Track sensitivity-based VSG transient stability discrimination method and system

Abstract

The invention provides a VSG transient stability discrimination method and system based on trajectory sensitivity. The method comprises the following steps: constructing a VSG trajectory sensitivity model; determining a transient stability index of the VSG based on the VSG trajectory sensitivity model; in the linear region of the critical value of the stability boundary of the system, two different parameter values are taken, and transient stability indexes, corresponding to the two different parameter values, of the VSG are calculated; obtaining a system parameter critical value according to the transient stability indexes of the VSG corresponding to the two different parameter values; and if the parameter reaches the critical value, the transient instability phenomenon occurs in the system, and the VSG transient stability is judged. And the design of related control strategies and electrical parameters of the VSG grid-connected system is guided.

Description

Technical Field

[0001] This invention relates to the field of new energy grid connection technology, specifically to a method and system for VSG transient stability discrimination based on trajectory sensitivity. Background Technology

[0002] In recent years, the penetration rate of new energy power generation has been increasing, leading to a lack of inertia and damping in large power grids. Virtual synchronous machine (VSG) strategy has attracted much attention. VSG control technology can provide inertia and damping support for power systems, but the premise is that the VSG itself can maintain stable operation under large disturbances. Therefore, studying the transient stability of VSG has important practical significance.

[0003] The main methods for transient stability analysis of VSG systems currently include the phase plane method, the equal area method, and the energy function method. In addition, the trajectory sensitivity analysis (TSA) method has been widely used by researchers to solve various problems related to power systems over the past few decades. However, there is currently no relatively mature method for applying the TSA method to the transient stability analysis of VSG grid-connected systems. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a VSG transient stability discrimination method based on trajectory sensitivity, comprising:

[0005] Construct a VSG trajectory sensitivity model;

[0006] Based on the VSG trajectory sensitivity model, the transient stability index of the VSG is determined;

[0007] Within the linear region of the critical value of the stability boundary of the system, two different parameter values ​​are taken, and the transient stability index of the VSG corresponding to the two different parameter values ​​is calculated; based on the transient stability index of the VSG corresponding to the two different parameter values, the critical value of the system parameter is obtained; if the parameter reaches the critical value, the system exhibits transient instability, thus realizing the determination of the transient stability of the VSG.

[0008] Furthermore, a VSG trajectory sensitivity model is constructed, including:

[0009] The expression for an nth-order nonlinear dynamic system is as follows:

[0010]

[0011] In the formula, t is the time variable, x is the state variable, α is the vector of p-dimensional system parameters, t0 is the initial time, and x0 is the initial value of the state variable;

[0012] Define the state variable x with respect to the system parameter α and the trajectory sensitivity x. α :

[0013]

[0014] In the formula, S is an n*p order trajectory sensitivity matrix;

[0015] Based on the trajectory sensitivity matrix, the dynamic model of trajectory sensitivity is obtained, which can be expressed as:

[0016]

[0017] In the formula, matrices A and B are calculated using the system parameter α = α0, and are expressed as follows:

[0018]

[0019] The second-order dynamic differential equation for VSG control is expressed as:

[0020]

[0021] In the formula, x1 is the power angle δ of the VSG, x2 is the angular velocity ω of the VSG, J is the virtual inertia, and D... p P is the damping coefficient, P0 is the input power, and P e The static power limit of the VSG is given by ω0, which is the rated angular frequency.

[0022] Choosing virtual inertia and damping coefficient as system parameters, we have α = [J, D] p The trajectory sensitivity matrix is ​​obtained as follows:

[0023]

[0024] Furthermore, based on the VSG trajectory sensitivity model, the transient stability index of the VSG is determined, including:

[0025] Based on the VSG trajectory sensitivity model, the L2 norm N of the system's trajectory sensitivity vector is derived. α Its mathematical expression is:

[0026]

[0027] In the formula, n is the number of system state variables;

[0028] When the system parameters reach a critical value, N α When it reaches its maximum value, the transient stability index σ of the VSG is defined. α for:

[0029]

[0030] Furthermore, within the linear region of the critical value of the system's stability boundary, two different parameter values ​​are taken, and the transient stability index of the VSG corresponding to the two different parameter values ​​is calculated; based on the transient stability index of the VSG corresponding to the two different parameter values, the critical value of the system parameters is obtained; if the parameter reaches the critical value, the system exhibits transient instability, thus realizing the determination of VSG transient stability, including:

[0031] Within the linear region of the critical value of the stability boundary of the system, two different parameter values ​​α1 and α2 are taken, and the transient stability index σ of the VSG corresponding to the two different parameter values ​​is calculated. a1 and σ a2 ;

[0032] Point (α1, σ) a1 ) and (α2, σ a2 By connecting the lines and extrapolating, we can obtain σ. a The critical value of the system parameter corresponding to the value of 0;

[0033] If the parameter reaches the critical value, the system will exhibit transient instability, thus realizing the determination of VSG transient stability.

