A voltage stability analysis method for single-machine infinite time-varying system

Abstract

The present invention provides a voltage stability analysis method for a single-machine infinite time-varying system, comprising the following steps: 1) collecting data of a time-varying system; 2) building a first-order differential model of an electric power system according to the data collected in step 1); 3) solving the equilibrium point of the first-order differential model of the electric power system in step 2); 4) combining the system in step 2) and the equilibrium point in step 3), calculating energy equation parameters of a Lyapunov system based on the Krasovsky method, and building a Lyapunov system based on the Krasovsky method; 5) calculating the output value of the Lyapunov system built in step 4) through an integral recursive neural network solver, and building a Lyapunov stability discriminator; 6) inputting the time-varying data of the system into the Lyapunov stability discriminator established in 5), and obtaining a voltage stability analysis result of the single-machine infinite bus system according to the change of its output value.

Description

Technical Field

[0001] The invention belongs to the field of power system dynamics analysis, and in particular relates to a single-machine infinite time-varying system voltage stability analysis method. Background Art

[0002] The power sector has been growing continuously for decades and it is essential to meet the growing demand for electricity in different sectors. This has led to the construction of many new power network lines every day, resulting in a large and complex framework. The complexity of the system makes it difficult to keep the power system stable. Stability or security assessment has become an important factor in making decisions to ensure the safe operation of power systems around the world. Post-fault stability analysis is a time-domain system dynamics analysis after an incident.

[0003] In recent years, a power system stability analysis method based on the Lyapunov stability criterion for single machine infinite bulk (SMIB) time-varying systems has been proposed. The Krasovsky method is used to linearize the nonlinear system. This method uses the Jacobian matrix coefficients of the time-varying dynamic system and the Lyapunov system to solve the problem, construct a time-varying Lyapunov stability discriminator, and use the time-varying Lyapunov stability discriminator to analyze the output value, thereby obtaining the stability status of the time-varying system. However, the application of the Jacobian matrix coefficients of the time-varying dynamic system and the Lyapunov system belongs to the problem of solving the output value of the time-varying system. In the past, the methods for solving time-varying problems, such as an article entitled "Comparison on neural solvers for the Lyapunovmatrix equation with stationary & nonstationary coefficients" published in the journal Applied Mathematical Modelling published by Elsevier, studied the method of using traditional neural network solvers (Zeroed Neural Network (ZNN) solver and Gradient Neural Network (GNN) solver) to solve the time-varying Lyapunov system. Although traditional neural network solvers can overcome the poor real-time performance of numerical methods to a certain extent, they still cannot effectively overcome the noise disturbance to the system when the system noise is large. Summary of the invention

[0004] The purpose of the present invention is to address the problems existing in the voltage stability analysis method of a single-machine infinite time-varying system. The present invention proposes a time-varying voltage stability analysis method based on an integral recursive neural network solver, which utilizes a more powerful integral recursive neural network solver to process and solve the time-varying system, thereby combining the time-varying Krasovsky method and the Lyapunov method to analyze the voltage stability of a time-varying single-machine infinite bus, which has the characteristics of higher computational efficiency, stronger real-time performance and better anti-interference ability.

[0005] The present invention is achieved by at least one of the following technical solutions.

[0006] A voltage stability analysis method for a single-machine infinite time-varying system includes the following steps:

[0007] 1) Collect the time-varying system network structure parameters, the generator power angle, power angular velocity, load voltage and system constant parameters in the system;

[0008] 2) Using the data collected in step 1) to build a first-order differential model of the power system;

[0009] 3) solving the equilibrium point of the first-order differential model of the power system in step 2);

[0010] 4) Combining the model of step 2) and the equilibrium point value of step 3), calculate the energy equation parameters of the Lyapunov system based on the Krasovsky method, and build the Lyapunov system based on the Krasovsky method;

[0011] 5) calculating the output value of the Lyapunov system constructed in step 4) by using an integral recursive neural network solver, and constructing a Lyapunov stability discriminator;

[0012] 6) Input the time-varying data of the system into the Lyapunov stability discriminator established in 5), and obtain the voltage stability analysis result of the single-machine infinite bus system according to the change of its output value.

