Compensation method-based fully-pure embedded power system security checking method

Abstract

The invention discloses an all-pure embedded power system security checking method based on a compensation method, and the method comprises the steps: firstly constructing an all-pure embedded power flow equation according to different node types based on an all-pure embedded theory; secondly, a compensation method is introduced to correct a coefficient matrix of the full-pure embedded power flow equation; and finally, a high-efficiency power system security checking algorithm is provided in combination with a full-pure embedded power flow equation and a compensation method, inversion of a high-dimensional matrix is avoided, and the calculation amount is greatly reduced. According to the method, the advantages of a full-pure embedding algorithm and a compensation method are combined, and the accuracy, the robustness and the high efficiency of safety checking of the power system can be considered.

Description

Technical Field

[0001] The invention relates to the technical field of power system safety verification, and in particular to a full-pure embedded power system safety verification method based on a compensation method. Background Art

[0002] During the operation of the power system, safety verification, as a core link to ensure the stability and reliability of the system, is of great significance for pre-identifying and preventing potential operating risks, and thus improving the overall safety and reliability of the power system. Traditional safety verification mainly relies on numerical calculation and simulation technology to evaluate the safety and stability of the system by considering the possible failure conditions of each component. This method can effectively discover potential problems in the system, but in large-scale power systems, the amount of calculation is large and it may take a long time. Its calculation efficiency has become a major obstacle to the practical application of power system safety verification.

[0003] In order to improve the efficiency of safety verification, many scholars have conducted extensive research. The literature "Virtual bus technology and its application (III): static safety verification method" (Tong Xing, Kang Chongqing, Chen Qixin, etc. Virtual bus technology and its application (III): static safety verification method [J]. Proceedings of the CSEE, 2014, 34 (10): 1592-8.) introduces virtual bus technology into static safety analysis, pre-identifies and constructs emergency line sets, effectively simplifies the safety constraints of redundant lines, ensures the retention of key constraints, and thus significantly reduces the size of the safety constraint set and effectively shortens the calculation time. The literature "Improved algorithm for fast static safety analysis of power systems" (Ding Ping, Li Yalou, Xu Dechao, etc. Improved algorithm for fast static safety analysis of power systems [J]. Proceedings of the CSEE, 2010, 30 (31): 77-82.) proposes a unified model processing criterion based on the PQ decomposition method, and combines the partial factor correction technology to introduce the factor table additional chain technology. These innovative strategies together accelerate the calculation process of single-period static safety verification. The paper "Application of Sparse Vector Technology in Static Safety Analysis" (He Yang, Hong Chao, Chen Kunwei. Application of Sparse Vector Technology in Static Safety Analysis [J]. Proceedings of the CSEE, 2003, (01): 42-5.) adopts a fast algorithm based on sparse vector technology. By combining the sparse vector method, the matrix partial refactorization method of the factor table path tree, and the fast forward / backward method, it fully utilizes the sparsity characteristics of the matrix and significantly improves the computational efficiency of static safety verification. The literature "Theoretical Analysis of Safety Constrained Optimal Power Flow Based on Nonlinear Interior Point Method (I)" (Li Yin, Zhang Boming, Sun Hongbin, etc. Theoretical Analysis of Safety Constrained Optimal Power Flow Based on Nonlinear Interior Point Method (I) [J]. Automation of Electric Power Systems, 2007, (19): 7-13.) proposes an interior point algorithm for safety constrained optimal power flow for multiple anticipated accident scenarios. The algorithm deeply analyzes the construction of the safety constrained optimal power flow model under multiple anticipated accidents and the division of control variables, and directly applies the nonlinear path tracking interior point theory based on the perturbation KKT condition, providing an effective solution to this large-scale nonlinear programming problem.

