Power system cascade fault sequence recovery method based on recovery probability matrix

Abstract

The invention provides a power system cascade fault sequence recovery method based on a recovery probability matrix, and the method specifically comprises the steps: 1, reading the information of a standard power grid system, and building a power grid topology model; 2, simulating a power grid fault, and randomly disconnecting K branches so as to set an initial fault; 3, setting a fault cascade model, and obtaining a steady-state network based on the fault cascade model; 4, generating a recovery probability matrix RPM; 5, calculating the weight of the fault branch, and selecting the branch with the maximum weight for recovery; step 5, judging whether all fault branches are recovered or not, if so, turning to step 6, and otherwise, turning to step 3; and step 6, obtaining an optimal recovery path under the condition that the K branches are disconnected. And step 7, result storage: recording a recovery path, an effect and an overload event.

Description

Technical Field

[0001] The present invention belongs to the technical field of power grids, and in particular relates to a method for sequentially restoring power system cascading faults based on a restoration probability matrix. Background Art

[0002] The power system is the core of critical infrastructure in modern society, and its stability and reliability are directly related to economic operations and public safety. With the large-scale integration of renewable energy, the widespread use of power electronics, and the increasing interconnectivity of power grids, the complexity and vulnerability of modern power grids have increased significantly. Traditional restoration methods (such as load restoration, black start, and transmission network reconfiguration) have the following limitations:

[0003] (1) Static model defects: ignoring the power flow redistribution caused by the recovery operation, resulting in the risk of secondary failure;

[0004] (2) Strong dependence on experience: relying on manually preset rules or node centrality indicators, lacking quantitative analysis of global influence;

[0005] (3) Inefficiency: The computational complexity of the traditional AC power flow model is O(N 3 ) is high, making it difficult to support online restoration decisions for large-scale power grids. Summary of the Invention

[0006] Purpose of the invention: In order to solve the problems existing in the above-mentioned prior art, the present invention provides a method for sequential restoration of cascading faults in a power system based on a restoration probability matrix.

[0007] Technical solution: The present invention provides a method for sequential restoration of power system cascading faults based on a restoration probability matrix, which specifically includes the following steps:

[0008] Step 1: Read standard power grid system information and establish a power grid topology model;

[0009] Step 2: Simulate a grid fault and randomly disconnect K branches to set an initial fault;

[0010] Step 3: Set up a fault cascade model, obtain a steady-state network based on the fault cascade model, and generate the adjacency matrix A0 of the steady-state network;

[0011] Step 4: Generate the recovery probability matrix RPM;

[0012] Step 5: Calculate the weight of the faulty branch and select the branch with the largest weight for restoration;

[0013] Step 6: Determine whether all faulty branches have been restored. If so, go to step 7; otherwise, go to step 3.

[0014] Step 7: Obtain the optimal restoration path when K branches are disconnected.

[0015] Furthermore, the fault cascade model in step 3 is:

[0016] Step 3.1: Determine whether the fault has multiple isolated subnets; if so, go to step 3.2; otherwise, end the test and directly obtain the steady-state network;

[0017] Step 3.2: Remove all nodes from isolated subnets where no autonomous nodes exist.

[0018] Step 3.3: Calculate the total generated power P for any of the remaining subgrids G and the total load P D , we get the power balance ΔP, ΔP=P G -P D , power scheduling of subnets is performed based on ΔP;

[0019] Step 3.4: Calculate the DC power flow P of each branch based on the dispatched power ij ;

[0020] Step 3.5: Remove the branch with overloaded DC power flow and go to step 3.2 until the power grid system reaches a steady state.

[0021] Furthermore, the step 3.3 performs power scheduling on the subgrid based on ΔP as follows: if ΔP<0, reduce part of the load on the load side so that ΔP=0; if ΔP>0, reduce the amount of power generated on the generation side so that ΔP=0.

