Partitioning and solving method for improving calculation efficiency of power system network equation

Abstract

The invention discloses a partitioning and solving method for improving the calculation efficiency of a network equation of a power system. The method comprises the following steps: constructing the network equation and a directed unweighted graph of the power system; generating an adjacent matrix according to a relationship between nodes in the directed unweighted graph; based on the adjacent matrix, an objective function with the aim of minimizing the number of edges used for dividing the power system is constructed, the objective function is optimized and solved, and two node sets and a cut set after division are obtained; dividing each divided node set, and generating a clustering tree according to each divided node set; traversing each layer in the clustering tree, and solving the network equation by adopting a layered off-diagonal low-rank algorithm; wherein parallel computing is carried out on node sets of all layers in the clustering number. The technical problem of low calculation efficiency in the prior art is solved.

Description

Technical Field

[0001] The present application relates to the technical field of power systems, and in particular to a partitioning and solving method for improving the computational efficiency of power system network equations. Background Art

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

[0003] Traditional partitioning and solving methods to improve the computational 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 decomposition and back substitution, they consume very high computing resources and time when facing large-scale power systems. Although the application of sparse technology and factored paths has reduced the amount of calculation to a certain extent, for dynamically changing power systems, frequent re-decomposition and calculation are still required, resulting in reduced efficiency. When dealing with complex power systems, iterative methods accelerate the convergence process through preprocessing technology. However, when dealing with high-impedance or low-impedance paths, iterative methods often face the problem of convergence difficulties or even divergence. In addition, with the increase in the number of nodes and connections in the power system, the convergence speed of iterative methods is also challenged. Although traditional preprocessing technology improves the solution efficiency, it still lacks targeted optimization means for the regional and low connectivity characteristics of power systems.

[0004] Although existing solution methods have met the needs of practical applications to a certain extent, with the continuous expansion of the scale and increase in complexity of power systems, these methods have gradually exposed their shortcomings in computational efficiency and adaptability. Existing solution methods generally ignore the characteristics existing in the power system, which is particularly obvious when the network scale is large. Therefore, relying solely on traditional solution methods has made it difficult to effectively respond to the increasingly complex power system analysis needs, especially in terms of computational efficiency. Summary of the invention

[0005] The present application provides a partitioning and solving method for improving the computational efficiency of power system network equations, which is used to solve the technical problem of low computational efficiency in the prior art.

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

[0007] Construct network equations and directed unweighted graphs for power systems;

[0008] Generate an adjacency matrix according to the relationship between nodes in the directed unweighted graph; construct an objective function based on the adjacency matrix with the goal of minimizing the number of edges used to divide the power system, optimize and solve the objective function, and obtain two node sets and a cut set after division;

[0009] Divide each node set after division, and generate a clustering tree according to each node set after division;

[0010] Each layer in the cluster tree is traversed, and the network equation is solved by using a hierarchical non-diagonal low-rank algorithm; wherein the node sets of each layer in the cluster tree are calculated in parallel.

[0011] Optionally, after generating an adjacency matrix according to the relationship between nodes in the directed unweighted graph, before constructing an objective function based on the adjacency matrix with the goal of minimizing the number of edges used to divide the power system, the method further includes:

[0012] Subtracting the diagonal elements in the adjacency matrix to obtain a preprocessed adjacency matrix;

[0013] Accordingly, the objective function constructed based on the adjacency matrix with the goal of minimizing the number of edges used to divide the power system includes:

[0014] An objective function is constructed based on the preprocessed adjacency matrix with the goal of minimizing the number of edges used to partition the power system.

[0015] Optionally, 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, includes:

[0016] S1, initialize the unbalanced amount d=0 of the two node sets formed by the power system network division;

[0017] S2. constructing an objective function based on the adjacency matrix with the goal of minimizing the number of edges used to divide the power system, and constructing corresponding constraints through the unbalanced amount;

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

[0019] Optionally, the objective function is:

[0020]

[0021] The constraints are:

[0022]

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

[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 using a hierarchical non-diagonal low-rank algorithm includes:

[0026] A low-rank decomposition method is used to decompose the non-diagonal blocks in the node admittance matrix in the network equation into a form of multiplication of a left low-rank basis and a right low-rank basis;

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

[0028] Based on the partitioned admittance matrix and the left low-rank basis large matrix, a non-recursive algorithm is used to solve the network equation.

