Power system fault prediction method based on fault location, line patrol and FISR model
By using fault location, line patrol and service recovery (FISR) models in power systems to coordinate RCS and MS operations, the problem of low fault isolation and recovery efficiency in the prior art is solved, and more efficient resource utilization and recovery capabilities are achieved .
Patent Information
- Application Number
- CN202410915139.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-07-09
- Publication Date
- 2024-12-13
AI Technical Summary
It is difficult for existing power systems to effectively coordinate fault location, fault isolation and service recovery in extreme events, resulting in slow resource waste and recovery speed and lack of flexibility.
The fault location, line patrol and service recovery (FISR) model is adopted to minimize the total system cost and failure duration, comprehensively consider fault location, isolation and recovery, and use the coordination of RCS and MS to optimize resource scheduling and patrol paths.
It enhances the recovery capability and flexibility of the distribution system, reduces system costs, improves the efficiency of fault isolation and recovery, and adapts to flexible strategies under different extreme events.
Smart Images
Figure CN119129168A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of power system fault prediction, and in particular relates to a power system fault prediction method based on a fault location, line patrol and service restoration (FISR) model. Background Art
[0002] In recent years, large-scale power outages caused by extreme events have attracted widespread attention from all walks of life. Climate change has led to an increase in the frequency and intensity of extreme natural disasters, and the resulting large-scale power outages have also increased. Power outages have led to huge economic losses and consumer dissatisfaction. A large number of restoration tasks will compete for limited personnel and facilities. In order to enhance the resilience of the distribution system, multiple resources should be fully coordinated, the coupling relationship between fault location, fault isolation and service restoration should be considered, and flexible strategies should be formulated for different situations faced by the distribution system.
[0003] In existing research, fault location, fault isolation, and service restoration are usually handled independently. Therefore, the coordination between fault location, fault isolation, and service restoration cannot be considered, and it is impossible to fully utilize and coordinate multiple resources, and to form flexible strategies for different situations under extreme events. This is not conducive to enhancing the resilience of the distribution system.
[0004] In addition, although a wide range of methods have been developed for fault location, fault isolation, and service recovery, these methods still have some shortcomings when forming a comprehensive recovery strategy for resilience, such as handling fault location, fault isolation, and service recovery separately, resulting in a lack of coordination between the various links. It is difficult to form an optimal comprehensive recovery strategy because the mutual influence between fault location and isolation and service recovery is not comprehensively considered. For example, after fault location, the fault isolation solution may affect the subsequent service recovery process, resulting in a waste of resources and time extension; some extreme weather may cause large-scale power grid failures. If the coordination and optimization between different links are not comprehensively considered, it is difficult to form a targeted recovery strategy, which in turn affects the overall recovery speed and quality. Summary of the invention
[0005] In order to cope with large-scale power outages in distribution systems under extreme conditions, the present invention provides a power system fault prediction method based on a fault location, line patrol and service restoration (FISR) model, which comprehensively considers and coordinates fault location, fault isolation and fault restoration to enhance the recovery capability of the distribution system.
[0006] The technical solution adopted by the present invention is:
[0007] The power system fault prediction method based on fault location, line patrol and FISR model includes the following steps:
[0008] Step 1: Taking the minimum total system cost as the objective function, establish a fault location model to determine the optimal SFI location and the area where the fault may occur;
[0009] Step 2: Based on the possible fault areas determined in step 1, with minimizing the duration of the line patrol process as the objective function and with the line patrol status and crew movement as constraints, a line patrol model is constructed to obtain the optimal patrol plan;
[0010] Step 3: Based on the fault location model established in step 1 and the line patrol model established in step 2, the objective function of minimizing the weighted value of load reduction power during the fault duration is established by considering the coordination between the remote control switch RCS and the manual switch MS;
[0011] Step 4: Considering the system operation constraints, crew scheduling constraints and related coupling constraints, combined with the objective function established in step 3, a fault isolation and service restoration (FISR) model is established to determine the RCS operation plan and MS operation plan;
[0012] Step 5: In the MATLAB environment, use the commercial solver GUROBI to solve the fault location model and obtain the possible fault area;
[0013] Next, solve the line patrol model to obtain the optimal patrol plan to patrol the fault area determined in step 1;
[0014] Then, the fault isolation and service restoration (FISR) model is solved to obtain the RCS operation plan, MS operation plan and unit scheduling plan to restore the patrolled areas that may fail in step 2;
[0015] Finally, the line patrol model and the fault isolation and service restoration (FISR) model are repeatedly solved until all areas where faults may occur have been patrolled.
