Method for identifying transient dominant instability link of new energy grid-connected system based on CUEP participation factor

Abstract

The invention discloses a method for identifying a transient dominant instability link of a new energy grid-connected system based on a CUEP participation factor, and belongs to the field of stable operation of a power system, and the method mainly comprises the steps: 1, carrying out the transient nonlinear modeling of a grid-connected system containing new energy equipment, and carrying out the linearization near a balance point, and obtaining a Jacobian matrix J; 2, calculating all unsteady equilibrium points (UEP) of the new energy grid-connected system, and finding out all I-class UEPs according to the number of positive feature roots; 3, numerically calculating an exit point (EP) of the trajectory, and identifying a dominant unsteady equilibrium point (CUEP) according to the distance between the EP and each class I UEP; and 4, calculating a participation factor of each state quantity of the system at the CUEP point to identify a dominant instability link. According to the method, the transient dominant instability link in the new energy grid-connected system can be effectively identified, and parameters are helped to be adjusted to ensure safe and stable operation of a power system.

Description

Technical Field

[0001] The present invention belongs to the field of transient stable operation and control of a new power system, and more specifically, relates to a method for identifying the transient dominant instability link of a new energy grid-connected system based on the participation factor at the critical unstable equilibrium point (CUEP). Background Art

[0002] The excessive consumption of traditional fossil fuels has brought environmental problems and energy crises. In order to improve the energy structure, China has vigorously developed new energy power generation. In recent years, the installed capacity of new energy has been continuously increasing, which has promoted the continuous evolution of the power system form and brought many new problems. The stable operation of the new power system faces many challenges.

[0003] New energy power generation mainly includes photovoltaic power generation and wind power generation. Both typical power generation equipment contain energy storage elements with different time scales and corresponding control links, and both have strong nonlinear and multi-time scale characteristics. When a disturbance event occurs in the power system, the terminal voltage and power output at each equipment node will jump. In a traditional synchronous machine, due to its physical characteristics, the amplitude / phase of its internal electromotive force does not jump accordingly, while in new energy equipment, due to its control structure, the amplitude / phase of its internal electromotive force will jump, showing discontinuous characteristics. In addition, new energy equipment usually operates faster than synchronous machines, and the relay protection control based on synchronous machines in traditional power systems will fail in new power systems. There are many control links in new energy equipment. For a multi-machine system containing new energy equipment, how to identify its transient dominant instability link has become a challenging problem.

[0004] The transient instability forms of synchronous generators usually have relatively clear definitions, and synchronous instability and voltage instability can be clearly distinguished. However, the coupling between links of new energy equipment is complex, making it difficult to identify the dominant instability form and the dominant instability link. The traditional power system has a relatively mature theory for identifying the dominant instability link near the operating point, but it is still very difficult to identify the dominant instability link during the transient process. The method for identifying the dominant instability equipment based on the impedance model usually regards all links inside the equipment as a whole, making it difficult to specifically determine the position of the control link and guide the optimization and adjustment. Moreover, when far from the stable equilibrium point, this method will be difficult to apply.

[0005] With the development of artificial intelligence algorithms, some studies have proposed the use of machine learning and other algorithms to identify data, but this method often regards the equipment as a black box model and lacks understanding at the mechanism level. At the same time, the use of machine learning to identify different dominant instability links often requires a large and high-quality data set, which is huge in terms of computational complexity. Therefore, this method has significant limitations: on the one hand, it lacks an intuitive explanation of the physical mechanism and it is difficult to reveal the deep-seated reasons behind the stability of the system; on the other hand, it is computationally intensive and time-consuming, making it difficult to meet the needs of real-time analysis and rapid decision-making for large-scale power grids.

[0006] It is urgent to propose a novel and efficient theoretical method for identifying the dominant instability link of the grid-connected system containing new energy equipment. This method should be able to adapt to the rapid response characteristics of new energy equipment and strong nonlinearity. Through this method, the dominant instability link can be located more quickly and accurately, providing a scientific basis and technical support for the safe and stable operation of the new energy power system. Summary of the invention

[0007] In view of the defects and improvement needs of the existing methods, the present invention provides a method for identifying the transient dominant instability link of the renewable energy grid-connected system based on the participation factor at CUEP, the purpose of which is to accurately identify the transient dominant instability link of the renewable energy grid-connected system, thereby ensuring the stable operation of the power system.

