Linear model analysis method and analysis system suitable for large-scale power electronic power system

Abstract

The invention belongs to the related technical field of power system analysis, and discloses a linear model analysis method and analysis system suitable for a large-scale power electronic power system, and the analysis method comprises the steps: constructing a system simulation model according to a topological structure of the power system, solving a steady-state periodic trajectory of a system state variable based on the system simulation model; selecting a series of sampling points in one period of the steady-state periodic trajectory; performing linearization processing on each sampling point to obtain a discrete state information matrix of the system linear model at each sampling moment; a series of discrete state information matrixes in a time domain are converted to a frequency domain based on fast Fourier transform, a plurality of Fourier coefficient matrixes Ah are obtained, and a continuous time function of a state information matrix of a system linear model in a corresponding period is constructed. The method is used for describing the evolution process of the system after small disturbance.

Description

Technical Field

[0001] The present invention belongs to the technical field related to power system analysis, and more specifically, relates to a linear model analysis method and analysis system suitable for large-scale power electronic power systems. Background Art

[0002] The power system is undergoing a transformation towards power electronics, and its safe and stable operation is directly related to the lifeblood of the national economy. In recent years, power electronics systems, including large-scale renewable energy and direct current transmission (DC), have continuously experienced broadband oscillations (ranging from a few hertz to several kilohertz), resulting in widespread grid disconnections and equipment damage. Linearized modeling and analysis have become a core requirement for ensuring the safety of modern power systems. However, positive and negative sequence control of renewable energy converters and DC transmission switch modulation introduce complex nonlinear time-varying characteristics into power electronics systems. Furthermore, the large-scale integration of diverse power electronic equipment, such as wind and solar power generation, results in significant high-order characteristics. This means that the small-disturbance stability problem of power electronics systems can be strictly formulated as the periodic solution stability problem of high-order nonlinear periodic time-varying systems. Given that nonlinearity and time-varying properties are widely present in nature as fundamental characteristics that determine evolutionary processes, corresponding modeling methods are of great significance for the safe and stable operation of new power systems.

[0003] Currently, there are two main technical approaches for constructing linear models of power systems. One is to eliminate the system's time-varying characteristics through time-invariant processing methods, thereby establishing a linear, time-invariant model of the system. Commonly used time-invariant processing methods include the Park transform, dynamic phasor, and harmonic state space. However, these methods face significant challenges when dealing with high-order and generalized periodic time-varying characteristics. Specifically, the Park transform can only handle time-varying characteristics with a single frequency component, the dynamic phasor has difficulty performing harmonic balance processing on Fourier series embedded with nonlinear relationships, and the harmonic state space approach based on series approximation results in an increase in model order, posing the risk of dimensionality curse for large-scale systems. Therefore, this technical approach is difficult to apply to linearizing large-scale nonlinear periodic time-varying systems. The other approach, based on Lyapunov theory, directly performs a first-order approximation on the steady-state periodic trajectory of the nonlinear periodic time-varying system. While this method offers high fidelity in linearizing the model, traditional linear modeling revolves around the equilibrium point. When applied to trajectory linearization, it can only obtain information about the Jacobian matrix of a single time slice, making it incapable of accurately analyzing the evolution of small perturbations within the trajectory neighborhood.

[0004] Therefore, there is an urgent need to provide an effective model analysis method that can accurately analyze the linearized model of large-scale power electronic power systems, so as to describe the evolution process of the system after being subjected to small disturbances and provide model support for subsequent stability analysis and control. Summary of the Invention

[0005] In response to the above-mentioned defects or improvement needs of the prior art, the present invention provides a linear model analysis method and analysis system suitable for large-scale power electronic power systems. The purpose is to accurately analyze the linear model of large-scale power electronic power systems to describe the evolution process of the system after being subjected to small disturbances, and provide model support for subsequent stability analysis and control.

[0006] To achieve the above objectives, according to a first aspect of the present invention, a linear model analysis method applicable to large-scale power electronic power systems is provided, which includes:

[0007] Building a system simulation model according to the topological structure of the power system, and solving the steady-state periodic trajectory of the system state variables based on the system simulation model;

[0008] selecting a series of sampling points within a period of the steady-state periodic trajectory;

[0009] Perform linearization on each sampling point to obtain each sampling time t i The discrete state information matrix A(t i ), t i =1,2,3,……,n, where n is the number of sampling points;

[0010] Based on the fast Fourier transform, a series of discrete state information matrices in the time domain are converted to the frequency domain to obtain multiple Fourier coefficient matrices A h , h is the order of the Fourier coefficient, based on the Fourier coefficient matrix A h Construct the continuous time function of the state information matrix of the system linear model within the corresponding period T is the period, t is the time, and j represents the imaginary unit.

