Line parameter identification method based on collaborative variance matrix

Abstract

The invention discloses a line parameter identification method based on a collaborative variance matrix, and the method comprises the following steps: S1, building a parameter model, and representing a line parameter as an undetermined coefficient; s2, constructing an optimization objective function about an undetermined coefficient by using historical measurement data and a power flow equation; s3, performing optimization solution of line parameters based on the collaborative variance matrix, adding physical constraint conditions, and searching the line parameters; and S4, judging according to the iteration condition of the optimization algorithm, and finally outputting the identified line parameters. According to the method, the line parameter identification technology based on the CMA-ES optimization algorithm is provided, and the population fitness is evaluated by adopting the Newton-Raphson method; a physical-information fusion driven power distribution network power flow state estimation model based on line parameter identification is designed, the problem of inaccurate or missing line parameters is effectively solved, and reliable data support is provided for planning and operation of a novel power system.

Description

Technical Field

[0001] The present invention relates to the technical field of line parameter identification of a distribution network, and in particular to a line parameter identification method based on a covariance matrix. Background Art

[0002] Currently, wind power, solar power, energy storage, and controllable loads are increasingly integrated into distribution networks. These uncertainties pose new challenges to the active optimization of distribution networks. However, since distribution networks have fewer monitoring devices than transmission networks, real-time information on their topology and line parameters is difficult to obtain. Therefore, correct topology identification and accurate line parameter estimation are key to future distribution network operation. Traditional power flow calculation and sensitivity analysis methods based on physical models are limited by the accuracy of the grid model and parameters, as well as the time-consuming iterative solution of implicit nonlinear equations. Under the conditions of clear grid topology and model parameters, an iterative numerical method is used to solve the nonlinear implicit function equation of the power flow. However, the inaccuracy of the model parameters and the time-consuming and convergence problems of the iterative solution will affect the accuracy and speed of the power flow calculation. In the context of large-scale access to new energy, these problems make it difficult for existing methods to meet the needs of grid development. Due to many factors such as the accuracy of the grid topology, the accuracy of the parameters, and the time required for iterative solution, the existing power flow calculation methods cannot fully meet the needs of the new power system. There is an urgent need for a line parameter identification method that can overcome the inaccuracy of the model parameters to provide reliable data support for the planning and operation of the new power system. Therefore, it is necessary to design a line parameter identification method based on the covariance matrix. Summary of the Invention

[0003] The purpose of the present invention is to provide a line parameter identification method based on the collaborative variance matrix to solve the problem that the existing power flow calculation method cannot fully meet the needs of the new power system due to many factors such as the accuracy of the grid topology, the accuracy of the parameters, and the time required for iterative solution. There is an urgent need for a line parameter identification method that can overcome the inaccuracy of model parameters to provide reliable data support for the planning and operation of the new power system.

[0004] To achieve the above object, the present invention provides the following technical solutions: In a first aspect, a line parameter identification method based on a covariance matrix is provided, comprising the following steps: S1. Establish a parameter model and express the line parameters as undetermined coefficients; S2. Using historical measurement data and the tidal flow equation, construct an optimization objective function for the undetermined coefficients; S3. Optimize the line parameters based on the covariance matrix and add physical constraints to find the line parameters that meet the optimization objective function. S4. Make a judgment based on the iteration of the optimization algorithm and finally output the identified line parameters.

[0005] As a further technical solution of the present invention, in step S1, given an N-node distribution network, for the line parameter vector Z: , Where L is the total number of lines. For a radial network with N nodes, L=N-1 , the total number of coefficients to be determined is 2L, and the line parameter vector Z contains the resistance R and reactance X of all lines.

[0006] As a further technical solution of the present invention, in step S2, given several sets of historical measurement data, including node voltage U, node active power P and reactive power Q, the line parameters are solved so that the sum of the deviations between the voltage results of the power flow equation calculated based on these line parameters and the voltage of the historical measurement data is minimized, expressed as the mean absolute error (MAE). The optimization objective function is: , in, Z is the line parameter vector, and They are t Example i The measured voltage of each node and the line parameter vector Z Calculated voltage.

[0007] As a further technical solution of the present invention, in step S2, the calculation of the power flow equation includes the following steps: 1) Use the Newton-Raphson method to perform power flow calculations and obtain the power imbalance equation for each PQ node; 2) Obtain the Jacobian matrix based on the power imbalance equation; 3) Solve the partial derivatives of the power imbalance equation and obtain the specific expressions of the Jacobian matrix elements.

[0008] As a further technical solution of the present invention, the power imbalance equation of each PQ node is: , , in, i=1,2,…,n , and Node i The amount of active power and reactive power injected, and Node i Initial active and reactive power injection amounts, is a nodei The voltage, is a node j The voltage, and They are lines ( i,j )’s conductance and susceptance; is a node i and nodes j The phase angle difference between them.

