A method for selecting target substations in power networks based on multi-dimensional indicators

Abstract

This invention discloses a method for selecting substation targets in a power network based on multi-dimensional indicators. The technical steps of this method are as follows: 1) Conducting intelligence research; 2) Constructing a weighted topology graph of the power network reflecting the network topology relationship and electrical distance characteristics based on complex network theory; 3) Constructing a power network energy flow graph reflecting the carrying capacity of the power network based on graph theory and graph maximum flow theory; 4) Calculating six key quantitative evaluation indicators for each substation in the target area's power system based on graph theory and complex network theory; 5) Calculating the entropy value of each key indicator and further calculating the entropy weight of multiple indicators based on the entropy weight algorithm; 6) Based on the key quantitative evaluation indicators of the substation in step 4) and the entropy weight of the indicators in step 5), conducting a comprehensive evaluation of the multi-dimensional key indicators, arranging them from largest to smallest according to the comprehensive evaluation indicator values, forming a preferred list of substations that could cause power network paralysis.

Description

Technical Field

[0001] This invention belongs to the field of power system automation technology, specifically relating to a method for optimizing the target of power network substations based on multi-dimensional indicators. Background Technology

[0002] Given the importance of power systems to modern society, attacks on and defenses against power systems are becoming increasingly crucial. Power networks consist of numerous power plants, hub substations, load substations, and transmission lines between them. When it is necessary to paralyze multiple power sources in a region or among multiple loads, even if the target region and the power supply substations for the loads are known, attacking them one by one would consume a significant amount of resources.

[0003] The following problems exist in existing power system attack and defense technologies:

[0004] 1. Difficulty in effectively identifying critical nodes in the power network. With limited information, it is impossible to accurately determine which substations are most critical to the operation of the entire power system.

[0005] 2. There is a lack of systematic analytical methods for the overall structure and function of the power network. A single indicator is insufficient to fully assess the importance of a substation.

[0006] 3. The complexity of power networks makes it difficult to accurately assess the impact of a single substation failure on the entire system.

[0007] To achieve precise paralysis of the power system and efficient restriction of power supply to target areas and facilities, there is an urgent need for a target optimization method for power network substations based on multi-dimensional indicators. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a target optimization method for power network substations based on multi-dimensional indicators, which can achieve precise paralysis of the power system and efficient restriction of target areas and facilities to ensure power supply.

[0009] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0010] In a first aspect, the present invention provides a target optimization method for power network substations based on multi-dimensional indicators, comprising the following steps:

[0011] S1: Obtain electrical and geographical distribution information of the power system in the target area;

[0012] S2: Based on complex network theory, and according to the electrical information and geographical distribution information, construct a weighted topology model of the power network that reflects the network topology relationship and electrical distance characteristics;

[0013] S3: Based on graph theory and graph maximum flow theory, construct a power network energy flow model that reflects the carrying capacity of the power network according to the weighted topology model of the power network.

[0014] S4: Based on graph theory and complex network theory, and according to the power network weighted topology model and power network energy flow model, calculate the values ​​of key quantitative evaluation indicators for each substation in the target area's power system.

[0015] S5: Based on the entropy weight algorithm, calculate the entropy value of key quantitative evaluation indicators for each substation and further calculate the entropy weight of multiple indicators;

[0016] S6: Based on the calculated values ​​of key quantitative evaluation indicators for substations and the entropy weights of multiple indicators, conduct a comprehensive evaluation of key indicators across multiple dimensions, arrange them from largest to smallest according to the comprehensive evaluation indicator values, and output the preferred list of targets that could cause substation paralysis in the power network.

[0017] Furthermore, the electrical information and geographical distribution information include information on power plants, substations or switching stations, transmission lines, and power loads.

[0018] Furthermore, obtain electrical and geographical distribution information of the power system in the target area, including:

[0019] S1-1: Obtain information about the power plant, including the power plant name, primary energy type, single unit capacity, total installed capacity, longitude, and latitude.

[0020] S1-2: Obtain information about the substation or switching station, including the station name, voltage level, longitude, and latitude;

[0021] S1-3: Obtain information about the transmission line, including: line name, voltage level, number of parallel circuits, line length, starting station, and ending station;

[0022] S1-4: Obtain information about the power load, including: load name, load type, maximum power consumption, upstream power supply substation, longitude, and latitude.

[0023] Furthermore, based on complex network theory, and according to the electrical information and geographical distribution information, a weighted topology model of the power network reflecting the network topology relationship and electrical distance characteristics is constructed, including:

[0024] Step S2-1: Construct the node set:

[0025] Identify all substations in the regional power network and construct nodes for each substation i. Traverse all substations to form a node set ,here This indicates the total number of substations.

[0026] Step S2-2: Construct the edge set:

[0027] Based on the constructed node set, edges between nodes are constructed according to the connection relationship between transmission lines and substations. For edges of the same voltage level, the line length is used as its weight, and the edge weight is calculated according to the following formula:

[0028] ;

[0029] In the formula, Let represent the edge weight of the k-th transmission line between substations i and j. This indicates the physical length of the transmission line. This indicates the voltage level of the transmission line. This indicates the highest voltage level of the regional power grid.

[0030] For any transmission line, calculate the weights according to the above formula and add the corresponding edges. Traverse all transmission lines to form an edge set. .

[0031] Step S2-3: Based on the node set and edge set, form a weighted topology model of the power network. .

[0032] Furthermore, based on graph theory and maximum flow theory, and according to the aforementioned weighted topology model of the power network, a power network energy flow model reflecting the carrying capacity of the power network is constructed, including:

[0033] Step S3-1: Construct the flow network:

[0034] Based on the weighted topology model of the power network, power plants and substations are abstracted as nodes of the power grid, and transmission lines are abstracted as edges of the power grid. Power flow is transmitted from generator nodes to load nodes through the edges of the power grid.

