Structure-maintained multi-station external power grid equivalence method and system

Abstract

The invention discloses a structure-maintained multi-station external power grid equivalence method and system, relates to the field of power systems, and aims to solve the problem of new energy high-permeability scene modeling caused by structure distortion, insufficient precision and unstable parameters in a traditional equivalence method. The method comprises the following steps: on the basis of a multi-station system topology, numbering new energy station nodes and other nodes in blocks, and constructing a block admittance matrix; carrying out load flow calculation by adopting a Newton-Raphson method to obtain node voltage and current vectors of the new energy field station; non-new energy node variables are eliminated through Kron order reduction, and an equivalent admittance matrix and equivalent balance node voltage which reserve tie line admittance are generated; and constructing a structure-maintained external power grid equivalent model. According to the technical scheme, through block admittance matrix construction and a Kron order reduction method, on the premise that new energy field inter-station tie line admittance and an original topological structure are reserved, the complexity of the model is remarkably reduced, and high-precision and high-efficiency multi-station external power grid equivalent modeling is achieved.

Description

Technical Field

[0001] The present invention relates to the field of power systems, and particularly to a method and system for equivalent external power grid of multiple stations with structure preservation. Background Art

[0002] China's power system has gradually evolved into a large-scale multi-region integrated system with a wide coverage and interconnection among regions. At the same time, with the vigorous development of new energy, many new energy stations have been connected to the grid. This complexity poses many challenges in analyzing various problems of the power system. Therefore, how to reasonably simplify the network equivalent of the power system has become a key link in the research. Through effective equivalent simplification, the calculation complexity can be reduced and the analysis efficiency can be improved, which has very important theoretical and engineering application values.

[0003] There are currently many methods for the static equivalent problem of power systems, but each has its own drawbacks. The simple equivalent machine hanging method is widely used in practical engineering, but it will cause large errors when there are disturbances in the internal network; the Ward equivalent method simplifies and eliminates the external network nodes based on the Gauss elimination method for the nodal admittance matrix, but it cannot reflect the voltage and reactive power support of the external power grid to the internal network; the idea of the REI equivalent method is to merge the injection power of a set of nodes to be eliminated into an REI node, but the equivalent admittance obtained by this method will change with the state of the external power grid. The above methods fail to effectively retain the key structural characteristics of the external power grid (such as the admittance of the tie lines between stations and the topological connection relationship) during the equivalent process, resulting in the equivalent model being unable to truly reflect the electrical influence of the external power grid on the internal network. Especially in the scenario of high penetration of new energy stations, the error is further amplified. Summary of the Invention

[0004] The technical problem to be solved and the technical task proposed by the present invention are to improve and refine the existing technical solutions, and provide a method and system for equivalent external power grid of multiple stations with structure preservation, aiming to solve the problems of structure distortion, insufficient accuracy, and parameter instability. For this purpose, the present invention adopts the following technical solutions.

[0005] A method for equivalent external power grid of multiple stations with structure preservation includes the following steps: 1) According to the topological structure of the multi-station power system, number the new energy station nodes and other nodes in the network in blocks to form a block admittance matrix; 2) Based on the block admittance matrix, use the Newton-Raphson method to perform system power flow calculation to obtain the voltage vector and current vector of each new energy station node; 3) Use the Kron reduction method to perform matrix transformation on the nodal voltage equation, and obtain the equivalent admittance matrix and the equivalent balanced nodal voltage by eliminating the variables corresponding to the non-new energy station nodes. The equivalent admittance matrix retains the tie line admittance information between new energy stations; 4) Output the equivalent system nodal admittance matrix YS and the equivalent balanced node voltage E. Based on the equivalent admittance matrix and the equivalent balanced node voltage, construct a structure-preserving equivalent model of the external power grid, and retain the original topological structure information among the new energy power stations.

[0006] Through the construction of the block admittance matrix, Kron reduction matrix transformation, and tie-line admittance retention technology, this technical solution simplifies the model while maintaining the topological structure and admittance relationship information of the original system, significantly reducing the model complexity and achieving high-precision and high-efficiency equivalent modeling of the multi-station external power grid. Specifically, the admittance information is retained through block numbering and matrix transformation to ensure that the equivalent model is consistent with the original system topology; avoid the dynamic response error caused by the replacement of the equivalent generator in the simple hanging equivalent machine method. Through the extraction of the equivalent balanced node voltage, accurately characterize the electrical interaction between the external power grid and the internal network, and overcome the limitation of the Ward equivalent method that ignores voltage support. Generate equivalent parameters based on power flow calculation and fixed admittance matrix to improve the model robustness. Compared with the REI equivalent method, the fixed admittance matrix design makes the equivalent parameters not affected by the fluctuations of the external network state.

