Vectorization Jacobian matrix construction method and system based on node voltage equation

Abstract

The invention discloses a vectorized Jacobian matrix construction method and system based on a node voltage equation, and relates to the field of power systems. At present, the calculation amount of Jacobian matrix construction is large, and the applicability is poor. The method comprises the following steps: establishing a corresponding system model according to a target power system structure, and establishing a system admittance matrix and a node voltage equation in combination with system parameters; then, on the basis of a system node voltage equation, mathematical derivation is carried out, a system power flow Jacobian matrix structure is obtained, and vectorization is realized in the construction process; and finally, calculating system power flow through a Newton-Raphson method, and substituting a calculation result to obtain a numerical system jacobian matrix in a corresponding scene. According to the technical scheme, the power flow Jacobian matrix construction method for realizing process vectorization is provided through mathematical derivation on the basis of the node voltage equation, so that a new practical method is provided for construction of the power flow Jacobian matrix.

Description

Technical Field

[0001] The present invention relates to the field of power systems, and particularly to a method and system for constructing a vectorized Jacobian matrix based on nodal voltage equations. Background Art

[0002] The stability, reliability, and economy of power systems, as the core objectives of modern power engineering, highly rely on accurate modeling and rapid calculation of the system operating state. In this process, the power flow Jacobian matrix, as a fundamental mathematical tool for power system power flow calculation, static stability analysis, and nonlinear equation solving, directly affects the accuracy of system state estimation, the efficiency of optimal dispatch, and the real-time performance of instability risk warning. Especially in the context of high penetration of new energy and complex power grid structures, the efficient construction and in-depth analysis of the Jacobian matrix have become the key technical bottlenecks for the safe and stable operation of large power grids.

[0003] Currently, the construction of the Jacobian matrix mostly relies on the differential transformation method, calculating the partial derivatives of each component with respect to the independent variables one by one and combining them to form the power flow Jacobian matrix. This method is simple and intuitive, but has a large amount of calculation, especially when dealing with large-scale systems, the calculation efficiency is low. With the development of artificial intelligence technology, a data-driven method for constructing the Jacobian matrix has been proposed. This method does not require line information and is not affected by changes in the network topology structure, but its applicability is still poor when dealing with different models. At the same time, The above methods all focus on the numerical generation of the Jacobian matrix, while ignoring the correlation between its internal structural characteristics and physical meanings. For example, the Jacobian matrix constructed by traditional methods is stored in the form of discrete elements, making it difficult to directly extract the coupling rules between active / reactive power sensitivities, and it also cannot efficiently support in-depth applications such as matrix eigenvalue analysis and weak node identification, resulting in a waste of resources of "constructed but not used". In addition, the existing technology has insufficient vectorization processing of the matrix construction process, restricting the application of parallel computing and hardware acceleration technologies, and it is difficult to meet the real-time requirements of UHV AC / DC hybrid power grids.

[0004] To address the above problems, there is an urgent need for a method for constructing a Jacobian matrix that combines high efficiency, scalability, and structural analyzability. Summary of the Invention

[0005] 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 constructing a vectorized Jacobian matrix based on nodal voltage equations, aiming to improve the calculation efficiency and facilitate subsequent analysis of structural characteristics. To this end, the present invention adopts the following technical solutions.

[0006] A method for constructing a vectorized Jacobian matrix based on nodal voltage equations, comprising the following steps: 1) Construct a target power system model, including eliminating the passive connection nodes in the system by Kron reduction method according to the target power system structure, and using Thevenin equivalent method to equivalent the external power grid as an infinite power grid to generate a simplified equivalent circuit model; 2) Based on the simplified equivalent circuit model, establish a system admittance matrix, and form a node voltage equation according to the product relationship between the node current vector, the admittance matrix, and the node voltage vector; 3) Convert the node voltage equation into a node injection complex power equation, and replace the product term of voltage amplitude and phase angle with the matrix multiplication of a diagonal matrix and a conjugate vector through vectorized matrix operation to obtain a vectorized expression of complex power; 4) Convert the complex power equation into a real power flow equation in polar coordinate system, take partial derivatives of the voltage amplitude vector and the phase angle vector respectively, and construct a block structure of the Jacobian matrix. The block structure includes the following four sub-matrices: the partial derivative matrix of active power with respect to phase angle, the partial derivative matrix of active power with respect to voltage amplitude, the partial derivative matrix of reactive power with respect to phase angle, and the partial derivative matrix of reactive power with respect to voltage amplitude; 5) Use the Newton-Raphson method to iteratively solve the power flow of the system, and substitute the converged voltage amplitude and phase angle into the block structure expression of the Jacobian matrix to generate a numerical Jacobian matrix.

