Big-Bang and Big-Crunch (BB-BC) and FireFly Optimization (FFO): Application and Comparison to Optimal Power flow with Continuous and Discrete Control Variables

Abstract

Big-Bang and Big-crunch (BB-BC), a heuristic optimization method is based on the concept of universal evolution. FireFly optimization (FFO), also a recent heuristic optimization method, is based on the concept of flashing behaviour of lightingbugs. Both the optimization methods are applied to obtain the solution of the Optimal Power Flow (OPF) with continuous and discrete control variables for quadratic generator output cost functions. The continuous control variables are generating unit active power outputs and generator bus voltage magnitudes, while the discrete ones are transformer- tap settings and switchable shunt devices. A number of functional constraints such as load bus voltage magnitudes, line flows and reactive power capabilities are included as quadratic penalties in the optimization function. A comparative simulation results for Ward -Hale 6 bus system with seven control variables and IEEE 30 bus system with twenty-three control variables are presented. F : total operating cost,NB: number of buses, NG: number of generator buses, NT: number of Transformers, NL: number of lines (branches),NSH: number of switchable shunts, NPQ: number of load buses NTR: number of transformers, ௜ : active power injection at bus i, ௜ : reactive power at bus i,NP: population size (number of fireflies in FFO/number of Big- Bangs BB-BC)NC: number of control variables (co-ordinates of fireflies FF0/dispersions in BB-BC)