[0013] Furthermore, the time-varying system network structure parameters and system constant parameters include the time variable t, the time-varying generator power angle δ m (t), time-varying generator speed ω(t), time-varying load angle δ(t), time-varying load voltage V(t), time-varying motor parameter K pv (t), the time-varying active power P of the motor 0 (t), time-varying rated PQ load P 1 (t), the time-varying characteristic time of the motor T(t), the time-varying infinite bus or relaxed bus admittance Y 0 ′(t), time-varying generator admittance Y m (t), time-varying infinite bus admittance angle θ 0 ′(t), time-varying generator admittance angle θ m (t), time-varying infinite bus or relaxed bus voltage E′ 0 (t), time-varying generator voltage E m (t), time-varying damping coefficient D(t), time-varying generator inertia M(t), time-varying mechanical power P m (t), time-varying power P(t).

[0014] Furthermore, in step 2), building a first-order differential model of the power system includes:

[0015] Determine a time-varying nonlinear dynamical system:

[0016]

[0017] Where t represents the time variable, x(t) is the time-varying state matrix of the system, is the first-order derivative of x(t) with respect to time t, f(x(t)) is the continuous function matrix with respect to x(t), f(x 1 (t))、f(x 2 (t))、f(x 3 (t)) are the three elements in f(x(t)), representing the three time-varying state variables x 1 (t), x 2 (t), x 3 (t) are respectively related continuous functions.

[0018] Furthermore, in step 2), the first-order differential model of the power system includes: establishing a first-order differential model based on a time-varying nonlinear dynamic system. Among them, the generator power angle speed:

[0019]

[0020] where δ m (t) represents the time-varying generator power angle, is δ m The time derivative of (t) represents the time-varying generator speed. The definition of ω(t) is the same as Consistent, x 1 (t) is the time-varying state quantity, f(x 1 (t)) is the value of f(x(t)) that is related to x 1 (t) related continuous functions;

[0021] Acceleration of generator speed:

[0022]

[0023] in is the derivative of ω(t) with respect to time t, M(t) represents the time-varying generator inertia, D(t) represents the time-varying damping coefficient, P m (t) represents the time-varying mechanical power, E m (t) represents the time-varying generator voltage, V(t) represents the time-varying load voltage, and Y m (t) represents the time-varying generator admittance, δ(t) represents the time-varying load angle, δ m (t) represents the time-varying generator power angle, θ m(t) represents the time-varying generator admittance angle, E m (t) represents the time-varying generator voltage, x 2 (t) is the time-varying state quantity, f(x 2 (t)) is the value of f(x(t)) that is related to x 2 (t) related continuous functions;

[0024] The first derivative of the load voltage:

[0025]

[0026] in represents the time-varying load voltage V(t) derivative with respect to time, T(t) represents the time-varying characteristic time of the motor, P 0 (t) represents the time-varying active power of the motor, P 1 (t) represents the time-varying rated PQ load, P W (t) represents the time-varying power of the generator, K pv (t) represents the time-varying motor parameters, x 3 (t) is the time-varying state quantity, f(x 3 (t)) is the value of f(x(t)) that is related to x 3 (t) related continuous functions;

[0027] Generator power size P W (t) is:

[0028] P(t)=(-E′ 0 (t)V(t)Y 0 ′(t)sin(δ(t)+θ′ 0 (t))-E m (t)V(t)Y m (t)sin(δ(t)-δ m (t)-θ m (t))+(Y 0 ′(t)sinθ′ 0 (t)+Y m (t)sin(θ m (t)))V 2 (t))

[0029] Where E′ 0 (t) Time-varying infinite bus or relaxed bus voltage, Y 0 ′(t) time-varying infinite bus or relaxed bus admittance, θ 0 ′(t) is the time-varying infinite bus admittance angle.