[0016] In step 1, the objective function is to minimize the total system cost, as shown below:
[0017] Min(C tz +C m +C in )(1);
[0018] In formula (1): C tz is the investment cost; C m is the maintenance cost; C in expected disruption costs;
[0019] 1) Investment cost C tz As shown below:
[0020]
[0021] In formula (2): N k is the line set; N z is the set of SFI positions in the line; is a binary variable indicating whether the SFI is installed at position z in feeder k, if yes, it is 1, otherwise it is 0; is a binary variable indicating whether the RCS is installed at position z in feeder k, if yes, it is 1, otherwise it is 0; is a binary variable indicating whether the MS is installed at position z in feeder k. If yes, it is 1, otherwise it is 0. represents the investment cost of SFI at position z in feeder k; represents the investment cost of RCS at position z in feeder k; represents the investment cost of the MS at position z in feeder k; k represents the feeder; z represents the position.
[0022] 2) Maintenance cost C m As shown below:
[0023]
[0024] In formula (3): represents the maintenance cost of the SFI at position z on feeder k; represents the maintenance cost of the RCS at position z on feeder k; N represents the maintenance cost of the MS at position z on feeder k; y is a set of years; AN is the annual discount rate; y represents the year.
[0025] 3) Expected disruption cost C in As shown below:
[0026]
[0027] In formula (4), N is the node set; N g is the set of possible fault locations; C y,k,i,g is the interruption cost at node i due to the g-segment fault and the feeder k fault in year y; y,k,i The failure rate of segments g and k in year y; Av y,k,g is the average customer load of node i and feeder k in year y; SH y,k,i,g (Y) represents the duration of customer outage; Y represents a set of years; i represents a node.
[0028] In step 1, the constraints of the fault location model include:
[0029]
[0030] In formula (5): Fk,g,ij is a binary variable indicating whether line ij is involved in a fault at position g in the fault zone at feeder k; SL k,g,ij is the number of SFIs between fault location g and section ij in feeder k;
[0031] is a binary variable indicating whether the RCS is installed at position z in feeder k.
[0032] a small auxiliary constant; Large auxiliary constant; g represents the fault location;
[0033] Indicates that the fault location g is upstream of line ij; Indicates that the fault location g is downstream of line ij; Indicates that the fault location g is at line ij.
[0034] In step 1, the optimal position of SFI is Figure 1 At lines (1-2), (2-3), (6-26), (8-9), (27-28), (30-31), (32-33), (14-15) and (16-17).
[0035] Areas where failures may occur, such as Figure 1 The area within the green dashed box.
[0036] In step 2, the objective function of the line patrol model is as follows:
[0037]
[0038] In formula (6): Φ t is a binary variable, indicating whether all routes are patrolled at time t, if yes, it is 0, otherwise it is 1; T Time collection; t represents time.
[0039] The constraints of the line patrol model include:
[0040] 1) The line patrol status constraints are as follows:
[0041] The constraints representing the initial patrol state of the line are as follows:
[0042] π ij,t =0 (7);
[0043] In formula (7): ij,t is a binary variable, which is 1 if the line ij has been patrolled at time t, otherwise it is 0; x The collection of routes that need to be patrolled; T XL,ij The time required to patrol route ij.
[0044] 2) If a route needs to be patrolled, it must be patrolled within a given time period T. The constraint is as follows:
[0045]
[0046] In formula (8): T is the time step set;
[0047] 3) If a line is patrolled, its patrol state will always be patrolled. The constraint is as follows:
[0048]
[0049] In formula (9): ij,t+1 is a binary variable, which is 1 if the route ij has been patrolled at time t+1, and 0 otherwise.
[0050] 4) The starting position and starting time of occupant b are as follows:
[0051] μ b,m,t =1,m=L C,b ,t=T P,b (10);
[0052] In formula (10): μ b,m,t is a binary variable, which is 1 if passenger b arrives at position m at t to patrol the line, otherwise it is 0; L C,b is the starting position of passenger b; O CY Assemble for patrol crew; T P,b The starting time for dispatching crew member b; m represents the position; t represents the time.
