A power distribution system fault recovery method based on switching timing actions
By optimizing the power distribution system fault recovery model based on the switching timing action method, the problem of switching operation simulation deviation in the existing technology is solved, and the fault isolation and load recovery capabilities of the power distribution network under extreme disasters are improved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- TIANJIN UNIV
- Filing Date
- 2022-12-23
- Publication Date
- 2026-07-24
AI Technical Summary
Existing research, when constructing resilient network reconfiguration models for distribution systems, typically assumes that switching operations can be completed in one step, leading to serious deviations in the simulation process and affecting the fault recovery performance of the distribution network under extreme disasters.
A fault recovery method for power distribution systems based on switching timing is proposed. By establishing fault propagation constraints, radial topology constraints, fault isolation constraints, power supply connection determination constraints, and operational constraints, the switching sequence operations in the actual fault recovery process of the power distribution network are simulated to optimize the load recovery strategy.
It improves the resilience and optimization of the distribution network under multiple fault conditions, and enhances the fault isolation and load recovery capabilities under extreme disasters.
Smart Images
Figure CN115776113B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of power system analysis, and in particular relates to a method for fault recovery of power distribution systems based on switching timing actions. Background Technology
[0002] With the increasing frequency of extreme disasters globally, building resilient distribution systems has become a crucial strategy for countries worldwide. Implementing recovery measures can enhance the rapid response and resilience of distribution systems under extreme disasters. However, when implementing distribution system recovery measures, the safe operation of the power grid must be fully considered, taking into account factors such as satisfying the distribution network's radial topology and reasonable switching sequence. Therefore, to build a resilient distribution network, it is essential to simultaneously emphasize the fault isolation process and load restoration methods after a distribution system accident under extreme disasters.
[0003] Network topology has a significant impact on the prevention and recovery processes of power distribution systems under extreme disasters. When a fault occurs, it propagates rapidly throughout the distribution network, and nodes connected to the fault lose all load. After an accident, all switches connected to the fault are typically disconnected to isolate the fault, and then the switches are gradually closed to restore the load. Therefore, proposing a power distribution system fault recovery method based on switch timing is of great importance for developing strategies for power distribution network recovery under extreme disasters. Summary of the Invention
[0004] To ensure the safe and reliable operation of the distribution network while further improving the survivability and recovery efficiency of critical loads in the distribution system, and thus to formulate a distribution network extreme disaster recovery strategy, a distribution system fault recovery method based on switch timing actions is proposed. The specific scheme includes the following steps:
[0005] Step 1: Collect initial information of the power distribution system and establish a power distribution system fault recovery model based on switch timing actions.
[0006] The power distribution system fault recovery model based on switching timing is represented as follows:
[0007]
[0008] The objective function is to minimize the active power loss load of the system during the recovery process, and its expression is as follows:
[0009]
[0010] Where C represents the set of scenes; p c ω represents the probability of a scenario. j Indicates node weight; Indicates the active power loss during the recovery process; Ω T B represents the set of time periods; B represents the set of nodes.
[0011] Step 3 solves the power distribution system fault recovery model based on switch timing action to obtain the power distribution system timing fault recovery calculation results.
[0012] Furthermore, the fault propagation constraint includes: establishing a first virtual network to determine the fault areas of the distribution network at each time period during the recovery process;
[0013] Establish fault propagation constraints:
[0014]
[0015]
[0016]
[0017]
[0018]
[0019]
[0020]
[0021]
[0022]
[0023]
[0024] in, This indicates whether the i-th side of the recovery process branch (i,j) is closed; if so, it is 1. N BUS This represents the number of distribution network nodes. (i,j) represents the distribution network branch number. i represents the distribution network node number. t represents the recovery process time period number. c represents the scenario number. This indicates whether vertex i in the first virtual network is a sink; if so, it is 1. ij,c This indicates whether a fault has occurred in branch (i,j) in scenario c; if so, it is 1. Let i represent the network flow on the i-th side of edge (i,j) in the first virtual network during time period t. This indicates whether edge (i,j) in the first virtual network during time period t is connected to the source node; if so, it is 1. N T This indicates the total number of time periods during the recovery process.
