solution adopted in this invention is as follows: A dynamic phasor-impedance joint modeling method for grid-type energy storage systems includes the following steps: S1: Construct the topology of the grid-type energy storage system and establish the benchmark mathematical model of each sub-module in the topology in its respective local reference coordinate system; S2: The dynamic phasor method is used to linearize the reference mathematical model of each sub-module into a small signal, establish the dynamic phasor small signal model of each sub-module, and then connect the dynamic phasor small signal models of each sub-module to a common reference coordinate system to construct the dynamic phasor state space model of the whole system. S3: The dq domain impedance model is established in complex vector form, taking into account the dynamic phase difference of the power synchronization loop between the control coordinate system and the stable coordinate system, and the equivalent output impedance model of the grid-type energy storage system is derived. S4: Based on the dynamic phasor state-space model, perform eigenvalue analysis and participation factor calculation to identify the dominant oscillation mode and associated state variables. Based on the equivalent output impedance model, use the generalized Nyquist criterion to determine the frequency domain stability, thereby achieving joint stability analysis combining the time and frequency domains.

[0010] S1 includes: S1.1: Construct the topology of the grid-type energy storage system. The main circuit of the topology includes a DC voltage source, a three-phase full-bridge inverter circuit, an LC filter, a π-type line equivalent circuit, and an AC grid. The control strategy of the topology includes a power control module, which consists of Pf droop control and QV droop control. S1.2: Based on the topology constructed in S1.1, establish the nonlinear equations for Pf droop control: ; ; in, For time; The angular velocity state variable is the control variable for Pf droop. Angular frequency in a common reference coordinate system; The angular frequency of the output is controlled by the droop of Pf; This is a reference value for angular frequency; It is a virtual inertial constant; The damping coefficient; The active power output of grid-type energy storage devices; This is a reference value for active power; S1.3: Based on the nonlinear equations for Pf droop control established in S1.2, establish the dynamic equations and output equations for QV droop control: ; ; in, These are the state variables of the PI controller; , These are the integral and proportional coefficients of the PI controller, respectively. The reactive power output of grid-type energy storage devices; This is a reference value for reactive power; This is the droop coefficient; , These are the voltage and reference value for QV droop control, respectively; This is the q-axis voltage output by the QV droop control.

[0011] S1 further includes: S1.4: Based on the topology constructed in S1.1, establish the dynamic equations of the LC filter: ; ; ; ; in, , These are the components of the filter inductor current of the LC filter on the d-axis and q-axis, respectively. , These are the components of the inverter output current on the d-axis and q-axis, respectively. , These are the components of the output current of the LC filter on the d-axis and q-axis, respectively. , These are the components of the inverter terminal voltage on the d-axis and q-axis, respectively. , These are the components of the filter capacitor voltage on the d-axis and q-axis, respectively. , , These are the equivalent series resistance, filter inductance, and filter capacitor of the LC filter, respectively. S1.5: Based on the dynamic equations of the LC filter established in S1.4, the dynamic equations of the equivalent circuit of the π-type line are established along the output side of the LC filter towards the AC power grid: ; ; ; ; in, , These are the current components on the d-axis and q-axis of the equivalent circuit of the π-type line, respectively. , These are the components of the load voltage on the d-axis and q-axis, respectively. , These are the components of the network voltage on the d-axis and q-axis after transformation from the common reference coordinate system; , These are the resistance and inductance of the equivalent circuit of the π-type circuit, respectively. It is the parallel capacitor in the equivalent circuit of a π-type circuit.

[0012] In S2, the dynamic phasor method is used to perform small-signal linearization on the baseline mathematical model of each sub-module, including: S2.1: Based on time-varying Fourier series, Fourier decomposition is performed on the time-domain waveforms of the state variables of each submodule within a sliding time window to extract the fundamental frequency component or specific harmonic components in phasor form. The k-th order dynamic phasor of the state variable is defined as: ; in, State variables of Dynamic phasor of order; The width of the sliding time window; For harmonic order; This is the system's fundamental angular frequency; For any of the aforementioned state variables; For integration variables; For time; The imaginary unit; is the base of the natural logarithm; S2.2: As defined in S2.1 The second-order dynamic phasor is used to transform the differential terms in the time-domain differential equations of each submodule into dynamic phasor form using the differential properties of dynamic phasors. The differential properties are as follows: ; S2.3: Regarding the two time-domain variables in the equation obtained by transformation in S2.2 , The product term, using the product property of dynamic phasors, is... The order of dynamic phasors is represented as the discrete convolution of each order of dynamic phasors: ; in, , Let them be any two time-domain variables; The harmonic order number is used to transform the time-domain differential equation into a combination of algebraic and differential equations about the dynamic phasors, thereby reducing the model order while preserving the high-frequency dynamic characteristics of the system.

[0013] S2 further includes: S2.4: The equations for the dynamic phasors of each submodule obtained from the transformation in S2.3 are linearized using small-signal methods at the steady-state operating point to establish the dynamic phasor small-signal model of each submodule; where: 1) The small-signal model for Pf droop control in the power control module is: ; in, For time; , , , These are the disturbances to the state vectors of the power control module, LC filter, π-type line equivalent circuit, and load, respectively. This is the self-coupling matrix of the power control module; , , These are the cross-coupling matrices of the power control module, LC filter, π-type line equivalent circuit, and load, respectively. This is the input matrix for Pf droop control; This represents the disturbance in the inverter terminal voltage. The linearized equation for the output voltage of the QV droop control in the power control module is: ; in, This represents the disturbance of the q-axis voltage output by the QV droop control. , These are the output matrix and the feedback matrix, respectively. 2) The small-signal model of the LC filter is: ; in, Here is the state space matrix of the LC filter; The disturbance amount of the angular frequency of the Pf droop control output; , These are the disturbances in the d-axis and q-axis components of the inverter terminal voltage, respectively. , These are the disturbances of the load voltage along the d-axis and q-axis, respectively. The input matrix is ​​the angular frequency perturbation matrix; This is the input matrix for inverter terminal voltage disturbance; This is the input matrix for the load voltage disturbance. 3) The small-signal model of the equivalent circuit of the π-type circuit is: ; in, The self-coupling matrix of the equivalent circuit of the π-type line; , , These are the cross-coupling matrices of the π-type line equivalent circuit and the power control module, LC filter, and load, respectively. The input matrix for the equivalent circuit of a π-type circuit; S2.5: Unify the dynamic phasor small-signal models of each submodule established in S2.4 to the common reference coordinate system through coordinate transformation. The transformation relationship between the variables of each submodule from the local reference coordinate system to the common reference coordinate system is as follows: ; ; in, This refers to the submodule number; For the first The variables of each submodule in the local reference coordinate system; These are the variables after transformation to a common reference coordinate system; For the first The coordinate transformation matrix of each submodule; For the first The angle between the local reference coordinate system and the common reference coordinate system of each submodule; S2.6: Connect the dynamic phasor small-signal models of each submodule after coordinate transformation in S2.5 through linear algebraic interconnections of input and output variables to construct the dynamic phasor state-space model of the entire system: ; in, These are the state variables of the entire system; The state space matrix of the entire system; The input perturbation vector; The input matrix is ​​denoted as .

