A detection method for critical loops in power networks based on simulated annealing algorithm

Abstract

The present invention provides a method for detecting critical loops in power networks based on a simulated annealing algorithm, comprising the following steps: Step 1: constructing a power network topology model; Step 2: constructing a solution space; Step 3: constructing an initial solution set; and Step 4: detecting critical loops. The present invention utilizes a simulated annealing algorithm that incorporates a neighborhood search strategy to detect critical loops in power networks. This method can successfully detect critical loops in power networks while effectively improving detection efficiency. It is adaptable to large networks, expanding its scope of application. The present invention utilizes a cascading failure process to simulate the failure process of a real power network, enabling detection of vulnerable structures in the power network and providing effective support for its security protection.

Description

Technical Field

[0001] The invention relates to a method for detecting a critical circle of an electric power network based on a simulated annealing algorithm, and belongs to the technical field of networks. Background Art

[0002] Complex networks, through the interactions of nodes and edges, reflect the structural patterns and dynamic characteristics of complex systems in the real world. Analysis of complex networks can reveal the system's topological structure, functional characteristics, and dynamic behavior, providing theoretical support for system optimization, risk control, and prediction. Identifying the network's critical structure is a core issue in the study of complex network robustness. In recent years, research has focused on identifying critical nodes. Cycle structure is an important component of networks and higher-order interactions. It not only provides a new approach for analyzing node influence but also plays an indispensable role in many key network properties, such as synchronization efficiency and survivability. However, existing metrics are calculated based on the global network, which means that the identification and search for critical cycles in large networks still requires further theoretical research and algorithm design. The existing detection methods for critical circles have the following main problems: (1) Low computational efficiency: The existing evaluation circle importance index is calculated based on the overall network, which is time-consuming; (2) Failure to consider the systemic 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 circles in the power grid do not fully consider the occurrence of cascading failures in the power grid, and it is difficult to effectively support the security protection of the power grid; (3) Poor applicability: Traditional algorithms do not consider the relationship between critical circles of different lengths, and lack the setting of search range, which limits their application in large networks. Summary of the Invention

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

[0004] In order to solve the above technical problems, the present invention provides a detection method for a power network critical circle based on a simulated annealing algorithm, comprising the following steps: Step 1, constructing a power network topology model: obtaining information about each load, each generator, and each branch of the power network, and constructing a power network topology model G(V, E) based on the information about each load, each generator, and each branch of the power network. The nodes of the power network topology model G(V, E) include generator nodes and load nodes. The total number of nodes of the power network topology model G(V, E) is N, and the N nodes of the power network topology model G(V, E) are sequentially denoted as v i, where i is a positive integer less than or equal to N, V ​​is a set of N nodes, and E is a set of edges; Step 2, construct the solution space: Use the depth-first search algorithm to traverse the power network topology model 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 constitute the solution space are denoted as D h , where h is a positive integer less than or equal to B; Step 3, construct the initial solution set: adopt a greedy strategy to expand all the first key circles with length less than L in the power network topology model G(V,E) to obtain multiple second key circles with length L, and add all the second key circles with length L obtained after expansion to the initial solution set, or extract multiple circles in the solution space and add them to the initial solution set, so that the number of circles in the initial solution set is A, to complete the construction of the initial solution set, and the A circles constituting the initial solution set are denoted as Q a , where a is a positive integer less than or equal to A, and A is a preset value for the number of cycles in the initial solution set; Step 4, detecting key cycles: Based on the initial solution set, a simulated annealing algorithm including a neighborhood search strategy is used to search for key cycles in the solution space to obtain key cycles.