[0030] Furthermore, in step 3), the equilibrium point of the first-order differential model of the power system includes:

[0031]

[0032] When f(x(t))=0, the equilibrium point is obtained:

[0033] x c (t)=(ω 0 (t), δ m0 (t), V 0 (t))

[0034] Among them, x c (t) is the equilibrium point, x(t) is the time-varying state matrix of the system, is the first-order derivative of x(t) with respect to time t, f(x(t)) is the continuous function matrix with respect to x(t), ω 0 (t), δ m0 (t) and V 0 (t) are the speed, load angle and load voltage of the time-varying generator balance point respectively.

[0035] Furthermore, in step 4), the energy equation coefficient and the Lyapunov system based on the Krasovsky method are constructed as follows:

[0036]

[0037] A(t) is the coefficient of the energy equation, x c (t) is the equilibrium point, x(t) is the time-varying state matrix of the system, and f(x(t)) is the continuous function matrix about x(t). According to A(t), build a Lyapunov system:

[0038] A T (t)P(t)+P(t)A(t)+Q(t)=0

[0039] Among them, A T (t) is the transposed matrix of A(t), Q(t) is the identity matrix, and P(t) is the value to be solved of the Lyapunov system.

[0040] Furthermore, in the step 5), the output value P(t) of the Lyapunov system constructed in step 4) is calculated by the integral recursive neural network solver, and a Lyapunov stability discriminator is constructed, including:

[0041] Build the deviation equation:

[0042] E(t): =A T (t)P(t)+P(t)A(t)+Q(t)

[0043] E(t) is the deviation value of the Lyapunov system, A(t) is the coefficient of the energy equation, and Q(t) is the unit matrix;

[0044] The value of P(t) is obtained by combining the solver of the integral recurrent neural network (IRNN), and the solver is:

[0045]

[0046] in, represents the convergence performance adjustment parameters of the involved annihilation neural network solver, σ and ρ represent the convergence performance adjustment parameters of the integral recursive neural network solver, and U(t) represents the convergence performance adjustment parameters of A(t) and I n The time-varying parameters obtained by Kronecker product and summation operations, I n is a 3×3 identity matrix, is the derivative of U(t) with respect to time t, U -1 (t) is the inverse matrix of U(t), They are P(t), Q(t), deviation value E(t), ε 0 The vector form of the matrix, for The derivative with respect to time t, ε 0 Denotes the parameter σ and The product of express about The partial derivative of , F(·) represents the activation function array.

[0047] Furthermore, in step 5), the output value P(t) of the Lyapunov system constructed in step 4) is calculated by an integral recursive neural network solver, and a Lyapunov stability discriminator is constructed, including:

[0048] The activation function type selected by the activation function array F(·) is a linear activation function, that is:

[0049] F(y)=y

[0050] Among them, the real number y is a temporary variable.

[0051] Furthermore, in step 5), the output value P(t) of the Lyapunov system constructed in step 4) is calculated by the integral recursive neural network solver, and a Lyapunov stability discriminator is constructed, including:

[0052] According to the output value P(t) of the Lyapunov system, the Lyapunov stability discriminator of the system is constructed. The form of the stability discriminator is:

[0053] V(x(t))=f T (x(t))P(t)f(x(t))

[0054] V(x(t)) represents the Lyapunov stability discriminator, x(t) is the time-varying state matrix of the system, f(x(t)) is the continuous function matrix about x(t), f T (x(t)) is the transposed matrix of f(x(t)).

[0055] Furthermore, in step 6), in the state space, if the stability discriminator satisfies V(x(t))→∞, ||x(t)||→∞, then the dynamic system is globally asymptotically stable.

