Power network key circle detection method based on simulated annealing algorithm

Abstract

The invention provides a power network key circle detection method based on a simulated annealing algorithm. The method comprises the following steps: step 1, constructing a power network topology model; step 2, constructing a solution space; 3, constructing an initial solution set; and step 4, detecting a key ring. According to the invention, the simulated annealing algorithm containing the neighborhood search strategy is adopted to detect the key circle of the power network, the key circle of the power network can be successfully detected, the detection efficiency is effectively improved, the method can be suitable for a large network, and the application range of the method is expanded; the cascade failure process is adopted to simulate the fault process of the real power network, the fragile structure of the power network can be detected, and effective support is provided for safety protection of the power network.

Description

Technical Field

[0001] The present invention relates to a method for detecting critical loops of a power network based on a simulated annealing algorithm, belonging to the field of network technology. Background Art

[0002] Complex networks reflect the structural patterns and dynamic characteristics of complex systems in the real world through the interaction of nodes and edges. By analyzing complex networks, the topological structure, functional characteristics, and dynamic behavior of the system can be revealed, thus providing theoretical support for system optimization, risk control, and prediction. In the study of the robustness of complex networks, identifying the key structures of the network is a core issue. In recent years, the research has mainly focused on the identification of key nodes. The loop structure is an important part of the network and higher-order interactions. It can not only provide a new path for analyzing the influence of nodes, but also play an indispensable role in many key attributes such as the synchronization efficiency and anti-destruction performance of the network. However, the existing indicators are calculated based on the entire network, which makes the identification and search of critical loops in large networks still require further theoretical research and algorithm design. The existing detection of critical loops mainly has the following problems: (1) Low computational efficiency: The existing evaluation indicators for loop importance are calculated based on the entire network, consuming a large amount of time; (2) Failure to consider the systematic risk of the power grid: Cascading failure is a serious chain reaction in the operation of the power grid, which may lead to large-scale power outages or even the collapse of the entire network. The existing methods for identifying critical loops in the power grid do not fully consider the occurrence of cascading failure phenomena in the power grid and are difficult to effectively support the safety protection of the power grid; (3) Poor applicability: Traditional algorithms do not consider the relationship between critical loops of different lengths and lack the setting of the search range, which limits their application in large networks. Summary of the Invention

[0003] The present invention provides a method for detecting critical loops of a power network based on a simulated annealing algorithm, which is suitable for large networks. It can successfully detect the critical loops of the power network and effectively improve the detection efficiency.

[0004] To solve the above technical problems, the present invention provides a method for detecting critical loops of a power network based on a simulated annealing algorithm, including the following steps: Step 1, construct a topological model of the power network: Obtain the information of each load, each generator, and each branch of the power network, and construct a topological model of the power network according to the information of each load, each generator, and each branch of the power network G(V, E) , the topological model of the power network G(V, E) The nodes of which include generator nodes and load nodes, and the topological model of the power network G(V, E) The total number of nodes is N , the topological model of the power network G (V, E) The N nodes of which are sequentially denoted asv i , where i is a positive integer less than or equal to N, V is a set composed of N nodes, E is a set composed of edges; Step 2, construct the solution space: Traverse the power network topology model using the depth-first search algorithm G(V, E) to generate B cycles of length L , and add the generated B cycles of length L to the solution space to complete the construction of the solution space. The B cycles that make up the solution space are sequentially denoted as D h , where h is a positive integer less than or equal to B ; Step 3, construct the initial solution set: Use the greedy strategy to expand all the first critical cycles with known lengths less than G(V, E) in the power network topology model L to obtain multiple second critical cycles of length L , and add all the second critical cycles of length L obtained after expansion to the initial solution set, or extract multiple cycles from the solution space and add them to the initial solution set so that the number of cycles in the initial solution set is A , to complete the construction of the initial solution set. The A cycles that make up the initial solution set are sequentially denoted as Q a , where a is a positive integer less than or equal to A , A is the preset value of the number of cycles in the initial solution set; Step 4, detect critical cycles: Based on the initial solution set, use the simulated annealing algorithm with the inclusion neighborhood search strategy to find critical cycles in the solution space to obtain critical cycles.