[0009] As a further technical solution of the present invention, the Jacobian matrix: , in, , , , .

[0010] As a further technical solution of the present invention, the specific expression of the Jacobian matrix element is: , Use the optimization algorithm to solve the problem so that the result satisfies the optimization objective function.

[0011] As a further technical solution of the present invention, in step S3, the optimization algorithm adopts the CMA-ES algorithm. First, the sample center point is randomly generated and the data is initialized. The nominal resistance and nominal reactance of the line are used as initial values to generate each sample point. In the gth generation, n individuals are generated: , in, The gth generation k samples, is the current population center, is the overall step length of the g-th generation, Indicates that the mean is 0, is the g-th generation covariance matrix; Sort all individuals by fitness value, the expression is: , Indicates the first k The fitness value of each individual, the sorting result means that the fitness value is arranged from small to large, that is is the individual with the lowest fitness, and It is the individual with the highest fitness; Before selection The best individuals are used to update the sample center, covariance matrix evolution path and step length evolution path, and the expressions are as follows: , , , , in, For the new population center, are weights assigned according to ranking, with better performing individuals having higher weights, For outstanding individuals in the evaluation, and is the g+1th generation covariance matrix and step-length evolution path vector, is the learning rate parameter, which controls the update speed. is the overall step size of the g+1 generation, which controls the search step size. is the g+1th generation covariance matrix, which describes the correlation between variables and the shape of the search space. exp is the exponential function. and are the matrix parameters and step size parameters respectively, is the simplified step size adaptation rate, is the length of the expected normal distribution vector, used to normalize the change in step size.

[0012] As a further technical solution of the present invention, in step S3, the physical constraints can ensure the physical rationality and engineering feasibility of the line parameters, and the constraints are: , in, R ij , X ij They are branches ( i,j ) of resistance and reactance, They are branches ( i,j )'s minimum and maximum resistance and minimum and maximum reactance.

[0013] As a further technical solution of the present invention, in step S4, it is determined whether the CMA-ES algorithm reaches the iteration upper limit or converges. If not, the iteration continues. If so, it indicates that the optimal sample point is found, and the sample point is output as the identified line parameter.

[0014] In a second aspect, a computer-readable medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the line parameter identification method based on the covariance matrix in the first aspect is implemented.

[0015] In a third aspect, an electronic device is provided, comprising a processor, a memory, and a computer program stored in the memory, wherein when the computer program is executed by the processor, the line parameter identification method based on the covariance matrix in the first aspect is implemented.

[0016] Compared with the existing technology, the line parameter identification method based on the covariance matrix has the following advantages: By proposing a line parameter identification technology based on the CMA-ES optimization algorithm and using the Newton-Raphson method to evaluate the population fitness, a distribution network flow state estimation model driven by physical-information fusion based on line parameter identification is designed, which integrates data-driven and physical constraints. It not only gives full play to the powerful learning ability of neural networks, but also maintains the constraint guidance of the physical model, providing a new method for distribution network parameter identification, which can effectively overcome the problem of inaccurate or missing line parameters and provide reliable data support for the planning and operation of new power systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a flow chart of the method of the present invention; Figure 2 It is the algorithm flow chart of the present invention; Figure 3 It is the standard IEEE33 node diagram in the present invention; Figure 4 A comparison diagram of line parameters in the present invention; Figure 5 It is the convergence curve diagram in the present invention. DETAILED DESCRIPTION

[0018] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0019] Please see the attached Figure 1 -Attached Figure 2 The present invention provides an embodiment of a line parameter identification method based on a covariance matrix, comprising the following steps: S1. Establish a parameter model and express the line parameters as undetermined coefficients; Given an N-node distribution network, for the line parameter vector Z: ,

[0020] Where L is the total number of lines. For a radial network with N nodes, L=N-1 , the total number of coefficients to be determined is 2L, and the line parameter vector Z contains the resistance R and reactance X of all lines; S2. Using historical measurement data and the tidal flow equation, construct an optimization objective function for the undetermined coefficients; Given several sets of historical measurement data, including node voltage U, node active power P, and reactive power Q, the line parameters are solved so that the deviation between the voltage results of the power flow equation calculated based on these line parameters and the voltage of the historical measurement data is minimized, expressed as the mean absolute error (MAE). The optimization objective function is: , in, Z is the line parameter vector, and They are t Example i The measured voltage of each node and the line parameter vector Z Calculated voltage.

[0021] The calculation of the power flow equation includes the following steps: 1) Use the Newton-Raphson method to perform power flow calculations and obtain the power imbalance equation for each PQ node; The power imbalance equation for each PQ node is: , , in, i=1,2,…,n , and Node i The amount of active power and reactive power injected, and Node i Initial active and reactive power injection amounts, is a node i The voltage, is a node j The voltage, and They are lines ( i,j )’s conductance and susceptance; is a node i and nodes j The phase angle difference between them.

