Reliability and Network Performance Enhancement by Reconfiguring Underground Distribution Systems
Abstract
:1. Introductions
2. Proposed Reliability Indices
3. Problem Formulation for Proposed NR
- Power Flow Constraint
- Node Voltage Constraint
- Feeder Current Limit Constraint
- Radial Topology Constraint
4. Handling Uncertainty in Load Demand and Renewable Power Generation
5. Simulation Results
6. Discussion
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
D(i) | System’s average duration interruption index for the ith candidate topology (hr/failure) |
DV(i,n) | Node voltage deviations for ith network topology during nth system state (p.u.) |
DVmin/DVmax | Minimum and maximum value of node voltage deviation index (p.u.) |
EL(i,n) | Energy losses for the ith network topology during nth system state (MWh) |
ELmin/ELmax | Minimum and maximum value of feeder energy loss index (MWh) |
ENS(i) | Energy not supplied for the ith candidate topology (MWh/yr) |
ENSmin/ENSmax | Minimum and maximum value of energy not supplied index (MWh/yr) |
F(i) | System’s average interruption frequency index for the ith candidate topology (failure/yr) |
F(i,n)/T(i,n)/ENS(i,n)/D(i,n) | F/T/ENS/D for ith topology at nth system state |
Fmin/Fmax | Minimum and maximum value of System average interruption frequency index (failure/yr) |
I(b,j,nom) | Current in the jth distribution feeder in base configuration during nominal load conditions (p.u.) |
I(i,j,n) | Current in the jth feeder for ith network topology during nth system state (p.u.) |
Maximum current of jth branch (p.u.) | |
Ijn | Current of jth line at nth system state (p.u.) |
ke(n) | Energy price prevailed at nth system state ($/kWh) |
KVA(j) | Apparent load demand of jth node (kVA) |
KVA(j,n) | Apparent load demand of jth node at nth system state (kVA) |
KW(j) | Active load demand on the jth distribution feeder (kW) |
KW(j,n) | Active load demand at jth system node for nth system state (kW) |
LD(n) | Load duration for the nth system state (hr) |
N/Nc | Set of system states/nodes |
r(j) | Repair time of jth feeder (hr) |
Rj | Line resistance of the jth line (Ω) |
T(i) | System’s average interruption unavailability index for the ith candidate topology (hr/yr) |
Tmin/Tmax | Minimum and maximum value of System average interruption unavailability index (hr/yr) |
U(j) | Unavailability index of jth feeder (failure) |
U(i,j,n) | U(j) for ith topology at nth system state (failure) |
Vjn | Voltage of jth node at nth system state (p.u.) |
Vmax,Vmin | Maximum/minimum limits of node voltage (p.u.) |
Vs | Absolute value of the source voltage (p.u.) |
ζ(i,j,n) | Failure rate in the jth distribution feeder for ith network topology at nth system state (failure/yr) |
λ(j) | Failure rate of jth feeder (failure/yr) |
Φn(i) | Closed path for ith network topology for nth state |