[0007] By block numbering the new energy power station nodes and other nodes to form a block admittance matrix, the boundary between the new energy power stations and the external power grid can be accurately divided, providing a structured data basis for subsequent matrix reduction. The block matrix is convenient for local operations and reduces the overall calculation complexity. The block design avoids the topological structure damage caused by directly eliminating nodes in traditional methods (such as the Ward equivalent method) and ensures the integrity of the tie-line admittance among the new energy power stations. Use the Newton-Raphson method for power flow calculation, combined with the Jacobian matrix to iteratively correct the voltage and phase, which can quickly converge to a high-precision solution. Use Kron reduction to perform matrix transformation on the node voltage equation, eliminate the non-new energy power station node variables, generate the equivalent admittance matrix and the equivalent balanced node voltage, eliminate the redundant non-new energy node variables, significantly reduce the model dimension, improve the calculation efficiency, and ensure that the equivalent model is consistent with the original system topology, avoiding the problem of admittance information loss in traditional methods. The constructed equivalent model retains the tie-line admittance and the original topological structure information among the new energy power stations. The model can truly reflect the electrical interaction characteristics of the external power grid with the internal network and is suitable for accurate analysis of high-penetration new energy scenarios. While reducing the model complexity, ensure the consistency of the simulation results with the full-system model by retaining key admittance and voltage parameters.

[0008] As a preferred technical means: in step 1), the new energy power station nodes are numbered as the first m nodes, and the remaining nodes are numbered as the last n - m nodes, where n is the total number of nodes and m is the number of new energy power station nodes; the construction method of the block admittance matrix is: The block admittance matrix includes the admittance sub-matrix between the new energy power station nodes , the mutual admittance submatrix between the new energy power station and other nodes and , as well as the admittance submatrix between other nodes , the form of which is: ; Among them, is an m×m matrix, is an (n - m)×(n - m) matrix.

[0009] By uniformly numbering the new energy power station nodes as the first m nodes and the remaining nodes as the last n - m nodes, a clear division of node types is achieved, clearly distinguishing the new energy power station from other parts of the power grid. It is convenient to quickly locate the association relationship between the new energy power station nodes and other nodes, providing an intuitive physical basis for the subsequent construction of block matrices. In a complex multi-power station system, node classification and numbering can reduce manual intervention errors and improve the automation level of model construction.

[0010] The admittance matrix Y is divided into four submatrices ( , , , ), and the mathematical properties of block matrices are used to optimize the operation. The independent processing of (the admittance between new energy power stations) and (the admittance of other nodes) avoids the complexity of full matrix operations. Significantly reduces the computational amount and improves the processing efficiency of large-scale systems. The submatrix completely retains all the admittance information (self-admittance and mutual admittance) between the new energy power station nodes, ensuring that the physical connection relationship between the new energy power stations (such as the admittance of tie lines) is fully reflected in the matrix, and avoiding the loss of topological information caused by node elimination in traditional methods. Provides accurate inter-station interaction parameters for the subsequent equivalent model, supporting accurate electrical characteristic analysis.

[0011] The submatrices and characterize the mutual admittance relationship between the new energy power station nodes and other nodes, distinguish the electrical interaction between the new energy power station and the external power grid (such as the power transmission path), and are convenient for analyzing the voltage and reactive power support effects of the external grid on the internal grid. By modifying and , the changes in the access position or quantity of new energy power stations can be quickly adapted, enhancing the scalability of the model.

[0012] The dimension division of the block admittance matrix naturally adapts to the requirements of subsequent order reduction operations. Through the block structure, subsequent steps (such as Kron reduction) can directly perform variable elimination on , avoiding redundant calculations for processing the full matrix. Block storage reduces the direct operation on large sparse matrices and reduces the memory requirement.

[0013] As a preferred technical means: The power flow calculation described in step 2) specifically includes: (a) Input the initial system parameters, including line admittance, active and reactive power of new energy power stations as PQ nodes, voltage amplitude and phase of the balancing node; (b) Iteratively calculate the active power error and the reactive power error , and solve the correction amounts of voltage amplitude and phase angle through the Jacobian matrix; (c) When the active power error and the reactive power error are less than the preset threshold, output the voltage amplitude and phase of each node, and substitute them into the node voltage equation to calculate the current vector ; (d) Calculate the current of the non-port nodes, which can be achieved by any of the following methods: ⅰ) Substitute the node voltages obtained from the power flow calculation into the block node voltage equation , and directly solve ; ⅱ) According to the node active power P, reactive power Q and voltage U in the power flow result, calculate the node current through the formula ; In the formula, the symbol is the conjugate operator, I is the node current, P is the node active power, Q is the node reactive power, U is the node voltage, and i = m + 1, m + 2,..., n are the corresponding node numbers.