[0011] Optionally, a series of sampling points may be selected by uniformly selecting the sampling points, or by performing non-uniform sampling according to the speed of change of the trajectory, where the faster the speed of change, the denser the sampling points.

[0012] Optionally, if the power system includes wind and solar power generation and flexible direct current transmission but does not include conventional direct current transmission, the number of sampling points is 800 to 1200; if the power system includes conventional direct current transmission, the number of sampling points is 3000 to 4000.

[0013] Optionally, a Simulink linearization toolbox is used to perform linearization processing on each of the sampling points.

[0014] Optionally, the method further includes:

[0015] The stability of the system in the corresponding period is analyzed based on the continuous time function A(t) of the state information matrix.

[0016] Optionally, if the power system includes wind and solar power generation and flexible DC transmission but does not include conventional DC transmission, h is selected from -5 to +5; if the system includes conventional DC transmission, h is selected from -15 to +15.

[0017] Optionally, a fast Fourier transform tool of Simulink is used to implement the fast Fourier transform.

[0018] According to a second aspect of the present invention, a linear model analysis system suitable for large-scale power electronic power systems is provided, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of any of the above methods when executing the computer program.

[0019] According to a third aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored, wherein when the computer program is executed by a processor, the steps of any of the above methods are implemented.

[0020] According to a fourth aspect of the present invention, there is provided a computer program product, comprising a computer program or instructions, wherein the computer program or instructions, when executed by a processor, implements the steps of any of the above methods.

[0021] In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:

[0022] The present invention selects a series of sampling points on the steady-state periodic trajectory for linearization, thereby obtaining a discrete state matrix under a series of time slices, and then performs Fourier transform to obtain relatively complete spectral information of the system matrix, thereby reconstructing an accurate continuous state matrix, and then realizing accurate analysis of the linearized model of the large-scale power electronic power system. The continuous state matrix can provide a basis for the long-term stability analysis of the system, thereby obtaining the evolution process of the system after a small disturbance. The above method makes up for the technical defect that the classical linearization modeling method is only applicable to nonlinear time-invariant systems, and provides a model support for the small-disturbance stability analysis of power electronic power systems with large-scale nonlinear periodic time-varying properties. In addition, the present invention does not need to perform time-invariant processing on the complex time-varying characteristics of the system, the operation is simpler, and the analysis has higher fidelity. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 is a flowchart of the steps of a linear model analysis method in one embodiment of the present invention;

[0024] Figure 2is a characteristic root locus diagram obtained based on a model analysis method in one embodiment of the present invention;

[0025] Figure 3 It is a verification diagram of the time domain response waveform in one embodiment. DETAILED DESCRIPTION

[0026] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0027] Example 1

[0028] The present invention provides a linear model analysis method suitable for large-scale power electronic power systems, such as Figure 1 The figure shows a flow chart of the steps of the linear model analysis method in one embodiment of the present invention, and the steps are described in detail below.

[0029] S1. Construct a system simulation model according to the topological structure of the power system, and solve the steady-state periodic trajectory of the system state variables based on the system simulation model.

[0030] Specifically, the Simulink simulation tool in MATLAB can be used to build a system simulation model. For example, mathematical models of various power equipment such as wind and solar power generation, DC transmission, and conventional power supply can be built based on the MATLAB / Simulink platform. According to the topology of the system to be analyzed, the diversified power equipment can be connected through the AC network to build a system model.

[0031] After the system simulation model is built, the steady-state periodic trajectory of the system can be solved according to existing methods. For example, the method for solving the steady-state periodic trajectory can be: numerical integration is used to solve the steady-state periodic trajectory of the system. Considering that the broadband oscillation involves faster system dynamics, the ode45 solver based on the Runge-Kutta method can generally be used, and a 1×10 -5 The solution step size is set to ensure the accuracy of the numerical integration.

[0032] S2. Select a series of sampling points within one cycle of the steady-state periodic trajectory.

[0033] In one embodiment, sampling points can be selected uniformly or non-uniformly based on the trajectory's rate of change, with denser sampling points in areas with faster rates of change. Uniform sampling is simpler, while based on the system's actual time-varying characteristics, sampling fidelity can be further improved by selecting more sampling points in areas where the trajectory changes more rapidly and fewer sampling points in areas where the trajectory changes more slowly.

