Power distribution network two-stage fault restoration optimization method and terminal based on variable time step

Abstract

The application discloses a power distribution network two-stage fault repair optimization method and a terminal based on variable time steps, determines damaged evaluation information of the power distribution network after extreme weather disasters occur, establishes a repair team scheduling decision model according to the damaged evaluation information, takes minimization of total active weighted loss of each scene under a known fault repair sequence as an objective function based on variable time steps, establishes a power distribution network operation strategy optimization model, solves the repair team scheduling decision model and the power distribution network operation strategy optimization model, obtains an optimal fault repair strategy, the repair team scheduling decision model is a first-stage problem, the power distribution network operation strategy optimization model is a second-stage problem, the two-stage optimization problem can give an effective and reliable fault repair strategy after the extreme weather disasters occur, and the second-stage problem adopts the variable time step idea for modeling, thereby improving the efficiency and accuracy of solving the fault repair strategy, and thus effectively enhancing the resilience level of the power distribution network.

Description

Technical Field

[0001] This invention relates to the field of distribution network fault repair technology, and in particular to a two-stage fault repair optimization method and terminal for distribution networks based on variable time step. Background Technology

[0002] With global climate change, the frequency and intensity of extreme weather disasters are continuously increasing, posing a serious threat to the safe and reliable power supply of the power system. How to enhance the resilience of the power distribution system to more effectively cope with extreme weather disasters has become a critical problem that urgently needs to be solved, attracting widespread attention from scholars and industries both domestically and internationally.

[0003] Unlike low-order faults such as N-1 (when a component in a power system fails or goes out of service, the system can still maintain stable operation and meet power demand) and N-2 (when two critical components in a power system fail simultaneously, the system cannot maintain stable operation) that are the focus of reliability assessments, extreme weather disasters often trigger high-order severe faults, causing large-scale power outages. Following large-scale power outages caused by extreme weather disasters, in order to restore load as quickly as possible, it is necessary to comprehensively coordinate power supply resources, switch resources, and human resources to enhance the rapid response and recovery capabilities of resilient distribution networks. Considering the severity of extreme weather disasters and the limited emergency resources, developing effective distribution network fault repair strategies is of great significance for enhancing the resilience of distribution networks. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a two-stage fault repair optimization method and terminal for distribution networks based on variable time step, which can effectively enhance the resilience of distribution networks.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0006] A two-stage fault repair optimization method for distribution networks based on variable time steps includes the following steps:

[0007] After extreme weather disasters occur, determine the damage assessment information of the power distribution network;

[0008] A maintenance team dispatch decision model is established based on the damage assessment information;

[0009] An optimization model for distribution network operation strategy is established based on the objective function of minimizing the total active power weighted loss in each scenario under the known fault repair sequence with variable time step.

[0010] The optimal fault repair strategy is obtained by solving the maintenance team dispatch decision model and the distribution network operation strategy optimization model.

[0011] To solve the above-mentioned technical problems, another technical solution adopted by the present invention is as follows:

[0012] A two-stage fault repair optimization terminal for distribution networks based on variable time steps includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it performs the following steps:

[0013] After extreme weather disasters occur, determine the damage assessment information of the power distribution network;

[0014] A maintenance team dispatch decision model is established based on the damage assessment information;

[0015] An optimization model for distribution network operation strategy is established based on the objective function of minimizing the total active power weighted loss in each scenario under the known fault repair sequence with variable time step.

[0016] The optimal fault repair strategy is obtained by solving the maintenance team dispatch decision model and the distribution network operation strategy optimization model.

[0017] The beneficial effects of this invention are as follows: After an extreme weather disaster occurs, the damage assessment information of the distribution network is determined, and a maintenance team dispatch decision model is established based on the damage assessment information. Based on a variable time step, a distribution network operation strategy optimization model is established with the objective function of minimizing the total active power weighted loss in each scenario under the known fault repair sequence. The optimal fault repair strategy is obtained by solving the maintenance team dispatch decision model and the distribution network operation strategy optimization model. The established maintenance team dispatch decision model is the first-stage problem, and the established distribution network operation strategy optimization model is the second-stage problem. Through the two-stage optimization problem, an effective and reliable fault repair strategy can be given after an extreme weather disaster occurs. Moreover, the second-stage problem adopts the variable time step idea for modeling, which improves the efficiency and accuracy of solving the fault repair strategy, thereby effectively enhancing the resilience of the distribution network. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the steps of a two-stage fault repair optimization method for distribution networks based on variable time steps, according to an embodiment of the present invention.

