Electric power system overload safety boundary description method and system based on gradient vector clustering

Abstract

The invention discloses a gradient vector clustering-based power system overload safety boundary depiction method and system, and the method comprises the steps: calculating an overload safety boundary gradient vector based on sensitivity analysis, clustering an overload safety boundary into a plurality of subsets based on a gradient vector Euclidean distance, calculating an overload safety boundary expression of each subset based on linear optimization, and carrying out the calculation of the overload safety boundary expression. And the optimal clustering number is determined through iterative calculation. According to the method, accurate description of the high-dimensional nonlinear boundary manifold is realized, and a foundation is laid for safe and economical operation of a power system.

Description

Technical Field

[0001] The invention relates to power system safety and stability analysis, in particular to a method and system for characterizing overload safety boundaries of a power system based on gradient vector clustering. Background Art

[0002] The safety and stability boundary of the power system is the premise and foundation of multi-time scale scheduling and real-time control. Its accuracy is directly related to the safety and economy of the power system. The overload safety boundary of the power system is an important part of the safety and stability boundary of the power system. With the large-scale grid connection of new energy sources, the operation mode of the new power system is complex and changeable. The influence of multi-dimensional variables on the system boundary tends to be strongly nonlinear and strongly coupled, and traditional characterization methods are difficult to deal with effectively.

[0003] At present, the overload safety boundary (thermal stability boundary) characterization methods mainly include three categories: one is the linear characterization method. As the nonlinearity of the system increases, the reliability and accuracy are difficult to meet the requirements; the second is the nonlinear characterization method, which has relatively high accuracy, but low computational efficiency, and the obtained nonlinear expression is difficult to apply in practice; the third is the piecewise linear characterization method, which improves the fitting accuracy without losing practicality and has certain application prospects. At present, the boundary segmentation and characterization in two-dimensional and three-dimensional space are mainly realized by calculating the curvature of the boundary manifold. For example, patent CN108493931A discloses an approximate method for the boundary of the static voltage stability domain of the power system based on the space tangent vector. In low-dimensional variable spaces such as two-dimensional and three-dimensional, the space tangent vector of the discrete boundary point and the boundary error are combined to realize the approximate characterization of the boundary. However, in this low-dimensional discrete method, the numerical accuracy and stability of the discrete point curvature calculation will be affected by multiple factors such as sample density and noise, and it is also difficult to calculate the curvature in high-dimensional space. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a method and system for characterizing overload safety boundaries of power systems based on gradient vector clustering, so as to achieve accurate characterization of high-dimensional nonlinear boundary manifolds.

[0005] Technical solution: The method for characterizing the overload safety boundary of a power system based on gradient vector clustering of the present invention comprises the following steps:

[0006] (1) Calculate the gradient vector of the power system overload safety boundary through AC sensitivity analysis, where the power system overload safety boundary is a set of overload safety critical points; set the initial clustering number K C ;

[0007] (2) Cluster the overload safety critical points into K according to the Euclidean distance of the gradient vector C subsets;

[0008] (3) Considering the envelope constraint under the overload safety boundary, the overload safety boundary expression of each subset is calculated based on linear optimization;

[0009] (4) Determine the current K according to the overload safety boundary expression of each subset and the preset residual requirement C Is it the optimal cluster number? If so, output the power system overload safety boundary; otherwise, adjust K C value and return to step (2).

[0010] Furthermore, in step (3), the objective function of linear optimization is:

[0011]

[0012] The envelope constraint under the overload safety boundary is:

[0013]

[0014] Among them, B k is the set of overload safety critical points in subset k, N k is the number of overload safety critical points in subset k, is the active power of adjustable device i at the critical point b3, I max is the current limit of the preset monitoring branch, α k,i is the active power coefficient of the adjustable device i in the subset k to be obtained.

[0015] Furthermore, in step (3), the overload safety boundary expression of each subset is:

[0016]

[0017] in, is the linear optimization result, that is, the active coefficient of adjustable device i in subset k obtained by linear optimization, P i ' is the active power of adjustable equipment i under the potential operating state of the power system.