[0007] Starting from the system node voltage equation, this technical solution realizes the vectorized reconstruction of the matrix construction process through mathematical derivation, breaks through the efficiency bottleneck of traditional methods, and retains the physical characteristic information of the matrix, providing direct support for subsequent stability analysis and optimal control. Through model reduction, vectorized operations, and block matrix construction, while ensuring accuracy, it significantly improves the calculation efficiency and structural analyzability of the Jacobian matrix, combining engineering practicality and theoretical rigor, and providing an efficient and reliable basic tool for real-time analysis, optimal control, and AI integration applications of power systems. Specifically, by replacing the element-by-element product of voltage amplitude and phase angle with the matrix multiplication of a diagonal matrix and a conjugate vector, the redundant operation of calculating element by element in traditional methods is avoided. Vectorized processing can make full use of the parallelism of matrix operations, especially in large-scale power systems, effectively improving the calculation speed. By using the Kron reduction method to eliminate passive connection nodes and the Thevenin equivalent external power grid, the system model is greatly simplified, the dimension of the admittance matrix is reduced, redundant calculations are avoided, and the electrical characteristics of key nodes are retained, which is applicable to various scenarios (such as power flow calculation, short-circuit analysis). Vectorized matrix operations replace traditional element-by-element partial derivative calculations, and utilize the parallel calculation characteristics of matrices to reduce the computational complexity. The Jacobian matrix is constructed in blocks (submatrices of the partial derivatives of active / reactive power with respect to voltage amplitude and phase angle), retaining the physical coupling characteristics of the matrix, facilitating the direct extraction of sensitivity coefficients or the analysis of matrix eigenvalues, and providing structured support for stability assessment; by generating the Jacobian matrix through a block structure, the matrix is decomposed into four submatrices, reducing the dimension of a single matrix, and reducing memory occupancy and computational complexity. Based on the mathematical derivation of the node voltage equation, it is ensured that the matrix elements strictly correspond to the power grid topology and parameters, avoiding the problem of model inaccuracy caused by training data deviation in data-driven methods, and at the same time avoiding the truncation error introduced by traditional numerical difference methods, improving the calculation accuracy. The Newton-Raphson method iterative solution is combined with the vectorized Jacobian matrix, and the symmetry of the matrix block structure is used to accelerate the iterative convergence, avoiding the oscillation or non-convergence problem caused by matrix ill-conditioning in traditional methods. By constructing the Jacobian matrix through the real power flow equation in the polar coordinate system, the cumulative error of complex number operations is avoided, and the numerical stability is better than the method of directly dealing with complex number equations. Avoiding the artificial partial derivative derivation in traditional differential transformation methods reduces the code implementation complexity and the risk of human errors. In addition, the block matrix structure is convenient for subsequent function expansion. For example, the voltage stability margin is evaluated through the minimum singular value of the Jacobian matrix; the sensitivity coefficients of active / reactive power with respect to voltage are extracted to guide generator voltage regulation or capacitor switching; the eigenvalues of the Jacobian matrix are used as the input of a deep learning model to predict the system stability boundary.

[0008] As a preferred technical means: The construction of the system admittance matrix in step 2) is specifically as follows: Assume that the system has a total of n nodes, and the dimension of the admittance matrix Y is n×n. The system admittance matrix Yas follows: (1) In the formula, For Node i With Node j The admittance value between When , it indicates the mutual admittance between nodes; When , it indicates the self-admittance of the node; Then the node voltage equation of the system is obtained as: (2) In the formula, is the node current vector, is the node voltage vector.

[0009] This technical solution realizes the precise mathematical representation of the grid topology and parameters through the systematic construction of the admittance matrix, which has both physical intuitiveness, computational efficiency and engineering practicality, and provides a reliable basic model for subsequent power flow calculation, stability analysis and optimization control, especially in large-scale complex power grid scenarios. Specifically, by constructing an admittance matrix Y with a dimension of n×n, the connection relationship of all nodes in the system is completely covered, ensuring the comprehensive mapping of the grid topology and parameters, and avoiding the omission of key node or branch information. The admittance matrix Y serves as the basic input for power flow calculation, short-circuit analysis, and stability evaluation, ensuring the mathematical consistency of the entire analysis process and reducing intermediate conversion errors.

[0010] As a preferred technical means: the complex power equation in step 3) is constructed as follows: multiply the two ends of the node voltage equation by the diagonal matrix , and the complex power equation of each node is obtained: (3) In the formula, the symbol It represents conjugate transpose for matrices and conjugate for vectors; S Inject complex power column vector into the node.