[0019] Figure 2 This is a schematic diagram of the structure of a two-stage fault repair optimization terminal for distribution networks based on variable time step, according to an embodiment of the present invention.

[0020] Figure 3 This is a schematic diagram of the IEEE 33-node system in the two-stage fault repair optimization method for distribution networks based on variable time step according to an embodiment of the present invention.

[0021] Figure 4This is a schematic diagram showing the duration of each fault repair period under different scenarios in the two-stage fault repair optimization method for distribution networks based on variable time steps according to an embodiment of the present invention. Detailed Implementation

[0022] To explain in detail the technical content, objectives, and effects of the present invention, the following description is provided in conjunction with the embodiments and accompanying drawings.

[0023] Please refer to Figure 1 A two-stage fault repair optimization method for distribution networks based on variable time steps includes the following steps:

[0024] After extreme weather disasters occur, determine the damage assessment information of the power distribution network;

[0025] A maintenance team dispatch decision model is established based on the damage assessment information;

[0026] An optimization model for distribution network operation strategy is established based on the objective function of minimizing the total active power weighted loss in each scenario under the known fault repair sequence with variable time step.

[0027] The optimal fault repair strategy is obtained by solving the maintenance team dispatch decision model and the distribution network operation strategy optimization model.

[0028] As can be seen from the above description, the beneficial effects of the present invention are as follows: After an extreme weather disaster occurs, the damage assessment information of the distribution network is determined, a maintenance team dispatch decision model is established based on the damage assessment information, and a distribution network operation strategy optimization model is established based on a variable time step with the objective function of minimizing the total active power weighted loss of each scenario under the known fault repair sequence. The maintenance team dispatch decision model and the distribution network operation strategy optimization model are solved to obtain the optimal fault repair strategy. The established maintenance team dispatch decision model is the first-stage problem, and the established distribution network operation strategy optimization model is the second-stage problem. Through the two-stage optimization problem, an effective and reliable fault repair strategy can be given after an extreme weather disaster occurs. Moreover, the second-stage problem adopts the variable time step idea for modeling, which improves the efficiency and accuracy of solving the fault repair strategy, thereby effectively enhancing the resilience of the distribution network.

[0029] Furthermore, the damage assessment information includes the location of the damaged component and the fault repair time;

[0030] The step of establishing a maintenance team dispatch decision model based on the damage assessment information includes:

[0031] A maintenance team scheduling decision model is established based on the location of the damaged component and the fault repair time.

[0032] As described above, establishing a maintenance team scheduling decision model based on the location of damaged components and the fault repair time, and treating it as the first-stage problem, allows for decision-making based on a given fault repair order, which helps in optimizing the solution in the next stage.

[0033] Furthermore, the step of establishing a maintenance team scheduling decision model based on the location of the damaged component and the fault repair time includes:

[0034]

[0035] In the formula, C E This indicates that the maintenance team has arrived at the warehouse and the location of all faulty lines, C. S λ represents the set of locations of the maintenance team's personnel from the departure warehouse and all faulty lines. m,n Indicates whether the maintenance personnel have moved from position m to position n, λ m,0 This indicates whether the maintenance personnel have moved from location m to the departure warehouse location n. This indicates whether the maintenance personnel have moved from location m to location n upon arrival at the warehouse.

[0036] As can be seen from the above description, the scheduling strategy that traverses all faulty components and maintenance personnel warehouses can be obtained based on the maintenance team scheduling decision model.

[0037] Furthermore, the establishment of the distribution network operation strategy optimization model based on variable time steps, with the objective function being to minimize the total active power weighted loss in each scenario under the known fault repair sequence, includes:

[0038] The objective function is to minimize the total active power weighted loss of each scenario under the known fault repair sequence based on the variable time step, and to establish constraints for fault component repair, network security operation, radial topology, fault area, and power generation unit output.

[0039] An optimization model for distribution network operation strategy is established based on the objective function, the fault component repair constraint, the network security operation constraint, the radial topology constraint, the fault area constraint, and the power generation unit output constraint.

[0040] As described above, the objective function is to minimize the total active power weighted loss in each scenario under the known fault repair sequence based on the variable time step. Constraints are established for fault component repair, network security operation, radial topology, fault area, and power generation unit output. This is used to establish a distribution network operation strategy optimization model as the second stage problem. In the second stage, the repair measures can minimize the active power loss in each scenario under the known repair sequence, ensuring the reliability of the final fault repair strategy.

