A distributed calculation method and system for power system characteristic values

Abstract

The present invention discloses a distributed calculation method and system for eigenvalues ​​of an electric power system. The nodes of the electric power system are partitioned according to a topological relationship, a system node admittance matrix is ​​established according to the nodes in different partitions, an equivalent node admittance equation is performed on the matrix, and an equivalent system corresponding to the equivalent node admittance equation is obtained. The state equation is established for the equivalent system, and a matrix inversion lemma is used based on the equivalent node admittance equation and the state equation to obtain a state matrix. The state matrix is ​​solved using a QR method to obtain the eigenvalues ​​of the electric power system. This reduces the scale of the processing matrix, avoids the inversion operation of a large-scale matrix, avoids the influence of the equivalent elimination external area, reduces the number of communications and the amount of calculation of partition transmission, and still has good convergence. The requirements for the communication conditions of the electric power system are reduced, thereby improving the efficiency and accuracy of eigenvalue calculation in the partition environment of the electric power system.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to a distributed calculation method and system for power system characteristic values. Background Art

[0002] The rapid development of renewable energy both domestically and internationally has placed greater demands on the regulation and support capabilities of power systems. As the proportion of renewable energy continues to rise, it rapidly depletes the flexible regulation resources of the power system. Its intermittent and volatile nature makes power system regulation more difficult, and safety and stability issues are becoming more prominent. Power system stability analysis remains a challenge, and a common strategy is to use distributed methods to calculate system-wide eigenvalues ​​for low-frequency oscillation analysis and small-disturbance stability analysis.

[0003] The operation and management of my country's power system is characterized by hierarchical and partitioned systems. Leveraging the partitioned computing environment of the power system to distribute computational and survey tasks to different partitions for coordinated resolution can significantly improve computational speed and the accuracy of partitioned information, while also protecting the integrity and security of that information. However, current research on small-disturbance stability analysis involving partitioned computational eigenvalues ​​is relatively limited. In particular, the characteristics of the partitioned power system environment are not well adapted to the independent security of information, and thus cannot guarantee the coordinated operation of the partitioned computations.

[0004] The analysis and calculation of power systems often involve localized changes in network structure, operating parameters, and other parameters. For example, in online power system analysis applications, calculations are performed for multiple operating conditions, but each condition only involves localized changes in the power grid, while the majority of other network components remain unchanged. In these cases, the results of the network changes must be calculated multiple times, and these calculations inevitably involve significant repetition. In such applications, effectively leveraging pre-change information to quickly calculate post-change information can significantly improve the speed and security of power grid calculations. For this application scenario, a modified solution to the network equations can be employed. The basic idea is to use a relatively small number of modified calculations based on a set of pre-change solutions to obtain the post-change solutions. This modified solution significantly improves computational speed and has therefore been widely used in power grid system-related computations.

[0005] The matrix inversion lemma is a proven and applied theorem that simplifies the computation of the inverse of a new matrix after a local transformation of the matrix. The basic idea is to calculate the inverse of a small-scale matrix related to the local transformation, based on the inverse of the original matrix. Then, through appropriate transformations, the inverse of the new matrix after the local transformation is obtained. Applying this theorem to a modified solution of the power system network equations can significantly reduce the computational complexity and the computational effort involved in power system analysis.

[0006] The matrix inversion lemma has a requirement for its application: the size of the locally modified matrix must be smaller than or equal to the size of the original matrix. This is difficult to guarantee in the context of small-disturbance stability calculations for power systems. Current power grid management and control is characterized by hierarchical and partitioned systems, with each partition independently managing its own dynamic grid data and parameters. The central data center can access dynamic data and parameters from each partition through a network of interconnecting lines between partitions. Furthermore, the type and quantity of data that can be communicated between partitions is limited. These factors restrict the application of the matrix inversion lemma in the context of partitioned power system calculations, making it difficult to guarantee computational efficiency and accuracy.

[0007] In response to the above problems, the applicability of the traditional matrix inversion lemma in the partitioned environment of the power network needs to be studied. It is urgent to propose a distributed computing technology that applies the matrix inversion lemma and is suitable for the operation and management of real power systems, and to improve the traditional matrix inversion lemma to adapt to the characteristics of the actual operation and management of power systems. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a distributed calculation method and system for power system eigenvalues, which can improve the efficiency and accuracy of eigenvalue calculation in a partitioned environment of the power system.

