# Reliability and Network Performance Enhancement by Reconfiguring Underground Distribution Systems

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## Abstract

**:**

## 1. Introductions

## 2. Proposed Reliability Indices

_{c}feeding nodes, the reliability indices for the ith radial topology, as adopted by the Chilean law, are defined by the Inter-American Committee of Regional Electricity-CIER [26] as

_{c}system load points as well as of the failure rate λ(j), repair time r(j) and the unavailability U(j) for each load point.

## 3. Problem Formulation for Proposed NR

- Power Flow Constraint$${g}_{j}\left(i\right)=0;\text{}\forall j\in {N}_{c}$$
- Node Voltage Constraint$${V}_{\mathrm{min}}\le {V}_{jn}\le {V}_{\mathrm{max}};\text{}\forall n\in N;\forall j\in {N}_{c}$$
- Feeder Current Limit Constraint$${I}_{jn}\le {I}_{j}^{\mathrm{max}};\text{}\forall n\in N,\forall j\in {N}_{c}$$
- Radial Topology Constraint$${\Phi}_{n}(i)=0;\forall n\in N$$

## 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.) |

${I}_{j}^{\mathrm{max}}$ | Maximum current of jth branch (p.u.) |

I_{jn} | Current of jth line at nth system state (p.u.) |

k_{e}(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/N_{c} | Set of system states/nodes |

r(j) | Repair time of jth feeder (hr) |

R_{j} | Line resistance of the jth line (Ω) |

T(i) | System’s average interruption unavailability index for the ith candidate topology (hr/yr) |

T_{min}/T_{max} | 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) |

V_{jn} | Voltage of jth node at nth system state (p.u.) |

Vmax,Vmin | Maximum/minimum limits of node voltage (p.u.) |

V_{s} | 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) |

Φ_{n}(i) | Closed path for ith network topology for nth state |

µ_{F}(i,n) | Overall fuzzy membership function for the ith network topology during nth system state |

µ_{DV}^{MIN}(b) | Minimum fuzzy membership function of µ_{DV}(b,n) for the base topology |

µ_{DV}^{MIN}(o) | Minimum fuzzy membership function of µ_{DV}(o,n) for the optimal topology |

µ_{F}(b,n)/µ_{T}(b,n)/µ _{ENS}(b,n)/µ_{EL}(b,n)/µ_{DV}(b,n) | Fuzzy membership function of reliability and power quality indices for the base topology during nth system state |

µ_{F}(i,n)/µ_{T}(i,n)/µ _{ENS}(i,n)/µ_{EL}(i,n)/µ _{DV}(i,n) | Fuzzy membership function for F(i,n)/T(i,n)/ENS(i,n)/EL(i,n)/DV(i,n) |

µ_{F}(o,n)/µ_{T}(o,n)/µ _{ENS}(o,n)/µ_{EL}(o,n)/µ_{DV}(o,n) | Fuzzy membership function of reliability and power quality indices for the optimal topology during nth system state |

µ_{F}^{M}(b)/µ_{T}^{M}(b)/µ _{ENS}^{M}(b)/µ_{EL}^{M}(b) | Mean fuzzy membership function of µ_{F}(b,n)/µ_{T}(b,n)/µ_{ENS}(b,n)/µ_{EL}(b,n) for the base topology |

µ_{F}^{M}(o)/µ_{T}^{M}(o)/µ _{ENS}^{M}(o)/µ_{EL}^{M}(o) | Mean fuzzy membership function of µ_{F}(o,n)/µ_{T}(o,n)/µ_{ENS}(o,n)/µ_{EL}(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 |

**Table 2.**Comparison of existing and proposed reliability indices without distributed resources (DRs) before network reconfiguration (NR).

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 |

F_{max} (Failure/yr) | T_{max} (h/yr) | ENS _{max} (USD/yr) | EL _{max} (USD) | DV_{max} (p.u.) |
---|---|---|---|---|

5 | 3 | 800 | 70 | 0.10 |

µ_{F}^{M}(b) | µ_{T}^{M}(b) | µ_{ENS}^{M}(b) | µ_{EL}^{M}(b) | µ_{DV}^{MIN}(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 |

µ_{F}^{M}(o) | µ_{T}^{M}(o) | µ_{ENS}^{M}(o) | µ_{EL}^{M}(o) | µ_{DV}^{MIN}(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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## Share and Cite

**MDPI and ACS Style**

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

**AMA Style**

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 Style**

Agrawal, 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