[0041] Furthermore, the objective function based on minimizing the total active power weighted loss of each scenario under the known fault repair sequence, using a variable time step, includes:

[0042]

[0043] In the formula, λ represents the decision vector of the maintenance team dispatch decision model, h(λ,ξ(s)) represents the optimal solution of the distribution network operation strategy optimization model, Ω represents the scenario set, and ρ s Let F(λ,s) represent the probability of scenario s, F(λ,s) represent the optimization objective of the second-stage problem, C represent the time period set, B represent the bus set, and Δτ represent the probability of scenario s. c,s ω represents the duration of the c-th time interval in scenario s. j This represents the weight of bus j. This represents the active power load loss of bus j within time period c under scenario s.

[0044] As described above, the resilience level of a power distribution system is often measured by the weighted load loss throughout the entire disaster process. Optimizing the system with the goal of minimizing the total active power weighted loss in each scenario under the known fault repair sequence can effectively improve the resilience level of the power distribution network. Furthermore, the objective function is constructed using a variable time step, which can effectively reduce the number of variables in the model and improve the optimization efficiency of the model.

[0045] Furthermore, the constraint for repairing the faulty component is:

[0046]

[0047] -M(1-λ m,n )+τ n,s -τ m,s ≤Vτ m,s ≤τ n,s -τ m,s +M(1-λ m,n );

[0048]

[0049] In the formula, M represents a preset maximum positive number, and λ m,n Indicates whether maintenance personnel have moved from position m to position n, τ m,s This represents the repair time for the fault at location m in scenario s. This represents the time it takes for a maintenance worker to move from position m to position n in scenario s. τ represents the time required to repair the fault at location n in scenario s. n,s Vτ represents the repair time for a fault at position n in scenario s. m,s f represents the duration from repairing a fault at position m to repairing a fault at the next position in scenario s. ij,c,sLet σ(m) represent the fault state of branch ij in the c-th time period under scenario s, and let σ(m) represent the branch number corresponding to the fault at position m. This represents the magnitude of the active power load shedding on bus j after the fault at location m is repaired in scenario s. This represents the magnitude of the active power load shedding on bus j after the fault at location n is repaired in scenario s. This represents the reactive load shearing magnitude of bus j at location n under scenario s after repair. This represents the amount of reactive load shedding on bus j after the fault at location m is repaired in scenario s.

[0050] As can be seen from the above description, the fault component repair constraint effectively describes the impact of maintenance team scheduling decisions on line fault status and bus load loss.

[0051] Furthermore, the network security operation constraints are as follows:

[0052]

[0053] In the formula, H represents the active power load demand of bus j, μ(j) represents the set of sub-buses of bus j, and H represents the active power load demand of bus j. ju,c,s Let H represent the active power of branch ju in the c-th time period under scenario s, and let π(j) represent the set of parent lines of bus j. ij,c,s Let represent the active power of branch ij in the c-th time period under scenario s. This represents the active power output of the power generation unit connected to bus j during the c-th time period in scenario s. This represents the reactive power load demand of bus j. G represents the reactive load loss of bus j within time period c under scenario s. ju,c,s G represents the reactive power of branch ju in the c-th time period under scenario s. ij,c,s This represents the reactive power of branch ij in the c-th time period under scenario s. This represents the reactive power output of the power generation unit connected to bus j during the c-th time period in scenario s, where M represents a preset maximum positive number, and z ij,c,s U represents the opening and closing state of branch ij in the c-th time period under scenario s. i,c,s U represents the voltage of bus i over c time periods in scenario s. j,c,s R represents the voltage of bus j over c time periods in scenario s. ij x represents the resistance of branch ij. ij U represents the reactance of branch ij, and U0 represents the reference voltage. This indicates the lower limit of the voltage at bus j. This indicates the upper limit of the voltage at bus j;

[0054] The radial topological constraints are:

[0055]

[0056] In the formula, ξ i,c,s Let π(i) represent whether bus i is the root node in the c-th time period under scenario s, and let π(i) represent the set of parent lines of bus i. Let δ(i) represent the virtual traffic on virtual edge ji during the c-th time period in scenario s. This represents the virtual traffic on virtual edge ij during the c-th time period in scenario s, where N0 represents the total number of buses, and E RCS This represents the set of branches equipped with remotely controllable switches; E represents the set of all branches in the power distribution system.

[0057] The output constraint of the power generation unit is:

[0058]

[0059] In the formula, φ k,j This indicates whether the k-th power generation unit is connected to bus j. This represents the upper limit of the active power output of the k-th power generation unit. This represents the upper limit of reactive power output of the k-th power generation unit.