[0005] In a specific implementation manner, Step 4 is specifically: Step 4.1, initialize the parameters in the simulated annealing algorithm, including the initial temperature T 0, the temperature reduction coefficient α , the termination temperature T end , the neighborhood search range m , and set the status of all cycles in the initial solution set to unvisited; Step 4.2, when all cycles in the initial solution set have been visited, execute Step 4.7. When there are unvisited cycles in the initial solution set, randomly select an unvisited cycle Q a from the initial solution set, and use Q a as the current solution C , and useQ a Mark as visited, and calculate the current solution based on the cascading failure process C The maximum connected component ratio R(C) ,calculate R(C) The formula is as follows: R(C) = N ’ / N ,in N ’ For the power network topology model G(V, E) Power network topology model after removing a loop and cascading failure process G(V, E) The total number of nodes remaining in the solution. The removed circle is the current solution. C ; Step 4.3, search range based on neighborhood m , based on the current solution C Search for cycles in the solution space to obtain the set S nei (C) , ,in, d r For the circle D h The nodes in q z Unlock the current circle C The nodes in d(d r ,q z ) Representation Node d r To Node q z The shortest path distance, min(d(d r ,q z )) Indicates circle D h To current solution C The shortest distance, S nei (Q a ) The circles in are denoted as O k ,in k is an integer greater than 0; Step 4.4, if S nei (C) If there are unvisited circles in S nei (C) Select an unvisited circle O k As a new solutionW and mark the loop O k as visited. If S nei (C) there is no unvisited loop in, then execute the steps in sequence starting from step 4.2; Step 4.5: Calculate the proportion of the largest connected component of the new solution W based on the cascade failure process R(W) , and the calculation formula of R(W) is as follows: R(W) = N ’’ / N , where N ’’ is the total number of remaining nodes in the power network topology model G(V, E) after removing a loop and performing the cascade failure process on the G(V, E) power network topology model, and the removed loop is the new solution W ; If R(W) is less than R(C) , then accept the new solution W as the current solution C , otherwise, accept the new solution J with probability W as the current solution C , J and the calculation formula of J = e (R(C)-R(W)) / T is as follows: T , where W represents the current temperature; Step 4.6: When accepting the new solution C as the current solution W , update the temperature. When the temperature reaches the termination temperature, execute step 4.7. When the temperature is not the termination temperature, execute the steps in sequence starting from step 4.3; When not accepting the new solution C as the current solution S nei (C) if there is an unvisited loop in, then execute the steps in sequence starting from step 4.4. If S nei (C) there is no unvisited loop in, execute the steps in sequence starting from step 4.2; Step 4.7: Mark the critical loop: Compare the proportion of the largest connected component of each loop obtained through steps 4.1 to 4.6, and mark the loop with the smallest proportion of the largest connected component as the critical loop.

[0006] In a specific implementation manner, in step 4, after removing a loop and performing the cascade failure process on the power network topology model G(V, E) the power network topology model G(V, E)The total number of remaining nodes in [model] is obtained through the following steps: Step 4.2.1: Calculate the active power of each edge in the power network topology model of the power network according to the parameters of each load, each generator, and each branch obtained in Step 1 G(V, E) in each edge P ; Step 4.2.2: Remove the corresponding loop, and remove all the edges connected to each node in the removed loop. The remaining nodes and edges in the power network topology model G(V, E) form multiple subnets; Step 4.2.3: Delete the subnets in the power network topology model G(V, E) that do not contain generator nodes or have only one node; Step 4.2.4: For each subnet in the power network topology model G(V, E) where the power generation and demand are unbalanced, execute the power rescheduling strategy to balance its power generation and demand, and update the active power of each remaining edge in the power network topology model G(V, E) and calculate the overload degree of each remaining edge in the power network topology model P， ; Step 4.2.5: If there are overloaded edges among the remaining edges in the power network topology model G(V, E) , delete the edge with the highest overload degree value, and retain the nodes at both ends of the edge with the highest overload degree value; Step 4.2.6: Execute Step 4.2.3 to Step 4.2.5 until there is no overload in each remaining edge in the power network topology model Z ; Step 4.2.7: Calculate the number of remaining nodes in the power network topology model when there is no overload in each remaining edge in the power network topology model G(V, E) . This is the total number of remaining nodes in the power network topology model G(V, E) after removing one loop and the cascading failure process G(V, E) from the power network topology model G(V, E) . G(V, E) G(V, E)

[0007] G(V, E) In a specific embodiment, Step 2 is specifically as follows: Step 2.1: Mark the status of each node in the power network topology model G(V, E) as unvisited; Step 2.2: Select a node with an unvisited status in the power network topology model G(V, E) i v , and set the recursion depth to L ; Step 2.3: Start a depth-first traversal from v i to search for a loop with a length of v i starting from L as the starting node, and mark the node v ​i The status of is marked as visited, and each search result is marked as visited. v i The length of the starting node is L The circles are added to the solution space; Step 2.4, repeat steps 2.2 to 2.3 to traverse the power network topology model G (V, E) The length of all nodes in the state that have not been visited is generated with the corresponding node as the starting node. L The circle is added to the solution space to complete the construction of the solution space.