[0025] Equations (2) to (10) represent the edge capacity, source point, and sink point constraints of the first virtual network. By establishing the first virtual network, all nodes and branches connected to the fault in the distribution network during each time period of the recovery process are determined. The necessary and sufficient condition for distribution network node i to be connected to the fault is that there exists a network flow distribution in the first virtual network that makes vertex i a sink point. Equation (11) indicates that if vertex i is not a sink point in the first virtual network during the (t-1)th time period of the recovery process, then vertex i should not be a sink point in the next time period. Equation (12) indicates that if edge (i,j) is not connected to the source point in the first virtual network during the (t-1)th time period of the recovery process, then edge (i,j) should not be connected to the source point in the next time period. That is, equations (11) and (12) indicate that the fault area of the distribution network should not expand due to the recovery measures of the recovery process.
[0026] Furthermore, the radial topological constraints:
[0027]
[0028]
[0029]
[0030]
[0031]
[0032]
[0033] Where E represents the set of distribution network branches. L k,ij This indicates whether branch (i,j) in the distribution network loop k is closed; if so, it is 1. This indicates whether the branch (i,j) in the recovery process is closed; a value of 1 indicates closure. E' represents the set of branches in the distribution network augmentation network. L represents the set of distribution network loops. {E\S3} i This indicates a distribution network branch set on side i that does not have an S3 switch installed. The S3 switch includes remote control switches, circuit breakers, etc. This indicates whether the branch (i,j) is closed in the first stage of the recovery process; if so, it is 1.
[0034] Equation (13) represents the radial topology constraint of the distribution network based on the idea of disconnecting loops. The radial topology is achieved by breaking the loop formation conditions of each loop in the distribution network. Equations (14) to (16) indicate that for each branch of the distribution network, if both switches on both sides are closed, the branch is closed; otherwise, the branch is open. Equations (17) and (18) indicate that the state of the side of the branch without the S3 collection switch remains unchanged during the recovery process.
[0035] Furthermore, the fault isolation constraints are as follows:
[0036] Based on the fault propagation constraints during the recovery process, all S3 group switches connected to the fault are disconnected during the first time period to isolate the fault. During the first time period of the recovery process, if the branch containing the S3 group switch or a node on one side of that branch is connected to the fault, the switch is disconnected; if neither the branch containing the S3 group switch nor a node on one side of that branch is connected to the fault, the switch remains inactive.
[0037]
[0038]
[0039]
[0040]
[0041]
[0042]
[0043] in, This indicates whether branch (i,j) is connected to the fault during the initial recovery phase; if so, it is 1. {S3} i This indicates a distribution network branch set with an S3 switch installed on side i. This indicates whether node i is connected to the fault in the stage before the recovery phase; if so, it is 1.
[0044] Equations (19) and (20) indicate that for a distribution network branch (i,j) with an S3 combined switch installed on side i, if the branch (i,j) or node i is in a fault area after the DEG stage switch automatically operates, then the i-side of the branch (i,j) is disconnected during the first time period of the recovery process. Equations (21) and (22) indicate that for a distribution network branch (i,j) with an S3 combined switch installed on side j, if the branch (i,j) or node j is in a fault area after the DEG stage switch automatically operates, then the j-side of the branch (i,j) is disconnected during the first time period of the recovery process. For a distribution network branch (i,j) with an S3 combined switch installed on side i, equation (23) indicates that if neither the branch (i,j) nor node i is in a fault area after the DEG stage switch automatically operates, then the i-side switch of the branch (i,j) does not operate during the first time period of the recovery process. Equation (24) indicates that if neither branch (i,j) nor node j is in the fault area after the DEG stage switch automatically operates, then the switch on the j-side of branch (i,j) will not operate during the first time period of the recovery process. Wherein, {S3} i This indicates a distribution network branch set with the S3 switch installed on side i.
[0045] Furthermore, power connection determination constraints:
[0046] Establish a second virtual network to determine the connection status of nodes and power supplies;
[0047]
[0048]
[0049]
[0050]
[0051]
[0052] in, This indicates whether vertex i in the second virtual network during time period t is a sink; if so, it is 1. This indicates whether node i has a power source; if so, it is 1. N BUS This indicates the number of nodes in the distribution network. This represents the size of the network flow injected into the network by source node i in the second virtual network during time period t. Let π(i) represent the network flow on edge (i,j) in the second virtual network during time period t. Let π(i) represent the set of parent vertices of vertex i. Let δ(i) represent the set of child vertices of vertex i.
