A Partitioning and Solving Method for Improving the Computational Efficiency of Power System Network Equations

Abstract

The present application discloses a partitioning and solving method for improving the calculation efficiency of the network equation of a power system. The method includes: constructing a network equation and a directed unweighted graph of the power system; generating an adjacency matrix according to the relationship between nodes in the directed unweighted graph; constructing an objective function based on the adjacency matrix with the goal of minimizing the number of edges used to partition the power system, optimizing and solving the objective function to obtain two node sets and a cut set after partitioning; partitioning each of the partitioned node sets, and generating a clustering tree according to each partitioned node set; traversing each layer in the clustering tree, and using a hierarchical non-diagonal low-rank algorithm to solve the network equation; wherein, parallel computing is performed on the node sets of each layer in the clustering tree. The present application solves the technical problem of low calculation efficiency existing in the prior art.

Description

Technical Field

[0001] This application relates to the technical field of power systems, and particularly to a partitioning and solution method for improving the calculation efficiency of power system network equations. Background Art

[0002] The calculation efficiency of power systems is crucial in power system analysis and optimization, especially when dealing with large-scale networks. Solving the power system network equations is the basis for key tasks such as analyzing the operating state of power systems, performing power flow calculations, and fault diagnosis.

[0003] Traditional partitioning and solution methods for improving the calculation efficiency of power system network equations include direct methods and iterative methods. Although direct methods (such as Gaussian elimination) can obtain accurate solutions through matrix factorization and back substitution, when dealing with large-scale power systems, the computational resources and time consumption are very high. Although the application of sparse technology and factorization paths reduces the amount of calculation to a certain extent, for dynamically changing power systems, frequent re-factorization and calculation are still required, resulting in reduced efficiency. When dealing with complex power systems, iterative methods accelerate the convergence process through preprocessing techniques. However, when dealing with high-impedance or low-impedance paths, iterative methods often face problems such as difficult convergence or even divergence. In addition, as the number of nodes and connections in power systems increases, the convergence speed of iterative methods is also challenged. Although traditional preprocessing techniques improve the solution efficiency, there are still no targeted optimization means for the regional and low connectivity characteristics of power systems.

[0004] Although existing solution methods meet the actual application requirements to a certain extent, with the continuous expansion of the scale and increasing complexity of power systems, these methods gradually expose deficiencies in computational efficiency and adaptability. Existing solution methods generally ignore the characteristics existing in power systems, which is particularly obvious when the network scale is large. Therefore, relying solely on traditional solution methods is difficult to effectively meet the increasingly complex power system analysis requirements, especially in terms of computational efficiency, where there are obvious deficiencies. Summary of the Invention

[0005] This application provides a partitioning and solution method for improving the calculation efficiency of power system network equations, which is used to solve the technical problem of low calculation efficiency existing in the prior art.

[0006] In view of this, the first aspect of this application provides a partitioning and solution method for improving the calculation efficiency of power system network equations, including:

[0007] Construct the network equations and directed unweighted graphs of the power system;

[0008] Generate an adjacency matrix based on the relationships between nodes in the directed unweighted graph; construct an objective function aiming to minimize the number of edges used to partition the power system based on the adjacency matrix, optimize and solve the objective function to obtain two partitioned node sets and a cut set;

[0009] Partition each of the partitioned node sets and generate a clustering tree based on each partitioned node set;

[0010] Traverse each layer in the clustering tree and solve the network equation using the hierarchical non - diagonal low - rank algorithm; wherein, parallel computing is performed on the node sets of each layer in the clustering tree.

[0011] Optionally, after generating the adjacency matrix according to the relationships between nodes in the directed unweighted graph and before constructing the objective function aiming to minimize the number of edges used to partition the power system based on the adjacency matrix, it further includes:

[0012] Subtract the diagonal elements in the adjacency matrix to obtain a pre - processed adjacency matrix;

[0013] Correspondingly, constructing the objective function aiming to minimize the number of edges used to partition the power system based on the adjacency matrix includes:

[0014] Construct an objective function aiming to minimize the number of edges used to partition the power system based on the pre - processed adjacency matrix.

