A method for solving power system network equations based on diagonal preconditioning

Abstract

The application discloses a kind of based on diagonal preprocessing power system network equation solving method, comprising: step 1, obtains power system network topology and element parameter, forms node admittance matrix and establishes network equation;Step 2, obtains the node injection current vector under the condition of current simulation time and corresponding network topology;Step 3, based on admittance matrix construction preprocessing matrix;Step 4, using preprocessing matrix to transform network equation, obtain the linear equation set after preprocessing;Step 5, solve the linear equation set after preprocessing, obtain node voltage vector;Compared with the diagonal preprocessing of traditional, the present application introduces regular term to avoid the numerical anomaly caused by too small diagonal element, enhances the robustness of algorithm under extreme ill-conditioned condition;Solve the node admittance matrix ill-conditioned caused by small impedance branch in the prior art, the problem of unstable or slow convergence of solution.

Description

Technical Field

[0001] This invention belongs to the field of power system simulation technology, and in particular relates to a method for solving power system network equations based on diagonal preprocessing. Background Technology

[0002] Transient simulation of power systems is a core tool for power grid planning, operation control, and safety analysis. In time-domain simulation, network equations need to be solved within each integration step. These equations are typically in the form of nodal voltage equations YU = I, where Y is the nodal admittance matrix, U is the nodal voltage vector, and I is the nodal injected current vector.

[0003] With the increasing cable coverage of urban power grids and the widespread application of power collection lines in new energy power plants, a large number of low-impedance branches (such as cable lines and low-resistance grounding systems) have emerged in power systems. These low-impedance branches have extremely high admittance values ​​(up to [missing information - likely referring to a value]). ~ The per-unit value leads to extreme numerical differences in the nodal admittance matrix Y, causing the matrix condition number to increase sharply and exhibiting severe ill-conditioned characteristics.

[0004] Ill-conditioned network equations present two challenges to numerical solutions: First, in direct methods, the ill-conditioned matrix is ​​prone to numerical overflow or amplified rounding errors due to excessively small pivot elements, leading to decomposition failure. Second, in iterative methods, the ill-conditioned matrix significantly reduces the convergence speed or even causes divergence. Existing simulation software often experiences simulation interruptions or slow convergence when dealing with systems containing low-impedance branches.

[0005] To address the aforementioned issues, various preprocessing methods have been proposed in the prior art, such as incomplete LU preprocessing and graph-based preprocessing. However, these methods typically require additional large-scale matrix factorization or filler meta-analysis, increasing computational complexity and making it difficult to balance numerical stability and computational efficiency. Diagonal preprocessing is widely used due to its simplicity and low computational cost, but traditional diagonal preprocessing only uses the inverse of the diagonal matrix as the preprocessor. When the diagonal elements of the admittance matrix are also small, this can further amplify numerical instability.

[0006] Therefore, there is an urgent need for a network equation solution method that can effectively reduce the condition number of the admittance matrix, maintain computational efficiency, and be numerically stable, so as to ensure the reliability and efficiency of time-domain simulation of power systems with low impedance branches. Summary of the Invention

[0007] The technical problem to be solved by this invention is to provide a method for solving power system network equations based on diagonal preprocessing, so as to solve the problems of ill-conditioned node admittance matrix, unstable solution or slow convergence caused by small impedance branches in the prior art.

[0008] Technical solution of the present invention:

[0009] A method for solving power system network equations based on diagonal preprocessing, the method comprising:

[0010] Step 1: Obtain the power system network topology and component parameters, form the node admittance matrix, and establish the network equations;

[0011] Step 2: Obtain the node injection current vector under the current simulation time and corresponding network topology conditions;

[0012] Step 3: Construct a preprocessing matrix based on the admittance matrix;

[0013] Step 4: Transform the network equations using the preprocessing matrix to obtain the preprocessed linear equation system;

[0014] Step 5: Solve the preprocessed linear equations to obtain the node voltage vectors.

[0015] The power system network topology and component parameters include: the name and rated voltage of the system bus, as well as the impedance and admittance parameters of the lines, transformers, parallel capacitors, and parallel reactors.