[0011] Using diagonal matrix multiplication , replacing element-by-element scalar operations, reducing the complexity of complex power calculations, especially suitable for rapid modeling of large-scale power grids. Complex power equations in matrix form naturally support parallel computing and can make full use of GPU or distributed computing resources to accelerate the solution. Complex power equations are directly generated through matrix operations, avoiding the tedious derivation of manually expanding node power equations in traditional methods and reducing the risk of human error. Complex conjugate operations and The data are processed uniformly in matrix form to avoid rounding errors in element-by-element operations.

[0012] As a preferred technical means: the block matrix construction in step 4) specifically includes: Convert the node voltage vector in complex form to polar coordinate system representation to obtain the Jacobian matrix of the power flow equation in real number form. Let: (4) In the formula, U and θ are order voltage amplitude and phase angle vectors. Denote the element-wise exponential operation on the phase angle vector θ, where j is the imaginary unit; The vector product of represents the Hadamard product between vectors; (5) In the formula, the derivatives of the complex voltage with respect to its phase and amplitude are defined as follows: (6) In the formula: j is the imaginary unit; Substitute Equation (2) and Equation (6) into Equation (5), we can get: (7) Among them, let the coupling matrix ; According to Equation (7), the Jacobian matrix J in real number form can be obtained: (8) In the formula, Re is to take the real part of each number, and Im is to take the imaginary part of each number; Let the complex power S = P +j Q , then the Jacobian matrix J can be re-expressed as: (9) In the formula, P is the column vector of nodal injected active power, Q is the column vector of nodal injected reactive power, Thus, the construction of the power flow Jacobian matrix with vectorized implementation process is obtained.

[0013] The block matrix construction separates the sensitivities of active power to phase angle and reactive power to voltage amplitude, intuitively reflecting the power-voltage coupling characteristics and providing a direct basis for stability analysis. Through Hadamard product and diagonal matrix operations, the partial derivative calculation is upgraded from element-wise scalar operation to matrix-level vectorized operation, with several times improvement in calculation efficiency and support for sparse matrix optimization. Introduce the coupling matrix Γ, and combine the network parameters ( Y S ) with the operating state (U , θ ), decouple, avoid repeated calculation of the admittance matrix, and reduce memory occupancy. The real-valued Jacobian matrix in polar coordinates circumvents the numerical oscillation problem in complex number operations, improves the convergence of the Newton-Raphson method, and is especially suitable for scenarios of high impedance ratio or heavily loaded power grids.

[0014] As a preferred technical means: after generating the numerical Jacobian matrix, it further includes any one of the following: 6) Perform static stability analysis of the power system based on the numerical Jacobian matrix, including: calculating the minimum singular value or eigenvalue of the Jacobian matrix to evaluate the voltage stability margin of the current operating section; locating the system instability mode according to the sign change of the eigenvalue, and identifying weak nodes or key transmission lines; 6) Construct a sensitivity matrix based on the numerical Jacobian matrix for optimizing dispatch decisions, including: extracting the sensitivity coefficients of the active / reactive power of nodes in the Jacobian matrix with respect to the voltage amplitude and phase; combining with the optimization objective function to generate preventive control strategies to adjust the generator output or reactive power compensation equipment; 6) Input the numerical Jacobian matrix into a deep learning model to train the mapping relationship between the power grid operating state and the stability boundary, including: using the eigenvalue of the Jacobian matrix, node voltage, and power data as input features; outputting the prediction results of the load growth limit or fault tolerance ability under the critical stable state of the system.

[0015] This technical solution can upgrade the Jacobian matrix from a basic mathematical tool to an intelligent analysis core engine, improve the active defense ability, economic operation level, and digital transformation speed of the power grid, and become a key technical support for building a new type of power system.