[0015] Optionally, constructing the objective function aiming to minimize the number of edges used to partition the power system based on the adjacency matrix, optimizing and solving the objective function to obtain two partitioned node sets and a cut set includes:

[0016] S1. Initialize the imbalance d = 0 of the two node sets formed by partitioning the power system network;

[0017] S2. Construct an objective function aiming to minimize the number of edges used to partition the power system based on the adjacency matrix and construct corresponding constraint conditions through the imbalance;

[0018] S3. Solve the objective function based on the constraint conditions. If there is no solution, let the imbalance d = d + 1 and return to step S2; if the solution is successful, obtain two partitioned node sets and a cut set.

[0019] Optionally, the objective function is:

[0020]

[0021] The constraint conditions are:

[0022]

[0023] Wherein, M is an adjacency matrix of order n; x is a vector of 0 or 1; is an all-ones vector of n dimensions.

[0024] Optionally, the network equation of the power system is a node voltage equation.

[0025] Optionally, traversing each layer in the clustering tree and solving the network equation by using a hierarchical non-diagonal low-rank algorithm includes:

[0026] Decomposing the non-diagonal blocks in the node admittance matrix in the network equation into a form of the product of a left low-rank basis and a right low-rank basis by using a low-rank decomposition method;

[0027] Traversing each non-leaf node in the clustering tree from the root node downwards, combining the left low-rank bases corresponding to each non-leaf node to form a large left low-rank basis matrix, and combining the right low-rank bases corresponding to each non-leaf node to form a large right low-rank basis matrix;

[0028] Based on the partitioned admittance matrix and the large left low-rank basis matrix, solving the network equation by using a non-recursive algorithm.

[0029] Optionally, the solving the network equation by using a non-recursive algorithm based on the partitioned admittance matrix and the large left low-rank basis matrix includes:

[0030] Initializing an intermediate large matrix by using the large left low-rank basis matrix; wherein, the intermediate large matrix is calculated from the partitioned admittance matrix and the left low-rank basis;

[0031] Traversing the leaf nodes of the clustering tree, and decomposing the diagonal block matrix corresponding to the leaf nodes by using the LU decomposition method to obtain an LU decomposition result;

[0032] Traversing each layer of the clustering tree from the root node downwards, and parallelly decomposing by using the LU decomposition method for each node in each layer to obtain a decomposition result, 、 being the non-diagonal block right low-rank bases corresponding to the child nodes of the current node 、 ; 、 being the non-diagonal block right low-rank bases corresponding to the child nodes of the current node 、 Calculating the results of and , wherein and is the corresponding diagonal block matrix, and is the corresponding non - diagonal block right low - rank basis, and I is the identity matrix;

[0033] Initialize the voltage of each node with the injection current of each node, and solve the network equation through the LU decomposition result and the decomposition result.

[0034] As can be seen from the above technical solutions, the present application has the following advantages:

[0035] The partitioning and solution method for improving the calculation efficiency of power system network equations in the present application generates a clustering tree by partitioning the power system. When traversing each layer of the clustering tree for solution, the node sets within each layer are solved in parallel, improving the calculation efficiency; since the goal is to minimize the number of edges used to partition the power system during partitioning, while making the size of each node set as balanced as possible after partitioning, the number of edges in the cut set is as small as possible, improving the calculation efficiency during the subsequent hierarchical non - diagonal low - rank algorithm solution process. Brief Description of the Drawings

[0036] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0037] Figure 1 is a flowchart of a partitioning and solution method for improving the calculation efficiency of power system network equations provided by an embodiment of the present application;

[0038] Figure 2 is a flowchart of a power system partitioning process provided by an embodiment of the present application;

[0039] Figure 3 is the partitioning result of a power system with 39 nodes provided by an embodiment of the present application;

[0040] Figure 4 is the partitioning result of the coefficient matrix provided by an embodiment of the present application;

[0041] Figure 5 is provided by an embodiment of the present application Figure 4 the hierarchical structure corresponding to the partitioning of the coefficient matrix;

[0042] Figure 6 is the flowchart of the hierarchical non - diagonal low - rank algorithm provided by an embodiment of the present application;

[0043] Figure 7Comparison graph of the calculation time of the hierarchical non - diagonal low - rank algorithm provided by the embodiments of this application and the calculation time of the Math Kernel Library algorithm. Detailed implementation manners

[0044] To enable those skilled in the art to better understand the solutions of this application, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of this application. Obviously, the described embodiments are only a part rather than all of the embodiments of this application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in this application without creative efforts shall fall within the scope of protection of this application.