[0060] As can be seen from the above description, network security operation constraints, radial topology constraints, and power generation unit output constraints can ensure the safe and stable operation of the power distribution system.

[0061] Furthermore, the fault region constraint is as follows:

[0062] n i,c,s ≥f ij,c,s +z ij,c,s -1;

[0063] n j,c,s ≥f ij,c,s +z ij,c,s -1;

[0064] z ij,c,s -1≤n i,c,s -n j,c,s ≤1-z ij,c,s ;

[0065]

[0066] In the formula, n i,c,s This indicates whether bus i is in the fault zone during the c-th time period in scenario s, f ij,c,s This represents the fault state of branch ij within the c-th time period under scenario s, where n j,c,s This indicates whether bus j is in the fault zone during the c-th time period under scenario s.

[0067] As described above, the fault area constraint can accurately describe the influence range of the faulty line and ensure the reliability of the final solution.

[0068] Furthermore, the process of solving the maintenance team dispatch decision model and the distribution network operation strategy optimization model to obtain the optimal fault repair strategy includes:

[0069] Solving the maintenance team scheduling decision model yields multiple sets of fault repair sequences;

[0070] The multiple fault repair sequences are substituted into the distribution network operation strategy optimization model as known fault repair sequences to obtain multiple distribution network operation strategies. The fault repair sequence corresponding to the distribution network operation strategy with the minimum total active power weighted loss is selected as the optimal fault repair strategy.

[0071] As described above, the multiple fault repair sequences obtained from solving the first-stage problem are substituted into the distribution network operation strategy optimization model as known fault repair sequences for solving, resulting in multiple distribution network operation strategies. The fault repair sequence corresponding to the distribution network operation strategy with the minimum total active power weighted loss is selected as the optimal fault repair strategy, ensuring the reliability of the optimal fault repair strategy.

[0072] The two-stage fault repair optimization method and terminal for distribution networks based on variable time step described above are applicable to distribution networks after extreme weather disasters. The following detailed implementation methods illustrate this:

[0073] Please refer to Figure 1 , Figure 3 and Figure 4 Embodiment 1 of the present invention is as follows:

[0074] A two-stage fault repair optimization method for distribution networks based on variable time steps includes the following steps:

[0075] S1. After an extreme weather disaster occurs, determine the damage assessment information of the power distribution network.

[0076] The damage assessment information includes the location of the damaged component and the time of fault repair.

[0077] For example, using fault indicators (FI) with communication capabilities, feeder and transformer monitoring equipment, smart meters, etc., can provide important basic information on the location of damaged components in the distribution network after extreme weather disasters. Furthermore, inspection teams or inspection drones can be dispatched to the faulty sections for on-site inspections to estimate the time required for each fault to be repaired.

[0078] S2. Establish a maintenance team dispatch decision model based on the damage assessment information.

[0079] Specifically, a maintenance team scheduling decision model is established based on the location of the damaged component and the fault repair time, as follows:

[0080]

[0081] In the formula, C E This indicates that the maintenance team has arrived at the warehouse and the location of all faulty lines, C. S λ represents the set of locations of the maintenance team's personnel from the departure warehouse and all faulty lines. m,n Indicates whether the maintenance personnel have moved from position m to position n, λ m,0 This indicates whether the maintenance personnel have moved from location m to the departure warehouse location n. Indicates whether maintenance personnel have moved from location m to location n upon arrival at the warehouse, C S ={0,1,2,K,N F}, C E ={1,2,K,N F N F +1},N F This indicates the total number of faulty lines.

[0082] The first and second equations above restrict maintenance personnel to starting only from the warehouse, repairing each faulty component sequentially, and ultimately returning to the warehouse. The third equation indicates that returning to the warehouse is not allowed ({0}), and the fourth equation indicates that the maintenance team ultimately returns to the warehouse ({N}). F +1} is used to avoid loops.

[0083] S3. Based on variable time steps, and with the objective function of minimizing the total active power weighted loss in each scenario under the known fault repair sequence, an optimization model for distribution network operation strategy is established, specifically including S31-S32:

[0084] In one alternative implementation, prior to S3, the following is also included:

[0085] A scene set is generated by sampling using a scene generation method to represent uncertainty. The scene set includes a scene set of damaged component repair time and a scene set of maintenance team relocation time.

[0086] S31. Based on the variable time step, the objective function is to minimize the total active power weighted loss of each scenario under the known fault repair sequence, and establishes the fault component repair constraints, network security operation constraints, radial topology constraints, fault area constraints, and power generation unit output constraints.