[0053] 5) The index transfer function from position to line is as follows;
[0054] ψ(m)=(i,j) (11);
[0055] In formula (11): ψ(m) is the index transfer function from position to line;
[0056] 6) The constraints that limit the movement of workers in different locations are as follows:
[0057]
[0058] In formula (12): T mn is the patrol time between positions m and n; T XL,ψ(m) is the patrol time from position m to line ψ(m); μ b,n,τ is a binary variable, which is 1 if passenger b arrives at position n at time τ to patrol the line, otherwise it is 0;XW patrol route location set; D is a large number, which is 99999 in the present invention; μ b,m,t is a binary variable, which is 1 if passenger b arrives at position m for line patrol at time τ, otherwise it is 0; τ represents time.
[0059] 7) The constraints restricting workers’ movement between warehouses and lines are as follows:
[0060]
[0061] In formula (13): CK A collection of warehouse locations.
[0062] 8) The coupling constraints are as follows:
[0063]
[0064] In formula (14): T XL,ψ(m)-1 represents the patrol time required from position m to line ψ(m)-1; is a binary variable, which is 1 if line ψ(m) is patrolled and 0 otherwise; is a binary variable, which is 1 if line ψ(m)-1 is patrolled and 0 otherwise.
[0065] 9) The constraints for determining whether all routes are patrolled are as follows:
[0066]
[0067] In formula (15): μ t is a binary variable, which is 1 if not all the routes that need to be patrolled have been patrolled at t, otherwise it is 0.
[0068] In step 2, the optimal patrol plan is: Figure 3 Indicated by the red dotted line.
[0069] In step 3, the coordination between the RCS and the MS is considered, and an objective function is established to minimize the weighted value of the load reduction power within the fault duration.
[0070] The objective function of the FISR model is as follows:
[0071]
[0072] In formula (16): is the active load reduction of bus i; ω i is the weight coefficient. B The busbar set.
[0073] The objective function of minimizing the weighted value of load reduction power during the fault duration is formula (16).
[0074] In step 4, system operation constraints, crew scheduling constraints and related coupling constraints are considered, including:
[0075] (1): Distribution system operation constraints:
[0076] ①. Initialize the initial network topology of the distribution system:
[0077]
[0078] In formula (17): is a binary variable, which is 1 if the end i of line ij is closed at time t, and 0 otherwise; is a binary variable, which is 1 if the end j of line ij is closed at time t, and 0 otherwise; is a binary variable, which is 1 if the end i of line ij starts to close, otherwise it is 0.
[0079] ②. When both ends of the line are closed and there is no fault on the line, the line is closed, which is indicated as follows:
[0080]
[0081] In formula (18): e ij,t is a binary variable, indicating whether the line is closed, 1 if closed, and 0 otherwise; ij,t is a binary variable, which is 1 if the line ij is closed, and 0 otherwise; σ ij It is a binary variable, which is 1 if the line is normal, and 0 otherwise.
[0082] Linearize equation (18):
[0083]
[0084] In formula (19): H ij,t is an auxiliary variable.
[0085] ③. The radial topology constraints are as follows:
[0086]
[0087] In formula (20): P L,i is the active load demand of bus i; Q L,i is the reactive load demand of bus i; P D,i,t is the active power output of the distributed generation at bus i; Q D,i,t is the reactive power output of the distributed generation at bus i; P C,i,t is the active load reduction at bus i; QC,i,t is the reactive load reduction at bus i; P F,hi,t is the active power flow of line hi; Q F,hi,t is the reactive power flow of line hi; P F,ij,t is the active power flow of line ij; Q F,ij,t is the reactive power flow of line ij. parent is the parent line set of busbar i; O child is the sub-bus set of bus i; h represents a node; j represents a node.
[0088] ④. The power flow equation based on the linearized flow splitting model is as follows:
[0089] -D(1-e ij,t )≤U i,t -U j,t -(r ij P F,ij,t +x ij Q F,ij,t ) / U R ≤D(1-e ij,t ) (twenty one); In formula (21): U i,t is the voltage amplitude of bus i; U j,t is the voltage amplitude of bus j; r ij is the resistance of line ij; x ij is the reactance of line ij; U R is the reference voltage.
[0090] ⑤. Line capacity constraints are as follows:
[0091]
[0092] In formula (22): is the capacity limit of line ij;
[0093] ⑥. The voltage amplitude constraints are as follows:
[0094]
[0095] In formula (23): is the minimum voltage amplitude of bus i; is the maximum voltage amplitude of busbar i; U i,t Indicates the bus voltage.