[0004] Most of the above correction algorithms for power system security verification require continuous iterative calculation of matrices, and the calculation efficiency is still low. In addition, there are problems such as sensitivity to initial values, singular Jacobian matrix, and poor convergence of traditional iterative methods. Therefore, it is necessary to further study and improve the relevant theories and algorithms for power system security verification, and develop mathematical models and calculation methods with high calculation efficiency in view of its complexity, nonlinearity, uncertainty, large-scale, coupling and other characteristics, so as to ensure the safe and reliable operation of the system under various working conditions. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art, and to provide a method for safety verification of a holomorphic embedded power system based on a compensation method, which can establish a holomorphic embedded power flow equation that does not require iterative solution based on the holomorphic embedding principle, and combine the compensation method based on the full rank decomposition theorem and the matrix inversion auxiliary theorem to perform safety verification on the power system, decompose the correction matrix of the coefficient matrix in the holomorphic embedded power flow equation, and reduce the computational complexity. This method combines the advantages of the holomorphic embedding algorithm and the compensation method, and can quickly and accurately solve the problem of power system safety verification.

[0006] To achieve the above purpose, the technical solution provided by the present invention is: a fully embedded power system safety verification method based on compensation method, the specific steps are as follows:

[0007] Step 1: Set the initial values ​​of the network parameters of the power system, construct a holomorphic embedded power flow equation according to the holomorphic embedding principle, and obtain the coefficient matrix and constant vector of the holomorphic embedded power flow equation;

[0008] Step 2: determine all fault scenarios for power system safety verification, and disconnect the kth branch of the power system in sequence;

[0009] Step 3, correcting the coefficient matrix and constant vector in the holomorphic embedded power flow equation under the kth accident state, and decomposing the correction matrix in the holomorphic embedded power flow equation by using the compensation method;

[0010] Step 4: Obtain the holomorphic embedded power flow equation based on the compensation method under the k-th accident state, solve its power series coefficients by recursive calculation, use the Padé approximation to solve the approximate solution, obtain the power flow solution under the k-th accident state, and determine whether it meets the convergence criterion;

[0011] Step 5. Repeat steps 2 to 4 to calculate the power flow solution after each branch is disconnected until the disconnection verification of all branches is completed. Finally, the safety verification results under each fault scenario are output, including node voltage, line power flow and whether there is an over-limit situation.

[0012] Furthermore, the constructed holomorphic embedded power flow equation is as follows:

[0013] Construct the holomorphic embedded power flow equations for each type of node, expand their relations, and derive the recursive relations as follows:

[0014]

[0015] Where N is the number of nodes; n is the order of the power series; V i re [n] is the real part of the n-order voltage power series at node i; V i im [n] is the imaginary part of the n-th order voltage power series at node i; is the real part of the n-1th order known vector of the PV node; is the imaginary part of the n-1th order known vector of the PV node; is the real part of the n-1th order known vector of the PQ node; is the imaginary part of the n-1th order known vector of the PQ node; is the real part of the initial value of the voltage at node i; is the imaginary part of the initial voltage value of node i; ii and β ii is the element in the recursive equation corresponding to the PV node in the coefficient matrix; and is the element of the real part of the recurrence equation in the coefficient matrix corresponding to the PQ node; and It is the element of the imaginary part of the recursive equation corresponding to the PQ node in the coefficient matrix; the calculation formula of each element is as follows:

[0016] When j≠i,

[0017]

[0018] When j = i,

[0019]

[0020] In the formula, is the real part of the initial value of the voltage at node j; is the imaginary part of the initial voltage value of node j; g ij is the conductance between nodes i and j; b ij is the susceptance between nodes i and j; g ii is the conductance of node i; b ii is the susceptance of node i.

[0021] Furthermore, the compensation method is used to decompose the correction matrix of the holomorphic embedded power flow equation, as follows:

[0022] The general linear power flow equations can be expressed as follows:

[0023] Ax=B(4)

[0024] In the formula, A is a coefficient matrix, which is related to the node type and network structure parameters of the power system; x is the variable vector to be determined, including voltage amplitude and voltage phase angle; B is a constant vector;

[0025] A and B will change due to changes in network parameters in the power system. When the network is disturbed, the coefficient matrix needs to be modified accordingly:

[0026] A k=A0+ΔA k (5)

[0027] A k x k =(A0+ΔA k )x k =B k (6)

[0028] Where A0 is the coefficient matrix before the accident; A k is the coefficient matrix under the kth accident state; ΔA k is the correction matrix under the kth accident state; x k is the solution under the kth accident state; the injection vector may also change accordingly, using B k express;