[0056] Compared with the existing single-machine infinite time-varying system voltage stability analysis method, the present invention has the following effects:

[0057] 1. Compared with the traditional post-fault stability analysis methods, which include pole arrangement, state feedback, root locus, Nyquist criterion, and Bode plot, these methods cannot be used directly due to their inherent nonlinear dynamic characteristics. The method based on Krasovsky method and Lyapunov stability criterion of the present invention introduces stability criteria for nonlinear systems, thereby being able to efficiently and in real time analyze the stability of the voltage of a single-machine infinite time-varying system;

[0058] 2. Compared with the numerical method solver, the present invention utilizes the integral neural network solver, which has fast calculation speed, higher efficiency and better real-time performance, so that the method based on Krasovsky method and Lyapunov stability criterion can achieve higher efficiency;

[0059] 3. Compared with the classic recursive neural network solver, the present invention adopts a new type of integral recursive neural network solver, which has the advantages of faster convergence speed, higher calculation accuracy and better anti-disturbance performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 This is a comparison diagram of the error between IRNN and ZNN in the embodiment;

[0061] Figure 2 The error comparison between IRNN and ZNN under different data in the embodiment;

[0062] Figure 3 A schematic diagram showing the comparison between the performance of the integrated recursive neural network solver of the present invention in solving a time-varying Lyapunov system and the traditional neural network method;

[0063] Figure 4 A flowchart of a method for analyzing voltage stability of a single-machine infinite time-varying system according to an embodiment of the present invention;

[0064] Figure 5The schematic diagram of the voltage stability detection system for a single-machine infinite time-varying system includes a power system circuit to be tested, a power system time-varying data acquisition function module, and a data analysis terminal. DETAILED DESCRIPTION

[0065] In order to enable those skilled in the art to better understand the scheme of the present invention, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation methods. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0066] Example 1

[0067] Figure 4 , Figure 5 A voltage stability analysis method for a single-machine infinite time-varying system shown in FIG. 1 includes the following steps:

[0068] S1. Collecting time-varying system network structure parameters, generator power angle, power angular velocity, load voltage and system constant parameters in the system;

[0069] S2. Use the collected data to build a first-order differential model of the power system;

[0070] S3, solving the equilibrium point of the first-order differential model of the power system;

[0071] S4. Calculate the energy equation coefficients of the Lyapunov system based on Krasovsky's method, and build a Lyapunov system based on Krasovsky's method;

[0072] S5. Solve the constructed time-varying Lyapunov system through the integral recursive neural network solver and construct the Lyapunov stability discriminator;

[0073] S6. Input the system's time-varying data into the established Lyapunov stability discriminator, and obtain the voltage stability analysis result of the single-machine infinite time-varying system according to the change trend of its output value. The details are as follows:

[0074] First, establish a time-varying nonlinear dynamic system

[0075]

[0076] Where t represents the time variable, x(t) is the time-varying state matrix of the system, is the first-order derivative of x(t) with respect to time t, f(x(t)) is the continuous function matrix with respect to x(t), f(x 1 (t))、f(x 2 (t))、f(x3 (t)) are the three elements in f(x(t)), representing the three time-varying state variables x 1 (t), x 2 (t), x 3 (t) are continuous functions related to each other. Considering the first-order differential equation model of a single machine infinite time-varying system is:

[0077]

[0078]

[0079]

[0080] in,

[0081] P(t)=(-E′ 0 (t)V(t)Y 0 ′(t)sin(δ(t)+θ′ 0 (t))-E m (t)V(t)Y m (t)sin(δ(t)-δ m (t)-θ m (t))+(Y 0 ′(t)sin(θ′ 0 (t))+Y m (t)sin(θ m (t)))V 2 (t)),

[0082] Among them, the time variable t, δ m (t) represents the time-varying generator power angle, is δ m The time derivative of (t) represents the time-varying generator speed. The definition of ω(t) is the same as Consistent, is the derivative of ω(t) with respect to time t, represents the time derivative of the time-varying load voltage V(t), the time-varying load angle δ(t), the time-varying load voltage V(t), and the time-varying motor parameter K pv (t), the time-varying active power P of the motor 0 (t), time-varying rated PQ load P 1 (t), the time-varying characteristic time of the motor T(t), the time-varying infinite bus or relaxed bus admittance Y 0 ′(t), time-varying generator admittance Y m (t), time-varying infinite bus admittance angle θ 0 ′(t), time-varying generator admittance angle θ m (t), time-varying infinite bus or relaxed bus voltage E′0 (t), time-varying generator voltage E m (t), time-varying damping coefficient D(t), time-varying generator inertia M(t), time-varying mechanical power P m (t), time-varying power P(t).