[0008] In a specific implementation, the step 3 is specifically as follows: Step 3.1, select the first key circle: from the power network topology model G(V, E) Select the length of F The first known key circle H = {h 1 ，h 2 ，…，h n ，…，h F } ,in 1≤ n ≤ F , n is an integer, , F Less than L ; Step 3.2, expand the first key circle: for the first key circle H Each pair of adjacent nodes h s and h g , both adopt greedy strategies in the power network topology model G(V, E) Search Node h s To Node h g If there are multiple paths between adjacent nodes containing R does not belong to the current first key circle H , then randomly select a path between a pair of adjacent nodes that contains R does not belong to the current first key circle H The path of the node is recorded as {j 1 ，…，j f ，…， j L-F } , the path {j 1 ，…，j f，…，j L-F } Add to the first critical circle H Middle node h s With the node h g Between to expand the first critical circle H to obtain the second critical circle H ’ ={h 1 ，…，h s ，j 1 ，j 2 ，…，j f ，…，j L-F ，h g ，…，h n ，…，h F } , the second critical circle H ’ The length of is L , add the second critical circle H ’ to the initial solution set. If no path to expand the first critical circle H is found between each pair of adjacent nodes of the first critical circle H , then select an unselected known first critical circle with a length less than L and repeat the above steps, where j f is V a node in 1 ≤ f ≤ L - F , f is an integer R = L - F ; Step 3.3. At the end of each execution of the action of adding the second critical circle H ’ to the initial solution set, compare the number of circles in the initial solution set with the preset value of the number of circles in the initial solution set. If the number of circles in the initial solution set is equal to the preset value of the number of circles in the initial solution set, the construction of the initial solution set is completed, and steps 3.1, 3.2, and 3.4 are no longer executed. Otherwise, select an unselected known first critical circle with a length less than L and execute step 3.2; Step 3.4. If the number of circles in the initial solution set obtained through steps 3.1 to 3.3 reaches the preset value of the number of circles in the initial solution set, the construction of the initial solution set is completed. Otherwise, extract multiple circles from the solution space and add them to the initial solution set until the number of circles in the initial solution set reaches the preset value of the number of circles in the initial solution set to complete the construction of the initial solution set.

[0009] In a specific embodiment, the parameters of the load include: load number, load type, active power and reactive power of the load, conductance and susceptance in parallel with the load, voltage amplitude of the load, and phase angle of the load; the parameters of the generator include: generator number, active power of the generator, reactive power of the generator, operating voltage of the generator, maximum allowable value of the generator's active power, and minimum allowable value of the generator's active power; the parameters of the branch include: starting node number of the branch, ending node number of the branch, resistance of the branch, reactance of the branch, charging susceptance of the branch, long-term allowable power of the branch, short-term allowable power of the branch, and emergency allowable power of the branch.

[0010] In a specific embodiment, the degree of overload Z is calculated by the following formula: Z = (P - U) / U , where U is the long-term allowable power of the edge, and the long-term allowable power of the edge is the long-term allowable power of the corresponding branch.

[0011] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. The present invention uses the simulated annealing algorithm to detect the critical circles of the power network, and by adopting the neighborhood search strategy, the algorithm can search globally in the early stage and easily jump out of the local optimal solution, while in the later stage of the algorithm, it can converge quickly. It can successfully detect the critical circles of the power network, and at the same time, effectively improve the detection efficiency. It can be adapted to large-scale networks and expand its application scope.

[0012] 2. The present invention uses the cascading failure process to simulate the fault process of the real power network, can detect the vulnerable structure of the power network, and provides effective support for the safety protection of the power network.

[0013] 3. The present invention constructs the initial solution set through the greedy strategy, utilizes the relationship of critical circles of different lengths, and improves the construction efficiency of the initial solution set. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is a schematic flow chart of the method for detecting critical circles of a power network based on the simulated annealing algorithm provided by an embodiment of the present invention.

[0015] Figure 2 is a schematic diagram of the power network topology model of the IEEE 118-bus power network provided by an embodiment of the present invention G(V, E) schematic diagram.

