Adaptive Sub-Network Method for Transient Simulation of Large Power Grids

Abstract

An adaptive sub-networking method for large power grid transient simulation. After mapping the power system into a graph structure based on the similarity between the original data of the power system and the graph structure, preprocess the graph structure by simplification; then, based on the k-way idea, use the improved density peak clustering method for initial segmentation; for the initial segmentation result, optimize the segmentation quality of the initial segmentation result based on the linear decision-making greedy method; finally, use the improved linear decision-making greedy method to optimize the inverse mapping of the graph structure segmentation result into the power system to obtain the power grid sub-networking result for electromagnetic transient parallel simulation. The sub-networking quantity obtained by the present invention has a higher degree of freedom, the scale of each sub-network is more uniform, and the number of inter-sub-network connection lines is less, which can greatly reduce the waiting time loss and communication time loss during the parallel simulation process, enabling the electromagnetic transient parallel simulation of large power grids to achieve an acceleration effect of several times to dozens of times, and the parallel simulation result is consistent with the serial simulation, having reliability.

Description

Technical Field

[0001] The present invention relates to a technology in the field of power system control, specifically an adaptive network partitioning method for large power grid transient simulation. Background Art

[0002] Due to the expansion of the scale and the complexity of the structure of the power system, the dynamic characteristics of the power system tend to be complex, and the operation stability also encounters challenges and tests, which requires research and analysis through electromagnetic transient simulation. The electromagnetic transient simulation of large-scale power systems generally takes a long time because of the small time step and large amount of calculation. Using network partitioning in parallel to accelerate is a common idea. However, the general network partitioning method manually partitions the network based on geographical location information, which not only lacks self-adaptability, but also the number of subnets decomposed is often limited, the sizes are uneven, and the number of associated lines is large, so it urgently needs to be improved. Summary of the Invention

[0003] Aiming at the above deficiencies of the existing technology, the present invention proposes an adaptive network partitioning method for large power grid transient simulation, which can adaptively partition a power grid with a large scale; the number of network partitions can have a high degree of freedom; it can reduce the number of lines associated with each other between subnets in the network partitioning result, which helps to reduce the communication time loss during electromagnetic transient parallel simulation; it can improve the uniformity of the scale of subnets in the network partitioning result, which helps to reduce the waiting time loss during electromagnetic transient parallel simulation; it can make the network partitioning result consistent with the result of serial simulation when applied to electromagnetic transient parallel simulation.

[0004] The present invention is realized through the following technical solutions:

[0005] The present invention relates to an adaptive network partitioning method for large power grid transient simulation. First, based on the similarity between the original data of the power system and the graph structure, the power system is mapped into a graph structure, and then the graph structure is simplified and preprocessed; then, based on the k-way idea, the improved Density Peak Clustering (DPC) method is used for initial partitioning; for the initial partitioning result, the Linear Deterministic Greedy method is used to optimize the partitioning quality of the initial partitioning result; finally, the improved Linear Deterministic Greedy method is used to optimize the inverse mapping of the graph structure partitioning result into the power system to obtain the power grid partitioning result for electromagnetic transient parallel simulation.

[0006] The present invention relates to a system for implementing the above method, including: a preprocessing unit for raw power system data, a power system network segmentation unit, and a parallel electromagnetic transient simulation unit for power systems. Among them: the preprocessing unit for raw power system data maps the power system network into a graph structure according to the input raw power system data, and then performs transformer condensation, vertex condensation, and multi-layer condensation in sequence to obtain a graph with a simplified structure and containing power system information; the power system network segmentation unit determines the initial aggregation center, initial clustering, and refinement and restoration operations according to the graph structure obtained by the preprocessing unit for raw power system data, and obtains a power system network segmentation result with uniform subnet scales and few inter-subnet connection lines; the parallel electromagnetic transient simulation unit for power systems performs parallel electromagnetic transient simulation of the power system according to the segmentation result of the power system network segmentation unit, and can complete the simulation with an acceleration ratio of several times or even dozens of times, and obtain a simulation result waveform as reliable as that of serial simulation.