[0005] In a specific embodiment, the step 4 is specifically as follows: Step 4.1, initializing the parameters in the simulated annealing algorithm, including the initial temperature T0, the cooling coefficient α, the termination temperature T end , neighborhood search range m, set the status of all circles in the initial solution set to unvisited; step 4.2, when all circles in the initial solution set have been visited, execute step 4.7, when there is an unvisited circle in the initial solution set, randomly select an unvisited circle Q from the initial solution set a , Q a As the current solution C, and Q a Mark as visited, calculate the maximum connected component ratio R(C) of the current solution C based on the cascading failure process, and the formula for calculating R(C) is as follows: R(C) = N' / N, where N' is the total number of nodes remaining in the power network topology model G(V,E) after removing a circle and performing the cascading failure process on the power network topology model G(V,E). The removed circle is the current solution C; Step 4.3, based on the neighborhood search range m, search for circles in the solution space based on the current solution circle C to obtain the set S nei (C), S nei (C)={D h |d r ∈D h ,q z ∈C,min(d(d r ,q z ))≤m}, where d r Circle D h Nodes in qz is the node in the current solution circle C, d(d r ,q z ) represents node d r To node q z The shortest path distance, min(d(d r ,q z )) indicates circle D h The shortest distance to the current solution circle C, S nei (Q a ) are marked as O k , where k is an integer greater than 0; Step 4.4, if S nei (C) has unvisited circles, then from S nei (C) Select an unvisited circle O k As the new solution W, and circle O k Mark as visited if S nei If there is no unvisited circle in (C), then the steps are executed sequentially starting from step 4.2; Step 4.5, calculate the maximum connected component ratio R(W) of the new solution W based on the cascading failure process, and the formula for calculating R(W) is as follows: R(W) = N" / N, where N" is the total number of nodes remaining in the power network topology model G(V,E) after removing a circle and performing the cascading failure process on the power network topology model G(V,E), and the removed circle 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 W as the current solution C with probability J, and 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 the new solution W is accepted 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 starting from step 4.3. When the new solution W is not accepted as the current solution C, if S nei (C) has unvisited circles, then start from step 4.4 and execute the steps in sequence. If S nei There are no unvisited circles in (C), and the steps are performed sequentially starting from step 4.2; Step 4.7, mark the key circle: compare the maximum connected component ratio of each circle obtained through steps 4.1 to 4.6, and mark the circle with the smallest maximum connected component ratio as the key circle.

[0006] In a specific embodiment, in step 4, the total number of nodes remaining in the power network topology model G (V, E) after removing a circle and performing a cascading failure process on the power network topology model G (V, E) is obtained by the following steps: step 4.2.1, using the parameters of each load, each generator and each branch of the power network obtained in step 1 to calculate the active power P of each edge in the power network topology model G (V, E) using DC power flow; step 4.2.2, removing the corresponding circle, removing all edges connected to each node in the removed circle, and the remaining nodes and edges in the power network topology model G (V, E) form multiple subnets; step 4.2.3, deleting the subnet that does not contain a generator node or has only one node in the power network topology model G (V, E); step 4.2.4, executing a power rescheduling strategy for each subnet in the power network topology model G (V, E) where the power generation and demand are unbalanced so that its power generation is unbalanced. The power and demand are balanced, and the active power P of each remaining edge in the power network topology model G(V,E) is updated using DC power flow, and the overload degree Z of each remaining edge in the power network topology model G(V,E) is calculated; Step 4.2.5: If there is an overloaded edge among the remaining edges of the power network topology model G(V,E), the edge with the highest overload degree value is deleted, and the nodes at both ends of the edge with the highest overload degree value are retained; Step 4.2.6: Execute Steps 4.2.3 to 4.2.5 until each remaining edge in the power network topology model G(V,E) is not overloaded; Step 4.2.7: Calculate the number of nodes remaining in the power network topology model G(V,E) when each remaining edge in the power network topology model G(V,E) is not overloaded, which is the total number of nodes remaining in the power network topology model G(V,E) after removing a circle and performing the cascading failure process on the power network topology model G(V,E).