[0018] Furthermore, in step (4), the number of clusters K is calculated based on the linear optimization results of each subset. C The maximum residual error when

[0019]

[0020] like If it is greater than the preset residual requirement ε, increase K C , otherwise reduce K C , return to step (2); through iterative calculation, find The minimum number of clusters not greater than ε is taken as the optimal number of clusters.

[0021] Furthermore, in step (1), the overload safety critical point is a critical operating mode in which the preset monitoring branch current is equal to the limit.

[0022] Furthermore, in step (1), for each overload safety critical point, the Jacobian matrix is ​​obtained by AC power flow calculation, and the sensitivity of the active power of the adjustable device to the preset monitoring branch current is calculated based on sensitivity analysis to obtain the gradient vector of the overload safety critical point:

[0023]

[0024] Among them, B is the set of overload safety critical points, D is the set of active adjustable equipment, T (b) is the gradient vector of the overload safety critical point b, It is the sensitivity of the active power of the adjustable device i to the preset monitoring branch current at the overload safety critical point b.

[0025] Furthermore, in step (2), the Euclidean distance between overload safety critical points is calculated based on the gradient vector:

[0026]

[0027] in, is the distance between critical points b1 and b2, They are the sensitivities of the active power of the adjustable device i to the preset monitoring branch current at the critical points b1 and b2 respectively.

[0028] The power system overload safety boundary characterization system based on gradient vector clustering of the present invention comprises:

[0029] The boundary gradient vector calculation module is used to calculate the gradient vector of the power system overload safety boundary through AC sensitivity analysis. The power system overload safety boundary is a set of overload safety critical points. The initial clustering number K is set. C ;

[0030] The boundary clustering calculation module is used to cluster the overload safety critical points into K according to the Euclidean distance of the gradient vector C subsets;

[0031] The boundary expression calculation module is used to consider the envelope constraints under the overload safety boundary and calculate the overload safety boundary expression of each subset based on linear optimization;

[0032] The boundary optimal clustering judgment module is used to judge the current K according to the overload safety boundary expression of each subset and the preset residual requirement. C Is it the optimal cluster number? If so, output the power system overload safety boundary; otherwise, adjust K C The value of and returns the boundary clustering calculation module.

[0033] The electronic device described in the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the method for characterizing the overload safety boundary of an electric power system based on gradient vector clustering is implemented.

[0034] The computer-readable storage medium of the present invention stores a computer program, and when the computer program is executed by a processor, the method for characterizing the overload safety boundary of a power system based on gradient vector clustering is implemented.

[0035] Beneficial effect: Compared with the prior art, the advantages of the present invention are: the present invention characterizes the gradient vector of the high-dimensional nonlinear boundary through analytical sensitivity, and then realizes the approximate characterization of the high-dimensional boundary based on gradient vector clustering and combining with the linear optimization algorithm, thereby overcoming the difficulty of calculating the high-dimensional curvature of traditional discrete points and realizing the accurate characterization of the high-dimensional nonlinear boundary manifold; compared with the traditional linear characterization method, the accuracy is improved, and compared with the traditional nonlinear or piecewise linear characterization method, the practicability is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a flow chart of the method for depicting overload safety boundaries of a power system according to the present invention. DETAILED DESCRIPTION

[0037] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0038] like Figure 1 As shown, the method for characterizing the overload safety boundary of the power system based on gradient vector clustering includes the following steps.

[0039] Step 1: Calculate the gradient vector of the overload safety margin based on AC sensitivity analysis and set the number of clusters K C is the initial value; the power system overload safety boundary is a set of overload safety critical points; the overload safety critical point is a critical operating mode in which the preset monitored branch current is equal to the limit.