[0035] Virtual source nodes and virtual sink nodes are introduced. Virtual edges are added between virtual source nodes and each power plant node to realize the connection relationship. At the same time, the virtual edge is defined as a unidirectional edge, which only allows power flow from the virtual source node to the power plant node, and the capacity of the virtual edge is equivalent to the available generation capacity of the corresponding power plant.

[0036] A virtual edge is added between the virtual sink and each load substation to establish a connection. This virtual edge is defined as a unidirectional edge, allowing power flow only from the load substation to the virtual sink. The capacity of this virtual edge is equivalent to the actual power demand of each load substation at each time.

[0037] Step S3-2: Solve for the maximum energy flow in the power network based on the Ford-Fulkerson algorithm:

[0038] Step 1: Settings Set the label function L for each node and the queue node set. Set Q is a sequential set and must satisfy the first-in, first-out (FIFO) principle;

[0039] Step 2: Take Find the node connecting i along the associated edges. , and Then record , , ,and and Then record , After all elements in J have been traversed, mark i as checked.

[0040] Where i: the node currently being processed;

[0041] s: Source node, i.e., the starting point of the flow network;

[0042] j: Neighboring nodes directly connected to node i (connected via forward or reverse edges);

[0043] f(i,j): The actual flow (current value) on edge (i,j);

[0044] c(i,j): capacity of edge (i,j) (maximum allowed flow);

[0045] L j : The label of node j, used to record its predecessor node and augmentation direction;

[0046] flow: The maximum flow that can be increased in the current augmenting path;

[0047] L t : The label of the target node (sink t).

[0048] Step 3: Repeat Step 2 until... or All have been checked;

[0049] Step 4: If If the saturation edges are found to be complete, the algorithm terminates, and all saturated edges form the minimum cut set of the network. The sum of the capacities of the saturated edges is the maximum flow of the network. Otherwise, an augmenting chain p is found along the label L, and the adjustment method is as follows: , ,and , After execution is complete, return to Step 2.

[0050] Step S3-3: Based on the maximum energy flow calculated in step S3-2, obtain the maximum power supply capacity of the target power system under the given grid structure;

[0051] If the minimum cut falls within the set of edges between the virtual source node and the power plant node, it means that the total available power generation capacity at that point in time is less than the load demand power, i.e., a situation of insufficient power supply.

[0052] If the minimum cut falls within the edge set of the power network, it means that at that point in time, the power transmission of the minimum cut is limited due to insufficient power transmission capacity of the power network.

[0053] If the minimum cut falls within the set of edges between the load substation and the virtual sink, then the maximum flow of the power network is equal to the total load demand, meaning that the power supply can meet the load demand.

[0054] Furthermore, the key quantitative evaluation indicators for the substation include indicators of the importance of the grid structure and indicators of the degree of performance degradation;

[0055] The network structure importance indicators include node centrality, node power degree, and network clustering coefficient; the performance degradation indicators include connectivity, shortest path change rate, and power supply capacity degradation.

[0056] Furthermore, based on graph theory and complex network theory, and according to the aforementioned power network weighted topology model and power network energy flow model, the values ​​of key quantitative evaluation indicators for each substation in the target region's power system are calculated, including:

[0057] S4-1: Calculate the node betweenness centrality index, which is the ratio of the number of shortest paths passing through that node to the total number of shortest paths. The calculation formula is as follows:

[0058] ;

[0059] In the formula, This represents the number of shortest paths connecting power node s and load node t that pass through node i. This represents the total number of shortest paths connecting power node s and load node t.

[0060] S4-2: Obtain the node power degree index, which represents the number of neighboring nodes directly connected to the current node. The calculation formula is shown below:

[0061] ;

[0062] In the formula, Let represent the set of downstream neighbor nodes j of node i. This represents the active power flowing from node i to its neighbor node j; if the actual active power calculated by the maximum flow model is the power flowing from node j to node i, then... Furthermore, it is not included in the calculation of the node power degree index. This represents the active power injected into the power grid by the g-th power plant. This represents the total number of power plants of all types in the power grid.

[0063] S4-3: Calculate the node clustering coefficient index. This index quantifies the degree to which the central node i and its first-order neighbors form tightly connected clusters. Mathematically, it is described as the proportion of closed triangles formed by node i and its first-order neighbors. The node clustering coefficient... The calculation formula is as follows:

[0064] ;

[0065] In the formula, This represents the first-order neighbor nodes of the node i of interest. This indicates that nodes j and k are both first-order neighbors of node i, and This indicates that there is a direct connection between two first-order neighbor nodes j and k.

[0066] S4-4: Calculate the connectivity index, which represents the interconnectivity of remaining nodes after node failure. The connectivity index is described using the source-load imbalance within the electrical island. The calculation formula is shown below:

[0067] ;

[0068] In the formula, Let L represent the active load at substation l, and L represent the total number of substations. D represents the number of electrical islands formed by the power network after node i fails. If the power network is still connected after node i fails, then D=1. This indicates that after node i fails, substation k belongs to the j-th electrical island. and These represent the active load and active power source connected to substation k, respectively. This indicates the operation of taking the larger number.

[0069] S4-5: Calculate the shortest path change rate index, which is defined as the rate of change of the average shortest path distance between the power network's sources and loads after any node i fails. The calculation formula is shown below:

[0070] ;

[0071] In the formula, and These represent the sets of power source nodes and load substation nodes in the power network, respectively. and denoted as source-load node pair st in the complete network configuration and in the network configuration after substation i fails, respectively, the shortest path distances are calculated in the weighted topology graph using Dijkstra's algorithm.

[0072] S4-6: Calculate the power supply capacity degradation index. The calculation formula is shown below:

[0073] ;

[0074] In the formula, This indicates the power supply capacity under the complete network structure. This represents the power supply capacity of the power network after the i-th substation fails;

[0075] Betweenness centrality, node power degree, node clustering coefficient, connectivity, shortest path change rate, and power supply capacity degradation are all positive indicators. The larger the indicator value, the more important the substation is in the power network topology.

