Optimal scheduling of short-term hydrothermal with integration of renewable energy resources using Lévy spiral flight artificial hummingbird algorithm

Abstract

Short-term hydrothermal scheduling (STHS) is taking an important consideration in the power system for economics operation. The solution to the STHS problem gives time-varying scheduling of power generation with available hydro and thermal units aims to attain the cost saving of thermal units for a given time period. It is a non-convex optimization problem with a set of inequality and equality constrains such as load balancing, transmission losses as well as valve-point effect to the thermal power units. The permeation of renewable energy is frequently used into the power networks aims to reduce the cost of generation and emissions. The two foremost resources such as wind and photo-voltaic are frequently used in the power networks. In the research, the use of both powers integrated into the STHS problem to reduce the fuel cost ($) by using the modified artificial hummingbird algorithm (MAHA). To modelled the uncertainty in solar irradiance and windspeed, the lognormal and Weibull distribution are used. The novel MAHA is based on two enhancing methods; (1). updating the positions of the hummingbirds in stochastic motion via Lévy flight walk and (2). updating the location of the hummingbirds via pitch adjustment motion. The MAHA is further tested on the four STHS cases such as; four hydro one thermal (non-vple and vple), four hydro three thermal (vple without and with losses), four hydro three thermal with integration of RERs including direct cost only (VPLE without and with losses) and four hydro three thermal with uncertainty of RERs including direct, reverse and penalty costs (vple without losses), respectively. Moreover, for validation the performance of MAHA is further compared to the outcomes of AHA and other state-of-the-arts techniques.