[0009] In order to solve the above technical problems, a technical solution adopted by the present invention is:

[0010] A distributed calculation method for power system characteristic values, comprising the steps of:

[0011] Partitioning the nodes of the power system according to the topological relationship to obtain an internal area, a boundary area, and an external area, and establishing a system node admittance matrix based on the nodes in the internal area, the boundary area, and the external area;

[0012] Performing equivalent simplification processing on the system node admittance matrix to obtain an equivalent node admittance equation, and determining an equivalent system corresponding to the equivalent node admittance equation, wherein the equivalent system is a power system with the external area eliminated;

[0013] Establishing a state equation for the equivalent system, and obtaining a state matrix using a matrix inversion lemma based on the equivalent node admittance equation and the state equation;

[0014] The state matrix is ​​solved using an orthogonal triangular decomposition method to obtain eigenvalues ​​of the power system.

[0015] In order to solve the above technical problems, another technical solution adopted by the present invention is:

[0016] A distributed computing system for power system characteristic values ​​includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the following steps are implemented:

[0017] Partitioning the nodes of the power system according to the topological relationship to obtain an internal area, a boundary area, and an external area, and establishing a system node admittance matrix based on the nodes in the internal area, the boundary area, and the external area;

[0018] Performing equivalent simplification processing on the system node admittance matrix to obtain an equivalent node admittance equation, and determining an equivalent system corresponding to the equivalent node admittance equation, wherein the equivalent system is a power system with the external area eliminated;

[0019] Establishing a state equation for the equivalent system, and obtaining a state matrix using a matrix inversion lemma based on the equivalent node admittance equation and the state equation;

[0020] The state matrix is ​​solved using an orthogonal triangular decomposition method to obtain eigenvalues ​​of the power system.

[0021] The beneficial effects of the present invention are as follows: the nodes of the power system are partitioned according to the topological relationship to obtain the internal area, the boundary area and the external area, and the system node admittance matrix is ​​established according to the nodes in different partitions, the system node admittance matrix is ​​subjected to equivalent simplification processing to obtain the equivalent node admittance equation, and the equivalent system corresponding to it is determined, the equivalent system has eliminated the external area, the state equation is established for the equivalent system, and the state matrix is ​​obtained by using the matrix inversion lemma based on the equivalent node admittance equation and the state equation, and the state matrix is ​​solved by using the orthogonal triangular decomposition method to obtain the characteristics of the power system The value is obtained by simplifying the equivalent value processing to reduce the scale of the processing matrix. By establishing the state equation for the equivalent system and introducing the matrix inversion lemma, the inversion operation of the large-scale matrix is ​​avoided. The orthogonal triangular decomposition method is used to solve the eigenvalue to avoid the influence of the external area of ​​the equivalent elimination. Each partition does not need to perform inversion calculation on the large-scale matrix, which reduces the number of communications and the amount of calculation of the partition transmission. At the same time, it can still have good convergence. In the calculation process, it can also reduce the requirements for the communication conditions of the power system, thereby improving the efficiency and accuracy of the eigenvalue calculation in the partition environment of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 A flowchart of a distributed calculation method for power system characteristic values ​​according to an embodiment of the present invention;

[0023] Figure 2 A schematic structural diagram of a distributed computing system for power system characteristic values ​​according to an embodiment of the present invention;

[0024] Figure 3 A calculation flow chart of a distributed calculation method for power system characteristic values ​​according to an embodiment of the present invention;

[0025] Figure 4 A system topology diagram of three machines and nine nodes in a distributed calculation method for power system characteristic values ​​according to an embodiment of the present invention;

[0026] Figure 5 A simplified equivalent diagram of system partitions in a distributed calculation method for power system characteristic values ​​according to an embodiment of the present invention;

[0027] Figure 6 Schematic diagram of the distribution of eigenvalues ​​calculated in the distributed calculation method of power system eigenvalues ​​according to an embodiment of the present invention. DETAILED DESCRIPTION

[0028] To illustrate the technical content, achieved objectives and effects of the present invention in detail, the following description is given in conjunction with the embodiments and accompanying drawings.