[0016] Another object of the present invention is to provide a vectorized Jacobian matrix construction system based on node voltage equations, and the system includes: A target power system model construction module, used to eliminate the passive connection nodes in the system by the Kron reduction method according to the target power system structure, and use the Thevenin equivalent method to equivalent the external power grid to an infinite power grid to generate a simplified equivalent circuit model; An admittance matrix generation module, connected to the target power system model construction module, used to construct a system admittance matrix based on the simplified equivalent circuit model, and form a node voltage equation according to the product relationship between the node current vector, the admittance matrix, and the node voltage vector; A complex power conversion module, connected to the admittance matrix generation module, used to convert the node voltage equation into a node injection complex power equation, and replace the product term of the voltage amplitude and phase angle with the matrix multiplication of a diagonal matrix and a conjugate vector through vectorized matrix operations to obtain a vectorized expression of complex power; The Jacobian matrix construction module, connected to the complex power conversion module, is used to convert the complex power equation into a real power flow equation in the polar coordinate system, respectively take partial derivatives of the voltage amplitude vector and the phase angle vector, and construct the block structure of the Jacobian matrix. The block structure includes the following four sub-matrices: the partial derivative matrix of active power with respect to phase angle, the partial derivative matrix of active power with respect to voltage amplitude, the partial derivative matrix of reactive power with respect to phase angle, and the partial derivative matrix of reactive power with respect to voltage amplitude; The power flow solution module, connected to the Jacobian matrix construction module, is used to iteratively solve the system power flow by the Newton-Raphson method, and substitute the converged voltage amplitude and phase angle into the block structure expression of the Jacobian matrix to generate a numerical Jacobian matrix.

[0017] Through the modular architecture, vectorized calculation and physical model drive, the high efficiency, high precision and strong scalability of the Jacobian matrix construction are realized. At the same time, it provides the full-scenario coverage ability from basic analysis to intelligent decision-making, and is the core technology platform to support the real-time monitoring, optimal operation and security defense of the new power system.

[0018] As a preferred technical means: the admittance matrix generation module is specifically configured as follows: assuming that the system has a total of n nodes and the dimension of the admittance matrix Y is n×n, the system admittance matrix Y is constructed as follows: (1) In the formula, is the admittance value between node i and node j . When , it represents the mutual admittance between nodes; when , it represents the self-admittance of this node; The admittance matrix generation module further generates the node voltage equation: (2) In the formula, is the node current vector, is the node voltage vector.

[0019] The admittance matrix generation module realizes the efficient and high-precision characterization of the power grid topology through systematic modeling and sparse optimization, and has both engineering practicability and scalability, providing a reliable basis for power flow calculation, stability analysis and intelligent decision-making, and is the core technical component of the digitalization of the power system.

[0020] As a preferred technical means: the complex power conversion module is specifically configured as follows: multiply both ends of the node voltage equation by the diagonal matrix to obtain the complex power equation of each node: (3) In the formula, the symbol The conjugate transpose is denoted for a matrix and the conjugate is denoted for a vector; S is the column vector of complex power injected at nodes.

[0021] As a preferred technical means: The Jacobian matrix construction module includes the following sub-modules: The polar coordinate conversion sub-module is used to convert the node voltage vector in complex form into polar coordinate system representation, and let: (4) In the formula, U and θ are order voltage amplitude and phase angle vectors, represents the element-by-element exponential operation on the phase angle vector θ, and j is the imaginary unit; The vector product of represents the Hadamard product between vectors; (5) In the formula, the derivatives of the complex voltage with respect to its phase and amplitude are defined as: (6) In the formula: j is the imaginary unit; The Jacobian matrix generation sub-module is used to substitute Equation (2) and Equation (6) into Equation (5) to obtain: (7) Among them, let the symbol ; According to Equation (7), the real-valued Jacobian matrix J is obtained: (8) In the formula, Re is to take the real part of each number, and Im is to take the imaginary part of each number; Let the complex power S = P + j Q , then the Jacobian matrix J is re-expressed as: (9) In the formula, P is the column vector of active power injected at nodes, Q is the column vector of reactive power injected at nodes, Thus, the construction of the power flow Jacobian matrix with the realization process vectorized is obtained.

[0022] Through vectorized complex power conversion and block Jacobi matrix construction, this technical solution achieves a step - up improvement in computational efficiency and enhanced numerical stability while ensuring physical interpretability. It provides an efficient and reliable basic tool and is a core technical breakthrough for supporting the secure and economic operation of new - type power systems.

[0023] As an optimal technical measure: It also includes any one of the following functional modules: A static stability analysis module, which is used to calculate the minimum singular value or eigenvalue based on the numerical Jacobi matrix, evaluate the voltage stability margin of the current operating section, and locate the system instability mode according to the sign change of the eigenvalue to identify weak nodes or key transmission lines; An optimal dispatch decision - making module, which is used to extract the sensitivity coefficients of nodal active / reactive power to voltage amplitude and phase based on the numerical Jacobi matrix, generate preventive control strategies in combination with the optimization objective function, and adjust the generator output or reactive power compensation equipment; A deep - learning prediction module, which is used to input the numerical Jacobi matrix into a deep - learning model, train the mapping relationship between the power grid operation state and the stability boundary, and use the Jacobi matrix eigenvalue, nodal voltage, and power data as input features to output the prediction results of the load growth limit or fault tolerance ability under the critical stable state of the system.