[0014] Through parameter input, Newton-Raphson method iteration, error control and seamless connection of the current vector, ensure the engineering-level accuracy of voltage, phase and current parameters; Design the Jacobian matrix and error criterion to optimize the convergence speed and robustness; Provide seamless connection of input data for subsequent equivalent steps.

[0015] Method ⅰ directly substitutes the node voltages , obtained from the Newton-Raphson power flow calculation into the block node voltage equation, and can quickly solve , without additional power data conversion, avoiding repeated calculations and significantly improving the calculation efficiency. Based on the solution of the linear equation of the admittance matrix Y, the algorithm is mature and has good convergence, especially suitable for the case of a large number of non-port nodes in a large-scale power grid, avoiding the divergence problem that may be caused by non-linear iteration. Directly reuse the voltage parameters in the power flow calculation result to ensure is strictly consistent with the real-time operating state of the system, and is applicable to the on-line dynamic equivalent scenario.

[0016] Method II When the external power grid parameters (such as branch admittance) are incomplete or there is measurement noise, the node measurement data can be directly used through the formula: Calculate , reducing the dependence on the integrity of the admittance matrix, and is applicable to the equivalent scenarios of parameter loss or measurement-driven. Update through real-time measurement of P and Q, which can capture dynamic characteristics such as wind and light power fluctuations and load time-variation, overcoming the limitation that the traditional non-topological method requires the external power grid to be stationary. Avoid complex block matrix operations, and only basic complex algebraic operations are required to complete the current calculation, reducing the difficulty of algorithm implementation, and is applicable to embedded devices or edge computing nodes.

[0017] Method I is applicable to scenarios with complete parameters and the pursuit of efficient calculation; Method II is applicable to scenarios with rich measurement data and the need to dynamically track the operating state. The combination of the two expands the applicable scope of the technical solution. In actual projects where external power grid parameters and measurement data are mixed and available, the calculation accuracy can be improved through cross-validation (such as comparing the results of the two methods) , enhancing the reliability of the equivalent model. Method I continues the classic admittance matrix modeling idea and is compatible with existing simulation platforms; Method II adapts to the measurement system with PMU (Phasor Measurement Unit) as the core and supports the high-frequency data assimilation requirements of the power system.

[0018] As a preferred technical means: The specific method of the matrix transformation described in step 3) is: First, eliminate the node voltage of non-new energy power stations through the formula , and substitute it into the original node voltage equation to obtain a simplified equation:

[0019] Then, perform different combined transformations on through the following two branches respectively: Branch 1:

[0020]

[0021]

[0022] Branch 2:

[0023]

[0024]

[0025] Among them, is the equivalent admittance matrix containing the admittance information of the tie line; Next, take the equivalent balanced node voltage E and the corresponding admittance parameters , and finally obtain the equivalent model equation: .

[0026] Through the formula Eliminate the node voltages of non-new energy power stations , and reduce the original high-dimensional node voltage equation to a simplified equation containing only the nodes of new energy power stations. Eliminating (n - m) non-new energy node variables significantly reduces the equation dimension and subsequent computational workload.

[0027] Equivalent admittance matrix Completely retain the tie line admittance between new energy power stations and the equivalent interaction admittance of the external power grid ( ). Avoid the loss of tie line admittance caused by directly eliminating nodes in traditional methods (such as Ward equivalent method), and ensure that the equivalent model is consistent with the original system topology. By retaining the key admittance parameters, the equivalent model can accurately represent the power interaction between new energy power stations and the electrical influence of the external power grid.

[0028] By extracting the equivalent balanced node voltage E and the admittance parameters , overcome the defect of the Ward equivalent method that ignores the voltage support of the external power grid, and improve the accuracy of the equivalent model in reactive power-voltage analysis. Generated based on a fixed admittance matrix, avoiding the limitation that the parameters fluctuate with the external network state in the REI equivalent method.

[0029] Through two branch methods, perform combined transformation on , and finally extract the equivalent balanced node voltage E and the admittance parameters . In branch one, by separating the equivalent current term X of the external power grid, the current contribution of the external power grid is intuitively reflected, facilitating the analysis of the equivalent current contribution of the external power grid. Branch two: directly generate through admittance matrix operation, simplify the parameter extraction process, reduce intermediate variables, and improve computational efficiency. Both branches simplify , ensuring interface standardization.

[0030] As an optimal technical means: the equivalent balanced node voltage E is calculated by the formula , where , is the element in the k-th row and p-th column of the equivalent admittance matrix ; is the k-th element of the equivalent current term X of the external power grid obtained from the power flow calculation; through the above calculation, make The error between its amplitude and the amplitude of the new energy power station node voltage does not exceed a preset threshold; then, compare the average values of the moduli of the elements in the equivalent balanced node voltage E obtained from the two branches, and select the branch result close to 1 as the output result.