[0029] Please refer to Figure 1, a distributed calculation method for power system characteristic values, comprising the steps of:

[0030] Partitioning the nodes of the power system according to the topological relationship to obtain an internal area, a boundary area, and an external area, and establishing a system node admittance matrix based on the nodes in the internal area, the boundary area, and the external area;

[0031] Performing equivalent simplification processing on the system node admittance matrix to obtain an equivalent node admittance equation, and determining an equivalent system corresponding to the equivalent node admittance equation, wherein the equivalent system is a power system with the external area eliminated;

[0032] Establishing a state equation for the equivalent system, and obtaining a state matrix using a matrix inversion lemma based on the equivalent node admittance equation and the state equation;

[0033] The state matrix is ​​solved using an orthogonal triangular decomposition method to obtain eigenvalues ​​of the power system.

[0034] From the above description, it can be seen that the beneficial effects of the present invention are: partitioning the nodes of the power system according to the topological relationship to obtain the internal area, the boundary area and the external area, and establishing the system node admittance matrix according to the nodes in different partitions, performing equivalent simplification processing on the system node admittance matrix to obtain the equivalent node admittance equation, and determining the equivalent system corresponding to it, the equivalent system has eliminated the external area, establishing the state equation for the equivalent system, and using the matrix inversion lemma based on the equivalent node admittance equation and the state equation to obtain the state matrix, using the orthogonal triangular decomposition method to solve the state matrix, and obtaining the power system The eigenvalues ​​of the system are obtained, thereby reducing the scale of the processing matrix through equivalent simplification. By establishing the state equation for the equivalent system and introducing the matrix inversion lemma, the inversion operation of the large-scale matrix is ​​avoided. The orthogonal triangular decomposition method is used to solve the eigenvalues ​​to avoid the influence of the external area of ​​the equivalent elimination. Each partition does not need to invert the large-scale matrix, which reduces the number of communications and the amount of calculation in the partition transmission. At the same time, it still has good convergence. In the calculation process, it can also reduce the requirements for the communication conditions of the power system, thereby improving the efficiency and accuracy of the eigenvalue calculation in the partition environment of the power system.

[0035] Furthermore, partitioning the nodes of the power system according to the topological relationship to obtain the internal area, the boundary area and the external area includes:

[0036] determining dynamic element nodes from the power system, and using the dynamic element nodes as internal nodes to form an internal area;

[0037] composing a boundary region with nodes directly associated with the internal nodes in the internal region;

[0038] The nodes that are not directly associated with the boundary nodes in the boundary area constitute an external area.

[0039] From the above description, it can be seen that by partitioning the power system, the set of power generation nodes and the set of boundary nodes in the power system can be determined, which facilitates the subsequent equivalent simplification of the power system to improve the efficiency of eigenvalue calculation.

[0040] Further, the internal area includes internal nodes;

[0041] The boundary area includes boundary nodes;

[0042] The external area includes external nodes;

[0043] The establishing of a system node admittance matrix according to the nodes in the inner area, the boundary area, and the outer area comprises:

[0044] ;

[0045] Where, represents the self-admittance of the internal node, represents the mutual admittance between internal nodes and boundary nodes, represents the mutual admittance between the boundary nodes and the internal nodes, represents the self-admittance of the boundary node, represents the mutual admittance between the boundary node and the external node, represents the mutual admittance between the external nodes and the boundary nodes, represents the self-admittance of the external node, represents the change in internal node voltage, represents the change in the boundary node current, Represents the change in external node current, represents the change in internal node current, represents the change in the boundary node current, Indicates the change in external node current.

[0046] From the above description, it can be seen that the system node admittance matrix is ​​established based on the nodes in the internal area, boundary area and external area. Through the system node admittance matrix, the voltage and power flow of each node in the power system can be calculated, which helps to evaluate the stability and load distribution of the power system and can be used for short-circuit analysis and voltage stability analysis.

[0047] Furthermore, performing equivalent simplification processing on the system node admittance matrix to obtain an equivalent node admittance equation includes:

[0048] ;

[0049] ;

[0050] Where, represents the equivalent admittance of the boundary nodes.

[0051] From the above description, it can be seen that by performing equivalent simplification on the node admittance matrix of the power system, the relationship between the node admittance, current and voltage in the external area can be eliminated, and the order and scale of the node admittance matrix can be reduced, so as to facilitate the subsequent establishment of the state equation of the power system.

[0052] Furthermore, establishing a state equation for the equivalent system includes:

[0053] ;

[0054] Where, Indicates a generator j The change in the state variable, A j Indicates a generator j The first coefficient matrix of B j Indicates a generator j The second coefficient matrix of Indicates the generator node voltage The change in the column vector consisting of the real and imaginary parts of Represents the generator node current The change in the column vector consisting of the real and imaginary parts of C j Indicates a generator j The third coefficient matrix of D j Indicates a generator j The fourth coefficient matrix of .