[0083] By f(x(t))=0, the equilibrium point x of the above system model can be calculated. c (t)=(ω 0 (t), δ m0 (t), V 0 (t)), which is the system The equilibrium point, where ω 0 (t),δ m0 (t) and V 0 (t) are the time-varying generator equilibrium point speed, load angle and load voltage respectively.

[0084] Define A(x(t)) to represent the Jacobian matrix of the system at the equilibrium point, that is,

[0085]

[0086] Then, a necessary condition for the equilibrium point to be asymptotically stable is that there exist two symmetric positive definite matrices P(t) and Q(t) satisfying

[0087] A(t) T P(t)+P(t)A(t)+Q(t)=0 (6) Where Q(t) is the identity matrix.

[0088] The goal is to calculate the output value P(t) of the Lyapunov system. First, build the integral recursive neural network deviation equation:

[0089] E(t):=A(t) T P(t)+P(t)A(t)+Q(t), (7)

[0090] When the deviation value E(t) of the Lyapunov system in equation (7) approaches 0, it is considered that the solution of P(t) in equation (6) is completed. Through the neurodynamic method, a composite solver based on an integral recurrent neural network (IRNN) is used to solve the deviation equation, and the following integral neural network deviation model is established:

[0091] ε(t):=ρ∫ 0 t E(τ)dτ-ε 0 +σF(E(t)), (8)

[0092] Among them, ε(t) is the deviation value of the integral neural network, ρ and σ represent the parameters of the integral neural network solver to adjust the convergence performance, and ε 0=σF(E(0)), where F(·) is the activation function, and a linear activation function is used here. In addition, when the integral neural network deviation value ε(t) approaches 0, it is considered that E(t) approaches 0, and the solution of equation (6) is also completed. Here, in order to solve the integral neural network of equation (8), the following neural dynamics model is introduced:

[0093]

[0094] in, represents the derivative of ε(t) with respect to time t, is the neural network convergence performance adjustment parameter. Substituting equation (8) into equation (9), we can get the integrated recurrent neural network (IRNN) solver, namely

[0095]

[0096] in, , σ, ρ are the performance adjustment parameters of the integral recurrent neural network solver, and is the identity matrix, represents the Kronecker product, is the derivative of U(t) with respect to time t, U -1 (t) is the inverse matrix of U(t), They are P(t), Q(t), E(t), ε 0 The vector form of the matrix, for The derivative with respect to time t is According to the above formula (9), the solution corresponding to time t can be obtained Thus, P(t) is obtained; according to P(t), the Lyapunov stability discriminator of the system is constructed

[0097]

[0098] According to the Krasovsky method and Lyapunov stability theorem, in the state space, if V(x(t))→∞, ||x(t)||→∞ is satisfied in equation (10), then the voltage of the time-varying single-machine infinite bus dynamic system is considered to be globally asymptotically stable.

[0099] In order to illustrate the characteristics and advantages of the present invention, the present invention is further described below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0100] This embodiment mainly compares the performance of the integral recursive neural network solver of the present invention in solving the Lyapunov time-varying system based on the Krasovsky method under noise disturbance with the traditional neural network method. Here, the zeroing neural network (ZNN) is selected as the traditional neural network for simulation experiments, that is:

[0101]

[0102] Among them, γ>0 is a parameter to adjust the convergence performance. In order to make the convergence speed of the integral recurrent neural network solver and the zeroing neural network solver consistent, γ=10 in ZNN, ρ=10 and σ=1 in IRNN. The constant noise perturbation is introduced as

[0103]

[0104] Therefore, the IRNN model after introducing constant noise perturbation is:

[0105]

[0106] in, is the vector form of W. The ZNN model after introducing constant noise perturbation is

[0107]

[0108] Three sets of specific embodiment data are given below, and simulation experiments are carried out with a 3×3 matrix P(0) with any element in the interval [-5, 5] as the starting value to illustrate that the novel integral recursive neural network solver adopted in the present invention has the advantages of faster convergence speed, higher calculation accuracy and better anti-disturbance performance.