[0096] ⑦. The power output limit constraints are as follows:
[0097]
[0098] In formula (24): i,tis a binary variable, which is 1 if bus i is in the fault area, otherwise it is 0; is the minimum active power output of the distributed generation at bus i; is the maximum active power output of the distributed generation at bus i; is the minimum reactive power output of the distributed generation at bus i; is the maximum reactive power output of the distributed generation at bus i; P D,i,t is the active power output of the distributed generation at bus i; Q D,i,t is the reactive power output of distributed generation at bus i.
[0099] ⑧. The constraints for all loads in the fault area to be cut off are as follows:
[0100]
[0101] In formula (25): P C,i,t is the active load reduction at bus i; Q C,i,t is the reactive load reduction at bus i; P L,i is the active load demand of bus i; Q L,i is the reactive load demand of bus i.
[0102] ⑨. The constraints indicating whether the bus is in the fault area are as follows:
[0103]
[0104] In formula (26): j,t is a binary variable, which is 1 if bus j is in the fault area, otherwise it is 0;
[0105] ⑩. At t <T MS When , the constraint indicating that the line end switch cannot operate is as follows:
[0106]
[0107] In formula (27): is a binary variable, which is 1 if the line ij terminal i is equipped with a remote control switch, otherwise it is 0; is a binary variable, which is 1 if the line ij terminal j is equipped with a remote control switch, otherwise it is 0; is a binary variable, which is 1 if the line ij terminal i is equipped with a manual switch, otherwise it is 0; is a binary variable, which is 1 if the line ij terminal j is equipped with a manual switch, otherwise it is 0; is a binary variable, which is 1 if the end i of line ij is closed at time t+1, and 0 otherwise; is a binary variable, which is 1 if the end j of line ij is closed at time t+1, and 0 otherwise; is a binary variable. If the end i of line ij starts to close at time t+1, it is 1, otherwise it is 0. t represents time; T MS is the average time required for MS operation.
[0108] (2): Manual switch operation crew scheduling constraints:
[0109]
[0110] In formula (28): b,m,t is a binary variable, which is 1 if passenger b operates the manual switch at position m at t, otherwise 0; SD Operate the manual switch to assemble the crew; AZ It is the installation position collection of the manual switch; b,n,τ is a binary variable, which is 1 if the occupant b operates the manual switch at position n at τ, otherwise it is 0; T P,b Indicates the start time when crew member b can be dispatched.
[0111] (3): Coupling constraints:
[0112] a: The formula describing the relationship between position and manual switch is as follows:
[0113] (i,l)=θ(m) (30);
[0114] In formula (30), θ(m) is the index transfer function from position to manual switch; (i,l)(i,l)
[0115] The above formula indicates that position m corresponds to the manual switch at end i of line l.
[0116] b: The coupling constraints are as follows
[0117]
[0118] In formula (31): ms (m) is a binary variable, which is 1 if a manual switch is provided at position m, otherwise it is 0; is a binary variable. If at t+T MS If the moment position m is closed, it is 1, otherwise it is 0; is a binary variable. If at t+T MS -1 If position m is closed at the moment, it is 1, otherwise it is 0; b Maintenance crew; Ω CM Indicates maintenance crew muster.
[0119] Linearize equation (31) into the following two formulas:
[0120]
[0121] Where: is an auxiliary integer variable; is an auxiliary binary variable; is an auxiliary integer variable; is an auxiliary binary variable; is a binary variable, which is 1 if the end i of line ij is closed at time t-1, and 0 otherwise; ms θ(m) is a binary variable, which is 1 if there is a manual switch at position θ(m), and 0 otherwise.
[0122] In step 4, the minimum weighted value of load reduction power within the fault duration of formula (16) is used as the objective function, and formulas (17)-(33) are used as constraints to establish a fault isolation and service restoration (FISR) model.
[0123] RCS operation plan: Turn on RCS on lines (2-3)(7-8)(12-13).
[0124] MS operation plan: Turn on the MS on lines (3-4)(5-6)(29-30)(31-32)(14-15)(16-17).
[0125] In step 5, the fault location model obtains possible fault areas: Figure 5 Shown in the green dashed box.