[0014] S3 includes: S3.1: Transform the voltage and current quantities of the grid-type energy storage system from the three-phase stationary coordinate system to the synchronous rotating coordinate system, and express them in complex vector form. Define the dq domain small-signal variable in complex vector form as: ; in, For small-signal variables in the dq domain in complex vector form; , These are the positive and negative order components of the small-signal variable in the dq domain, respectively. , These are the small-signal components of the d-axis and q-axis in the stable coordinate system, respectively; the superscript s is the identifier of the stable coordinate system based on the grid voltage. The imaginary unit; S3.2: Based on the complex vector form defined in S3.1, establish the small-signal equivalent circuit on the AC side of the main circuit, and derive the filter inductor impedance matrix, line impedance matrix, and filter capacitor impedance matrix: ; ; ; in, , , These are the filter inductor impedance matrix, the line impedance matrix, and the filter capacitor impedance matrix, respectively. For the Laplace operator; This is the system's fundamental angular frequency; , , These are the equivalent series resistance, filter inductance, and filter capacitor of the LC filter, respectively. , These represent the resistance and inductance of the equivalent circuit of the π-type line, respectively; the superscript m is the identifier of the complex vector matrix.

[0015] S3 further includes: S3.3: The control coordinate system is the rotating coordinate system used by the control loop of the grid-type energy storage system, i.e., the c-coordinate system; the stable coordinate system is the rotating coordinate system used by the main circuit, i.e., the s-coordinate system; the two rotate synchronously in steady state, and a dynamic phase difference is generated due to the different rotational angular velocities when subjected to small disturbances; based on the small-signal equivalent circuit established in S3.2, the small disturbances to the output phase angle of the power synchronization loop are determined. for: ; Among them, the transfer function , They are respectively: ; ; in, This is a small disturbance to the output phase angle of the power synchronization loop; , These are the output current, port voltage, and small disturbance, respectively. The transfer function matrix; , These are the small-signal complex vectors of the output current and port voltage in the c-coordinate system, respectively. This is the active power droop coefficient; The transfer function of the low-pass filter; , These are the positive-sequence and negative-sequence components of the port voltage steady-state complex vector, respectively. , These are the positive-sequence and negative-sequence components of the steady-state complex vector of the output current, respectively; the superscript c is the identifier of the c-coordinate system. S3.4: The small perturbation determined according to S3.3 Establish the relationship between voltage and current small-signal quantities in the c-coordinate system and the s-coordinate system, and perform small-signal linearization: ; in, , These are the small-signal complex vectors of the output current and the port voltage in the s-coordinate system, respectively. S3.5: By combining equations S3.3 and S3.4, we obtain the direct linear transformation relationship between small-signal voltage and current quantities in the c-coordinate system and the s-coordinate system: ; ; in, , The output current and port voltage in the s-coordinate system are respectively under small disturbance. The transfer function matrix; , , , It is the transfer function matrix for the transformation of small-signal voltage and current quantities between the c-coordinate system and the s-coordinate system.

[0016] S3 further includes: S3.6: Based on the direct linear transformation relationship obtained in S3.5, after simplification, the equivalent output impedance model of the grid-type energy storage system in complex vector form is obtained: ; in, The equivalent output impedance of a grid-type energy storage system; This is the equivalent open-loop impedance matrix; , The small-signal transfer function matrix from output current to duty cycle; The small-signal transfer function matrix from port voltage to duty cycle; It is the identity matrix; S3.7: Convert the equivalent output impedance model of the network-type energy storage system in complex vector form obtained in S3.6 into a dq-domain impedance model in real transfer function form: ; ; in, For small-signal variables in the dq domain in the form of real transfer functions; The impedance matrix is ​​in complex vector form; This is the equivalent output impedance in the standard dq coordinate system.

[0017] S4 includes: S4.1: The state-space matrix of the entire system in the dynamic phasor state-space model constructed from S2. Find the eigenvalues: ; in, The eigenvalue index; For the first One eigenvalue; The real part of the eigenvalue represents the damping of the oscillation mode and determines the decay or divergence characteristics of the oscillation. The imaginary part of the eigenvalue represents the angular frequency of the oscillation mode and determines the period of the oscillation. When hour, Corresponding to an oscillation mode; when When, it is determined that the system has experienced small-signal instability; when When the system is stable in the oscillation mode, it is determined that the system is stable. S4.2: Based on the eigenvalues ​​obtained in S4.1, calculate the participating factors that characterize the correlation between the state variables and the eigenvalues: ; in, For the first State variables With the eigenvalues Factors involved in the correlation; For state variable index; and They are respectively The left and right eigenvectors; and Left eigenvectors and right eigenvectors The first in There are 10 elements; the superscript T denotes matrix transpose. The larger the value of the participation factor, the greater the degree of participation of the corresponding state variable in the corresponding oscillation mode.

[0018] S4.3: Based on the equivalent output impedance model derived in S3, the grid-type energy storage is equivalent to the parallel connection of an ideal current source and the equivalent output impedance, and the power grid is equivalent to the series connection of an ideal voltage source and the grid impedance. The generalized Nyquist criterion is applied to determine whether the eigenvalue locus of the levitational matrix encloses (…). The system stability is determined at point (j0), and the time-domain analysis results of S4.1 and S4.2 are combined with the frequency-domain determination results to achieve joint stability analysis combining the time and frequency domains.