[0109] Example 2

[0110] In this embodiment, the specific Lyapunov system time-varying coefficient matrix A(t), the unit matrix Q(t), and the corresponding theoretical value P are given. * (t), the matrices are all diagonal matrices. By comparing the solver output value with the theoretical value P * (t) The deviation between them is verified by examples. The integral recursive neural network solver mentioned in the present invention has the characteristics of stronger convergence, higher calculation accuracy and better anti-disturbance performance than the traditional neural network solver in the past.

[0111]

[0112]

[0113] Where, S = sin(t), C = cos(t). *(t) is the solution corresponding to the Lyapunov time-varying system, and P(t) is the output value of the neural network solver. Figure 1 In the figure, the vertical axis is ||P * (t)-P(t)|| F The deviation between the reaction output value and the correct solution, the horizontal axis is time t, the unit is seconds. Figure 1 It can be seen that under the interference of noise, the traditional neural network solver method ZNN cannot complete convergence, while the integral recursive neural network solver method IRNN can quickly achieve ||P * (t)-P(t)|| F The result that converges to 0 has the advantages of faster convergence speed, higher calculation accuracy and better anti-disturbance performance.

[0114] Example 3

[0115] In this embodiment, from the perspective of comprehensiveness, a specific Lyapunov system time-varying coefficient matrix A(t), a unit matrix Q(t), and a corresponding theoretical value P are given, which are different from those in Embodiment 2 in terms of element distribution. * (t), by comparing the solver output value with the theoretical value P * (t) The deviation between them is verified by examples. The integral recursive neural network solver mentioned in the present invention has the characteristics of stronger convergence, higher calculation accuracy and better anti-disturbance performance than the traditional neural network solver in the past.

[0116]

[0117]

[0118] Where H = (4S + 12C + 4C 2 +17) / (8(S-2)(S+2)).

[0119] Among them, P * (t) is the solution corresponding to the Lyapunov time-varying system, and P(t) is the output value of the neural network solver. Figure 2 In the figure, the vertical axis is ||P * (t)-P(t)|| F Reflects the deviation between the output value and the correct solution, and the horizontal axis is time t, in seconds. Figure 2 It can be seen that under the interference of noise, the traditional neural network solver method ZNN cannot complete convergence, while the integral recursive neural network solver method IRNN can quickly achieve ||P * (t)-P(t)|| F The result that converges to 0 has the advantages of faster convergence speed, higher calculation accuracy and better anti-disturbance performance.

[0120] Example 4

[0121] In this embodiment, from the perspective of comprehensiveness, a specific Lyapunov system time-varying coefficient matrix A(t), a unit matrix Q(t), and a corresponding theoretical value P are given, which are different from those in Embodiments 2 and 3. * (t), by comparing the solver output value with the theoretical value P * (t) The deviation between them is verified by examples. The integral recursive neural network solver mentioned in the present invention has the characteristics of stronger convergence, higher calculation accuracy and better anti-disturbance performance than the traditional neural network solver in the past.

[0122]

[0123]

[0124] Where K = (S 2 +C+3) / ((2C 2 +4)(C 2 +S 2 +S+4)), J = -(S 2 +C+3) / ((2S 2 -4)(C 2 -S 2 +4)).

[0125] Among them, P * (t) is the solution corresponding to the Lyapunov time-varying system, and P(t) is the output value of the neural network solver. Figure 3 In the figure, the vertical axis is ||P * (t)-P(t)|| F The deviation between the reaction output value and the correct solution, the horizontal axis is time t, the unit is seconds. Figure 3 It can be seen that under the interference of noise, the traditional neural network solver method ZNN cannot complete convergence, while the integral recursive neural network solver method IRNN can quickly achieve ||P * (t)-P(t)|| F The result that converges to 0 has the advantages of faster convergence speed, higher calculation accuracy and better anti-disturbance performance.

[0126] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principles of the present invention shall be equivalent replacement methods and shall be included in the protection scope of the present invention.