[0016] Forming the nodal admittance matrix Methods for establishing network equations include:

[0017] Step 1.1: Read the information of all buses in the system and assign a unique node number to each bus. The number can be from 0 to N, where N is the total number of nodes.

[0018] Step 1.2: Initialize an N×N all-zero matrix as the initial admittance matrix;

[0019] Step 1.3: Traverse all static components in the system, and append the admittance values ​​of the components to the corresponding positions in the node admittance matrix Y according to the component type and connection status.

[0020] Step 1.4: After constructing the node admittance matrix, establish the network equations. The specific network equations are as follows:

[0021] ;

[0022] In the formula: Y is the node admittance matrix, U is the node voltage vector to be determined, and I is the node injected current vector.

[0023] The method for appending the admittance value of a component to the corresponding position in the nodal admittance matrix Y is as follows:

[0024] For lines and transformer components connected between two nodes, read the node numbers q and j corresponding to the two ends of the connection, as well as the series impedance z of the component. bThe admittance value is calculated as follows: The admittance value y is accumulated at positions (q,q) and (j, j) of the matrix, and the cross admittance value -y is accumulated at positions (q, j) and (j, q) of the matrix.

[0025] For parallel capacitors and parallel reactance components, read the node number p corresponding to the connection node and the admittance parameter y. shunt The admittance value y shunt Accumulate it to position (p, p) of Y.

[0026] The node injection current vector I is obtained by summing the injection currents of all grid-connected devices in the current alternating iteration step of the power system time-domain simulation; the implementation methods include:

[0027] Step 2.1: Initialize a zero-current vector with a dimension equal to the total number of nodes N. Let the zero-current vector be I.

[0028] Step 2.2: Initialize the current search node number K to 1;

[0029] Step 2.3: Determine whether node K is connected to a grid-connected device. If it is connected, add the current injected into the network by the grid-connected device to the corresponding position of the Kth element of the current vector I; otherwise, do not perform any operation.

[0030] Step 2.4: Calculate the updated search node number K. new The calculation method is K new = K + 1; Update the search node number K, using the update method K = K new； After updating the search node number, if K ≤ N, return to step S203; if K > N, then the current current vector I is the final node injection current vector.

[0031] Step 3 describes the method for constructing the preprocessing matrix, which includes:

[0032] Step 3.1: Extract the diagonal elements of the admittance matrix to form a diagonal matrix D:

[0033] ;

[0034] In the formula This indicates that the diagonal elements of the admittance matrix Y are used to form a diagonal matrix;

[0035] ;

[0036] In the formula This represents the value of the element at the i-th row and i-th column of the admittance matrix Y;

[0037] Step 3.2: Perform the inverse operation on matrix D to obtain the diagonal inverse matrix:

[0038] ;

[0039] This is the diagonal inverse matrix obtained by inverting matrix D; for matrix D... Each element in the matrix is ​​introduced with a regularization term to form a preprocessing matrix M;

[0040] ;

[0041] In the formula, ε is the given regularization coefficient.

[0042] The value of ε is 0.001.

[0043] Methods for transforming network equations using preprocessing matrices to obtain a preprocessed system of linear equations include:

[0044] Step 4.1: Perform preprocessing operations on the admittance matrix and current vector in the network equations, specifically:

[0045] ;

[0046] Y is the nodal admittance matrix, and I is the nodal injected current vector. This is the preprocessed nodal admittance matrix. Inject current vectors into the preprocessed nodes;

[0047] Step 4.2: Based on the nodal admittance matrix and nodal injected current vector obtained after preprocessing, construct the preprocessed network equations. The specific method for constructing the preprocessed network equations is as follows:

[0048] ;

[0049] Where U is the node voltage vector to be solved.

[0050] Methods for solving nodal voltage vectors include:

[0051] Step 5.1: Process the preprocessed nodal admittance matrix Perform triangular decomposition to obtain an upper triangular matrix A1 and a lower triangular matrix A2;

[0052] Step 5.2: Execute the previous process to solve the system of equations. ,in The intermediate vector obtained from the previous process;

[0053] Step 5.3: Perform the back-substitution process to solve the system of equations. , where U is the node voltage vector.