[0016] Figure 3 is a schematic diagram of the critical circles of the IEEE 118-bus power network provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0017] The present invention will be described in detail below in conjunction with embodiments and the accompanying drawings. It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0018] Reference Figure 1 , a method for detecting critical loops in a power network based on a simulated annealing algorithm, includes the following steps: Step 1, construct a power network topology model G(V, E) : Obtain the information of each load, each generator, and each branch in the power network. Preferably, obtain the information of each load, each generator, and each branch in the power network through the PYPOWER library, and construct a power network topology model according to the information of each load, each generator, and each branch in the power network G(V, E), Power network topology model G(V, E) Subject to topological constraints, the voltage of each node and the current of each edge both satisfy Kirchhoff's theorem. In the power network topology model G(V, E) , the nodes include generator nodes and load nodes. Each load in the power network corresponds one-to-one with each load node in the power network topology model G(V, E) , each generator in the power network corresponds one-to-one with each generator node in the power network topology model G(V, E) , each branch in the power network corresponds one-to-one with each edge in the power network topology model G(V, E) , the power network topology model G(V, E) The total number of nodes is N , the power network topology model G(V, E) The N nodes of the power network topology model are denoted in sequence as v i , where i is a positive integer less than or equal to N, V is a set composed of N nodes, E is a set composed of edges.

[0019] In this embodiment, the critical loops of the IEEE 118-bus power network are detected. Through the information of each load, each generator, and each branch in the IEEE 118-bus power network, a generated power network topology model G(V, E) , as Figure 2 shown, the squares are generator nodes and the circles are load nodes.

[0020] Further, the parameters of the load include: load number, load type, active power and reactive power of the load, conductance and susceptance in parallel with the load, voltage amplitude of the load, and phase angle of the load; the parameters of the generator include: generator number, active power of the generator, reactive power of the generator, operating voltage of the generator, maximum allowable value of the generator's active power, and minimum allowable value of the generator's active power; the parameters of the branch include: starting node number of the branch, ending node number of the branch, resistance of the branch, reactance of the branch, charging susceptance of the branch, long-term allowable power of the branch, short-term allowable power of the branch, and emergency allowable power of the branch.

[0021] Step 2: Construct the solution space: Traverse the power network topology model using the depth-first search algorithm G(V, E) , to generate B circles with a length of L , and add the generated B circles with a length of L to the solution space to complete the construction of the solution space. The B circles that make up the solution space are sequentially denoted as D h , where h is a positive integer less than or equal to B .

[0022] Further, the specific steps of Step 2 are as follows: Step 2.1: Mark the status of each node in the power network topology model G(V, E) as unvisited.

[0023] Step 2.2: Select an unvisited node G(V, E) in the power network topology model v i , and set the recursion depth to L .

[0024] Step 2.3: Start depth traversal from v i to search for a circle with a length of v i starting from L . Mark the status of the node v i as visited, and add each circle with a length of v i starting from L to the solution space.

[0025] Step 2.4: Repeat Step 2.2 to Step 2.3 to traverse all unvisited nodes in the power network topology model G(V, E) to generate circles with a length of L starting from the corresponding nodesThe loop is circled and added to the solution space to complete the construction of the solution space.

[0026] Step 3, construct the initial solution set: Adopt the greedy strategy for the power network topology model G(V, E) All the known first critical loops with lengths less than L in it are expanded to obtain multiple second critical loops with lengths of L All the second critical loops with lengths of L obtained after expansion are added to the initial solution set, or multiple loops in the solution space are extracted and added to the initial solution set, so that the number of loops in the initial solution set is A to complete the construction of the initial solution set. The A loops that make up the initial solution set are successively denoted as Q a where a is a positive integer less than or equal to A , A is the preset value of the number of loops in the initial solution set; Furthermore, the specific steps of Step 3 are as follows: Step 3.1, select the first critical loop: Select from the power network topology model G (V, E) a known first critical loop F with a length of H = {h 1 ，h 2 ，…，h n ，…，h F } where 1 ≤ n ≤ F , n is an integer, , F is less than L .

[0027] Step 3.2, expand the first critical loop: For each pair of adjacent nodes H of the first critical loop h s and h g , use the greedy strategy to search for the path from node G(V, E) in the power network topology model h s to node h g . If there are multiple paths between adjacent nodes that contain R nodes not belonging to the current first critical loop H , randomly select one path between a pair of adjacent nodes that contains R nodes not belonging to the current first critical loop H . This path is denoted as {j 1，…，j f ，…，j L-F } , add the path {j 1 ，…，j f ，…，j L-F } to the first critical circle H the middle node h s and the node h g to expand the first critical circle H to obtain the second critical circle H ’ ={h 1 ，…，h s ，j 1 ，j 2 ，…，j f ，…，j L-F ，h g ，…，h n ，…，h F } , the second critical circle H ’ has a length of L , add the second critical circle H ’ to the initial solution set. If no path to expand the first critical circle H is found between each pair of adjacent nodes of the first critical circle H , then select an unselected first critical circle with a length less than L and repeat the above steps, where j f is V the node in 1 ≤ f ≤ L - F , f is an integer, R = L - F .