[0029] According to the full rank decomposition theorem, any non-zero matrix can be decomposed into the product of a matrix with full row rank and a matrix with full column rank. Therefore, ΔA can be k This breaks down into:

[0030] ΔA k =M k N k (7)

[0031] In the formula, ΔA k is an m×m square matrix, where m is the dimension of the matrix. If ΔA k The rank of is r, then M k is an m×r column-full rank matrix, N k is an r×m full row rank matrix;

[0032] The interruption of a power system branch is a small disturbance event, and only the elements related to the corresponding branch in its coefficient matrix will change. Therefore, the correction matrix ΔA k It is a very sparse matrix, that is, ΔA k The rank r is very small. If r = 1, then equation (4) is the same as the traditional compensation method. If r ≠ 1, according to the full rank decomposition theorem, an r × r unit matrix E is added to it. k It can still satisfy the decomposition form of the auxiliary theorem of matrix inversion, that is:

[0033] ΔA k =M k E k N k (8).

[0034] Furthermore, the holomorphic embedded power flow equation based on the compensation method is as follows:

[0035] When a branch (i, j) in the power system is interrupted, the elements related to branch (i, j) in the coefficient matrix A will also change accordingly. For the convenience of discussion, it is assumed that i and j are both PQ nodes, and the elements in ΔA will change as follows:

[0036]

[0037] In the formula, is the non-zero submatrix of ΔA, and the arrows represent the relationship between the non-zero submatrix and the original matrix; is the element of the real part of the recursive equation corresponding to node i in the coefficient matrix A; is the element of the imaginary part of the recursive equation corresponding to node i in the coefficient matrix A; is the element of the real part of the recursive equation corresponding to node j in the coefficient matrix A; is the element of the imaginary part of the recursive equation corresponding to node j in the coefficient matrix A; 2*i-1, 2*i represents the number of rows or columns corresponding to the elements related to node i in the correction coefficient matrix; 2*j-1, 2*j represents the number of rows or columns corresponding to the elements related to node j in the correction coefficient matrix; if the corresponding nodes i and j in the interrupt branch (i, j) contain PV nodes, the PV node can also be corrected as above. The formula of the PV node is different from the above formula only in that the following parameters are modified to the parameters pointed by the arrow:

[0038] By observing the calculation formulas (2) and (3) of the coefficient matrix, we can see that when the initial voltage values ​​of node i and node j are equal, that is, V i0 =V j0 hour, But when V i0 ≠V j0 When , their calculation formulas are not the same, so they should be corrected respectively;

[0039] Since each element in ΔA has no clear physical meaning, when the matrix elements change, ΔA will be decomposed based on the full rank decomposition theorem; considering V i ≠V k In the case of node i and node j, the coefficients corresponding to node i and node j are modified respectively to obtain:

[0040]

[0041] Where ΔA1 and ΔA2 are correction matrices; and are the non-zero sub-matrices of M1E1N1 and M2E2N2 respectively, and the arrow symbols are used to represent the relationship between the non-zero sub-matrices and the original matrix; M1 and M2 are matrices with full column rank; N1 and N2 are matrices with full row rank; E1 and E2 are identity matrices of small dimensions;

[0042] Substituting equations (6), (10) and (11) into the matrix inversion auxiliary theorem, the solution of the equation under the kth accident state can be obtained:

[0043]

[0044] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0045] 1. The method of the present invention realizes efficient solution of power flow calculation by fully embedding the power flow equation. Compared with the traditional iterative method, the method of the present invention is less sensitive to initial values, has better convergence performance, and reduces calculation time.

[0046] 2. The method of the present invention is applicable to large-scale complex power systems, and can effectively handle both single-branch faults and multi-branch faults. Through rapid correction of branch faults and accurate calculation of power flow solutions, it is ensured that the operating status of the system after the fault can be accurately reflected.

[0047] 3. The method of the present invention introduces a compensation method to convert the inverse solution of a high-dimensional coefficient matrix into the inverse solution of a modified matrix of smaller dimension, which greatly reduces the computational complexity and thus improves the overall computational efficiency.