[0076] Furthermore, based on the entropy weight algorithm, the entropy values ​​of key quantitative evaluation indicators for each substation are calculated, and the entropy weights of multiple indicators are further calculated, including:

[0077] Step S5-1: Given m substation objects and n evaluation indicators, obtain the indicator set after indicator calculation. The index set of the i-th object is Meanwhile, the sample set for the j-th indicator is defined as follows: .

[0078] like If it is a positive indicator, then perform standardized preprocessing as follows:

[0079] ;

[0080] like If it is a negative indicator, then perform standardized preprocessing as follows:

[0081] ;

[0082] In the above formula, and Representing the j-th indicator The maximum and minimum values ​​in the sample set.

[0083] After preprocessing, a new set of indicators is obtained. .

[0084] Step S5-2: For the j-th index after standardization... Calculate the i-th substation sample sequentially. weight in this set of indicators :

[0085] ;

[0086] ;

[0087] Step S5-3: According to the definition of information entropy, calculate the information entropy of the j-th index in sequence:

[0088] ;

[0089] ;

[0090] Among them, when When, define .therefore, Heng was established.

[0091] Step S5-4: Using information entropy Calculate the weight of each indicator using the following formula. :

[0092] ;

[0093] .

[0094] Furthermore, based on the calculated values ​​of key quantitative evaluation indicators for substations and the entropy weights of multiple indicators, a comprehensive evaluation of multi-dimensional key indicators is conducted. These indicators are then ranked from largest to smallest, and a preferred list of substation-related targets for power network paralysis is output, including:

[0095] After calculating the weights of each indicator, the indicators are fused using the following formula to obtain the comprehensive evaluation indicator value:

[0096] ;

[0097] ;

[0098] In the formula, This is the comprehensive evaluation index value of the i-th substation;

[0099] After calculating the comprehensive evaluation index values ​​of each node, the optimal list of targets that could cause power grid substation paralysis is obtained by arranging them from largest to smallest.

[0100] Secondly, the present invention provides a target optimization device for power network substations based on multi-dimensional indicators, including a processor and a storage medium;

[0101] The storage medium is used to store instructions;

[0102] The processor is configured to operate according to the instructions to perform the steps of the method according to the first aspect.

[0103] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0104] 1. This invention discloses a target optimization method for power network substations based on multi-dimensional indicators. Based on complex network theory and graph theory, this invention constructs a weighted topology model of the power network reflecting the electrical connections of power facilities, and a maximum flow model of the power network reflecting the maximum power supply capacity of the power system. Using these models, the impact and criticality of any substation or transmission line on the overall power transmission capacity of the power system can be analyzed.

[0105] 2. Based on the constructed model, a comprehensive evaluation using multiple indicators is conducted from two aspects: the importance of the network structure and the degree of performance degradation. The indicators for network structure importance include node centrality, node power degree, and network clustering coefficient, while the indicators for performance degradation include connectivity, shortest path rate of change, and power supply capacity degradation. Finally, based on the entropy weight algorithm, the weights of each key indicator are calculated to achieve a quantitative evaluation of the substation's criticality, ultimately outputting a preferred list of substation-related targets that could cause power network paralysis.

[0106] 3. The method of this invention can be used for the selection of key targets for attacks on power systems under limited intelligence data, effectively identifying key links in the opponent's power system and providing a basis for decision-making to restrict the opponent's power supply. Furthermore, the method of this invention can also be used to identify key links in one's own power system. By implementing proactive protection measures such as physical hardening and network defense for key links, it helps to improve the survivability and continuous power supply capability of one's own power system in emergency situations. Attached Figure Description

[0107] Figure 1 This is a schematic diagram of the flow network of a power grid;

[0108] Figure 2A schematic diagram of the power flow network under conditions of insufficient power supply.

[0109] Figure 3 This is a schematic diagram of a power flow network under grid-side capacity constraints.

[0110] Figure 4 A schematic diagram of the power flow network assuming that the load's electricity demand is fully met;

[0111] Figure 5 This is a flowchart of the method of the present invention. Detailed Implementation

[0112] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0113] Example 1:

[0114] This invention provides a target optimization method for power network substations based on multi-dimensional indicators. The main technical steps of the method are as follows:

[0115] 1) Through intelligence research, collect information on power plants, substations or switching stations, transmission lines, land use and main power loads in the target area's power system;

[0116] 2) Based on complex network theory, construct a weighted topology diagram of the power network that reflects the network topology relationship and electrical distance characteristics;

[0117] 3) Based on graph theory and maximum flow theory, construct an energy flow graph of the power network that reflects the carrying capacity of the power network;

[0118] 4) Based on graph theory and complex network theory, six key quantitative evaluation indicators for each substation in the target area's power system are calculated sequentially.

[0119] 5) Based on the entropy weight algorithm, calculate the entropy value of each key indicator and further calculate the entropy weight of multiple indicators;

[0120] 6) Based on the key quantitative evaluation indicators of substations in step 4) and the entropy weight of indicators in step 5), conduct a comprehensive evaluation of key indicators in multiple dimensions, arrange them from largest to smallest according to the comprehensive evaluation indicator values, and form a preferred list of power network substations that could cause paralysis.

[0121] Specifically, this embodiment provides a target optimization method for power network substations based on multi-dimensional indicators, such as... Figure 5 As shown, it includes the following steps:

[0122] S1: Through intelligence research, collect electrical and geographical distribution information of power plants, substations or switching stations, transmission lines, and power loads in the target area's power system;

[0123] S2: Based on complex network theory, a weighted topology model of power network reflecting the network topology relationship and electrical distance characteristics is constructed;

[0124] S3: Based on graph theory and graph maximum flow theory, construct a power network energy flow model that reflects the carrying capacity of the power network;

[0125] S4: Based on graph theory and complex network theory, six key quantitative evaluation indicators for each substation in the target area's power system are calculated sequentially.