[0045] For ease of understanding, please refer to Figure 1 , the embodiments of this application provide a partitioning and solving method for improving the calculation efficiency of power system network equations, including:

[0046] Step 110: Construct the network equation and the directed unweighted graph of the power system.

[0047] The network equation of the power system refers to the equation that can reflect the mutual relationship between the current and voltage in the power grid. For a determined power system network, the node voltage equation or loop current equation of the power grid can be written. However, in the actual power grid, due to many grounding branches, the number of loop current equations is more than that of node voltage equations. In addition, it is difficult to find independent loops in large and complex power grids, while the node voltage equation is easy to form and can be conveniently modified when the network structure changes. Therefore, this application adopts the construction of node voltage equations.

[0048] The node voltage equation describes the mathematical relationship between the injected current of each node in the power grid and the voltage of each node. For an -order power system, when taking the ground (the rd node) as the reference node, the -order node voltage equation can be written as:

[0049]

[0050] In the formula, is the vector composed of the injected current of each node, ; is the vector composed of the voltage of each node, ; is the node admittance matrix of the network.

[0051] The matrix expression is:

[0052]

[0053] Wherein: is the self - admittance of node , and its value is equal to the sum of the admittances of the branches connected to this node; is the mutual - admittance between node and node , and its value is equal to the negative value of the admittance of the connected branch.

[0054] The node - voltage equation can also be written as:

[0055]

[0056] Wherein, represents the set of all nodes directly connected to node i through branches.

[0057] The node - admittance matrix has the following characteristics:

[0058] 1) The node - admittance matrix is a complex - number matrix, and is usually a non - singular matrix when the power grid has at least one grounded branch.

[0059] 2) The node - admittance matrix is a symmetric matrix, that is , so when storing in a computer, only the elements of the corresponding upper - triangular (or lower - triangular) part can be stored, thus saving computer memory.

[0060] 3) When there is no directly - connected branch between node i and node j, , so the topological relationship of the power grid can be obtained from the admittance matrix. In addition, each busbar in an actual power system is connected to 3 - 5 lines or transformers on average. Therefore, there are a large number of non - diagonal elements in the admittance matrix that are 0, that is, the admittance matrix is a sparse matrix.

[0061] 4) In an actual power grid, regions are often connected by only a few lines. Therefore, after dividing the admittance matrix into diagonal blocks and non - diagonal blocks, the non - diagonal blocks correspond to the inter - regional connection lines and can be represented by the product of low - rank bases.

[0062] The network of the power system can be abstracted as a directed unweighted graph composed of several nodes and edges, that is, the nodes of the power system correspond to the nodes of the directed unweighted graph, the transmission lines of the power system correspond to the edges of the directed unweighted graph, and the division of the power system is equivalent to the division problem of the directed unweighted graph.

[0063] Step 120: Generate an adjacency matrix according to the relationship between nodes in the directed unweighted graph, construct an objective function with the goal of minimizing the number of edges used to divide the power system based on the adjacency matrix, optimize and solve the objective function to obtain two divided node sets and a cut set.

[0064] A power system network with n nodes, and its corresponding directed unweighted graph G can be described by an adjacency matrix M of order n. If , it means there is a connection line between node i and node j. If , it means there is no connection line between node i and node j.

[0065] Suppose the directed unweighted graph can be divided into two non-empty and complementary node sets and . Use a vector to represent the node set where each node is located. If , it means node . If , it means node .