[0034] This invention also provides a VSG transient stability discrimination system based on trajectory sensitivity, comprising:

[0035] The sensitivity model building module is used to build VSG trajectory sensitivity models;

[0036] The stability index determination module determines the transient stability index of the VSG based on the VSG trajectory sensitivity model.

[0037] The transient stability determination module is used to take two different parameter values ​​within the linear region of the critical value of the stability boundary of the system, and calculate the transient stability index of the VSG corresponding to the two different parameter values; based on the transient stability index of the VSG corresponding to the two different parameter values, the critical value of the system parameter is obtained; if the parameter reaches the critical value, the system exhibits transient instability, thus realizing the determination of the transient stability of the VSG.

[0038] Furthermore, the sensitivity model building module includes:

[0039] The expression for an nth-order nonlinear dynamic system is as follows:

[0040]

[0041] In the formula, t is the time variable, x is the state variable, α is the vector of p-dimensional system parameters, t0 is the initial time, and x0 is the initial value of the state variable;

[0042] The trajectory sensitivity definition submodule is used to define the trajectory sensitivity x of the state variable x relative to the system parameter α. α :

[0043]

[0044] In the formula, S is an n*p order trajectory sensitivity matrix;

[0045] The dynamic model acquisition submodule is used to obtain the trajectory sensitivity dynamic model based on the trajectory sensitivity matrix, which can be represented as:

[0046]

[0047] In the formula, matrices A and B are calculated using the system parameter α = α0, and are expressed as follows:

[0048]

[0049] The second-order dynamic differential equation for VSG control is expressed as:

[0050]

[0051] In the formula, x1 is the power angle δ of the VSG, x2 is the angular velocity ω of the VSG, J is the virtual inertia, and D... p P is the damping coefficient, P0 is the input power, and P e The static power limit of the VSG is given by ω0, which is the rated angular frequency.

[0052] The sensitivity matrix acquisition submodule is used to select virtual inertia and damping coefficients as system parameters, with α = [J, D]. p The trajectory sensitivity matrix is ​​obtained as follows:

[0053]

[0054] Furthermore, the stability metric determination module includes:

[0055] The norm derivation submodule is used to derive the L2-norm N of the system's trajectory sensitivity vector based on the VSG trajectory sensitivity model. α Its mathematical expression is:

[0056]

[0057] In the formula, n is the number of system state variables;

[0058] The stability index determination submodule is used to determine the system parameters when they reach critical values, N. α When it reaches its maximum value, the transient stability index σ of the VSG is defined. α for:

[0059]

[0060] Furthermore, the transient stability determination module includes:

[0061] The stability index calculation submodule is used to take two different parameter values ​​α1 and α2 within the linear region of the critical value of the stability boundary of the system, and calculate the transient stability index σ of the VSG corresponding to the two different parameter values. a1 and σ a2 ;

[0062] The critical value acquisition submodule is used to obtain the point (α1, σ). a1 ) and (α2, σ a2 By connecting the lines and extrapolating, we can obtain σ. a The critical value of the system parameter corresponding to the value of 0;

[0063] The determination submodule is used to determine the transient stability of the VSG if the parameter reaches a critical value and the system exhibits transient instability.

[0064] This invention also provides a computer device, comprising: one or more processors;

[0065] The processor is used to store one or more programs;

[0066] When the one or more programs are executed by the one or more processors, the VSG transient stability discrimination method based on trajectory sensitivity as described in any of the preceding claims is implemented.

[0067] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed, it implements the VSG transient stability discrimination method based on trajectory sensitivity as described in any one of the preceding claims.

[0068] This invention provides a VSG transient stability assessment method and system based on trajectory sensitivity. By constructing a trajectory sensitivity model of the VSG, the influence of parameters on system stability is dynamically described. The transient stability assessment index derived from the L-2 norm of the trajectory sensitivity vector can determine the critical values ​​of relevant parameters at the stability boundary, thereby guiding the design of relevant control strategies and electrical parameters for VSG grid-connected systems. Attached Figure Description

[0069] Figure 1 This is a flowchart illustrating a VSG transient stability discrimination method based on trajectory sensitivity provided in an embodiment of the present invention;

[0070] Figure 2 This is a model and control of the VSG grid-connected system involved in the embodiments of the present invention;

[0071] Figure 3 This is a schematic diagram of the structure of a VSG transient stability discrimination system based on trajectory sensitivity provided in an embodiment of the present invention;

[0072] Figure 4 This is a method for determining the critical values ​​of system parameters involved in the embodiments of the present invention. Detailed Implementation

[0073] Numerous specific details are set forth in the following description to provide a full understanding of the invention. However, the invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0074] like Figure 1 As shown, the present invention provides a VSG transient stability discrimination method based on trajectory sensitivity, which includes the following steps.