[0054] A method for applying a power system network equation solving method based on diagonal preprocessing to power system time-domain simulation includes:

[0055] Step 6.1: Initialize system variables, simulation algorithm, algorithm parameters, and simulation parameters;

[0056] Step 6.2: Enter the main loop of time-domain simulation and update the simulation time;

[0057] Step 6.3: In each time step of the alternating iteration, solve the equipment-side equations, update the equipment variables, and calculate the injection current of each grid-connected device based on the updated equipment variables;

[0058] Step 6.4: Using the network equation solving method described in steps S1 to S5, the node voltage vector U is obtained;

[0059] Step 6.5: Determine whether the alternating iteration has converged. If it has converged, proceed to the next time step; otherwise, return to step 6.3.

[0060] Step 6.6: Determine if the simulation end time has been reached. If yes, end the simulation; otherwise, return to step S6.2.

[0061] The beneficial effects of this invention are:

[0062] This invention constructs a preprocessing matrix by extracting the diagonal elements of the nodal admittance matrix and introducing regularization terms, which effectively reduces the condition number of ill-conditioned linear equations, significantly improves the stability of numerical solutions, and avoids simulation divergence or interruption caused by small impedance branches.

[0063] The preprocessing matrix used in this invention is a diagonal matrix, which has minimal overhead for inversion and storage, and is updated only when the network topology changes, resulting in high computational efficiency and suitability for online or offline simulation of large-scale power systems.

[0064] The preprocessing method of this invention does not change the physical meaning of the original network equations, and the solution results are strictly equivalent to those of traditional methods (within the range of numerical accuracy), thus ensuring the accuracy of the simulation results.

[0065] This invention can be seamlessly embedded into existing alternating solution simulation frameworks with minimal changes to the original code, exhibiting good compatibility and practicality.

[0066] Compared to traditional diagonal preprocessing, this invention introduces a regularization term to avoid numerical anomalies caused by excessively small diagonal elements, thereby enhancing the robustness of the algorithm under extreme ill-conditioned conditions.

[0067] This solves the problems of ill-conditioned nodal admittance matrix, unstable solution, or slow convergence caused by small impedance branches in the existing technology. Attached Figure Description

[0068] Figure 1 This is a schematic diagram of the power system network equation solving method based on diagonal preprocessing provided in an embodiment of the present invention;

[0069] Figure 2 This is a test system topology diagram used in the embodiments of the present invention;

[0070] Figure 3 This is a comparison chart of the iteration number curves of the network equation between the embodiment of the present invention and the traditional method under the test system conditions in a specific embodiment;

[0071] Figure 4 This is a comparison graph of simulation results curves of the present invention and the traditional method under the test system conditions in a specific embodiment.

[0072] Figure 5 This is a comparison graph of simulation results between the embodiments of the present invention and the traditional method under the IEEE39 system conditions. Detailed Implementation

[0073] A method for solving power system network equations based on diagonal preprocessing includes the following steps:

[0074] S1. Obtain the power system network topology and component parameters to form the node admittance matrix;

[0075] S2. Obtain the node injection current vector I under the current simulation time and corresponding network topology conditions;

[0076] S3. Construct a preprocessing matrix based on the admittance matrix;

[0077] S4. Transform the network equations using the preprocessing matrix to obtain the preprocessed linear equation system;

[0078] S5. Solve the preprocessed linear equations to obtain the node voltage vectors.

[0079] Further, in step S1, the power system network topology and component parameters include the name and rated voltage of the system bus, as well as the impedance and admittance parameters of the lines, transformers, parallel capacitors, and parallel reactances;

[0080] Further, in step S1, the formation of the node admittance matrix The method is as follows:

[0081] S101. Read the information of all buses in the system and assign a unique node number to each bus. The number ranges from 0 to N, where N is the total number of nodes.