[0053] Equations (25) to (29) determine all nodes in the distribution network connected to the power source during each time period of the recovery process. The necessary and sufficient condition for node i in the distribution network to be connected to the power source is that there exists a network flow distribution in the second virtual network that makes vertex i a sink. Equation (25) indicates that if node i in the distribution network has a power source, then vertex i in the second virtual network is a sink. Equation (26) indicates that if branch (i,j) in the distribution network is closed, then the two vertices at both ends of edge (i,j) in the second virtual network are either both sinks or neither is a sink. Equation (27) constrains the injection of network flow in the second virtual network 2. If node i in the distribution network has a power source, then vertex i in the second virtual network is a source; otherwise, vertex i is not a source. Here, since the total flow of the second virtual network is at most N BUS Therefore, the maximum value of the injection amount at each source point is limited to N. BUS Equation (28) constrains the balance and absorption of network flows in the second virtual network. For each vertex in the second virtual network, the sum of the injection of the source vertex (if the vertex is a source vertex) and the inflow of the edge should be equal to the sum of the absorption of the sink vertex (if the vertex is a sink vertex) and the outflow of the edge. In the second virtual network, each sink vertex absorbs a unit network flow. Equation (29) constrains the capacity of the edges in the second virtual network. If the branch (i,j) in the distribution network is closed, then the capacity of the edge (i,j) in the second virtual network is N. BUS Otherwise, it is 0. Wherein, the total traffic of the second virtual network is at most N.BUS Therefore, the flow of each edge is at most N. BUS .
[0054] Load recovery constraints:
[0055]
[0056]
[0057]
[0058] in, This indicates the recovery status of the load of node i during the recovery phase t. If the load has been recovered, it is 1.
[0059] Equations (30) to (32) determine the recovery status of the distribution network node in each time period of the recovery process. They indicate that if node i is connected to the power source and is not in the fault area, then node i has been recovered; otherwise, node i has not been recovered.
[0060]
[0061]
[0062] Equations (33) and (34) restrict the switching action during the recovery process. For a distribution network branch (i,j), the branch (i,j) can only be closed during time period t if at least one node at both ends of the branch (i,j) has been restored during time period t-1.
[0063] Furthermore, the operational constraints are as follows:
[0064]
[0065]
[0066]
[0067]
[0068]
[0069]
[0070]
[0071]
[0072]
[0073]
[0074]
[0075]
[0076] Among them, P L,j and Q L,j These represent the active and reactive loads of node j, respectively. and These represent the active / reactive load deficit at node j, respectively. and These represent the active and reactive power flows of branch (i,j), respectively. and These represent the active and reactive power of substation node i, respectively. and These represent the active and reactive power of the distributed power source k at node i, respectively. and These represent the maximum and minimum voltage values at node j, respectively. express. This represents the voltage at node j. ij This represents the resistance of branch (i,j). ij This represents the reactance of branch (i,j). and These represent the maximum active and reactive power of the substation at node j, respectively. and Ω represents the maximum active / reactive power of the distributed power source k. DG This represents a collection of distributed power sources. i,k This indicates whether the distributed power source k is connected to node j; if so, it is 1.
[0077] Equations (35) and (36) represent the active and reactive power balance equations for nodes considering load loss, respectively. Equation (37) is the node voltage relationship constraint. Equation (38) limits the node voltage range. Equations (39) and (40) are the active and reactive capacity constraints for branches. Equations (41) and (42) are the active and reactive power output constraints for substations. Equations (43) and (44) are the active and reactive power output constraints for distributed generation. Equations (45) and (46) represent the loss of all load by nodes in the fault area of the distribution network.
[0078] Beneficial effects
[0079] Compared with the prior art, the beneficial effects of the present invention are:
[0080] Following extreme disasters, and assuming the power distribution system meets operational and topological constraints, a series of reconfiguration operations are typically performed in a specific sequence to isolate faults and restore loads. However, existing research, when constructing reconfiguration models for power distribution system resilient networks, mostly considers the two-stage process of isolation and restoration during actual load restoration. Furthermore, during restoration, switches are usually closed sequentially to gradually restore loads, while existing research generally assumes that switch closure can be completed in one step; this assumption and simulation process contain significant biases. Therefore, this invention proposes a power distribution system fault recovery method based on switch timing actions, simulating the switch sequence operations during actual power distribution network fault recovery, thereby improving the power distribution network's ability to respond to severe faults.
[0081] In summary, this invention further improves the optimality of the post-disaster recovery and reconfiguration strategy of the distribution system when multiple faults occur in the distribution network, thereby promoting the formulation of extreme disaster recovery strategies for the distribution network. Attached Figure Description
[0082] Figure 1 To verify the IEEE 123 node power distribution system diagram of this invention;
[0083] Figure 2 This refers to the state before the switching sequence of the IEEE 123 node power distribution system is activated;
[0084] Figure 3 This refers to the state after the switching sequence of the IEEE 123 node power distribution system is activated. Detailed Implementation
[0085] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific implementation examples.