[0029] Optionally, the adopting a non-recursive algorithm to solve the network equation based on the divided admittance matrix and the left low-rank basis large matrix includes:

[0030] The left low-rank basis large matrix is ​​used to initialize the intermediate large matrix; wherein the intermediate large matrix is ​​calculated by the divided admittance matrix and the left low-rank basis;

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

[0032] Traverse each layer of the clustering tree from the root node downward, and decompose each node in each layer in parallel using the LU decomposition method ,get Decomposition results, , For the current node Child nodes of , The corresponding off-diagonal block right low-rank basis, , For the current node Child nodes of , calculate and The results, among which and is the corresponding diagonal block matrix, and is the corresponding off-diagonal block right low-rank basis, I is the identity matrix;

[0033] The voltage of each node is initialized by the injection current of each node, and the LU decomposition result and the The decomposition results in solving the network equations.

[0034] It can be seen from the above technical solutions that this application has the following advantages:

[0035] The partitioning and solving method for improving the computational efficiency of the 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 solving, the node sets in each layer are solved in parallel, thereby improving the computational efficiency. Since the goal of partitioning is to minimize the number of edges used to divide the power system, the size of each node set after the partition is made as balanced as possible, and the number of edges in the cut set is as small as possible, thereby improving the computational efficiency of the subsequent layered non-diagonal low-rank algorithm solution process. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

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

[0038] Figure 2 A schematic diagram of a power system division process provided in an embodiment of the present application;

[0039] Figure 3 The division result of the power system including 39 nodes provided in the embodiment of the present application;

[0040] Figure 4 The coefficient matrix partitioning result provided in the embodiment of the present application;

[0041] Figure 5 Provided in the embodiments of this application Figure 4 The hierarchical structure corresponding to the partitioning of the coefficient matrix;

[0042] Figure 6 A flowchart of a layered non-diagonal low-rank algorithm provided in an embodiment of the present application;

[0043] Figure 7A comparison chart of the computation time of the layered non-diagonal low-rank algorithm provided in an embodiment of the present application and the computation time of the Math Kernel Library algorithm. DETAILED DESCRIPTION

[0044] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0045] For easier understanding, please refer to Figure 1 , the embodiment of the present application provides a partitioning and solving method for improving the calculation efficiency of power system network equations, including:

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

[0047] The network equation of the power system refers to the equation that can reflect the relationship between the current and voltage in the power grid. For a certain power system network, the node voltage equation or loop current equation of the power grid can be listed, but in the actual power grid, due to the large number of grounding branches, the number of loop current equations is greater than the number 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 easily 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 and the voltage of each node in the power grid. The power system of the first stage, when the earth ( nodes) as reference nodes, we can write The node voltage equation of order:

[0049]

[0050] In the formula, A vector of currents injected into each node, ; is the vector composed of the voltages at each node, ; is the node admittance matrix of the network.

[0051] The matrix expression is:

[0052]

[0053] Where: For Node The self-admittance of the node is equal to the sum of the admittances of the branches connected to the node; For Node and nodes The mutual admittance between them is equal to the negative value of the admittance of the connected branches.

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

[0055]

[0056] In the formula, 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 The complex matrix of 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 Therefore, when storing it in a computer, only the corresponding elements of the upper triangle (or lower triangle) can be stored, thus saving computer memory.

[0060] 3) When there is no direct 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 the actual power system is connected to 3 to 5 lines or transformers on average. Therefore, a large number of non-diagonal elements in the admittance matrix are 0, that is, the admittance matrix is ​​a sparse matrix.

[0061] 4) In actual power grids, regions are often connected by only a few lines. Therefore, after the admittance matrix is ​​divided into diagonal blocks and off-diagonal blocks, the off-diagonal blocks correspond to the connection lines between regions and can be represented by low-rank basis products.