[0007] In a specific embodiment, the step 2 is specifically as follows: step 2.1, marking the state of each node in the power network topology model G (V, E) as unvisited; step 2.2, selecting a node v in the power network topology model G (V, E) as unvisited i , set the recursive depth to L; step 2.3, from v i Start a depth traversal to search for v i For a circle with a length of L as the starting node, move node v i The state of is marked as visited, and each search result with v i All circles with a length of L starting from the starting node are added to the solution space; step 2.4, repeat steps 2.2 to 2.3 to traverse all nodes in the power network topology model G(V,E) that are in the unvisited state to generate a circle with a length of L starting from the corresponding node and add it to the solution space to complete the construction of the solution space.

[0008] In a specific embodiment, the step 3 is specifically as follows: Step 3.1, select the first key circle: select the first key circle H = {h1, h2, ..., h n ,…,h F}, where 1≤n≤F, n is an integer, h n ∈V, F is less than L; Step 3.2, expand the first critical circle: for each pair of adjacent nodes h in the first critical circle H s and h g , both use greedy strategies to search for node h in the power network topology model G(V,E) s To node h g If there are multiple paths between adjacent nodes that contain R nodes that do not belong to the current first critical circle H, then a path between a pair of adjacent nodes that contains R nodes that do not belong to the current first critical circle H is randomly selected and recorded as {j1,…,j f ,…,j L-F}, the path {j1,…,j f ,…,j L-F}Add to node h in the first key circle H s With node h g By expanding the first key circle H, we can get the second key circle H'={h1,…,h s ,j1,j2,…,j f ,…,j L-F , h g ,…,h n ,…,h F}, the length of the second key circle H' is L, the second key circle H' is added to the initial solution set, if no path that can extend the first key circle H is found between each pair of adjacent nodes of the first key circle H, then a known first key circle with a length less than L that has not been selected is selected and the above steps are repeated, where j fis a node in V, 1≤f≤LF, f is an integer, and R=LF; Step 3.3, at the end of each execution of the action of adding the second key 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 has been completed, and Step 3.1, Step 3.2 and Step 3.4 are no longer executed. Otherwise, select a known first key circle with a length less than L that has not been selected to 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 has been completed. Otherwise, extract multiple circles in 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 active power of the generator, and minimum allowable value of active power of the generator; 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 overload degree Z is calculated by the following formula: Z=(PU) / 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 present invention has the following beneficial effects:

[0012] 1. The present invention adopts a simulated annealing algorithm to detect the critical circle of the power network. By adopting a neighborhood search strategy, the algorithm can search globally in the early stage and easily jump out of the local optimal solution, while the algorithm can converge quickly in the later stage. It can successfully detect the critical circle of the power network and effectively improve the detection efficiency. It is adaptable to large networks and expands its application range.

[0013] 2. The present invention uses a cascading failure process to simulate the failure process of a real power network, which can detect the fragile structure of the power network and provide effective support for the safety protection of the power network.

[0014] 3. The present invention constructs the initial solution set through a greedy strategy, utilizes the relationship between key cycles of different lengths, and improves the efficiency of constructing the initial solution set. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 A schematic flow chart of a method for detecting a critical loop in a power network based on a simulated annealing algorithm provided in an embodiment of the present invention.

[0016] Figure 2 A schematic diagram of a power network topology model G(V, E) of an IEEE 118 bus power network provided in an embodiment of the present invention.

[0017] Figure 3 A schematic diagram of a critical loop of an IEEE 118 bus power network provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0018] The present invention will be described in detail below with reference to the embodiments and accompanying drawings. It should be noted that the embodiments and features of the embodiments of the present invention can be combined with each other without conflict.

[0019] refer to Figure 1 The detection method of the critical circle of the power network based on the simulated annealing algorithm includes the following steps: Step 1, constructing the power network topology model G (V, E): obtaining the information of each load, each generator and each branch of the power network, preferably, obtaining the information of each load, each generator and each branch of the power network through the PYPOWER library, and constructing the power network topology model G (V, E) according to the information of each load, each generator and each branch of the power network. The power network topology model G (V, E) is subject to topology constraints, and the voltage of each node and the voltage of each branch are the same. The currents of the edges all 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 to each load node in the power network topology model G(V,E), each generator in the power network corresponds one-to-one to each generator node in the power network topology model G(V,E), and each branch in the power network corresponds one-to-one to each edge in the power network topology model G(V,E). The total number of nodes in the power network topology model G(V,E) is N, and the N nodes of the power network topology model G(V,E) are denoted as v i , where i is a positive integer less than or equal to N, V ​​is the set of N nodes, and E is the set of edges.