[0024] This technical solution can upgrade the Jacobi matrix from a basic mathematical tool to the core of power grid intelligent analysis, effectively improving the stability, economy, and digital level of the system, and is a key technical pillar for building a new - type power system.

[0025] Beneficial effects: This technical solution simplifies the power grid model through Kron reduction method and Thevenin equivalence, significantly reducing the computational complexity; uses vectorized matrix operations to replace element - by - element operations to improve computational efficiency; constructs the Jacobi matrix by block in the polar coordinate system, clearly separating the sensitivity of active / reactive power to voltage amplitude and phase angle, with clear physical meaning and supporting parallel computing, strong numerical stability, and combines the Newton - Raphson method to accelerate convergence. At the same time, it provides a high - precision and highly compatible mathematical basis for static stability assessment, optimal dispatch, and AI prediction, significantly improving the real - time performance, economy, and intelligence level of power grid analysis.

[0026] Starting from the system nodal voltage equation, this technical solution realizes the vectorized reconstruction of the matrix construction process through mathematical derivation, breaks through the efficiency bottleneck of traditional methods, and retains the physical characteristic information of the matrix, providing direct support for subsequent stability analysis and optimal control. Description of the drawings

[0027] Figure 1 It is a partial schematic diagram of an AC power grid.

[0028] Figure 2 This is the equivalent circuit diagram of the power grid of the present invention.

[0029] Figure 3 This is the flow chart of the present invention. Specific embodiments

[0030] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings of the specification.

[0031] Embodiment 1: As Figure 3 shown, this embodiment includes the following steps: 1. Construct a target power system model Taking Figure 1 the partial schematic diagram of the AC power grid as an example for illustration, Figure 1 it includes a local AC network, a new energy power station, a synchronous generator, etc. Among them, the AC network contains loads, passive connection nodes, etc. When analyzing the system power flow or the static voltage stability of the system, etc., it is necessary to construct a system Jacobian matrix. To reduce the complexity of the calculation, first simplify the system structure. The Kron reduction method can be used to eliminate the passive connection nodes in the system, and the external power grid is equivalent to an infinite power grid by using Thevenin equivalence. The equivalent circuit after system simplification is as Figure 2 shown.

[0032] Based on the above system equivalent circuit model structure and parameters, assuming that the system has a total of n nodes, construct a system admittance matrix Y as follows: (1) In the formula, is the admittance value between the corresponding nodes, i, j is the node number, when, it represents the mutual admittance between nodes; when, it represents the self-admittance of this node.

[0033] Furthermore, the system node voltage equation is obtained as: (2) In the formula, I S is the n ×1 order matrix composed of the currents of each node of the system, U S is the n ×1 order matrix composed of the voltages of each node of the system.

[0034] 2. Construction of the vectorized Jacobian matrix Next, construct the power flow equation of the local power grid according to the equivalent circuit. Multiply both ends of the equivalent circuit formula (2) by respectively, and the complex power of each node can be obtained, as shown in formula (3).

[0035] (3) In the formula, the symbol represents the conjugate transpose for a matrix and the conjugate for a vector. The symbol diag represents taking the diagonal matrix, S is the column vector composed of the complex power injection values at each node.

[0036] By changing the rectangular coordinate system in Equation (3) to the polar coordinate system, the Jacobian matrix of the traditional real - type power flow equation can be obtained. Let: (4) In the formula, U and θ are order voltage amplitude and phase angle vectors. The vector product of

[0037] represents the Hadamard product between vectors. The Hadamard product between vectors represents the element - by - element product of the corresponding elements. and Let Equation (3) be differentiated with respect to the (5) In the formula, the derivatives of the complex voltage with respect to its phase and amplitude are defined as follows (j is the imaginary unit): (6) Substituting Equation (2) and Equation (6) into Equation (5), we can get: (7) Among them, let the symbol .

[0038] According to Equation (7), the real - type Jacobian matrix J is obtained: (8) In the formula, Re represents taking the real part of each number, and Im represents taking the imaginary part of each number.

[0039] Observing Equations (7) and (8), it can be seen that there is a correlation among the four block matrices in the Jacobian matrix. To further analyze the structural characteristics of the Jacobian matrix, let the complex power S = P +j Q , then the Jacobian matrix J can be re - expressed as: (9) In the formula P is the column vector of the active power injection at the node, Q is the column vector of the reactive power injection at the node. Thus, the construction of the power flow Jacobian matrix with the realization process vectorized is obtained.