[0019] Following S4, the following is also included: 5.1: Construct an electromagnetic transient time-domain simulation model of a grid-type energy storage system, and verify the results of the joint stability analysis described in S4 through time-domain simulation; 5.2: Construct a small-signal impedance model of the grid-type energy storage system, measure the output impedance of the grid-type energy storage system using the frequency sweep method, and compare the frequency sweep measurement results with the theoretical calculation value of the equivalent output impedance model derived in S3 to verify the accuracy of the equivalent output impedance model; 5.3: Based on the verification in 5.1 and 5.2, a hardware-in-the-loop experimental platform was built to conduct semi-physical experimental verification. By setting typical operating conditions with different grid strengths, energy storage penetration rates and fault types, the state variables of voltage, current and power at the grid connection point were collected to verify the effectiveness of the joint stability analysis.

[0020] This invention provides a dynamic phasor-impedance joint modeling method for grid-type energy storage systems, with the following technical advantages: 1) Addressing the issue that existing impedance modeling does not fully encompass the multiple control loops of grid-type energy storage, this invention establishes a complete benchmark mathematical model covering the power synchronization loop (Pf droop control and QV droop control), LC filter, and π-type line equivalent circuit. It integrates each control loop and main circuit component into the unified modeling framework, overcoming the shortcomings of existing impedance modeling that only considers the power loop or simplifies grid-type energy storage as a controlled voltage source. This enables the model to fully reflect the dynamic coupling relationships between multiple loops and parameters in grid-type energy storage, providing a complete model foundation for stability analysis.

[0021] 2) Addressing the issues of high state matrix dimension and large computational load in existing state-space eigenvalue analysis methods, this invention employs the dynamic phasor method to perform small-signal linearization processing on the time-domain differential equations of each submodule. It extracts time-varying phasor information of state variables through sliding-time-window Fourier decomposition, effectively reducing the model order while preserving the high-frequency dynamic characteristics of the system. This significantly reduces the computational load of constructing and solving the entire system's state-space model while maintaining modeling accuracy, thus balancing modeling accuracy and analysis efficiency.

[0022] 3) Addressing the issue that existing impedance modeling for grid-type energy storage neglects the dynamic characteristics of the power synchronization loop and the dynamic phase difference between the control and stable coordinate systems. This invention, when establishing the dq-domain impedance model, explicitly considers the dynamic phase difference between the two coordinate systems introduced by the power synchronization loop output phase angle disturbance. Through coordinate transformation and small-signal linearization, an equivalent output impedance model is derived, overcoming the accuracy deficiencies of existing impedance models in the low-frequency range. This allows for accurate characterization of the broadband impedance characteristics of grid-type energy storage, thereby improving the accuracy of frequency domain stability determination based on impedance.

[0023] 4) Addressing the limitations of existing technologies that lack joint time-domain and frequency-domain analysis methods and the limitations of single analysis methods, this invention combines eigenvalue analysis and participation factor calculation based on a dynamic phasor state-space model with a generalized Nyquist criterion based on an impedance model. This achieves joint stability analysis that mutually verifies the time and frequency domains: time-domain analysis can identify the dominant oscillation modes and their associated state variables, while the frequency-domain criterion can intuitively determine the stability boundary. The two complement each other, overcoming the limitations of single methods in simultaneously capturing dynamic details and revealing interaction mechanisms, and enabling more accurate identification of oscillation risks in grid-connected energy storage systems.

[0024] 5) Addressing the issues of unclear influence of control parameters on stability and the lack of quantitative models to guide parameter optimization, this invention quantifies the degree of participation of each state variable in each oscillation mode through participation factor calculation. This allows for the identification of control loops and key parameters strongly correlated with instability modes. By combining eigenvalue trajectories and impedance frequency characteristics, the impact of multiple control loop parameters and grid conditions on stability can be systematically evaluated, providing a clear quantitative basis for the optimized design of grid-type energy storage control parameters.

[0025] 6) Addressing the issues of unclear interaction mechanisms among multiple grid-connected energy storage devices operating in parallel and the lack of quantitative analysis methods for the coupling of control parameters and network parameters, this invention unifies the sub-module models of each parallel device to a common reference coordinate system through coordinate transformation and interconnection, constructing a full-system model that includes the line network and load. This model can characterize the interaction of parallel devices through line impedance and the coupling mechanism of control parameters and network parameters, thereby effectively revealing the broadband interaction mechanism between grid-connected energy storage and the power grid system, providing reliable technical support for the stability analysis and stable operation of high-penetration grid-connected energy storage systems. Attached Figure Description

[0026] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is a schematic diagram of the topology of a grid-type energy storage device parallel system in an embodiment of the present invention.

[0027] Figure 2 This is a schematic diagram of the AC side small-signal equivalent circuit of the main circuit in the complex vector form of the present invention.

[0028] Figure 3 This is a comparison chart of the theoretically calculated value of the equivalent output impedance of the grid-connected energy storage system of the present invention and the results of frequency sweep measurement.

[0029] Figure 4 This is the eigenvalue locus diagram of the cyclicity matrix under different power grid intensities according to the present invention.

[0030] Figure 5 This is a waveform diagram of the dynamic response of the grid-type energy storage system of the present invention under small disturbance.

[0031] Figure 6 This is a trajectory diagram of the dominant oscillation mode of the system when the filter inductance changes according to the present invention. Detailed Implementation

[0032] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Example 1: like Figure 1 , Figure 2 As shown, this embodiment provides a dynamic phasor-impedance joint modeling method for a grid-type energy storage system, including the following steps S1 to S5.

[0033] S1: Construct the topology of the grid-type energy storage system and establish the benchmark mathematical model of each sub-module in the topology in its respective local reference coordinate system.

[0034] S1.1: Construct the topology of a grid-type energy storage system. For example... Figure 1 As shown, taking a parallel system of two grid-connected energy storage devices as an example, the main circuit of the topology includes a DC voltage source, a three-phase full-bridge inverter circuit, an LC filter, a π-type line equivalent circuit, and an AC grid. The control strategy of the topology includes a power control module, which consists of Pf droop control and QV droop control. The load is connected to the parallel node of the π-type line equivalent circuit, and its state vector is denoted as... The load can be established using a constant power load model or a constant impedance load model.

[0035] S1.2: Based on the topology constructed in S1.1, establish the nonlinear equation for Pf droop control: (1); (2); in, For time; The angular velocity state variable is the control variable for Pf droop. Angular frequency in a common reference coordinate system; The angular frequency of the output is controlled by the droop of Pf; This is a reference value for angular frequency; It is a virtual inertial constant; The damping coefficient; The active power output of grid-type energy storage devices; This is a reference value for active power.

[0036] The aforementioned nonlinear equations characterize the working principle of the power control module, which simulates the inertia and damping characteristics of a synchronous generator, enabling the grid-type energy storage device to exhibit external voltage source characteristics and autonomously establish a frequency reference.