[0082] S102. Initialize an N×N all-zero matrix as the initial admittance matrix Y;

[0083] S103. Traverse all static components in the system, and based on the component type and connection status, append the component's admittance value to the corresponding position in the admittance matrix Y. The specific method for appending the component's admittance value to the corresponding position in the admittance matrix Y is as follows:

[0084] For lines and transformer components connected between two nodes, read the node numbers q and j corresponding to the two connected nodes, as well as the series impedance z of the component. b The admittance value is calculated as follows: The admittance value y is accumulated in the q-th row and q-th column and the j-th row and j-th column of the matrix, and the mutual admittance value -y is accumulated in the q-th row and j-th column and the j-th row and q-th column of the matrix.

[0085] For parallel capacitors and parallel reactance components, read the node number p corresponding to their connection node and the admittance parameter y. shunt The admittance value y shunt The sum is added to the p-th row and p-th column position of Y.

[0086] After constructing the node admittance matrix using the above method, the network equations can be established. The specific method for establishing the network equations is as follows:

[0087]

[0088] Where Y is the node admittance matrix, U is the node voltage vector to be determined, and I is the node injected current vector.

[0089] Further, in step S2, the node injection current vector I is obtained by summarizing the injection currents of all grid-connected devices in the current alternating iteration step of the power system time-domain simulation. The specific calculation method of the node injection current vector I is as follows:

[0090] S201 initializes a zero current vector with a dimension equal to the total number of nodes N, and denots this current vector as I.

[0091] S202 Initialize the current search node number K to 1;

[0092] S203 Determine whether node number K is connected to a grid-connected device. If it is connected to a grid-connected device, add the current injected into the network by the grid-connected device to the corresponding position of the Kth element of the current vector I. Otherwise, do not perform any operation.

[0093] S204 Update the search node number. Calculate the updated search node number K. new Its calculation method is K new = K + 1; Update the search node number K, using the update method K = K newAfter updating the search node number, if K ≤ N, return to step S203; if K > N, the current vector I finally becomes the node injection current vector.

[0094] Furthermore, in step S3, the specific method for constructing the preprocessing matrix is ​​as follows: first, extract the diagonal elements of the admittance matrix to form a diagonal matrix D:

[0095]

[0096] Where, diag(Y) represents taking the diagonal elements of the nodal admittance matrix Y to form a diagonal matrix, and the specific calculation method is as follows:

[0097]

[0098] in, This represents the value of the element at the i-th row and i-th column of the admittance matrix Y.

[0099] Inverting matrix D yields its inverse matrix:

[0100]

[0101] in, This is the diagonal inverse matrix obtained by inverting matrix D. Each element in the matrix is ​​introduced with a regularization term to form a preprocessing matrix M. The specific calculation method of the preprocessing matrix M is as follows:

[0102]

[0103] In the formula, ε is a given regularization coefficient. The main purpose of introducing a regularization term on the basis of the diagonal inverse matrix in this invention is to stabilize and compensate for excessively small preprocessing matrix elements.

[0104] Specifically, in power systems containing low-impedance branches, the self-admittance element of the relevant nodes typically increases significantly, making its reciprocal term very small; if only... As a preprocessing matrix, the equation corresponding to this node may be over-compressed during preprocessing, resulting in an imbalance in the numerical scale between different node equations, thus affecting the improvement effect of preprocessing on ill-conditioned network equations. Through... The addition of a regularization term ε on top of the preprocessing matrix can provide a moderate lower bound compensation for the diagonal elements of the preprocessing matrix, so that the equations of each node maintain more reasonable values ​​after preprocessing, thereby improving the scale balance of the preprocessed equations and enhancing the stability and robustness of solving the network equations.

[0105] Furthermore, in step S4, the admittance matrix and current vector in the network equation are preprocessed as follows:

[0106]

[0107] Where Y is the nodal admittance matrix and I is the nodal injected current vector. This is the preprocessed nodal admittance matrix. Inject current vectors into the preprocessed nodes.