[0028] Step 3.3. Each time when executing to add the second critical circle H ’When the action of adding the initial solution set ends, compare the number of cycles in the initial solution set with the preset value of the number of cycles in the initial solution set. If the number of cycles in the initial solution set is equal to the preset value of the number of cycles in the initial solution set, the construction of the initial solution set is completed, and steps 3.1, 3.2, and 3.4 are no longer executed. Otherwise, select an unselected known first critical cycle with a length less than L and execute step 3.2.

[0029] Step 3.4: If the number of cycles in the initial solution set obtained through steps 3.1 to 3.3 reaches the preset value of the number of cycles in the initial solution set, the construction of the initial solution set is completed. Otherwise, extract multiple cycles from the solution space and add them to the initial solution set until the number of cycles in the initial solution set reaches the preset value of the number of cycles in the initial solution set to complete the construction of the initial solution set.

[0030] Figure 2 In, the cycle {49, 66, 65, 68, 69} can be expanded to the cycle {49, 66, 65, 68, 69, 47} and then added to the initial solution set. When searching for critical cycles with a length of 6, the cycle {4966, 65, 68, 69, 47} can be used as the second critical cycle in the initial solution set in step 3. H ’ 。

[0031] Step 4: Detect critical cycles: Based on the initial solution set, use a simulated annealing algorithm with a neighborhood search strategy to find critical cycles in the solution space to obtain critical cycles.

[0032] Preferably, step 4 is specifically: Step 4.1: Initialize the parameters in the simulated annealing algorithm, including the initial temperature T 0, the temperature reduction coefficient α , the termination temperature T end , the neighborhood search range m , and set the status of all cycles in the initial solution set to unvisited.

[0033] Step 4.2: When all cycles in the initial solution set have been visited, execute step 4.7. When there are unvisited cycles in the initial solution set, randomly select an unvisited cycle from the initial solution set Q a , and use Q a as the current solution C , and mark Q a as visited. Calculate the maximum connected component ratio C of the current solution R(C) based on the cascading failure process. The maximum connected component ratio is an index to measure the importance of the cycle. The smaller the maximum connected component ratio, the more important the cycle. Calculate R(C)The formula is as follows: R(C) = N ’ / N , where N ’ is the total number of remaining nodes in the power network topology model G(V, E) after performing the process of removing a cycle and cascading failure on the power network topology model G(V, E) , and the removed cycle is the current solution C .

[0034] Step 4.3: According to the neighborhood search range m , search for cycles in the solution space based on the current solution cycle C to obtain the set S nei (C) , , where d r is the node in the cycle D h , q z is the node in the current solution cycle C , min(d(d r ,q z )) represents the shortest path distance from node d r to node q z , min(d(d r ,q z )) represents the shortest path distance from the cycle D h to the current solution cycle C , S nei (C) The cycles in O k are sequentially denoted as k , where m is an integer greater than 0. Let C = 1, the cycle S nei (C)= selected from the initial solution set is {49, 66, 65, 68, 69, 47}, and through step 4.3, we get​​​{{30, 17, 15, 33, 37, 38}, {49, 50, 57, 56, 58, 51}, {49, 50, 57, 56, 55, 54}, {49, 50, 57, 56, 59, 54}, {49, 51, 58, 56, 55, 54}, {49, 51, 58, 56, 59, 54}, {49, 54, 59, 60, 62, 66}, {49, 54, 59, 61, 62, 66}, {64, 61, 60, 62, 66, 65}, {64, 61, 62, 67, 66, 65}, {64, 61, 62, 60, 59, 63}, {70, 69, 77, 76, 118, 75}, {77, 78, 79, 80, 96, 82}, {51, 52, 53, 54, 56, 58}, {68, 69, 75, 77, 80, 81}}。

[0035] Step 4.4, Step 4.4, If S nei (C) there are unvisited loops, then select an unvisited loop from S nei (C) as the new solution O k and mark the loop W as visited. If O k there are no unvisited loops in S nei (C) then start executing the steps sequentially from Step 4.2.

[0036] Step 4.5, Calculate the proportion of the largest connected component of the new solution W The formula for calculating R(W) is as follows: R(W) R(W) = N ’’ / N where N ’’ is the total number of remaining nodes in the power network topology model G(V, E) after removing a loop and performing the cascading failure process on the power network topology model G(V, E) The removed loop is the new solution W ; If R(W) is less than R (C) (C) then accept the new solution W as the current solution C otherwise, accept the new solution with probability J W ​As the current solution C , J The calculation formula of J =e (R(C)-R(W)) / T is as follows: T represents the current temperature.