[0037] S1.3: Based on the nonlinear equations established in S1.2, establish the dynamic equations and output equations for QV droop control. The dynamics of the PI controller in the QV droop control utilize state variables. Modeling: (3); (4); in, These are the state variables of the PI controller; , These are the integral and proportional coefficients of the PI controller, respectively. The reactive power output of grid-type energy storage devices; This is a reference value for reactive power; This is the droop coefficient; , These are the voltage and reference value for QV droop control, respectively; This refers to the q-axis voltage output by the QV droop control. The QV droop control generates voltage commands through the reactive power-voltage droop characteristic and PI regulation, thereby enabling voltage support for grid-type energy storage devices.

[0038] S1.4: Based on the topology constructed in S1.1, establish the dynamic equations of the LC filter (including the transformer) in the stationary coordinate system: (5); (6); (7); (8); in, , These are the components of the filter inductor current of the LC filter on the d-axis and q-axis, respectively. , These are the components of the inverter output current on the d-axis and q-axis, respectively. , These are the components of the LC filter output current on the d-axis and q-axis, respectively. , These are the components of the inverter terminal voltage on the d-axis and q-axis, respectively. , These are the components of the filter capacitor voltage on the d-axis and q-axis, respectively. , , These represent the equivalent series resistance, filter inductance, and filter capacitor of the LC filter, respectively.

[0039] S1.5: Based on the dynamic equations of the LC filter established in S1.4, the dynamic equations of the equivalent circuit of the π-type line are established along the output side of the LC filter towards the AC power grid: (9); (10); (11); (12); in, , These are the current components on the d-axis and q-axis of the equivalent circuit of the π-type line, respectively. , These are the components of the load voltage on the d-axis and q-axis, respectively. , These are the components of the network voltage on the d-axis and q-axis after transformation from the common reference coordinate system; , These are the resistance and inductance of the equivalent circuit of the π-type circuit, respectively. This is the parallel capacitor in the equivalent circuit of the π-type line. At this point, the baseline mathematical model for the power control module, LC filter, and equivalent circuit of the π-type line is complete, fully covering the multiple control loops and main circuit components of the grid-type energy storage system.

[0040] S2: The dynamic phasor method is used to linearize the baseline mathematical model of each sub-module into a small signal, establish the dynamic phasor small signal model of each sub-module, and interconnect them to construct the dynamic phasor state space model of the whole system.

[0041] S2.1: The dynamic phasor method, based on time-varying Fourier series, performs Fourier decomposition on the time-domain waveforms of each state variable in the system within a sliding time window, extracting its fundamental frequency component or specific harmonic components in phasor form. The definition of a dynamic phasor is: (13); in, State variables of Dynamic phasor of order; The width of the sliding time window is taken in this embodiment as the system fundamental period, i.e. ; The harmonic order is taken when performing fundamental frequency dynamic analysis. When analyzing the dynamics of a specific harmonic, the corresponding order should be selected; This is the system's fundamental angular frequency; Let it be any state variable; For integration variables; For time; The imaginary unit; is the base of the natural logarithm.

[0042] S2.2: As defined in S2.1 The second-order dynamic phasor is used to transform the differential terms in the time-domain differential equations of each submodule into dynamic phasor form using the differential properties of dynamic phasors. The differential properties are as follows: (14); S2.3: Regarding the two time-domain variables in the equation obtained by transformation in S2.2 , The product term, using the product property of dynamic phasors, is used to... The order of dynamic phasors is represented as the discrete convolution of each order of dynamic phasors: (15); in, , Let them be any two time-domain variables; The harmonic order is represented by the above transformation. This transforms the time-domain differential equation into a combination of algebraic and differential equations concerning dynamic phasors, thereby reducing the model order while preserving the high-frequency dynamic characteristics of the system, thus balancing modeling accuracy and computational efficiency.

[0043] S2.4: Before performing small-signal linearization, the steady-state values ​​of each state variable are solved based on the given operating conditions of the system (active power reference value, reactive power reference value, and grid voltage) to determine the steady-state operating point. Then, at the steady-state operating point, the equations of each sub-module obtained from S2.3 regarding the dynamic phasors are linearized using small-signal linearization to establish the dynamic phasor small-signal model of each sub-module, as detailed below: 1) Small-signal model of the power control module: The small-signal model for Pf droop control is: (16); in, , , , These are the disturbances to the state vectors of the power control module, LC filter, π-type line equivalent circuit, and load, respectively. This is the self-coupling matrix of the power control module; , , These are the cross-coupling matrices of the power control module and the LC filter, the equivalent circuit of the π-type line, and the load, respectively. This is the input matrix for Pf droop control; This represents the disturbance in the inverter terminal voltage.

[0044] The linearized equation for the output voltage of the QV droop control is: (17); in, This represents the disturbance of the q-axis voltage output by the QV droop control. , These are the output matrix and the feedback matrix, respectively.

[0045] (2) Small-signal model of LC filter: (18); in, Here is the state space matrix of the LC filter; The disturbance amount of the angular frequency of the Pf droop control output; , These are the disturbances in the d-axis and q-axis components of the inverter terminal voltage, respectively. , These are the disturbances of the load voltage along the d-axis and q-axis, respectively. The input matrix is ​​the angular frequency perturbation matrix; This is the input matrix for inverter terminal voltage disturbance; This is the input matrix for load voltage disturbance.

[0046] (3) Small-signal model of the equivalent circuit of π-type circuit: (19); in, The self-coupling matrix of the equivalent circuit of the π-type line; , , These are the cross-coupling matrices of the π-type line equivalent circuit and the power control module, LC filter, and load, respectively. This is the input matrix of the equivalent circuit of the π-type circuit.

[0047] S2.5: After each submodule has been modeled in its own local reference coordinate system, it is unified to a common reference coordinate system through coordinate transformation. The transformation relationship between the variables of each submodule from the local reference coordinate system to the common reference coordinate system is as follows: (20); (twenty one); in, This refers to the submodule number; For the first The variables of each submodule in the local reference coordinate system; These are the variables after transformation to the common reference coordinate system; For the first The coordinate transformation matrix of each submodule; For the first The angle between the local reference coordinate system of each submodule and the common reference coordinate system.

