A Holopure Embedded Power System Security Verification Method Based on Compensation Method

Abstract

This invention discloses a holomorphic embedded power system security verification method based on the compensation method. First, based on the holomorphic embedding theory, a holomorphic embedded power flow equation is constructed according to different node types. Second, a compensation method is introduced to correct the coefficient matrix of the holomorphic embedded power flow equation. Finally, combining the holomorphic embedded power flow equation and the compensation method, an efficient power system security verification algorithm is proposed, which avoids the inversion of high-dimensional matrices and greatly reduces the amount of calculation. The method of the present invention combines the advantages of the holomorphic embedding algorithm and the compensation method, and can take into account the accuracy, robustness, and efficiency of power system security verification.

Description

Technical Field

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

[0002] During power system operation, safety verification, as a core component in ensuring system stability and reliability, is crucial for proactively identifying and preventing potential operational risks, thereby enhancing the overall safety and reliability of the power system. Traditional safety verification relies primarily on numerical calculations and simulation techniques, assessing the safety and stability of the system by considering the potential failure scenarios of each component. This approach can effectively identify potential problems in the system, but in large-scale power systems, the computational complexity is high and can be time-consuming. This computational inefficiency 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 paper "Virtual Bus Technology and Its Application (III): Static Safety Verification Method" (Tong Xing, Kang Chongqing, Chen Qixin, et al. 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 an emergency line set, 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 paper "Improved Algorithm for Fast Static Safety Analysis of Power Systems" (Ding Ping, Li Yalou, Xu Dechao, et al. 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 it with 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 / back substitution method, it fully utilizes the sparsity characteristics of the matrix and significantly improves the computational efficiency of static safety verification. The document "Theoretical Analysis of Safety Constrained Optimal Power Flow Based on Nonlinear Interior Point Method (I)" (Li Yin, Zhang Boming, Sun Hongbin, et al. 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 aforementioned correction algorithms for power system security verification require continuous iterative matrix calculations, resulting in low computational efficiency. Traditional iterative methods also suffer from issues such as sensitivity to initial values, singular Jacobian matrices, and poor convergence. Therefore, further research is needed to improve the relevant theories and algorithms for power system security verification. This requires developing efficient mathematical models and methods to address the complexity, nonlinearity, uncertainty, large-scale, and coupled nature of power system security verification, thereby ensuring safe and reliable system operation under various operating conditions. Summary of the Invention

[0005] The present invention aims to overcome the shortcomings and deficiencies of the prior art by providing a holomorphic embedded power system security verification method based on a compensation method. This method, based on the principle of holomorphic embedding, establishes a holomorphic embedded power flow equation that does not require iterative solution. This method, combined with a compensation method based on the full-rank decomposition theorem and the matrix inversion auxiliary theorem, performs power system security verification. The correction matrix of the coefficient matrix in the holomorphic embedded power flow equation is decomposed, reducing computational complexity. This method combines the advantages of the holomorphic embedding algorithm and the compensation method to quickly and accurately solve power system security verification problems.

[0006] To achieve the above objectives, the present invention provides a technical solution: a fully embedded power system security verification method based on a compensation method, the specific steps of which 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: Correct the coefficient matrix and constant vector in the holomorphic embedded power flow equation under the k-th accident state, and decompose the correction matrix in the holomorphic embedded power flow equation 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, recursively calculate and solve its power series coefficients, 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 for 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 equation for each type of node, expand its relation, and derive the recursive relation 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-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; δ 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 corresponding to the PQ node in the coefficient matrix; and is the imaginary element in the recursive equation corresponding to the PQ node in the coefficient matrix; the calculation formula for each element is as follows:

[0016] When j≠i,

[0017]

[0018] When j=i,

[0019]

[0020] Where, 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] Where A is the coefficient matrix, which is related to the power system node type and network structure parameters; x is the variable vector to be determined, including voltage amplitude and voltage phase angle; B is the constant vector;

[0025] 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:

[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 k-th accident state; x k is the solution under the k-th 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 decomposed into k Breaks down to:

[0030] ΔA k =M k N k (7)

[0031] Where 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 power system branch interruption 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. For the convenience of discussion, it is assumed that i and j are both PQ nodes. The elements in ΔA will change as follows:

[0036]

[0037] Where, 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 imaginary element in the recursive equation corresponding to node j in the coefficient matrix A; 2*i-1 and 2*i represent the number of rows or columns corresponding to the elements related to node i in the correction coefficient matrix; 2*j-1 and 2*j represent 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 only difference between the PV node formula and the above formula is that the following parameters are changed to the parameters pointed by the arrows:

[0038] From 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 different, so they should be modified 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 the nodes are modified respectively, and the results are:

[0040]

[0041] Where ΔA1 and ΔA2 are correction matrices; and are the non-zero submatrices of M1E1N1 and M2E2N2 respectively, and the arrow symbols represent the relationship between the non-zero submatrices 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, we can obtain the solution of the equation under the k-th accident state:

[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 achieves efficient solution to the tidal flow calculation by fully embedding the tidal flow equation. Compared with the traditional iterative method, the method of the present invention is less sensitive to the initial value, has better convergence performance, and reduces the calculation time.

[0046] 2. The method of the present invention is applicable to large-scale and complex power systems and can effectively handle both single-branch and multi-branch faults. By quickly correcting branch faults and accurately calculating power flow solutions, it ensures that the system's operating status after a 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 heavy load and other operating conditions of 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 Flowchart of the method of the present invention. DETAILED DESCRIPTION

[0050] The present invention will be described in further detail below with reference to the 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 computational 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 based on 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] Where, 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 nodes i and j; “*” represents the conjugate operator.

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

[0056] (1) Holomorphic embedded 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 embedded model of equilibrium node equations:

[0060]

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

[0062] (3) Holomorphic embedded 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 sorted to obtain 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-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; δ 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 corresponding to the PQ node in the coefficient matrix; and is the element of the imaginary part of the recursive equation corresponding to the PQ node in the coefficient matrix; the calculation formula for the elements in the coefficient matrix is ​​as follows:

[0068] When j≠i,

[0069]

[0070] When j=i,

[0071]

[0072] Where, 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 do 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] Where, I PV Represents the set of PV nodes; IPQ Represents a set of PQ nodes; [] are the orders corresponding to 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] Where, 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] Where ΔY k is the modified admittance matrix; is the corrected node voltage; is the corrected node current; subscript k represents the kth fault state. Use the branch correlation matrix to describe ΔY k :

[0084]

[0085] Where 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 incidence matrix corresponding to the k-th changing element of the interrupted branch; the superscript T indicates 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 the elements in an m×m matrix A change:

[0088] ΔA=M′aN′ T (13)

[0090]

[0091] Where 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 formula (12), which satisfies the form of formula (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 power system node type and network structure parameters; 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 k-th accident state; x kis the solution under the k-th 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. Therefore, ΔA can be k Breaks down to:

[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 coefficient matrix after the change The expression:

[0108]

[0109] Here, the smaller the dimension of the identity matrix E, the less computational effort required for the auxiliary theorem for matrix inversion. The full-rank decomposition theorem ensures that E and ΔA have the same rank r, achieving a minimum value. This allows only the rows and columns associated with the interrupted branch to be modified, significantly reducing the computational effort.

[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 security 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 sake of discussion, it is assumed that i and j are both PQ nodes. The elements in ΔA will change as follows:

[0112]

[0113] Where, 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 imaginary element in the recursive equation corresponding to node k in the coefficient matrix A; 2*i-1 and 2*i represent the number of rows or columns corresponding to the elements related to node i in the correction coefficient matrix; 2*j-1 and 2*j represent 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 only difference between the PV node formula and the above formula is that the following parameters are changed 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 will be 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 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 unit matrices of small dimensions.

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

[0119]

[0120] The embodiments of the present invention use test systems of different scales to perform simulation tests. When a branch is disconnected, it will cause changes in system network parameters. The embodiments of the present invention analyze the faulty branch that forms the Unicom system. Detailed data of the specific test system is 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, each branch was disconnected in turn to simulate a branch fault. The power flow calculation results from the compensation-based holomorphic embedded power flow equation were compared with those from the original holomorphic embedded power flow equation. Due to the large number of branch data, only the calculation results for the top 20 branches with the highest maximum absolute errors in voltage amplitude and voltage phase angle are shown. The resulting voltage amplitude and voltage phase angle errors are shown in Tables 2 and 3.