[0007] Technical effects

[0008] For the graph structure obtained by mapping the raw power system data of the present invention, transformer condensation is performed, and a vertex cluster connected by a transformer is fused into one vertex, simplifying the graph structure and avoiding segmentation at the transformer, so as not to affect the implementation of subsequent parallel electromagnetic transient simulation; for the graph structure after transformer condensation, vertex condensation is performed, and a vertex cluster connected by a line with a length not meeting the critical length corresponding to the electromagnetic transient simulation step length is fused into one vertex, simplifying the graph structure and avoiding segmentation at the overly short line, so as not to affect the implementation of subsequent parallel electromagnetic transient simulation; for the graph structure after vertex condensation, multi-layer condensation is performed to further simplify the graph structure, and there are two constraint conditions to avoid over-condensation, and finally a preprocessed, concise graph structure suitable for graph segmentation for the purpose of parallel electromagnetic transient simulation is obtained.

[0009] Compared with the prior art, the present invention can simplify the graph structure and avoid segmentation at the transformer, so as not to affect the implementation of subsequent parallel electromagnetic transient simulation; for the preprocessed graph structure, the improved DPC algorithm for power systems is used to determine the initial aggregation center, and a better and more uniform initial clustering result can be obtained. For the initial clustering result, the improved LDG algorithm is used for refinement and restoration, which can help reduce invalid vertex allocation operations and optimize the initial clustering result, obtaining a more balanced subgraph scale and fewer edges across subgraphs. Description of the drawings

[0010] Figure 1 is the flowchart of the present invention;

[0011] Figure 2 is the schematic diagram of transformer condensation of the present invention;

[0012] Figure 3 Schematic diagram of line concentration of the present invention;

[0013] Figure 4 Flow chart of multi-layer concentration of the present invention;

[0014] Figure 5 Schematic diagram of multi-layer concentration of the present invention;

[0015] Figure 6 Flow chart of initial clustering of the present invention;

[0016] Figure 7 and Figure 8 Schematic diagram of the effect of the embodiment. Specific implementation manner

[0017] As Figure 1 shown, this embodiment relates to an adaptive sub-network method for large power grid transient simulation. After mapping the power system into a graph structure based on the similarity between the original power system data and the graph (Graph) structure, preprocessing is performed on the graph structure to simplify it; then, based on the k-way idea, an improved density peak clustering method is used for initial segmentation; for the initial segmentation result, the segmentation quality is optimized based on the linear decision greedy method; finally, the improved linear decision greedy method is used to optimize the inverse mapping of the graph structure segmentation result into the power system, and the final large power grid sub-network result is obtained. Its sub-network quantity has a higher degree of freedom, the scale of each sub-network is more uniform, the number of inter-sub-network tie lines is less, which can greatly reduce the waiting time loss and communication time loss during the parallel simulation process, enabling the electromagnetic transient parallel simulation of the large power grid to achieve an acceleration effect of several times to dozens of times, and the parallel simulation result is consistent with the serial simulation, with reliability.

[0018] The mapping described above includes: ① mapping the busbars into vertices (Vertex), ② mapping the transmission lines and transformers into edges (Edge), and ③ incorporating the remaining components into the vertices mapped by the busbars without affecting the topological structure of the graph.

[0019] In the mapping described above, the computational amount of all components is converted into the form of the point weight of the vertex, and the point weight is: Where: W i refers to the point weight of vertex v i and is equal to the sum of the computational amounts of all four main components included in this vertex. Since the transformers and lines are shared by both ends of the nodes, the computational amount for one side is only half of it.

[0020] The simplified preprocessing described above includes:

[0021] 1) Transformer concentration: As Figure 2In the mapping process from the power system to the graph structure, nodes are mapped to vertices, and the transmission lines and transformer connection relationships between nodes are mapped to edges. However, since the present invention selects the Bergeron numerical calculation model only for long lines to decouple subgraphs, it is necessary to avoid segmentation at transformers.

[0022] In the transmission network architecture of the power system, transformers generally exist in clusters (substations). Therefore, the nodes associated with the transformer cluster can be fused into one vertex (i.e., the T vertex, and the other vertices are the N vertices). In this way, not only is segmentation at transformers avoided, but the graph structure is also simplified to a certain extent.