[0031] is the sum of the admittances of the new energy power station nodes, reflecting the admittance contribution among the power stations. E is obtained by normalizing the external power grid equivalent current term and directly characterizes the voltage support effect of the external power grid on the new energy power station. Through the sum of admittances normalize the current term to ensure that the amplitude of E is close to the actual voltage amplitude of the new energy power station nodes. The amplitude of E is close to the actual voltage of the new energy power station nodes, avoiding the model distortion caused by ignoring voltage support in traditional methods (such as the Ward equivalent method). Based on the calculation of the column sums of the fixed admittance matrix , rather than the dynamic external power grid state parameters. The admittance matrix is a static parameter and does not change with the operation state of the external power grid, ensuring that the generation process of E is not affected by the fluctuations of the external network; compared with the REI equivalent method, it avoids the problem of the equivalent admittance fluctuating with the external network power, improving the long-term applicability of the model. The formula only needs to calculate the column sums of the admittance matrix without complex iteration or matrix decomposition. Compared with the methods that require dynamic update of admittance parameters (such as the REI equivalent method), the computational amount of this formula is significantly reduced, making it suitable for real-time or large-scale system analysis. By retaining the sum of the admittances of the new energy power stations , the model can accurately reflect the electrical interaction characteristics among the new energy power stations, is applicable to the multi-power station grid connection scenario, and ensures the accuracy of the equivalent model under high penetration. Through multi-path verification, reduce the possible calculation errors or numerical instability problems of a single method; with the voltage modulus close to 1 as the benchmark (the ideal voltage amplitude in the per-unit value system), ensure the rationality of the model output result.

[0032] Another technical solution of the present invention is: a structure-preserving multi-power station external power grid equivalent system, the system includes: A partitioning module, configured to partition and number the new energy power station nodes and other nodes in the network according to the topological structure of the multi-power station power system, and generate a partitioned admittance matrix; A power flow calculation module, based on the partitioned admittance matrix, uses the Newton-Raphson method to perform system power flow calculation to obtain the voltage vector and current vector of each new energy power station node; A matrix transformation module, which uses the Kron reduction method to perform matrix transformation on the node voltage equation, and by eliminating the variables corresponding to the non-new energy power station nodes, obtains an equivalent admittance matrix and an equivalent balanced node voltage, and the equivalent admittance matrix retains the tie-line admittance information among the new energy power stations; The equivalent model construction module constructs a structure-preserving equivalent model of the external power grid based on the equivalent admittance matrix and the equivalent balanced node voltage, retaining the original topological structure information among new energy power stations.

[0033] The block module generates a structured admittance matrix, and the matrix transformation module eliminates redundant variables based on Kron reduction. The two cooperate to reduce the operation dimension. The matrix transformation module maintains the original topological structure by retaining the tie-line admittance ( ), and the equivalent balanced node voltage (E). The equivalent model construction module avoids the structure distortion problem of traditional equivalent methods and accurately represents the electrical interaction among new energy power stations and the supporting role of the external power grid.

[0034] As an optimal technical means: In the block module, the node numbers of new energy power stations are the first m nodes, and the remaining node numbers are the last n - m nodes, where n is the total number of nodes and m is the number of nodes of new energy power stations; the block module includes: The admittance sub-matrix generation unit between new energy power station nodes generates an m×m matrix ; The mutual admittance sub-matrix generation unit generates the mutual admittance sub-matrix between new energy power stations and other nodes and ; The admittance sub-matrix generation unit between other nodes generates an (n - m)×(n - m) matrix ; The form of the block admittance matrix is: .

[0035] As an optimal technical means: The power flow calculation module includes: (a) A parameter input interface for receiving the initial parameters of the system, including line admittance, active and reactive power of new energy power stations as PQ nodes, voltage amplitude and phase of the balanced node; (b) An iterative calculation unit that iteratively calculates the active power error and the reactive power error , and solves the correction amounts of voltage amplitude and phase angle through the Jacobian matrix; (c) An error judgment unit that outputs the voltage amplitude and phase of each node when max(| |, |Δ |) < , where is the preset error threshold; (d) A current calculation unit, including a first current calculation sub-module and a second current calculation sub-module. The first current calculation sub-module substitutes the voltage amplitude and phase into the node voltage equation to calculate the current vector ; The second current calculation sub-module is used to calculate the node current according to the active power P, reactive power Q, and voltage U of the nodes in the power flow result through the formula Calculate the node current ; In the formula, the symbol is the conjugate operator, I is the node current, P is the active power of the node, Q is the reactive power of the node, U is the node voltage, and i = m + 1, m + 2,..., n is the corresponding node number.