µF(i,n) | Overall fuzzy membership function for the ith network topology during nth system state |
µDVMIN(b) | Minimum fuzzy membership function of µDV(b,n) for the base topology |
µDVMIN(o) | Minimum fuzzy membership function of µDV(o,n) for the optimal topology |
µF(b,n)/µT(b,n)/ µENS(b,n)/µEL(b,n)/µDV(b,n) | Fuzzy membership function of reliability and power quality indices for the base topology during nth system state |
µF(i,n)/µT(i,n)/ µENS(i,n)/µEL(i,n)/ µDV(i,n) | Fuzzy membership function for F(i,n)/T(i,n)/ENS(i,n)/EL(i,n)/DV(i,n) |
µF(o,n)/µT(o,n)/ µENS(o,n)/µEL(o,n)/µDV(o,n) | Fuzzy membership function of reliability and power quality indices for the optimal topology during nth system state |
µFM(b)/µTM(b)/ µENSM(b)/µELM(b) | Mean fuzzy membership function of µF(b,n)/µT(b,n)/µENS(b,n)/µEL(b,n) for the base topology |
µFM(o)/µTM(o)/ µENSM(o)/µELM(o) | Mean fuzzy membership function of µF(o,n)/µT(o,n)/µENS(o,n)/µEL(o,n) for the optimal topology |
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Particular | Value |
---|---|
Line voltage (kV) | 12.66 |
Nominal active power demand (kW) | 3715 |
Nominal reactive power demand (kVAr) | 2300 |
Sectionalizing switches | 1–32 |
Tie-switches | 33–37 |
Base configuration with open lines | 33 to 37 |
Power loss (kW) | 202.5 |
Minimum node voltage (pu) | 0.9131 |
Reliability Index | F (Failure/yr) | T (hr/yr) | ENS (MWh/yr) | ||
---|---|---|---|---|---|
Load level | 1 | F(i) | 3.18 | 1.86 | 437.67 |
F(i,n) | 3.18 | 1.86 | 437.67 | ||
%ΔF | 0 | 0 | 0 | ||
1.1 | T(i) | 3.18 | 1.86 | 481.43 | |
T(i,n) | 3.91 | 2.29 | 591.41 | ||
%ΔT | 22.97 | 22.89 | 22.84 | ||
0.9 | ENS(i) | 3.18 | 1.86 | 393.9 | |
ENS(i,n) | 2.53 | 1.49 | 314.41 | ||
%ΔENS | –20.26 | –20.20 | –20.18 |
SPV (Size in kWp/Site) | WT (Size in kWp/Site) | MT (Size in kW/Site) | SC (Size in kVAr/Site) |
---|---|---|---|
280/14, 840/24, 560/30 | 420/14, 700/24, 420/30 | 800/24 | 300/12, 300/25, 600/30 |
State | Load/Generation Factor | State | Load/Generation Factor | ||||
---|---|---|---|---|---|---|---|
Load | WT | SPV | Load | WT | SPV | ||
1 | 0.5421 | 0.556 | 0 | 13 | 0.8711 | 0.896 | 0.967 |
2 | 0.5421 | 0.507 | 0 | 14 | 0.8000 | 0.894 | 0.921 |
3 | 0.5421 | 0.484 | 0 | 15 | 0.8711 | 0.799 | 0.820 |
4 | 0.5421 | 0.454 | 0 | 16 | 0.8711 | 0.688 | 0.625 |
5 | 0.5421 | 0.45 | 0 | 17 | 0.8711 | 0.704 | 0.398 |
6 | 0.6132 | 0.49 | 0 | 18 | 0.8711 | 0.728 | 0.158 |
7 | 0.6829 | 0.397 | 0.008 | 19 | 0.9303 | 0.763 | 0 |
8 | 0.6829 | 0.435 | 0.203 | 20 | 1.0000 | 0.784 | 0 |
9 | 0.6829 | 0.587 | 0.453 | 21 | 1.0000 | 0.806 | 0 |
10 | 0.7421 | 0.698 | 0.563 | 22 | 0.7513 | 0.823 | 0 |
11 | 0.7421 | 0.748 | 0.794 | 23 | 0.5421 | 0.88 | 0 |
12 | 0.7421 | 0.796 | 0.934 | 24 | 0.5421 | 0.911 | 0 |
00AM-6AM | 6AM-5PM | 5PM-9PM | 9PM-00AM |
---|---|---|---|
0.02 | 0.06 | 0.12 | 0.09 |