[0048] 4. The insensitivity of the method of the present invention to parameter disturbances and initial conditions makes it highly robust. When faced with operating conditions such as heavy loads in actual power systems, it can ensure the stability and accuracy of safety verification and improve the reliability of system operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0050] The present invention is further described in detail below in conjunction with embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0051] like Figure 1 As shown, this embodiment discloses a holomorphic embedded power system safety verification method based on the compensation method, which can decompose the correction matrix of the holomorphic embedded coefficient matrix, avoid multiple calculations of the inverse of the high-dimensional coefficient matrix in the safety verification, and only invert the compensated matrix with a smaller dimension, thereby reducing the calculation complexity and achieving accuracy, robustness and efficiency of the power system safety verification, which are described in detail below.

[0052] The first step is to construct the holomorphic embedding power flow equation according to the holomorphic embedding principle. For a power system network with N nodes, the power flow equation of the power system can be written as:

[0053]

[0054] In the formula, represents the injected power of node i; represents the voltage vector of node i; represents the voltage vector of node j; Y ij represents the admittance between node i and node j; “*” represents the conjugate operator.

[0055] Different embedding models are established for different node types:

[0056] (1) Holomorphic embedding model of load node equations:

[0057]

[0058] Where s is the embedding factor, is the voltage holomorphic function of node i; is the voltage holomorphic function of node j; c i 、c j is any given non-zero negative constant, and in the initial state s=0, we get V i (0) = c i . That is, c i is the initial value of the voltage at node i, which can take any initial value. In the target state s=1, equation (2) is completely equal to the original equation (1).

[0059] (2) Holomorphic embedding model of equilibrium node equations:

[0060]

[0061] Where V i sp is the given voltage at the equilibrium node.

[0062] (3) Holomorphic embedding model of generator node equations:

[0063]

[0064] Where P i is the active injected power of node i.

[0065] The obtained holomorphic embedded power flow equations of various types of nodes can be derived and organized into a recursive matrix relationship in the form of Ax=B:

[0066]

[0067] Where N is the number of nodes; n is the order of the power series; V i re [n] is the real part of the n-order voltage power series at node i; V i im [n] is the imaginary part of the n-th order voltage power series at node i; is the real part of the n-1th order known vector of the PV node; is the imaginary part of the n-1th order known vector of the PV node; is the real part of the n-1th order known vector of point PQ; is the imaginary part of the n-1th order known vector of the PQ node; is the real part of the initial value of the voltage at node i; is the imaginary part of the initial voltage value of node i; ii and β ii is the element in the recursive equation corresponding to the PV node in the coefficient matrix; and is the element of the real part of the recurrence equation in the coefficient matrix corresponding to the PQ node; and is the element of the imaginary part of the recursive equation corresponding to the PQ node in the coefficient matrix; the calculation formula of the elements in the coefficient matrix is ​​as follows:

[0068] When j≠i,

[0069]

[0070] When j = i,

[0071]

[0072] In the formula, is the real part of the initial value of the voltage at node i; is the imaginary part of the initial value of the voltage at node i; is the real part of the initial value of the voltage at node j; is the imaginary part of the initial voltage value of node j; g ij is the conductance between nodes i and j; b ij is the susceptance between nodes i and j; g ii is the conductance of node i; b ii is the susceptance of node i; the elements in the coefficient matrix will not change during the recursive process. The calculation formula for the known vector on the right side of the linear equation system is as follows:

[0073]

[0074] In the formula, I PV Represents the set of PV nodes; IPQ Represents a set of PQ nodes; [] are the orders of the power series coefficients.

[0075] The second step is to obtain the compensation method for solving the general coefficient matrix correction equation, which is as follows:

[0076] Taking the power system network equation as an example, when there is an n-dimensional power system network equation:

[0077]

[0078] Where Y is the node admittance matrix; is the node voltage; is the node injection current. The state before the network structure or parameter changes can be obtained:

[0079]

[0080] In the formula, It is the inverse of the node admittance matrix; the subscript 0 indicates the state before the network structure or parameters change.