[0008] To achieve the above object, according to a first aspect of the present invention, a method for identifying a transient dominant instability link of a new energy grid-connected system is provided, comprising the following steps:

[0009] (1) For a grid-connected system containing new energy equipment, a differential equation group is written for all state quantities, an algebraic equation group is written in combination with the topological structure of the grid-connected system, the differential equation group and the algebraic equation group are combined to obtain a state space equation group, and the differential equation group and the algebraic equation group are combined to obtain a state space equation group; the state space equation group is linearized to obtain the Jacobian matrix J of the grid-connected system;

[0010] (2) setting the derivative terms of the state space equations to 0, solving all equilibrium points, bringing the equilibrium points into the Jacobian matrix J to solve the characteristic roots, and searching for all type I UEPs based on the number of positive characteristic roots obtained;

[0011] (3) The classic fourth-order Runge-Kuta method is used to analyze the fault trajectory of the calculation system and find the exit point EP where the trajectory leaves the attraction domain; the distance between EP and each type I UEP is calculated, and the closest one is the dominant unstable equilibrium point CUEP;

[0012] (4) Calculate the participation factor at the CUEP, where the state quantity with the highest proportion at the positive characteristic root represents the dominant instability link.

[0013] Furthermore, the type-I UEP is an equilibrium point with one positive eigenvalue root and n-1 negative eigenvalue roots; where n is the number of state variables.

[0014] Furthermore, parsing and calculating the system fault trajectory to find the exit point EP where the trajectory leaves the attraction domain includes: parsing and calculating the system fault trajectory using the classical fourth-order Runge-Kutta method; setting the fault duration to increase from small to large, and when the trajectory just becomes unstable, recording the state point information at the fault clearing moment, and this point is the trajectory exit point EP.

[0015] Furthermore, calculating the participation factor at the CUEP includes: decomposing the Jacobian matrix J using the SVD method to obtain J = VDW; where V is the left eigenmatrix, W is the right eigenmatrix, and D is the diagonal matrix of eigenvalue roots, and the participation factor p ij = v ij w ji ; v ij is the element in the i-th row and j-th column of the V matrix, and w ji is the element in the j-th row and i-th column of the W matrix.

[0016] Beneficial effects: The present invention performs transient non-linear modeling on the grid-connected system containing new energy equipment, and linearizes it near the equilibrium point to obtain the Jacobian matrix J; calculates all the unstable equilibrium points (UEPs) of the new energy grid-connected system, and finds all the type-I UEPs according to the number of positive eigenvalue roots; then numerically calculates the exit point (EP) of the trajectory, and identifies the dominant unstable equilibrium point (CUEP) according to the distance between the EP and each type-I UEP; finally, calculates the participation factor of each state variable of the system at the CUEP point to identify the dominant instability link. The type-I UEP has the characteristic of being on the boundary of the attraction domain, and if the system becomes unstable, its phase trajectory in the state space must penetrate from the boundary of the attraction domain. Among them, the position of the penetration point is the closest to the CUEP. If the CUEP is identified and linearized near this point, then the non-linear dynamic behavior during the instability process can be approximately characterized by its linearized system. And the linearized system is easy to analyze, and the dominant instability link can be known. Therefore, it is necessary to find the CUEP, linearize it, and use the participation factor method commonly used in the linearized system to identify the dominant instability link.

[0017] The present invention also provides an electronic device, including: a computer-readable storage medium and a processor;

[0018] The computer-readable storage medium is used to store executable instructions;

[0019] The processor is used to read the executable instructions stored in the computer-readable storage medium and execute the above method.

[0020] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a processor to execute the above method.

[0021] The present invention also provides a computer program product, comprising a computer program or instructions, wherein the computer program or instructions implement the above method when executed by a processor.

[0022] Through the above technical scheme conceived by the present invention, compared with the prior art, the present invention is aimed at a grid-connected system containing new energy equipment, writes a differential equation group for all state quantities, writes an algebraic equation group in combination with the topological structure of the grid-connected system, and combines the differential equation group and the algebraic equation group to obtain a state space equation group, thereby completing the transient nonlinear modeling of the grid-connected system containing new energy equipment. Based on Hartman's theorem, the linear space near the equilibrium point can approximately describe its nonlinear behavior, and linearization is used to approximately characterize the nonlinear behavior of the system near the equilibrium point. For nonlinear systems, linearization based on UEP can explain the nonlinear dynamic behavior of the system near a specific point (UEP) in the state space, identify and process CUEP, and approximate the original nonlinear system after linearization, so as to approximately describe the transient dynamic behavior of the trajectory leaving the attraction domain, and can find the dominant instability link of the transient instability process based on the linearized participation factor analysis. The present invention can effectively identify the transient-dominated instability link in the renewable energy grid-connected system, accurately characterize the dynamic behavior of the system under disturbance, improve the accuracy of evaluating the transient-dominated instability link in the renewable energy grid-connected system, and help adjust parameters to ensure the safe and stable operation of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 A flow chart of a method for evaluating transient stability of a multi-machine system of new energy equipment provided by an embodiment of the present invention;