[0048] S2.6: The dynamic phasor small-signal models of each submodule described in S2.5 after coordinate transformation are connected through linear algebraic interconnections of input and output variables. For a parallel system of two grid-type energy storage devices, the dynamic phasor state-space model of the entire system is uniformly represented as: (twenty two); in, These are the state variables of the entire system; The state space matrix of the entire system; The input perturbation vector; The input matrix is ​​defined as follows. The dynamic phasor state-space model fully preserves the interaction between parallel devices through the line network and the coupling relationship between control parameters and network parameters, providing model support for time-domain eigenvalue analysis.

[0049] S3: The dq domain impedance model is established in complex vector form, taking into account the dynamic phase difference between the power synchronization loop in the control coordinate system and the stable coordinate system, and the equivalent output impedance model of the grid-type energy storage system is derived.

[0050] S3.1: The voltage and current quantities of the grid-type energy storage system are transformed from the three-phase stationary coordinate system to the synchronous rotating coordinate system and expressed in complex vector form. The small-signal variables in the dq domain in complex vector form are defined as follows: (twenty three); in, For small-signal variables in the dq domain in complex vector form; , These are the positive and negative order components of the small-signal variable in the dq domain, respectively. , These are the small-signal components of the d-axis and q-axis in the stable coordinate system, respectively; the superscript s is the identifier of the stable coordinate system based on the grid voltage.

[0051] S3.2: Based on the complex vector form defined in S3.1, establish the small-signal equivalent circuit on the AC side of the main circuit, such as... Figure 2 As shown, the impedance matrix of the filter inductor, the line impedance matrix, and the impedance matrix of the filter capacitor are derived: (twenty four); (25); (26); in, , , These are the filter inductor impedance matrix, the line impedance matrix, and the filter capacitor impedance matrix, respectively. is the Laplace operator; the superscript m is the identifier of the complex vector form matrix; , , , , , The meaning is consistent with that in S1 and S2.

[0052] S3.3: The control coordinate system is the rotating coordinate system used by the control loop of the grid-type energy storage system, i.e., the c-coordinate system; the stable coordinate system is the rotating coordinate system used by the main circuit, i.e., the s-coordinate system. Both rotate synchronously in steady state, but a dynamic phase difference arises due to their different rotational angular velocities when subjected to small disturbances. Based on the small-signal equivalent circuit established in S3.2, small disturbances to the output phase angle of the power synchronization loop are determined. for: (27); Among them, the transfer function , They are respectively: (28); (29); in, This is a small disturbance to the output phase angle of the power synchronization loop; , These are output current, port voltage, and small disturbances, respectively. The transfer function matrix; $m'$ is the active droop coefficient; Here is the transfer function of the low-pass filter; , These are the positive-sequence and negative-sequence components of the port voltage steady-state complex vector, respectively. , These are the positive-sequence and negative-sequence components of the steady-state complex vector of the output current, respectively. , These are small-signal complex vectors of output current and port voltage in the c-coordinate system, respectively; the superscript c is the identifier of the c-coordinate system.

[0053] S3.4: Small perturbation determined according to S3.3 The voltage and current small-signal quantities in the c-coordinate system and the s-coordinate system satisfy the following relationship: (30); Applying small-signal linearization to the above equation, we get: (31); in, , These are the small-signal complex vectors of the output current and port voltage in the s-coordinate system, respectively.

[0054] S3.5: By combining equations S3.3 and S3.4, we obtain the direct linear transformation relationship between small-signal voltage and current quantities in the c-coordinate system and the s-coordinate system: (34); (35); in, , The output current and port voltage in the s-coordinate system are respectively under small disturbance. The transfer function matrix; , , , This is the transfer function matrix for the transformation of small-signal voltage and current quantities between the c-coordinate system and the s-coordinate system. The above transformation relationship introduces the dynamic characteristics of the power synchronization loop and the dynamic phase difference between the two coordinate systems into the impedance derivation process, overcoming the defect of insufficient accuracy in the low-frequency band caused by neglecting it in existing impedance modeling.

[0055] S3.6: Based on the direct linear transformation relationship obtained in S3.5, after simplification, the equivalent output impedance model of the grid-type energy storage system in complex vector form is obtained: (36); in, The equivalent output impedance of a grid-type energy storage system; This is the equivalent open-loop impedance matrix; , The small-signal transfer function matrix from output current to duty cycle; The small-signal transfer function matrix from port voltage to duty cycle; It is an identity matrix.

[0056] S3.7: Convert the equivalent output impedance model in complex vector form obtained in S3.6 into a dq domain impedance model in real transfer function form: (37); (38); in, For small-signal variables in the dq domain in the form of real transfer functions; The impedance matrix is ​​in complex vector form; This is the equivalent output impedance in the standard dq coordinate system.

[0057] S4: Based on the dynamic phasor state-space model, eigenvalue analysis and participation factor calculation are performed, and based on the equivalent output impedance model, the generalized Nyquist criterion is used to determine the frequency domain stability, realizing joint stability analysis combining the time domain and frequency domain.

[0058] S4.1: The state-space matrix of the entire system based on the dynamic phasor state-space model constructed from S2.6. Find the eigenvalues: (39); in, The eigenvalue index; For the first One eigenvalue; The real part of the eigenvalue represents the damping of the oscillation mode and determines the decay or divergence characteristics of the oscillation. The imaginary part of the eigenvalue represents the oscillation angular frequency of the oscillation mode and determines the oscillation period. When hour, Corresponding to an oscillation mode; when When, it is determined that the system has experienced small-signal instability; when When the system is stable in the oscillation mode, it is determined that the system is stable.

[0059] S4.2: Based on the eigenvalues ​​obtained in S4.1, calculate the participating factors that characterize the correlation between the state variables and the eigenvalues: (40); in, For the first State variables With the eigenvalues Factors involved in the correlation; For state variable index; and They are respectively The left and right eigenvectors; and The left feature vectors are respectively and the right feature vector The first in There are 10 elements; the superscript T indicates matrix transpose. The larger the value of the participation factor, the greater the participation of the corresponding state variable in the corresponding oscillation mode. Based on this, the associated state variables and key control links of the dominant oscillation mode can be identified, providing a quantitative basis for the optimization of control parameters.

[0060] S4.3: Based on the equivalent output impedance model derived in S3, the grid-type energy storage is equivalent to a parallel connection of an ideal current source and an equivalent output impedance, and the power grid is equivalent to a series connection of an ideal voltage source and a grid impedance, forming a closed-loop system with impedance interaction. Its hysteresis matrix is: (41); in, This is the return matrix; Let the impedance be the grid impedance. Applying the generalized Nyquist criterion, determine whether the eigenvalue locus of the levitational matrix encloses (the grid impedance). The stability of the system is determined when the feature root trajectory does not enclose (j0) points. When the system reaches point (j1, j0), it is determined to be stable; when the feature root locus encloses (j0, j0), the system is considered stable. When the system reaches point (j1, j0), it is determined to be unstable. The time-domain analysis results of S4.1 and S4.2 are combined with the frequency-domain determination results of S4.3, and the two are mutually verified to achieve joint stability analysis combining the time and frequency domains.