[0022] Furthermore, the DC power flow P of the branch is calculated by the following formula: ij :

[0023]

[0024] Among them, i and j represent nodes, x ij is the reactance of the branch formed by nodes i and j, P ij is the power flow of the branch formed by nodes i and j, θ i is the voltage phase angle at node i, θ j is the voltage phase angle at node j.

[0025] Furthermore, the step 4 is specifically as follows:

[0026] Step 4.1: Restore all isolated subnets in A0 that do not have autonomous nodes and generate the adjacency matrix A1; the adjacency matrix of the power grid before disconnecting K branches is recorded as A (0) ;

[0027] Step 4.2: Perform the tth iteration, randomly select M branches from the faulty branches and actively restore them, and generate the adjacency matrix

[0028] Step 4.3: Generate a steady-state network based on the cascading failure model and obtain the corresponding adjacency matrix

[0029] Step 4.4: Calculate the adjacency matrix Will actively restore the branch Set to zero, thus retaining only The passive recovery branch in the current iteration is obtained by (t) ;

[0030] Step 4.4: Calculate the incremental matrix A accumulated at the tth iteration (t) =A (t-1) +ΔA (t) ;

[0031] Step 4.5: Based on A (t) Calculate the impact of the mth branch on other branches and obtain the cumulative impact matrix:

[0032]

[0033] Among them, if the mth branch is an active recovery branch at the tth iteration, then otherwise Under the premise that m branches are active recovery branches, Indicates that in A (t) The impact of the active restoration of the mth branch on the nth branch is as follows: if the nth branch is passively restored due to the active restoration of the mth branch, then If there is no impact on the nth branch, then If the restoration of the nth branch is inhibited, then

[0034] Step 4.6: Determine whether the maximum number of iterations has been reached. If so, go to step 4.7. Otherwise, increase the number of iterations by 1 and go to step 4.2.

[0035] Step 4.7: Obtain the probability matrix of the impact of the mth branch on the restoration of other branches:

[0036]

[0037] Furthermore, the weight of the branch is calculated by the following formula in step 5:

[0038]

[0039] Among them, JC(m) represents the weight of the mth branch, α and β are coefficients, represents the normalized out-degree centrality d out (m), represents the normalized in-degree centrality d in (n):

[0040]

[0041] Wherein, L represents the total number of branches.

[0042] Beneficial effects: The present invention embeds the recovery operation into the cascading fault propagation model, and simulates the power flow redistribution process after the branch is restored in real time. The probability of passive recovery of the branch is defined, and the RPM matrix integrates historical data and real-time simulation results to provide a quantitative basis for path selection, overcoming the limitations of traditional methods that rely on experience. The path weight is dynamically updated by combining the branch influence weight and real-time power flow sensitivity. Subgroups that do not contain power generation nodes are restored first to avoid voltage instability caused by power imbalance. The present invention helps to solve the pain point that traditional static models ignore the dynamic disturbance of the system state caused by the recovery operation, resulting in frequent secondary faults (such as overload of other lines after the restoration of a branch). The chain effect of branch recovery on the power flow of the entire network can be effectively quantified. After each recovery operation, the RPM matrix and branch weight are updated through real-time power flow calculation, supporting online dynamic scheduling of large-scale power grids, and providing an innovative solution for the rapid recovery of power grids under cascading faults. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is the overall flow chart of the present invention;

[0044] Figure 2 This is a flow chart of the cascading failure model proposed by the present invention;

[0045] Figure 3 This is a flow chart of generating a recovery probability matrix provided by the present invention;

[0046] Figure 4 The present invention provides a recovery path generation diagram and a dynamic recovery flow chart based on a recovery probability matrix. DETAILED DESCRIPTION

[0047] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0048] The key terms are described below:

[0049] 1) DC power flow model: The DC power flow model is an approximate model used for power system power flow calculation. By ignoring the influence of reactive power, the AC power flow model is simplified to a DC power flow model to reduce the calculation complexity and improve the calculation speed.