[0062] The network of the power system can be abstracted as a directed unweighted graph consisting of several nodes and edges, that is, the nodes of the power system correspond to the nodes of the directed unweighted graph, and the transmission lines of the power system correspond to the edges of the directed unweighted graph. The division of the power system can be 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 based on the adjacency matrix with the goal of minimizing the number of edges used in the partitioned power system, optimize and solve the objective function, and obtain two node sets and a cut set after the partition.

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

[0065] Suppose there is a directed unweighted graph can be partitioned into two non-empty and complementary sets of nodes and , use one vector Represents the node set where each node is located. If , indicating a node ,like , then it means the node .

[0066] make ,in is an n-dimensional all-1 vector, then:

[0067]

[0068] like , then it represents the node set Nodes in pass Edge and Node Sets Connection, proof is as follows:

[0069] when When

[0070]

[0071] Then we have:

[0072]

[0073] Right now , and exists Different nodes , so that:

[0074]

[0075] From the above formula, we can get: and , i.e. node And node Connect. Proof.

[0076] The directed unweighted graph corresponding to the power system Use some edges to divide into two node sets and , the number of edges It can be expressed as follows:

[0077]

[0078] After transformation, we can expand it to get:

[0079]

[0080] In order to ensure that the two node sets after division are as balanced as possible, a known feasible node number deviation is set as d, and the constraints are as follows:

[0081]

[0082] Expand to get:

[0083]

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

[0085]

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

[0087] S1, initialize the unbalanced amount (i.e., node number deviation) of the two node sets formed by the power system network division to d=0;

[0088] S2. Based on the adjacency matrix, an objective function is constructed to minimize the number of edges used in the partitioned power system, and corresponding constraints are constructed through the unbalanced amount;

[0089] The purpose of solving the optimization problem is to reduce the number of edges used for partitioning, so the objective function is defined as ; In order to make the unbalanced amount of the two node sets divided by the power system network as small as possible, the constraint is defined as ;

[0090] S3. Solve the objective function based on the constraints. If there is no solution, set d=d+1 and return to step S2. If the solution is successful, two node sets and one cut set are obtained after the division.

[0091] After each execution of the power system partitioning algorithm, two node sets and one cut set are obtained, which ensure that the node set is as balanced as possible and the edges in the cut set are as few as possible.

[0092] Step 130: partition each node set after partitioning, and generate a clustering tree according to each node set after partitioning.

[0093] The node sets obtained after the division are further divided. The specific division process is similar to the division process in step 120. The division is terminated until the node sets after the division cannot be further divided or the value of the imbalance d exceeds the preset threshold. A clustering tree is generated for all the node sets obtained after the division. Each node in the clustering tree represents an index set of a node set.

[0094] The results obtained by testing the example of 39 nodes in this application are as follows: Figure 3 As shown, 39 nodes are divided into Region 1 and Region 2, where 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 of the matrix structure in step 140.

[0095] Step 140: traverse each layer in the clustering tree and use a hierarchical non-diagonal low-rank algorithm to solve the network equation.

[0096] A low-rank decomposition method is used to decompose the non-diagonal blocks in the node admittance matrix in the network equation into the form of multiplication of a left low-rank basis and a right low-rank basis; each non-leaf node in the clustering tree is traversed downward from the root node, and the left low-rank basis corresponding to each non-leaf node is combined to form a large left low-rank basis matrix, and the right low-rank basis corresponding to each non-leaf node is combined to form a large right low-rank basis matrix; based on the partitioned admittance matrix and the large left low-rank basis matrix, a non-recursive algorithm is used to solve the network equation.

[0097] For a linear system of equations, we need to solve:

[0098]

[0099] Among them, A corresponds to Y in the network equation, and x corresponds to , b corresponds to the network equation . Assume that the coefficient matrix of the equation has the following form: the coefficient matrix A of the equation is divided twice in succession. The first division divides the matrix into two diagonal blocks and two non-diagonal blocks. The second division divides the diagonal blocks obtained by 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 Figure 4 The structure shown is used as an example to introduce the hierarchical non-diagonal low-rank algorithm (in practical applications, 3, 4 or more divisions can be performed). Figure 4In the matrix, D represents the diagonal block in the original matrix, and the corresponding off-diagonal block has the characteristics of low rank and sparseness.

