Service Restoration Strategy for Distribution Networks Considering Multi-Source Collaboration and Incomplete Fault Information
Abstract
1. Introduction
2. Mathematic Formulation of the Proposed Strategy
2.1. Framework of the Proposed Strategy
2.2. Upper-Layer Model
2.2.1. Master Problem of the Upper-Layer Model
2.2.2. Subproblem of the Upper-Layer Model
2.2.3. Dual Model of the Upper-Layer Model
2.3. Lower-Layer Model
2.3.1. Scheduling Model of MDGs
2.3.2. Scheduling Model of WTs and PVs
2.3.3. Scheduling Model of ESSs
2.3.4. Radiality Constraints [19]
2.3.5. Operation Constraints of the Distribution Networks
3. Results and Discussion
3.1. Simulation Parameters
3.2. Result Analysis
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Sets and Indexes | |
Set of positive real numbers for the scenario probability distribution. | |
Feasible domain of subproblem of the upper-layer model, including Equation (11). | |
Set of distribution network buses. | |
Set of charging station buses. | |
Set of depots. | |
Set of ESSs. | |
Set of fault areas. | |
Set of generators. | |
Set of potential fault locations. | |
Set of distribution network lines. | |
Set of MDGs. | |
Set of PVs. | |
Set of fault scenarios. | |
Set of substation buses. | |
Set of time steps. | |
Feasible domain of master problem of the upper-layer model, including Equations (2)–(10). | |
Set of WTs. | |
Parameters | |
Maximum number of connections for charging station bus i. | |
Number of RCs in depot d. | |
Capacity of ESS i. | |
Initial state-of-charge level of ESS i. | |
Minimum and maximum state-of-charge levels of ESS i, respectively. | |
Square of the rated current of the line. | |
A large parameter. | |
Minimum and maximum active charging power of ESS i, respectively. | |
Minimum and maximum active discharging power of ESS i, respectively. | |
Minimum and maximum active power of the generator at bus i, respectively. | |
Predicted power of the new energy source at bus i at time t. | |
Upper limit of the active power output of MDG m. | |
Ramp rate upper and lower limits of the generator at bus i, respectively. | |
Actual power of the new energy source at bus i. | |
Rated active and reactive power transmitted by the line, respectively. | |
Minimum and maximum reactive charging power of ESS i, respectively. | |
Minimum and maximum reactive discharging power of ESS i, respectively. | |
Minimum and maximum reactive power of the generator at bus i, respectively. | |
Reactive power demand of bus i at time t. | |
Upper limit of the reactive power output of MDG m. | |
Resistance line ij. | |
Time for RC to inspect potential fault location k to check for a fault. | |
Time required for RC to repair potential fault location k. | |
Travel time of RC between potential fault locations k′ and k. | |
Travel time of an MDG between charging station buses i and j. | |
Square of the lower and upper limits of the bus voltage, respectively. | |
Weight of buses. | |
Reactance of line ij. | |
A positive number approaching zero. | |
Maximum values of the first-order norm and infinite norm of the scenario probability deviation, respectively. | |
Robustness parameter of new energy source. | |
Maximum prediction error of the new energy output. | |
Charging and discharging loss coefficients of ESS i, respectively. | |
Time duration of one step. | |
Variables | |
Binary variable indicating whether potential fault location k belongs to scenario s, where 1 means it belongs to scenario s and 0 otherwise. | |
Remaining energy of ESS i at time t. | |
Binary variable, where 1 indicates that a RC travels from a potential fault location k′ to k, and 0 otherwise. | |
Square of the current transmitted by line ij at time t. | |
Probability of scenario s. | |
Charging and discharging power of ESS i, respectively. | |
Active and reactive power of the generator at bus i at time t, respectively. | |
Active power demand of bus i at time t. | |
Active power output of MDG m at charging station bus i at time t. | |