[0050] 2) Active Recovery: After a power grid failure, the system proactively intervenes in the power system's recovery process through dynamic optimization and manual intervention to optimize the recovery path, shorten recovery time, and improve system security and stability.

[0051] 3) Passive Recovery: After a power grid failure, the system relies on its own automatic protection mechanisms and established recovery processes to gradually restore the power system to normal operation without additional human intervention or optimization decisions.

[0052] 4) Restoration Probability Matrix (RPM): The RPM is typically used to describe the probability of recovery of each component after a power system fault. It plays an important role in fault analysis and the design of power grid restoration strategies. By using the RPM, the probability of recovery of each component under different times and conditions can be quantified, and the restoration strategy can be optimized.

[0053] 5) Restoration path: The design of the restoration path needs to consider the optimal restoration sequence to restore the normal operation of the power grid in the shortest time.

[0054] 6) Dynamic recovery: The process of gradually restoring system operation. Unlike static recovery, dynamic recovery not only considers the timing and steps of system recovery, but also considers the changes and dynamic characteristics of the system state during the fault recovery process.

[0055] The structural diagram of the power system cascading fault sequential restoration method based on the restoration probability matrix provided by the present invention is as follows: Figure 1 The main steps are as follows:

[0056] Step 1: Read the standard power grid system information, establish the power grid topology model, and set the initial operating status.

[0057] Step 2: Simulate the power grid fault through simulation to obtain the initial fault state.

[0058] Step 3: Perform cascading failure simulation and iterate T simulation experiments to generate the recovery probability matrix RPM.

[0059] Step 4: Calculate the influence of each branch, select the optimal restoration path, and give priority to restoring the sub-cluster without power generation nodes.

[0060] Step 5: Based on the optimal restoration path, perform dynamic grid restoration and store data.

[0061] Among them, in step 1, the standard test system containing information such as nodes, branches, and generator parameters is read to provide initial data of grid topology and operating parameters for subsequent analysis.

[0062] In step 2, an initial fault setting is performed on the simulation environment, and K branches are randomly selected to be disconnected, so that a specific area of ​​the standard test system enters a fault failure state due to branch disconnection, thereby providing the required initial fault grid operation state for the generation of the restoration probability matrix path.

[0063] Grid Modeling:

[0064] The unweighted and undirected network G = (V, E) is constructed using graph theory, where V represents the node set and E represents the link set. Furthermore, the node set can be divided into autonomous node subsets and load node subset Satisfying V = V g ∪V d .

[0065] The DC power flow equation is used to describe the steady-state operation of the power grid:

[0066]

[0067] Where, P ij is the active power from node i to node j, θ i -θ j is the voltage phase angle difference, X ij is the reactance of the line formed by nodes i and j. Computational efficiency: the complexity is reduced from O(N 3 )(AC power flow) is reduced to O(N)(DC power flow).

[0068] In this model, the following two criteria are set as the fault triggering mechanism:

[0069] (1) Autonomous node constraint: Some nodes in the network are autonomous. If the connected subgroup Does not contain any autonomous nodes, that is ( is a set of autonomous nodes), then the sub-cluster is considered unable to operate independently and all its links need to be disconnected;

[0070] (2) Capacity overload criterion: When the link capacity exceeds the rated maximum capacity, it is considered failed and removed.

[0071] The flow chart of the cascading fault model based on the DC power flow model provided by the present invention is as follows: Figure 2 As shown, based on the above modeling, the cascading failure process is defined as follows:

[0072] 1. Subnet detection: Detects whether the power grid has split into multiple isolated subnets due to a fault. Detects the connected components of the network, with each subnet representing an isolated subnet.

[0073] 2. Autonomous subnet identification: Determine whether each subnet has the ability to operate independently. For each subnet G s , check whether there is at least one autonomous node. If not, all nodes and their connections in the subnet are removed; if so, power rescheduling is initiated.

[0074] 3. Power rescheduling: For the sub-grids that are still connected, define the total generated power P G , total load P D Calculate the power balance ΔP = P G -P D If ΔP=0, no scheduling is required; if ΔP<0, the load side will reduce part of the load; if ΔP>0, the power generation side will reduce part of the output.

