# Solution of the Optimal Power Flow Problem Considering FACTS Devices by Using Lightning Search Algorithm

- 47 Downloads

## Abstract

In this study, the optimal power flow (OPF) problem including flexible AC transmission systems (FACTS) devices, ever increasing in the planning and operating of the modern power systems has been addressed. The thyristor-controlled series capacitor and the thyristor-controlled phase shifter are used as FACTS devices. The solution to this problem is proposed by using a new heuristic algorithm known as the lightning search algorithm (LSA) based on the phenomenon of lighting. The LSA method is generalized from the mechanism of step leader propagation. The performance, success and robustness in the solution of this problem of the LSA are evaluated and tested on IEEE test systems, which are the modified IEEE 30-bus and IEEE 57-bus test systems. The multi-objective functions are used in the solution analysis processes of this problem. These objective functions are defined as the minimization of the fuel cost, minimization of the emission and minimization of the active power loss of the test system. The numerical results of the LSA are compared to different methods presented in the recent literature, which are ant lion optimizer, grey wolf optimizer, dragonfly algorithm, moth-flame optimization. The outcomes obtained from simulation study indicate the potential of the LSA method in solving the OPF problem including FACTS devices for operating and planning of the modern power systems.

## Keywords

Lightning search algorithm Optimal power flow FACTS devices Power systems Optimization## List of Symbols

*δ*_{i},*δ*_{j}Angles of the

*i*th and*j*th buses*V*_{i},*V*_{j}Voltage magnitudes of the

*i*th and*j*th buses*P*_{ij},*Q*_{ij}Active and reactive power flows between the

*i*th and*j*th buses*R*_{ij},*X*_{ij}Resistance and reactance of transmission line between the

*i*th and*j*th buses*X*_{new}Reactance of transmission line with TCSC integrated in between the

*i*th and*j*th buses*f*Objective function of the problem

*g*Equality limitations of the problem

*h*Inequality limitations of the problem

*h*_{l},*h*_{u}Represented minimum and maximum limits of the inequality constraints

*P*_{slack}The active power value of generator in the slack bus

*V*_{L}The voltage magnitude values of all the load buses of the test system

*Q*_{G}The reactive power of the generating units of the test system

- NL
The total number of the all load buses of the test system

- NG
The total number of the generating units of the test system

- NTL
The total number of transmission lines of the test system

*P*_{G}The active power output values of the generating units excluding at the slack bus in test system

*V*_{G}The terminal voltage values of the generating units

*Q*_{C}Shunt VAR compensator

*T*The transformer tap ratio

- TCSC
The operating range value of TCSC device

*Φ*Phase shift angle of the TCPS

- NC
The number of shunt VAR compensator

- NT
The number of tap regulating transformers

*N*The total number of TCSC devices installed in the test systems

- NTCPS
The total number of TCPS devices in the test systems

*P*_{Li},*Q*_{Li}Demand active and reactive power in the

*i*th load bus*P*_{Gi},*Q*_{Gi}Active and reactive power of the

*i*th generating unit*P*_{is},*Q*_{is}Injected active and reactive power of TCPS at

*i*th bus- NB
The number of all buses in the test system

*Y*_{ij}Admittance value of the transmission line connected between

*i*th and*j*th buses*θ*_{ij}Admittance angle of the transmission line connected between