[0100] Figure 4 The partitioning shown actually performs hierarchical processing on the matrix, which can be described by a tree structure. Figure 5 Due to the sparse low-rank structure of the non-diagonal blocks, the non-diagonal blocks can be decomposed into the form of two low-rank bases multiplied together, that is, for ,like , then there exists , so that ,say is a left low-rank basis, is a right low-rank basis, is the adjoint matrix of V. In order to conveniently describe the hierarchical non-diagonal low-rank algorithm, it is assumed that the maximum rank of all non-diagonal blocks formed by the two partitions is ,say is the rank of the hierarchical non-diagonal low-rank matrix.

[0101] Depend on Figure 4 and Figure 5 From the tree structure, we can see that the first division can be obtained:

[0102]

[0103] in, , The diagonal blocks formed by the partition; , is the left low-rank basis formed by the off-diagonal block decomposition after partitioning; , is the right low-rank basis formed by the off-diagonal block decomposition after partitioning; , Solve the original equation The upper and lower parts of , are the upper and lower halves of the right-hand side vector of the original equation to be solved.

[0104] Ride both sides , then:

[0105]

[0106] Where I represents the identity matrix that adapts to the size of two off-diagonal blocks;

[0107] in , , and from the Woodbury equation we know:

[0108]

[0109] Solving equations , , are the solution corrections for nodes 2 and 3 respectively, then the solution can be transformed into solving the following two sub-problems:

[0110]

[0111] Then the solution to the original equation is obtained by calculating:

[0112]

[0113] right and Divide again to get:

[0114]

[0115] Where 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 non-diagonal blocks corresponding to nodes 4, 5, 6, and 7 respectively; V4, V5, V6, and V7 are the right low-rank bases of the non-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; express The upper part of express the lower part; express The upper part of express the lower part; express The upper part of express the lower part; express The upper part of express The lower half of the above problem is transformed into solving the following system of equations:

[0116]

[0117] Then substitute ,right and Make corrections.

[0118] Note that on the right side of the four sub-problems above, The matrices are partitioned and then connected together. This structure inspires all left low-rank bases Connect together to form a large matrix. Traverse the tree structure from the root node downward to create , for each non-leaf node There are two child nodes and ,Will and , i.e. node and The corresponding non-diagonal block left low-rank basis is placed vertically. If the number of columns is different, it is required to be left-aligned and placed on the left. , expressed as:

[0119]

[0120] For ease of representation, and right low-rank basis This data structure is also used to represent and , is the decomposition matrix. For each node in the clustering tree, it is only necessary to store the corresponding low-rank basis , and The index of the , without having to store the specific value.

[0121] For the admittance matrix and , we can write a non-recursive algorithm based on the for loop, which consists of a decomposition phase and a solution phase. This data structure allows the algorithm to calculate multiple left low-rank bases at different levels in the clustering tree structure with only one BLAS or LAPACK call, and no unnecessary data movement will occur. Figure 6 .

[0122] Decomposition stage:

[0123] 1. ,Will use Initialization, subsequent solutions are performed directly in place;

[0124] 2. Traverse the leaf nodes of the clustering tree ,implement:

[0125] 1) LU decomposes the diagonal block matrix corresponding to the leaf node and stores the decomposition result in place

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

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

[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 node voltage collection.

[0146] When traversing each layer of the tree structure, the nodes in the layer do not have data dependencies, so the node operations in the layer can be parallelized to improve the computing efficiency. By overwriting the input with the output result, the computing process only needs to use additional memory, which is easy to get , so the rank of the hierarchical non-diagonal low-rank matrix is When is small, this algorithm requires very little additional memory.

[0147] The results of the test on 280k and 560k nodes are compared. Figure 7 As shown in the figure, the Hierarchical Off-Diagonal Low-Rank Direct Solver (HODLR) algorithm is about 10% faster than the Math Kernel Library (MKL) and can achieve better performance on machines with parallel capabilities.

[0148] This solution algorithm based on hierarchical non-diagonal low-rank structured matrices converts the problem of solving linear equations with larger dimensions into solving several sub-problems with smaller dimensions and LU decomposition in parallel. , and due to , and the rank of the hierarchical non-diagonal low-rank matrix It is very small, so the calculation time can be greatly reduced and the efficiency can be greatly improved.