[0034] In one embodiment, the number of sampling points can be set based on the structure of the power system. If the power system includes wind and solar power generation and flexible direct current transmission but does not include conventional direct current transmission, the number of sampling points is 800-1200. If the power system includes conventional direct current transmission, the number of sampling points is 3000-4000. When the system primarily includes wind and solar power generation and flexible direct current transmission, since the time-varying characteristics involved only have low-frequency components, selecting 800-1200 sampling points can more accurately characterize the time-varying characteristics. When conventional direct current transmission is also considered in the system, due to the inclusion of 12th harmonic components, selecting 3000-4000 sampling points is required to more accurately characterize the time-varying characteristics.

[0035] S3, perform linear processing on each sampling point to obtain each sampling time t i The discrete state information matrix A(t i ), t i =1,2,3,……,n, where n is the number of sampling points.

[0036] Among them, linearizing each sampling point is actually establishing a system linear module on a single time slice. The implementation process is: solving the expression of the first-order partial derivative of the differential equation of the system mathematical model with respect to the system state vector, substituting the state vector value corresponding to the set sampling point, thereby obtaining the system linearization model at the sampling point, and thus obtaining the state information matrix at the sampling point.

[0037] Based on the sampling points selected on the steady-state periodic trajectory in S2, the system is linearized at each sampling point using the Simulink linearization toolbox to obtain the state information matrix under a series of time slices within a cycle, and A(t i ) represents, where i = 1, 2, ..., n.

[0038] S4, based on the fast Fourier transform, a series of discrete state information matrices in the time domain are converted to the frequency domain to obtain multiple Fourier coefficient matrices A h , h is the order of the Fourier coefficient, based on the Fourier coefficient matrix A h Construct the continuous time function of the state information matrix of the system linear model within the corresponding period T is the period, t is the time, and j represents the imaginary unit.

[0039] Specifically, the state information matrix A(t i ), use fast Fourier transform to extract the spectrum information of its matrix, and use A h Represents the h-order Fourier coefficient matrix of the matrix, and then based on A h By constructing the continuous time function A(t) of the system state information matrix, the continuous time function A(t) of the system state information matrix can be obtained, and the continuous time system linear model can be determined. Its expression is as follows:

[0040]

[0041] Where x(t)=[x1(t),…,x n (t)] T is an n-order column vector of the system's state variables. State variables refer to a set of variables that can fully describe the system's dynamic evolution, such as voltage and current in the capacitance and inductance equations. Δx(t) represents the linear form of the state variables with small perturbations, and A(t) represents the state matrix of the system's linear model, with a period of T.

[0042] In one embodiment, the required Fourier coefficient order h can be selected based on the system structure. If the power system includes wind and solar power generation and flexible DC transmission but does not include conventional DC transmission, h is selected from -5 to +5. If the system includes conventional DC transmission, h is selected from -15 to +15. If the system does not include conventional DC transmission but only includes wind and solar power generation and flexible DC transmission, h is selected from -5 to +5 to more accurately characterize the time-varying characteristics. If the system includes conventional DC transmission, h is selected from -15 to +15 to more accurately characterize the time-varying characteristics.

[0043] Specifically, the fast Fourier transform tool of Simulink can be used to implement the fast Fourier transform.

[0044] After obtaining the continuous time function A(t) of the system state information matrix, the long-term stability analysis of the system over the entire period can be realized.

[0045] Therefore, the analysis method also includes:

[0046] S4. Analyze the stability of the system within the corresponding period based on the continuous time function A(t) of the state information matrix.

[0047] Specifically, stability analysis can be performed with reference to existing methods. For example, reference can be made to Chinese patent CN112909931B “A method and device for dynamic stability analysis of a linear periodic time-varying system”, which calculates the state transition matrix Φ(T,0) of the linearized model within one period, and then uses the eigenvalue of ln(Φ(T,0)) / T to perform system stability analysis.

[0048] Example 2

[0049] The present invention also relates to a linear model analysis system suitable for large-scale power electronic power systems, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above method when executing the computer program.

[0050] The analysis system can be installed on computing devices such as desktop computers, notebooks, PDAs and cloud servers. The processor can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The memory can be used to store computer programs and / or modules, and the processor can run or execute computer programs and / or modules stored in the memory, as well as call data stored in the memory, to realize various functions of the electronic device.

[0051] Example 3

[0052] The present invention also relates to a computer-readable storage medium having a computer program stored thereon, which implements the steps of the above method when the computer program is executed by a processor.

[0053] Specifically, the memory may include a high-speed random access memory, and may also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other volatile solid-state storage device.

[0054] Example 4

[0055] An embodiment of the present invention provides a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the steps of the method of the above embodiment of the present invention.