[0040] Finally, the Newton-Raphson method is used to solve the power flow of the system, and substituting the parameter results into Equation (9) can obtain the corresponding Jacobian matrix.

[0041] Specific implementation example The specific example of the present invention is described with a 3-machine system. The system nodes are numbered. The 3 generator nodes are numbered as Nodes 1, 2, and 3, and the remaining nodes are numbered in sequence. The impedance parameters of each line in the system are shown in Table 1.

[0042] Table 1 Impedance parameters of each line

[0043] Relying on the line parameter data, the system Jacobian matrix is constructed according to the method proposed in the present invention as follows: (10) To verify the effectiveness of the method proposed in the present invention, a comparison is made with the traditional method for calculating the Jacobian matrix. The traditional method is as follows: (11) In the formula, H , N , M , L are the sub-matrix blocks that make up the Jacobian matrix, represents the Jacobian matrix constructed by the traditional method.

[0044] 1) When , the calculation methods of each element are as follows:

[0045]

[0046]

[0047] (12) In the formula, P i is the active power of each node, Q i is the reactive power of each node, represents the conductance value of the corresponding line, represents the susceptance value of the corresponding line, is the voltage amplitude of Node i , is the voltage amplitude of Node j , is the voltage amplitude of Node i, jPhase angle difference between them.

[0048] 2) When , the calculation methods of each element are as follows:

[0049]

[0050]

[0051] (13) In the formula, Σ is the summation symbol.

[0052] Based on the same line model as above, the Jacobian matrix obtained by the traditional method is: (14) Compared with the matrix obtained by the method of the present invention, it can be seen that the Jacobian matrices obtained by the method of the present invention and the traditional method are the same, which proves the accuracy of the method proposed by the present invention. However, the method proposed by the present invention realizes the vectorization of the construction process, providing a basis for further deconstructing the Jacobian matrix or further transformation.

[0053] Embodiment 2: A vectorized Jacobian matrix construction system based on node voltage equations, comprising: A target power system model construction module, configured to eliminate passive connection nodes in the system by Kron reduction method according to the structure of the target power system, and equivalent the external power grid to an infinite power grid by Thevenin equivalent method to generate a simplified equivalent circuit model; An admittance matrix generation module, connected to the target power system model construction module, configured to construct a system admittance matrix based on the simplified equivalent circuit model, and form a node voltage equation according to the product relationship between the node current vector, the admittance matrix, and the node voltage vector; A complex power conversion module, connected to the admittance matrix generation module, configured to convert the node voltage equation into a node injected complex power equation, and replace the product term of the voltage amplitude and phase angle with the matrix multiplication of a diagonal matrix and a conjugate vector through vectorized matrix operations to obtain a vectorized expression of complex power; A Jacobian matrix construction module, connected to the complex power conversion module, configured to convert the complex power equation into a real power flow equation in polar coordinates, respectively obtain partial derivatives of the voltage amplitude vector and the phase angle vector, and construct a block structure of the Jacobian matrix, the block structure including the following four sub-matrices: the partial derivative matrix of active power with respect to phase angle, the partial derivative matrix of active power with respect to voltage amplitude, the partial derivative matrix of reactive power with respect to phase angle, and the partial derivative matrix of reactive power with respect to voltage amplitude; A power flow solution module, connected to the Jacobian matrix construction module, is used to iteratively solve the power flow of the system by the Newton-Raphson method, and substitute the converged voltage amplitude and phase angle into the block structure expression of the Jacobian matrix to generate a numerical Jacobian matrix.

[0054] In this embodiment, through a modular architecture, vectorized calculation, and physical model drive, the high efficiency, high precision, and strong scalability of Jacobian matrix construction are achieved. At the same time, it provides the full-scenario coverage ability from basic analysis to intelligent decision-making, and is the core technology platform for supporting the real-time monitoring, optimal operation, and security defense of the new power system.

[0055] It can be understood that the detailed function implementation of the above modules can be referred to the introduction in the foregoing method embodiments, and no other elaboration will be made here.

[0056] The above-described method and system for constructing a vectorized Jacobian matrix based on node voltage equations 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., which are all within the protection scope of this solution.