[0108] Based on the admittance matrix and nodal injection current vectors obtained after preprocessing, the preprocessed network equations are constructed. The specific method for constructing the preprocessed network equations is as follows:

[0109]

[0110] Where U is the node voltage vector to be solved. Constructing the preprocessing matrix in the above form can not only reduce the condition number of ill-conditioned linear equations and reduce the risks of principal component anomalies, rounding error amplification, slow convergence or divergence caused by ill-conditioned matrices during direct decomposition or iterative solution, thus improving solution stability; at the same time, this diagonal matrix only requires storage of diagonal elements and element-wise operations, without the need for additional large-scale matrix decomposition or filling element analysis, which can minimize the computational load of preprocessing operations.

[0111] Furthermore, in step S5, when solving the preprocessed network equations, the direct method is used to solve for the nodal voltage vector U. The specific calculation method is as follows:

[0112] S501. Preprocessed node admittance matrix Perform triangular decomposition to obtain an upper triangular matrix A1 and a lower triangular matrix A2;

[0113] S502, Execute the previous process to solve the system of equations. ,in The intermediate vector obtained from the previous process;

[0114] S503, Perform the back-substitution process to solve the system of equations. , where U is the node voltage vector.

[0115] This embodiment uses a modified IEEE 39-bus system with low-impedance branches as an example to verify the proposed power system network equation solving method based on diagonal regularization preprocessing. Based on the IEEE 39 system network topology and system parameters, two photovoltaic devices and three wind turbine devices are added. The test system topology is as follows: Figure 2 As shown, the system's rated frequency is 50Hz. Meanwhile, to construct a low-impedance test scenario, the impedance values ​​of some lines in the system were adjusted according to Table 1.

[0116] Table 1 Line Parameter Adjustment

[0117]

[0118] S1. Forming the nodal admittance matrix

[0119] Read the information of 39 buses and assign a unique node number (1 to 39) to each bus, with a total number of nodes N=39.

[0120] Initialize a 39×39 all-zero matrix as the initial admittance matrix Y.

[0121] Iterate through all static components in the system, and based on the component type and connection configuration, append the component's admittance value to the corresponding position in the admittance matrix Y. The specific method for appending the component's admittance value to the corresponding position in the admittance matrix Y is as follows:

[0122] For lines and transformer components connected between two nodes, read the node numbers q and j corresponding to the two connected nodes, as well as the series impedance z of the component. b The admittance value is calculated as follows: The admittance value y is accumulated in the q-th row and q-th column and the j-th row and j-th column of the matrix, and the mutual admittance value -y is accumulated in the q-th row and j-th column and the j-th row and q-th column of the matrix.

[0123] For parallel capacitors and parallel reactance components, read the node number p corresponding to their connection node and the admittance parameter y. shunt The admittance value y shunt The sum is added to the p-th row and p-th column position of Y.

[0124] After constructing the node admittance matrix using the above method, the network equations can be established. The specific method for establishing the network equations is as follows:

[0125]

[0126] Where Y is the node admittance matrix, U is the node voltage vector to be determined, and I is the node injected current vector.

[0127] S2. Obtain the node injection current vector

[0128] In the current alternating iteration step of the time-domain simulation, the node injection current vector I is obtained. The specific process is as follows:

[0129] S201: Initialize a 39-dimensional zero current vector I.

[0130] S202: Initialize the current search node number K to 1.

[0131] S203: Determine whether node K is connected to a grid-connected device. If it is connected, add the current injected into the network by the grid-connected device to the corresponding position of the Kth element of the current vector I. Otherwise, do not perform any operation.

[0132] S204: Update the search node number. Calculate the updated search node number K. new Its calculation method is K new = K + 1; Update the search node number K, using the update method K = K new After updating the search node number, if K ≤ 39, return to step S203; if K > 39, the current vector I will eventually become the node injection current vector.

[0133] S3. Construct the preprocessing matrix

[0134] The specific method for constructing the preprocessing matrix is ​​as follows: First, extract the diagonal elements of the admittance matrix to form a diagonal matrix D:

[0135]

[0136] Where diag(Y) represents taking the diagonal elements of the admittance matrix Y to form a diagonal matrix, and the specific calculation method is as follows:

[0137]

[0138] in, This represents the value of the element at the i-th row and i-th column of the admittance matrix Y.