[0056] Example 5

[0057] This example verifies the effect of the present invention.

[0058] The topology and parameter design of the power system refer to the document "Research on Voltage Stability Mechanism after Integration of Large-Scale Wind Power / Photovoltaic Power Generation Clusters". The parameter settings for wind and solar power generation and conventional DC transmission are shown in the following table:

[0059] Table 1 Wind and solar power generation parameter settings

[0060]

[0061] Table 2 Conventional DC transmission parameter settings

[0062]

[0063]

[0064] After the state information matrix A(t) of the linear model is obtained by the method of the present invention, stability analysis is performed based on A(t), such as Figure 2 The following is the characteristic root locus diagram obtained based on the model analysis method. As the wind farm positive sequence current loop proportional coefficient k pi+ As the proportional coefficient k decreases, the dominant mode λ1 and its conjugate complex root gradually move to the right half plane of the complex plane, indicating that the stability of the system gradually weakens. Further analysis shows that when the proportional coefficient k pi+ When it drops to 0.4, the eigenvalue λ1 is (0.12+j2.97×2π), and its real part is positive, indicating that the system has the risk of instability at this time.

[0065] Furthermore, the analysis results of the above mode damping were verified, such as Figure 3 As shown, when the system is in steady state operation at 1.0s, the positive sequence current loop proportional coefficient k of the wind farm is pi+ When the value is set to 0.4, the system experiences an amplified oscillation after being subjected to a small disturbance. It can be seen that the actual verification results are very consistent with the analysis results output by the present invention, indicating that the present invention can accurately perform stability analysis.

[0066] In summary, the present invention can reconstruct an accurate continuous state matrix, and then realize accurate analysis of the linearized model of a large-scale power electronic power system. The continuous state matrix can provide a basis for the long-term stability analysis of the system; the present invention makes up for the technical defect that the classical linearization modeling method is only applicable to nonlinear time-invariant systems, and provides a model support for the small-disturbance stability analysis of power electronic power systems with large-scale nonlinear periodic time-varying properties; and the present invention does not need to perform time-invariant processing on the complex time-varying characteristics of the system, the operation is simpler, and the analysis has higher fidelity.

[0067] The technical features of the above embodiments can be combined in any manner. To simplify the description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification. It should be noted that the phrases "in one embodiment", "for example", "and another example", etc. of the present invention are intended to illustrate the present invention and are not intended to limit the present invention.

[0068] The above embodiments merely illustrate several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, and all such variations and improvements fall within the scope of protection of the present invention.

Claims

1. A linear model analysis method suitable for large-scale power electronic power systems, characterized in that: include: Building a system simulation model according to the topological structure of the power system, and solving the steady-state periodic trajectory of the system state variables based on the system simulation model; selecting a series of sampling points within a period of the steady-state periodic trajectory; Perform linearization on each sampling point to obtain each sampling time t i The discrete state information matrix A(t i ), t i =1,2,3,……,n, where n is the number of sampling points; Based on the fast Fourier transform, a series of discrete state information matrices in the time domain are converted to the frequency domain to obtain multiple Fourier coefficient matrices A h , h is the order of the Fourier coefficient, based on the Fourier coefficient matrix A h Construct the continuous time function of the state information matrix of the system linear model within the corresponding period T is the period, t is the time, and j represents the imaginary unit.

2. The linear model analysis method according to claim 1, wherein: The method of selecting a series of sampling points is to select sampling points uniformly, or to perform non-uniform sampling according to the change speed of the trajectory. The faster the change speed, the denser the sampling points.

3. The linear model analysis method according to claim 1, wherein: If the power system includes wind and solar power generation and flexible direct current transmission but does not include conventional direct current transmission, the number of sampling points is 800 to 1200. If the power system includes conventional direct current transmission, the number of sampling points is 3000 to 4000.

4. The linear model analysis method according to claim 1, wherein: The Simulink linearization toolbox is used to perform linearization processing on each of the sampling points.

5. The linear model analysis method according to claim 1, wherein: The method further comprises: The stability of the system in the corresponding period is analyzed based on the continuous time function A(t) of the state information matrix.

6. The linear model analysis method according to claim 1, wherein: If the power system includes wind and solar power generation and flexible DC transmission but does not include conventional DC transmission, h is selected from -5 to +5. If the system includes conventional DC transmission, h is selected from -15 to +15.

7. The linear model analysis method according to claim 1, wherein: The fast Fourier transform tool of Simulink is used to implement the fast Fourier transform.

8. A linear model analysis system suitable for large-scale power electronic power systems, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program or instructions, characterized in that When the computer program or instruction is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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