[0023] 2) Vertex condensation: As Figure 3 shown, since the length of the line applying the Bergeron numerical calculation model should be greater than or equal to the equivalent length of one simulation step, for the case of a common simulation step of 50 microseconds, the corresponding critical length is 15 km. In other words, the transmission delay of the line must be greater than or equal to one simulation step, that is: τ≥t step . To avoid the situation of decomposition at short lines that do not meet the requirements, it is necessary to condense the vertices connected by short lines. For these condensed vertices, they are the C vertices (C Vertex, Complex Vertex). Since the power system is generally composed of a large number of small networks connected by high-voltage and long-distance transmission lines, the above condensation steps will not infinitely condense the entire network into a small number of vertices, resulting in excessive simplification of the graph structure.

[0024] 3) Multi-layer condensation / coarsening: As Figure 4 and Figure 5 shown, before graph segmentation, a multi-layer condensation operation can be performed on the existing undirected graph G = G(V, E) to further simplify the graph structure. Since the condensation operation increases the granularity and coarseness of the vertices in the undirected graph G = G(V, E), the multi-layer condensation is the multi-layer coarsening.

[0025] The multi-layer coarsening can orderly condense the vertices in the graph and moderately coarsen the graph structure. It has the following advantages: greatly reducing the number of vertices in the graph during segmentation, simplifying the complexity of the graph, and helping to accelerate the segmentation process; the multi-layer coarsening increases the equivalent distance between vertices, which helps to select the initial aggregation center of the subgraph later. To ensure that the multi-layer coarsening will not be excessive, certain constraints need to be imposed on it. The constraint conditions include:

[0026] a) The scale of the coarsened vertices cannot exceed a given size, which is: where: N total is the total number of nodes in the network; K is the number of subnets decomposed; E represents the minimum number of vertices that can be tolerated in each subnet.

[0027] b) During a single coarsening process, a vertex is only allowed to be condensed once.

[0028] The improved density peak clustering method performs an initial segmentation, including: selecting the density peak clustering method to determine the initial aggregation center, and using the one with a relatively high local density and a large distance from a higher density point as the basis for selecting the clustering center. Specifically, it includes: the local density ρ i = ∑ j χ(d ij - d c ), where: ρ i is the local density of the data point x i ; d ij is the Euclidean distance between the data points x i , x j ; d c = max(d ij ) × α is the cut-off distance, and α is the adjustment coefficient. During the use for the power system, let α = 1, so that the local density ρ i degenerates into the outgoing line degree of the vertex (the number of edges associated with the vertex); the function For each data point x i the distance to the data point with a higher local density that is, the sum of the minimum values of the distances from the data point x i to all points with a higher density than it; for the point x k with the highest local density, that is, the maximum value of the distances from the data point x k to any other point.

[0029] The local density ρ i and the distance δ i of the data point selected as the clustering center by the DPC method are both higher than those of other ordinary vertices.

[0030] As Figure 6 shown, the initial segmentation further includes:

[0031] 1) Since the vertices in the graph do not have coordinates, for two directly connected vertices v i , v j , d ij is directly the average length of the edge between the vertices v i , v j , specifically: Due to the aforementioned condensation operation, there may be more than one edge between the vertices v i , v j , so the set E ij is used to represent it.

[0032] 2) For the truncation distance d c = max(d ij ) × α, where: α is an adjustment coefficient, α ∈ (0, 1]. In actual use, for simplicity, α can be set to 1. At this time, the local density ρ i degenerates into the out-degree of the vertex.

[0033] 3) Plot the vertices according to the two attributes of local density ρ i and distance δ i , and select K initial aggregation centers from the upper right corner of the graph.

[0034] For the initial segmentation mentioned above, after obtaining the initial aggregation centers, the initial center expansion is carried out in the following way to obtain a small network with a certain scale. Specifically: retrieve all the directly adjacent vertices of the initial aggregation centers and assign them to the corresponding subgraphs, so that each subnet is expanded to a certain extent, enabling more reference vertices in the subsequent vertex assignment process and ensuring that the adjacent vertices of the initial aggregation centers are closely related to them and should be assigned to the same subgraph, thus accelerating the network segmentation process.