[0087] The objective function is:

[0088]

[0089] In the formula, λ represents the decision vector of the maintenance team dispatch decision model, λ∈Λ, h(λ,ξ(s)) represents the optimal solution of the distribution network operation strategy optimization model, Ω represents the scenario set, and ρ s Let F(λ,s) represent the probability of scenario s, F(λ,s) represent the optimization objective of the second-stage problem, C represent the time period set, B represent the bus set, and Δτ represent the probability of scenario s. c,s ω represents the duration of the c-th time interval in scenario s. j This represents the weight of bus j. This represents the active power load loss of bus j within time period c under scenario s.

[0090] In existing research, the fault recovery process of distribution networks is typically discretized into N equal time intervals. Rapid system response and power restoration are achieved through methods such as scheduling mobile resources, repairing damaged components, and dynamic network reconfiguration. This type of method is called the fixed-time-step method. However, the time intervals for personnel movement, fault repair, manual switching operations, and remote switching actions vary significantly, potentially ranging from hours to minutes. Using a fixed-time-step modeling approach to couple these temporal actions results in numerous periods where the system state remains unchanged. As the number of time intervals increases, this method may compromise the optimality of the solution and increase computational complexity. Furthermore, extreme weather events significantly increase the uncertainty of fault repair times for different components and the transfer times of maintenance teams between different locations, further expanding the model's time dimension and increasing the computational burden of decision-making. Simply put, the difference between fixed-time-step and variable-time-step methods lies primarily in the description of model variables. Variables in the fixed-time-step method are defined based on time intervals, while variables in the variable-time-step method are defined based on events. In the variable-time-step method of this invention, the variable-time-step method uses... This represents the active power load loss of bus j within time period c under scenario s, with the length of each time period being Δτ. c,s It is variable and is calculated from the faulty component repair constraints.

[0091] Suppose three faults occur simultaneously in a power distribution system, with an estimated system recovery time of 10 hours. Using a fixed-time-step method requires dividing the system recovery process into 10 equal periods, each lasting 1 hour, with a power flow check performed within each period. Therefore, 10 variables are needed to represent the active power load loss of bus j during the recovery process. However, using the variable-time-step method of this invention, the system recovery process will experience four main events: fault not repaired, repair of the first fault, repair of the second fault, and repair of all faults. A power flow check is performed only after each event occurs. Therefore, only four variables are needed to represent the active power load loss of bus j during the recovery process. It is evident that the method of this invention effectively reduces the number of variables in the model, improves the optimization efficiency of the model, can flexibly handle different combinations of discrete events such as fault repair, and effectively reduces the computational burden of decision-making.

[0092] The constraints for repairing the faulty component are:

[0093]

[0094] -M(1-λ m,n )+τ n,s -τ m,s ≤Vτ m,s ≤τ n,s -τ m,s +M(1-λ m,n );

[0095]

[0096] In the formula, M represents a preset maximum positive number, τ m,s This represents the repair time for the fault at location m in scenario s. This represents the time it takes for a maintenance worker to move from position m to position n in scenario s. τ represents the time required to repair the fault at location n in scenario s. n,s Vτ represents the repair time for a fault at position n in scenario s. m,s f represents the duration from repairing a fault at position m to repairing a fault at the next position in scenario s. ij,c,s This represents the fault status of branch ij within the c-th time period under scenario s. A value of 1 indicates that the branch is faulty, and a value of 0 indicates that the branch is normal, i.e., no fault has occurred or the fault has been repaired. σ(m) represents the branch number corresponding to the fault at position m. This represents the magnitude of the active power load shedding on bus j after the fault at location m is repaired in scenario s. This represents the magnitude of the active power load shedding on bus j after the fault at location n is repaired in scenario s. This represents the reactive load shearing magnitude of bus j at location n under scenario s after repair. This represents the reactive power load shedding magnitude of bus j after fault repair at location m in scenario s. In one optional implementation, the preset maximum positive number is 10000.

[0097] The first constraint in the fault component repair constraint is the coupling constraint between the fault component repair times, indicating that if the maintenance team repairs the faults at positions m and n sequentially, i.e., λ m,n =1, then the repair of the nth faulty component lags behind the repair of the mth faulty component, and the time difference is . This includes the time to move from location m to location n and the time required to repair the fault at location n; the second constraint indicates that if the maintenance team repairs the faults at locations m and n sequentially, the duration of the m-th time interval is τ. n,s -τ m,s The third constraint represents the relationship between the fault state and fault repair time of branch ij within the time period n. If the nth faulty component is repaired before the mth faulty component, i.e., τ m,s >τ n,s Then, in the nth time period, the state of line ij corresponding to the mth faulty component is normal (f ij,c,s =0); the fourth and fifth constraints indicate that once the load is restored during the recovery process, it cannot be shut down again.