[0036] As a preferred technical means: The matrix transformation module includes: The voltage elimination unit eliminates the node voltage of non-new energy power stations through the formula ; ; The equation simplification unit substitutes the eliminated result into the original node voltage equation to generate a simplified equation: Branch 1:

[0037] Branch 2:

[0038] The equivalent parameter extraction unit extracts the equivalent balanced node voltage E and admittance parameters from the simplified equation to generate an equivalent model equation: ; where is the equivalent admittance matrix that retains the tie-line admittance.

[0039] As a preferred technical means: In the equivalent parameter extraction unit, the calculation module of the equivalent balanced node voltage E calculates through the formula: where , is the equivalent admittance matrix the element in the k-th row and p-th column; is the k-th element of the equivalent current term X of the external power grid obtained from the power flow calculation; through the above calculation, the error between the amplitude of and the amplitude of the new energy power station node voltage does not exceed the preset threshold; finally, compare the average value of the modulus of each element in the equivalent balanced node voltage E obtained from the two branches, and select a set of branch results close to 1 as the output result.

[0040] Beneficial effects: This technical solution simplifies the model while maintaining the topological structure and admittance relationship of the original system through the construction of a block admittance matrix, Kron reduction matrix transformation, and tie-line admittance retention technology.

[0041] This technical solution preserves the admittance through block numbering and matrix transformation, ensuring that the equivalent model is topologically consistent with the original system; it avoids the dynamic response errors caused by the equivalent generator substitution in the simple equivalent machine connection method.

[0042] This technical solution accurately characterizes the electrical interaction between the external power grid and the internal network through the extraction of the equivalent balanced node voltage; by extracting the equivalent balanced node voltage, it overcomes the limitation of the Ward equivalent method that ignores voltage support.

[0043] This technical solution generates equivalent parameters based on power flow calculation and fixed admittance matrix, improving the robustness of the model. Compared with the REI equivalent method, the design of the fixed admittance matrix makes the equivalent parameters unaffected by the fluctuations of the external network state. Description of the Drawings

[0044] Figure 1 It is a schematic diagram of a multi-machine grid-connected system.

[0045] Figure 2 It is a flow chart of the present invention.

[0046] Figure 3 It is a topological diagram of the 3-machine 9-node system adopted in the embodiment of the present invention. Detailed Implementation Manner

[0047] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings of the specification.

[0048] Embodiment 1: As Figure 2 shown, the present invention includes the following steps: S1: According to the topological structure of the multi-station power system, number the new energy station nodes and other nodes in the network in blocks to form a block admittance matrix; As Figure 1 shown is a schematic diagram of a new energy multi-station grid-connected system, including a local AC network and the nodes where new energy power generation stations are connected. Among them, the AC network contains loads, connection nodes, and the remaining possible synchronous generators, etc. First, number the system nodes according to the research object. Assume that there are n nodes in the system and m new energy stations. Number the new energy station nodes as , and number the remaining nodes as . Thus, the system admittance matrix is formed as: (1) In the formula, is the admittance value between the corresponding nodes. When , it represents the mutual admittance between the nodes; when , it represents the self-admittance of the node.

[0049] Meanwhile, according to the model parameters, the corresponding conductance values and susceptance values between each node are obtained, and let:

[0050] (2) In the formula, represents the corresponding conductance value, represents the corresponding susceptance value, represents taking the real part of the corresponding number, represents taking the imaginary part of the corresponding number.

[0051] Further construct the node voltage equation of the multi-station system as shown in Equation (2).

[0052] (3) In the formula, for the current matrix I and the voltage matrix U, the subscript S represents the new energy station node, and the subscript L represents other nodes in the network, such as load nodes, connection nodes, etc., etc. are the block matrices composed of the elements at the corresponding positions of the system total admittance matrix Y, and the order of each matrix is determined by the number of each type of node.

[0053] S2: Based on the block admittance matrix, use the Newton-Raphson method to perform system power flow calculation to obtain the voltage vector and current vector of each new energy station node; According to the corresponding structure of the system, input system parameters such as admittance values and power values of each node into the power flow calculation program, and use the Newton-Raphson method to solve the system power flow. The power flow calculation method is as follows.

[0054] (1) Input the initial data of the system. Such as the admittance values of each line, the active power and reactive power given by each load point and the new energy station as the PQ node, the voltage amplitude and phase given by the balance node, etc. And set the iteration number l = 0.

[0055] (2) Apply the given system parameter values and other initial values, and calculate the active power error from Equation (4) and the reactive power error. Judge whether the maximum error is less than the allowable value. If it is satisfied, go to step (6) to output the voltage of each node. If it is not satisfied, proceed to step (3).

[0056]

[0057] (4) In the formula, i and j represent the node numbers, is the active power of each node, is the reactive power of each node, is the voltage phase of each node, is the phase angle difference between nodes i and j, and n is the total number of nodes in the system.

[0058] (3) Substitute the numerical values of each parameter, and calculate the values of each element of the Jacobian matrix J from equations (6) and (7) to form the Jacobian matrix.