[0037] Step 4.6: When accepting the new solution W as the current solution C , update the temperature. The cooling coefficient follows the geometric decay rule. When the temperature is the termination temperature, execute Step 4.7. When the temperature is not the termination temperature, start from Step 4.3 and execute the steps in sequence; when not accepting the new solution W as the current solution C , if S nei (C) there are unvisited loops, start from Step 4.4 and execute the steps in sequence. If S nei (C) there are no unvisited loops, start from Step 4.2 and execute the steps in sequence.

[0038] Step 4.7: Mark the critical loop: Compare the maximum connected component ratio of each loop obtained through Steps 4.1 to 4.6, and mark the loop with the minimum maximum connected component ratio as the critical loop.

[0039] Preferably, in Step 4, for the power network topology model G(V, E) after performing the process of removing one loop and cascading failure on the power network topology model G(V, E) , the total number of remaining nodes in it is obtained through the following steps: Step 4.2.1: Calculate the active power G(V, E) of each edge in the power network topology model P according to the parameters of each load, each generator and each branch of the power network obtained in Step 1 by using the DC power flow.

[0040] Ignore the changes in the reactive power and voltage amplitude of all nodes. For each load node x in the power network, given that the active power is P x , and the active power of the load node x is equal to the sum of the active powers flowing out of it, that is , then the active power E xy of the edge P xy can be calculated as P xy =b xy (θx -θ y ) , where is the set of neighbor nodes of node x y is a neighbor node of x, b xy is the charging susceptance of branch E xy . θ x is the voltage phase angle of node x . θ y is the voltage phase angle of node y .

[0041] Step 4.2.2, Remove the corresponding loop, and remove all the edges connected to each node in the removed loop. The remaining nodes and edges in the power network topology model G(V, E) form multiple subnets.

[0042] Step 4.2.3, Delete the subnets in the power network topology model G(V, E) that do not contain generator nodes or have only one node.

[0043] Step 4.2.4, For each subnet in the power network topology model G(V, E) where the power generation and demand are unbalanced, execute the power rescheduling strategy to balance its power generation and demand, specifically by increasing or decreasing the power generation of the corresponding generator, and update the active power of each remaining edge in the power network topology model G(V, E) using the DC power flow and calculate the overload degree of each remaining edge in the power network topology model P， . G(V, E) The overload degree of each remaining edge in the power network topology model Z is calculated as follows:

[0044] Furthermore, the overload degree Z is obtained by the following formula: Z = (P - U) / U , where U is the long-term allowable power of the edge, and the long-term allowable power of the edge is the long-term allowable power of the corresponding branch.

[0045] Step 4.2.5, If there is an overloaded edge among the remaining edges in the power network topology model G(V, E) , delete the edge with the highest overload degree value, and retain the nodes at both ends of the edge with the highest overload degree value.

[0046] Step 4.2.6, Execute steps 4.2.3 to 4.2.5 until there is no overload for each remaining edge in the power network topology model G(V, E) .

[0047] Step 4.2.7. Calculate the number of remaining nodes in the power network topology model when each of the remaining edges in the power network topology model G(V, E) does not have overload. This is the total number of remaining nodes in the power network topology model G(V, E) after performing the process of removing a cycle and cascading failure on the power network topology model G(V, E) . G(V, E) Refer to

[0048] , in the IEEE 118-bus network power grid, the critical cycle with a length of 6 is {68, 69, 75, 77, 80, 81}, and the maximum connected component ratio is 0.644. Figure 3

[0049] The above content is a further detailed description of the present invention in combination with specific preferred embodiments. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions and substitutions can still be made, which should all be regarded as belonging to the protection scope of the present invention.​

Claims

1. A detection method for critical loops in a power network based on the simulated annealing algorithm, characterized in that, Including the following steps: Step 1: Construct a power network topology model: Obtain the information of each load, each generator, and each branch in the power network, and construct a power network topology model based on the information of each load, each generator, and each branch in the power network G(V,E) , the power network topology model G(V,E) 's nodes include generator nodes and load nodes, and the power network topology model G(V,E) 's total number of nodes is N , the power network topology model G(V,E) 's N nodes are sequentially denoted as v i , where i is a positive integer less than or equal to N, V is a set composed of N nodes, E is a set composed of edges; Step 2, construct the solution space: traverse the power network topology model using the depth-first search algorithm G(V,E) , to generate B cycles of length L , and add the generated B cycles of length L to the solution space to complete the construction of the solution space. The B cycles that make up the solution space are denoted in sequence as D h , where h is a positive integer less than or equal to B ; Step 3, construct an initial solution set: Use the greedy strategy for the power network topology model G(V,E) to expand all the first critical cycles with known lengths less than L to obtain multiple second critical cycles with a length of L and add all the second critical cycles with a length of L after expansion to the initial solution set, or extract multiple cycles from the solution space and add them to the initial solution set, so that the number of cycles in the initial solution set is A , to complete the construction of the initial solution set. The A cycles that make up the initial solution set are denoted in sequence as Q a , where a is a positive integer less than or equal to A , and A is the preset value of the number of cycles in the initial solution set; Step 4, Detect critical loop: Based on the initial solution set, use a simulated annealing algorithm with a neighborhood search strategy to find critical loops in the solution space to obtain critical loops.