[0081] When the network structure or parameters change, the network equation becomes:

[0082]

[0083] In the formula, ΔY k is the modified admittance matrix; is the corrected node voltage; is the corrected node current; subscript k represents the kth accident state. Use the branch association matrix to describe ΔY k :

[0084]

[0085] In the formula, δy k represents the series admittance of the interrupted branch k, which is a d×d-order matrix, where d is the dimension of the matrix; M′ k represents the m×d-order node-branch association matrix corresponding to the k-changed elements of the interrupted branch; the superscript T represents the transpose of the matrix.

[0086] According to the auxiliary theorem of matrix inversion, using the known and ΔY k The matrix sparsity of into a less computationally intensive process.

[0087] When an element in an m×m matrix A changes:

[0088] ΔA=M′aN′ T (13)

[0090]

[0091] Among them, a is a d×d matrix; M′ and N′ are m×d matrices; and d≤m. Then:

[0092]

[0093] In the formula, the value of a can be positive or negative. -1 It is known that the inverse of the changed matrix can be quickly solved using formula (15): When the order of matrix A is high and the order of matrix a is low, the order of the terms in the brackets on the right side of equation (15) is the same as the order of matrix a, which is low, thus achieving a fast solution.

[0094] If the above formula is established, a must be satisfied -1 +N′ T A -1 M′ is reversible. Consider the modified node admittance matrix ΔY k , can be decomposed into equation (12), which satisfies the form of equation (14). Therefore, the compensation method can be used to correct the network equation.

[0095] The general linear power flow equations can be expressed as follows:

[0096] Ax=B(16)

[0097] Among them, A is the coefficient matrix, which is related to the node type and network structure parameters of the power system; x is the variable vector to be determined, including voltage amplitude and voltage phase angle; B is the constant vector.

[0098] A and B will change due to changes in network parameters in the power system. When a disturbance occurs in the network, the coefficient matrix needs to be modified accordingly:

[0099] A k =A0+ΔA k (17)

[0100] A k =(A0+ΔA k )x k =B k (18)

[0101] Where A0 is the coefficient matrix before the accident; A k is the coefficient matrix under the kth accident state; ΔA k is the correction matrix under the kth accident state; x kis the solution under the kth accident state; the injection vector may also change accordingly, using B k express.

[0102] According to the full rank decomposition theorem, any non-zero matrix can be decomposed into the product of a matrix with full row rank and a matrix with full column rank. k This breaks down into:

[0103] ΔA k =M k N k (19)

[0104] Where ΔA k is an m×m square matrix, if ΔA k The rank of is r, then M k is an m×r column-full rank matrix, N k is an r×m full row rank matrix.

[0105] If r is any other smaller number, according to the full rank decomposition theorem, add an r×r identity matrix E k It can still satisfy formula (12), that is:

[0106] ΔA k =M k E k N k (20)

[0107] Substituting formula (20) into the auxiliary theorem of matrix inversion, we can get the inverse of the changed coefficient matrix: The expression is:

[0108]

[0109] In the formula, the smaller the dimension of the unit matrix E, the smaller the computational complexity of the matrix inversion auxiliary theorem. The full rank decomposition theorem ensures that E and ΔA have the same rank r, reaching the minimum value, so that only the rows and columns of the elements related to the interrupted branch need to be corrected, which greatly reduces the computational complexity.

[0110] In the third step, when each branch is disconnected in turn, the corresponding correction matrix ΔA of the kth accident state is obtained. k Combining the holomorphic embedding model and the compensation method, the holomorphic embedding power system safety verification process based on the compensation method is obtained, as follows:

[0111] When a branch (i, j) in the power system is interrupted, the elements related to branch (i, j) in the coefficient matrix A will also change. For the convenience of discussion, it is assumed that i and j are both PQ nodes. The elements in ΔA will change as follows:

[0112]