[0040] For each overload safety critical point, the Jacobian matrix is ​​obtained through AC power flow calculation, and the sensitivity of the active power of the adjustable equipment to the preset monitoring branch current is calculated based on sensitivity analysis to obtain the gradient vector of the overload safety critical point, specifically,

[0041]

[0042] Among them, B is the set of overload safety critical points, D is the set of active adjustable equipment, T (b) is the gradient vector of the overload safety critical point b, It is the sensitivity of the active power of the adjustable device i to the preset monitoring branch current at the overload safety critical point b.

[0043] Step 2: Calculate the Euclidean distance between overload safety critical points based on the gradient vector:

[0044]

[0045] in, is the distance between critical points b1 and b2, They are the sensitivities of the active power of the adjustable device i to the preset monitoring branch current at the critical points b1 and b2 respectively.

[0046] According to the set number of clusters K C , cluster the overload safety critical point set based on the Euclidean distance of the gradient vector, and obtain K C A subset of overload safety critical points.

[0047] Step 3: Considering the envelope constraint under the overload safety boundary, the overload safety boundary expression of each subset is calculated based on linear optimization.

[0048] For each subset of overload safety critical points, the objective function of linear optimization is:

[0049]

[0050] The constraints of linear optimization include the envelope constraints under the overload safety boundary, specifically,

[0051]

[0052] Among them, B k is the set of overload safety critical points in subset k, N k is the number of overload safety critical points in subset k, is the active power of adjustable device i at the critical point b3, I max is the current limit of the preset monitoring branch, α k,i is the active power coefficient of the adjustable device i in the subset k to be obtained.

[0053] The lower envelope constraint of the overload safety boundary ensures that the piecewise linear manifold of the power system overload safety boundary completely covers the nonlinear manifold of the real overload safety boundary.

[0054] Overload safety boundary expression, specifically:

[0055]

[0056] in, is the active power coefficient of adjustable device i in subset k obtained by linear optimization in claim 5, P i' is the active power of adjustable equipment i under the potential operating state of the power system.

[0057] Step 4: Determine whether it is the optimal number of clusters based on the optimization results and the preset residual requirements, and calculate the number of clusters K based on the optimization results of each subset. C The maximum residual error when The specific formula is:

[0058]

[0059] like If it is greater than the preset residual requirement ε, increase K C , otherwise reduce K C , return to step 2; through iterative calculation, find The minimum number of clusters less than or equal to ε is taken as the optimal number of clusters.

[0060] The power system overload safety boundary characterization system based on gradient vector clustering of the present invention comprises:

[0061] The boundary gradient vector calculation module is used to calculate the gradient vector of the power system overload safety boundary through AC sensitivity analysis. The power system overload safety boundary is a set of overload safety critical points. The initial clustering number K is set. C ;

[0062] The boundary clustering calculation module is used to cluster the overload safety critical points into K according to the Euclidean distance of the gradient vector C Subset;

[0063] The boundary expression calculation module is used to consider the envelope constraints under the overload safety boundary and calculate the overload safety boundary expression of each subset based on linear optimization;

[0064] The boundary optimal clustering judgment module is used to judge the current K according to the overload safety boundary expression of each subset and the preset residual requirement. C Is it the optimal cluster number? If so, output the power system overload safety boundary; otherwise, adjust K C The value of and returns the boundary clustering calculation module.

[0065] The electronic device described in the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the method for characterizing the overload safety boundary of an electric power system based on gradient vector clustering is implemented.

[0066] The computer-readable storage medium of the present invention stores a computer program, and when the computer program is executed by a processor, the method for characterizing the overload safety boundary of a power system based on gradient vector clustering is implemented.

[0067] The computer-readable storage media may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, flash memory, or any other medium that can be used to store the desired program code in the form of instructions or data structures and that can be accessed by a computer.

[0068] The processor is used to execute the computer program stored in the memory to implement each step of the method involved in the above embodiment.