[0022] 2) Obtain the Jacobian matrix based on the power imbalance equation; Jacobian matrix: , in, , , , .

[0023] 3) Solve the partial derivatives of the power imbalance equation to obtain the specific expressions of the Jacobian matrix elements; The specific expression of Jacobian matrix elements: , Use the optimization algorithm to solve the problem so that the result satisfies the optimization objective function.

[0024] S3. Optimize the line parameters based on the covariance matrix and add physical constraints to find the line parameters that meet the optimization objective function. The optimization algorithm uses the CMA-ES algorithm. First, the sample center point is randomly generated and the data is initialized. The nominal resistance and nominal reactance of the line are used as the initial values to generate each sample point. In the gth generation, n individuals are generated: , in, The gth generation k samples, is the current population center, is the overall step length of the g-th generation, Indicates that the mean is 0, is the g-th generation covariance matrix; Sort all individuals by fitness value, the expression is: , Indicates the first k The fitness value of each individual, the sorting result means that the fitness value is arranged from small to large, that is is the individual with the lowest fitness, and It is the individual with the highest fitness; Before selection The best individuals are used to update the sample center, covariance matrix evolution path and step length evolution path, and the expressions are as follows: , , , , in, For the new population center, are weights assigned according to ranking, with better performing individuals having higher weights, For outstanding individuals in the evaluation, and is the g+1th generation covariance matrix and step-length evolution path vector, is the learning rate parameter, which controls the update speed. is the overall step size of the g+1 generation, which controls the search step size. is the g+1th generation covariance matrix, describing the correlation between variables and the shape of the search space, exp is the exponential function, and are the matrix parameters and step size parameters respectively, is the simplified step size adaptation rate, is the length of the expected normal distribution vector, used to normalize the change in step size; Physical constraints can ensure the physical rationality and engineering feasibility of line parameters. The constraints are as follows: , in, R ij , X ij They are branches ( i,j ) of resistance and reactance, They are branches ( i,j )'s minimum and maximum resistance and minimum and maximum reactance.

[0025] S4. Judging whether the CMA-ES algorithm has reached the iteration limit or converged based on the iteration status of the optimization algorithm, if not, continuing the iteration, and if so, indicating that the optimal sample point has been found, outputting the sample point as the identified line parameter; An embodiment of the present invention provides: a computer-readable medium having a computer program stored thereon, which, when executed by a processor, implements a line parameter identification method based on a covariance matrix; An embodiment of the present invention provides an electronic device, comprising a processor, a memory, and a computer program stored in the memory, wherein when the computer program is executed by the processor, a line parameter identification method based on a covariance matrix is implemented; Please see the attached Figure 3 -Attached Figure 5 ,An embodiment provided by the present invention: a line parameter identification method based on the covariance matrix,verifies the effectiveness of the algorithm in optimizing line parameter identification, and verifies the algorithm performance through simulation analysis on a standard IEEE33 node; To simulate the actual operation of the power system, we first used MATLAB to extract the impedance parameters and load parameters of the IEEE33-node system from Matpower. Based on the actual load distribution characteristics, we generated 30 sets of load data and their flow calculation results. The impedance, load, and voltage data of the 33 nodes were extracted to form 30 sets of high-quality initial data sets. This data set was transferred to the Python environment as the input basis for subsequent calculations to support further analysis and modeling. In the process of identifying resistance and reactance, several sets of nominal resistance and reactance were set as unknown parameters and no initial values were passed in to simulate the situation where line parameters were missing.

[0026] The nominal impedance, active load, reactive load, and actual voltage value of the node are introduced as initial variables, and the power flow equation is calculated using pandapower. There is a deviation between the calculated voltage and the actual voltage. Then the CMA-ES optimization algorithm is used for optimization. The power flow equation is calculated using the optimized impedance. The optimization goal is to minimize the deviation between the calculated voltage and the actual voltage. Then the optimized parameters are extracted and divided into identification resistance and identification reactance. The results are as follows Figure 4 As shown; In summary, the line parameter identification method based on the collaborative variance matrix provided by the present invention proposes a line parameter identification technology based on the CMA-ES optimization algorithm, and adopts the Newton-Raphson method to evaluate the population fitness; designs a distribution network flow state estimation model driven by physical-information fusion based on line parameter identification, and integrates data drive with physical constraints, which not only exerts learning ability but also maintains the constraint guidance of the physical model. Finally, simulation verification is carried out on the IEEE33-node system. The results show that the flow estimation model under predicted impedance achieves higher accuracy in voltage prediction, injection power prediction and line power flow prediction, verifying the advantages of the proposed method in computational efficiency and accuracy, providing a new method for distribution network parameter identification, which can effectively overcome the problem of inaccurate or missing line parameters, and provide reliable data support for the planning and operation of new power systems.

