Power system high-dimensional static security boundary identification method and system based on state variable dimensionality reduction

Abstract

The invention discloses an electric power system high-dimensional static safety boundary identification method and system based on state variable dimensionality reduction. The method comprises the following steps: determining an anticipated fault set of an electric power system, and determining a static safety analysis range, a power injection node and a safety constraint branch; sensitivity vectors of branch currents are arranged into a matrix by using power injection, and row vectors are clustered; according to a clustering result, constructing a reduced sensitivity matrix of the associated branches; calculating a Pearson matrix based on a column vector of the reduced sensitivity matrix, constructing a new state variable, and realizing dimension reduction of a power injection space; fitting the security boundary of each out-of-limit mode by using a plurality of hyperplanes in the state variable space after dimensionality reduction, constructing a high-dimensional static security domain model, and realizing high-dimensional static security boundary identification; according to the method provided by the invention, the dimensionality of the state variable can be greatly reduced, the security boundary is fitted in the dimensionality-reduced state variable space by using hyperplane segments, and the problem of dimensionality disaster in construction of the static security domain of the power system is solved.

Description

Technical Field

[0001] The present invention relates to a method and system for identifying a high-dimensional static safety boundary of an electric power system, and in particular to a method and system for identifying a high-dimensional static safety boundary of an electric power system based on state variable dimensionality reduction, and belongs to the technical field of electric power system automation. Background Art

[0002] As the penetration rate of new energy sources continues to increase, the structure of the power grid becomes more complex, the number of power injections that need to be paid attention to in the static safety analysis of the power grid is getting larger and larger, and the possible power growth direction shows strong uncertainty, which brings many difficulties to the static safety analysis of the power grid. Therefore, it is necessary to develop dimensionality reduction and simplification methods suitable for static safety analysis of power systems, reduce the dimension of state variables while ensuring the authenticity of the analysis and calculation results, and identify the boundaries of high-dimensional static safety domains, which is of great significance to support the static safety analysis of power systems.

[0003] Traditional high-dimensional static safety boundary identification methods based on state variable dimensionality reduction mainly include the cut set method and the projection method. The cut set method divides the power grid into several cut sets, performs static safety analysis in each cut set, optimizes the connecting lines between the cut sets, and iterates alternately to ensure the overall static safety of the power grid. However, the large-scale and complex modern power system network is difficult to simply divide into several cut sets for analysis, and each cut set often contains a large number of new energy state variables, which requires further dimensionality reduction. The projection method is to fix other state variables of the power grid, and only construct a projection of the complete static safety domain for 2 to 3 state variables at a time for analysis, and peek into the full picture of the static safety domain of the power grid by calculating different combinations of state variables multiple times. However, this type of method has large computational complexity and limitations, and is overly conservative and prone to risk omissions. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a method and system for identifying high-dimensional static safety boundaries of power systems based on state variable dimensionality reduction, which can improve the accuracy of static safety domain.

[0005] Technical solution: The present invention provides a method for identifying high-dimensional static safety boundaries of a power system based on state variable dimensionality reduction, comprising:

[0006] Step 1: Determine the expected fault set i = [1, ..., F] of the power system, determine the scope of static safety analysis, the node n (n = 1, ..., N) for power injection, and the branch l (l = 1, ..., M) for safety constraints;

[0007] Step 2: According to different expected fault types, the sensitivity vectors of branch currents are arranged into a matrix S using power injection i ;

[0008] Step 3: For the sensitivity matrix [S1 ,..., S F T Among the M·F row vectors, perform clustering using the k-means algorithm under cosine metric;

[0009] Step 4: According to the clustering results, sort the risks of branch over-limit in each cluster from large to small, retain the top R branches with large over-limit risks as the associated branch set, and construct the reduced sensitivity matrix S of the associated branches R ′ ×N ;

[0010] Step 5: Based on S R ′ ×N Calculate the Pearson matrix from the N column vectors of, and merge the power injections corresponding to the elements in the Pearson matrix that are greater than the preset threshold ρ 0 to construct new state variables to replace the merged node power injections, realizing the dimensionality reduction of the power injection space;

[0011] Step 6: Fit the safety boundaries of each over-limit mode with several hyperplanes in the dimensionality-reduced state variable space, construct a high-dimensional static security region model, and realize the identification of high-dimensional static safety boundaries.