[0125] Table 2 Voltage amplitude errors of faults in some branches of a 30-bus system

[0126]

[0127]

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

[0129]

[0130] The data in the table shows that the maximum absolute error in voltage amplitude for branch faults is 0.002419, corresponding to a maximum relative error of 0.2537%. The maximum absolute error in voltage phase angle is 0.050389, corresponding to a maximum relative error of 1.3347%. Only a few branch faults exhibit errors of this magnitude, indicating that the calculated voltage amplitude and phase angle for these branch faults exhibit small errors within an acceptable range. For all other branch faults, the maximum absolute error in voltage amplitude is less than 1e-05, and the maximum relative error is less than 1e-03%. The maximum absolute error in voltage phase angle is less than 1e-03, and the maximum relative error is less than 1e-01%, representing negligible errors. The results of the two algorithms are essentially consistent. This is because when a power system fault occurs, the network parameters of the power system change, and the elements in the coefficient matrix change accordingly. The compensation method modifies the coefficient matrix so that it is essentially identical to the coefficient matrix that changes when a fault occurs. Therefore, it can obtain a more accurate solution to this system of equations. These results demonstrate the high accuracy of the algorithm's calculations for branch fault safety checks.

[0131] To compare the computational efficiency of the holomorphic embedded power flow equation based on the compensation method with the original holomorphic embedded power flow equation for safety verification, we conducted validation on five test systems of varying sizes: 14-bus, 30-bus, 118-bus, 300-bus, and 1354-bus. Each test system was repeatedly solved 10 times using both methods, and the average computational time was taken as the execution time for the corresponding method. The computation times for different examples are 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 the compensation method and the original holomorphic embedded power flow equation

[0133]

[0134] The table shows that, across test systems of varying scale, the computation time of the holomorphic embedded tidal flow equation based on the compensation method is consistently longer than that of the original holomorphic embedded tidal flow equation. The computational efficiency of the holomorphic embedded tidal flow equation based on the compensation method is significantly higher than that of the original holomorphic embedded tidal flow equation. Furthermore, as the scale of the calculation case increases, the computational speed of the holomorphic embedded tidal flow equation based on the compensation method increases significantly, with an average improvement in computational efficiency of over 50%. In a 1354-node system, the computational efficiency of the holomorphic embedded tidal flow equation based on the compensation method exceeds that of the original holomorphic embedded tidal flow equation by over 80%. This is because the matrix dimension increases significantly with the scale of the calculation case. During safety checks, the original holomorphic embedded tidal flow equation requires repeated inversion of the high-dimensional matrix, which is computationally intensive and time-consuming. However, the holomorphic embedded tidal flow equation based on the compensation method avoids this high-dimensional matrix inversion, thereby shortening the computational time required to solve the linear system.

[0135] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of this application. Therefore, the scope of protection of this application should be based on the scope of protection of the claims.

Claims

1. A fully embedded power system security verification method based on compensation method, characterized by: 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: Correct the coefficient matrix and constant vector in the holomorphic embedded power flow equation under the k-th accident state, and decompose the correction matrix in the holomorphic embedded power flow equation using the compensation method, as follows: The general linear power flow equations can be expressed as follows: Ax=B (4) Where A is the coefficient matrix, which is related to the power system node type and network structure parameters; x is the variable vector to be determined, including voltage amplitude and voltage phase angle; B is the constant vector; 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: A k =A0+ΔA k (5) A k x k =(A0+ΔA k )x k =B k (6) 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 k-th accident state; x k is the solution under the k-th 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 decomposed into k Breaks down to: ΔA k =M k N k (7) Where 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 power system branch interruption 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) Step 4: Obtain the holomorphic embedded power flow equation based on the compensation method under the k-th accident state, recursively calculate and solve its power series coefficients, 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 for 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 security 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 equation for each type of node, expand its relation, and derive the recursive relation as follows: 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-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; δ 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 corresponding to the PQ node in the coefficient matrix; and is the imaginary element in the recursive equation corresponding to the PQ node in the coefficient matrix; the calculation formula for each element is as follows: When j≠i, When j=i, Where, 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. The method for safety verification of a fully embedded power system based on the compensation method according to claim 2 is 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. For the convenience of discussion, it is assumed that i and j are both PQ nodes. The elements in ΔA will change as follows: Where, 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 and 2*i represent the number of rows or columns corresponding to the elements related to node i in the correction coefficient matrix; 2*j-1 and 2*j represent 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 interrupted branch (i, j) contain PV nodes, the PV node can also be corrected as above. The only difference between the PV node formula and the above formula is that the following parameters are modified to the parameters pointed by the arrows: From 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 different, so they should be modified 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 the nodes are modified respectively, and the results are: Where ΔA1 and ΔA2 are correction matrices; and are the non-zero submatrices of M1E1N1 and M2E2N2 respectively, and the arrow symbols represent the relationship between the non-zero submatrices 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, we can obtain the solution of the equation under the k-th accident state:

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