Renewable Energy-Based Economic Load Dispatch Using Two-Step Biogeography-Based Optimization and Butterfly Optimization Algorithm

1. Introduction

Due to increment in energy demand, the electrical power market, in recent years, has become highly competitive and more liberal. Economic load dispatch (ELD) is an important and effective tool in the sphere of energy management system operation and planning. ELD is a process that allocates generating units in accordance to load demand, minimizes total generation cost and thus, maintains the power system economy. The primary objective of ELD technique is scheduling control variables of power system in order to share the total load and simultaneously, meeting all equality and inequality constraints; so that highest economical operation of the overall system is achieved. ELD integrated with renewable energy sources is an emerging trend that can be implemented with various optimization techniques. Renewable energy sources are most crucial prospects of energy nowadays. They can reduce the threats, to some extent, coming up from excessive environmental pollution, discharge of greenhouse gases and other hazardous gases (e.g. CO, NO_x, SO_x, etc.) emitting from conventional thermal power plants for satisfying the ever-growing electrical energy demand. The exhaust gas contains several toxic pollutants and they are released into the open air directly. Thus, the environment is degrading day by day and posing a great threat to the mankind. A few renowned organizations like UNFCCC are trying to control these emissions by some protocols such as Kyoto protocol and doing their best to maintain the global warming within a limit by cutting down the carbon output. Thus, to meet the energy demand, both the developing and developed countries will feel the urge of incorporating various sources of renewable energy like solar energy, biogas energy, tidal energy, wind energy etc. with the traditional thermal plants.

, , , ,	fuel cost coefficients of the i-th thermal generating unit
	fuel cost function for thermal power generation of i-th unit
	lower bound of thermal power generation of i-th unit
	upper bound of thermal power generation of i-th unit
, ,	number of thermal generator plants, wind plants and solar PV plants respectively
,	active power output of the i-th wind and solar PV unit respectively
,	direct cost coefficient related to i-th wind and solar PV unit respectively
	penalty/underestimation cost coefficient due to underestimation of wind power for i-th wind unit
	reserve/overestimation cost coefficient due to overestimation of wind power for i-th wind unit
,	rated power from i-th wind and solar PV unit respectively
,	actual available power from wind and solar PV unit respectively
,	scheduled power from wind and solar PV unit respectively
	penalty/ underestimation cost coefficient due to underestimation of solar power for i-th solar unit
	reserve/overestimation cost coefficient due to overestimation of solar power for i-th solar unit
	total system load
	total transmission losses
, ,	cut-in, rated and cut-out wind speeds respectively
,	scale and shape parameters of Weibull PDF, respectively
,	mean and standard deviation of Lognormal PDF, respectively
	intermediary parameter
TGU, WGU, SGU	conventional thermal generator units, wind generator units and solar PV generator units, respectively
FC, WC, SC, TC	fuel cost, wind cost, solar cost and total cost in $/hr, respectively
TL	transmission loss in MW
	probability