# Differential Evolution algorithm for contingency analysis-based optimal location of FACTS controllers in deregulated electricity market

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## Abstract

In this paper, a novel heuristic optimization algorithm called differential evolution (DE) technique has been proposed to solve the optimal location of FACTS devices in deregulated electricity market using contingency analysis. The proposed approach deals with the optimal injection of real and reactive power using FACTS devices with an aim to minimize the total system cost, the total number of overloads, excess power flow, the severity of overload and real power loss of the network. To enhance the search behavior of the DE approach, the scaling factor and crossover parameters are empirically selected. To show the superiority of the proposed DE approach and as a step ahead to prove its novelty, the same optimization problem is solved using evolutionary programming method, and the results are compared. The results indicate the proposed DE algorithm is superior in terms of final solution quality, efficiency, convergence rate and robustness. A sample four-bus system and 24-bus EHV southern region of Indian grid system has been considered to illustrate the proposed methodology.

## Keywords

Contingency analysis Deregulated electricity market Differential evolution FACTS Optimal placement## List of symbols

- \(Q_{i}\)
Reactive power injection at \({i}{\mathrm{th} }\) bus

- \(C_{1} (P_{\mathrm{G}})\)
Total generation cost

- \(C_{2 }(f) \)
Average investment cost of FACTS devices

- \(P_{dj}^{gi} \)
Power contract of the customer at bus

*j*from the supplier at bus*i*- \(F_{i} (P_{\mathrm{G}i})\)
Fuel cost for the \({i}{\mathrm{th} }\) generator

- \(C_{\mathrm{TCSC}}\)
Cost function of TCSC device in $/kVAR

- \(C_{\mathrm{SVC}}\)
Cost function of SVC device in $/kVAR

*S*Operating range in MVAR

- \(P_{\mathrm{G}i}\)
Power output of the \({i}{\mathrm{th} }\) generator

- \(\eta _{i}\)
Uniformly distributed random number between [0,1]

- \(P_{ij, \hbox {cont} }\)
Power flow through line “

*j*” during \({i}{\mathrm{th} }\) contingency- \(P_{ij, \hbox {base} }\)
Base case power flow through line “

*j*”- \(P_{i }\)
Probability of occurrence of \({i}{\mathrm{th} }\) contingency

*m*Number of contingencies

- \(U_{ij}\)
Elements of participation matrix

- \(W_{ij }\)
Elements of ratio matrix

*n*Number of lines

- Ng
Number of generators

- \(\hbox {nb}\)
Number of bus

- \(P_{k}\)
Real power flow in the \({k}{\mathrm{th}}\) line

- \(P_{k\,\mathrm{max}}\)
Thermal limit of the \({k}{\mathrm{th}}\) line

## Notes

### Compliance with ethical standards

### Conflict of interest

Authors declare that they have no conflict of interest.

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