[0126] S5: Based on the entropy weight algorithm, calculate the entropy value of each key indicator and further calculate the entropy weight of multiple indicators;

[0127] S6: Based on steps S4 and S5, conduct a comprehensive evaluation of key indicators across multiple dimensions, arrange them from largest to smallest according to the comprehensive evaluation indicator values, and output a preferred list of targets that could cause power grid substation paralysis.

[0128] Step S1 includes: collecting electrical and geographical distribution information of power plants, substations or switching stations, transmission lines, and power loads in the target area's power system through intelligence research. Specifically:

[0129] S1-1: Power Plant Information

[0130] The required power plant information is shown in Table 1:

[0131] Table 1 Information on Required Power Plants

[0132]

[0133] S1-2: Substation or switching station information:

[0134] Information on the required substations or switching stations is shown in Table 2:

[0135] Table 2 Information on Required Substations or Switching Stations

[0136]

[0137] S1-3: Transmission line information:

[0138] Information on the required transmission lines is shown in Table 3:

[0139] Table 3 Information on Required Transmission Lines

[0140]

[0141] S1-4: Electrical Load

[0142] The required power load information is shown in Table 4:

[0143] Table 4 Information on Required Power Load

[0144]

[0145] Step S2 includes: constructing a weighted topology model of the power network that reflects the network topology relationship and electrical distance characteristics based on complex network theory, specifically:

[0146] Step S2-1: Construct the node set

[0147] Identify all substations in the regional power network and construct nodes for each substation i. Traverse all substations to form a node set ,here This indicates the total number of substations.

[0148] Step S2-2: Construct the edge set

[0149] Based on the constructed node set, edges between nodes are constructed according to the connection relationship between transmission lines and substations. Conventional weighted topology models generally use the reactance parameters of transmission lines as edge weights, but in practical applications of power system attack and defense, it is often difficult to obtain the precise parameters of each transmission line. On the other hand, transmission lines of the same voltage level have similar physical parameters such as resistance and reactance per unit length; therefore, for edges of the same voltage level, their line length can be used as their weight. Furthermore, in power grid flow calculations, the resistance, reactance, and other parameters of transmission lines are generally converted to per-unit values ​​based on the highest voltage level for calculation. Analogous to the per-unit value calculation process, the edge weights can be calculated using the following formula:

[0150] ;

[0151] In the formula, Let k represent the edge weight of the k-th transmission line between substations i and j (k is introduced mainly because there may be multiple parallel transmission lines between substations). This indicates the physical length of the transmission line. This indicates the voltage level of the transmission line (in kV). This indicates the highest voltage level of the regional power grid (in kV).

[0152] For any transmission line, calculate the weights according to the above formula and add the corresponding edges. Traverse all transmission lines to form an edge set. .

[0153] Step S2-3: Form a weighted graph .

[0154] Finally, based on the node set and edge set, a weighted topology model of the power network is formed. .

[0155] Step S3 includes: constructing a power network energy flow model reflecting the carrying capacity of the power network based on graph theory and graph maximum flow theory, specifically:

[0156] Power flow calculations in power networks, whether AC or DC, have mature theoretical foundations and solution algorithms. However, these methods require high-precision model parameters for each branch of the power network, which is difficult to meet the needs of practical power system attack and defense applications. However, considering that practical power system attack and defense applications primarily focus on ensuring the supply of target loads in a specific region, the power network mainly plays a role in path dependence and transmission capacity constraints in this problem. To address these requirements, the maximum flow algorithm from graph theory can be used for approximate modeling, without the need to construct a precise mathematical model of the power network.

[0157] Step S3-1: Construct the flow network

[0158] Power networks have a graph structure, where power plants and substations can be abstracted as nodes in the grid, and transmission lines as edges. Power flow is transmitted from generator nodes to load nodes via these edges. However, existing algorithms such as the Ford-Fulkerson algorithm are typically only applicable to maximum flow problems in single-source-single-sink networks, while real-world power networks usually contain numerous power plants and load substations. Clearly, each power plant is a source of injected power, while each load substation is a sink; thus, the power network is a multi-source-multi-sink network.

[0159] To address this, virtual source points and virtual sink points are introduced. Virtual edges are added between the virtual source points and each power plant node to establish connections. These virtual edges are defined as unidirectional, allowing power flow only from the virtual source point to the power plant node, and their capacity is equivalent to the available generating capacity of the corresponding power plant. Similarly, virtual edges are added between the virtual sink points and each load substation to establish connections. Likewise, these virtual edges are defined as unidirectional, allowing power flow only from the load substation to the virtual sink point, and their capacity is equivalent to the actual power demand of each load substation at each time point. Specifically, as follows... Figure 1 As shown.

[0160] Figure 1 middle, This represents the available generating capacity of power plant G1, and also the capacity of the one-way edge from the virtual source point to this power plant node. This represents the power capacity of the transmission line between hub substations T1 and T4, which is used as the capacity of this bidirectional side. This represents the active power load demand of the load substation L1 at a certain moment, and is used as the capacity of the one-way side from the load substation to the virtual load point.

[0161] Step S3-2: Solve for the maximum energy flow of the power network based on the Ford-Fulkerson algorithm.

[0162] The basic idea of ​​the Ford-Fulkerson algorithm is to find augmenting paths under the constraint of flow conservation. When no augmenting path can be found, the algorithm terminates. The specific process is as follows:

[0163] Step 1: Place Set the label function L for each node and the queue node set. (Set Q is a sequential set and must satisfy the first-in, first-out principle).

[0164] Step 2: Take Find the node connecting i along the associated edges. , and Then record , , ,and and Then record , After all elements in J have been traversed, mark i as checked.