[0066] Let , where is an n-dimensional all-ones vector. Then there is:

[0067]

[0068] If , it means the node in the node set is connected to the node set through edges. The proof is as follows:

[0069] When , that is:

[0070]

[0071] Then there is:

[0072]

[0073] That is , and there exist different nodes , such that:

[0074]

[0075] From the above formula, it can be obtained that and , that is, node and is connected to node . Q.E.D.

[0076] Divide the directed unweighted graph corresponding to the power system into two node sets and , the number of edges can be expressed by the following formula:

[0077]

[0078] After transformation and expansion, we get:

[0079]

[0080] To ensure that the two node sets after partitioning are as balanced as possible, a known feasible node number deviation d is set, and the constraint conditions are as follows:

[0081]

[0082] Expanding, we get:

[0083]

[0084] Therefore, the partitioning problem of the power system is equivalent to the integer programming problem shown below:

[0085]

[0086] The process of power system partitioning can refer to Figure 2 , first load the adjacency matrix M of the system from the file, then remove the self-loops by subtracting the diagonal elements, define a binary variable x, and perform partitioning according to the following steps:

[0087] S1. Initialize the imbalance (i.e., the node number deviation) d = 0 of the two node sets formed by the power system network partitioning;

[0088] S2. Based on the adjacency matrix, construct an objective function aiming to minimize the number of edges used in partitioning the power system, and construct the corresponding constraint conditions through the imbalance;

[0089] The purpose of solving the optimization problem is to reduce the number of edges used in partitioning, so the objective function is defined as ; To make the imbalance of the two node sets in the power system network partitioning as small as possible, the constraint is defined as ;

[0090] S3. Solve the objective function based on the constraint conditions. If there is no solution, let d = d + 1 and return to step S2; if the solution is successful, obtain the two partitioned node sets and a cut set.

[0091] After each execution of the power system partitioning algorithm, two node sets and a cut set are obtained, satisfying that the node sets are as balanced as possible while the number of edges in the cut set is as small as possible.

[0092] Step 130: Divide each of the divided node sets and generate a clustering tree based on each divided node set.

[0093] Divide each of the obtained node sets after division again. The specific division process is similar to the division process in Step 120 until the divided node sets can no longer be divided or the value of the imbalance measure d exceeds a preset threshold, then end the division, and generate a clustering tree for all the divided node sets. Each node in the clustering tree represents an index set of a node set.

[0094] The results obtained by testing with an example of 39 nodes in the embodiments of the present application are as Figure 3 shown. Divide the 39 nodes to obtain Region 1 and Region 2. Among them, Region 1 includes 20 nodes and Region 2 includes 19 nodes. The number of edges (Cut Edges) used for division is 3, that is, the number of edges in the cut set is 3, which can meet the requirements for the matrix structure in Step 140.

[0095] Step 140: Traverse each layer in the clustering tree and solve the network equations using a hierarchical non - diagonal low - rank algorithm.

[0096] Use a low - rank decomposition method to decompose the non - diagonal blocks in the node admittance matrix in the network equations into the form of the product of a left low - rank basis and a right low - rank basis; traverse each non - leaf node in the clustering tree from the root node downwards, combine the left low - rank bases corresponding to each non - leaf node to form a large left low - rank basis matrix, and combine the right low - rank bases corresponding to each non - leaf node to form a large right low - rank basis matrix; based on the divided admittance matrix and the large left low - rank basis matrix, use a non - recursive algorithm to solve the network equations.

[0097] For a system of linear equations, it is necessary to solve:

[0098]

[0099] Among them, A corresponds to Y in the network equations, x corresponds to in the network equations, and b corresponds to in the network equations. Assume that the coefficient matrix of the equation has the following form: Divide the coefficient matrix A of the equation twice. The first division divides the matrix into two diagonal blocks and two non - diagonal blocks, and the second division divides the diagonal blocks obtained from the first division into two diagonal blocks and two non - diagonal blocks again. The two divisions can divide the coefficient matrix corresponding to the linear system into the structure as Figure 4 shown. Take this structure as an example to introduce the hierarchical non - diagonal low - rank algorithm (in actual applications, more divisions such as 3 times, 4 times, etc. can be performed). Figure 4In this, D represents the diagonal block in the original matrix, and the corresponding off-diagonal blocks are of low rank and sparse.