[0075] 4. Power flow recalculation: Based on the power after scheduling, recalculate the power flow P of each line ij , and update the line load status.

[0076] 5. Detect line overload: If any link is overloaded, remove the most severely overloaded link (or links) and return to step 2; if all links meet the capacity constraints, the system reaches a stable state.

[0077] The flow chart of the method for generating the recovery probability matrix provided by the present invention is as follows: Figure 3 Specifically, it includes the following contents:

[0078] I. Recovery mechanism and mathematical model:

[0079] ① Active recovery: The set of branches restored by human operation L active ;

[0080] ② Passive recovery: The branch set L that is automatically recovered due to changes in the standard test system status other than human operation passive ;

[0081] Assuming that T independent recovery simulations are performed, the cumulative number of times that the active recovery of link m and the passive recovery of link n satisfy their respective recovery states in the same round in the t-th simulation is:

[0082]

[0083] Among them, if the mth branch is an active recovery branch at the tth iteration, then otherwise Under the premise that m branches are active recovery branches, Indicates that in A (t)The impact of the active restoration of the mth branch on the nth branch is as follows: if the nth branch is passively restored due to the active restoration of the mth branch, then If there is no impact on the nth branch, then If the restoration of the nth branch is inhibited, then

[0084] Therefore, the recovery probability matrix is ​​defined as follows:

[0085]

[0086] In order to reflect the impact of topology changes on passive recovery during simulation, the accumulated incremental matrix is ​​dynamically updated after each round of simulation:

[0087] A (t) =A (t-1) +ΔA (t)

[0088] Among them, A (0) The adjacency matrix of the power grid before attacking branch K, L is the total number of links, ΔA (t) It represents the incremental matrix corresponding to the latest restored link in the t-th simulation.

[0089] The recovery probability matrix satisfies the following probability constraints:

[0090]

[0091] Positive impact P ij >0 indicates link e i Active recovery helps link e j Passive recovery, negatively affecting P ij <0 means link e i Active recovery of the link may induce j failure or inhibit its recovery.

[0092] II. Method for constructing the recovery probability matrix (RPM):

[0093] ① Initialization phase: Construct the initial state adjacency matrix A0, which is derived from the state after attacking several links in the system and triggering cascading failures.

[0094] ② Autonomous node priority recovery: Based on the initial matrix A0, prioritize the recovery of subclusters that do not contain autonomous nodes to generate the restored initial state matrix A1. This step can effectively improve the recovery efficiency and enhance the stability of the recovery process.

[0095] ③ Passive recovery matrix construction (each round of simulation):

[0096] For each simulation t∈{1,2,...,T}, perform the following operations:

[0097] Active recovery selection: Randomly select M links from the current fault link set as active recovery links to restore and generate an adjacency matrix Form the corresponding recovery topology matrix.

[0098] Cascading failure assessment: Through repeated iterations, detect and remove secondary failure links caused by recovery until the set of failure links no longer changes, forming the final matrix after cascading failures

[0099] Passive recovery extraction: calculation Actively restore the link Set zero in the middle and keep only the passive recovery link, so as to obtain the incremental matrix ΔA of the current iteration (t) .

[0100] Incremental matrix calculation: Count the impact of newly added and removed links in this round of recovery simulation and construct the corresponding incremental matrix.

[0101] Matrix accumulation: add positive and negative increments to C respectively ij , used for the final recovery probability matrix calculation.

[0102] ④ Recovery probability matrix statistics: After completing T rounds of recovery simulation, calculate the overall recovery probability matrix.

[0103] The flow chart of selecting the optimal recovery path provided by the present invention is as follows: Figure 4 As shown in the figure, the power grid based on the optimal restoration path is dynamically restored; a branch influence weight map is constructed based on RPM, and the high-probability passive restoration branches in the power system are restored; during the restoration process, the key paths of the sub-clusters without power generation nodes are restored first to ensure power balance and voltage stability.