[0098] The network security operation constraints are as follows:

[0099]

[0100]

[0101] In the formula, H represents the active power load demand of bus j, μ(j) represents the set of sub-buses of bus j, and H represents the active power load demand of bus j. ju,c,s Let H represent the active power of branch ju in the c-th time period under scenario s, and let π(j) represent the set of parent lines of bus j. ij,c,s Let represent the active power of branch ij in the c-th time period under scenario s. This represents the active power output of the power generation unit connected to bus j during the c-th time period in scenario s. This represents the reactive power load demand of bus j. G represents the reactive load loss of bus j within time period c under scenario s. ju,c,s G represents the reactive power of branch ju in the c-th time period under scenario s. ij,c,s This represents the reactive power of branch ij in the c-th time period under scenario s. This represents the reactive power output of the power generation unit connected to bus j during the c-th time period in scenario s. ij,c,s U represents the opening and closing state of branch ij in the c-th time period under scenario s.i,c,s U represents the voltage of bus i over c time periods in scenario s. j,c,s R represents the voltage of bus j over c time periods in scenario s. ij x represents the resistance of branch ij. ij U represents the reactance of branch ij, and U0 represents the reference voltage. This indicates the lower limit of the voltage at bus j. This indicates the upper limit of the voltage at bus j.

[0102] The radial topological constraints are:

[0103]

[0104] In the formula, ξ i,c,s Let π(i) represent whether bus i is the root node in the c-th time period under scenario s, and let π(i) represent the set of parent lines of bus i. Let δ(i) represent the virtual traffic on virtual edge ji during the c-th time period in scenario s. This represents the virtual traffic on virtual edge ij during the c-th time period in scenario s, where N0 represents the total number of buses, and E RCS This represents the set of branches equipped with remotely controllable switches, and E represents the set of all branches in the power distribution system.

[0105] The output constraint of the power generation unit is:

[0106]

[0107]

[0108] In the formula, φ k,j This indicates whether the k-th power generation unit is connected to bus j. This represents the upper limit of the active power output of the k-th power generation unit. This represents the upper limit of reactive power output of the k-th power generation unit.

[0109] The fault region constraint is as follows:

[0110] n i,c,s ≥f ij,c,s +z ij,c,s -1;

[0111] n j,c,s ≥f ij,c,s +z ij,c,s -1;

[0112] z ij,c,s -1≤n i,c,s -n j,c,s ≤1-z ij,c,s ;

[0113]

[0114] In the formula, n i,c,s This indicates whether bus i is in the fault zone during the c-th time period in scenario s, n j,c,s This indicates whether bus j is in the fault zone during the c-th time period under scenario s.

[0115] The first and second constraints in the fault region constraint indicate that if a closed branch experiences a fault, both buses at its ends are included within the fault region. The third constraint is a fault state propagation constraint, meaning the fault region extends along the closed branch. The fourth and fifth constraints indicate that buses within the fault region lose all load. The fault region constraint characterizes the system's fault isolation process; that is, during network reconfiguration during distribution network fault repair, faulty components must be isolated from non-faulty areas to prevent the fault's impact area from expanding.

[0116] S32. Establish a distribution network operation strategy optimization model based on the objective function, the fault component repair constraint, the network security operation constraint, the radial topology constraint, the fault area constraint, and the power generation unit output constraint.

[0117] S4. Solve the maintenance team dispatch decision model and the distribution network operation strategy optimization model to obtain the optimal fault repair strategy, specifically including:

[0118] S41. Solve the maintenance team scheduling decision model to obtain multiple sets of fault repair sequences.

[0119] S42. Substitute the multiple sets of fault repair sequences as known fault repair sequences into the distribution network operation strategy optimization model for solution to obtain multiple distribution network operation strategies. Then, select the fault repair sequence corresponding to the distribution network operation strategy with the minimum total active power weighted loss from the multiple distribution network operation strategies as the optimal fault repair strategy.

[0120] The optimal fault repair strategy is the fault repair strategy with the minimum active power loss. The above solution is achieved using solvers such as Cplex or Gurobi.