[0100] Figure 4 The shown partitioning actually performs a hierarchical processing on the matrix, which can be described by a tree structure, and reference can be made to Figure 5 . Due to the sparse low-rank structure of the off-diagonal blocks, the off-diagonal blocks can be decomposed into the form of the product of two low-rank bases, that is, for , if , then there exists such that , and is called the left low-rank base, is called the right low-rank base, is the adjoint matrix of V. To facilitate the description of the hierarchical off-diagonal low-rank algorithm, assume that the maximum rank of all off-diagonal blocks formed by the two partitions is , and is called the rank of the hierarchical off-diagonal low-rank matrix.

[0101] From Figure 4 and Figure 5 's tree structure, it can be obtained that after the first partition:

[0102]

[0103] Among them, , is the diagonal block formed by the partition; , is the left low-rank base formed by the decomposition of the off-diagonal block after the partition; , is the right low-rank base formed by the decomposition of the off-diagonal block after the partition; , are the upper and lower parts of the solution of the original equation; , are the upper and lower parts of the right-side vector to be solved in the original equation.

[0104] Multiply both sides by , then there is:

[0105]

[0106] In the formula, I represents the identity matrix adapted to the sizes of the two off-diagonal blocks;

[0107] Among them , , and from the Woodbury identity, it can be known that:

[0108]

[0109] Solve the equation , , which are the solution correction amounts of nodes 2 and 3 respectively. Then the solution can be transformed into solving the following two sub-problems:

[0110]

[0111] Then the solution of the original equation is obtained by calculating the following formula:

[0112]

[0113] For and re-partitioning gives:

[0114]

[0115] In the formula, D4, D5, D6, and D7 are the diagonal blocks corresponding to nodes 4, 5, 6, and 7 respectively; U4, U5, U6, and U7 are the left low-rank bases of the off-diagonal blocks corresponding to nodes 4, 5, 6, and 7 respectively; V4, V5, V6, and V7 are the right low-rank bases of the off-diagonal blocks corresponding to nodes 4, 5, 6, and 7 respectively; z4, z5, z6, and z7 are the solutions to be corrected corresponding to nodes 4, 5, 6, and 7 respectively; b4, b5, b6, and b7 are the vectors to be solved on the right side of the original equation corresponding to nodes 4, 5, 6, and 7 respectively. represents the upper half of represents the lower half of represents the upper half of represents the lower half of represents the upper half of represents the lower half of represents the upper half of represents the lower half of. The problem of the above formula is transformed into solving the following system of equations:

[0116]

[0117] Then substitute into , and correct and .

[0118] Note that on the right side of the above four sub-problems, the matrix is partitioned and then connected together. This structure inspires combining all the left low-rank bases The idea of connecting them together to form a large matrix. Traverse the tree structure downward from the root node to create For each non-leaf node There are two child nodes and Align the left low-rank bases of the non-diagonal blocks corresponding to nodes and vertically. If the number of columns is different, it is stipulated to align to the left and place on the left and as follows: It is expressed as:

[0119]

[0120] For the sake of easy representation, and the right low-rank basis are also represented by this data structure and are denoted as and respectively. is the matrix to be decomposed. For each node in the clustering tree, only the indices of the corresponding low-rank bases in , and need to be stored, rather than the specific values.

[0121] For the admittance matrix that has been partitioned and , a non-recursive algorithm based on a for loop can be written. This non-recursive algorithm consists of a decomposition stage and a solution stage. This data structure enables this algorithm to calculate multiple left low-rank bases at different levels in the clustering tree with only one BLAS or LAPACK call and without generating unnecessary data movement. Please refer to Figure 6 .