[0126] The present invention provides a method for predicting power system faults based on a fault location, line patrol and service restoration (FISR) model, and the technical effects are as follows:
[0127] 1) The present invention takes minimizing the total system cost as the objective function and establishes a fault location model, which can reduce the system cost and SFI deployment cost;
[0128] 2) The present invention comprehensively considers and coordinates fault location, fault isolation and fault recovery under extreme events, which helps to enhance the recovery capability of the power distribution system.
[0129] 3) The present invention comprehensively considers MS operation and RCS operation as well as the coordination between them, which helps to speed up the process of fault isolation and fault recovery.
[0130] 4) The present invention can cope with different situations under extreme events, utilize and coordinate multiple resources, form flexible strategies, and enhance the resilience of the distribution system. BRIEF DESCRIPTION OF THE DRAWINGS
[0131] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:
[0132] Figure 1 This is a 33-node power distribution network diagram.
[0133] Figure 2 The figure is a flow chart of the fault prediction method for intelligent power system.
[0134] Figure 3 This is the fault location diagram.
[0135] Figure 4 This is the best patrol plan diagram.
[0136] Figure 5 This is a fault isolation and recovery diagram.
[0137] Figure 6 It is a comparison diagram between the method of the present invention and the traditional method. DETAILED DESCRIPTION
[0138] A power system fault prediction method based on the fault location, line patrol and service restoration (FISR) model, firstly, with the minimization of the total system cost as the objective function, a fault location model is established to determine the optimal SFI location and fault area; secondly, with the minimization of the duration of the line patrol process as the objective function, the line patrol state and the crew movement are used as constraints to construct a line patrol model to obtain the optimal patrol plan; then, considering the coordination of RCS and MS, an objective function with the minimum weighted value of load reduction power within the fault duration is established; then, considering the system operation constraints, crew scheduling constraints and related coupling constraints, combined with the objective function, the FISR model is established to determine the RCS operation plan, MS operation plan and unit scheduling plan; finally, in the MATALB environment, the commercial solver GUROBI is used to solve, and the line patrol model and FISR model are repeatedly solved until all possible fault areas are patrolled. Taking a 33-node distribution system as an example, the present invention compares and analyzes the proportion of restored loads by the traditional method and the method of the present invention. According to the empirical results in the embodiments of the present invention, the method proposed by the present invention has a significant improvement in reducing system costs and can also enhance the flexibility of the distribution system.
[0139] Example:
[0140] by Figure 1 Take the 33-node power distribution system shown in the figure as an example. The power distribution system includes 1 main power supply, 5 remote switches, 2 distributed power supplies, and 37 lines. Two controllable distributed power supplies are installed on busbars 10 and 18, respectively, with a capacity of 0.5MVA, a voltage amplitude between [0.95, 1.05] pu, a line capacity limit of 5MVA, and various line parameters as shown in Table 1. The reference voltage in the network is 23KV, and the system reference capacity is 100MVA. The steps of the comprehensive method of the present invention are as follows: Figure 2 shown.
[0141] Table 1 Line parameters
[0142]
[0143]
[0144] like Figure 3 As shown, assuming that lines (4-5), (15-16), (30-31), and (32-33) are faulty, the fault location model can determine that SFI should be installed on lines (1-2), (2-3), (6-26), (8-9), (27-28), (30-31), (32-33), (14-15), and (16-17). The direction of the fault current can be obtained from the SFI indication, and the possible fault area can be determined based on the opposite direction of the fault current in a certain area. Then, through the line patrol model, personnel are dispatched as soon as possible to determine the fault status of the uncertain line and determine the optimal personnel dispatch plan. Figure 4 The optimal patrol route for the crew is shown in the figure.
[0145] Solution 1: After a fault occurs, implement fault isolation and fault recovery in advance, and immediately implement fault isolation and fault recovery based on RCSs, such as Figure 5 As shown, the RCS on lines (2-3) (7-8) (12-13) are turned on to isolate the fault area. If the distributed generation on bus 10 cannot provide all these loads, the RCS on line (12-25) will be turned off to help restore service between lines (8-12). Option 2: After the fault occurs, all lines have been patrolled and staff operate MSs on lines (3-4) (5-6) (29-30) (31-32) (14-15) (16-17). If the fault on line (4-5) is isolated, the RCSs on lines (2-3) (7-8) (27-28) can be operated immediately to restore service to the bus isolated from the fault area.