[0020] This embodiment detects the critical loop of the IEEE 118 bus power network and generates a power network topology model G(V, E) based on the information of each load, each generator, and each branch of the IEEE 118 bus power network. Figure 2 As shown, the squares are generator nodes and the circles are load nodes.

[0021] Furthermore, 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 active power of the generator, and minimum allowable value of active power of the generator; 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.

[0022] Step 2: Construct the solution space: Use the depth-first search algorithm to traverse the power network topology model 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 constitute the solution space are denoted as D h , where h is a positive integer less than or equal to B.

[0023] Furthermore, the step 2 is specifically as follows: Step 2.1, marking the state of each node in the power network topology model G (V, E) as unvisited.

[0024] Step 2.2: Select a node v in the power network topology model G(V,E) that is in the unvisited state. i , set the recursion depth to L.

[0025] Step 2.3, from v i Start a depth traversal to search for v i For a circle with a length of L as the starting node, add node v i The state of is marked as visited, and each search result with v i All circles of length L starting from the starting node are added to the solution space.

[0026] Step 2.4: Repeat steps 2.2 to 2.3 to traverse all nodes in the power network topology model G(V,E) that are in the unvisited state to generate a circle of length L with the corresponding node as the starting node and add it to the solution space to complete the construction of the solution space.

[0027] Step 3: Construct the initial solution set: Use the greedy strategy to expand all the first key circles with length less than L in the power network topology model G(V,E) to obtain multiple second key circles with length L, and add all the second key circles with length L obtained after expansion to the initial solution set, or extract multiple circles in the solution space and add them to the initial solution set, so that the number of circles in the initial solution set is A, to complete the construction of the initial solution set. The A circles that constitute the initial solution set are denoted as Q in sequence.a , where a is a positive integer less than or equal to A, and A is the preset value of the number of circles in the initial solution set;

[0028] Furthermore, the step 3 is specifically as follows: Step 3.1, select the first key circle: select the first key circle H = {h1, h2, ..., h n ,…,h F}, where 1≤n≤F, n is an integer, h n ∈V, F is smaller than L.

[0029] Step 3.2: Expand the first critical circle: For each pair of adjacent nodes h in the first critical circle H s and h g , both use greedy strategies to search for node h in the power network topology model G(V,E) s To node h g If there are multiple paths between adjacent nodes that contain R nodes that do not belong to the current first critical circle H, then a path between a pair of adjacent nodes that contains R nodes that do not belong to the current first critical circle H is randomly selected and recorded as {j1,…,j f ,…,j L-F}, the path {j1,…,j f ,…,j L-F}Add to node h in the first key circle H s With node h g By expanding the first key circle H, we can get the second key circle H'={h1,…,h s ,j1,j2,…,j f ,…,j L-F , h g ,…,h n ,…,h F}, the length of the second key circle H' is L, the second key circle H' is added to the initial solution set, if no path that can extend the first key circle H is found between each pair of adjacent nodes of the first key circle H, then a known first key circle with a length less than L that has not been selected is selected and the above steps are repeated, where j f is a node in V, 1≤f≤LF, f is an integer, and R=LF.

[0030] Step 3.3: At the end of each execution of the action of adding the second key loop H' to the initial solution set, compare the number of loops in the initial solution set with the preset number of loops in the initial solution set. If the number of loops in the initial solution set is equal to the preset 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 a known first key loop with a length less than L that has not been selected before and execute step 3.2.

[0031] 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 has been completed; otherwise, multiple circles in the solution space are extracted and added 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.