[0055] From the above description, it can be seen that the scale of the state equation is greatly reduced at this time, which is conducive to the subsequent rapid calculation of the eigenvalue.

[0056] Furthermore, obtaining a state matrix using a matrix inversion lemma based on the equivalent node admittance equation and the state equation includes:

[0057] The state equation is combined with the equivalent node admittance equation to obtain a linearized equation of the system at a steady-state operating point;

[0058] Eliminating the system node voltage variation in the linearized equation;

[0059] Calculate auxiliary inversion factors;

[0060] The matrix inversion lemma is used to obtain a state matrix based on the linearized equation after eliminating the system node voltage variation and the auxiliary inversion factor.

[0061] From the above description, it can be seen that the application of the equivalent system and matrix inversion lemma reduces the difficulty of calculating all the eigenvalues ​​of the system. There is no need to exchange internal information between partitions. Instead, one-way intersection and boundary area are used for calculation and evaluation, which further reduces the number of communications for information exchange between partitions. The requirements for power system communication conditions during the calculation process are lowered, while the algorithm still has good accuracy.

[0062] Furthermore, the state equation is combined with the equivalent node admittance equation to obtain a linearized equation of the system at a steady-state operating point, which includes:

[0063] ;

[0064] ;

[0065] ;

[0066] ;

[0067] ;

[0068] ;

[0069] Where, represents the change of all state variables of the system, represents the fifth coefficient matrix, represents the sixth coefficient matrix, represents the seventh coefficient matrix, represents the eighth coefficient matrix, Represents the change in system node voltage, represents the simultaneous first coefficient matrix of the system generators, represents the simultaneous second coefficient matrix of the system generators, represents the simultaneous third coefficient matrix of the system generators, represents the simultaneous fourth coefficient matrix of the system generators, represents the self-admittance of the internal node, represents the mutual admittance between internal nodes and boundary nodes, represents the mutual admittance between the boundary nodes and the internal nodes, represents the equivalent admittance of the boundary nodes, Indicates the n The first coefficient matrix of the generator, Indicates the n The second coefficient matrix of the generator, Indicates the n The third coefficient matrix of the generator, Indicates the n The fourth coefficient matrix of the generator.

[0070] From the above description, it can be seen that by combining the state equation with the equivalent node admittance equation, the linearized equation of the system at the steady-state operating point is obtained, which is beneficial to the subsequent calculation of the state matrix and improves the overall calculation efficiency.

[0071] Furthermore, eliminating the system node voltage variation in the linearized equation includes:

[0072] ;

[0073] Where, A represents the state matrix;

[0074] The calculation-assisted inversion factor includes:

[0075] ;

[0076] Where, a represents the auxiliary inversion factor, From , .

[0077] From the above description, it can be seen that by using the matrix inversion lemma, the amount of computation required to calculate the auxiliary inversion factor is significantly lower than that required to calculate the original inversion matrix, thereby improving the computation speed.

[0078] Furthermore, the use of the matrix inversion lemma to obtain a state matrix based on the linearized equation after eliminating the system node voltage variation and the auxiliary inversion factor includes:

[0079] .

[0080] From the above description, it can be seen that in the equivalent system, the matrix order of the operation is greatly reduced, and all the accurate eigenvalues ​​of the system can be calculated based on the state matrix, which reduces the difficulty of the operation.

[0081] Please refer to Figure 2 Another embodiment of the present invention provides a distributed computing system for power system characteristic values, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, each step in the above-mentioned distributed computing method for power system characteristic values ​​is implemented.

[0082] The above-mentioned distributed calculation method and system of power system characteristic values ​​of the present invention can be applied to power systems, and are described below through specific implementation methods:

[0083] Please refer to Figure 1 、 Figure 3-Figure 6 , embodiment 1 of the present invention is:

[0084] A distributed calculation method for power system characteristic values, comprising the steps of:

[0085] S1. Partition the nodes of the power system according to the topological relationship to obtain the internal area, the boundary area and the external area, and establish the system node admittance matrix according to the nodes in the internal area, the boundary area and the external area, such as Figure 3 As shown, specifically including S11-S14:

[0086] S11 . Determine dynamic element nodes (such as generator nodes) from the power system, and use the dynamic element nodes as internal nodes to form an internal region, where the internal region includes internal nodes.

[0087] S12. Nodes directly associated with the internal nodes in the internal area are grouped into a boundary area, where the boundary area includes boundary nodes.