[0024] Figure 2 A topological structure diagram of a doubly-fed wind turbine single-machine infinite system provided by an embodiment of the present invention;

[0025] Figure 3 A time domain simulation diagram of system stability and instability under different terminal voltage parameters when a power grid fault occurs provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail 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 intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0027] In the present invention, the terms "first", "second", etc. (if any) in the present invention and the accompanying drawings are used to distinguish similar objects but not necessarily to describe a specific order or sequence.

[0028] The new power system containing new energy equipment shows completely different characteristics from the traditional power system with synchronous generators as the core in terms of transient stability. The traditional synchronous generator system can be accurately described by the classical swing equation, and its physical mechanism is clear. In contrast, new energy equipment generally adopts a complex sequential control strategy involving multiple time scales, which contains many nonlinear control links. This characteristic not only aggravates the nonlinearity and strong coupling of the system, but also makes the dominant influencing factors unclear, thereby greatly increasing the difficulty of identifying the transient dominant instability link of the new energy grid-connected system. Therefore, in order to identify the transient dominant instability link of the grid-connected system containing new energy equipment and ensure the stable and safe operation of the power system, the present invention proposes a method for identifying the transient dominant instability link of the new energy grid-connected system based on the participation factor at CUEP, which can improve the accuracy of evaluating the transient dominant instability link of the new energy grid-connected system, and guide parameter adjustment to ensure the safe and stable operation of the power system. The specific implementation process is as follows: Figure 1 As shown, it mainly includes the following steps:

[0029] (1) For a grid-connected system containing new energy equipment, a differential equation group is written for all state quantities, and an algebraic equation group is written in combination with the topological structure of the grid-connected system. The differential equation group and the algebraic equation group are combined to obtain a state space equation group; the state space equation group is linearized to obtain the Jacobian matrix J of the grid-connected system.

[0030] Specifically, for the new energy grid-connected system, due to the large number of control links and the mutual coupling between them, it is necessary to write a differential equation system for all state quantities. The state quantity x=[x1,x2,……,x n ], n is the number of state quantities. Then write the algebraic equation group u=Cx for the network topology structure, and combine the differential equation group and the algebraic equation group to obtain the state space equation group: All state variables are represented by column vector x, B and C represent transfer matrices, Denotes the differential of the state variable, where \(x\) is the state variable and \(f(x)\) is the system of non - linear equations related to the state variable. For the state - space equations Linearization is carried out to obtain the Jacobian matrix \(J\) expression of the new - energy grid - connected system:

[0031] (2) Set the derivative terms of the state - space equations to 0, solve for all equilibrium points, substitute each of the equilibrium points into the Jacobian matrix \(J\) to solve for the eigenvalues, and search for all type - I UEP according to the number of positive eigenvalues obtained.

[0032] Specifically, set the derivative terms of the state - space equations to 0, that is, \(0 = f(x)+BCx\). Solving this equation can obtain all equilibrium points. Further, combined with the already - calculated expression of the Jacobian matrix \(J\), substitute each equilibrium point into it to solve for the eigenvalues. The equilibrium point with exactly one positive eigenvalue and \(n - 1\) negative eigenvalues is the type - I unstable equilibrium point, thus obtaining all type - I unstable equilibrium points.

[0033] (3) Use the classical fourth - order Runge - Kutta method to analytically calculate the system fault trajectory, find the exit point \(EP\) where the trajectory leaves the attraction domain; calculate the distances between \(EP\) and each type - I UEP, and the one with the shortest distance is the dominant unstable equilibrium point \(CUEP\).

[0034] Specifically, use the classical fourth - order Runge - Kutta method to calculate the multi - machine system fault trajectory, with the step size set as \(\Delta t\), which can be corrected according to the requirements of calculation accuracy and speed. When the system undergoes critical instability, mark this point as the exit point (\(EP\)). Calculate the distances between \(EP\) and each type - I unstable equilibrium point, and the one with the minimum distance is the dominant unstable equilibrium point (\(CUEP\)).