[0059] (5) In the formula, H, N, M, and L are the submatrix blocks that make up the Jacobian matrix.

[0060] 1) When the calculation methods of each element are as follows:

[0061]

[0062]

[0063] (6) 2) When the calculation methods of each element are as follows:

[0064]

[0065]

[0066] (7) (4) Solve the correction equation using equation (8) to obtain the correction amounts of the voltage amplitude and phase angle.

[0067] (8) (5) Calculate the corresponding corrected parameter values according to equation (9), that is, the new initial values, increment the iteration count by 1, and return to step (2) to continue execution.

[0068]

[0069] (9) (6) Output the calculation results

[0070] Use the Newton-Raphson method to solve the power flow of the system to obtain the voltage amplitude of each node and the voltage phase of each node thus forming the voltage of each node

[0071] Obtain the current based on the power flow results of the system , for use in the following equivalent simplification steps of the present invention. The present invention provides two methods for obtaining the required current through power flow calculation. Two methods.

[0072] Method 1: According to the voltage magnitudes of each node and the voltage phases of each node , thus forming the voltage of each node .

[0073] Substitute the obtained voltage values of each node into Equation (3), and the current can be obtained, for use in the following equivalent simplification steps of the present invention.

[0074] Method 2: Use the Newton-Raphson method to solve the system power flow. Similar to Method 1, the voltage of each node and the active power P and reactive power Q of each node are obtained. The method for calculating the current is as follows: (10) In the formula, the symbol is the conjugate operator, I is the node current, P is the node active power, Q is the node reactive power, U is the node voltage, and i = m + 1, m + 2,..., n are the corresponding node numbers.

[0075] S3: Use the Kron reduction method to perform matrix transformation on the node voltage equation. By eliminating the variables corresponding to the non-new energy power station nodes, an equivalent admittance matrix and an equivalent balanced node voltage are obtained. The equivalent admittance matrix retains the tie-line admittance between new energy power stations; Looking from each new energy power station side, the external power grid part is equivalent. According to the Kron reduction method, the original system node voltage equation is processed. First, the following changes are made to : (11) Substitute Equation (10) into Equation (3) to eliminate , and obtain: (12) Then, through the following two branches, different combined transformations are performed on : Branch 1:

[0076] (13) Let:

[0077] (14) Branch two:

[0078] (15) Let:

[0079] (16) By this method, the information of the admittance part of the original connection lines between stations is retained, and it has a certain structure-preserving characteristic. In addition, further process each matrix, and transform X equivalently into the form of. By this method, the equivalent balanced nodes of the system are extracted. E is the voltage matrix composed of the balanced nodes, and the calculation method of each element is described as follows.

[0080] Assume the matrix is order. According to the characteristics of the self-admittance and mutual-admittance in the total admittance matrix of the system, then the elements in are: (17) In the formula, both k and p indicate the position of the element in the matrix.

[0081] The voltages of each balanced node are: (18) Finally, the nodal voltage equation of the equivalent simplified system model is obtained as: (19) Thus, the admittance matrix of the equivalent simplified system 、 and the equivalent balanced node voltage E extracted can be output, realizing the multi-station external power grid equivalence considering structure preservation.

[0082] S4: Based on the equivalent admittance matrix and the equivalent balanced node voltage, construct an external power grid equivalent model with structure preservation, and retain the original topological structure between new energy stations.

[0083] By this method, the external power grid equivalence seen from the side of multiple new energy stations is realized, providing a new reliable method for the external power grid equivalence of the power system.

[0084] Specific implementation example The specific example of the present invention is described by using a 3-machine 9-node system. Number the system nodes. The 3 generator nodes are used as new energy stations and numbered as nodes 1, 2, and 3, and the remaining nodes are numbered in sequence. After numbering, the schematic diagram of the system topological structure is as Figure 3 shown, and the parameters of each system are already inFigure 3 It is marked that the initial parameters of each power generation station are shown in Table 1.

[0085] Table 1 Initial parameters of each power generation station

[0086] From the parameters of the 3-machine 9-node system, the total admittance matrix Y of the system can be obtained, and it is partitioned according to the number of each type of node to obtain each submatrix. Using the Newton-Raphson method to solve the system power flow according to the system parameters, the voltage vectors of each node are obtained, and further solved by the method described in step two , and the obtained results are shown in Table 2.

[0087] Table 2 The current values of each node in

[0088] Then, the system equivalent simplification is carried out. Through matrix transformation and comparing the results of the two branches, the output is as shown in Equation (20). (20) The matrix is obtained from Equation (17) as: (21) Furthermore, the corresponding voltage values are calculated and output from Equation (18) as shown in Equation (22). The amplitudes of the elements in E are: 1.1764, 1.1796, 1.1545. (22) Thus, a structure-preserving multi-station external power grid equivalence is realized, the original interconnection admittance between each station is retained, and the admittance between the equilibrium node and the output is and the equilibrium node voltage E, and the amplitudes of the elements in E are close to 1, verifying the effectiveness of the method of the present invention.