Active power of the PVs at bus i at time t. | |
Active power of the WTs at bus i at time t | |
Active and reactive power transmitted by the line, respectively. | |
Charging and discharging reactive power of ESS i, respectively. | |
Reactive power output of MDG m at charging station bus i at time t. | |
Time for an RC to arrive at potential fault location k in scenario s. | |
Robust fault repair time of the upper-layer model. | |
Repair completion time for potential fault location k in scenario s, which is an integer variable. | |
Binary variable for the energized status of bus i at time step t, where 1 indicates the bus is energized and 0 otherwise. | |
Square of the bus voltage. | |
Binary variable indicating charging and discharging status of ESS i, respectively, where 1 indicates that ESS i is in a charging or discharging state. | |
Binary variable for the energized status of line ij at time t, where 1 means it is energized and 0 otherwise. | |
Binary variable indicating whether bus i is the parent bus of bus j at time t, where 1 means bus i is the parent bus of bus j, and 0 otherwise. | |
Binary variable indicating whether MDG m is connected to charging station bus i at time t. | |
Repair completion time of all faults under scenario s. | |
Auxiliary variable introduced for the linearized absolute value calculation. | |
Dual variables. |
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[8] | [10] | [19] | [23] | [25] | [26] | [27] | [28] | This Work | |
---|---|---|---|---|---|---|---|---|---|
RC | √ | √ | √ | √ | × | × | × | √ | √ |
ESS | × | √ | √ | × | √ | √ | √ | √ | √ |
MDG | √ | × | × | × | × | × | × | √ | √ |
Incomplete Fault Information | × | × | × | × | × | × | × | × | √ |
Uncertainty of fault scenario | √ | × | √ | × | × | × | × | × | √ |
Robust optimization | × | × | √ | × | × | × | √ | × | √ |
Type | Bus No. | Maximum and Minimum Power Outputs | Other Parameters |
---|---|---|---|
Substation and DG | 0/4/29 | = 2000/1000/800 kW = 0/0/0 kW = 1500/600/600 kVar = −(1500/600/600) kVar | = 350/100/100) kW/15 min = −(350/100/100) kW/15 min |
MDG | / | = 200/100 kW = 150/100 kVar | / |
Bus No. | Parameters | |
---|---|---|
11/23 | = 200/300 kW = 200/300 kW = 100/200 kVar = 100/200 kVar = 600/900 kWh | = 0.1/0.1 = 0.9/0.9 = 0.5/0.5 = 0.9/0.95 = 0.9/0.95 |
Priority | Bus No. | Weight |
---|---|---|
Priority 1 | 2, 4, 12, 16, 20, 22, 24, 28 | 100 |
Priority 2 | 0, 3, 8–10, 13–15, 17, 18, 21, 23, 26, 30, 32 | 10 |
Priority 3 | 1, 5–7, 11, 19, 25, 27, 29, 31 | 1 |
= 0.2 | = 0.4 | = 0.6 | = 0.8 | = 1 | |
---|---|---|---|---|---|
μ = 0.1 | 8.718 | 8.718 | 8.759 | 8.792 | 8.806 |
μ = 0.2 | 8.718 | 8.759 | 8.803 | 8.947 | 8.997 |
μ = 0.4 | 8.759 | 8.947 | 9.013 | 9.087 | 9.196 |
μ = 0.6 | 8.803 | 9.013 | 9.150 | 9.231 | 9.342 |
μ = 0.8 | 8.947 | 9.087 | 9.231 | 9.342 | 9.359 |
μ = 1 | 8.997 | 9.196 | 9.342 | 9.359 | 9.457 |
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Wang, X.; Xie, C.; Xia, L.; Li, J.; Wang, H.; Sun, L. Service Restoration Strategy for Distribution Networks Considering Multi-Source Collaboration and Incomplete Fault Information. Processes 2025, 13, 3075. https://doi.org/10.3390/pr13103075
Wang X, Xie C, Xia L, Li J, Wang H, Sun L. Service Restoration Strategy for Distribution Networks Considering Multi-Source Collaboration and Incomplete Fault Information. Processes. 2025; 13(10):3075. https://doi.org/10.3390/pr13103075
Chicago/Turabian StyleWang, Xunting, Cheng Xie, Lingzhi Xia, Jianlin Li, Han Wang, and Lei Sun. 2025. "Service Restoration Strategy for Distribution Networks Considering Multi-Source Collaboration and Incomplete Fault Information" Processes 13, no. 10: 3075. https://doi.org/10.3390/pr13103075
APA StyleWang, X., Xie, C., Xia, L., Li, J., Wang, H., & Sun, L. (2025). Service Restoration Strategy for Distribution Networks Considering Multi-Source Collaboration and Incomplete Fault Information. Processes, 13(10), 3075. https://doi.org/10.3390/pr13103075