Claims

1. A voltage stability analysis method for a single-machine infinite time-varying system, characterized in that: The steps include: 1) Collect the time-varying system network structure parameters, the generator power angle, power angular velocity, load voltage and system constant parameters in the system; 2) Using the data collected in step 1) to build a first-order differential model of the power system; The first-order differential model of the power system includes: establishing a first-order differential model based on a time-varying nonlinear dynamic system, where the generator power angle speed is: where δ m (t) represents the time-varying generator power angle, is δ m The time derivative of (t) represents the time-varying generator speed. The definition of ω(t) is the same as Consistent, x1(t) is the time-varying state quantity, and f(x1(t)) is the continuous function related to x1(t) in f(x(t)); Acceleration of generator speed: in is the derivative of ω(t) with respect to time t, M(t) represents the time-varying generator inertia, D(t) represents the time-varying damping coefficient, P m (t) represents the time-varying mechanical power, E m (t) represents the time-varying generator voltage, V(t) represents the time-varying load voltage, and Y m (t) represents the time-varying generator admittance, δ(t) represents the time-varying load angle, δ m (t) represents the time-varying generator power angle, θ m (t) represents the time-varying generator admittance angle, E m (t) represents the time-varying generator voltage, x2(t) is the time-varying state quantity, and f(x2(t)) is the continuous function related to x2(t) in f(x(t)); The first derivative of the load voltage: in represents the time-varying derivative of the load voltage V(t), T(t) represents the time-varying characteristic time of the motor, P0(t) represents the time-varying active power of the motor, P1(t) represents the time-varying rated PQ load, P W (t) represents the time-varying power of the generator, K pv (t) represents the time-varying motor parameter, x3(t) is the time-varying state quantity, and f(x3(t)) represents the continuous function related to x3(t) in f(x(t)); The generator power P(t) is: P(t)=(-E′0(t)V(t)Y0′(t)sin(δ(t)+θ′0(t))-E m (t)V(t)Y m (t)sin(δ(t)-δ m (t)-θ m (t))+(Y0′(t)sinθ′0(t)+Y m (t)sin(θ m (t))V 2 (t)) Where E′0(t) is the time-varying infinite bus or relaxed bus voltage, Y0′(t) is the time-varying infinite bus or relaxed bus admittance, and θ′0(t) is the time-varying infinite bus admittance angle; 3) solving the equilibrium point of the first-order differential model of the power system in step 2); 4) Combining the model of step 2) and the equilibrium point value of step 3), calculate the energy equation parameters of the Lyapunov system based on the Krasovsky method, and build the Lyapunov system based on the Krasovsky method; 5) calculating the output value of the Lyapunov system constructed in step 4) by using an integral recursive neural network solver, and constructing a Lyapunov stability discriminator; 6) Input the time-varying data of the system into the Lyapunov stability discriminator established in 5), and obtain the voltage stability analysis result of the single-machine infinite bus system according to the change of its output value.

2. The voltage stability analysis method for a single-machine infinite time-varying system according to claim 1 is characterized in that: The time-varying system network structure parameters and system constant parameters include time variable t, time-varying generator power angle δ m (t), time-varying generator speed ω(t), time-varying load angle δ(t), time-varying load voltage V(t), time-varying motor parameter K pv (t), the time-varying active power P0(t) of the motor, the time-varying rated PQ load P1(t), the time-varying characteristic time T(t) of the motor, the time-varying infinite bus or relaxed bus admittance Y0′(t), the time-varying generator admittance Y m (t), time-varying infinite bus admittance angle θ0′(t), time-varying generator admittance angle θ m (t), time-varying infinite bus or relaxed bus voltage E′0(t), time-varying generator voltage E m (t), time-varying damping coefficient D(t), time-varying generator inertia M(t), time-varying mechanical power P m (t), time-varying power P(t).

3. The voltage stability analysis method for a single machine infinite time-varying system according to claim 1 is characterized in that: In the step 2), building a first-order differential model of the power system includes: Determine a time-varying nonlinear dynamical system: Where t represents the time variable, x(t) is the time-varying state matrix of the system, is the first-order derivative of x(t) with respect to time t, f(x(t)) is the continuous function matrix with respect to x(t), f(x1(t)), f(x2(t)), and f(x3(t)) are the three elements in f(x(t)), representing three continuous functions related to the time-varying state quantities x1(t), x2(t), and x3(t), respectively.