[0149] The time consumption of the calculation of the solution algorithm in step 140 mainly depends on the size of each node set and the number of tie lines (i.e., the size of the cut set) after the division. The fewer tie lines, the higher the calculation efficiency. Since there is no data dependency between the multiple regions formed after the division, parallel calculation can be used, so the calculation time of each region independently solving depends on the region with the largest number of nodes. In the aforementioned division process of the power system, it is ensured that the size of each node set is as balanced as possible during the division, thereby improving the calculation efficiency.

[0150] This application proposes an algorithm for decomposing the admittance matrix and efficiently solving network equations by performing hierarchical analysis on the power system network and taking advantage of the regional and low connectivity characteristics of the network. This method divides the power system into multiple regions and performs optimization processing within and between regions to reduce the amount of calculation and improve the efficiency of the solution; through reasonable partitioning and optimization solution, the overall calculation efficiency is significantly improved and it adapts to the dynamically changing power system structure.

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

[0152] The present application provides a partitioning and solving device for improving the calculation efficiency of power system network equations, including:

[0153] Construction unit for constructing network equations and directed unweighted graphs of power systems;

[0154] A partitioning unit is used to generate an adjacency matrix according to the relationship between nodes in the directed unweighted graph; an objective function is constructed based on the adjacency matrix to minimize the number of edges used in the partitioned power system, and the objective function is optimized to obtain two node sets and a cut set after the partition;

[0155] A tree generation unit, used for dividing each node set after division, and generating a clustering tree according to each node set after division;

[0156] The solving unit is used to traverse each layer in the clustering tree and solve the network equation using a hierarchical non-diagonal low-rank algorithm; wherein the node sets of each layer in the clustering tree are calculated in parallel.

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

[0158] The preprocessing unit is used to subtract the diagonal elements in the adjacency matrix to obtain the preprocessed adjacency matrix.

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

[0160] Initialization subunit, used to initialize the unbalanced amount d=0 of two node sets formed by power system network division;

[0161] A model building subunit, for building an objective function based on the adjacency matrix with the goal of minimizing the number of edges used in the partitioned power system, and building corresponding constraints through the unbalanced amount;

[0162] The solving subunit is used to solve the objective function based on the constraints. If there is no solution, the imbalance d=d+1 is set and the model building subunit is triggered. If the solution is successful, two node sets and a cut set are obtained after the division.

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

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

[0165] Traverse each non-leaf node in the clustering tree from the root node downward, combine the left low-rank basis corresponding to each non-leaf node to form a left low-rank basis large matrix, and combine the right low-rank basis corresponding to each non-leaf node to form a right low-rank basis large 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] The present application generates a clustering tree by dividing the power system, and when traversing each layer of the clustering tree for solution, the node sets in each layer are solved in parallel, thereby improving the computational efficiency; since the goal during division is to minimize the number of edges used to divide the power system, the size of each node set after division is made as balanced as possible, and the number of edges in the cut set is as small as possible, thereby improving the computational efficiency in the subsequent layered non-diagonal low-rank algorithm solution process.

[0168] The embodiment of the present application also provides an electronic device, the device comprising a processor and a memory;

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

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

[0171] An embodiment of the present application 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 solving method for improving the calculation efficiency of the power system network equations in the aforementioned 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 aforementioned method embodiments and will not be repeated here.

[0173] The terms "first", "second", "third", "fourth", etc. (if any) in the specification of this application and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are 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 "plurality" means two or more. "And / or" is used to describe the association relationship of associated objects, indicating that three relationships may exist. For example, "A and / or B" can mean: only A exists, only B exists, and A and B exist at the same time, where A and B can be singular or plural. The character " / " generally indicates that the objects associated before and after are in an "or" relationship. "At least one of the following" or similar expressions refers to any combination of these items, including any combination of single or plural items. For example, at least one of a, b or c can mean: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, c can be single or multiple.