[0146] like Figure 6 As shown, by comparing the integrated approach based on the utilization of various resources with the traditional approach, it is obvious that under extreme events, the full coordination and utilization of multiple resources such as SFIs, MSs, RCSs and crews are the key to achieving rapid fault location, fault isolation and service restoration, thereby enhancing the resilience of the distribution system.
Claims
1. A power system fault prediction method based on fault location, line patrol and FISR model, characterized by The following steps are involved: Step 1: Taking the minimum total system cost as the objective function, establish a fault location model to determine the optimal SFI location and the area where the fault may occur; Step 2: Based on the possible fault areas determined in step 1, with minimizing the duration of the line patrol process as the objective function and with the line patrol status and crew movement as constraints, a line patrol model is constructed to obtain the optimal patrol plan; Step 3: Based on the fault location model established in step 1 and the line patrol model established in step 2, the objective function of minimizing the weighted value of load reduction power during the fault duration is established by considering the coordination between the remote control switch RCS and the manual switch MS; Step 4: Considering the system operation constraints, crew scheduling constraints and related coupling constraints, combined with the objective function established in step 3, a fault isolation and service restoration (FISR) model is established to determine the RCS operation plan and MS operation plan.
2. The method for predicting power system faults based on fault location, line patrol and FISR model according to claim 1 is characterized in that: Also includes step 5: In the MATLAB environment, the commercial solver GUROBI is used to solve the fault location model and obtain the possible fault area; Next, solve the line patrol model to obtain the optimal patrol plan and patrol the fault area determined in step 1; Then, the fault isolation and service restoration (FISR) model is solved to obtain the RCS operation plan, MS operation plan and unit scheduling plan to restore the patrolled areas that may fail in step 2; Finally, the line patrol model and the fault isolation and service restoration (FISR) model are repeatedly solved until all areas where faults may occur have been patrolled.
3. The power system fault prediction method based on fault location, line patrol and FISR model according to claim 1 is characterized by: In step 1, the objective function is to minimize the total system cost, as shown below: Min(C tz +C m +C in )(1); In formula (1): C tz is the investment cost; C m is the maintenance cost; C in expected disruption costs; 1) Investment cost C tz As shown below: In formula (2): N k is the line set; N z is the set of SFI positions in the line; is a binary variable indicating whether the SFI is installed at position z in feeder k, if yes, it is 1, otherwise it is 0; is a binary variable indicating whether the RCS is installed at position z in feeder k, if yes, it is 1, otherwise it is 0; is a binary variable indicating whether the MS is installed at position z in feeder k, if yes, it is 1, otherwise it is 0; represents the investment cost of SFI at position z in feeder k; represents the investment cost of RCS at position z in feeder k; represents the investment cost of the MS at position z in feeder k; k represents the feeder; z represents the position; 2) Maintenance cost C m As shown below: In formula (3): represents the maintenance cost of the SFI at position z on feeder k; represents the maintenance cost of the RCS at position z on feeder k; N represents the maintenance cost of the MS at position z on feeder k; y is a set of years; AN is the annual discount rate; y represents the year; 3) Expected disruption cost C in As shown below: In formula (4), N is the node set; N g is the set of possible fault locations; C y,k,i,g is the interruption cost at node i due to the g-segment fault and the feeder k fault in year y; y,k,i The failure rate of segments g and k in year y; Av y,k,g is the average customer load of node i and feeder k in year y; SH y,k,i,g (Y) represents the duration of customer outage; Y represents a set of years; i represents a node.
4. The method for predicting power system faults based on fault location, line patrol and FISR model according to claim 3 is characterized by: In step 1, the constraints of the fault location model include: In formula (5): F k,g,ij is a binary variable indicating whether line ij is involved in a fault at position g in the fault zone at feeder k; SL k,g,ij is the number of SFIs between fault location g and section ij in feeder k; is a binary variable indicating whether the RCS is installed at position z in feeder k; a is a small auxiliary constant; Large auxiliary constant; g represents the fault location; Indicates that the fault location g is upstream of line ij; Indicates that the fault location g is downstream of line ij; Indicates that the fault location g is at line ij.
5. The method for predicting power system faults based on fault location, line patrol and FISR model according to claim 1 is characterized in that: In step 2, the objective function of the line patrol model is as follows: In formula (6): Φ t is a binary variable, indicating whether all routes are patrolled at time t, if yes, it is 0, otherwise it is 1; T Time collection; t represents time.