[0139] Inverting matrix D yields its inverse matrix:

[0140]

[0141] in, This is the diagonal inverse matrix obtained by inverting matrix D. Each element in the matrix is ​​introduced with a regularization term to form a preprocessing matrix M. The specific calculation method of the preprocessing matrix M is as follows:

[0142]

[0143] In the formula, ε is the given regularization coefficient.

[0144] In this embodiment, the value of ε in the method of the present invention is 0.001. This value is chosen because: firstly, it can adequately compensate for the excessively small preprocessing coefficients formed by the reciprocal terms of large admittance elements, avoiding insufficient scaling of local equations due to excessively small preprocessing coefficients; secondly, this value is still relatively small compared to the normal reciprocal terms of admittance, so it will not affect the original diagonal preprocessing effect, nor will it change the physical solution object of the network equations. If the value of ε is too small, the compensation effect for the excessively small preprocessing coefficients will be insignificant; if the value of ε is too large, it may weaken the effect of differentiated preprocessing based on the diagonal elements of the admittance matrix. Therefore, the present invention uses ε = 0.001 to balance numerical stability and solution accuracy.

[0145] S4. Transform the network equations using the preprocessing matrix.

[0146] The admittance matrix and current vector in the network equations are preprocessed as follows:

[0147]

[0148] Where Y is the nodal admittance matrix and I is the nodal injected current vector. This is the preprocessed nodal admittance matrix. Inject current vectors into the preprocessed nodes.

[0149] Based on the admittance matrix and nodal injection current vectors obtained after preprocessing, the preprocessed network equations are constructed. The specific method for constructing the preprocessed network equations is as follows:

[0150]

[0151] Here, U is the nodal voltage vector to be solved. Through the above preprocessing transformation, while keeping the nodal voltage vector to be solved unchanged, the numerical conditions of the linear equation system can be improved, and the risks of principal component anomalies, rounding error amplification, slow convergence or divergence caused by matrix ill-conditioning during direct decomposition or iterative solution can be reduced, thereby improving the stability of the solution.

[0152] S5. Solve the preprocessed linear equations.

[0153] When solving the preprocessed network equations, the direct method is used to solve for the nodal voltage vector U. The specific calculation method is as follows:

[0154] S501. Preprocessed node admittance matrix Perform triangular decomposition to obtain an upper triangular matrix A1 and a lower triangular matrix A2;

[0155] S502, Execute the previous process to solve the system of equations. ,in The intermediate vector obtained from the previous process;

[0156] S503, Perform the back-substitution process to solve the system of equations. , where U is the node voltage vector.

[0157] Time-domain simulation calculation process

[0158] Applying the above-mentioned method for solving network equations based on diagonal regularization preprocessing to power system time-domain simulation includes the following steps:

[0159] S601. Initialize system variables, simulation algorithm, algorithm parameters, and simulation parameters;

[0160] S602. Enter the main loop of time-domain simulation and update the simulation time;

[0161] S603. In each time step of the alternating iteration, the equipment-side equations are solved, the equipment variables are updated, and the injection current of each grid-connected device is calculated based on the updated equipment variables.

[0162] S604. Using the network equation solving method described in steps S1 to S5, the node voltage vector U is obtained;

[0163] S605. Determine whether the alternating iteration has converged. If it has converged, proceed to the next step; otherwise, return to step S603.

[0164] S606. Determine whether the simulation end time has been reached. If yes, end the simulation; otherwise, return to step S602.

[0165] In this embodiment, the initialization of system variables in step S601 includes setting a given alternating iteration convergence threshold, simulation time step, and total simulation duration. In this embodiment, the convergence threshold is set to 10. -6 The simulation step size was set to 0.001 s, and the total simulation time was set to 10 s.