[0035] (4) Calculate the participation factors at \(CUEP\), and the state variable with the highest proportion at the positive eigenvalue represents the dominant instability link.

[0036] Specifically, for the dominant unstable equilibrium point, calculate the Jacobian matrix with specific numerical values at this point. And calculate the participation factors of each state variable at the positive eigenvalue. The state variable with the highest participation factor proportion is the dominant instability link.

[0037] Furthermore, the search for all type - I UEP of the system includes: setting the derivative terms of the state - space equations to 0, solving to obtain all equilibrium points; linearizing at each equilibrium point and separately solving to obtain the Jacobian matrix \(J\) corresponding to each equilibrium point; for type - I unstable equilibrium points, having 1 positive eigenvalue and \(n - 1\) negative eigenvalues, and all equilibrium points satisfying this condition are type - I unstable equilibrium points; where \(n\) is the number of state variables.

[0038] Further, the finding of the exit point EP where the trajectory leaves the attraction domain includes: obtaining the system fault trajectory using the classical fourth-order Runge-Kutta method with a step size of Δt; setting the fault duration to increase from small to large, and when the trajectory just becomes unstable, recording the state point information at the fault clearing moment, and this point is the trajectory exit point EP.

[0039] Further, the calculation of the participation factor at CUEP includes: decomposing the Jacobian matrix J using the SVD method, that is, for any matrix, it can always be obtained that J = VDW, where V is the left eigenmatrix, W is the right eigenmatrix, and D is the eigenvalue diagonal matrix, then the participation factor is equal to p ij = v ij w ji ; where, v ij is the element in the i-th row and j-th column of the V matrix, w ji is the element in the j-th row and i-th column of the W matrix, p ij represents the degree of participation of the i-th state variable in the j-th mode.

[0040] The embodiment of the present invention adopts a doubly-fed wind turbine single-machine infinite grid-connected system, and its topological structure and control block diagram are as Figure 2 shown. The specific process of the method for identifying the transient dominant instability link of the new energy grid-connected system based on the participation factor at CUEP includes:

[0041] (1) For the control block diagram and topological structure of the doubly-fed wind turbine single-machine infinite system as Figure 2 shown, its differential equation set is as follows:

[0042]

[0043] The algebraic equation set is:

[0044]

[0045] Among them, the state variables respectively represent the rotor speed, rotor active current, rotor reactive current, PLL frequency, and PLL phase; P m is the mechanical input power, P t is the electromagnetic output power, H is the rotor inertia, k pw and k iw are respectively the proportional coefficient and integral coefficient of the rotor speed PI controller; k pV and k iV are respectively the proportional coefficient and integral coefficient of the terminal voltage PI controller; k ppll and k ipll are respectively the proportional coefficient and integral coefficient of the PLL PI controller. U t is the terminal voltage amplitude, u td and utq are the projections of the terminal voltage in the dq coordinate system, i td and i tq are the total active current and reactive current output by the equipment, U g is the grid voltage, X g is the grid reactance, X m is the mutual reactance of the wind turbine, X s is the stator reactance.

[0046] Furthermore, the above system of equations can be written as a system of differential equations: The algebraic system of equations is: u = Cx. All state variables are represented by the column vector x, and B and C represent the transfer matrices respectively. By linearizing the differential equations and algebraic equations at the equilibrium point, the Jacobian matrix J expression of the new energy grid-connected system can be obtained.

[0047] (2) Solve all Type-I unstable equilibrium points (UEP) of the differential equations and algebraic equations of the system. Further, combined with the obtained expression of the Jacobian matrix J, substitute each equilibrium point and solve for its characteristic roots. The equilibrium point that satisfies one positive characteristic root and n - 1 negative characteristic roots is the Type-I UEP, thus obtaining all Type-I UEP.

[0048] (3) Set the step size as Δt, give the initial values of the system for stable operation, set the fault occurrence time, set multiple simulations, and let the fault clearing time change from small to large. Use the classical fourth-order Runge-Kutta method to calculate the fault trajectory of the system after the fault occurs. When the fault trajectory just shows transient instability, record the state point information at the fault clearing time, and this point is the trajectory exit point (EP).