[0122] Decomposition stage:

[0123] 1. Initialize with , and subsequent solutions are performed in-place;

[0124] 2. Traverse the leaf nodes of the clustering tree and execute:

[0125] 1) Perform LU decomposition on the diagonal block matrix corresponding to the leaf node and store the decomposition result in-place

[0126] 2) Solve multiple right-hand sides in-place, that is

[0127] 3. Traverse each layer of the clustering tree from bottom to top and traverse each node in this layer and execute:

[0128] 1) Let the child nodes of this node be and

[0129] 2) LU decomposition , and store the result in place

[0130] 3) Application The result of LU decomposition solves the following equation:

[0131]

[0132] 4) Calculate the following formula:

[0133]

[0134] Solution phase:

[0135] 1. ,use Initialize the value of , the subsequent solution is carried out in situ;

[0136] 2. Traverse the leaf nodes. Let the node being traversed be , apply the LU decomposition result of the decomposition stage and solve it in situ:

[0137]

[0138] in For Node The corresponding diagonal block matrix, is the right-hand side vector to be solved The number of rows corresponding to the node's corresponding index.

[0139] 3. Traverse each layer of the tree from bottom to top and traverse each node of that layer

[0140] 1) Order The child nodes are and

[0141] 2) Application decomposition phase The LU decomposition result is solved:

[0142]

[0143] 3) Calculation:

[0144]

[0145] In the formula, For Node The index collection of For Node The set of nodal voltages.

[0146] When traversing each layer of the tree structure, the nodes within a layer do not have data dependencies. Therefore, the operations of the nodes within a layer can all be parallelized to improve the computational efficiency. By overwriting the input with the output result, the calculation process only requires additional memory that is easy to obtain. Therefore, when the rank of the hierarchical off-diagonal low-rank matrix is very small, this algorithm only requires very little additional memory.

[0147] The comparison of the test results at 280k and 560k nodes is as Figure 7 shown. The direct solution algorithm for hierarchical off-diagonal low-rank matrices (HODLR) has a computational speed increase of approximately 10% compared to the Math Kernel Library (MKL), and better performance can also be achieved on machines with parallel capabilities.

[0148] This solution algorithm based on hierarchical off-diagonal low-rank structured matrices converts the problem of solving linear equations with a large dimension into parallelly solving several sub-problems with smaller dimensions and LU decomposition. And because , and the rank of the hierarchical off-diagonal low-rank matrix is very small, the computational time can be greatly reduced and the efficiency can be well improved.

[0149] The time consumption of the calculation of the solution algorithm in step 140 mainly depends on the size of each node set after partitioning and the number of tie lines (i.e., the size of the cut set). The fewer the tie lines, the higher the computational efficiency. Also, since there are no data dependencies between the multiple regions formed after partitioning, parallel computing can be used. Therefore, the computational time for independent solution of each region depends on the region with the largest number of nodes. And in the partitioning process of the aforementioned power system, it is ensured that the sizes of each node set are as balanced as possible during partitioning, thereby improving the computational efficiency.

[0150] This application conducts a hierarchical analysis of the power system network, utilizes the regional and low connectivity characteristics of the network, and proposes a decomposition of the admittance matrix and an efficient solution algorithm for network equations. This method divides the power system into multiple regions and performs optimization processing within and between regions to reduce the computational amount and improve the solution efficiency; through reasonable partitioning and optimized solution, the overall computational efficiency is significantly improved, and it adapts to the dynamically changing power system structure.

[0151] The above is an embodiment of a partitioning and solution method for improving the computational efficiency of power system network equations provided by this application. The following is an embodiment of a partitioning and solution device for improving the computational efficiency of power system network equations provided by this application.

[0152] A partitioning and solving device for improving the calculation efficiency of power system network equations provided by an embodiment of the present application includes:

[0153] A construction unit for constructing the network equation and the directed unweighted graph of the power system;

[0154] A partitioning unit for generating an adjacency matrix according to the relationship between nodes in the directed unweighted graph; constructing an objective function with the goal of minimizing the number of edges used to partition the power system based on the adjacency matrix, optimizing and solving the objective function to obtain two partitioned node sets and a cut set;

[0155] A tree generation unit for partitioning each of the partitioned node sets and generating a clustering tree according to each partitioned node set;

[0156] A solving unit for traversing each layer in the clustering tree and solving the network equation using a hierarchical non-diagonal low-rank algorithm; wherein, parallel computing is performed on the node sets of each layer in the clustering number.