[0165] Where i: the node currently being processed;

[0166] s: Source node, i.e., the starting point of the flow network;

[0167] j: Neighboring nodes directly connected to node i (connected via forward or reverse edges);

[0168] f(i,j): The actual flow (current value) on edge (i,j);

[0169] c(i,j): capacity of edge (i,j) (maximum allowed flow);

[0170] L j : The label of node j, used to record its predecessor node and augmentation direction;

[0171] flow: The maximum flow that can be increased in the current augmenting path;

[0172] L t : The label of the target node (sink t).

[0173] Step 3: Repeat Step 2 until... or All have been checked;

[0174] Step 4: If If the saturation edges are found to be complete, the algorithm terminates, and all saturated edges form the minimum cut set of the network. The sum of the capacities of the saturated edges is the maximum flow of the network. Otherwise, an augmenting chain p is found along the label L, and the adjustment method is as follows: , ,and , After execution is complete, return to Step 2.

[0175] Step S3-3: Based on the maximum energy flow calculated in step S3-2, obtain the maximum power supply capacity of the target power system under the given grid structure.

[0176] By introducing virtual source and virtual sink points, the traditional Ford-Fulkerson algorithm can be adapted to the problem of power supply capacity assessment in power networks. It is worth noting that, for this problem, the algorithm results may exhibit three different outcomes, explained in detail below:

[0177] The minimum cut lies in the set of edges between the virtual source node and the power plant node, such as... Figure 2 As shown, this means that the total available generating capacity at this point in time is less than the load demand, i.e., a situation of insufficient power supply.

[0178] The minimum cut lies within the set of edges in the power network, such as... Figure 3 As shown, this means that at this point in time, due to insufficient power transmission capacity of the power network, the power transmission at the minimum cut-off section is limited. This situation often occurs when the power network is deliberately attacked, or when some key substations or transmission lines are out of service.

[0179] The minimum cut lies in the set of edges between the load substation and the virtual sink, such as... Figure 4 As shown, this is the case where the maximum flow of the power network is equal to the total load demand, meaning that the power supply can meet the load demand.

[0180] Through maximum flow calculation, the flow of the edge between the load substation and the virtual sink is the actual power supply at that point in time. The difference between the power supply and the demand power is the load shedding of the corresponding load substation. The flow of the edge between the virtual source and the power plant node is the active power output of the power plant at that point in time. For coal-fired, gas-fired, and oil-fired power plants, the primary energy consumption for the corresponding period can be calculated based on this active power output, and the primary capacity reserve of the power plant can be updated.

[0181] Step S4 includes: based on graph theory and complex network theory, calculating six key quantitative evaluation indicators for each substation in the target area's power system, specifically:

[0182] This invention, based on graph theory and complex network theory, comprehensively evaluates network structures from two aspects: the importance of the network structure and the degree of performance degradation. The network structure importance indicators include node centrality, node power degree, and network clustering coefficient, while the performance degradation indicators include connectivity, shortest path rate of change, and power supply capacity degradation. The definitions and mathematical expressions of each of these indicators are explained in detail below.

[0183] S4-1: Node Betweenness Centrality Index

[0184] Betweenness centrality is the ratio of the shortest path through a given node to the total number of shortest paths. The shortest path is defined as the path with the minimum total weight among all paths between node s and node t. Considering that power flow originates from power source nodes to load nodes, this project, unlike traditional complex network analysis which identifies shortest paths between any two nodes, only identifies the shortest path between any power source-load node pair in the weighted topology graph, reflecting the substation's role as an energy transfer hub for power supply. Node Betweenness Indicators The calculation formula is as follows:

[0185] ;

[0186] In the formula, This represents the number of shortest paths connecting power node s and load node t that pass through node i. This represents the total number of shortest paths connecting power node s and load node t.

[0187] A higher betweenness centrality index for a node (substation) indicates that the node is located on a main branch of the source-load electrical connection, meaning that the node has a significant impact on power transmission efficiency. Therefore, betweenness centrality is a positive indicator; the higher the index value, the more important the substation is in the power network topology.

[0188] S4-2: Node Power Scale

[0189] Node degree represents the number of neighboring nodes directly connected to a given node. This project improves upon the traditional node degree metric by proposing a node power degree metric, defined as the proportion of active power flowing out of that node relative to the total active power flow in the power network. Node Power Degree Metric The calculation formula is shown below:

[0190] ;

[0191] In the formula, Let represent the set of downstream neighbor nodes j of node i. This represents the active power flowing from node i to its neighbor node j; if the actual active power calculated by the maximum flow model is the power flowing from node j to node i, then... Furthermore, it is not included in the calculation of the node power degree index. This represents the active power injected into the power grid by the g-th power plant. This represents the total number of power plants of all types in the power grid.

[0192] A higher node power index for a substation indicates that the hub substation / load substation is handling a higher power transmission capacity. If this node fails, it will cause a large-scale power flow shift, with a higher probability of cascading failures and widespread power outages. Therefore, the node power index is a positive indicator; the higher the value, the more important the substation is in the power network topology.

[0193] S4-3: Node Clustering Coefficient Indicator

[0194] The clustering coefficient quantifies the degree to which a central node i and its first-order neighbors form a tightly connected cluster. Mathematically, it is described as the proportion of closed triangles formed by node i and its first-order neighbors. The calculation formula is as follows:

[0195] ;

[0196] In the formula, This represents the first-order neighbor nodes of the node i of interest. This indicates that nodes j and k are both first-order neighbors of node i, and This indicates that there is a direct connection between two first-order neighbor nodes j and k.

[0197] The node clustering coefficient quantifies the tightness of connections between a group of nodes. In the context of power network problems, if there are many edges and close connections between nodes, then when node i fails, the more backup paths its neighbors have, the smaller the impact on power supply reliability. Conversely, if the connections between nodes are weak, in the extreme case where all neighbors are only connected to node i and there are no edges between neighbors, then when node i fails, its neighbors may lack backup paths and lose power supply. Therefore, the node clustering coefficient is a negative indicator; the larger the coefficient, the smaller the impact on the power network's supply capacity when that node fails, and thus the relatively lower the importance of that substation.