[0032] Figure 2 In step 3, the circle {49, 66, 65, 68, 69} can be expanded to the circle {49, 66, 65, 68, 69, 47} and added to the initial solution set. When searching for a key circle with a length of 6, the circle {49, 66, 65, 68, 69, 47} can be used as the second key circle H' in the initial solution set in step 3.

[0033] Step 4: Detect key circles: Based on the initial solution set, a simulated annealing algorithm with a neighborhood search strategy is used to find key circles in the solution space to obtain the key circles.

[0034] Preferably, the step 4 is specifically as follows: step 4.1, initializing the parameters in the simulated annealing algorithm, including the initial temperature T0, the cooling coefficient α, the termination temperature T end , neighborhood search range m, set the status of all circles in the initial solution set to unvisited.

[0035] Step 4.2: When all circles in the initial solution set have been visited, execute step 4.7. If there are unvisited circles in the initial solution set, randomly select an unvisited circle Q from the initial solution set. a , Q a As the current solution C, and Q a Mark as visited, and calculate the maximum connected component ratio R(C) of the current solution C based on the cascading failure process. The maximum connected component ratio is an indicator to measure the importance of the circle. The smaller the maximum connected component ratio, the more important the circle. The formula for calculating R(C) is as follows: R(C) = N' / N, where N' is the total number of nodes remaining in the power network topology model G(V,E) after removing a circle and executing the cascading failure process. The removed circle is the current solution C.

[0036] Step 4.3: Based on the neighborhood search range m, search for circles in the solution space based on the current solution circle C to obtain the set S nei (C), S nei (C)={D h |d r ∈D h ,q z ∈C,min(d(d r ,q z ))≤m}, where d r Circle D h Nodes in q z is the node in the current solution circle C, min(d(d r ,q z )) represents node d r To node q z The shortest path distance, min(d(d r ,q z )) indicates circle D h The shortest path distance to the current solution circle C, S nei The circles in (C) are marked as O k , where k is an integer greater than 0. Assume that when m=1, the circle C selected in the initial solution set is {49, 66, 65, 68, 69, 47}, and S is obtained through step 4.3. nei (C)={{30, 17, 15, 33, 37, 38}, {49, 50, 57, 56, 58, 51}, {49, 50, 57, 56, 55, 54}, {49, 50, 57, 5 6, 59, 54}, {49, 51, 58, 56, 55, 54}, {49, 51, 58, 56, 59, 54}, {49, 54, 59, 60, 62, 66}, {49, 54, 5 9, 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}}.

[0037] Step 4.4, Step 4.4, If S nei (C) has unvisited circles, then from S nei (C) Select an unvisited circle O k As the new solution W, and circle O k Mark as visited if S nei If there is no unvisited circle in (C), then execute the steps starting from step 4.2.

[0038] Step 4.5: Calculate the maximum connected component ratio R(W) of the new solution W based on the cascading failure process. The formula for calculating R(W) is as follows: R(W) = N” / N, where N” is the total number of nodes remaining in the power network topology model G(V,E) after removing a circle and performing the cascading failure process on the power network topology model G(V,E). The removed circle 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 W as the current solution C with probability J. The calculation formula for J is as follows: J = e (R(C)-R(W)) / T , where T represents the current temperature.

[0039] Step 4.6: When the new solution W is accepted as the current solution C, update the temperature. The cooling coefficient follows the geometric attenuation rule. When the temperature is the termination temperature, execute step 4.7. When the temperature is not the termination temperature, execute the steps starting from step 4.3. When the new solution W is not accepted as the current solution C, if S nei (C) has unvisited circles, then start from step 4.4 and execute the steps in sequence. If S nei There are no unvisited circles in (C), and the steps are performed sequentially starting from step 4.2.

[0040] Step 4.7, mark the key circle: compare the maximum connected component ratio of each circle obtained through steps 4.1 to 4.6, and mark the circle with the smallest maximum connected component ratio as the key circle.