*i*th and*j*th buses*v*_{p}The current velocities of the projectile

*v*_{0}The initial velocities of the projectile

*c*The speed of light

*F*_{i}The constant ionization rate

*m*The mass of the projectile

*s*The length of the path traveled

## References

- Abido MA (2002) Optimal power flow using tabu search algorithm. Electr Power Compon Syst 30:469–483CrossRefGoogle Scholar
- Babu AVN, Suresh CV, Sivanagaraju S, Rama Mohana Rao M (2014) A two initialization based particle swarm optimization algorithm for optimal power flow solution with TCSC. In: 2014 international conference on smart electric grid (ISEG), 19–20 Sept 2014Google Scholar
- Banu RN, Devaraj D (2008) Genetic algorithm approach for optimal power flow with FACTS devices. In: 4th international IEEE conference intelligent systems, 6–8 Sept 2008Google Scholar
- Basu M (2011) Multi-objective optimal power flow with FACTS devices. Energy Convers Manag 52:903–910CrossRefGoogle Scholar
- Bhattacharyya B, Gupta VK, Kumar S (2014) UPFC with series and shunt FACTS controllers for the economic operation of a power system. Ain Shams Eng J 5(3):775–787CrossRefGoogle Scholar
- Bouchekara HREH (2014) Optimal power flow using black-hole-based optimization approach. Appl Soft Comput 24:879–888CrossRefGoogle Scholar
- Bouchekara HREH, Chaib AE, Abido MA, El-Sehiemy RA (2016) Optimal power flow using an improved colliding bodies optimization algorithm. Appl Soft Comput 42:119–131CrossRefGoogle Scholar
- Cai LJ, Erlich I, Stamtsis G (2004) Optimal choice and allocation of FACTS devices in deregulated electricity market using genetic algorithms. In: IEEE PES power systems conference and exposition, 10–13 Oct 2004Google Scholar
- Chaib AE, Bouchekara HREH, Mehasni R, Abido MA (2016) Optimal power flow with emission and non-smooth cost functions using backtracking search optimization algorithm. Int J Electr Power Energy Syst 81:64–77CrossRefGoogle Scholar
- Daryani N, Hagh MT, Teimourzadeh S (2016) Adaptive group search optimization algorithm for multi-objective optimal power flow problem. Appl Soft Comput 38:1012–1024CrossRefGoogle Scholar
- Dubey HM, Pandit M, Panigrahi BK (2016) Ant lion optimization for short-term wind integrated hydrothermal power generation scheduling. Int J Electr Power Energy Syst 83:158–174CrossRefGoogle Scholar
- Duman S (2016) Symbiotic organisms search algorithm for optimal power flow problem based on valve-point effect and prohibited zones. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2265-0 CrossRefGoogle Scholar
- Edward JB, Rajasekar N, Sathiyasekar K, Senthilnathan N, Sarjila R (2013) An enhanced bacterial foraging algorithm approach for optimal power flow problem including FACTS devices considering system loadability. ISA Trans 52:622–628CrossRefGoogle Scholar
- Elmitwally A, Eladl A (2016) Planning of multi-type FACTS devices in restructured power systems with wind generation. Int J Electr Power Energy Syst 77:33–42CrossRefGoogle Scholar
- Huneault M, Galina FD (1991) A survey of the optimal power flow literature. IEEE Trans Power Syst 6(2):762–770CrossRefGoogle Scholar
- IEEE 30-bus test system data http://www.ee.washington.edu/research/pstca/pf30/pg_tca30bus.htm
- IEEE 57-bus test system data https://www2.ee.washington.edu/research/pstca/pf57/ieee57cdf.txt
- Kılıç U (2015) Backtracking search algorithm based optimal power flow with valve point effect and prohibited zones. Electr Eng 97:101–110CrossRefGoogle Scholar
- Mahdad B, Srairi K (2014) Multi objective large power system planning under sever loading condition using learning DE-APSO-PS strategy. Energy Convers Manag 87:338–350CrossRefGoogle Scholar
- Mahdad B, Srairi K (2016) Security constrained optimal power flow solution using new adaptive partitioning flower pollination algorithm. Appl Soft Comput 46:501–522CrossRefGoogle Scholar
- Mahdad B, Srairi K, Bouktir T (2010) Optimal power flow for large-scale power system with shunt FACTS using efficient parallel GA. Int J Electr Power Energy Syst 32:507–517CrossRefGoogle Scholar
- Mirjalili S (2015a) The ant lion optimizer. Adv Eng Softw 83:80–98CrossRefGoogle Scholar
- Mirjalili S (2015b) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl Based Syst 89:228–249CrossRefGoogle Scholar
- Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27:1053–1073CrossRefGoogle Scholar
- Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61CrossRefGoogle Scholar
- Mohamed A-AA, Mohamed YS, El-Gaafary AAM, Hemeida AM (2017) Optimal power flow using moth swarm algorithm. Electr Power Syst Res 142:190–206CrossRefGoogle Scholar
- Monticelli A, Liu WHE (1992) Adaptive movement penalty method for the newton optimal power flow. IEEE Trans Power Syst 7(1):334–342CrossRefGoogle Scholar
- Mukherjee A, Mukherjee V (2015) Solution of optimal power flow using chaotic krill herd algorithm. Chaos, Solitons Fractals 78:10–21MathSciNetCrossRefGoogle Scholar
- Mukherjee A, Mukherjee V (2016) Solution of optimal power flow with FACTS devices using a novel oppositional krill herd algorithm. Int J Electr Power Energy Syst 78:700–714CrossRefGoogle Scholar
- Niknam T, Narimani MR, Abarghooee RA (2012) A new hybrid algorithm for optimal power flow considering prohibited zones and valve point effect. Energy Convers Manag 58:197–206CrossRefGoogle Scholar
- Ongsakul W, Bhasaputra P (2002) Optimal power flow with FACTS devices by hybrid TS/SA approach. Int J Electr Power Energy Syst 24:851–857CrossRefGoogle Scholar
- Prasad D, Mukherjee V (2016) A novel symbiotic organisms search algorithm for optimal power flow of power system with FACTS devices. Eng Sci Technol Int J 19:79–89CrossRefGoogle Scholar
- Reddy SS, Rathnam CS (2016) Optimal power flow using glowworm swarm optimization. Int J Electr Power Energy Syst 80:128–139CrossRefGoogle Scholar
- Shareef H, Ibrahim AA, Mutlag AH (2015) Lightning search algorithm. Appl Soft Comput 36:315–333CrossRefGoogle Scholar
- Singh RP, Mukherjee V, Ghoshal SP (2015) Particle swarm optimization with an aging leader and challengers algorithm for optimal power flow problem with FACTS devices. Int J Electr Power Energy Syst 64:1185–1196CrossRefGoogle Scholar
- Sonmez Y, Guvenc U, Duman S, Yorukeren N (2012) Optimal power flow incorporating FACTS devices using gravitational search algorithm. In: 2012 international symposium on innovations in intelligent systems and applications (INISTA), Trabzon, TURKEY, 2–4 July 2012Google Scholar
- Yan X, Quantana VH (1999) Improving an interior point based OPF by dynamic adjustments of step sizes and tolerances. IEEE Trans Power Syst 14(2):709–717CrossRefGoogle Scholar
- Zhang S, Irving MR (1994) Enhanced Newton–Raphson algorithm for normal, controlled and optimal power flow solutions using column exchange techniques. IEE Proc Gener Transm Distrib 141(6):647–657CrossRefGoogle Scholar
- Zimmerman RD, Murillo-Sanchez CE, Thomas RJ (2011) MATPOWER: steady-state operations, planning, and analysis tools for power systems research and education. IEEE Trans Power Syst 26(1):12–19CrossRefGoogle Scholar