[0027] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the invention is defined by the appended claims, not the foregoing description, and all variations within the meaning and range of equivalents of the claims are intended to be included therein. Any reference sign in a claim should not be construed as limiting the claim to which it relates.

Claims

1. A line parameter identification method based on a covariance matrix, characterized by: The following steps are involved: S1. Establish a parameter model and express the line parameters as undetermined coefficients; S2. Using historical measurement data and the tidal flow equation, construct an optimization objective function for the undetermined coefficients; S3. Optimize the line parameters based on the covariance matrix and add physical constraints to find the line parameters that meet the optimization objective function. S4. Make a judgment based on the iteration of the optimization algorithm and finally output the identified line parameters.

2. The line parameter identification method based on the covariance matrix according to claim 1, characterized in that: In step S1, given an N-node distribution network, for the line parameter vector Z: ， Where L is the total number of lines. For a radial network with N nodes, L=N-1 , the total number of coefficients to be determined is 2L, and the line parameter vector Z contains the resistance R and reactance X of all lines.

3. The line parameter identification method based on the covariance matrix according to claim 1, characterized in that: In step S2, given several sets of historical measurement data, including node voltage U, node active power P, and reactive power Q, the line parameters are solved so that the sum of the deviations between the voltage results of the power flow equation calculated based on these line parameters and the voltage of the historical measurement data is minimized, expressed as the mean absolute error (MAE). The optimization objective function is: ， in, Z is the line parameter vector, and They are t Example i The measured voltage of each node and the line parameter vector Z Calculated voltage.

4. The line parameter identification method based on the covariance matrix according to claim 3, characterized in that: In step S2, the calculation of the power flow equation includes the following steps: 1) Use the Newton-Raphson method to perform power flow calculations and obtain the power imbalance equation for each PQ node; 2) Obtain the Jacobian matrix based on the power imbalance equation; 3) Solve the partial derivatives of the power imbalance equation and obtain the specific expressions of the Jacobian matrix elements.

5. The line parameter identification method based on the covariance matrix according to claim 4, characterized in that: The power imbalance equation of each PQ node is: ， ， in, i=1,2,…,n , and Node i The amount of active power and reactive power injected, and Node i Initial active and reactive power injection amounts, is a node i The voltage, is a node j The voltage, and They are lines ( i,j )’s conductance and susceptance; is a node i and nodes j The phase angle difference between them.

6. The line parameter identification method based on the covariance matrix according to claim 4, characterized in that: The Jacobian matrix: ， in, , , , .

7. The line parameter identification method based on the covariance matrix according to claim 4, characterized in that: The specific expression of the Jacobian matrix elements is: ， Use the optimization algorithm to solve the problem so that the result satisfies the optimization objective function.

8. The line parameter identification method based on the covariance matrix according to claim 1, characterized in that: In step S3, the optimization algorithm adopts the CMA-ES algorithm. First, the sample center point is randomly generated and various data are initialized. The nominal resistance and nominal reactance of the line are used as initial values to generate each sample point. In the gth generation, n individuals are generated: ， in, The gth generation k samples, is the current population center, is the overall step length of the g-th generation, Indicates that the mean is 0, is the g-th generation covariance matrix; Sort all individuals by fitness value, the expression is: ， Indicates the first k The fitness value of each individual, the sorting result means that the fitness value is arranged from small to large, that is is the individual with the lowest fitness, and It is the individual with the highest fitness; Before selection The best individuals are used to update the sample center, covariance matrix evolution path and step length evolution path, and the expressions are as follows: ， ， ， ， in, For the new population center, are weights assigned according to ranking, with better performing individuals having higher weights, For outstanding individuals in the evaluation, and is the g+1th generation covariance matrix and step-length evolution path vector, is the learning rate parameter, which controls the update speed. is the overall step size of the g+1 generation, which controls the search step size. is the g+1th generation covariance matrix, describing the correlation between variables and the shape of the search space, exp is the exponential function, and are the matrix parameters and step size parameters respectively, is the simplified step size adaptation rate, is the length of the expected normal distribution vector, used to normalize the change in step size.

9. The line parameter identification method based on the covariance matrix according to claim 1, characterized in that: In step S3, the physical constraints can ensure the physical rationality and engineering feasibility of the line parameters, and the constraints are: ， in, R ij , X ij They are branches ( i,j ) of resistance and reactance, They are branches ( i,j )'s minimum and maximum resistance and minimum and maximum reactance.

10. The line parameter identification method based on the covariance matrix according to claim 1, characterized in that: In step S4, it is determined whether the CMA-ES algorithm has reached the iteration limit or converged. If not, the iteration continues. If yes, it indicates that the optimal sample point has been found, and the sample point is output as the identified line parameter.

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