[0086] The present invention provides a power distribution system fault recovery method based on switch timing action, which is described in detail below:
[0087] Step 1: Input initial information, including: given fault information, substation location information, distributed power source location information, network topology information, switch installation information, etc.; Establish a power distribution system fault recovery model based on switch timing actions, with the objective function being the minimum active power load loss during the recovery process: The objective function for the minimum active power load loss during the recovery process is expressed as follows:
[0088]
[0089] Where C represents the set of scenes. c ω represents the probability of a scenario. j This represents the node weight. This indicates the active power loss during the recovery process. Ω TB represents the set of time periods. B represents the set of nodes.
[0090] Step 2: Establish a constraint group for the power distribution system fault recovery model based on switch timing actions. The constraint group includes: fault propagation constraints, radial topology constraints, fault isolation constraints, power supply connection determination constraints, load recovery constraints, and operational constraints. The constraint group includes: fault propagation constraints:
[0091] A first virtual network is established to identify the fault areas of the distribution network at different times during the recovery process.
[0092]
[0093]
[0094]
[0095]
[0096]
[0097]
[0098]
[0099]
[0100]
[0101]
[0102]
[0103] in, This indicates whether the i-th side of the recovery process branch (i,j) is closed; if so, it is 1. N BUS This represents the number of distribution network nodes. (i,j) represents the distribution network branch number. i represents the distribution network node number. t represents the recovery process time period number. c represents the scenario number. This indicates whether vertex i in the first virtual network is a sink; if so, it is 1. ij,c This indicates whether a fault has occurred in branch (i,j) in scenario c; if so, it is 1. Let i represent the network flow on the i-th side of edge (i,j) in the first virtual network during time period t. This indicates whether edge (i,j) in the first virtual network during time period t is connected to the source node; if so, it is 1. N T This indicates the total number of time periods during the recovery process.
[0104] Equations (2) to (10) represent the edge capacity, source point, and sink point constraints of the first virtual network. By establishing the first virtual network, all nodes and branches connected to the fault in the distribution network during each time period of the recovery process are determined. The necessary and sufficient condition for distribution network node i to be connected to the fault is that there exists a network flow distribution in the first virtual network that makes vertex i a sink point. Equation (11) indicates that if vertex i is not a sink point in the first virtual network during the (t-1)th time period of the recovery process, then vertex i should not be a sink point in the next time period. Equation (12) indicates that if edge (i,j) is not connected to the source point in the first virtual network during the (t-1)th time period of the recovery process, then edge (i,j) should not be connected to the source point in the next time period. That is, equations (11) and (12) indicate that the fault area of the distribution network should not expand due to the recovery measures of the recovery process.
[0105] The radial topological constraints:
[0106]
[0107]
[0108]
[0109]
[0110]
[0111]
[0112] Where E represents the set of distribution network branches. L k,ij This indicates whether branch (i,j) in the distribution network loop k is closed; if so, it is 1. This indicates whether the branch (i,j) in the recovery process is closed; a value of 1 indicates closure. E' represents the set of branches in the distribution network augmentation network. L represents the set of distribution network loops. {E\S3} i This indicates a distribution network branch set on side i that does not have an S3 switch installed. The S3 switch includes remote control switches, circuit breakers, etc. This indicates whether the branch (i,j) is closed in the first stage of the recovery process; if so, it is 1.
[0113] Equation (13) represents the radial topology constraint of the distribution network based on the idea of disconnecting loops. The radial topology is achieved by breaking the loop formation conditions of each loop in the distribution network. Equations (14) to (16) indicate that for each branch of the distribution network, if both switches on both sides are closed, the branch is closed; otherwise, the branch is open. Equations (17) and (18) indicate that the state of the side of the branch without the S3 collection switch remains unchanged during the recovery process.
[0114] Fault isolation constraints:
[0115] Based on the fault propagation constraints during the recovery process, all S3 group switches connected to the fault are disconnected during the first time period to isolate the fault. During the first time period of the recovery process, if the branch containing the S3 group switch or a node on one side of that branch is connected to the fault, the switch is disconnected; if neither the branch containing the S3 group switch nor a node on one side of that branch is connected to the fault, the switch remains inactive.