[0166] Test Results and Analysis

[0167] To verify the effectiveness of the method of the present invention, in Figure 2 Simulation tests were conducted on the test system shown to compare the simulation performance of the traditional network equation solving method with that of the present invention. Specifically, the traditional network equation solving method is implemented by replacing step S604 in steps S601-S606 with directly solving the linear equation system. Update the node network vector U. The test system fault configuration is shown in Table 2:

[0168] Table 2 System Fault Configuration

[0169]

[0170] Figure 3A comparison of the number of iterations required to solve the network equations during the fault period is presented between the traditional method and the method of this invention. Figure 4 A comparison of the number of iterations required to solve the network equations during a fault is presented between the traditional method and the method of this invention.

[0171] Traditional methods often fail to converge after a fault occurs, with the simulation ending around 1.02 seconds later. However, using the preprocessing method of this invention, the simulation completes successfully, verifying the numerical stability of the invention.

[0172] To further verify the accuracy of the calculation results obtained by the method of this invention, a comparative analysis was conducted between the traditional network equation solving method and the method of this invention under the classical parameter conditions of the IEEE 39 system. Figure 5 A comparison of the number of iterations required to solve the network equations during a fault is presented under the classic parameters of the IEEE 39 system, comparing the traditional method with the method of this invention. The fault configurations are shown in Table 2. Figure 5 It can be concluded that, under the classical parameter conditions of the IEEE39 system, the curve obtained by the method of this invention basically coincides with the curve obtained by the traditional method, which verifies the calculation accuracy of the method proposed in this invention.

[0173] The above test results demonstrate that the proposed method for solving power system network equations based on diagonal preprocessing can effectively address the ill-conditioned solution problem of network equations in time-domain simulations involving branches with small impedances. It offers the following advantages: high numerical stability; the introduction of regularization terms avoids numerical overflow caused by small diagonal elements, ensuring stable solution even after preprocessing; the preprocessing matrix is ​​a diagonal matrix, resulting in low storage and update costs; recalculation only occurs when the network topology changes, minimizing computational overhead; and the preprocessing transformation is mathematically rigorously equivalent to the original equation, with simulation results consistent with the baseline results under the non-ill-conditioned condition.

Claims

1. A method for solving power system network equations based on diagonal preprocessing, characterized in that: The method includes: Step 1: Obtain the power system network topology and component parameters, form the node admittance matrix, and establish the network equations; Step 2: Obtain the node injection current vector under the current simulation time and corresponding network topology conditions; Step 3: Construct a preprocessing matrix based on the admittance matrix; Step 4: Transform the network equations using the preprocessing matrix to obtain the preprocessed linear equation system; Step 5: Solve the preprocessed linear equations to obtain the node voltage vectors.

2. The method for solving power system network equations based on diagonal preprocessing according to claim 1, characterized in that: The power system network topology and component parameters include: the name and rated voltage of the system bus, as well as the impedance and admittance parameters of the lines, transformers, parallel capacitors, and parallel reactors.

3. The method for solving power system network equations based on diagonal preprocessing according to claim 1, characterized in that: Forming the nodal admittance matrix Methods for establishing network equations include: Step 1.1: Read the information of all buses in the system and assign a unique node number to each bus. The number ranges from 0 to N, where N is the total number of nodes. Step 1.2: Initialize an N×N all-zero matrix as the initial admittance matrix; Step 1.3: Traverse all static components in the system, and append the admittance values ​​of the components to the corresponding positions in the node admittance matrix Y according to the component type and connection status. Step 1.4: After constructing the node admittance matrix, establish the network equations. The specific network equations are as follows: ； In the formula: Y is the node admittance matrix, U is the node voltage vector to be determined, and I is the node injected current vector.

4. The method for solving power system network equations based on diagonal preprocessing according to claim 1, characterized in that: The method for appending the admittance value of a component to the corresponding position in the nodal admittance matrix Y is as follows: For lines and transformer components connected between two nodes, read the node numbers q and j corresponding to the two ends of the connection, as well as the series impedance z of the component. b The admittance value is calculated as follows: The admittance value y is accumulated at positions (q, q) and (j, j) of the matrix, and the cross admittance value -y is accumulated at positions (q, j) and (j, q) of the matrix. For parallel capacitors and parallel reactance components, read the node number p corresponding to the connection node and the admittance parameter y. shunt , the admittance value y shunt Accumulate it to position (p, p) of Y.