[0049] (4) For each Type-I unstable equilibrium point, substitute it into the expression J of the Jacobian matrix to obtain the specific value of J. Decompose the J matrix using the Singular Value Decomposition (SVD) method, that is, for any matrix, it can always be obtained that J = VDW, where V is the left eigenmatrix, W is the right eigenmatrix, and D is the diagonal matrix of characteristic roots. Thus, the participation factor p ij = v ij w ji can be calculated. The larger the numerical value of the participation factor of a certain state variable, the higher the degree of influence on this mode. There is only one positive characteristic root in the D matrix, assumed to be the first characteristic root λ1. For the participation factors on this characteristic root, the state variable with the highest proportion represents the dominant instability link.

[0050] Since there is only one stable equilibrium point and one unstable equilibrium point in the doubly-fed induction generator (DFIG) single-machine infinite-bus grid-connected system, this unstable equilibrium point is the CUEP. The participation factors of each state variable are calculated at the CUEP according to the above calculation method, as shown in Table 1. Among them, the phase-locked loop (PLL) link has the highest proportion of participation factors at the positive characteristic root. To verify the effectiveness of the method, under the same fault conditions (the voltage of bus 1 drops to 0.5 p.u. at 1 s and the fault duration is 0.127 s), the time-domain simulation between the second-order model of the PLL and the original fifth-order model is compared, as Figure 3 shown. It can be seen that the phases of the PLL are basically in agreement, indicating that the PLL link plays a dominant role in transient instability. The method proposed in the present invention for identifying the transient dominant instability link of a new energy grid-connected system can effectively judge the stability of the system.

[0051] Table 1 Calculation results of participation factors at CUEP

[0052]

[0053] In summary, the present invention proposes a method for identifying the transient dominant instability link of a new energy grid-connected system based on the participation factors at the CUEP, which can improve the accuracy of identifying the transient dominant instability link of a new energy grid-connected system and guide the parameter adjustment design to ensure the safe and stable operation of the power system.

[0054] It is easy for those skilled in the art to understand that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for identifying the transient dominant instability link of a renewable energy grid-connected system based on the participation factor at CUEP, characterized in that: The following steps are involved: (1) For a grid-connected system containing new energy equipment, a differential equation group is written for all state quantities, and an algebraic equation group is written in combination with the topological structure of the grid-connected system, and the differential equation group and the algebraic equation group are combined to obtain a state space equation group; Linearize the state space equations to obtain the Jacobian matrix J of the grid-connected system; (2) setting the derivative terms of the state space equations to 0, solving all equilibrium points, bringing the equilibrium points into the Jacobian matrix J to solve the characteristic roots, and searching for all type I UEPs based on the number of positive characteristic roots obtained; (3) Analyze the fault trajectory of the computing system and find the exit point EP where the trajectory leaves the attraction domain; Calculate the distance between EP and each type I UEP, where the closest distance is the dominant unstable equilibrium point CUEP; (4) Calculate the participation factor at the CUEP, where the state quantity with the highest proportion at the positive characteristic root represents the dominant instability link.

2. The method for identifying the transient dominant instability link of the renewable energy grid-connected system based on the CUEP participation factor according to claim 1, characterized in that: The type I UEP is an equilibrium point with 1 positive characteristic root and n-1 negative characteristic roots; where n is the number of state quantities.

3. The method for identifying the transient dominant instability link of the new energy grid-connected system based on the CUEP participation factor according to claim 1, characterized in that: The method of analyzing the fault trajectory of the computing system and finding the exit point EP of the trajectory leaving the attraction domain includes: using the classic fourth-order Runge-Kuta method to analyze the fault trajectory of the computing system; setting the fault duration from small to large, and when the trajectory just becomes unstable, recording the state point information at the moment of fault removal, which is the trajectory exit point EP.

4. The method for identifying the transient dominant instability link of the renewable energy grid-connected system based on the CUEP participation factor according to claim 1, characterized in that: The calculation of the participation factor at the CUEP includes: decomposing the Jacobi matrix J using the SVD method to obtain J=VDW; wherein V is the left characteristic matrix, W is the right characteristic matrix, D is the characteristic root diagonal matrix, and the participation factor p ij =v ij w ji ;v ij is the element in the i-th row and j-th column of the V matrix, w ji is the element in the jth row and ith column of the W matrix.

5. An electronic device, characterized in that: include: A computer readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is used to read the executable instructions stored in the computer-readable storage medium and execute the method according to any one of claims 1 to 4.

6. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a processor to execute the method according to any one of claims 1 to 4.

7. 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 method according to any one of claims 1 to 4 is implemented.

Images