6. The method for predicting power system faults based on fault location, line patrol and FISR model according to claim 5 is characterized by: The constraints of the line patrol model include: 1) The line patrol status constraints are as follows: The constraints representing the initial patrol state of the line are as follows: π ij,t ＝0 (7)； In formula (7): ij,t is a binary variable, which is 1 if the line ij has been patrolled at time t, otherwise it is 0; x The collection of routes that need to be patrolled; T XL,ij The time required to patrol route ij; 2) If a route needs to be patrolled, it must be patrolled within a given time period T. The constraint is as follows: In formula (8): T is the time step set; 3) If a line is patrolled, its patrol state will always be patrolled. The constraint is as follows: In formula (9): ij,t+1 is a binary variable, which is 1 if the line ij has been patrolled at time t+1, otherwise it is 0; 4) The starting position and starting time of occupant b are as follows: μ b,m,t =1,m=L C,b ,t=T P,b (10); In formula (10): μ b,m,t is a binary variable, which is 1 if passenger b arrives at position m at t to patrol the line, otherwise it is 0; L C,b is the starting position of passenger b; O CY Assemble for patrol crew; T P,b The starting time of dispatching crew member b; m represents the position; t represents the time; 5) The index transfer function from position to line is as follows; ψ(m)=(i,j) (11); In formula (11): ψ(m) is the index transfer function from position to line; 6) The constraints that limit the movement of workers in different locations are as follows: In formula (12): T mn is the patrol time between positions m and n; T XL,ψ(m) is the patrol time from position m to line ψ(m); μ b,n,τ is a binary variable, which is 1 if passenger b arrives at position n at time τ to patrol the line, otherwise it is 0; XW The patrol route location set; D is a large number; μ b,m,t is a binary variable, which is 1 if passenger b arrives at position m for line patrol at time τ, otherwise it is 0; τ represents time; 7) The constraints restricting workers’ movement between warehouses and lines are as follows: In formula (13): CK The warehouse location collection; 8) The coupling constraints are as follows: In formula (14): T XL,ψ(m)-1 represents the patrol time required from position m to line ψ(m)-1; is a binary variable, which is 1 if line ψ(m) is patrolled and 0 otherwise; is a binary variable, which is 1 if line ψ(m)-1 is patrolled and 0 otherwise; 9) The constraints for determining whether all routes are patrolled are as follows: In formula (15): μ t is a binary variable, which is 1 if not all the routes that need to be patrolled have been patrolled at t, otherwise it is 0.
7. The method for predicting power system faults based on fault location, line patrol and FISR model according to claim 1 is characterized by: In step 3, considering the coordination between RCS and MS, an objective function is established to minimize the weighted value of load reduction power within the fault duration; The objective function is as follows: In formula (16): is the active load reduction of bus i; ω i is the weight coefficient; O B The busbar set.
8. The method for predicting power system faults based on fault location, line patrol and FISR model according to claim 7 is characterized by: In step 4, system operation constraints, crew scheduling constraints and related coupling constraints are considered, including: (1): Distribution system operation constraints: ①. Initialize the initial network topology of the distribution system: In formula (17): is a binary variable, which is 1 if the end i of line ij is closed at time t, and 0 otherwise; is a binary variable, which is 1 if the end j of line ij is closed at time t, and 0 otherwise; is a binary variable, which is 1 if the end i of line ij starts to close, otherwise it is 0; ②. When both ends of the line are closed and there is no fault on the line, the line is closed, which is indicated as follows: In formula (18): e ij,t is a binary variable, indicating whether the line is closed, 1 if closed, and 0 otherwise; ij,t is a binary variable, which is 1 if the line ij is closed, and 0 otherwise; σ ij It is a binary variable, which is 1 if the line is normal, and 0 otherwise. Linearize equation (18): In formula (19): H ij,t is an auxiliary variable; ③. The radial topology constraints are as follows: In formula (20): P L,i is the active load demand of bus i; Q L,i is the reactive load demand of bus i; P D,i,t is the active power output of the distributed generation at bus i; Q D,i,t is the reactive power output of the distributed generation at bus i; P C,i,t is the active load reduction at bus i; Q C,i,t is the reactive load reduction at bus i; P F,hi,t is the active power flow of line hi; Q F,hi,t is the reactive power flow of line hi; P F,ij,t is the active power