[0088] S13. Nodes that are not directly associated with the boundary nodes in the boundary area form an external area, where the external area includes external nodes.

[0089] Among them, the internal node set can be expressed as , each generator node stores the parameters and dynamic data of the power grid where the generator is located. The boundary node set can be expressed as , the boundary node set has the parameters and dynamic data of the inter-regional contact line network, and the external node set can be expressed as , the external node set includes loads and user terminals. And satisfy m=n , x Represents node-related variables, including node voltage changes , node current change and the corresponding admittance blocks Y . Reflected in the system node admittance matrix formula, x G and x W 、 x W and x B The correlation matrix between the expressions of is non-zero, x G and x W The incidence matrix of all nodes is zero matrix.

[0090] S14, establishing a system node admittance matrix according to the nodes in the inner area, the boundary area, and the outer area includes:

[0091] After being divided into regions, the node admittance equation of the entire system can be expressed in blocks as follows:

[0092] ;

[0093] Where, Represents an internal node i The current change, Represents a boundary node i The current change, Represents an external node i The current change, Represents an internal node i The voltage change, Represents a boundary node i The voltage change, Represents an external node i The voltage change, Represents an internal node i The self-admittance, Represents a boundary node i The self-admittance, Represents an external node i The self-admittance, Represents an internal node i With boundary nodes i The mutual admittance, Represents a boundary node i With internal nodes i The self-admittance, Represents an external node i 、 j The mutual admittance, Represents an external node i With boundary nodes i The mutual admittance, Represents a boundary node i With external nodes i The self-admittance, Represents an external node i The self-admittance of .

[0094] Integrating the above formula, we can get the system node admittance matrix, which is:

[0095] ;

[0096] Where, represents the self-admittance of the internal node, represents the mutual admittance between internal nodes and boundary nodes, represents the mutual admittance between the boundary nodes and the internal nodes, represents the self-admittance of the boundary node, represents the mutual admittance between the boundary node and the external node, represents the mutual admittance between the external nodes and the boundary nodes, represents the self-admittance of the external node, represents the change in internal node voltage, represents the change in the boundary node current, Represents the change in external node current, represents the change in internal node current, represents the change in the boundary node current, Indicates the change in external node current.

[0097] Among them, it can be seen from the above formula that, 、 、 、 、 is a diagonal block matrix, and .

[0098] By partitioning the power system according to topological relationships and dividing the nodes into three categories, the set of power generation nodes and the set of boundary nodes in the power system can be determined, so as to facilitate the subsequent simplification of the node admittance equation of the power system.

[0099] S2. Perform equivalent simplification processing on the system node admittance matrix to obtain an equivalent node admittance equation, and determine an equivalent system corresponding to the equivalent node admittance equation, where the equivalent system is a power system with the external area eliminated.

[0100] The equivalent simplification processing of the system node admittance matrix to obtain the equivalent node admittance equation includes:

[0101] From the third row of the system node admittance matrix, we can get:

[0102] ;

[0103] Substituting the above formula into the second row of the system node admittance matrix, we can eliminate ,get:

[0104] ;

[0105] Since the external nodes consist of load nodes, In dynamic modeling, take 0 to integrate the information of the boundary area and the external area 、 、 、 , so the equivalent node admittance equation is specifically:

[0106] ;

[0107] ;

[0108] Where, represents the equivalent admittance of the boundary nodes.

[0109] Observing the symmetry relationship in the above matrix topology, we can get , can be merged and stored. Since the subsequent generator modeling will not involve the nodes in the external area, an equivalent system with the external area eliminated has been obtained.

[0110] By simplifying the node admittance equation of the power system, the relationship between the node admittance, current and voltage in the external area can be eliminated, and the order and scale of the node admittance equation can be reduced, so as to facilitate the subsequent establishment of the state equation of the power system.

[0111] S3, establish a state equation for the equivalent system, and use the matrix inversion lemma based on the equivalent node admittance equation and the state equation to obtain a state matrix, such as Figure 3 As shown, specifically including S31-S35:

[0112] S31, establishing a state equation for the equivalent system, specifically:

[0113] ;

[0114] Where, Indicates a generator j The change in the state variables (including angular velocity, rotor angle, etc.), A j Indicates a generator j The first coefficient matrix of B j Indicates a generator j The second coefficient matrix of Indicates the generator node voltage The change in the column vector consisting of the real and imaginary parts of Represents the generator node current The change in the column vector consisting of the real and imaginary parts of C j Indicates a generator j The third coefficient matrix of D j Indicates a generator j The fourth coefficient matrix, the first coefficient matrix, the second coefficient matrix, the third coefficient matrix and the fourth coefficient matrix are related to the structure, parameters and operating conditions of the system.