[0041] Preferably, in step 4, the total number of nodes remaining in the power network topology model G(V,E) after performing a cycle removal and cascading failure process on the power network topology model G(V,E) is obtained by the following steps:

[0042] Step 4.2.1: Based on the parameters of each load, each generator, and each branch of the power network obtained in step 1, the active power P of each edge in the power network topology model G(V, E) is calculated using DC power flow.

[0043] Ignore the changes in reactive power and voltage amplitude of all nodes. For each load node x in the power network, the active power is known to be P x , the active power of load node x is equal to the sum of its outflow active power, that is, Then we can calculate the edge E xy Active power P xy , P xy =b xy (θ x -θ y ), where Γ x is the set of neighbor nodes of node x, y is the neighbor node of x, b xy It is branch E xyThe charging susceptance, θ x is the voltage phase angle at node x, θ y is the voltage phase angle at node y.

[0044] Step 4.2.2: Remove the corresponding circle and all edges connected to each node in the removed circle. The remaining nodes and edges in the power network topology model G(V, E) form multiple subnets.

[0045] Step 4.2.3: Delete the subnet that does not contain a generator node or has only one node in the power network topology model G(V,E).

[0046] Step 4.2.4: For each subgrid in the power network topology model G(V,E) where the power generation and demand are unbalanced, a power rescheduling strategy is implemented to balance the power generation and demand. Specifically, the power generation of the corresponding generator is increased or decreased, and the DC power flow is used to update the active power P of each remaining edge in the power network topology model G(V,E), and the overload degree Z of each remaining edge in the power network topology model G(V,E) is calculated.

[0047] Furthermore, the overload degree Z is calculated by the following formula: Z=(PU) / 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.

[0048] Step 4.2.5: If there is an overloaded edge among the remaining edges of the power network topology model G(V,E), delete the edge with the highest overload value and retain the nodes at both ends of the edge with the highest overload value.

[0049] Step 4.2.6: Execute steps 4.2.3 to 4.2.5 until all remaining edges in the power network topology model G(V, E) are free of overload.

[0050] Step 4.2.7. Calculate the number of remaining nodes in the power network topology model G(V,E) when each remaining edge in the power network topology model G(V,E) is not overloaded. This is the total number of remaining nodes in the power network topology model G(V,E) after removing a circle and performing the cascading failure process on the power network topology model G(V,E).

[0051] See Figure 3 ,The critical cycle of length 6 in the IEEE 118 bus power network is {68, 69, 75, 77, 80, 81}, and the maximum connected component ratio is 0.644.

[0052] The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, several simple deductions and substitutions can be made without departing from the concept of the present invention, and all of these should be considered to fall within the scope of protection of the present invention.

Claims

1. A method for detecting critical loops in power networks based on simulated annealing algorithm, characterized in that: The following steps are involved: Step 1: Construct a power network topology model: Obtain information about each load, each generator, and each branch of the power network, and construct a power network topology model G(V,E) based on the information about each load, each generator, and each branch of the power network. The nodes of the power network topology model G(V,E) include generator nodes and load nodes. The total number of nodes of the power network topology model G(V,E) is N, and the N nodes of the power network topology model G(V,E) are denoted as v i , where i is a positive integer less than or equal to N, V ​​is the set of N nodes, and E is the set of edges; Step 2: Construct the solution space: Use the depth-first search algorithm to traverse the power network topology model 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 constitute the solution space are 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 key circles with length less than L in the power network topology model G(V,E) to obtain multiple second key circles with length L, and add all the second key circles with length L obtained after expansion to the initial solution set, or extract multiple circles in the solution space and add them to the initial solution set, so that the number of circles in the initial solution set is A, to complete the construction of the initial solution set. The A circles that constitute the initial solution set are denoted as Q in sequence. a , where a is a positive integer less than or equal to A, and A is the preset value of the number of circles in the initial solution set; Step 4: Detect key circles: Based on the initial solution set, a simulated annealing algorithm with a neighborhood search strategy is used to find key circles in the solution space to obtain key circles. When there are unvisited circles in the initial solution set, an unvisited circle Q is randomly selected from the initial solution set. a , Q a As the current solution C, and Q a Mark as visited, and calculate the maximum connected component ratio R(C) of the current solution C based on the cascading failure process. The formula for calculating R(C) is as follows: R(C) = N' / N, where N' is the total number of nodes remaining in the power network topology model G(V,E) after removing a circle and performing the cascading failure process on the power network topology model G(V,E). The removed circle is the current solution C.