[0121] use Figure 3 The effectiveness of the proposed method is verified using an IEEE 33-bus system. In the system, bus 1 is connected to a substation, and controllable distributed power sources are installed on bus 14 and bus 33. Assume six faults occur in the system, and the expected repair time intervals for each fault are shown in Table 1.

[0122] Table 1 Location of damaged components and repair time in the system

[0123] Faulty branch Repair time interval (h) L6 [2,4] L14 [1,2] L21 [2,6] L23 [2,4] L28 [2,4] L31 [1,2]

[0124] The optimal fault repair strategy finally obtained by the above method of the present invention is: L23→L6→L21→L28→L14→L31. For example... Figure 4 As shown, Figure 4 The results show that the duration of each fault repair period is different under different scenarios, indicating that the above-mentioned method of the present invention achieves the function of variable time step.

[0125] Please refer to Figure 2 Embodiment two of the present invention is as follows:

[0126] A two-stage fault repair optimization terminal for distribution networks based on variable time steps includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements each step of the two-stage fault repair optimization method for distribution networks based on variable time steps in Embodiment 1.

[0127] In summary, this invention provides a two-stage fault repair optimization method and terminal for distribution networks based on variable time steps. After an extreme weather disaster, the damage assessment information of the distribution network is determined. Based on the damage assessment information, a maintenance team dispatch decision model is established. Using a variable time step, a distribution network operation strategy optimization model is established with the objective function of minimizing the total active power weighted loss in each scenario under a known fault repair sequence. The optimal fault repair strategy is obtained by solving both the maintenance team dispatch decision model and the distribution network operation strategy optimization model. The established maintenance team dispatch decision model is the first-stage problem, and the established distribution network operation strategy optimization model is the second-stage problem. Through two-stage... The segment optimization problem can provide effective and reliable fault repair strategies after extreme weather disasters. The second-stage problem adopts the concept of variable time step modeling, which improves the efficiency and accuracy of solving fault repair strategies, thereby effectively enhancing the resilience of the distribution network. In addition, the multiple fault repair sequences obtained from solving the first-stage problem are substituted into the distribution network operation strategy optimization model as known fault repair sequences for solving, resulting in multiple distribution network operation strategies. The fault repair sequence corresponding to the distribution network operation strategy with the minimum total active power weighted loss is selected as the optimal fault repair strategy, ensuring the reliability of the optimal fault repair strategy.

[0128] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent modifications made based on the content of the present invention specification and drawings, or direct or indirect applications in related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A variable time step based two-stage fault restoration optimization method for power distribution network, characterized in that, The method comprises the steps of: determining damage assessment information of a power distribution network after an extreme weather disaster occurs; establishing a repair team scheduling decision model according to the damage assessment information; establishing a power distribution network operation strategy optimization model based on variable time steps to minimize the total active power weighted loss of each scenario under a known fault repair sequence as an objective function; solving the repair team scheduling decision model and the power distribution network operation strategy optimization model to obtain an optimal fault repair strategy; the damage assessment information includes the location of damaged elements and fault repair time; the repair team scheduling decision model is established according to the location of damaged elements and the fault repair time; the repair team scheduling decision model is established according to the location of damaged elements and the fault repair time; the power distribution network operation strategy optimization model is established based on variable time steps to minimize the total active power weighted loss of each scenario under a known fault repair sequence as an objective function, and includes fault element repair constraints, network safe operation constraints, radial topology constraints, fault area constraints and power generation unit output constraints; where C E represents the set of locations where the repair crew arrives at the warehouse and all the faulty lines, C S represents the set of locations where the repair crew departs from the warehouse and all the faulty lines, λ m,n represents whether the repair crew moves from location m to location n, λ m,0 represents whether the repair crew moves from location m to the departure warehouse location n, represents whether the repair crew moves from the arrival warehouse location m to location n; the power distribution network operation strategy optimization model is established according to the objective function, the fault element repair constraints, the network safe operation constraints, the radial topology constraints, the fault area constraints and the power generation unit output constraints; the objective function based on variable time steps to minimize the total active power weighted loss of each scenario under a known fault repair sequence includes: solving the repair team scheduling decision model to obtain multiple fault repair sequences; substituting the multiple fault repair sequences into the power distribution network operation strategy optimization model as known fault repair sequences to obtain multiple power distribution network operation strategies, and selecting the fault repair sequence corresponding to the power distribution network operation strategy with the minimum total active power weighted loss as the optimal fault repair strategy. In the formula, λ represents a decision vector of a maintenance team scheduling decision model, h(λ, ξ(s)) represents an optimal solution of a distribution network operation strategy optimization model, Ω represents a scenario set, ρ s represents a probability of scenario s, F(λ, s) represents an optimization objective of a second-stage problem, C represents a time period set, B represents a bus set, Δτ c,s represents a duration of a cth time period under scenario s, ω j represents a weight of bus j, represents an active load loss of bus j in a time period c under scenario s; the fault element repair constraints are: the network safe operation constraints are: the radial topology constraints are:

2. The method of claim 1, wherein, the power generation unit output constraints are: - M(1 - λ m,n ) + τ n,s - τ m,s ≤ Δτ m,s ≤ τ n,s - τ m,s + M(1 - λ m,n ); where M represents a preset maximum positive number, λ m,n represents whether the maintenance personnel is transferred from position m to position n, τ m,s represents the repair time of the fault at position m under scenario s, represents the transfer time of the maintenance personnel from position m to position n under scenario s, represents the time required to repair the fault at position n under scenario s, τ n,s represents the repair time of the fault at position n under scenario s, Δτ m,s represents the duration from repairing the fault at position m to repairing the fault at the next position under scenario s, f ij,c,s represents the fault state of branch ij in the cth time period under scenario s, σ(m) represents the branch number corresponding to the fault at position m, represents the active cut load size of bus j after the fault at position n is repaired under scenario s, represents the active cut load size of bus j after the fault at position m is repaired under scenario s, represents the reactive cut load size of bus j after the fault at position n is repaired under scenario s, represents the reactive cut load size of bus j after the fault at position m is repaired under scenario s.

3. The method of claim 1, wherein, the fault area constraints are: M(z ij,c,s -1)≤U i,c,s -U j,c,s -(H ij,c,s r ij +G ij,c,s x ij ) / U0≤M(1-z ij,c,s ); wherein, P(j) represents the active load demand of bus j, μ(j) represents the set of child buses of bus j, H ju,c,s P(ju) represents the active power of branch ju in the cth time period under scenario s, π(j) represents the set of parent buses of bus j, H ij,c,s P(ij) represents the active power of branch ij in the cth time period under scenario s, P(ju) represents the active power of branch ju in the cth time period under scenario s, π(j) represents the set of parent buses of bus j, H Q(j) represents the reactive load demand of bus j, Q(j) represents the reactive load demand of bus j, ju,c,s Q(ju) represents the reactive power of branch ju in the cth time period under scenario s, G ij,c,s Q(ij) represents the reactive power of branch ij in the cth time period under scenario s, Q(ju) represents the reactive power of branch ju in the cth time period under scenario s, M represents a preset maximum positive number, z ij,c,s U(ij) represents the on-off state of branch ij in the cth time period under scenario s, U i,c,s U(i) represents the voltage of bus i in the c time periods under scenario s, U j,c,s U(j) represents the voltage of bus j in the c time periods under scenario s, r ij R(ij) represents the resistance of branch ij, x ij X(ij) represents the reactance of branch ij, U0 represents a reference voltage, Umin(j) represents the lower limit of the voltage of bus j, Umax(j) represents the upper limit of the voltage of bus j; the processor executes the computer program to realize each step in the two-stage fault repair optimization method for a power distribution network based on variable time steps according to any one of claims 1 to 4. wherein ξ i,c,s denotes whether bus i is a root node in the cth time period under scenario s, π(i) denotes the parent bus set of bus i, denotes the virtual flow on virtual edge ji in the cth time period under scenario s, δ(i) denotes, denotes the virtual flow on virtual edge ij in the cth time period under scenario s, N0 denotes the total number of buses, E RCS denotes the branch set equipped with remotely controllable switches, E denotes the branch set of the entire distribution system; ​ where φkjis the phase angle of the kth generator, k,j denotes whether the kth generator is connected to bus j, denotes the active power upper limit of the kth generator, denotes the reactive power upper limit of the kth generator.

4. The method of claim 3, wherein, ​ n i,c,s ≥f ij,c,s +z ij,c,s -1; n j,c,s ≥f ij,c,s +z ij,c,s -1; z ij,c,s -1≤n i,c,s -n j,c,s ≤1-z ij,c,s ; where n i,c,s denotes whether bus i is in the fault zone in the cth time period under scenario s, f ij,c,s denotes the fault state of branch ij in the cth time period under scenario s, n j,c,s denotes whether bus j is in the fault zone in the cth time period under scenario s.

5. A variable time step based two-stage fault restoration optimization terminal for power distribution network, comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that, ​

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