Claims

1. A method for constructing a vectorized Jacobian matrix based on node voltage equations, characterized in that It includes the following steps: 1) Construct a target power system model, including eliminating passive connection nodes in the system by the Kron reduction method according to the target power system structure, and equivalenting the external power grid to an infinite power grid by the Thevenin equivalent method to generate a simplified equivalent circuit model; 2) Based on the simplified equivalent circuit model, establish a system admittance matrix, and form a node voltage equation according to the product relationship between the node current vector, the admittance matrix, and the node voltage vector; 3) Convert the node voltage equation into a node injection complex power equation, and replace the product term of the voltage amplitude and phase angle with the matrix multiplication of a diagonal matrix and a conjugate vector through vectorized matrix operations to obtain a vectorized expression of the complex power; 4) Convert the complex power equation into a real power flow equation in the polar coordinate system, respectively take partial derivatives of the voltage amplitude vector and the phase angle vector, and construct a block structure of the Jacobian matrix. The block structure includes the following four sub-matrices: the partial derivative matrix of active power with respect to the phase angle, the partial derivative matrix of active power with respect to the voltage amplitude, the partial derivative matrix of reactive power with respect to the phase angle, and the partial derivative matrix of reactive power with respect to the voltage amplitude; 5) Use the Newton-Raphson method to iteratively solve the power flow of the system, and substitute the converged voltage amplitude and phase angle into the block structure expression of the Jacobian matrix to generate a numerical Jacobian matrix.

2. The vectorized Jacobi matrix construction method based on the nodal voltage equation according to claim 1, characterized in that: The construction of the system admittance matrix in step 2) is specifically as follows: Assume that the system has a total of n nodes, and the dimension of the admittance matrix Y is n×n. The system admittance matrix Y is constructed as follows: （1） Wherein, is the admittance value between node i and node j ; when , it represents the mutual admittance between nodes; when , it represents the self-admittance of this node Furthermore, the node voltage equation of the system is obtained as: （2） In the formula, is the node current vector, is the node voltage vector.

3. A method for constructing a vectorized Jacobian matrix based on the nodal voltage equation according to claim 2, characterized in that: The construction of the complex power equation in step 3) is specifically as follows: Multiply both ends of the node voltage equation by the diagonal matrix , and the complex power equations of each node are obtained: （3） where the symbol represents conjugate transpose for matrices and conjugate for vectors; S Inject a complex power column vector into the node.

4. A method for constructing a vectorized Jacobian matrix based on nodal voltage equations according to claim 3, characterized in that: The specific construction of the block matrix in step 4) includes: Convert the complex node voltage vector into a polar coordinate system representation to obtain a real power flow equation Jacobian matrix, and let: （4） In the formula, U , θ are order voltage amplitude and phase angle vectors, represents element-wise exponentiation of the phase angle vector θ, where j is the imaginary unit; The vector product of represents the Hadamard product between vectors; Take partial derivatives of the complex power equation with respect to the voltage amplitude vector and the phase angle vector respectively, （5） In the formula, the derivatives of the complex voltage with respect to its phase and amplitude are defined as follows: （6） In the formula: j is the imaginary unit; Substitute formula (2) and formula (6) into formula (5), and we can get: （7） Among them, let the coupling matrix ; The real-valued Jacobian matrix can be obtained according to Equation (7). J : （8） In the formula, Re is to take the real part of each number, and Im is to take the imaginary part of each number; Let the complex power S = P +j Q , then the Jacobian matrix J is re-expressed as: （9） wherein, P is the column vector of the active power injected into the nodes, Q is the column vector of the reactive power injected into the nodes, Thus, the construction of the vectorized power flow Jacobian matrix of the implementation process is obtained.

5. A method for constructing a vectorized Jacobian matrix based on the nodal voltage equation according to claim 1, characterized in that: After generating the numerical Jacobian matrix, it further includes any one of the following: 6) Conduct static stability analysis of the power system based on the numerical Jacobian matrix, including: calculating the minimum singular value or eigenvalue of the Jacobian matrix, and evaluating the voltage stability margin of the current operating section; locating the system instability mode according to the sign change of the eigenvalue, and identifying weak nodes or key transmission lines; 6) Construct a sensitivity matrix based on the numerical Jacobian matrix for optimizing dispatching decisions, including: extracting the sensitivity coefficients of node active / reactive power with respect to voltage amplitude and phase in the Jacobian matrix; combining the optimization objective function to generate a preventive control strategy to adjust generator output or reactive power compensation equipment; 6) Input the numerical Jacobian matrix into a deep learning model to train the mapping relationship between the power grid operating state and the stability boundary, including: using the Jacobian matrix eigenvalue, node voltage, and power data as input features; outputting the prediction result of the load growth limit or fault tolerance ability under the critical stable state of the system.