[0061] S5: The stability analysis conclusions are verified through time-domain simulation and semi-physical experiments, and the equivalent output impedance model is verified by sweep frequency impedance measurement.

[0062] 5.1: Construct an electromagnetic transient time-domain simulation model of a grid-type energy storage system, and verify the results of the joint stability analysis described in S4 through time-domain simulation; 5.2: Construct a small-signal impedance model of a grid-type energy storage system, measure the output impedance of the grid-type energy storage system using the frequency sweep method, and compare the frequency sweep measurement results with the theoretical calculation value of the equivalent output impedance model derived in S3 to verify the accuracy of the equivalent output impedance model; 5.3: Based on the verification in 5.1 and 5.2, a hardware-in-the-loop experimental platform was built to conduct semi-physical experimental verification. By setting typical operating conditions with different grid strengths, energy storage penetration rates and fault types, the state variables of voltage, current and power at the grid connection point were collected to verify the effectiveness of the joint stability analysis.

[0063] Example 2: This embodiment provides a specific parameter setting for implementing the method described in Embodiment 1, to support implementation by those skilled in the art. Taking a parallel system of two grid-connected energy storage devices with the same parameters as an example, the two grid-connected energy storage devices are connected in parallel after passing through their respective LC filters, and then connected to the AC power grid through a π-type line equivalent circuit. The main parameters of the system are shown in Table 1.

[0064]

[0065] The grid strength is characterized by the short-circuit ratio (SCR), and different grid strength conditions (strong grid, weak grid) are set by changing the grid impedance; the filter inductor... Three values, 60μH, 80μH, and 110μH, were selected to cover the two ends and the middle of the parameter variation range, in order to examine the impact of changes in control parameters and main circuit parameters on system stability.

[0066] Example 3: This embodiment verifies the joint modeling method and stability analysis results described in Embodiment 1 based on an electromagnetic transient simulation platform and a hardware-in-the-loop experimental platform. Figures 3-6 As shown.

[0067] 1) Accuracy Verification of Impedance Model: The output impedance of the grid-connected energy storage system was measured using a frequency sweep method, and the results were compared with the theoretical calculations of the dq-domain impedance model established in this invention. For example... Figure 3 As shown, the comparison results indicate that the theoretical impedance model and the frequency sweep measurement results are in high agreement across the entire frequency band, proving the accuracy of the complex vector form dq domain impedance model established in this invention.

[0068] 2) Frequency Domain Stability Verification: Based on the established impedance model, the generalized Nyquist criterion is applied to determine the frequency domain stability. For example... Figure 4 As shown, the eigenvalue trajectories of the eigenvalue matrix under different power grid intensities are presented: Under strong power grid conditions, the eigenvalue trajectories do not enclose ( At point (j0), the system exhibits good stability; as the grid strength decreases, the characteristic root locus gradually shifts towards (j0). The eigenvalue locus moves across (j0) points; when the power grid strength is weak, the eigenvalue locus crosses (j0). At point (j0), the system becomes unstable. The above results demonstrate that the generalized Nyquist criterion based on the impedance model in this invention can accurately determine the stability boundary of a grid-connected energy storage system.

[0069] 3) Time-domain dynamic response verification: Based on the hardware-in-the-loop simulation platform of the grid-connected energy storage system, typical disturbance conditions such as grid strength changes and power command step jumps are set, and the time-domain response waveforms of state variables such as voltage, current, and power at the grid connection point are collected. For example... Figure 5As shown, the oscillation waveforms of active power, terminal voltage, and AC current rapidly decay and tend to stabilize after the disturbance is eliminated, which is consistent with the stability analysis conclusion of S4, verifying the accuracy of the joint analysis method of the present invention in assessing system stability.

[0070] 4) Eigenvalue analysis and time-domain simulation verification: Eigenvalue analysis is performed based on the dynamic phasor state-space model. Figure 6 The filter inductor is given. The trajectory of the system's dominant oscillation mode as adjusted from 60 μH to 110 μH. Figure 6 It can be seen that, with With the increase of [variable name], the damping ratio of the dominant oscillation mode increases significantly, and the system stability is enhanced, while the oscillation frequency remains almost unchanged; different [variable names] The time-domain response waveform under the given values ​​is consistent with the eigenvalue analysis conclusions. The increased size of the system accelerates its convergence speed after being disturbed, verifying the correctness of the dynamic phasor state space model and its eigenvalue analysis method established in this invention.

[0071] Based on the above verification results, it can be seen that the joint modeling method established in this invention can accurately characterize the dynamic characteristics of grid-connected energy storage systems. The time-domain eigenvalue analysis results, frequency-domain Nyquist determination results, time-domain simulation results, and semi-physical experiment results corroborate each other, proving the effectiveness of the joint modeling and stability analysis method.

Claims

1. A dynamic phasor-impedance joint modeling method for a grid-type energy storage system, characterized in that... Includes the following steps: S1: Construct the topology of the grid-type energy storage system and establish the benchmark mathematical model of each sub-module in the topology in its respective local reference coordinate system; S2: The dynamic phasor method is used to linearize the reference mathematical model of each sub-module into a small signal, establish the dynamic phasor small signal model of each sub-module, and then connect the dynamic phasor small signal models of each sub-module to a common reference coordinate system to construct the dynamic phasor state space model of the whole system. S3: The dq domain impedance model is established in complex vector form, taking into account the dynamic phase difference of the power synchronization loop between the control coordinate system and the stable coordinate system, and the equivalent output impedance model of the grid-type energy storage system is derived. S4: Based on the dynamic phasor state-space model, perform eigenvalue analysis and participation factor calculation to identify the dominant oscillation mode and associated state variables. Based on the equivalent output impedance model, use the generalized Nyquist criterion to determine the frequency domain stability, thereby achieving joint stability analysis combining the time and frequency domains.