[0115] The state equation is the generator j ( j =1,…,n) of the state equation.

[0116] S32, the state equation is combined with the equivalent node admittance equation to obtain the linearized equation of the system at the steady-state operating point, specifically:

[0117] ;

[0118] ;

[0119] ;

[0120] ;

[0121] ;

[0122] ;

[0123] Where, represents the change of all state variables of the system, represents the fifth coefficient matrix, represents the sixth coefficient matrix, represents the seventh coefficient matrix, represents the eighth coefficient matrix, Represents the change in system node voltage, represents the simultaneous first coefficient matrix of the system generators, represents the simultaneous second coefficient matrix of the system generators, represents the simultaneous third coefficient matrix of the system generators, represents the simultaneous fourth coefficient matrix of the system generators, Indicates the n The first coefficient matrix of the generator, Indicates the n The second coefficient matrix of the generator, Indicates the n The third coefficient matrix of the generator, Indicates the n The fourth coefficient matrix of the generator.

[0124] S33, eliminating the system node voltage variation in the linearized equation, specifically:

[0125] ;

[0126] Where, A Represents the state matrix.

[0127] Among them, the state matrix A The calculation formula is:

[0128] .

[0129] S34. Calculate auxiliary inversion factors, including:

[0130] From the matrix inversion lemma, we know that: , known A for n × n non-singular matrix of order, M 、 N for n × m rank matrix, a for m × m is a non-singular matrix with m ≤ n If the matrix auxiliary inversion factor is a reversible matrix, then The inverse matrix can be transformed into:

[0131] ;

[0132] In the original power system, m for Y BB The order of n for Y GG The order of , obviously cannot satisfy m ≤ n ; But in the above equivalent system, m = n , so we can apply the matrix inversion lemma.

[0133] From , , then the auxiliary inversion factor is:

[0134] ;

[0135] Where, a Represents the auxiliary inversion factor.

[0136] S35. Using the matrix inversion lemma, a state matrix is ​​obtained based on the linearized equation after eliminating the system node voltage variation and the auxiliary inversion factor. Specifically, the state matrix is:

[0137] .

[0138] S4. Solve the state matrix using an orthogonal triangular decomposition (QR) method to obtain eigenvalues ​​of the power system.

[0139] The following provides a specific application scenario, namely an IEEE 3-machine 9-node system, using the above method of the present invention.

[0140] Reference Figure 4 and Figure 5 The IEEE 3-machine 9-node system is divided into three regions: the inner region, the boundary region, and the outer region. The inner region contains nodes 1, 2, and 3; the boundary region contains nodes 4, 7, and 9; and the inner region contains nodes 5, 6, and 8. Node 1 is connected to generator 1; region 3 contains nodes 3, 6, and 9, and node 3 is connected to generator 3.

[0141] System parameters are shown in Tables 1 to 3. T J represents the inertia time constant, R a represents the excitation resistance, X d represents the direct-axis reactance, represents the direct-axis transient reactance, X q represents the quadrature-axis reactance, represents the quadrature-axis transient reactance, represents the stator open-circuit time constant of the direct-axis excitation winding, represents the stator open-circuit time constant of the quadrature-axis damping winding, D represents the damping coefficient, T R 、 K A 、 T A 、 T B are the parameters of the generator self-shunt static excitation system, T R represents the time measurement constant, K A It represents the gain of the comprehensive amplification link, T A It represents the time constant of the comprehensive amplification link, T B Indicates the inherent equivalent time constant of the excitation regulator.

[0142] Table 1 Generator data

[0143]

[0144] Table 2 Flow data of normal operation

[0145]

[0146] Table 3 Branch data

[0147]

[0148] Divide the nodes into partitions to establish the system node admittance matrix:

[0149] ;

[0150] ;

[0151] ;

[0152] ;

[0153] ;

[0154] ;

[0155] ;

[0156] The boundary area integrates the information of the boundary area and the external area 、 、 、 , calculate the equivalent admittance of the boundary nodes:

[0157] ;

[0158] From this we can obtain the equivalent nodal admittance equation of the equivalent system.