[0198] S4-4: Connectivity Indicators

[0199] Connectivity represents the interoperability of remaining nodes after a node failure. In the context of a power network, if a node (substation) fails and causes grid disconnection, the resulting two or more electrical islands may have insufficient generating capacity to support the electricity load demand, leading to load shedding. While connectivity is a binary 0-1 result, it cannot reflect the source-load balance capability within each electrical island. Therefore, this project uses the source-load imbalance within the electrical islands to describe connectivity. The calculation formula is shown below:

[0200] ;

[0201] In the formula, Let L represent the active load at substation l, and L represent the total number of substations. D represents the number of electrical islands formed by the power network after node i fails. If the power network is still connected after node i fails, then D=1. This indicates that after node i fails, substation k belongs to the j-th electrical island. and These represent the active load and active power source connected to substation k, respectively. This indicates the operation of taking the larger number.

[0202] The connectivity index, considering the source-load imbalance within an electrical island, reflects the impact of node i on the power network connectivity and the degree of matching of source-load distribution after its failure. A larger connectivity index value indicates a higher degree of source-load mismatch, leading to a larger-scale load loss. Therefore, the connectivity index is a positive indicator; a larger value indicates higher node importance.

[0203] S4-5: Shortest Path Change Rate Indicator

[0204] The Shortest Path Change Rate (SPR) is defined as the rate of change of the average shortest path distance between power source and load nodes in a power network after the failure of any node i. Similar to SPR1, since power flow is unidirectional from power source nodes to load nodes, the calculation of the shortest path only considers the shortest path between power source and load node pairs. The calculation formula is shown below:

[0205] ;

[0206] In the formula, and These represent the sets of power source nodes and load substation nodes in the power network, respectively. and denoted as source-load node pair st in the complete network configuration and in the network configuration after substation i fails, respectively, the shortest path distances are calculated in the weighted topology graph using Dijkstra's algorithm.

[0207] A larger shortest path change rate index means that the electrical distance between the source and load increases after node i fails, resulting in a decrease in transmission efficiency. Therefore, the shortest path change rate index is a positive indicator; the larger the index value, the more important the corresponding substation is in the power network topology.

[0208] S4-6: Power Supply Capacity Degradation Indicator

[0209] Using the power network supply capacity assessment algorithm based on maximum flow proposed in step S3, the power supply capacity degradation index is defined as the rate of change of the power network supply capacity after any substation failure compared to the supply capacity under the complete network condition. Power Supply Capacity Degradation Index The calculation formula is shown below:

[0210] ;

[0211] In the formula, This indicates the power supply capacity under the complete network structure. This represents the power supply capacity of the power network after the i-th substation fails.

[0212] A larger power supply capacity decline index means a decrease in the power flow transmission capacity of the power network after the failure of the i-th substation, which is detrimental to load supply. Therefore, the power supply capacity decline index is a positive indicator; the larger the index value, the more important the corresponding substation.

[0213] Step S5 includes: calculating the entropy value of each key indicator based on the entropy weight algorithm and further calculating the entropy weight of multiple indicators, specifically:

[0214] The indicators proposed in step S4 differ in numerical dimensions. In multi-indicator comprehensive evaluation, another key aspect is determining the weight of each indicator within the overall evaluation. Compared to subjective weighting methods such as the analytic hierarchy process (AHP), the entropy weight method can measure the distinguishing power of indicators on the evaluation object and objectively set the weights of each indicator based on this distinguishing power. Therefore, the entropy weight method is used to achieve multi-indicator comprehensive evaluation, thereby obtaining the ranking results of the substation's importance.

[0215] The calculation process of the multi-index comprehensive evaluation model based on the entropy weight method is explained as follows:

[0216] Step S5-1: Data Standardization

[0217] Given m objects to be evaluated (i.e., substations) and n evaluation indicators, the indicator set is obtained after indicator calculation. The index set of the i-th object is Meanwhile, the sample set for the j-th indicator is defined as follows: .

[0218] like If it is a positive indicator, then perform standardized preprocessing as follows:

[0219] ;

[0220] like If it is a negative indicator, then perform standardized preprocessing as follows:

[0221] ;

[0222] In the above formula, and Representing the j-th indicator The maximum and minimum values ​​in the sample set.

[0223] After preprocessing, a new set of indicators is obtained. .

[0224] Step S5-2: Calculate the weight of each indicator under each scheme.

[0225] For the j-th index after standardization Calculate the sample of the i-th object (i.e., the substation) in sequence. weight in this set of indicators :

[0226] ;

[0227] ;

[0228] Step S5-3: Calculate the information entropy of each indicator

[0229] According to the definition of information entropy, the information entropy of the j-th index is calculated sequentially:

[0230] ;

[0231] ;

[0232] Among them, when When, define .therefore, Heng was established.

[0233] Step S5-4: Calculate the weight of each indicator

[0234] Through information entropy Calculate the weight of each indicator using the following formula. :

[0235] ;

[0236] ;

[0237] Step S6 includes: based on steps S4 and S5, performing a comprehensive evaluation of multi-dimensional key indicators, arranging them from largest to smallest according to the comprehensive evaluation indicator values, and outputting a preferred list of targets that could cause power grid substation paralysis, specifically:

[0238] After calculating the weights of each indicator, the indicators can be fused using the following formula to obtain the comprehensive evaluation indicator value:

[0239] ;

[0240] ;

[0241] In the formula, This is the comprehensive evaluation index value of the i-th substation.

[0242] After calculating the comprehensive evaluation index values ​​of each node, the substation paralysis list is obtained by arranging them from largest to smallest.