Fmax (Failure/yr) | Tmax (h/yr) | ENS max (USD/yr) | EL max (USD) | DVmax (p.u.) |
---|---|---|---|---|
5 | 3 | 800 | 70 | 0.10 |
µFM(b) | µTM(b) | µENSM(b) | µELM(b) | µDVMIN(b) |
---|---|---|---|---|
0.8882 | 0.8660 | 0.8891 | 0.9743 | 0.5598 |
F(b) (failure/yr) | T(b) (hr/yr) | ENS(b) (USD/yr) | EL(b) (USD/yr) | DV(b) (p.u.) |
0.5590 | 0.4021 | 88.7287 | 15757.7700 | 0.0440 |
State | Optimal Configuration | State | Optimal Configuration |
---|---|---|---|
1 | 33-37-35-13-36 | 13 | 20-37-35-13-8 |
2 | 33-37-35-13-36 | 14 | 20-37-33-10-34 |
3 | 33-37-35-13-36 | 15 | 33-37-35-9-34 |
4 | 33-37-35-13-36 | 16 | 33-37-35-11-34 |
5 | 33-37-35-13-36 | 17 | 33-37-35-12-36 |
6 | 33-37-35-13-36 | 18 | 33-37-35-12-36 |
7 | 33-37-35-14-36 | 19 | 33-37-35-14-36 |
8 | 33-37-35-13-36 | 20 | 33-37-35-14-36 |
9 | 33-37-35-13-36 | 21 | 33-37-35-14-36 |
10 | 20-37-11-34-36 | 22 | 33-37-35-12-36 |
11 | 20-37-8-12-36 | 23 | 20-37-35-34-36 |
12 | 20-37-8-12-36 | 24 | 20-37-35-34-36 |
µFM(o) | µTM(o) | µENSM(o) | µELM(o) | µDVMIN(o) |
---|---|---|---|---|
0.8967 | 0.8732 | 0.8954 | 0.9812 | 0.5699 |
F(o) (failure/yr) | T(o) (hr/yr) | ENS(o) (USD/yr) | EL(o) (USD/yr) | DV(o) (p.u.) |
0.5167 | 0.3804 | 83.6887 | 13122.48 | 0.0316 |
F(%) | T(%) | ENS (%) | EL(%) | DV(%) |
7.57 | 5.40 | 5.68 | 16.72 | 28.18 |
Scenario | Network Topology | F (Failure/yr) | T (h/yr) | ENS (USD/yr) | EL (USD/yr) | DV (p.u.) |
---|---|---|---|---|---|---|
Distribution system without DR | Before NR | 1.7123 | 1.0055 | 229.0578 | 70722.99 | 0.0869 |
After NR | 1.5300 | 0.9123 | 207.92 | 66282.78 | 0.0803 | |
Distribution system with DR | Before NR | 0.5590 | 0.4021 | 88.7287 | 15757.77 | 0.0440 |
After NR | 0.5167 | 0.3804 | 83.6887 | 13122.48 | 0.0316 |
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Agrawal, P.; Kanwar, N.; Gupta, N.; Niazi, K.R.; Swarnkar, A.; Meena, N.K.; Yang, J. Reliability and Network Performance Enhancement by Reconfiguring Underground Distribution Systems. Energies 2020, 13, 4719. https://doi.org/10.3390/en13184719
Agrawal P, Kanwar N, Gupta N, Niazi KR, Swarnkar A, Meena NK, Yang J. Reliability and Network Performance Enhancement by Reconfiguring Underground Distribution Systems. Energies. 2020; 13(18):4719. https://doi.org/10.3390/en13184719
Chicago/Turabian StyleAgrawal, Praveen, Neeraj Kanwar, Nikhil Gupta, Khaleequr Rehman Niazi, Anil Swarnkar, Nand K. Meena, and Jin Yang. 2020. "Reliability and Network Performance Enhancement by Reconfiguring Underground Distribution Systems" Energies 13, no. 18: 4719. https://doi.org/10.3390/en13184719
APA StyleAgrawal, P., Kanwar, N., Gupta, N., Niazi, K. R., Swarnkar, A., Meena, N. K., & Yang, J. (2020). Reliability and Network Performance Enhancement by Reconfiguring Underground Distribution Systems. Energies, 13(18), 4719. https://doi.org/10.3390/en13184719