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

- 61 Downloads

## 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.

## References

- Acharya N, Mithulananthan N (2007a) Influence of TCSC on congestion and spot price in electricity market with bilateral contract. Electr Power Syst Res 77:1010–1018CrossRefGoogle Scholar
- Acharya N, Mithulananthan N (2007b) Locating series FACTS devices for congestion management in deregulated electricity markets. Electr Power Syst Res 77:352–360CrossRefGoogle Scholar
- Akter S, Saha A, Das P (2012) Modelling, simulation and comparison of various FACTS devices in power system. Int J Eng Res Technol 1:1–12CrossRefGoogle Scholar
- Balamurugan K, Dharmalingam V, Muralisachithanandam R (2013a) Active power loss minimization by optimal placement of SVC devices using evolutionary programming technique. Int J Appl Eng Res 8:895–908Google Scholar
- Balamurugan K, Dharmalingam V, Muralisachithanandam R, Sankaran R (2013b) Differential evolution based optimal choice and location of FACTS devices in restructured power system. Int J Electr Electron Sci Eng 7:829–837Google Scholar
- Balamurugan K, Muralisachithanandam R, Dharmalingam V, Srikanth R (2013c) Optimal choice and location of multi-type facts devices in deregulated electricity market using evolutionary programming method. Int J Electr Electron Sci Eng 7:96–102Google Scholar
- Balamurugan K, Muralisachithanandam R, Krishnan SR (2014) Differential evolution based solution for combined economic and emission power dispatch with valve loading effect. Int J Electr Eng Inform 6:74–92CrossRefGoogle Scholar
- Balamurugan K, Muralisachithanandam R, Dharmalingam V (2016) Evolutionary programming based simulation of bilateral real power contracts by optimal placement of flexible AC transmission system devices using contingency analysis. Electr Power Compon Syst 44(7):806–819CrossRefGoogle Scholar
- Biskas PN, Bakirtzis AG (2002) Decentralised congestion management of interconnected power systems. IEEE Proc Gener Transm Distrib 149(4):432–438CrossRefGoogle Scholar
- Cai L, Erlich I, Stamtsis G, Luo Y (2004) Optimal choice and allocation of FACTS devices in deregulated electricity market using genetic algorithms. In: Bulk power system dynamics and control—VI, Italy, pp 22–27Google Scholar
- Gerbex S, Cherkaoui R, Germond AJ (2001) Optimal location of multi-type FACTS devices in a power system by means of genetic algorithms. IEEE Trans Power Syst 16:537–544CrossRefGoogle Scholar
- Habur K, O’Leary D (2018) FACTS for cost-effective and reliable transmission of electrical energy. www.worldbank.org/html/fpd/em/transmission/facts_siemens.pdf. Accessed 15 Jan 2018
- Jeevarathinam B (2006) Genetic algorithm and fuzzy logic based optimal location of FACTS devices in a power system network. Int J Emerg Electr Power Syst 5(2):1–11Google Scholar
- Kazemia A, Badrzadeh B (2004) Modeling and simulation of SVC and TCSC to study their limits on maximum loadability point. Electr Power Energy Syst 26:381–388CrossRefGoogle Scholar
- Nabavi SMH, Hajforoosh S (2010) Social welfare maximization of optimal locating and sizing of TCSC for congestion management in deregulated power markets. Int J Comput Appl 6:16–20Google Scholar
- Ramasubramanian P, Uma Prasana G, Sumathi K (2012) Optimal location of FACTS devices by evolutionary programming based OPF in deregulated power systems. Br J Math Comput Sci 2:21–30CrossRefGoogle Scholar
- Singh H, Hao S, Papalexopoulos A (1998) Transmission congestion management in competitive electricity markets. IEEE Trans Power Syst 13(2):672–680CrossRefGoogle Scholar
- Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359MathSciNetCrossRefzbMATHGoogle Scholar
- Sutha S, Kamaraj N (2008) Optimal location of multi-type facts devices for multiple contingencies using particle swarm optimization. Int J Electr Comput Energ Electron Commun Eng 2(10):2275–2281Google Scholar
- Taher SA, Besharat H (2008) Transmission congestion management by determining optimal location of FACTS devices in deregulated power systems. Am J Appl Sci 5:242–247CrossRefGoogle Scholar
- Tiwari R, Niazi KR, Gupta V (2012) Optimal location of FACTS devices for improving performance of the power systems. In: IEEE power and energy society general meeting, pp 1–8Google Scholar
- Tuan LA, Bhattacharya K, Daalder J (2005) Transmission congestion management in bilateral markets: an interruptible load auction solution. Electr Power Syst Res 74:379–389CrossRefGoogle Scholar
- Vaisakh K, Rao GVSK (2010) Linear programming based determination of optimal bilateral real power contracts in open access. Electr Power Energy Syst 32:1143–1150CrossRefGoogle Scholar
- Vijayakumar K (2011) Optimal location of FACTS devices for congestion management in deregulated power systems. Int J Comput Appl 16:29–37Google Scholar