[0243] This invention discloses a target optimization method for power network substations based on multi-dimensional indicators. Based on complex network theory and graph theory, this method constructs a weighted topology model of the power network reflecting the electrical connections of power facilities, and a maximum flow model of the power network reflecting the maximum power supply capacity of the power system. Using these models, the impact and criticality of any substation or transmission line on the overall power transmission capacity of the power system can be analyzed.

[0244] Example 2:

[0245] This embodiment provides a target optimization device for power network substations based on multi-dimensional indicators, including a processor and a storage medium;

[0246] The storage medium is used to store instructions;

[0247] The processor is configured to operate according to the instructions to perform the steps of the method according to Embodiment 1.

[0248] Example 3:

[0249] This invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0250] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0251] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0252] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0253] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0254] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for selecting target substations in a power network based on multi-dimensional indicators, characterized in that, Includes the following steps: S1: Obtain electrical and geographical distribution information of the power system in the target area; S2: Based on complex network theory, and according to the electrical information and geographical distribution information, construct a weighted topology model of the power network that reflects the network topology relationship and electrical distance characteristics; S3: Based on graph theory and graph maximum flow theory, construct a power network energy flow model that reflects the carrying capacity of the power network according to the weighted topology model of the power network. S4: Based on graph theory and complex network theory, and according to the power network weighted topology model and power network energy flow model, calculate the values ​​of key quantitative evaluation indicators for each substation in the target area's power system. S5: Based on the entropy weight algorithm, calculate the entropy value of key quantitative evaluation indicators for each substation and further calculate the entropy weight of multiple indicators; S6: Based on the calculated values ​​of key quantitative evaluation indicators for substations and the entropy weights of multiple indicators, conduct a comprehensive evaluation of key indicators across multiple dimensions, arrange them from largest to smallest according to the comprehensive evaluation indicator values, and output a preferred list of targets that could cause substation paralysis in the power network. Based on graph theory and maximum flow theory, and according to the weighted topology model of the power network, a power network energy flow model reflecting the carrying capacity of the power network is constructed, including: Step S3-1: Based on the weighted topology model of the power network, power plants and substations are abstracted as nodes of the power grid, and transmission lines are abstracted as edges of the power grid. Power flow is transmitted from generator nodes to load nodes through the edges of the power grid. Virtual source points and virtual sink points are introduced; virtual edges are added between virtual source points and each power plant node to realize the connection relationship. At the same time, the virtual edge is defined as a unidirectional edge, which only allows power flow from the virtual source point to the power plant node, and the capacity of the virtual edge is equivalent to the available power generation capacity of the corresponding power plant. A virtual edge is added between the virtual sink and each load substation to establish a connection. This virtual edge is defined as a unidirectional edge, allowing power flow only from the load substation to the virtual sink. The capacity of this virtual edge is equivalent to the actual power demand of each load substation at each time. Step S3-2: Solve for the maximum energy flow in the power network based on the Ford-Fulkerson algorithm: Step 1: Settings Set the label function L for each node and the queue node set. Set Q is a sequential set and must satisfy the first-in, first-out (FIFO) principle; Step 2: Take Find the node connecting i along the associated edges. , and Then record , , ,and and Then record , After all elements in J have been traversed, mark i as checked. Step 3: Repeat Step 2 until... or All have been checked; Where i is the node currently being processed; Let be the first node in set Q, s be the source node, i.e., the starting point of the flow network; j be the neighboring node directly connected to node i; f(i,j) be the actual flow on edge (i,j); c(i,j) be the capacity of edge (i,j); L j Here is the label for node j, used to record its predecessor node and augmentation direction; flow is the maximum augmentable flow of the current augmentation path; L t Label for load node t; L i Let i be the label of node i; Step 4: If If the saturation edges are found to be complete, the algorithm terminates, and all saturated edges form the minimum cut set of the network. The sum of the capacities of the saturated edges is the maximum flow of the network. Otherwise, an augmenting chain p is found along the label L, and the adjustment method is as follows: , ,and , After execution is complete, return to Step 2. Step S3-3: Based on the maximum energy flow calculated in step S3-2, obtain the maximum power supply capacity of the target power system under the given grid structure; If the minimum cut falls within the set of edges between the virtual source node and the power plant node, it means that at this point in time, the power generation capacity is always less than the load demand, i.e., the power supply is insufficient. If the minimum cut falls within the edge set of the power network, it means that at that moment, the power transmission of the minimum cut is limited due to insufficient power transmission capacity of the power network. If the minimum cut falls within the set of edges between the load substation and the virtual sink, then the maximum flow of the power network is equal to the total load demand, which means that the power supply can meet the load demand. The key quantitative evaluation indicators for the substation include indicators of the importance of the grid structure and indicators of the degree of performance degradation; The network structure importance indicators include node centrality, node power degree, and network clustering coefficient; the performance degradation indicators include connectivity, shortest path change rate, and power supply capacity degradation. Based on graph theory and complex network theory, and according to the aforementioned power network weighted topology model and power network energy flow model, the values ​​of key quantitative evaluation indicators for each substation in the target region's power system are calculated, including: S4-1: Calculate the node betweenness centrality index, which is the ratio of the number of shortest paths passing through that node to the total number of shortest paths. The calculation formula is as follows: ； In the formula, This represents the number of shortest paths connecting power node s and load node t that pass through node i. This represents the total number of shortest paths connecting power node s and load node t. These parameters are obtained using a weighted topology model of the power network. S4-2: Obtain the node power degree index, which represents the number of neighboring nodes directly connected to the current node. The calculation formula is shown below: ； In the formula, Let j represent the set of downstream neighbor nodes j of node i. This represents the active power flowing from node i to its neighbor node j; if the actual active power calculated by the maximum flow model is the power flowing from node j to node i, then... And it is not included in the calculation of the node power degree index; This represents the active power injected into the power grid by the g-th power plant. This represents the total number of power plants of all types in the power network. The above parameters are obtained using the power network energy flow model. S4-3: Calculate the node clustering coefficient index. This index quantifies the degree to which the central node i and its first-order neighbors form tightly connected clusters. Mathematically, it is described as the proportion of closed triangles formed by node i and its first-order neighbors. The node clustering coefficient... The calculation formula is as follows: ； In the formula, This represents the first-order neighbor nodes of the node i of interest. This indicates that nodes j and k are both first-order neighbors of node i, and This indicates that there is a direct connection between two first-order neighbor nodes j and k. The above parameters are obtained using a weighted topology model of the power network. S4-4: Calculate the connectivity index, which represents the interconnectivity of remaining nodes after node failure; the connectivity index is described using the source-load imbalance within the electrical island. The calculation formula is shown below: ； In the formula, Let L represent the active load at substation l, and L represent the total number of substations. D represents the number of electrical islands formed by the power network after node i fails. If the power network is still connected after node i fails, then D=1. This indicates that after node i fails, substation k belongs to the j-th electrical island. and These represent the active load and active power source connected to substation k, respectively. This indicates the operation of taking the larger number; the above parameters are obtained using the power network energy flow model. S4-5: Calculate the shortest path change rate index, which is defined as the rate of change of the average shortest path distance between the power network's source and load after any node i fails. The calculation formula is shown below: ； In the formula, and These represent the sets of power source nodes and load substation nodes in the power network, respectively. and These represent the shortest path distances for source-load node pair st in the complete network configuration and in the network configuration after substation i fails, respectively. The above parameters are calculated in the weighted topology graph using Dijkstra's algorithm. S4-6: Calculate the power supply capacity degradation index. The calculation formula is shown below: ； In the formula, This indicates the power supply capacity under the complete network structure. This represents the power supply capacity of the power network after the i-th substation fails; Betweenness centrality, node power degree, node clustering coefficient, connectivity, shortest path change rate, and power supply capacity degradation are all positive indicators. The larger the indicator value, the more important the substation is in the power network topology.