5. The method for solving power system network equations based on diagonal preprocessing according to claim 1, characterized in that: The node injection current vector I is obtained by summing the injection currents of all grid-connected devices in the current alternating iteration step of the power system time-domain simulation. Implementation methods include: Step 2.1: Initialize a zero-current vector with a dimension equal to the total number of nodes N. Let the zero-current vector be I. Step 2.2: Initialize the current search node number K to 1; Step 2.3: Determine whether node K is connected to a grid-connected device. If it is connected, add the current injected into the network by the grid-connected device to the corresponding position of the Kth element of the current vector I; otherwise, do not perform any operation. Step 2.4: Calculate the updated search node number K new The calculation method is K new = K + 1; Update the search node number K, using the update method K = K new； After updating the search node number, if K ≤ N, return to step S203; if K > N, then the current current vector I is the final node injection current vector.

6. The method for solving power system network equations based on diagonal preprocessing according to claim 1, characterized in that: Step 3 describes the method for constructing the preprocessing matrix, which includes: Step 3.1: Extract the diagonal elements of the admittance matrix to form a diagonal matrix D: ； In the formula This indicates that the diagonal elements of the admittance matrix Y are used to form a diagonal matrix; ； In the formula This represents the value of the element at the i-th row and i-th column of the admittance matrix Y; Step 3.2: Perform the inverse operation on matrix D to obtain the diagonal inverse matrix: ； This is the diagonal inverse matrix obtained by inverting matrix D; for matrix D... Each element in the matrix is ​​introduced with a regularization term to form a preprocessing matrix M; ； In the formula, ε is the given regularization coefficient.

7. The method for solving power system network equations based on diagonal preprocessing according to claim 6, characterized in that: The value of ε is 0.

001.

8. The method for solving power system network equations based on diagonal preprocessing according to claim 1, characterized in that: Methods for transforming network equations using preprocessing matrices to obtain a preprocessed system of linear equations include: Step 4.1: Perform preprocessing operations on the admittance matrix and current vector in the network equations, specifically: ； Y is the nodal admittance matrix, and I is the nodal injected current vector. This is the preprocessed nodal admittance matrix. Inject current vectors into the preprocessed nodes; Step 4.2: Based on the nodal admittance matrix and nodal injected current vector obtained after preprocessing, construct the preprocessed network equations. The specific method for constructing the preprocessed network equations is as follows: ； Where U is the node voltage vector to be solved.

9. The method for solving power system network equations based on diagonal preprocessing according to claim 1, characterized in that: Methods for solving nodal voltage vectors include: Step 5.1: Process the preprocessed nodal admittance matrix Perform triangular decomposition to obtain an upper triangular matrix A1 and a lower triangular matrix A2; Step 5.2: Execute the previous process to solve the system of equations. ,in The intermediate vector obtained from the previous process; Step 5.3: Perform the back-substitution process to solve the system of equations. , where U is the node voltage vector.

10. A method for applying the power system network equation solving method based on diagonal preprocessing as described in claim 1 to power system time-domain simulation includes: Step 6.1: Initialize system variables, simulation algorithm, algorithm parameters, and simulation parameters; Step 6.2: Enter the main loop of time-domain simulation and update the simulation time; Step 6.3: In each time step of the alternating iteration, solve the equipment-side equations, update the equipment variables, and calculate the injection current of each grid-connected device based on the updated equipment variables; Step 6.4: Using the network equation solving method described in steps S1 to S5, the node voltage vector U is obtained; Step 6.5: Determine whether the alternating iteration has converged. If it has converged, proceed to the next time step; otherwise, return to step 6.

3. Step 6.6: Determine if the simulation end time has been reached. If yes, end the simulation; otherwise, return to step S6.2.

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