[0089] Embodiment 2: A structure-preserving multi-station external power grid equivalence system, the system includes: A partitioning module, configured to partition and number the new energy station nodes and other nodes in the network according to the topological structure of the multi-station power system, and generate a partitioned admittance matrix; A power flow calculation module, based on the partitioned admittance matrix, using the Newton-Raphson method to perform system power flow calculation to obtain the voltage vectors and current vectors of each new energy station node; The matrix transformation module uses the Kron reduction method to perform matrix transformation on the nodal voltage equation. By eliminating the variables corresponding to the non-new energy power station nodes, an equivalent admittance matrix and an equivalent balanced nodal voltage are obtained. The equivalent admittance matrix retains the admittance information of the tie lines between the new energy power stations; The equivalent model construction module constructs a structure-preserving equivalent model of the external power grid based on the equivalent admittance matrix and the equivalent balanced nodal voltage, retaining the original topological structure between the new energy power stations.

[0090] The block module generates a structured admittance matrix, and the matrix transformation module eliminates redundant variables based on Kron reduction. The two cooperate to reduce the operation dimension. The matrix transformation module retains the tie line admittance ( ), information and the equivalent balanced nodal voltage (E). The equivalent model construction module maintains the original topological structure, avoiding the structure distortion problem of the traditional equivalent method, and accurately characterizing the electrical interaction between the new energy power stations and the support function of the external power grid.

[0091] The specific functions of each module correspond to the foregoing method and will not be repeated here.

[0092] The above-described structure-preserving multi-station external power grid equivalent method and system are specific embodiments of the present invention, which have already reflected the substantial features and progress of the present invention. According to actual usage needs, under the inspiration of the present invention, equivalent modifications can be made to its shape, structure, etc., and all are within the protection scope of this solution.

Claims

1. A structure-preserving multi-station off-grid power grid equivalent method, characterized in that It includes the following steps: 1) According to the topological structure of the multi-station power system, number the new energy station nodes and other nodes in the network in blocks to form a block admittance matrix; 2) Based on the block admittance matrix, use the Newton-Raphson method to perform system power flow calculation to obtain the voltage vector and current vector of each new energy station node; 3) Use the Kron reduction method to perform matrix transformation on the node voltage equation. By eliminating the variables corresponding to non-new energy station nodes, obtain the equivalent admittance matrix and the equivalent balanced node voltage. The equivalent admittance matrix retains the tie-line admittance information between new energy stations; 4) Output the equivalent system node admittance matrix YS and the equivalent balanced node voltage E. Based on the equivalent admittance matrix and the equivalent balanced node voltage, construct a structure-preserving external power grid equivalent model, retaining the original topological structure information between new energy stations.

2. The multi-station off-grid equivalent method for structure maintenance according to claim 1, wherein: In step 1), the new energy station nodes are numbered as the first m nodes, and the remaining nodes are numbered as the last n - m nodes, where n is the total number of nodes and m is the number of new energy station nodes; the method for constructing the block admittance matrix is: The block admittance matrix includes the admittance sub-matrix between new energy power station nodes , the mutual admittance sub-matrix between new energy power stations and other nodes and , and the admittance sub-matrix between other nodes , and its form is: Among them, is a matrix of order m×m, is a matrix of order (n - m)×(n - m).

3. The structure-preserving multi-station off-grid power grid equivalent method according to claim 2, characterized in that: The power flow calculation in step 2) specifically includes: a) Input the initial system parameters, including line admittance, active and reactive power of the new energy station as a PQ node, voltage amplitude and phase of the balanced node; (b) Iteratively calculate the active power error and the reactive power error , and solve for the corrections of the voltage magnitude and phase angle through the Jacobian matrix; (c) When the active power error and the reactive power error are less than a preset threshold, output the voltage magnitudes and phases ; (d) Calculate the current of non-port nodes , which is implemented by any of the following methods: ⅰ) Substitute the nodal voltages obtained from the power flow calculation into the block nodal voltage equation , and directly solve ; ⅱ) According to the active power P, reactive power Q, and voltage U of the nodes in the power flow result, through the formula calculate the node current ; where the symbol is the conjugate operator, I is the node current, P is the active power of the node, Q is the reactive power of the node, U is the node voltage, and i = m + 1, m + 2, …, n are the corresponding node numbers.