[0159] The state equation is established for the equivalent system, specifically:

[0160] ;

[0161] ;

[0162] ;

[0163] ;

[0164] ;

[0165] ;

[0166] ;

[0167] ;

[0168] ;

[0169] ;

[0170] ;

[0171] ;

[0172] The above data of each generator node is collected from the boundary area to obtain the coefficient matrix:

[0173] ;

[0174] ;

[0175] ;

[0176] Calculate the auxiliary inversion factor:

[0177] ;

[0178] Recalculate the state matrix A .

[0179] All characteristic values ​​of the original power system are calculated according to the QR method, as shown in Table 4 and Figure 6 shown.

[0180] Table 4 Calculated eigenvalue results

[0181]

[0182] By comparing with the original power system characteristic values, it was found that the error of all the calculated characteristic values ​​was less than one ten-thousandth, so the accuracy of the above method of the present invention was verified.

[0183] The distributed calculation method for power system eigenvalues ​​described above in the present invention performs equivalent simplification on the power system. Therefore, when calculating the state matrix, the equivalent admittance of the boundary nodes is inverted. This is the boundary nodes excluding the generator nodes and external nodes, resulting in a small scale and a diagonal block matrix. Compared to directly calculating the state matrix of the original system, the block admittance matrix of all nodes excluding the generator nodes must be inverted. The order of the block admittance matrix is ​​the sum of the number of boundary nodes and external nodes, resulting in a large scale and computational complexity. In addition, the admittance matrix used in the calculation of the state matrix of the equivalently processed system is of the same scale as the generator node admittance block and contains a set of duplicate data, which reduces data storage and improves computational efficiency.

[0184] Furthermore, the method of the present invention only requires that each partition transmit a small amount of processed data from each generator node within the internal area to the boundary area in a one-way manner. It does not require that generator nodes within the internal area exchange information between nodes within the partition, especially generator and load information of important nodes. Because the present method does not require the exchange of detailed power data between important internal nodes during the calculation process, it can maintain the security independence of each partition under the hierarchical and zoned management system of my country's power system, which is of practical significance.

[0185] In addition, the accuracy of the characteristic values ​​calculated using the above method of the present invention is verified by comparing them with the original power system characteristic values. The above method of the present invention improves the accuracy of characteristic value calculation.

[0186] Please refer to Figure 2 , the second embodiment of the present invention is:

[0187] A distributed computing system for power system characteristic values ​​includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, each step of the distributed computing method for power system characteristic values ​​in the first embodiment is implemented.

[0188] In summary, the present invention provides a distributed calculation method and system for the eigenvalues ​​of an electric power system, which partitions the nodes of the electric power system according to the topological relationship to obtain internal areas, boundary areas and external areas, and establishes a system node admittance matrix according to the nodes in different partitions, performs equivalent simplification processing on the system node admittance matrix to obtain an equivalent node admittance equation, and determines an equivalent system corresponding to it, which has eliminated the external area, establishes a state equation for the equivalent system, and uses the matrix inversion lemma based on the equivalent node admittance equation and the state equation to obtain a state matrix, uses the orthogonal triangular decomposition method to solve the state matrix, and obtains the eigenvalues ​​of the electric power system, thereby reducing the scale of the processing matrix through equivalent simplification processing, and avoiding the problem of simplification by establishing a state equation for the equivalent system and introducing the matrix inversion lemma. The inversion operation of large-scale matrices is performed, and then the orthogonal triangular decomposition method is used to solve the eigenvalues, avoiding the influence of the external area of ​​equivalence elimination. Each partition does not need to perform inversion calculation on the large-scale matrix, reducing the number of communications and the amount of calculation for partition transmission, while still having good convergence. During the calculation process, the requirements for the communication conditions of the power system can also be reduced, thereby improving the efficiency and accuracy of the eigenvalue calculation in the partition environment of the power system; moreover, the application of the equivalent system and matrix inversion lemma reduces the difficulty of calculating all the eigenvalues ​​of the system. There is no need to exchange internal information between partitions, but a one-way intersection with the boundary area is used for calculation and evaluation, which further reduces the number of communications for exchanging information between partitions, reduces the requirements for the communication conditions of the power system during the calculation process, and the algorithm still has good accuracy.