[0175] In the several embodiments provided in the present 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 only schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation, such as 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 mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

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

[0177] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0178] If 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 the present application is essentially or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium, including a number of instructions for executing all or part of the steps of the method described in each embodiment of the present application through a computer device (which can be a personal computer, server, or network device, etc.). The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (full name in English: Read-Only Memory, English abbreviation: ROM), random access memory (full name in English: Random Access Memory, English abbreviation: RAM), disk or optical disk and other media that can store program codes.

[0179] As described above, the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A partitioning and solving method for improving the computational efficiency of power system network equations, characterized in that: include: Construct network equations and directed unweighted graphs for power systems; Generate an adjacency matrix based on the relationship between nodes in the directed unweighted graph; Based on the adjacency matrix, an objective function is constructed with the goal of minimizing the number of edges used to divide the power system, and the objective function is optimized and solved to obtain two node sets and a cut set after division; Divide each node set after division, and generate a clustering tree according to each node set after division; Each layer in the cluster tree is traversed, and the network equation is solved by using a hierarchical non-diagonal low-rank algorithm; wherein the node sets of each layer in the cluster tree are calculated in parallel.

2. The method for solving the force system network equation according to claim 1, characterized in that: After generating an adjacency matrix according to the relationship between nodes in the directed unweighted graph, and before constructing an objective function based on the adjacency matrix with the goal of minimizing the number of edges used to divide the power system, the method further includes: Subtracting the diagonal elements in the adjacency matrix to obtain a preprocessed adjacency matrix; Accordingly, the objective function constructed based on the adjacency matrix with the goal of minimizing the number of edges used to divide the power system includes: An objective function is constructed based on the preprocessed adjacency matrix with the goal of minimizing the number of edges used to partition the power system.

3. The method for solving the force system network equation according to claim 1, characterized in that: The objective function is constructed based on the adjacency matrix to minimize the number of edges used to divide the power system, and the objective function is optimized to obtain two node sets and a cut set after division, including: S1, initialize the unbalanced amount d=0 of the two node sets formed by the power system network division; S2. constructing an objective function based on the adjacency matrix with the goal of minimizing the number of edges used to divide the power system, and constructing corresponding constraints through the unbalanced amount; S3. Solve the objective function based on the constraint conditions; if there is no solution, set the imbalance d=d+1 and return to step S2; if the solution is successful, obtain two node sets and a cut set after division.

4. The partitioning and solving method for improving the calculation efficiency of power system network equations according to claim 3 is characterized in that: The objective function is: The constraints are: Where M is an n-order adjacency matrix; x is a vector of 0 or 1; is an n-dimensional vector of all ones.

5. The partitioning and solving method for improving the calculation efficiency of power system network equations according to any one of claims 1 to 4, characterized in that: The network equation of the power system is a node voltage equation.

6. The partitioning and solving method for improving the calculation efficiency of power system network equations according to claim 5 is characterized in that: The traversing each layer in the clustering tree and solving the network equation using a hierarchical non-diagonal low-rank algorithm includes: A low-rank decomposition method is used to decompose the non-diagonal blocks in the node admittance matrix in the network equation into a form of multiplication 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 downward, combine the left low-rank basis corresponding to each non-leaf node to form a left low-rank basis large matrix, and combine the right low-rank basis corresponding to each non-leaf node to form a right low-rank basis large matrix; Based on the partitioned admittance matrix and the left low-rank basis large matrix, a non-recursive algorithm is used to solve the network equation.

7. The partitioning and solving method for improving the calculation efficiency of power system network equations according to claim 6 is characterized in that: The method of solving the network equation based on the divided admittance matrix and the left low-rank basis large matrix using a non-recursive algorithm includes: The left low-rank basis large matrix is ​​used to initialize the intermediate large matrix; wherein the intermediate large matrix is ​​calculated by the divided 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, and obtaining the LU decomposition result; Traverse each layer of the clustering tree from the root node downward, and decompose each node in each layer in parallel using the LU decomposition method ,get Decomposition results, , For the current node Child nodes of , The corresponding off-diagonal block right low-rank basis, , For the current node Child nodes of , calculate and The results, among which and is the corresponding diagonal block matrix, and is the corresponding off-diagonal block right low-rank basis, I is the identity matrix; The voltage of each node is initialized by the injection current of each node, and the LU decomposition result and the The decomposition results in solving the network equations.

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