2. The method for selecting target substations in a power network based on multi-dimensional indicators according to claim 1, characterized in that, The electrical and geographic distribution information includes information on power plants, substations or switching stations, transmission lines, and power loads.

3. The method for selecting target substations in a power network based on multi-dimensional indicators according to claim 2, characterized in that, Obtain electrical and geographical distribution information of the power system in the target area, including: S1-1: Obtain information about the power plant, including the power plant name, primary energy type, single unit capacity, total installed capacity, longitude, and latitude. S1-2: Obtain information about the substation or switching station, including the station name, voltage level, longitude, and latitude; S1-3: Obtain information about the transmission line, including: line name, voltage level, number of parallel circuits, line length, starting station, and ending station; S1-4: Obtain information about the power load, including: load name, load type, maximum power consumption, upstream power supply substation, longitude, and latitude.

4. The method for selecting target substations in a power network based on multi-dimensional indicators according to claim 3, characterized in that, Based on complex network theory, and according to the aforementioned electrical and geographical distribution information, a weighted topology model of the power network reflecting the grid topology relationships and electrical distance characteristics is constructed, including: Step S2-1: Identify all substations in the regional power network and construct a node for the i-th substation. Traverse all substations to form a node set , Indicates the total number of substations; Step S2-2: Based on the constructed node set, construct the edges between nodes according to the connection relationship between the transmission line and the substation. For edges of the same voltage level, use the line length as its weight, and calculate the edge weight according to the following formula: ； In the formula, Let represent the edge weight of the k-th transmission line between substation i and substation j. This indicates the physical length of the transmission line. This indicates the voltage level of the transmission line. Indicates the highest voltage level of the regional power grid; For any transmission line, calculate the weights according to the above formula and add the corresponding edges. Traverse all transmission lines to form an edge set. ;e (i,j) This represents the edge between substations i and j; Step S2-3: Based on the node set and edge set, form a weighted topology model of the power network. .

5. The method for selecting target substations in a power network based on multi-dimensional indicators according to claim 4, characterized in that, Based on the entropy weight algorithm, the entropy values ​​of key quantitative evaluation indicators for each substation are calculated, and further, the entropy weights of multiple indicators are calculated, including: Step S5-1: Given m substation objects and n evaluation indicators, obtain the indicator set after indicator calculation. The index set of the i-th object is Meanwhile, the sample set for the j-th indicator is defined as follows: ; like If it is a positive indicator, then perform standardized preprocessing as follows: ； like If it is a negative indicator, then perform standardized preprocessing as follows: ； In the above formula, and Representing the j-th indicator The maximum and minimum values ​​in the sample set; After preprocessing, a new set of indicators is obtained. ; Step S5-2: For the j-th index after standardization... Calculate the i-th substation sample sequentially. weight in this set of indicators : ； ； Step S5-3: According to the definition of information entropy, calculate the information entropy of the j-th index in sequence: ； ； Among them, when When, define ;therefore, Heng is established; Step S5-4: Using information entropy Calculate the weight of each indicator using the following formula. : ； 。 6. The method for selecting target substations in a power network based on multi-dimensional indicators according to claim 5, characterized in that, Based on the calculated values ​​of key quantitative evaluation indicators for substations and the entropy weights of multiple indicators, a comprehensive evaluation of key indicators across multiple dimensions is conducted. The indicators are then ranked from largest to smallest, and a preferred list of substation-related targets for power network paralysis is output, including: After calculating the weights of each indicator, the indicators are fused using the following formula to obtain the comprehensive evaluation indicator value: ； ； In the formula, This is the comprehensive evaluation index value of the i-th substation; After calculating the comprehensive evaluation index values ​​of each node, the optimal list of targets that could cause power grid substation paralysis is obtained by arranging them from largest to smallest.

7. A target optimization device for power network substations based on multi-dimensional indicators, characterized in that, Including processor and storage media; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to any one of claims 1-6.

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