[0113] In the formula, is the non-zero submatrix of ΔA, and the arrows represent the relationship between the non-zero submatrix and the original matrix; is the element of the real part of the recursive equation corresponding to node i in the coefficient matrix A; is the element of the imaginary part of the recursive equation corresponding to node i in the coefficient matrix A; is the element of the real part of the recursive equation corresponding to node k in the coefficient matrix A; is the element of the imaginary part of the recursive equation corresponding to node k in the coefficient matrix A; 2*i-1, 2*i represents the number of rows or columns corresponding to the elements related to node i in the correction coefficient matrix; 2*j-1, 2*j represents the number of rows or columns corresponding to the elements related to node j in the correction coefficient matrix; if the corresponding nodes i and j in the interrupt branch (i, j) contain PV nodes, the PV nodes can also be corrected as above. The formula of the PV node is different from the above formula only in that the following parameters are modified to the parameters pointed by the arrows:

[0114] From the calculation formulas (6) and (7) of the coefficient matrix, we can see that when the initial voltage values ​​of node i and node j are equal, that is, V i0 =V j0 hour, But when V i0 ≠V j0 , their calculation formulas are not the same.

[0115] Since each element in ΔA has no clear physical meaning, it is difficult to decompose it based on the physical meaning of the matrix when the matrix elements change. Therefore, ΔA is decomposed based on the full rank decomposition theorem. Consider V i ≠V k In the case of node i and node k, the coefficients corresponding to the nodes are modified respectively, and the following can be obtained:

[0116]

[0117] Where ΔA1 and ΔA2 are correction matrices; and are the non-zero sub-matrices of M1E1N1 and M2E2N2 respectively, and the relationship between the non-zero sub-matrices and the original matrix is ​​represented by arrow symbols; M1 and M2 are matrices with full column rank; N1 and N2 are matrices with full row rank; E1 and E2 are unit matrices of small dimension.

[0118] Substituting equations (23), (24) and (21) into equation (18), we can obtain the solution of the equation under the kth accident state:

[0119]

[0120] The embodiment of the present invention uses test systems of different scales to perform simulation tests. When a branch is disconnected, the system network parameters will change. The embodiment of the present invention analyzes the fault branch that forms the Unicom system. The detailed data of the specific test system are as follows:

[0121] Table 1 Configuration of the test system

[0122] Test system Number of nodes Number of generators Number of branches 14-node system 14 5 21 30-node system 30 6 44 118-node system 118 54 194 300-node system 300 69 411 1354 Node System 1354 260 1991

[0123] A complete safety check is performed on the 30-node system to verify branch faults. Performance indicators include node voltage amplitude error and node voltage phase angle error.

[0124] First, disconnect each branch in turn to simulate the situation where the branch fails, and compare the power flow calculation results of the full pure embedded power flow equation based on the compensation method with the original full pure embedded power flow equation. Due to the large amount of branch data, only the calculation results of the top 20 branches with the highest maximum absolute error values ​​of voltage amplitude and voltage phase angle are shown. The obtained voltage amplitude and voltage phase angle errors are shown in Tables 2 and 3.

[0125] Table 2 Voltage amplitude error of some branch faults in 30-bus system

[0126]

[0127]

[0128] Table 3 Voltage phase angle error of some branch faults in 30-bus system

[0129]

[0130] From the data in the table, it can be seen that the maximum absolute error value of the voltage amplitude in the branch fault is 0.002419, and the corresponding maximum relative error value is 0.2537%; the maximum absolute error value of the voltage phase angle is 0.050389, and the corresponding maximum relative error value is 1.3347%. Only a few branch faults have error values ​​of this order of magnitude, which shows that there are small errors in the calculation results of the voltage amplitude and voltage phase angle in a few branch faults, and the errors are within an acceptable range. The maximum absolute error of the voltage amplitude in all other branch faults is less than 1e-05, and the maximum relative error is less than 1e-03%; the maximum absolute error of the voltage phase angle is less than 1e-03, and the maximum relative error is less than 1e-01%, the error is almost negligible, and the calculation results of the two algorithms are basically the same. This is because when a fault occurs in the power system, the network parameters of the power system change, and the elements in the coefficient matrix change accordingly. When the compensation method modifies the coefficient matrix, it can make the modified matrix basically consistent with the coefficient matrix that changes when a fault occurs, so a more accurate result can be obtained when solving the equation group. The above results verify that the calculation results of the algorithm have high accuracy when performing branch fault safety verification.