4. The voltage stability analysis method for a single-machine infinite time-varying system according to claim 1 is characterized in that: In step 3), the equilibrium point of the first-order differential model of the power system includes: When f(x(t))=0, the equilibrium point is obtained: x c (t)=(ω0(t),δ m0 (t),V0(t)) Among them, x c (t) is the equilibrium point, x(t) is the time-varying state matrix of the system, is the first-order derivative of x(t) with respect to time t, f(x(t)) is the continuous function matrix with respect to x(t), ω0(t), δ m0 (t) and V0(t) are the speed, load angle and load voltage of the time-varying generator equilibrium point, respectively.

5. The voltage stability analysis method for a single-machine infinite time-varying system according to claim 1 is characterized in that: In the step 4), the energy equation coefficient and the Lyapunov system based on the Krasovsky method are: A(t) is the coefficient of the energy equation, x c (t) is the equilibrium point, x(t) is the time-varying state matrix of the system, and f(x(t)) is the continuous function matrix about x(t). According to A(t), build a Lyapunov system: A T (t)P(t)+P(t)A(t)+Q(t)=0 Among them, A T (t) is the transposed matrix of A(t), Q(t) is the identity matrix, and P(t) is the value to be solved of the Lyapunov system.

6. The voltage stability analysis method for a single machine infinite time-varying system according to claim 1 is characterized in that: In the step 5), the output value P(t) of the Lyapunov system constructed in step 4) is calculated by the integral recursive neural network solver, and a Lyapunov stability discriminator is constructed, including: Build the deviation equation: E(t):=A T (t)P(t)+P(t)A(t)+Q(t) E(t) is the deviation value of the Lyapunov system, A(t) is the coefficient of the energy equation, and Q(t) is the unit matrix; The value of P(t) is obtained by combining the solver of the integral recurrent neural network (IRNN), and the solver is: Wherein, θ represents the convergence performance adjustment parameter of the involved annihilation neural network solver, σ and ρ represent the convergence performance adjustment parameters of the integral recursive neural network solver, and U(t) represents the convergence performance adjustment parameters of A(t) and I n The time-varying parameters obtained by Kronecker product and summation operations, I n is a 3×3 identity matrix, is the derivative of U(t) with respect to time t, U -1 (t) is the inverse matrix of U(t), are the vector forms of P(t), Q(t), deviation value E(t), and ε0 matrix, for The derivative with respect to time t, ε0, represents the relationship between parameter σ and The product of express about The partial derivative of , F(·) represents the activation function array.

7. The voltage stability analysis method for a single machine infinite time-varying system according to claim 1 is characterized in that: In the step 5), the output value P(t) of the Lyapunov system constructed in step 4) is calculated by an integral recursive neural network solver, and a Lyapunov stability discriminator is constructed, including: The activation function type selected by the activation function array F(·) is a linear activation function, that is: F(y)=y Among them, the real number y is a temporary variable.

8. The voltage stability analysis method for a single machine infinite time-varying system according to claim 1 is characterized in that: In step 5), the output value P(t) of the Lyapunov system constructed in step 4) is calculated by the integral recursive neural network solver, and a Lyapunov stability discriminator is constructed, including: According to the output value P(t) of the Lyapunov system, the Lyapunov stability discriminator of the system is constructed. The form of the stability discriminator is: V(x(t))=f T (x(t))P(t)f(x(t)) V(x(t)) represents the Lyapunov stability discriminator, x(t) is the time-varying state matrix of the system, f(x(t)) is the continuous function matrix about x(t), f T (x(t)) is the transposed matrix of f(x(t)).

9. The voltage stability analysis method for a single-machine infinite time-varying system according to any one of claims 1 to 8, characterized in that: In step 6), in the state space, if the stability discriminator satisfies V(x(t))→∞, ||x(t)||→∞, then the dynamic system is globally asymptotically stable.

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