flow of line ij; Q F,ij,t is the reactive power flow of line ij; parent is the parent line set of busbar i; O child is the sub-bus set of bus i; h represents a node; j represents a node; ④. The power flow equation based on the linearized flow splitting model is as follows: -D(1-e ij,t )≤U i,t -U j,t -(r ij P F,ij,t +x ij Q F,ij,t ) / U R ≤D(1-e ij,t ) (21); In formula (21): U i,t is the voltage amplitude of busbar i; U j,t is the voltage amplitude of bus j; r ij is the resistance of line ij; x ij is the reactance of line ij; U R is the reference voltage; ⑤. Line capacity constraints are as follows: In formula (22): is the capacity limit of line ij; ⑥. The voltage amplitude constraints are as follows: In formula (23): is the minimum voltage amplitude of bus i; is the maximum voltage amplitude of busbar i; U i,t Indicates bus voltage; ⑦. The power output limit constraints are as follows: In formula (24): i,t is a binary variable, which is 1 if bus i is in the fault area, otherwise it is 0; is the minimum active power output of the distributed generation at bus i; is the maximum active power output of the distributed generation at bus i; is the minimum reactive power output of the distributed generation at bus i; is the maximum reactive power output of the distributed generation at bus i; P D,i,t is the active power output of the distributed generation at bus i; Q D,i,t is the reactive power output of distributed generation at bus i; ⑧. The constraints for all loads in the fault area to be cut off are as follows: In formula (25): P C,i,t is the active load reduction at bus i; Q C,i,t is the reactive load reduction at bus i; P L,i is the active load demand of bus i; Q L,i is the reactive load demand of bus i; ⑨. The constraints indicating whether the bus is in the fault area are as follows: In formula (26): j,t is a binary variable, which is 1 if bus j is in the fault area, otherwise it is 0; ⑩. At t <T MS When , the constraint indicating that the line end switch cannot operate is as follows: In formula (27): is a binary variable, which is 1 if the line ij terminal i is equipped with a remote control switch, otherwise it is 0; is a binary variable, which is 1 if the line ij terminal j is equipped with a remote control switch, otherwise it is 0; is a binary variable, which is 1 if the line ij terminal i is equipped with a manual switch, otherwise it is 0; is a binary variable, which is 1 if the line ij terminal j is equipped with a manual switch, otherwise it is 0; is a binary variable, which is 1 if the end i of line ij is closed at time t+1, and 0 otherwise; is a binary variable, which is 1 if the end j of line ij is closed at time t+1, and 0 otherwise; is a binary variable. If the end i of line ij starts to close at time t+1, it is 1, otherwise it is 0. t represents time; T MS is the average time required for MS operation; (2): Manual switch operation crew scheduling constraints: In formula (28): b,m,t is a binary variable, which is 1 if passenger b operates the manual switch at position m at t, otherwise 0; SD Operate the manual switch to assemble the crew; AZ It is the installation position collection of manual switch; b,n,τ is a binary variable, which is 1 if the occupant b operates the manual switch at position n at τ, otherwise it is 0; T P,b Indicates the start time when crew member b can be dispatched; (3): Coupling constraints: a: The formula describing the relationship between position and manual switch is as follows: (i,l)=θ(m) (30); In formula (30), θ(m) is the index transfer function from position to manual switch; (i,l)(i,l) The above formula indicates that position m corresponds to the manual switch at end i of line l; b: The coupling constraints are as follows In formula (31): ms (m) is a binary variable, which is 1 if a manual switch is provided at position m, otherwise it is 0; is a binary variable. If at t+T MS If the moment position m is closed, it is 1, otherwise it is 0; is a binary variable. If at t+T MS -1 If position m is closed at the moment, it is 1, otherwise it is 0; b Maintenance crew; Ω CM Indicates the maintenance crew muster; Linearize equation (31) into the following two formulas: Where: is an auxiliary integer variable; is an auxiliary binary variable; is an auxiliary integer variable; is an auxiliary binary variable; is a binary variable, which is 1 if the end i of line ij is closed at time t-1, otherwise it is 0; ms θ(m) is a binary variable, which is 1 if there is a manual switch at position θ(m), and 0 otherwise.
9. The method for predicting power system faults based on fault location, line patrol and FISR model according to claim 8, characterized in that: Taking the minimum weighted value of load reduction power within the fault duration of formula (16) as the objective function and formulas (17) to (33) as the constraints, the fault isolation and service recovery FISR model is established.