6. A vectorized Jacobian matrix construction system based on nodal voltage equations, characterized in that, It includes: A target power system model construction module, which is used to eliminate passive connection nodes in the system by the Kron reduction method according to the target power system structure, and use the Thevenin equivalent method to equivalent the external power grid to an infinite power grid, so as to generate a simplified equivalent circuit model; An admittance matrix generation module, connected to the target power system model construction module, is used to construct a system admittance matrix based on the simplified equivalent circuit model, and form a node voltage equation according to the product relationship between the node current vector, the admittance matrix, and the node voltage vector; A complex power conversion module, connected to the admittance matrix generation module, is used to convert the node voltage equation into a node injection complex power equation, and replace the product term of the voltage amplitude and phase angle with the matrix multiplication of a diagonal matrix and a conjugate vector through vectorized matrix operations to obtain a vectorized expression of complex power; A Jacobian matrix construction module, connected to the complex power conversion module, is used to convert the complex power equation into a real power flow equation in polar coordinates, respectively take partial derivatives of the voltage amplitude vector and the phase angle vector, and construct a block structure of the Jacobian matrix. The block structure includes the following four sub-matrices: the partial derivative matrix of active power with respect to phase angle, the partial derivative matrix of active power with respect to voltage amplitude, the partial derivative matrix of reactive power with respect to phase angle, and the partial derivative matrix of reactive power with respect to voltage amplitude; A power flow solution module, connected to the Jacobian matrix construction module, is used to iteratively solve the system power flow by the Newton-Raphson method, and substitute the converged voltage amplitude and phase angle into the block structure expression of the Jacobian matrix to generate a numerical Jacobian matrix.

7. A vectorized Jacobian matrix construction system based on node voltage equations according to claim 6, characterized in that: The admittance matrix generation module is specifically configured as follows: Assume that the system has a total of n nodes, and the dimension of the admittance matrix Y is n×n. The system admittance matrix Y is constructed as follows: （1） wherein, is the admittance value i between node j and node , when , it represents the mutual admittance between nodes; when The admittance matrix generation module further generates a node voltage equation: （2） wherein, is the node current vector, is the node voltage vector.

8. A vectorized Jacobi matrix construction system based on node voltage equations according to claim 7, characterized in that: The complex power conversion module is specifically configured to multiply both ends of the node voltage equation by a diagonal matrix to obtain the complex power equations of each node: （3） where the symbol represents conjugate transpose for matrices and conjugate for vectors; S is a column vector of node injection complex power.

9. A vectorized Jacobian matrix construction system based on node voltage equations according to claim 8, characterized in that: The Jacobian matrix construction module includes the following sub-modules: A polar coordinate conversion sub-module, which is used to convert the complex node voltage vector into a polar coordinate system representation, and let: （4） In the formula, U and θ are order voltage amplitude and phase angle vectors, denotes element-by-element exponentiation of the phase angle vector θ, where j is the imaginary unit; The vector product of represents the Hadamard product between vectors; A partial derivative calculation sub-module, which is used to take partial derivatives of the complex power equation with respect to the voltage amplitude vector and the phase angle vector respectively: （5） In the formula, the derivative of the complex voltage with respect to its phase and amplitude is defined as: （6） In the formula: j is the imaginary unit; A Jacobian matrix generation sub-module, which is used to substitute Equation (2) and Equation (6) into Equation (5) to obtain: （7） Among them, let the coupling matrix ; The real-valued Jacobian matrix can be obtained according to Equation (7). J : （8） In the formula, Re is to take the real part of each number, and Im is to take the imaginary part of each number; Let the complex power S = P +j Q , then the Jacobian matrix J is re-expressed as: （9） wherein, P is the column vector of the active power injected into the nodes, Q is the column vector of the reactive power injected into the nodes, Thus, the construction of the power flow Jacobian matrix with vectorized implementation process is obtained.

10. A vectorized Jacobi matrix construction system based on node voltage equations according to claim 9, characterized in that It further includes any one of the following function modules: A static stability analysis module, which is used to calculate the minimum singular value or eigenvalue of the numerical Jacobian matrix, evaluate the voltage stability margin of the current operating section, and locate the system instability mode according to the sign change of the eigenvalue, and identify weak nodes or key transmission lines; An optimal dispatch decision-making module, which is used to extract the sensitivity coefficients of node active / reactive power with respect to voltage amplitude and phase based on the numerical Jacobian matrix, generate a preventive control strategy in combination with the optimization objective function, and adjust the generator output or reactive power compensation equipment; A deep learning prediction module for inputting the numerical Jacobian matrix into a deep learning model, training the mapping relationship between the power grid operation state and the stability boundary, using the Jacobian matrix eigenvalue, node voltage, and power data as input features, and outputting the prediction result of the load growth limit or fault tolerance ability under the critical stable state of the system.

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