2. The detection method of critical loops in a power grid based on the simulated annealing algorithm according to claim 1, wherein The specific content of the said Step 4 is: Step 4.1: Initialize the parameters in the simulated annealing algorithm, including the initial temperature T 0, the cooling coefficient α , the termination temperature T end , the neighborhood search range m , and set the status of all cycles in the initial solution set to unvisited; Step 4.2: When all the loops in the initial solution set have been visited, execute Step 4.

7. When there are unvisited loops in the initial solution set, randomly select an unvisited loop Q from the initial solution set a , and take Q a as the current solution C , and mark Q a as visited. Calculate the proportion of the largest connected component of the current solution C based on the cascading failure process. The formula for calculating R(C) is as follows: R(C) R(C)=N ’ / N , where N ’ is the total number of remaining nodes in the power network topology modelafter removing a loop and performing the cascading failure process on the power network topology model G(V,E) . The removed loop is the current solution G(V,E) C ;​ Step 4.

3. According to the neighborhood search range m , based on the current solution loop C search for loops in the solution space to obtain the set S nei (C) , , where d r is a node in the loop D h , q z is a node in the current solution loop C , d(d r ,q z ) represents the shortest path distance from node d r to node q z , min(d(d r ,q z )) represents the shortest distance from the loop D h to the current solution loop C , S nei (Q a ) The loops in O k are sequentially denoted as k , where is an integer greater than 0; Step 4.

4. If S nei (C) there are unvisited loops, then select an unvisited loop from S nei (C) as the new solution O k and mark the loop W as visited. If O k there are no unvisited loops in S nei (C) then execute the steps sequentially starting from Step 4.2; Step 4.5: Calculate a new solution based on the cascading failure process W of the largest connected component ratio R(W) and calculate R(W) using the following formula: R(W)=N ’’ / N where N ’’ is the total number of remaining nodes in the power grid topology model G(V,E) after removing a loop and performing the cascading failure process on the power grid topology model G(V,E) , and the removed loop is the new solution W ; if R(W) is less than R(C) , then accept the new solution W as the current solution C , otherwise, accept the new solution J as the current solution W with probability C . The calculation formula of J is as follows: J=e (R(C )-R(W)) / T where T represents the current temperature; Step 4.

6. When accepting the new solution W as the current solution C update the temperature. When the temperature is the termination temperature, execute Step 4.

7. When the temperature is not the termination temperature, execute the steps in sequence starting from Step 4.3; when not accepting the new solution W as the current solution C if S nei (C) there are unvisited loops, execute the steps in sequence starting from Step 4.

4. If S nei (C) there are no unvisited loops, execute the steps in sequence starting from Step 4.2; Step 4.7, Mark critical loop: Compare the maximum connected component ratio of each loop obtained through Steps 4.1 to 4.6, and mark the loop with the minimum maximum connected component ratio as the critical loop.

3. The detection method of the critical loop of the power network based on the simulated annealing algorithm according to claim 2, characterized in that, In step 4, for the power network topology model G(V,E) After performing the process of removing a loop and cascading failure on the power network topology model G(V,E) The total number of remaining nodes in is obtained through the following steps: Step 4.2.1: Calculate the active power of each edge in the G(V,E) power network topology model by using the direct current power flow according to the parameters of each load, each generator and each branch of the power network obtained in Step 1 P ; Step 4.2.2, Remove the corresponding loop, and remove all the edges connected to each node in the removed loop. The remaining nodes and edges in the power network topology model G(V,E) form multiple subnets; Step 4.2.3, delete the subnets in the power network topology model G(V,E) that do not contain generator nodes or have only one node; Step 4.2.4, for the power network topology model G(V,E) Execute the power rescheduling strategy for each subnet with unbalanced power generation and demand to make its power generation and demand balanced, and update the power network topology model using DC power flow G(V, E) The active power of each remaining edge in P， And calculate the overload degree of each remaining edge in the power network topology model G(V,E) ; Z ; Step 4.2.