[0189] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent transformations made using the contents of the present invention's description and drawings, or directly or indirectly applied in related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A distributed calculation method for power system characteristic values, characterized in that: Including steps: Partitioning the nodes of the power system according to the topological relationship to obtain an internal area, a boundary area, and an external area, and establishing a system node admittance matrix based on the nodes in the internal area, the boundary area, and the external area; Performing equivalent simplification processing on the system node admittance matrix to obtain an equivalent node admittance equation, and determining an equivalent system corresponding to the equivalent node admittance equation, wherein the equivalent system is a power system with the external area eliminated; Establishing a state equation for the equivalent system, and obtaining a state matrix using a matrix inversion lemma based on the equivalent node admittance equation and the state equation; Solving the state matrix using an orthogonal triangular decomposition method to obtain eigenvalues ​​of the power system; The obtaining of a state matrix by using a matrix inversion lemma based on the equivalent node admittance equation and the state equation comprises: The state equation is combined with the equivalent node admittance equation to obtain a linearized equation of the system at a steady-state operating point; Eliminating the system node voltage variation in the linearized equation includes: ； Where, A represents the state matrix, Indicates the change in all state variables of the system; Compute auxiliary inversion factors, including: ； Where, a represents the auxiliary inversion factor, represents the equivalent admittance of the boundary nodes, represents the mutual admittance between internal nodes and boundary nodes, represents the mutual admittance between the boundary nodes and the internal nodes, From , , represents the eighth coefficient matrix, represents the self-admittance of the internal node, represents the simultaneous fourth coefficient matrix of the system generators; The matrix inversion lemma is used to obtain a state matrix based on the linearized equation after eliminating the system node voltage variation and the auxiliary inversion factor, including: ； Where, represents the simultaneous first coefficient matrix of the system generators, represents the simultaneous second coefficient matrix of the system generators, Represents the simultaneous third coefficient matrix of the system generators.

2. A distributed calculation method for power system characteristic values ​​according to claim 1, characterized in that: Partitioning the nodes of the power system according to the topological relationship to obtain the internal area, the boundary area and the external area includes: determining dynamic element nodes from the power system, and using the dynamic element nodes as internal nodes to form an internal area; composing a boundary region with nodes directly associated with the internal nodes in the internal region; The nodes that are not directly associated with the boundary nodes in the boundary area constitute an external area.

3. A distributed calculation method for power system characteristic values ​​according to claim 1, characterized in that: The internal area includes internal nodes; The boundary area includes boundary nodes; The external area includes external nodes; The establishing of a system node admittance matrix according to the nodes in the inner area, the boundary area, and the outer area comprises: ； Where, represents the self-admittance of the internal node, represents the mutual admittance between internal nodes and boundary nodes, represents the mutual admittance between the boundary nodes and the internal nodes, represents the self-admittance of the boundary node, represents the mutual admittance between the boundary node and the external node, represents the mutual admittance between the external nodes and the boundary nodes, represents the self-admittance of the external node, represents the change in internal node voltage, represents the voltage change at the boundary node, Represents the external node voltage change, represents the change in internal node current, represents the change in the boundary node current, Indicates the change in external node current.

4. A distributed calculation method for power system characteristic values ​​according to claim 3, characterized in that: The equivalent simplification processing of the system node admittance matrix to obtain the equivalent node admittance equation includes: ； ； Where, represents the equivalent admittance of the boundary nodes.

5. A distributed calculation method for power system characteristic values ​​according to claim 1, characterized in that: The establishing of the state equation for the equivalent system comprises: ； Where, Indicates a generator j The change in the state variable, A j Indicates a generator j The first coefficient matrix of B j Indicates a generator j The second coefficient matrix of Indicates the generator node voltage The change in the column vector consisting of the real and imaginary parts of Represents the generator node current The change in the column vector consisting of the real and imaginary parts of C j Indicates a generator j The third coefficient matrix of D j Indicates a generator j The fourth coefficient matrix of .

6. A distributed calculation method for power system characteristic values ​​according to claim 1, characterized in that: The state equation is combined with the equivalent node admittance equation to obtain the linearized equation of the system at the steady-state operating point, which includes: ； ； ； ； ； ； Where, represents the fifth coefficient matrix, represents the sixth coefficient matrix, represents the seventh coefficient matrix, Represents the change in system node voltage, Indicates the n The first coefficient matrix of the generator, Indicates the n The second coefficient matrix of the generator, Indicates the n The third coefficient matrix of the generator, Indicates the n The fourth coefficient matrix of the generator.

7. A distributed computing system for power system characteristic values, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, each step of the distributed calculation method of power system characteristic values ​​according to any one of claims 1 to 6 is implemented.

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