[0104] The dynamic restoration of the power grid based on the optimal restoration path includes the following steps:

[0105] i. Optimal recovery path selection model;

[0106] Definition of branch influence weight: The restoration weight of each branch l is:

[0107] In order to comprehensively evaluate the importance of links, the following three centrality metrics are introduced:

[0108] Out-Degree Centrality:

[0109]

[0110] Measures the direct influence of link m on the recovery of other links, that is, the number and degree of other links that can be activated after the link m is restored.

[0111] In-Degree Centrality:

[0112]

[0113] Measures the degree of dependence of link n on other links during the recovery process, that is, the probability that the recovery of this link requires the recovery of other links.

[0114] In order to comprehensively evaluate the initiative and dependency of the link, this embodiment further introduces the joint centrality

[0115] Centrality, JC):

[0116]

[0117] in, and are the normalized out-degree and in-degree centralities, respectively; α and β are weight coefficients used to weigh the importance of the link between active impact and passive recovery.

[0118] Based on the joint centrality, the key link set can be further filtered out:

[0119] E key ={e i ∈E|JC(i)≥τ}

[0120] Here, τ is a threshold used to screen links that have both broad influence during the recovery process and are susceptible to the recovery of other links. These links play a central role in network recovery and significantly impact overall recovery efficiency and stability.

[0121] ii. Recovery chain generation and dynamic recovery mechanism;

[0122] Recovery Chain is a sequence of links arranged in order of priority c = {e1,e1,...,e k}, used to guide link reconstruction during system recovery to maximize overall recovery efficiency. Considering that static recovery chains are difficult to cope with sudden failures in practical applications, this embodiment further proposes a dynamic recovery mechanism to achieve an organic combination of local optimal selection and global state feedback.

[0123] Its design covers link selection, real-time status updates, and dynamic path adjustment, and mainly includes the following steps:

[0124] Initialize the chain head: from the key edge set E keyThe link with the highest JC value is selected as the initial recovery object to ensure that the recovery process starts from the link with the greatest influence.

[0125] Iterative expansion and dynamic optimization: After each round of recovery, the JC value of each link is recalculated based on the updated RPM to ensure that the recovery path always reflects the latest system status. The link with the highest priority is selected to join the recovery chain to capture dynamic changes in the network topology.

[0126] Real-time status updates: Cascading failure simulation results and RPM changes are integrated in real time to dynamically optimize and adjust the recovery path, ensuring the adaptability and robustness of the recovery chain. Through fine-grained control in small steps, the risk of secondary failures caused by uncertainty is reduced, improving overall recovery efficiency.

[0127] The present invention provides a method for sequential restoration of power system cascading faults based on a restoration probability matrix. The method includes both real-time and research modes. Its basic functions include: reading standard network system information and simulating the fault environment to obtain the initial fault operating state of the power grid; performing cascading fault simulation on the initial operating state of the power grid; iterating T simulation experiments to generate a restoration probability matrix, effectively quantifying the influence and importance of each branch within the network; selecting the optimal restoration path and prioritizing the restoration of subclusters without power generation nodes; dynamically restoring the post-fault power grid based on the optimal restoration path; and finally, storing the data obtained after the dynamic restoration of the power system.

[0128] Finally, it should be noted that the above embodiments are intended only to illustrate the technical solutions of the present invention and are not intended to limit the same. Although the present invention has been described in detail with reference to these embodiments, those skilled in the art will appreciate that modifications or equivalent substitutions may be made to the specific embodiments without departing from the spirit and scope of the present invention, and all such modifications or equivalent substitutions are intended to be encompassed by the claims of the present invention.