[0157] As a further improvement, the device further includes:

[0158] A preprocessing unit for subtracting the diagonal elements in the adjacency matrix to obtain a preprocessed adjacency matrix.

[0159] As a further improvement, the partitioning unit is specifically used for:

[0160] An initialization subunit for initializing the imbalance d = 0 of the two node sets formed by partitioning the power system network;

[0161] A model construction subunit for constructing an objective function with the goal of minimizing the number of edges used to partition the power system based on the adjacency matrix and constructing corresponding constraint conditions through the imbalance;

[0162] A solving subunit for solving the objective function based on the constraint conditions. If there is no solution, the imbalance d is set to d + 1, and the model construction subunit is triggered; if the solution is successful, two partitioned node sets and a cut set are obtained.

[0163] As a further improvement, the solving unit is specifically used for:

[0164] Using a low-rank decomposition method to decompose the non-diagonal blocks in the node admittance matrix of the network equation into the form of the product of a left low-rank basis and a right low-rank basis;

[0165] Traversing each non-leaf node in the clustering tree from the root node downwards, combining the left low-rank bases corresponding to each non-leaf node to form a large left low-rank basis matrix, and combining the right low-rank bases corresponding to each non-leaf node to form a large right low-rank basis matrix;

[0166] Based on the partitioned admittance matrix and the left low-rank basis large matrix, a non-recursive algorithm is used to solve the network equations.

[0167] In this application, a clustering tree is generated by partitioning the power system. When traversing each layer of the clustering tree for solution, the node sets within each layer are solved in parallel, improving the calculation efficiency. Since the goal of partitioning is to minimize the number of edges used in partitioning the power system, while making the size of each node set as balanced as possible after partitioning, the number of edges in the cut set is as small as possible, which improves the calculation efficiency in the subsequent hierarchical non-diagonal low-rank algorithm solution process.

[0168] This application embodiment also provides an electronic device, which includes a processor and a memory.

[0169] The memory is used to store program code and transmit the program code to the processor.

[0170] The processor is used to execute the partitioning and solution method for improving the calculation efficiency of the power system network equation in the foregoing method embodiment according to the instructions in the program code.

[0171] This application embodiment also provides a computer-readable storage medium, which is used to store program code. When the program code is executed by a processor, it implements the partitioning and solution method for improving the calculation efficiency of the power system network equation in the foregoing method embodiment.

[0172] Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the above-described devices and units can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated herein.

[0173] The terms "first", "second", "third", "fourth", etc. (if any) in the specification of this application and the above drawings are used to distinguish similar objects and do not necessarily need to describe a specific order or sequence. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products, or devices.

[0174] It should be understood that in this application, "at least one (item)" means one or more, and "a plurality" means two or more. "And / or" is used to describe the association relationship of associated objects and indicates that three relationships may exist. For example, "A and / or B" may mean: only A exists, only B exists, and both A and B exist at the same time. Among them, A and B can be singular or plural. The character " / " generally represents an "or" relationship between the associated objects before and after. "At least one (or more) of the following" or its similar expressions refer to any combination of these items, including any combination of single items (or more) or plural items (or more). For example, at least one (or more) of a, b, or c may mean: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0175] In several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the units is only a logical function division. In actual implementation, there may be other division methods. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed coupling or direct coupling or communication connection to each other can be through some interfaces. The indirect coupling or communication connection of the devices or units can be in electrical, mechanical or other forms.

[0176] The units described as separate components may or may not be physically separated. The components displayed as units may or may not be physical units, that is, they may be located in one place, or may be distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0177] In addition, each functional unit in various embodiments of this application can be integrated in a processing unit, or each unit can exist physically alone, or two or more units can be integrated in one unit. The above integrated units can be implemented in the form of hardware or in the form of software functional units.

[0178] When the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of this application. The aforementioned storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memories (English full name: Read-Only Memory, English abbreviation: ROM), random access memories (English full name: Random Access Memory, English abbreviation: RAM), magnetic disks, or optical discs.