2. The method for detecting a critical loop in a power network based on a simulated annealing algorithm according to claim 1, wherein: The step 4 is specifically as follows: Step 4.1, initialize the parameters in the simulated annealing algorithm, including the initial temperature T0, the cooling coefficient α, and the termination temperature T end , neighborhood search range m, set the status of all circles in the initial solution set to be unvisited; Step 4.2: When all circles in the initial solution set have been visited, execute step 4.

7. If there are unvisited circles in the initial solution set, randomly select an unvisited circle Q from the initial solution set. a , Q a As the current solution C, and Q a Mark as visited, calculate the maximum connected component ratio R(C) of the current solution C based on the cascading failure process, and calculate R(C) using the following formula: R(C) = N' / N, where N' is the total number of nodes remaining in the power network topology model G(V,E) after removing a circle and performing the cascading failure process on the power network topology model G(V,E). The removed circle is the current solution C. Step 4.3: Based on the neighborhood search range m, search for circles in the solution space based on the current solution circle C to obtain the set S nei (C), S nei (C)={D h |d r ∈D h ,q z ∈C,min(d(d r ,q z ))≤m}, Among them, d r Circle D h Nodes in q z is the node in the current solution circle C, d(d r ,q z ) represents node d r To node q z The shortest path distance, min(d(d r ,q z )) indicates circle D h The shortest distance to the current solution circle C, S nei (Q a ) are marked as O k , where k is an integer greater than 0; Step 4.4: If S nei (C) has unvisited circles, then from S nei (C) Select an unvisited circle O k As the new solution W, and circle O k Mark as visited if S nei If there is no unvisited circle in (C), then the steps are executed sequentially starting from step 4.2; Step 4.5: Calculate the maximum connected component ratio R(W) of the new solution W based on the cascading failure process. The formula for calculating R(W) is as follows: R(W) = N” / N, where N” is the total number of nodes remaining in the power network topology model G(V,E) after removing a circle and performing the cascading failure process on the power network topology model G(V,E). The removed circle 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 W as the current solution C with probability J. The calculation formula for J is as follows: J = e (R (C)-R(W)) / T , where T represents the current temperature; Step 4.6: When the new solution W is accepted as the current solution C, update the temperature. If the temperature is the termination temperature, execute step 4.

7. If the temperature is not the termination temperature, execute the steps starting from step 4.

3. If the new solution W is not accepted as the current solution C, if S nei (C) has unvisited circles, then start from step 4.4 and execute the steps in sequence. If S nei (C) There are no unvisited circles, and the steps are performed sequentially starting from step 4.2; Step 4.7, mark the key circle: compare the maximum connected component ratio of each circle obtained through steps 4.1 to 4.6, and mark the circle with the smallest maximum connected component ratio as the key circle.