Claims

1. A method for sequential restoration of power system cascading faults based on a restoration probability matrix, characterized in that: The specific steps include: Step 1: Read standard power grid system information and establish a power grid topology model; Step 2: Simulate a grid fault and randomly disconnect K branches to set an initial fault; Step 3: Set up a fault cascade model, obtain a steady-state network based on the fault cascade model, and generate the adjacency matrix A0 of the steady-state network; Step 4: Generate the recovery probability matrix RPM; Step 5: Calculate the weight of the faulty branch and select the branch with the largest weight for restoration; Step 6: Determine whether all faulty branches have been restored. If so, go to step 7; otherwise, go to step 3. Step 7: Obtain the optimal restoration path when K branches are disconnected.

2. A method for sequential restoration of power system cascading failures based on a restoration probability matrix according to claim 1, characterized in that: The fault cascade model in step 3 is: Step 3.1: Determine whether the fault has multiple isolated subnets; if so, go to step 3.2; otherwise, end the test and directly obtain the steady-state network; Step 3.2: Remove all nodes from isolated subnets where no autonomous nodes exist. Step 3.3: Calculate the total generated power P for any of the remaining subgrids G and the total load P D , we get the power balance ΔP, ΔP=P G -P D , power scheduling of subnets based on ΔP; Step 3.4: Calculate the DC power flow P of each branch based on the dispatched power ij ; Step 3.5: Remove the branch with overloaded DC power flow and go to step 3.2 until the power grid system reaches a steady state.

3. The method for sequential restoration of power system cascading failures based on a restoration probability matrix according to claim 2, characterized in that: The step 3.3 performs power scheduling on the subgrid based on ΔP as follows: if ΔP < 0, reduce part of the load on the load side so that ΔP = 0; if ΔP > 0, reduce the amount of power generated on the generation side so that ΔP = 0.

4. The method for sequential restoration of power system cascading failures based on a restoration probability matrix according to claim 2, characterized in that: The DC power flow P of the branch is calculated by the following formula in step 3.4: ij : Among them, i and j represent nodes, x ij is the reactance of the branch formed by nodes i and j, P ij is the power flow of the branch formed by nodes i and j, θ i is the voltage phase angle at node i, θ j is the voltage phase angle at node j.

5. The method for sequential restoration of power system cascading failures based on a restoration probability matrix according to claim 1, characterized in that: The step 4 is specifically as follows: Step 4.1: Restore all isolated subnets in A0 that do not have autonomous nodes and generate the adjacency matrix A1; the adjacency matrix of the power grid before disconnecting K branches is recorded as A( 0) ; Step 4.2: Perform the tth iteration, randomly select M branches from the faulty branches and actively restore them, and generate the adjacency matrix Step 4.3: Generate a steady-state network based on the cascading failure model and obtain the corresponding adjacency matrix Step 4.4: Calculate the adjacency matrix Will actively restore the branch Set to zero, thus retaining only The passive recovery branch in the current iteration is obtained by (t) ; Step 4.4: Calculate the incremental matrix A accumulated at the tth iteration (t) =A (t-1) +ΔA (t) ; Step 4.5: Based on A (t) Calculate the impact of the mth branch on other branches and obtain the cumulative impact matrix: Among them, if the mth branch is an active recovery branch at the tth iteration, then otherwise Under the premise that m branches are active recovery branches, Indicates that in A (t) The impact of the active restoration of the mth branch on the nth branch is as follows: if the nth branch is passively restored due to the active restoration of the mth branch, then If there is no impact on the nth branch, then If the restoration of the nth branch is inhibited, then Step 4.6: Determine whether the maximum number of iterations has been reached. If so, go to step 4.

7. Otherwise, increase the number of iterations by 1 and go to step 4.

2. Step 4.7: Obtain the probability matrix of the impact of the mth branch on the restoration of other branches:

6. The method for sequential restoration of power system cascading failures based on a restoration probability matrix according to claim 1, characterized in that: The step 5 calculates the weight of the branch using the following formula: Among them, JC(m) represents the weight of the mth branch, α and β are coefficients, represents the normalized out-degree centrality d out (m), represents the normalized in-degree centrality d in (n): Wherein, L represents the total number of branches.

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