4. A method for equivalent external power grid of multiple substations with structure maintenance according to claim 3, characterized in that: The specific method of the matrix transformation in step 3) is: First, through the formula Eliminate the node voltages of non-new energy power stations , and after substituting into the original node voltage equation, a simplified equation is obtained: Then, different combinatorial transformations are performed through the following two branches respectively: ​ Branch 1: Branch 2: Among them, is an equivalent admittance matrix containing tie-line admittance information; Next, extract the equivalent equilibrium node voltage E and the corresponding admittance parameters , and finally obtain the equivalent model equation: .

5. A method for equivalent external power grid of multiple substations with structure maintenance according to claim 4, characterized in that: The equivalent balanced node voltage E is calculated by the formula where , is the element in the k-th row and p-th column of the equivalent admittance matrix ; is the k-th element of the equivalent current term X of the external power grid obtained by power flow calculation; through the above calculation, the error between the amplitude of and the amplitude of the node voltage of the new energy power station does not exceed the preset threshold; Then compare the average of the modulus values of each element in the equivalent balanced node voltage E obtained from the two branches, and select a set of branch results close to 1 as the output result.

6. A structure-preserving multi-station off-grid equivalent system, characterized in that It includes: A block module, which is used to number the new energy station nodes and other nodes in the network in blocks according to the topological structure of the multi-station power system to generate a block admittance matrix; A power flow calculation module, which based on the block admittance matrix, uses the Newton-Raphson method to perform system power flow calculation to obtain the voltage vector and current vector of each new energy station node; A matrix transformation module, which uses the Kron reduction method to perform matrix transformation on the node voltage equation. By eliminating the variables corresponding to non-new energy station nodes, obtain the equivalent admittance matrix and the equivalent balanced node voltage. The equivalent admittance matrix retains the tie-line admittance between new energy stations; An equivalent model construction module, which based on the equivalent admittance matrix and the equivalent balanced node voltage, constructs a structure-preserving external power grid equivalent model, retaining the original topological structure between new energy stations.

7. A structure-maintained multi-station off-grid equivalent system according to claim 6, characterized in that: In the block module, the new energy station nodes are numbered as the first m nodes, and the remaining nodes are numbered as the last n - m nodes, where n is the total number of nodes and m is the number of new energy station nodes; the block module includes: A susceptance sub-matrix generation unit between nodes of a new energy power station generates an m×m order matrix ; Mutual admittance sub-matrix generation unit, which generates the mutual admittance sub-matrix between the new energy power station and other nodes and ; An admittance submatrix generation unit between other nodes generates an (n - m)×(n - m) order matrix ; The form of the block admittance matrix is as follows: 。 8. A structure-maintained multi-station off-grid equivalent system according to claim 7, characterized in that: The power flow calculation module includes: A parameter input interface, which is used to receive the initial system parameters, including line admittance, active and reactive power of the new energy station as a PQ node, voltage amplitude and phase of the balanced node; An iterative calculation unit iteratively calculates the active power error based on the input parameters and the reactive power error , and solves the correction amounts of the voltage amplitude and phase angle through the Jacobian matrix; Error judgment unit, when max(| |, | |) < , output the voltage amplitude and phase of each node, being a preset error threshold; The current calculation unit includes a first current calculation sub-module and a second current calculation sub-module. The first current calculation sub-module substitutes the voltage amplitude and phase into the nodal voltage equation to calculate the current vector ; The second current calculation sub-module is used to calculate the nodal current according to the nodal active power P, reactive power Q and voltage U in the power flow result through the formula to calculate the nodal current ; In the formula, the symbol is the conjugate operator, I is the nodal current, P is the nodal active power, Q is the nodal reactive power, U is the nodal voltage, and i = m + 1, m + 2, …, n are the corresponding node numbers.

9. A structure-maintained multi-station off-grid equivalent system according to claim 8, characterized in that: The matrix transformation module includes: Voltage elimination unit, which eliminates the node voltage of non-new energy power stations through the formula Eliminate the node voltage of non-new energy power stations ; An equation simplification unit, which substitutes the eliminated result into the original node voltage equation to generate a simplified equation: Branch 1: Branch 2: The equivalent parameter extraction unit extracts the equivalent balanced node voltage E and admittance parameters from the simplified equation , and generates an equivalent model equation: Among them, is the equivalent admittance matrix for retaining the admittance of the tie line.

10. A structure-maintained multi-station off-grid equivalent system according to claim 9, characterized in that: In the equivalent parameter extraction unit, the calculation module of the equivalent balanced node voltage E uses the formula: Calculation, where , is the equivalent admittance matrix and the element in the k-th row and p-th column of; is the k-th element of the equivalent current term X of the external power grid obtained by power flow calculation; through the above calculation, the amplitude error from the node voltage amplitude of the new energy power station does not exceed the preset threshold; finally, compare the average values of the moduli of the elements in the equivalent balanced node voltage E obtained from the two branches, and select the branch result closer to 1 as the output result.

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