5. If there are overloaded edges among the remaining edges in the power network topology model G(V,E) delete the edge with the highest overload degree value and retain the nodes at both ends of the edge with the highest overload degree value; Step 4.2.

6. Execute Steps 4.2.3 to 4.2.5 until there is no overload on each remaining edge in the G(V,E) power grid topology model; Step 4.2.7, calculate the power network topology model when G(V,E) each remaining edge in the G(V,E) does not have overload, and calculate the number of remaining nodes in the power network topology model G(V,E) after performing the process of removing a loop and cascading failure on the power network topology model G(V,E) This is the total number of remaining nodes in the power network topology model.

4. The detection method of the key loop of the power network based on the simulated annealing algorithm according to claim 3, characterized in that, The specific content of the said Step 2 is: Step 2.

1. Mark the status of each node in the power network topology model G(V,E) as unvisited; Step 2.

2. Select a node with an unvisited status in the power network topology model G(V,E) and set the recursion depth to v i ; L ​ Step 2.

3. Starting from v i perform a depth-first traversal to search for cycles of length v i starting from L . Mark the status of node v i as visited, and add each cycle of length v i starting from L found in the search to the solution space; Step 2.

4. Repeat Step 2.2 to Step 2.3 to traverse all nodes in the power network topology model G(V,E) with the status of unvisited to generate cycles with the corresponding nodes as the starting nodes and with a length of L and add them to the solution space to complete the construction of the solution space.

5. The detection method of the key circle of the power network based on the simulated annealing algorithm according to claim 4, characterized in that The specific content of the said Step 3 is: Step 3.

1. Select the first key loop: Select a known first key loop with a length of G(V,E) from the power grid topology model F . Among them, H={h 1 ，h 2 ，…，h n ，…，h F } , where 1≤n≤F , n is an integer, , F is less than L ; Step 3.2, Expand the first critical circle: For the first critical circle H of each pair of adjacent nodes h s and h g , the greedy strategy is used to search for the path from node G(V,E) in the power network topology model h s to node h g . If there are multiple paths between adjacent nodes that contain R nodes not belonging to the current first critical circle H , then randomly select one path between a pair of adjacent nodes that contains R nodes not belonging to the current first critical circle H . This path is denoted as {j 1 ，…，j f ，…，j L-F } . Add the path {j 1 ，…， j f ，…，j L-F } to the first critical circle H between nodes h s and node h g to expand the first critical circle H to obtain the second critical circle H ’ ={h 1 ，…，h s ，j 1 ，j 2 ，…，j f ，…，j L-F ，h g ，…，h n ，…，h F } . The length of the second critical circle H ’ is L . Add the second critical circle H ’ to the initial solution set. If the first critical circle H No expandable first critical circle is found between each pair of adjacent nodes H for the path, then select an unselected known first critical circle with a length less than L and repeat the above steps, where j f is V a node in 1≤f≤L - F , f is an integer R = L - F ; Step 3.

3. At the end of each operation of adding the second critical loop H ’ to the initial solution set, compare the number of loops in the initial solution set with the preset value of the number of loops in the initial solution set. If the number of loops in the initial solution set is equal to the preset value of the number of loops in the initial solution set, the construction of the initial solution set has been completed, and steps 3.1, 3.2, and 3.4 are no longer executed. Otherwise, select an unselected known first critical loop with a length less than L and execute step 3.2; Step 3.4, If the number of loops in the initial solution set obtained through Steps 3.1 to 3.3 reaches the preset value of the number of loops in the initial solution set, the construction of the initial solution set is completed; otherwise, extract multiple loops from the solution space and add them to the initial solution set until the number of loops in the initial solution set reaches the preset value of the number of loops in the initial solution set to complete the construction of the initial solution set.

6. The detection method of the key loop of the power grid based on the simulated annealing algorithm according to claim 5, characterized in that, The parameters of the load include: load number, load type, active power and reactive power of the load, conductance and susceptance in parallel with the load, voltage amplitude of the load, phase angle of the load; the parameters of the generator include: generator number, active power of the generator, reactive power of the generator, operating voltage of the generator, maximum allowable value of the generator active power, and minimum allowable value of the generator active power; the parameters of the branch include: starting node number of the branch, terminating node number of the branch, resistance of the branch, reactance of the branch, charging susceptance of the branch, long-term allowable power of the branch, short-term allowable power of the branch, emergency allowable power of the branch.

7. The detection method of the critical loop of the power network based on the simulated annealing algorithm according to claim 6, characterized in that, The degree of overload Z is calculated by the following formula: Z=(P - U) / U , where U is the long-term allowable power of the side, and the long-term allowable power of the side is the long-term allowable power of the corresponding branch.

Images