[0012] Furthermore, the matrix S described in Step 2 i , is the sensitivity matrix after simulating the removal of the assumed fault i, and is a matrix with M rows and N columns. The calculation formula is as follows:

[0013] S i = [s i,1 , …, s i,M T ,

[0014] where, I i,l represents the current value of branch l, and P i,n represents the power injection of node n; dI i,l / dP i,n is the sensitivity value of the power injection of node n to the current of branch l after simulating the removal of the assumed fault i.

[0015] Furthermore, the cosine metric described in Step 3 is specifically a method for calculating the distance between two vectors, and the calculation formula is as follows:

[0016]

[0017] where, and respectively represent [[S 1 ,..., S F ​​​T The mth 1 and mth 2 row vector, m 1 ,m 2 =1,…,M·F, for and The distance between.

[0018] Furthermore, the step 4 comprises:

[0019] Step 4.1: Calculate the safe space index D m :

[0020] D m =I m / |s m |

[0021] Among them, s m For [S 1 ,...,S F ] T The s m row vector; I m Indicates the rated current of the branch corresponding to the row vector;

[0022] Step 4.2: D in each cluster m Sort from small to large, retain the first R branches in each cluster according to the accuracy requirements, and update the sensitivity matrix to obtain the reduced sensitivity matrix S R ′ ×N .

[0023] Further, step 5 is based on S R ′ ×N The N column vectors are used to calculate the Pearson matrix. Specifically:

[0024] The calculation formula for the element in the ath row and bth column of the Pearson matrix is ​​as follows:

[0025]

[0026] Among them, cov() represents the covariance of the two sensitivity vectors, and σ represents the standard deviation of the vectors.

[0027] Furthermore, in step 5, the merged Pearson matrix is ​​greater than the preset threshold value ρ 0 The power injection corresponding to the elements of is used to construct a new state variable to replace the merged node power injection and realize the dimensionality reduction of the power injection space. Specifically:

[0028] Based on the correlation coefficient in the Pearson matrix, K power injection variables are used to construct a new state variable d, which is calculated as follows:

[0029]

[0030] Among them, P k represents the kth power injection variable among the K nodes that can be combined, s k,r The element in the kth row and rth column in the sensitivity matrix of the K mergeable node power injections to the screened R branches.

[0031] Based on the same inventive concept, the present invention also provides a high-dimensional static safety boundary identification system for a power system based on state variable dimensionality reduction, comprising:

[0032] Initialization module, used to determine the expected fault set i = [1, ..., F] of the power system, determine the scope of static safety analysis, the node n (n = 1, ..., N) for power injection and the branch l (l = 1, ..., M) of safety constraints;

[0033] The matrix calculation module is used to arrange the sensitivity vectors of branch currents into a matrix S according to different expected fault types using power injection i ;

[0034] Clustering module for sensitivity matrix [S 1 ,...,S F ] T The M·F row vectors are clustered using the k-means algorithm under the cosine metric;

[0035] The matrix reduction module is used to sort the risk of each branch in each cluster from large to small according to the clustering results, retain the first R branches with large risk of crossing the limit as the associated branch set, and construct the reduced sensitivity matrix S of the associated branches. R ′ ×N ;

[0036] Dimensionality reduction module for S-based R ′ ×N Calculate the Pearson matrix based on the N column vectors of 0 The power injection corresponding to the elements of is used to construct a new state variable to replace the merged node power injection, thus achieving dimensionality reduction of the power injection space;

[0037] The identification module is used to fit the safety boundaries of each crossing mode with several hyperplanes in the state variable space after dimensionality reduction, construct a high-dimensional static safety domain model, and realize high-dimensional static safety boundary identification.

[0038] Based on the same inventive concept, the present invention also provides a computer program product, including a computer program / instructions, which when executed by a processor, implement the steps of the method for identifying a high-dimensional static security boundary of a power system based on state variable dimension reduction according to any one of the above.

[0039] Based on the same inventive concept, the present invention also provides a computing device, including: one or more processors, one or more memories, and one or more programs, where the programs are stored in the memory and configured to be executed by the processor, and when the programs are loaded into the processor, they implement the steps of the method for identifying a high-dimensional static security boundary of a power system based on state variable dimension reduction according to any one of the above.