2. The dynamic phasor-impedance joint modeling method for a grid-type energy storage system according to claim 1, characterized in that: S1 includes: S1.1: Construct the topology of the grid-type energy storage system. The main circuit of the topology includes a DC voltage source, a three-phase full-bridge inverter circuit, an LC filter, a π-type line equivalent circuit, and an AC grid. The control strategy of the topology includes a power control module, which consists of Pf droop control and QV droop control. S1.2: Based on the topology constructed in S1.1, establish the nonlinear equations for Pf droop control: ； ； in, For time; The angular velocity state variable is controlled by the droop of Pf; Angular frequency in a common reference coordinate system; The angular frequency of the output is controlled by the droop of Pf; This is a reference value for angular frequency; It is a virtual inertial constant; The damping coefficient; The active power output of grid-type energy storage devices; This is a reference value for active power; S1.3: Based on the nonlinear equations for Pf droop control established in S1.2, establish the dynamic equations and output equations for QV droop control: ； ； in, These are the state variables of the PI controller; , These are the integral and proportional coefficients of the PI controller, respectively. The reactive power output of grid-type energy storage devices; This is a reference value for reactive power; This is the droop coefficient; , These are the voltage and reference value for QV droop control, respectively; This is the q-axis voltage output by the QV droop control.

3. The dynamic phasor-impedance joint modeling method for a grid-type energy storage system according to claim 2, characterized in that: S1 further includes: S1.4: Based on the topology constructed in S1.1, establish the dynamic equations of the LC filter: ； ； ； ； in, , These are the components of the filter inductor current of the LC filter on the d-axis and q-axis, respectively. , These are the components of the inverter output current on the d-axis and q-axis, respectively. , These are the components of the output current of the LC filter on the d-axis and q-axis, respectively. , These are the components of the inverter terminal voltage on the d-axis and q-axis, respectively. , These are the components of the filter capacitor voltage on the d-axis and q-axis, respectively. , , These are the equivalent series resistance, filter inductance, and filter capacitor of the LC filter, respectively. S1.5: Based on the dynamic equations of the LC filter established in S1.4, the dynamic equations of the equivalent circuit of the π-type line are established along the output side of the LC filter towards the AC power grid: ； ； ； ； in, , These are the current components on the d-axis and q-axis of the equivalent circuit of the π-type line, respectively. , These are the components of the load voltage on the d-axis and q-axis, respectively. , These are the components of the network voltage on the d-axis and q-axis after transformation from the common reference coordinate system; , These are the resistance and inductance of the equivalent circuit of the π-type circuit, respectively. It is the parallel capacitor in the equivalent circuit of a π-type circuit.

4. The dynamic phasor-impedance joint modeling method for a grid-type energy storage system according to claim 3, characterized in that: In S2, the dynamic phasor method is used to perform small-signal linearization on the baseline mathematical model of each sub-module, including: S2.1: Based on time-varying Fourier series, Fourier decomposition is performed on the time-domain waveforms of the state variables of each submodule within a sliding time window to extract the fundamental frequency component or specific harmonic components in phasor form. The k-th order dynamic phasor of the state variable is defined as: ； in, State variables of Dynamic phasor of order; The width of the sliding time window; For harmonic order; This is the system's fundamental angular frequency; For any of the aforementioned state variables; For integration variables; For time; The imaginary unit; is the base of the natural logarithm; S2.2: As defined in S2.1 The second-order dynamic phasor is used to transform the differential terms in the time-domain differential equations of each submodule into dynamic phasor form using the differential properties of dynamic phasors. The differential properties are as follows: ； S2.3: Regarding the two time-domain variables in the equation obtained by transformation in S2.2 , The product term, using the product property of dynamic phasors, is... The order of dynamic phasors is represented as the discrete convolution of each order of dynamic phasors: ； in, , Let them be any two time-domain variables; The harmonic order number is used to transform the time-domain differential equation into a combination of algebraic and differential equations about the dynamic phasors, thereby reducing the model order while preserving the high-frequency dynamic characteristics of the system.

5. The dynamic phasor-impedance joint modeling method for a grid-type energy storage system according to claim 4, characterized in that: S2 further includes: S2.4: The equations for the dynamic phasors of each submodule obtained from the transformation in S2.3 are linearized using small-signal methods at the steady-state operating point to establish the dynamic phasor small-signal model of each submodule; where: 1) The small-signal model for Pf droop control in the power control module is: ； in, For time; , , , These are the disturbances to the state vectors of the power control module, LC filter, π-type line equivalent circuit, and load, respectively. This is the self-coupling matrix of the power control module; , , These are the cross-coupling matrices of the power control module, LC filter, π-type line equivalent circuit, and load, respectively. This is the input matrix for Pf droop control; This represents the disturbance in the inverter terminal voltage. The linearized equation for the output voltage of the QV droop control in the power control module is: ； in, This represents the disturbance of the q-axis voltage output by the QV droop control. , These are the output matrix and the feedback matrix, respectively. 2) The small-signal model of the LC filter is: ； in, Here is the state space matrix of the LC filter; The disturbance amount of the angular frequency of the Pf droop control output; , These are the disturbances in the d-axis and q-axis components of the inverter terminal voltage, respectively. , These are the disturbances of the load voltage along the d-axis and q-axis, respectively. The input matrix is ​​the angular frequency perturbation matrix; This is the input matrix for inverter terminal voltage disturbance; This is the input matrix for the load voltage disturbance. 3) The small-signal model of the equivalent circuit of the π-type circuit is: ； in, The self-coupling matrix of the equivalent circuit of the π-type line; , , These are the cross-coupling matrices of the π-type line equivalent circuit and the power control module, LC filter, and load, respectively. The input matrix for the equivalent circuit of a π-type circuit; S2.5: Unify the dynamic phasor small-signal models of each submodule established in S2.4 to the common reference coordinate system through coordinate transformation. The transformation relationship between the variables of each submodule from the local reference coordinate system to the common reference coordinate system is as follows: ； ； in, This refers to the submodule number; For the first The variables of each submodule in the local reference coordinate system; These are the variables after transformation to a common reference coordinate system; For the first The coordinate transformation matrix of each submodule; For the first The angle between the local reference coordinate system and the common reference coordinate system of each submodule; S2.6: Connect the dynamic phasor small-signal models of each submodule after coordinate transformation in S2.5 through linear algebraic interconnections of input and output variables to construct the dynamic phasor state-space model of the entire system: ； in, These are the state variables of the entire system; The state space matrix of the entire system; The input perturbation vector; The input matrix is ​​denoted as .