[0131] In order to compare the computational efficiency of the safety check of the holomorphic embedded power flow equation based on the compensation method with that of the original holomorphic embedded power flow equation, verification was performed on five different scale test systems: 14-node system, 30-node system, 118-node system, 300-node system, and 1354-node system. Each test system was repeatedly solved 10 times using the two methods, and the average calculation time was taken as the execution time of the corresponding method. The time consumed for calculating different examples is shown in the table below.

[0132] Table 4 Comparison of computational time for branch fault safety check between the holomorphic embedded power flow equation based on compensation method and the original holomorphic embedded power flow equation

[0133]

[0134] It is found from the table that in test systems of different scales, the calculation time of the holomorphic embedded power flow equation based on the compensation method is longer than that of the original holomorphic embedded power flow equation. The calculation efficiency of the holomorphic embedded power flow equation based on the compensation method is significantly higher than that of the original holomorphic embedded power flow equation. And as the scale of the example increases, the calculation speed of the holomorphic embedded power flow equation based on the compensation method increases more and more significantly, and the calculation efficiency increases by more than 50% on average. In the 1354-node system, the calculation efficiency of the holomorphic embedded power flow equation based on the compensation method increases by more than 80% compared with the original holomorphic embedded power flow equation. This is because as the scale of the example increases, the dimension of the matrix increases greatly. In the safety check, the original holomorphic embedded power flow equation needs to repeatedly invert the high-dimensional matrix, which is very computationally intensive and time-consuming. The holomorphic embedded power flow equation based on the compensation method avoids the inversion of the high-dimensional matrix through the compensation method, thereby shortening the calculation time of solving the linear equation system.

[0135] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A fully embedded power system security verification method based on compensation method, characterized in that: The specific steps are as follows: Step 1: Set the initial values ​​of the network parameters of the power system, construct a holomorphic embedded power flow equation according to the holomorphic embedding principle, and obtain the coefficient matrix and constant vector of the holomorphic embedded power flow equation; Step 2: determine all fault scenarios for power system safety verification, and disconnect the kth branch of the power system in sequence; Step 3, correcting the coefficient matrix and constant vector in the holomorphic embedded power flow equation under the kth accident state, and decomposing the correction matrix in the holomorphic embedded power flow equation by using the compensation method; Step 4: Obtain the holomorphic embedded power flow equation based on the compensation method under the k-th accident state, solve its power series coefficients by recursive calculation, use the Padé approximation to solve the approximate solution, obtain the power flow solution under the k-th accident state, and determine whether it meets the convergence criterion; Step 5. Repeat steps 2 to 4 to calculate the power flow solution after each branch is disconnected until the disconnection verification of all branches is completed. Finally, the safety verification results under each fault scenario are output, including node voltage, line power flow and whether there is an over-limit situation.

2. A fully embedded power system safety verification method based on compensation method according to claim 1, characterized in that: The constructed holomorphic embedded power flow equation is as follows: Construct the holomorphic embedded power flow equations for each type of node, expand their relations, and derive the recursive relations as follows: Where N is the number of nodes; n is the order of the power series; is the real part of the n-order voltage power series at node i; is the imaginary part of the n-order voltage power series at node i; is the real part of the n-1th order known vector of the PV node; is the imaginary part of the n-1th order known vector of the PV node; is the real part of the n-1th order known vector of the PQ node; is the imaginary part of the n-1th order known vector of the PQ node; is the real part of the initial value of the voltage at node i; is the imaginary part of the initial voltage value of node i; ii and β ii is the element in the recursive equation corresponding to the PV node in the coefficient matrix; and is the element of the real part of the recurrence equation in the coefficient matrix corresponding to the PQ node; and It is the element of the imaginary part of the recursive equation corresponding to the PQ node in the coefficient matrix; the calculation formula of each element is as follows: When j≠i, When j = i, In the formula, is the real part of the initial value of the voltage at node j; is the imaginary part of the initial voltage value of node j; g ij is the conductance between nodes i and j; b ij is the susceptance between nodes i and j; g ii is the conductance of node i; b ii is the susceptance of node i.