[0040] Based on the same inventive concept, the present invention also provides a storage medium, where the storage medium stores a computer program, and the computer program includes program instructions, which when executed by a processor, cause the processor to execute the steps of the method for identifying a high-dimensional static security boundary of a power system based on state variable dimension reduction according to any one of the above.

[0041] Beneficial effects: Compared with the prior art, the present invention identifies associated branches and clusters according to the sensitivity matrix under pre-conceived faults, can effectively screen out the set of associated branches that may form the boundary of the static security region, and improve the subsequent calculation efficiency of the static security region; according to the sensitivity matrix formed by the set of associated branches, linearly related node power injections are merged to achieve dimension reduction of the state space of the static security region, improve the accuracy of the static security region after dimension reduction, and use hyperplanes to piecewise fit the security boundary in the state variable space after dimension reduction, solving the problem of dimensionality disaster in the construction of the power system static security region. Description of the Drawings

[0042] Figure 1 It is a flowchart of the method of the embodiment of the present invention. Detailed Embodiments

[0043] In order to enable those skilled in the art to better understand the solution of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application.

[0044] As shown in the Figure 1 accompanying drawings, the method for identifying a high-dimensional static security boundary of a power system based on state variable dimension reduction in this embodiment includes:

[0045] Step 1: Determine the set of pre-conceived faults i = [1,..., F] of the power system, determine the scope of static security analysis, the nodes n (n = 1,..., N) of power injection, and the branches l (l = 1,..., M) of security constraints;

[0046] Step 2: According to different expected fault types, the sensitivity vectors of branch currents are arranged into a matrix S using power injection i ;

[0047] Step 3: For the sensitivity matrix [S 1 ,...,S F ] T The M·F row vectors are clustered using the k-means algorithm under the cosine metric;

[0048] Step 4: According to the clustering results, sort the risks of each branch in each cluster from large to small, retain the first R branches with large risks of crossing the limit as the associated branch set, and construct the reduced sensitivity matrix S of the associated branches R ′ ×N ;

[0049] Step 5: Based on S R ′ ×N Calculate the Pearson matrix based on the N column vectors of 0 The power injection corresponding to the elements of is used to construct a new state variable to replace the merged node power injection, thus achieving dimensionality reduction of the power injection space;

[0050] Step 6: Use several hyperplanes to fit the safety boundaries of each crossing mode in the state variable space after dimensionality reduction, construct a high-dimensional static safety domain model, and realize high-dimensional static safety boundary identification.

[0051] Specifically, the matrix S in step 2 i , is the sensitivity matrix after the simulated expected fault i is removed, which is a matrix with M rows and N columns. The calculation formula is as follows:

[0052] S i =[s i,1 ,…,s i,M ] T ,

[0053] Among them, I i,l Indicates the current value of branch l, P i,n represents the power injection into node n; dI i,l / dP i,n This is to simulate the sensitivity of the power injection of node n to the current of branch l after the anticipated fault i is removed.

[0054] Furthermore, the cosine metric in step 3 is specifically a method for calculating the distance between two vectors, and the calculation formula is as follows:

[0055]

[0056] Among them, and respectively represent the 1 ,..., S F T the m 1 and the m 2 th row vectors, where m 1 , m 2 = 1, …, M·F, is and the distance between.

[0057] Furthermore, step 4 includes:

[0058] Step 4.1: Calculate the safety space index D m :

[0059] D m = I m / |s m |

[0060] where s m is the 1 ,..., S F T the s m th row vector; I m represents the rated current of the branch corresponding to this row vector;

[0061] Step 4.2: Sort the D m values within each cluster from small to large, screen and retain the first R branches in each cluster according to the accuracy requirement, and update the sensitivity matrix to obtain the reduced sensitivity matrix S R ′ ×N .

[0062] Furthermore, step 5 calculates the Pearson matrix based on the N column vectors of S R ′ ×N Specifically:

[0063] The formula for calculating the element in the a-th row and b-th column of the Pearson matrix is as follows:

[0064]

[0065] where cov() represents the covariance of two sensitivity vectors, and σ represents the standard deviation of the vector.