6. The dynamic phasor-impedance joint modeling method for a grid-type energy storage system according to claim 5, characterized in that: S3 includes: S3.1: Transform the voltage and current quantities of the grid-type energy storage system from the three-phase stationary coordinate system to the synchronous rotating coordinate system, and express them in complex vector form. Define the dq domain small-signal variable in complex vector form as: ； in, For small-signal variables in the dq domain in complex vector form; , These are the positive and negative order components of the small-signal variable in the dq domain, respectively. , These are the small-signal components of the d-axis and q-axis in the stable coordinate system, respectively; the superscript s is the identifier of the stable coordinate system based on the grid voltage. The imaginary unit; S3.2: Based on the complex vector form defined in S3.1, establish the small-signal equivalent circuit on the AC side of the main circuit, and derive the filter inductor impedance matrix, line impedance matrix, and filter capacitor impedance matrix: ； ； ； in, , , These are the filter inductor impedance matrix, the line impedance matrix, and the filter capacitor impedance matrix, respectively. For the Laplace operator; This is the system's fundamental angular frequency; , , These are the equivalent series resistance, filter inductance, and filter capacitor of the LC filter, respectively. , These represent the resistance and inductance of the equivalent circuit of the π-type line, respectively; the superscript m is the identifier of the complex vector matrix.

7. The dynamic phasor-impedance joint modeling method for a grid-type energy storage system according to claim 6, characterized in that: S3 further includes: S3.3: The control coordinate system is the rotating coordinate system used by the control loop of the grid-type energy storage system, i.e., the c-coordinate system; the stable coordinate system is the rotating coordinate system used by the main circuit, i.e., the s-coordinate system; the two rotate synchronously in steady state, and a dynamic phase difference is generated due to the different rotational angular velocities when subjected to small disturbances; based on the small-signal equivalent circuit established in S3.2, the small disturbances to the output phase angle of the power synchronization loop are determined. for: ； Among them, the transfer function , They are respectively: ； ； in, This is a small disturbance to the output phase angle of the power synchronization loop; , These are the output current, port voltage, and small disturbance, respectively. The transfer function matrix; , These are the small-signal complex vectors of the output current and port voltage in the c-coordinate system, respectively. This is the active power droop coefficient; The transfer function of the low-pass filter; , These are the positive-sequence and negative-sequence components of the port voltage steady-state complex vector, respectively. , These are the positive-sequence and negative-sequence components of the steady-state complex vector of the output current, respectively; the superscript c is the identifier of the c-coordinate system. S3.4: The small perturbation determined according to S3.3 Establish the relationship between voltage and current small-signal quantities in the c-coordinate system and the s-coordinate system, and perform small-signal linearization: ； in, , These are the small-signal complex vectors of the output current and the port voltage in the s-coordinate system, respectively. S3.5: By combining equations S3.3 and S3.4, we obtain the direct linear transformation relationship between small-signal voltage and current quantities in the c-coordinate system and the s-coordinate system: ； ； in, , The output current and port voltage in the s-coordinate system are respectively under small disturbance. The transfer function matrix; , , , It is the transfer function matrix for the transformation of small-signal voltage and current quantities between the c-coordinate system and the s-coordinate system.

8. The dynamic phasor-impedance joint modeling method for a grid-type energy storage system according to claim 7, characterized in that: S3 further includes: S3.6: Based on the direct linear transformation relationship obtained in S3.5, after simplification, the equivalent output impedance model of the grid-type energy storage system in complex vector form is obtained: ； in, The equivalent output impedance of a grid-type energy storage system; This is the equivalent open-loop impedance matrix; , The small-signal transfer function matrix from output current to duty cycle; The small-signal transfer function matrix from port voltage to duty cycle; It is the identity matrix; S3.7: Convert the equivalent output impedance model of the network-type energy storage system in complex vector form obtained in S3.6 into a dq-domain impedance model in real transfer function form: ； ； in, For small-signal variables in the dq domain in the form of real transfer functions; The impedance matrix is ​​in complex vector form; This is the equivalent output impedance in the standard dq coordinate system.

9. The dynamic phasor-impedance joint modeling method for a grid-type energy storage system according to claim 8, characterized in that: S4 includes: S4.1: The state-space matrix of the entire system in the dynamic phasor state-space model constructed from S2. Find the eigenvalues: ； in, The eigenvalue index; For the first One eigenvalue; The real part of the eigenvalue represents the damping of the oscillation mode and determines the decay or divergence characteristics of the oscillation. The imaginary part of the eigenvalue represents the angular frequency of the oscillation mode and determines the period of the oscillation; when hour, Corresponding to an oscillation mode; when When, it is determined that the system has experienced small-signal instability; when When the system is stable in the oscillation mode, it is determined that the system is stable. S4.2: Based on the eigenvalues ​​obtained in S4.1, calculate the participating factors that characterize the correlation between the state variables and the eigenvalues: ； in, For the first State variables With the eigenvalues Factors involved in the correlation; For state variable index; and They are respectively The left and right eigenvectors; and Left eigenvectors and right eigenvectors The first in There are 10 elements; the superscript T indicates matrix transpose; the larger the value of the participation factor, the greater the participation of the corresponding state variable in the corresponding oscillation mode; S4.3: Based on the equivalent output impedance model derived in S3, the grid-type energy storage is equivalent to the parallel connection of an ideal current source and the equivalent output impedance, and the power grid is equivalent to the series connection of an ideal voltage source and the grid impedance. The generalized Nyquist criterion is applied to determine whether the eigenvalue locus of the levitational matrix encloses (…). The system stability is determined at point (j0), and the time-domain analysis results of S4.1 and S4.2 are combined with the frequency-domain determination results to achieve joint stability analysis combining the time and frequency domains.

10. The dynamic phasor-impedance joint modeling method for a grid-type energy storage system according to claim 9, characterized in that: Following S4, the following is also included: 5.1: Construct an electromagnetic transient time-domain simulation model of a grid-type energy storage system, and verify the results of the joint stability analysis described in S4 through time-domain simulation; 5.2: Construct a small-signal impedance model of the grid-type energy storage system, measure the output impedance of the grid-type energy storage system using the frequency sweep method, and compare the frequency sweep measurement results with the theoretical calculation value of the equivalent output impedance model derived in S3 to verify the accuracy of the equivalent output impedance model; 5.3: Based on the verification in 5.1 and 5.2, a hardware-in-the-loop experimental platform was built to conduct semi-physical experimental verification. By setting typical operating conditions with different grid strengths, energy storage penetration rates and fault types, the state variables of voltage, current and power at the grid connection point were collected to verify the effectiveness of the joint stability analysis.

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