3. The method for detecting a critical loop in a power network based on a simulated annealing algorithm according to claim 2, wherein: In step 4, the total number of nodes remaining in the power network topology model G(V,E) after performing a cycle removal and cascading failure process on the power network topology model G(V,E) is obtained by the following steps: Step 4.2.1, using the DC power flow to calculate the active power P of each edge in the power network topology model G(V,E) based on the parameters of each load, each generator, and each branch of the power network obtained in step 1; Step 4.2.2: Remove the corresponding circle and all edges connected to each node in the removed circle. The remaining nodes and edges in the power network topology model G(V,E) form multiple subnets. Step 4.2.3, delete the subnet that does not contain a generator node or has only one node in the power network topology model G(V,E); Step 4.2.4: For each subgrid in the power network topology model G(V,E) where generation and demand are unbalanced, a power rescheduling strategy is implemented to balance generation and demand. The active power P of each remaining edge in the power network topology model G(V,E) is updated using DC power flow, and the overload level Z of each remaining edge in the power network topology model G(V,E) is calculated. Step 4.2.5: If there is an overloaded edge among the remaining edges of the power network topology model G(V,E), delete the edge with the highest overload value and retain the nodes at both ends of the edge with the highest overload value; Step 4.2.6: Execute steps 4.2.3 to 4.2.5 until all remaining edges in the power network topology model G(V, E) are free of overloads. Step 4.2.

7. Calculate the number of remaining nodes in the power network topology model G(V,E) when each remaining edge in the power network topology model G(V,E) is not overloaded. This is the total number of remaining nodes in the power network topology model G(V,E) after removing a circle and performing the cascading failure process on the power network topology model G(V,E).

4. The method for detecting a critical loop of a power network based on a simulated annealing algorithm according to claim 3, wherein: The step 2 is specifically as follows: Step 2.1: Mark the state of each node in the power network topology model G(V,E) as unvisited; Step 2.2: Select a node v in the power network topology model G(V,E) that is in the unvisited state. i , set the recursion depth to L; Step 2.3, from v i Start a depth traversal to search for v i For a circle with a length of L as the starting node, add node v i The state of is marked as visited, and each search result with v i Add all circles of length L starting from the starting node to the solution space; Step 2.4: Repeat steps 2.2 to 2.3 to traverse all nodes in the power network topology model G(V,E) that are in the unvisited state to generate a circle of length L with the corresponding node as the starting node and add it to the solution space to complete the construction of the solution space.

5. The method for detecting a critical loop of a power network based on a simulated annealing algorithm according to claim 4, characterized in that: The step 3 is specifically as follows: Step 3.1, select the first key loop: select the first key loop H = {h1, h2, ..., h n ,…,h F }, where 1≤n≤F, n is an integer, h n ∈V, F is less than L; Step 3.2: Expand the first critical circle: For each pair of adjacent nodes h in the first critical circle H s and h g , both use greedy strategies to search for node h in the power network topology model G(V,E) s To node h g If there are multiple paths between adjacent nodes that contain R nodes that do not belong to the current first critical circle H, then a path between a pair of adjacent nodes that contains R nodes that do not belong to the current first critical circle H is randomly selected and recorded as {j1,…,j f ,…,j L-F }, the path {j1,…,j f ,…,j L-F }Add to node h in the first key circle H s With node h g By expanding the first key circle H, we can get the second key circle H'={h1,…,h s ,j1,j2,…,j f ,…,j L-F , h g ,…,h n ,…,h F }, the length of the second key circle H' is L, the second key circle H' is added to the initial solution set, if no path that can extend the first key circle H is found between each pair of adjacent nodes of the first key circle H, then a known first key circle with a length less than L that has not been selected is selected and the above steps are repeated, where j f is a node in V, 1≤f≤LF, f is an integer, R=LF; Step 3.3: At the end of each execution of the action of adding the second key loop H' to the initial solution set, compare the number of loops in the initial solution set with the preset number of loops in the initial solution set. If the number of loops in the initial solution set is equal to the preset number of loops in the initial solution set, the construction of the initial solution set is complete, and Steps 3.1, 3.2, and 3.4 are no longer executed. Otherwise, select a known first key loop of length less than L that has not been selected before 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 has been completed; otherwise, multiple circles in the solution space are extracted and added 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.

6. The method for detecting a critical loop in a power network based on a simulated annealing algorithm according to claim 5, wherein: 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 active power of the generator, and minimum allowable value of active power of the generator; 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.

7. The method for detecting a critical loop in a power network based on a simulated annealing algorithm according to claim 6, wherein: The overload degree Z is calculated by the following formula: Z=(PU) / 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.

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