[0035] For the optimization of the segmentation quality of the initial segmentation result based on the linear decision greedy method, it specifically includes: Where: V k is a vertex set; ω(V k ) is the total calculation amount of the vertex set V k ; C = |V 0 | / K, |V 0 | is the sum of the calculation amounts of all vertices; Adj(v) refers to the set of adjacent vertices of vertex v i . For each vertex v i , |V k ∩ Adj(v i )|(1 - ω(V k ) / C) corresponding to each vertex set V k (k = 1, 2,......, K) can be obtained, and the largest of these K values is the value of the constraint function f(v i ). In the components of the constraint function f(v i ), |V k ∩ Adj(v)| represents the magnitude of the association between vertex v i and the set V k ; 1 - ω(V k ) / C plays a role in balancing the calculation amounts of each vertex set (subgraph).

[0036] The inverse mapping performs multi-layer refinement for multi-layer concentration to optimize the sub-network division result, specifically including: for the initial clustering result, mapping the sub-graph back to the upper level to refine the graph structure; using the multi-layer refinement LDG function to optimize the refined graph to improve the segmentation quality; continuously repeating the above steps until the influence of multi-layer concentration is completely offset.

[0037] The specific form of the multi-layer refinement LDG function is as follows: Where: n average is the average computational amount of all vertices in the graph; σ n is the standard deviation of the vertex computational amount; C = N total / K, representing the average scale size of each sub-network; Adj(v i 1 ) are the adjacent vertices directly connected to vertex v i , while Adj(v i 2 ) are the adjacent vertices directly connected to V k ∩Adj(v i 1 ); w is the weight of the indirect adjacent vertices, which is linearly positively correlated with the total number of nodes in the network. For some vertices that are both in the definition of Adj(v i 1 ) and Adj(v i 2 ), they are uniformly placed into Adj(v i 1 ).

[0038] In addition to improving the part of calculating the computational amount of the balanced sub-graph, the multi-layer refinement LDG function expands the consideration scope of the greedy method by introducing Adj(v i 2 ) from single-layer to double-layer: for cases with a relatively large overall scale of the network, unnecessary allocation operations can be avoided; for cases with a relatively small overall scale of the network, since the maximum scale allowed for the sub-network itself may already be very small, an overly large scope involved in the LDG method may instead interfere with the effective allocation of vertices. Therefore, the weight w should be linearly positively correlated with the total number of nodes in the network.

[0039] Through specific experiments, adaptive sub-network division and electromagnetic transient parallel simulation are respectively carried out for the cases of East China Power Grid and Yunnan Power Grid. Among them, the results obtained from the adaptive sub-network division are as follows:

[0040] Table 1 Sub-network division results obtained by using the adaptive sub-network division algorithm for the case of East China Power Grid

[0041]

[0042] Table 2 Sub-network Division Results of Yunnan Power Grid Example Using Adaptive Sub-network Algorithm

[0043]

[0044] The sub-network division results of the above two examples are used for electromagnetic transient parallel simulation on a computer with an Intel Xeon Gold 6140 processor with a main frequency of 2.30 GHz and 256G of memory. This processor has 18 cores and 36 logical processors. The waveform of the simulation results of representative nodes (the number of nodes is too large to list them all here) is as Figure 7 and Figure 8 shown, which are the A-phase voltage waveforms of Hulinran in East China Power Grid (the three cases have been overlapped); the A-phase voltage waveforms of MW-HLZ in Yunnan Power Grid (the three cases have been overlapped). Using the sub-network division results of the above adaptive sub-network algorithm for electromagnetic transient parallel simulation, the results are consistent with the serial simulation results and are reliable.

[0045] Table 3 Comparison of Simulation Efficiency of East China Power Grid Example

[0046]

[0047] Table 4 Comparison of Simulation Efficiency of Yunnan Power Grid Example

[0048]

[0049] Using the sub-network division results of the above adaptive sub-network algorithm for electromagnetic transient parallel simulation, the simulation rate can be effectively improved.

[0050] Compared with the existing technology, the sub-network division results of large power grids obtained by this method have a higher degree of freedom in the number of sub-networks, more uniform sub-network scales, and fewer tie lines between sub-networks; applying this high-quality sub-network division result to electromagnetic transient parallel simulation can obtain the following advantages: reducing the waiting time in the parallel simulation process, reducing the communication time in the parallel simulation process, enabling the electromagnetic transient parallel simulation of large power grids to obtain a higher simulation rate, and the simulation results can be consistent with the serial simulation and are reliable.