[0179] As described above, the above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit them; although this application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of various embodiments of this application.

Claims

1. A partitioning and solution method for improving the calculation efficiency of power system network equations, characterized in that Including: Constructing the network equations and the directed unweighted graph of the power system; Generating an adjacency matrix according to the relationship between nodes in the directed unweighted graph; Constructing an objective function aiming to minimize the number of edges used for partitioning the power system based on the adjacency matrix, and optimizing and solving the objective function to obtain two node sets and a cut set after partitioning, including: S1. Initializing the imbalance d = 0 of the two node sets formed by the network partitioning of the power system; S2. Constructing an objective function aiming to minimize the number of edges used for partitioning the power system based on the adjacency matrix, and constructing corresponding constraint conditions through the imbalance; the objective function is: ； The constraint conditions are: ； Where M is an adjacency matrix of order n; x is a vector of 0 or 1; is an all-ones vector of n dimensions; S3. Solving the objective function based on the constraint conditions; if there is no solution, let the imbalance d = d + 1, and return to step S2; if the solution is successful, obtain two node sets and a cut set after partitioning; Partitioning each node set after partitioning, and generating a clustering tree according to each partitioned node set; Traversing each layer in the clustering tree, and solving the network equations by using the hierarchical non - diagonal low - rank algorithm; wherein, parallel computing is performed on the node sets of each layer in the clustering tree.

2. The zoning and solution method for improving the calculation efficiency of the power system network equation according to claim 1, characterized in that, After generating the adjacency matrix according to the relationship between nodes in the directed unweighted graph and before constructing the objective function aiming to minimize the number of edges used for partitioning the power system based on the adjacency matrix, it further includes: Subtracting the diagonal elements in the adjacency matrix to obtain a pre - processed adjacency matrix; Correspondingly, constructing the objective function aiming to minimize the number of edges used for partitioning the power system based on the adjacency matrix includes: Constructing an objective function aiming to minimize the number of edges used for partitioning the power system based on the pre - processed adjacency matrix.

3. The partitioning and solution method for improving the calculation efficiency of the power system network equation according to any one of claims 1 to 2, characterized in that, The network equation of the power system is the node voltage equation.

4. The partitioning and solution method for improving the calculation efficiency of the power system network equation according to claim 3, characterized in that, Traversing each layer in the clustering tree and solving the network equations by using the hierarchical non - diagonal low - rank algorithm includes: Using the low - rank decomposition method to decompose the non - diagonal blocks in the node admittance matrix in the network equation into the form of the product of a left low - rank basis and a right low - rank basis; Traversing each non - leaf node in the clustering tree from the root node downwards, combining the left low - rank bases corresponding to each non - leaf node to form a large left low - rank basis matrix, and combining the right low - rank bases corresponding to each non - leaf node to form a large right low - rank basis matrix; Based on the partitioned admittance matrix and the large left low - rank basis matrix, using a non - recursive algorithm to solve the network equations.

5. The partitioning and solution method for improving the calculation efficiency of the power system network equation according to claim 4, wherein Using the non - recursive algorithm to solve the network equations based on the partitioned admittance matrix and the large left low - rank basis matrix includes: Initializing an intermediate large matrix with the large left low - rank basis matrix; wherein, the intermediate large matrix is calculated through the partitioned admittance matrix and the left low - rank basis; Traversing the leaf nodes of the clustering tree, decomposing the diagonal block matrix corresponding to the leaf nodes by using the LU decomposition method to obtain the LU decomposition result; Traverse each layer of the clustering tree downward from the root node, and decompose in parallel for each node in each layer using the LU decomposition method , obtaining the decomposition result, , being the right low-rank bases of the off-diagonal blocks corresponding to the child nodes of the current node , ; , being the right low-rank bases of the off-diagonal blocks corresponding to the child nodes of the current node , Calculate and results, where and are the corresponding diagonal block matrices, and are the corresponding right low-rank bases of the off-diagonal blocks, and I is the identity matrix; Initialize the voltages of each node with the injection currents of each node, and solve the network equations through the LU decomposition result and the decomposition result.

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