[0116]
[0117]
[0118]
[0119]
[0120]
[0121]
[0122] in, This indicates whether branch (i,j) is connected to the fault during the initial recovery phase; if so, it is 1. {S3} i This indicates a distribution network branch set with an S3 switch installed on side i. This indicates whether node i is connected to the fault in the stage before the recovery phase; if so, it is 1.
[0123] Equations (19) and (20) indicate that for a distribution network branch (i,j) with an S3 combined switch installed on side i, if the branch (i,j) or node i is in a fault area after the DEG stage switch automatically operates, then the i-side of the branch (i,j) is disconnected during the first time period of the recovery process. Equations (21) and (22) indicate that for a distribution network branch (i,j) with an S3 combined switch installed on side j, if the branch (i,j) or node j is in a fault area after the DEG stage switch automatically operates, then the j-side of the branch (i,j) is disconnected during the first time period of the recovery process. For a distribution network branch (i,j) with an S3 combined switch installed on side i, equation (23) indicates that if neither the branch (i,j) nor node i is in a fault area after the DEG stage switch automatically operates, then the i-side switch of the branch (i,j) does not operate during the first time period of the recovery process. Equation (24) indicates that if neither branch (i,j) nor node j is in the fault area after the DEG stage switch automatically operates, then the switch on the j-side of branch (i,j) will not operate during the first time period of the recovery process. Wherein, {S3} i This indicates a distribution network branch set with the S3 switch installed on side i.
[0124] Power connection determination constraints:
[0125] Establish a second virtual network to determine the connection status of nodes and power supplies.
[0126]
[0127]
[0128]
[0129]
[0130]
[0131] in, This indicates whether vertex i is a sink in the second virtual network during time period t; if so, it is 1. This indicates whether node i has a power source; if so, it is 1. N BUS This indicates the number of nodes in the distribution network. This represents the size of the network flow injected into the network by source node i in the second virtual network during time period t. Let π(i) represent the network flow on edge (i,j) in the second virtual network during time period t. Let π(i) represent the set of parent vertices of vertex i. Let δ(i) represent the set of child vertices of vertex i.
[0132] Equations (25) to (29) determine all nodes in the distribution network connected to the power source during each time period of the recovery process. The necessary and sufficient condition for node i in the distribution network to be connected to the power source is that there exists a network flow distribution in the second virtual network that makes vertex i a sink. Equation (25) indicates that if node i in the distribution network has a power source, then vertex i in the second virtual network is a sink. Equation (26) indicates that if branch (i,j) in the distribution network is closed, then the two vertices at both ends of edge (i,j) in the second virtual network are either both sinks or neither is a sink. Equation (27) constrains the injection of network flow in the second virtual network. If node i in the distribution network has a power source, then vertex i in the second virtual network is a source; otherwise, vertex i is not a source. Here, since the total flow of the second virtual network is at most N BUS Therefore, the maximum value of the injection amount at each source point is limited to N. BUS Equation (28) constrains the balance and absorption of network flows in the second virtual network. For each vertex in the second virtual network, the sum of the injection of the source vertex (if the vertex is a source vertex) and the inflow of the edge should be equal to the sum of the absorption of the sink vertex (if the vertex is a sink vertex) and the outflow of the edge. In the second virtual network, each sink vertex absorbs a unit network flow. Equation (29) constrains the capacity of the edges in the second virtual network. If the branch (i,j) in the distribution network is closed, then the capacity of the edge (i,j) in the second virtual network is N. BUS Otherwise, it is 0. Wherein, the total traffic of the second virtual network is at most N. BUSTherefore, the flow of each edge is at most N. BUS .
[0133] Load recovery constraints:
[0134]
[0135]
[0136]
[0137] in, This indicates the recovery status of the load of node i during the recovery phase t. If the load has been recovered, it is 1.
[0138] Equations (30) to (32) determine the recovery status of the distribution network node in each time period of the recovery process. They indicate that if node i is connected to the power source and is not in the fault area, then node i has been recovered; otherwise, node i has not been recovered.
[0139]
[0140]
[0141] Equations (33) and (34) restrict the switching action during the recovery process. For a distribution network branch (i,j), the branch (i,j) can only be closed during time period t if at least one node at both ends of the branch (i,j) has been restored during time period t-1.