[0051] The present invention can automatically partition power grids with the number of nodes ranging from dozens, hundreds, thousands to tens of thousands. The number of sub-grids in the present invention can have a high degree of freedom, and the number of sub-grids is not restricted by the geographical information corresponding to the power grid itself, nor does it require the additional assistance of such information. Based on the DPC method and the LDG method, the present invention can effectively reduce the number of interconnected lines between sub-grids in the sub-network partitioning result, which helps to reduce the communication time loss during electromagnetic transient parallel simulation. It can also improve the uniformity of the scale of sub-grids in the sub-network partitioning result, which helps to reduce the waiting time loss during electromagnetic transient parallel simulation, enabling the sub-network partitioning result to play a good acceleration role when applied to electromagnetic transient parallel simulation. The present invention uses the Bergeron transmission line model as the decoupling port of the sub-grid, which can make the sub-network partitioning result consistent with the result of serial simulation when applied to electromagnetic transient parallel simulation, ensuring the reliability of parallel simulation.

[0052] Those skilled in the art can make partial adjustments to the above specific implementation in different ways without departing from the principles and purposes of the present invention. The protection scope of the present invention is subject to the claims and is not limited by the above specific implementation. All implementation solutions within its scope are subject to the present invention.

Claims

1. An adaptive sub-networking method for large power grid transient simulation, characterized in that, after mapping the power system into a graph structure based on the similarity between the original data of the power system and the graph structure, preprocess the graph structure by simplification; then, based on the k-way idea, use the improved density peak clustering method for initial segmentation; for the initial segmentation result, optimize the segmentation quality of the initial segmentation result based on the linear decision greedy method; finally, use the improved linear decision greedy method to optimize the inverse mapping of the graph structure segmentation result into the power system to obtain the power grid sub-networking result for electromagnetic transient parallel simulation; The initial segmentation using the improved density peak clustering method includes: selecting the density peak clustering method to determine the initial aggregation center, and using the data points with higher local density and larger distance from higher density points as the basis for selecting the clustering center. Specifically, the local density ρ i = ∑ j χ(d ij - d c ), where: ρ i is the local density of the data point x i ; d ij is the Euclidean distance between the data points x i , x j ; d c = max(d ij ) × α is the cut-off distance, α is the adjustment coefficient, and the function is the sum of the minimum distances from each data point x i to the data points with higher local density, that is, the minimum value of the sum of the distances from the data point x to all points with higher density than it; for the point x i with the maximum local density, k , is the maximum value of the distances from the data point x k to any other point; The local density ρ of the data points selected as the clustering centers by the improved density peak clustering method described above i and the distance δ i are both higher than those of other ordinary vertices; For the inverse mapping, multi-layer refinement is performed on multi-layer condensation to optimize the sub-networking result, specifically including: for the initial clustering result, map the sub-graph back to the upper level to refine the graph structure; then use the multi-layer refinement LDG function to optimize the refined graph to improve the segmentation quality; continuously repeat the above steps until the influence of multi-layer condensation is completely offset; The multi-layer refined LDG function is specifically as follows: Among them: V k is a vertex set; ω(V k ) is the total computational amount of the vertex set V k ; n average is the average computational amount of all vertices in the graph; σ n is the standard deviation of the vertex computational amounts; C = N total / K, representing the average scale size of each subnet; Adj(v i 1 ) are the adjacent vertices directly connected to the vertex v i , while Adj(v i 2 ) are the adjacent vertices directly connected to V k ∩Adj(v i 1 ); w is the weight of the indirect adjacent vertices, linearly positively correlated with the total number of nodes in the network; for some vertices that are defined to belong to both Adj(v i 1 ) and Adj(v i 2 ), they are uniformly placed into Adj(v i 1 ).

2. The adaptive sub-networking method for large power grid transient simulation according to claim 1, characterized in that, The mapping described above includes: ① mapping the busbars to vertices, ② mapping the transmission lines and transformers to edges, and ③ incorporating the remaining components into the vertices formed by mapping the busbars without affecting the topological structure of the graph. The computational load of all components is converted into the form of vertex point weights, and the point weight is: Where: W i refers to the point weight of vertex v i which is equal to the sum of the computational loads of all four main components included in the vertex. Since the transformers and lines are shared by the two end nodes, the computational load for one side is only half of it.