[0075] Step S101: Construct the VSG trajectory sensitivity model.

[0076] The expression for an nth-order nonlinear dynamic system is as follows:

[0077]

[0078] In the formula, t is the time variable, x is the state variable, α is the vector of p-dimensional system parameters, t0 is the initial time, and x0 is the initial value of the state variable;

[0079] Define the state variable x with respect to the system parameter α and the trajectory sensitivity x. α :

[0080]

[0081] In the formula, S is an n*p order trajectory sensitivity matrix;

[0082] Based on the trajectory sensitivity matrix, the dynamic model of trajectory sensitivity is obtained, which can be expressed as:

[0083]

[0084] In the formula, matrices A and B are calculated using the system parameter α = α0, and are expressed as follows:

[0085]

[0086] VSG grid-connected system structure and control structure as follows: Figure 2 As shown in the figure, the second-order dynamic differential equation controlled by the VSG can be obtained, expressed as:

[0087]

[0088] In the formula, x1 is the power angle δ of the VSG, x2 is the angular velocity ω of the VSG, J is the virtual inertia, and D... p P is the damping coefficient, P0 is the input power, and P e The static power limit of the VSG is given by ω0, which is the rated angular frequency.

[0089] Choosing virtual inertia and damping coefficient as system parameters, we have α = [J, D] p The trajectory sensitivity matrix is ​​obtained as follows:

[0090]

[0091] Step S102: Based on the VSG trajectory sensitivity model, determine the transient stability index of the VSG.

[0092] Transient stability assessment methods typically require quantitative characterization of the system's stability boundary; therefore, a VSG transient stability index needs to be constructed. Firstly, based on the aforementioned VSG trajectory sensitivity model, the L2 norm N of the system's trajectory sensitivity vector is derived. α Its mathematical expression is:

[0093]

[0094] In the formula, n is the number of system state variables;

[0095] When the system parameters reach a critical value, N α When it reaches its maximum value, the transient stability index σ of the VSG is defined. α for:

[0096]

[0097] Step S103: Within the linear region of the critical value of the stability boundary of the system, take two different parameter values ​​and calculate the transient stability index of the VSG corresponding to the two different parameter values; obtain the critical value of the system parameters based on the transient stability index of the VSG corresponding to the two different parameter values; if the parameter reaches the critical value, the system will experience transient instability, thus realizing the determination of the transient stability of the VSG.

[0098] At the stability boundary, max(N) α The value of ) is very large, so σ a It can be approximated as 0. Therefore, to estimate the critical value of a parameter, within the linear region of the critical value of the stability boundary of the system, two different parameter values ​​α1 and α2 are taken, and the transient stability index σ of the VSG corresponding to the two different parameter values ​​is calculated. a1 and σ a2 ; point (α1, σ a1) and (α2, σ a2 By connecting the lines and extrapolating, we can obtain σ. a The critical value of the system parameter α corresponding to the position = 0 c α c like Figure 4 As shown; if the parameter reaches the critical value, the system will experience transient instability, thus realizing the determination of VSG transient stability.

[0099] Based on the same inventive concept, this invention also provides a VSG transient stability discrimination system 300 based on trajectory sensitivity, such as... Figure 3 As shown, it includes:

[0100] Sensitivity model building module 310 is used to build a VSG trajectory sensitivity model;

[0101] The stability index determination module 320 determines the transient stability index of the VSG based on the VSG trajectory sensitivity model.

[0102] The transient stability determination module 330 is used to take two different parameter values ​​within the linear region of the critical value of the stability boundary of the system, and calculate the transient stability index of the VSG corresponding to the two different parameter values; obtain the critical value of the system parameters based on the transient stability index of the VSG corresponding to the two different parameter values; if the parameter reaches the critical value, the system exhibits transient instability, thereby realizing the determination of the transient stability of the VSG.