[0142] Operational constraints:
[0143]
[0144]
[0145]
[0146]
[0147]
[0148]
[0149]
[0150]
[0151]
[0152]
[0153]
[0154]
[0155] Among them, P L,j and Q L,j These represent the active and reactive loads of node j, respectively. and These represent the active / reactive load deficit at node j, respectively. and These represent the active and reactive power flows of branch (i,j), respectively. and These represent the active and reactive power of substation node i, respectively. and These represent the active and reactive power of the distributed power source k at node i, respectively. and These represent the maximum and minimum voltage values at node j, respectively. express. This represents the voltage at node j. ij This represents the resistance of branch (i,j). ij This represents the reactance of branch (i,j). and These represent the maximum active and reactive power of the substation at node j, respectively. and Ω represents the maximum active / reactive power of the distributed power source k. DG This represents a collection of distributed power sources. i,k This indicates whether the distributed power source k is connected to node j; if so, it is 1.
[0156] Equations (35) and (36) represent the active and reactive power balance equations for nodes considering load loss, respectively. Equation (37) is the node voltage relationship constraint. Equation (38) limits the node voltage range. Equations (39) and (40) are the active and reactive capacity constraints for branches. Equations (41) and (42) are the active and reactive power output constraints for substations. Equations (43) and (44) are the active and reactive power output constraints for distributed generation. Equations (45) and (46) represent the loss of all load by nodes in the fault area of the distribution network.
[0157] Step 3 solves the power distribution system fault recovery model based on switch timing action to obtain the power distribution system timing fault recovery calculation results.
[0158] Example:
[0159] Step 101:
[0160] Adopting such Figure 1The effectiveness and correctness of the proposed method are verified using the IEEE 123 node power distribution system shown. This is based on line fault information as shown in Table 1. In this table, CB represents a circuit breaker, RCS represents a remote control switch, FU represents a fuse, MS represents a manual switch, DG represents a distributed generation source, and SCF represents a short-circuit fault.
[0161] Table 1
[0162]
[0163] Step 2:
[0164] A power distribution system fault recovery model based on switch timing action is established with the objective function of minimizing the active power loss during the recovery process.
[0165] Step 3:
[0166] Solving the power distribution system fault recovery model based on the switching timing action yields a power distribution system timing fault recovery method. The model includes fault propagation constraints, radial topology constraints, fault isolation constraints, power supply connection determination constraints, load recovery constraints, and operation constraints.
[0167] Taking fault scenario 10 as the research object, the state of the power distribution system before the switching sequence operation is as follows: Figure 2 As shown. The state of the power distribution system after the switching sequence is as follows. Figure 3 As shown in Table 2, the timing sequence of the switching actions is as follows.
[0168] Table 2
[0169]
[0170] During the recovery process, the distribution network utilizes S3 switchgear for further fault isolation and load restoration. S3 switchgear includes remote control switches and circuit breakers. In the first time period, all S3 switchgear connected to nodes in the fault area are disconnected to isolate the fault. In the second time period, CB 64-65 and RCS 43-45 are closed to restore the loads of nodes 61, 62, 63, and 64; CB 79-81 is closed to restore the loads of nodes 78, 79, and 80. In the third time period, RCS 61-118 is closed to restore the loads of nodes 68, 98, 99, and 118. In the fourth time period, RCS 99-100 is closed to restore the loads of nodes 100, 101, and 116; RCS 98-122 is closed to restore the loads of nodes 102, 103, 104, 105, 106, 107, and 108. In the fifth time period, CB115-116 is closed to restore the load at nodes 114 and 115. After the restoration process is completed, the distribution network status is as follows: Figure 3 As shown.