3. The adaptive sub-networking method for large power grid transient simulation according to claim 1, characterized in that, The said simplification preprocessing includes: 1) Transformer condensation: In the mapping process from the power system to the graph structure, nodes are mapped to vertices, and the transmission lines and transformer connection relationships between nodes are mapped to edges, and segmentation at the transformer is avoided; 2) Vertex condensation: The transmission delay of the circuit must be greater than or equal to one simulation step, i.e., τ≥t step , and condense the vertices connected by short circuits to obtain the condensed vertices, i.e., C vertices; 3) Multi-layer condensation / coarsening: Before graph segmentation, multi-layer condensation operation can be performed on the existing undirected graph G = G(V, E) to further simplify the graph structure.

4. The adaptive sub-networking method for large power grid transient simulation according to claim 3, characterized in that, To ensure that multi-layer coarsening will not be excessive, the constraint conditions for multi-layer condensation / coarsening include: a) The scale of the coarsened vertices cannot exceed the threshold, where the threshold where: N total is the total number of nodes in the network; K is the number of subnets decomposed; E represents the minimum number of vertices that can be tolerated in each subnet; b) During a single coarsening process, a vertex is only allowed to be condensed once.

5. The adaptive sub-networking method for large power grid transient simulation according to claim 3, characterized in that, The said initial segmentation further includes: 1) Since the vertices in the graph do not have coordinates, for two directly connected vertices v i and v j , d ij is directly the average length of the edge between vertices v i and v j , specifically: Due to the condensation operation, there may be more than one edge between vertices v i , v j , so the set E ij is used to represent it; 2) For the truncation distance d c = max(d ij ) × α, where: α is an adjustment coefficient, α ∈ (0, 1]; in actual use, for simplicity, let α = 1, and at this time the local density ρ i degenerates into the out-degree of the vertex; 3) Plot the vertices according to the two attributes of the local density ρ i and the distance δ i to obtain K initial aggregation centers by selecting from the upper right corner of the graph.

6. The adaptive sub-networking method for large power grid transient simulation according to claim 5, characterized in that, after obtaining the initial aggregation center, perform initial center expansion in the following way to obtain a small network with a certain scale, specifically: retrieve all the directly adjacent vertices of the initial aggregation center and allocate them into the corresponding sub-graphs, so that each sub-network is expanded to a certain extent, enabling more reference vertices in the subsequent vertex allocation process and the adjacent vertices of the initial aggregation center being closely related to it and should be allocated into the same sub-graph, thus accelerating the sub-networking process.

7. The adaptive sub-networking method for large power grid transient simulation according to claim 1, characterized in that, The segmentation quality of the initial segmentation result is optimized based on the linear decision greedy method, specifically including: Where: C = |V 0 | / K, |V 0 | is the sum of the computational amounts of all vertices; Adj(v i ) refers to the set of adjacent vertices of vertex v i ; for each vertex v i , |V k ∩ Adj(v i )|(1 - ω(V k ) / C) corresponds to the values of each vertex set V k (k = 1, 2, ……, K); the largest of the K values is the value of the constraint function f(v i ); in the components of the constraint function f(v i ), |V k ∩ Adj(v i )| represents the magnitude of the relevance between vertex v i and the set V k ; 1 - ω(V k ) / C plays a role in balancing the computational amounts of each vertex set.

8. A system for implementing the adaptive sub-networking method for large power grid transient simulation according to any one of claims 1 to 7, characterized in that, comprising: Power system raw data preprocessing unit, power system network segmentation unit and power system electromagnetic transient parallel simulation unit, where: the power system raw data preprocessing unit maps the power system network to a graph structure according to the input power system raw data, and on this basis, performs transformer condensation, vertex condensation and multi-layer condensation in sequence to obtain a graph with a simplified structure and containing power system information; the power system network segmentation unit determines the initial aggregation center, initial clustering, and refinement reduction operations according to the graph structure obtained by the power system raw data preprocessing unit to obtain a power system network segmentation result with uniform subnet scale and few inter-subnet tie lines; the power system electromagnetic transient parallel simulation unit performs power system electromagnetic transient parallel simulation according to the segmentation result of the power system network segmentation unit, and can complete the simulation with an acceleration ratio of several times or even dozens of times to obtain a simulation result waveform as reliable as the serial simulation.

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