[0103] Furthermore, the sensitivity model building module includes:

[0104] The expression for an nth-order nonlinear dynamic system is as follows:

[0105]

[0106] In the formula, t is the time variable, x is the state variable, α is the vector of p-dimensional system parameters, t0 is the initial time, and x0 is the initial value of the state variable;

[0107] The trajectory sensitivity definition submodule is used to define the trajectory sensitivity x of the state variable x relative to the system parameter α. α :

[0108]

[0109] In the formula, S is an n*p order trajectory sensitivity matrix;

[0110] The dynamic model acquisition submodule is used to obtain the trajectory sensitivity dynamic model based on the trajectory sensitivity matrix, which can be represented as:

[0111]

[0112] In the formula, matrices A and B are calculated using the system parameter α = α0, and are expressed as follows:

[0113]

[0114] The second-order dynamic differential equation for VSG control is expressed as:

[0115]

[0116] In the formula, x1 is the power angle δ of the VSG, x2 is the angular velocity ω of the VSG, J is the virtual inertia, and D... p P is the damping coefficient, P0 is the input power, and P e The static power limit of the VSG is given by ω0, which is the rated angular frequency.

[0117] The sensitivity matrix acquisition submodule is used to select virtual inertia and damping coefficients as system parameters, with α = [J, D]. p The trajectory sensitivity matrix is ​​obtained as follows:

[0118]

[0119] Furthermore, the stability metric determination module includes:

[0120] The norm derivation submodule is used to derive the L2-norm N of the system's trajectory sensitivity vector based on the VSG trajectory sensitivity model. α Its mathematical expression is:

[0121]

[0122] In the formula, n is the number of system state variables;

[0123] The stability index determination submodule is used to determine the system parameters when they reach critical values, N. α When it reaches its maximum value, the transient stability index σ of the VSG is defined. α for:

[0124]

[0125] Furthermore, the transient stability determination module includes:

[0126] The stability index calculation submodule is used to take two different parameter values ​​α1 and α2 within the linear region of the critical value of the stability boundary of the system, and calculate the transient stability index σ of the VSG corresponding to the two different parameter values. a1 and σ a2 ;

[0127] The critical value acquisition submodule is used to obtain the point (α1, σ). a1) and (α2, σ a2 By connecting the lines and extrapolating, we can obtain σ. a The critical value of the system parameter α corresponding to the position = 0 c α c like Figure 4 As shown;

[0128] The determination submodule is used to determine the transient stability of the VSG if the parameter reaches a critical value and the system exhibits transient instability.

[0129] This invention provides a VSG transient stability assessment method and system based on trajectory sensitivity. By constructing a trajectory sensitivity model of the VSG, the influence of parameters on system stability is dynamically described. The transient stability assessment index derived from the L-2 norm of the trajectory sensitivity vector can determine the critical values ​​of relevant parameters at the stability boundary, thereby guiding the design of relevant control strategies and electrical parameters for VSG grid-connected systems.

[0130] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0131] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0132] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0133] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0134] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A VSG transient stability discrimination method based on trajectory sensitivity, characterized in that, include: Construct a VSG trajectory sensitivity model; Based on the VSG trajectory sensitivity model, the transient stability index of the VSG is determined; Within the linear region of the critical value of the stability boundary of the system, two different parameter values ​​are taken, and the transient stability index of the VSG corresponding to the two different parameter values ​​is calculated; based on the transient stability index of the VSG corresponding to the two different parameter values, the critical value of the system parameter is obtained; if the parameter reaches the critical value, the system exhibits transient instability, thus realizing the determination of the transient stability of the VSG.

2. The method according to claim 1, characterized in that, Constructing a VSG trajectory sensitivity model includes: The expression for an nth-order nonlinear dynamic system is as follows: In the formula, t is the time variable, x is the state variable, α is the vector of p-dimensional system parameters, t0 is the initial time, and x0 is the initial value of the state variable; Define the state variable x with respect to the system parameter α and the trajectory sensitivity x. α : In the formula, S is an n*p order trajectory sensitivity matrix; Based on the trajectory sensitivity matrix, the dynamic model of trajectory sensitivity is obtained, which can be expressed as: In the formula, matrices A and B are calculated using the system parameter α = α0, and are expressed as follows: The second-order dynamic differential equation for VSG control is expressed as: In the formula, x1 is the power angle δ of the VSG, x2 is the angular velocity ω of the VSG, J is the virtual inertia, and D... p P is the damping coefficient, P0 is the input power, and P e The static power limit of the VSG is given by ω0, which is the rated angular frequency. Choosing virtual inertia and damping coefficient as system parameters, we have α = [J, D] p The trajectory sensitivity matrix is ​​obtained as follows:

3. The method according to claim 1, characterized in that, Based on the VSG trajectory sensitivity model, the transient stability indices of the VSG are determined, including: Based on the VSG trajectory sensitivity model, the L2 norm N of the system's trajectory sensitivity vector is derived. α Its mathematical expression is: In the formula, n is the number of system state variables; When the system parameters reach a critical value, N α When it reaches its maximum value, the transient stability index σ of the VSG is defined. α for:

4. The method according to claim 1, characterized in that, Within the linear region of the critical value of the stability boundary of the system, two different parameter values ​​are taken, and the transient stability index of the VSG corresponding to the two different parameter values ​​is calculated; based on the transient stability index of the VSG corresponding to the two different parameter values, the critical value of the system parameter is obtained. If the parameters reach a critical value, the system will exhibit transient instability. The determination of VSG transient stability includes: Within the linear region of the critical value of the stability boundary of the system, two different parameter values ​​α1 and α2 are taken, and the transient stability index σ of the VSG corresponding to the two different parameter values ​​is calculated. a1 and σ a2 ; Point (α1, σ) a1 ) and (α2, σ a2 By connecting the lines and extrapolating, we can obtain σ. a The critical value of the system parameter corresponding to the value of 0; If the parameter reaches the critical value, the system will exhibit transient instability, thus realizing the determination of VSG transient stability.

5. A VSG transient stability discrimination system based on trajectory sensitivity, characterized in that, include: The sensitivity model building module is used to build VSG trajectory sensitivity models; The stability index determination module determines the transient stability index of the VSG based on the VSG trajectory sensitivity model. The transient stability determination module is used to take two different parameter values ​​within the linear region of the critical value of the stability boundary of the system, and calculate the transient stability index of the VSG corresponding to the two different parameter values; based on the transient stability index of the VSG corresponding to the two different parameter values, the critical value of the system parameter is obtained; if the parameter reaches the critical value, the system exhibits transient instability, thus realizing the determination of the transient stability of the VSG.

6. The system according to claim 5, characterized in that, The sensitivity model building module includes: The expression for an nth-order nonlinear dynamic system is as follows: In the formula, t is the time variable, x is the state variable, α is the vector of p-dimensional system parameters, t0 is the initial time, and x0 is the initial value of the state variable; The trajectory sensitivity definition submodule is used to define the trajectory sensitivity x of the state variable x relative to the system parameter α. α : In the formula, S is an n*p order trajectory sensitivity matrix; The dynamic model acquisition submodule is used to obtain the trajectory sensitivity dynamic model based on the trajectory sensitivity matrix, which can be represented as: In the formula, matrices A and B are calculated using the system parameter α = α0, and are expressed as follows: The second-order dynamic differential equation for VSG control is expressed as: In the formula, x1 is the power angle δ of the VSG, x2 is the angular velocity ω of the VSG, J is the virtual inertia, and D... p P is the damping coefficient, P0 is the input power, and P e The static power limit of the VSG is given by ω0, which is the rated angular frequency. The sensitivity matrix acquisition submodule is used to select virtual inertia and damping coefficients as system parameters, with α = [J, D]. p The trajectory sensitivity matrix is ​​obtained as follows:

7. The system according to claim 5, characterized in that, The stability index determination module includes: The norm derivation submodule is used to derive the L2-norm N of the system's trajectory sensitivity vector based on the VSG trajectory sensitivity model. α Its mathematical expression is: In the formula, n is the number of system state variables; The stability index determination submodule is used to determine the system parameters when they reach critical values, N. α When it reaches its maximum value, the transient stability index σ of the VSG is defined. α for:

8. The system according to claim 5, characterized in that, The transient stability determination module includes: The stability index calculation submodule is used to take two different parameter values ​​α1 and α2 within the linear region of the critical value of the stability boundary of the system, and calculate the transient stability index σ of the VSG corresponding to the two different parameter values. a1 and σ a2 ; The critical value acquisition submodule is used to obtain the point (α1, σ). a1 ) and (α2, σ a2 By connecting the lines and extrapolating, we can obtain σ. a The critical value of the system parameter corresponding to the value of 0; The determination submodule is used to determine the transient stability of the VSG if the parameter reaches a critical value and the system exhibits transient instability.

9. A computer device, characterized in that, include: One or more processors; The processor is used to store one or more programs; When the one or more programs are executed by the one or more processors, the VSG transient stability discrimination method based on trajectory sensitivity as described in any one of claims 1 to 4 is implemented.

10. A computer-readable storage medium, characterized in that, It contains a computer program, which, when executed, implements the VSG transient stability discrimination method based on trajectory sensitivity as described in any one of claims 1 to 4.

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