[0066] Furthermore, step 5 merges the elements in the Pearson matrix that are greater than the preset threshold ρ 0 ​​The power injection corresponding to the elements is used to construct new state variables to replace the combined node power injection, achieving dimensionality reduction of the power injection space. Specifically:

[0067] Based on the correlation coefficients in the Pearson matrix satisfying K power injection variables, a new state variable d is constructed, and the calculation method is as follows:

[0068]

[0069] where P k represents the k-th power injection variable among the K combinable node power injections, and s k,r represents the element in the r-th column of the k-th row of the sensitivity matrix of the K combinable node power injections to the selected R branches.

[0070] Based on the same inventive concept, this embodiment also provides a high-dimensional static security boundary identification system for a power system based on state variable dimensionality reduction, including:

[0071] An initialization module for determining the set of pre-faults i = [1,..., F] of the power system, determining the scope of static security analysis, the nodes n (n = 1,..., N) of power injection, and the branches l (l = 1,..., M) of security constraints;

[0072] A matrix calculation module for arranging the sensitivity vectors of power injection to branch current into a matrix S i ;

[0073] A clustering module for clustering the M·F row vectors in the sensitivity matrix [S 1 ,..., S F using the k-means algorithm under cosine metric; T A matrix reduction module for sorting the risks of branch violations in each cluster from large to small according to the clustering results, retaining the top R branches with large violation risks as the associated branch set, and constructing a reduced sensitivity matrix S

[0074] R ′ ×N R ;

[0075] A dimensionality reduction module for calculating the Pearson matrix based on the N column vectors of S R ′ ×N 0 merging the power injections corresponding to the elements in the Pearson matrix greater than the preset threshold ρto construct new state variables to replace the combined node power injections, achieving dimensionality reduction of the power injection space;

[0076] An identification module, which is used to fit the safety boundaries of each over-limit mode with a number of hyperplanes in the state variable space after dimensionality reduction, construct a high-dimensional static security region model, and realize the identification of high-dimensional static safety boundaries.

[0077] Based on the same inventive concept, the present invention also provides a computer program product, including computer programs / instructions, and when the computer programs / instructions are executed by a processor, the steps of the method for identifying high-dimensional static safety boundaries of a power system based on state variable dimensionality reduction according to any one of the above are implemented.

[0078] Based on the same inventive concept, this embodiment also provides a computing device, including: one or more processors, one or more memories, and one or more programs, the programs are stored in the memory and configured to be executed by the processor, and when the programs are loaded into the processor, the steps of the method for identifying high-dimensional static safety boundaries of a power system based on state variable dimensionality reduction according to any one of the above are implemented.

[0079] Based on the same inventive concept, this embodiment also provides a storage medium, the storage medium stores a computer program, the computer program includes program instructions, and when the program instructions are executed by a processor, the processor is caused to execute the steps of the method for identifying high-dimensional static safety boundaries of a power system based on state variable dimensionality reduction according to any one of the above.

Claims

1. A method for identifying high-dimensional static safety boundaries of power systems based on state variable dimensionality reduction, characterized in that: include: Step 1: Determine the expected fault set i = [1, ..., F] of the power system, determine the scope of static safety analysis, the node n (n = 1, ..., N) for power injection, and the branch l (l = 1, ..., M) for safety constraints; Step 2: According to different expected fault types, the sensitivity vectors of branch currents are arranged into a matrix S using power injection i ; Step 3: For the sensitivity matrix [S1,...,S F ] T The M·F row vectors are clustered using the k-means algorithm under the cosine metric; Step 4: According to the clustering results, sort the risks of each branch in each cluster from large to small, retain the first R branches with large risks of crossing the limit as the associated branch set, and construct the reduced sensitivity matrix S of the associated branches R ′ ×N ; Step 5: Based on S R ′ ×N The N column vectors of are used to calculate the Pearson matrix, merge the power injections corresponding to the elements in the Pearson matrix that are greater than the preset threshold ρ0, construct a new state variable, replace the merged node power injection, and achieve dimensionality reduction of the power injection space; Step 6: Use several hyperplanes to fit the safety boundaries of each crossing mode in the state variable space after dimensionality reduction, construct a high-dimensional static safety domain model, and realize high-dimensional static safety boundary identification.

2. The method for identifying high-dimensional static safety boundaries of power systems based on state variable dimensionality reduction according to claim 1 is characterized in that: Step 2: Matrix S i , is the sensitivity matrix after the simulated expected fault i is removed, which is a matrix with M rows and N columns. The calculation formula is as follows: Among them, I i,l Indicates the current value of branch l, P i,n represents the power injection into node n; dI i,l / dP i,n This is to simulate the sensitivity of the power injection of node n to the current of branch l after the anticipated fault i is removed.