Claims
1. A method for fault recovery in a power distribution system based on switch timing actions, characterized in that, The method includes the following steps: Step 1: Collect initial information of the power distribution system and establish a power distribution system fault recovery model based on switch timing. The objective function is to minimize the active power loss during the recovery process, and its expression is as follows: (1) in: C Represents a set of scenes; Represents the probability of a scenario; Indicates node weight; This indicates the amount of active power lost during the recovery process; Represents a set of time periods; B Represents a set of nodes; Step 2: Establish a constraint group for the power distribution system fault recovery model based on switch timing actions. The constraint group includes: fault propagation constraints, radial topology constraints, fault isolation constraints, power supply connection determination constraints, load recovery constraints, and operational constraints. The fault propagation constraints include: Establish a first virtual network to identify the fault areas of the distribution network at different stages of the recovery process; Establish fault propagation constraints: (2) （3） (4) (5) (6) (7) (8) (9) (10) (11) (12) in, Indicates the branch in the recovery process ( i , j )of i Whether the side is closed; if so, the value is 1. Indicates the number of nodes in the distribution network; Indicates the branch number of the distribution network; Indicates the distribution network node number Indicates the time period number of the recovery process; Indicates the scene number; Represents the vertices in the first virtual network. i Is it a sink? If so, then set it to 1. Representing a scene c Middle Branch Road ( i , j ) Whether a fault has occurred; if so, the value is 1. express t In the first virtual network of the time period, the edge ( i , j )of i Side network flow; express t In the first virtual network of the time period, the edge ( i , j Is it connected to the source node? If so, the value is 1. The total number of time periods in the recovery process is represented by equations (2) to (10); the edge capacity, source point, and sink point constraints of the first virtual network are represented by equations (2) to (10); by establishing the first virtual network, all nodes and branches connected to the fault in the distribution network during each time period of the recovery process are determined; distribution network nodes i The necessary and sufficient condition for a fault to be associated with a vertex is: in the first virtual network, there exists a vertex such that... i The network flow distribution at the sink; Equation (11) represents the flow distribution at the sink during the recovery process. t -1 time period, if the vertex in the first virtual network i If it is not the sink, then it will be the peak in the next time period. i It should not be the sink; Equation (12) indicates the first step in the recovery process. t -1 time period, if the edge in the first virtual network ( i,j If the edge is not connected to the source node, then in the next time interval... i,j ) should not be connected to the source point; that is, equations (11) and (12) indicate that the fault area of the distribution network should not be expanded due to the restoration measures during the restoration process; Step 3: Solve the power distribution system fault recovery model based on switch timing action and output the power distribution system timing fault recovery calculation results.
2. The power distribution system fault recovery method based on switch timing action according to claim 1, characterized in that, The radial topological constraints include: (13) (14) (15) (16) (17) (18) in, E Represents the set of branches in a distribution network; Indicates distribution network loop k Middle Branch Road ( i , j If the closure is closed, then the value is 1; Indicates the branch in the recovery process ( i , j If the closure is closed, then the value is 1; E` This represents the set of branches in the distribution network augmentation network; Represents the set of distribution network loops; express i Side not installed S 3. Distribution network branch collection of switchgear S 3. The combined switch includes remote control switches and circuit breakers; Indicates the branch in the early stage of the recovery process ( i , j ) Whether it is closed, if so, it is 1; Equation (13) is the radial topology constraint of the distribution network based on the idea of breaking the loop, and the radial topology is realized by destroying the loop formation condition of each loop in the distribution network; Equations (14)~(16) indicate that for each branch of the distribution network, if both of its two sides are closed, the branch is closed, otherwise the branch is open; Equations (17) and (18) indicate that the branch is not equipped with S The state on one side of the 3-channel switch remains unchanged during the recovery process.
3. The power distribution system fault recovery method based on switch timing action according to claim 1, characterized in that, The fault isolation constraint is based on the fault propagation constraint during the recovery process, which determines the distribution network branches and nodes connected to the fault. In the first time period, all fault-connected branches and nodes are disconnected. S 3. A combined switch is used to isolate the fault; during the first phase of the recovery process, if... S If the branch where the 3-channel switch is located, or a node on one side of the branch where it is located, is connected to a fault, then the switch is disconnected; if S If neither the branch where the 3-channel switch is located nor any node on one side of that branch is connected to a fault, then the switch will not operate; the fault isolation constraints include: (19) (20) (21) (22) (23) (24) in, Indicating the branch road (in the pre-recovery phase) i , j Is it connected to a fault? If so, then the value is 1. Indicate i Side-mounted S 3. Distribution network branch collection of switch; Represents nodes in the pre-recovery phase. i Whether it is connected to a fault, if so, then it is 1; Equations (19) and (20) indicate that for i Side-mounted S 3. Distribution network branch of the combined switch ( i,j If the DEG stage switch automatically activates, the branch ( i,j ) or node i If the fault is located in the fault area, then in the first time period of the recovery process, the branch ( i,j )of i The side is disconnected; equations (21) and (22) indicate that for j Side-mounted S 3. Distribution network branch of the combined switch ( i,j If the DEG stage switch automatically activates, the branch ( i,j ) or node j If the fault is located in the fault area, then in the first time period of the recovery process, the branch ( i,j )of j The side is disconnected; for i Side-mounted S 3. Distribution network branch of the combined switch ( i,j Equation (23) indicates that if the DEG stage switch automatically operates, the branch ( i,j ) and nodes i If none of them are in the fault area, then in the first time period of the recovery process, the branch ( i,j )of i The side switch does not operate; Equation (24) indicates that if the DEG stage switch operates automatically, the branch ( i,j ) and nodes j If none of them are in the fault area, then in the first time period of the recovery process, the branch ( i,j )of j The side switch does not operate; among them, express i Side-mounted S 3. Distribution network branch collection of the switch.