Claims

1. A method for characterizing overload safety boundaries of power systems based on gradient vector clustering, characterized in that: The steps include: (1) Calculate the gradient vector of the power system overload safety boundary through AC sensitivity analysis, where the power system overload safety boundary is a set of overload safety critical points; set the initial clustering number K C ; (2) Cluster the overload safety critical points into K according to the Euclidean distance of the gradient vector C subsets; (3) Considering the envelope constraint under the overload safety boundary, the overload safety boundary expression of each subset is calculated based on linear optimization; (4) Determine the current K according to the overload safety boundary expression of each subset and the preset residual requirement C Is it the optimal cluster number? If so, output the power system overload safety boundary; otherwise, adjust K C value and return to step (2).

2. The method for characterizing the overload safety boundary of a power system based on gradient vector clustering according to claim 1 is characterized in that: In step (3), the objective function of linear optimization is: The envelope constraint under the overload safety boundary is: Among them, B k is the set of overload safety critical points in subset k, N k is the number of overload safety critical points in subset k, is the active power of adjustable device i at the critical point b3, I max is the current limit of the preset monitoring branch, α k,i is the active power coefficient of the adjustable device i in the subset k to be obtained.

3. The method for characterizing the overload safety boundary of a power system based on gradient vector clustering according to claim 2 is characterized in that: In step (3), the overload safety boundary expression of each subset is: in, is the linear optimization result, that is, the active coefficient of adjustable device i in subset k obtained by linear optimization, P i ' is the active power of adjustable equipment i under the potential operating state of the power system.

4. The method for characterizing the overload safety boundary of a power system based on gradient vector clustering according to claim 3 is characterized in that: In step (4), the number of clusters K is calculated based on the linear optimization results of each subset. C The maximum residual error when like If the residual error is greater than the preset requirement ε, increase K C , otherwise reduce K C , return to step (2); through iterative calculation, find The minimum number of clusters not greater than ε is taken as the optimal number of clusters.

5. The method for characterizing the overload safety boundary of a power system based on gradient vector clustering according to claim 1 is characterized in that: In step (1), the overload safety critical point is a critical operating mode in which the preset monitoring branch current is equal to the limit.

6. The method for characterizing the overload safety boundary of a power system based on gradient vector clustering according to claim 1 is characterized in that: In step (1), for each overload safety critical point, the Jacobian matrix is ​​obtained by AC power flow calculation, and the sensitivity of the active power of the adjustable device to the preset monitoring branch current is calculated based on sensitivity analysis to obtain the gradient vector of the overload safety critical point: Among them, B is the set of overload safety critical points, D is the set of active adjustable equipment, T (b) is the gradient vector of the overload safety critical point b, It is the sensitivity of the active power of the adjustable device i to the preset monitoring branch current at the overload safety critical point b.

7. The method for characterizing the overload safety boundary of a power system based on gradient vector clustering according to claim 1 is characterized in that: In step (2), the Euclidean distance between overload safety critical points is calculated based on the gradient vector: in, is the distance between critical points b1 and b2, They are the sensitivities of the active power of the adjustable device i to the preset monitoring branch current at the critical points b1 and b2 respectively.

8. A power system overload safety boundary characterization system based on gradient vector clustering, characterized in that: include: A boundary gradient vector calculation module, used to calculate the gradient vector of the overload safety boundary of the power system through AC sensitivity analysis, wherein the overload safety boundary of the power system is a set of overload safety critical points; Set the initial number of clusters K C ; The boundary clustering calculation module is used to cluster the overload safety critical points into K according to the Euclidean distance of the gradient vector C subsets; The boundary expression calculation module is used to consider the envelope constraints under the overload safety boundary and calculate the overload safety boundary expression of each subset based on linear optimization; The boundary optimal clustering judgment module is used to judge the current K according to the overload safety boundary expression of each subset and the preset residual requirement. C Is it the optimal cluster number? If so, output the power system overload safety boundary; otherwise, adjust K C The value of and returns the boundary clustering calculation module.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the computer program is loaded into a processor, the method for characterizing the overload safety boundary of a power system based on gradient vector clustering according to any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method for characterizing the overload safety boundary of a power system based on gradient vector clustering according to any one of claims 1 to 7 is implemented.

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