3. The method for identifying high-dimensional static safety boundaries of power systems based on state variable dimensionality reduction according to claim 1 is characterized in that: The cosine metric described in step 3 is specifically a method for calculating the distance between two vectors, and the calculation formula is as follows: in, and They represent [S1,...,S F ] T The m1th and m2th row vectors of , m1, m2 = 1, ..., M·F, for and The distance between.

4. The method for identifying high-dimensional static safety boundaries of power systems based on state variable dimensionality reduction according to claim 1 is characterized in that: The step 4 comprises: Step 4.1: Calculate the safe space index D m : D m =I m / |s m | Among them, s m is [S1,...,S F ] T The s m row vector; I m Indicates the rated current of the branch corresponding to the row vector; Step 4.2: D in each cluster m Sort from small to large, retain the first R branches in each cluster according to the accuracy requirements, and update the sensitivity matrix to obtain the reduced sensitivity matrix S R ′ ×N .

5. The method for identifying high-dimensional static safety boundaries of power systems based on state variable dimensionality reduction according to claim 1, characterized in that: Step 5 is based on S R ′ ×N The N column vectors are used to calculate the Pearson matrix. Specifically: The calculation formula for the element in the ath row and bth column of the Pearson matrix is ​​as follows: Among them, cov() represents the covariance of the two sensitivity vectors, and σ represents the standard deviation of the vectors.

6. The method for identifying high-dimensional static safety boundaries of power systems based on state variable dimensionality reduction according to claim 1, characterized in that: Step 5 merges the power injections corresponding to the elements in the Pearson matrix that are greater than the preset threshold ρ0, constructs a new state variable, replaces the merged node power injection, and realizes the dimensionality reduction of the power injection space. Specifically: Based on the correlation coefficient in the Pearson matrix, K power injection variables are used to construct a new state variable d, which is calculated as follows: Among them, P k represents the kth power injection variable among the K nodes that can be combined, s k,r The element in the kth row and rth column in the sensitivity matrix of the K mergeable node power injections to the screened R branches.

7. A high-dimensional static safety boundary identification system for power systems based on state variable dimensionality reduction, characterized in that: include: Initialization module, used to determine the expected fault set i = [1, ..., F] of the power system, determine the scope of static safety analysis, the node n (n = 1, ..., N) for power injection and the branch l (l = 1, ..., M) of safety constraints; The matrix calculation module is used to arrange the sensitivity vectors of branch currents into a matrix S according to different expected fault types using power injection i ; Clustering module for the sensitivity matrix [S1,...,S F ] T The M·F row vectors are clustered using the k-means algorithm under the cosine metric; The matrix reduction module is used to sort the risk of each branch in each cluster from large to small according to the clustering results, retain the first R branches with large risk of crossing the limit as the associated branch set, and construct the reduced sensitivity matrix S of the associated branches. R ′ ×N ; Dimensionality reduction module for S-based R ′ ×N The N column vectors of are used to calculate the Pearson matrix, merge the power injections corresponding to the elements in the Pearson matrix that are greater than the preset threshold ρ0, construct a new state variable, replace the merged node power injection, and achieve dimensionality reduction of the power injection space; The identification module is used to fit the safety boundaries of each crossing mode with several hyperplanes in the state variable space after dimensionality reduction, construct a high-dimensional static safety domain model, and realize high-dimensional static safety boundary identification.

8. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, the steps of the method for identifying high-dimensional static safety boundaries of a power system based on state variable dimensionality reduction according to any one of claims 1 to 6 are implemented.

9. A computing device, characterized in that include: One or more processors, one or more memories and one or more programs, wherein the programs are stored in the memories and configured to be executed by the processors, and when the programs are loaded into the processors, the steps of the method for identifying high-dimensional static safety boundaries of power systems based on state variable dimensionality reduction according to any one of claims 1 to 6 are implemented.

10. A storage medium, characterized in that: The storage medium stores a computer program, which includes program instructions. When the program instructions are executed by a processor, the processor executes the steps of the method for identifying high-dimensional static safety boundaries of a power system based on state variable dimensionality reduction according to any one of claims 1 to 6.

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