4. The power distribution system fault recovery method based on switch timing action according to claim 1, characterized in that, The power connection determination constraints include: (25) (26) (27) (28) (29) in, This indicates whether vertex i in the second virtual network during time period t is a sink; if so, it is 1. Indicates whether node i has a power source; if so, the value is 1. Indicates the number of nodes in the distribution network; This represents the size of the network flow injected into the network by source node i in the second virtual network during time period t; Let represent the network flow on edge (i, j) in the second virtual network during time period t; Represents the set of parent vertices of vertex i; Let i represent the set of subvertices of vertex i; equations (25) to (29) determine all nodes in the distribution network connected to the power source in each time period of the recovery process; distribution network nodes i The necessary and sufficient condition for a vertex to be connected to a power source is that, in the second virtual network, there exists a vertex such that... i The network flow distribution at the sink; Equation (25) represents the distribution of nodes in the distribution network. i If a power source exists, then the vertices in the second virtual network... i For the sink; Equation (26) indicates that if the branch in the distribution network ( i,j If the edge () is closed, then the edge () in the second virtual network is closed. i,j Both vertices are either both sinks or neither is a sink; Equation (27) constrains the injection of network flow into the second virtual network; if nodes in the distribution network i If there is power, then the vertices in the virtual network i If it is the source point, otherwise it is the vertex. i Not the source; where, since the total traffic of the second virtual network is at most... Therefore, the maximum value of the injection amount at each source point is limited to . That is, Equation (28) constrains the balance and absorption of network flow in the second virtual network; for each vertex in the second virtual network, the sum of the injection amount of the source vertex and the inflow amount of the edge should be equal to the sum of the absorption amount of the sink vertex and the outflow amount of the edge; where, the sink vertex in the second virtual network absorbs a unit network flow; Equation (29) constrains the capacity of the edge in the second virtual network; if the branch in the distribution network ( i,j If the edge () is closed, then the edge () in the second virtual network is closed. i,j The capacity is Otherwise, it is 0; where, since the total traffic of the second virtual network is at most 0. Therefore, the flow of each edge is at most 1. .
5. The power distribution system fault recovery method based on switch timing action according to claim 1, characterized in that, The load recovery constraints include: (30) (31) (32) in, Indicates recovery phase t Time period nodes i The recovery status of the load is 1 if it has been restored; Equations (30) to (32) determine the recovery status of the distribution network nodes in each time period of the recovery process, indicating that if the node i If the node is connected to the power supply and is not located in the fault area, then... i It has been restored, otherwise the node i Not recovered; (33) (34) Equations (33) and (34) restrict the switching action during the recovery process; for distribution network branches ( i , j ), only when t -1 time period branch ( i , j When at least one node at each end has been recovered, t Time-of-use branch ( i , j Only then can it be closed.
6. The power distribution system fault recovery method based on switch timing action according to claim 1, characterized in that, The operational constraints include: (35) (36) (37) 38) (39) (40) (41) (42) (43) (44) (45) (46) in, and Representing nodes respectively j Active / reactive load; and Representing nodes respectively j The amount of active / reactive load deficit; and They represent the branches ( i , j The active / reactive current flow; and Representing nodes respectively i Active / reactive power of the substation; and Representing nodes respectively i Distributed power supply k Active / reactive power; and Representing nodes respectively j Maximum / minimum voltage values; Represents a node j The voltage; Indicates branch ( i , j The resistance of ) Indicates branch ( i , j The reactance of ) and Representing nodes respectively j The maximum active / reactive power of the substation; and These represent distributed power sources. k Maximum active / reactive power; Represents a collection of distributed power sources; Distributed power sources k Connect to node j If so, then it is 1; Equations (35) and (36) are the active and reactive power balance equations of the node considering the load loss of the node, respectively; Equation (37) is the node voltage relationship constraint; Equation (38) limits the node voltage range; Equations (39) and (40) are the active and reactive capacity constraints of the branch; Equations (41) and (42) are the active and reactive output constraints of the substation; Equations (43) and (44) are the active and reactive output constraints of the distributed power source; Equations (45) and (46) indicate that the node in the fault area of the distribution network loses all the load.