3. A fully embedded power system safety verification method based on compensation method according to claim 2, characterized in that: The compensation method is used to decompose the correction matrix of the holomorphic embedded power flow equation as follows: The general linear power flow equations can be expressed as follows: Ax=B(4) In the formula, A is a coefficient matrix, which is related to the node type and network structure parameters of the power system; x is a vector of variables to be determined, including voltage amplitude and voltage phase angle; B is a constant vector; A and B will change due to changes in network parameters in the power system. When the network is disturbed, the coefficient matrix needs to be modified accordingly: A k =A0+ΔA k (5) A k x k =(A0+ΔA k )x k =B k (6) In the formula, A0 is the coefficient matrix before the accident; A k is the coefficient matrix under the kth accident state; ΔA k is the correction matrix under the kth accident state; x k is the solution under the kth accident state; the injection vector may also change accordingly, using B k express; According to the full rank decomposition theorem, any non-zero matrix can be decomposed into the product of a matrix with full row rank and a matrix with full column rank. Therefore, ΔA can be k This breaks down into: ΔA k =M k N k (7) In the formula, ΔA k is an m×m square matrix, where m is the dimension of the matrix. If ΔA k The rank of is r, then M k is an m×r column-full rank matrix, N k is an r×m full row rank matrix; The interruption of a power system branch is a small disturbance event, and only the elements related to the corresponding branch in its coefficient matrix will change. Therefore, the correction matrix ΔA k It is a very sparse matrix, that is, ΔA k The rank r is very small. If r = 1, then equation (4) is the same as the traditional compensation method. If r ≠ 1, according to the full rank decomposition theorem, an r × r unit matrix E is added to it. k It can still satisfy the decomposition form of the auxiliary theorem of matrix inversion, that is: ΔA k =M k E k N k (8)。 4. A method for safety verification of a fully embedded power system based on a compensation method according to claim 3, characterized in that: The holomorphic embedded power flow equation based on the compensation method is as follows: When a branch (i, j) in the power system is interrupted, the elements related to branch (i, j) in the coefficient matrix A will also change accordingly. For the convenience of discussion, it is assumed that i and j are both PQ nodes, and the elements in ΔA will change as follows: In the formula, is the non-zero submatrix of ΔA, and the arrows represent the relationship between the non-zero submatrix and the original matrix; is the element of the real part of the recursive equation corresponding to node i in the coefficient matrix A; is the element of the imaginary part of the recursive equation corresponding to node i in the coefficient matrix A; is the element of the real part of the recursive equation corresponding to node j in the coefficient matrix A; is the element of the imaginary part of the recursive equation corresponding to node j in the coefficient matrix A; 2*i-1, 2*i represents the number of rows or columns corresponding to the elements related to node i in the correction coefficient matrix; 2*j-1, 2*j represents the number of rows or columns corresponding to the elements related to node j in the correction coefficient matrix; if the corresponding nodes i and j in the interrupt branch (i, j) contain PV nodes, the PV node can also be corrected as above. The formula of the PV node is different from the above formula only in that the following parameters are modified to the parameters pointed by the arrows: By observing the calculation formulas (2) and (3) of the coefficient matrix, we can see that when the initial voltage values ​​of node i and node j are equal, that is, V i0 =V j0 hour, But when V i0 ≠V j0 When , their calculation formulas are not the same, so they should be corrected respectively; Since each element in ΔA has no clear physical meaning, when the matrix elements change, ΔA will be decomposed based on the full rank decomposition theorem; considering V i ≠V k In the case of node i and node j, the coefficients corresponding to node i and node j are modified respectively to obtain: Where ΔA1 and ΔA2 are correction matrices; and are the non-zero sub-matrices of M1E1N1 and M2E2N2 respectively, and the arrow symbols are used to represent the relationship between the non-zero sub-matrices and the original matrix; M1 and M2 are matrices with full column rank; N1 and N2 are matrices with full row rank; E1 and E2 are identity matrices of small dimensions; Substituting equations (6), (10) and (11) into the matrix inversion auxiliary theorem, the solution of the equation under the kth accident state can be obtained:

Images