Evaluating the effectiveness of normal boundary intersection method for short-term environmental/economic hydrothermal self-scheduling

The problem of the optimal scheduling of available hydro and thermal generating units considering a short scheduling period (one day-one week) in order to maximize the total profit is denoted as short-term hydro thermal self-scheduling (SHTSS). Mixed-integer linear programming (MILP) method is proposed to model the SHTSS problem in the day-ahead energy and reserve markets. MILP formulation allows for considering a precise model for the prohibited working zones, dynamic ramp rate constraints and operating services of thermal generating units, as well as the characteristics of multi-head power discharge for hydro generating units and reservoirs' spillage. This problem is modelled as a multi-objective (MO) optimization one, having two objectives, i.e. maximization of the profit of Generation Company's (GENCO's) and minimization of emissions from thermal units. In order to solve the problem and generate the non-inferior solutions, normal boundary intersection (NBI) method is applied. The main advantage is the provision of set of uniformly distributed non-dominated solutions regardless of the scales of objective functions values. Then, a fuzzy based decision maker is employed in order to select a non-inferior solution. In order to demonstrate the effectiveness of the presented method, several numerical simulations are presented. Furthermore, the obtained results are compared with those obtained considering different methods for obtaining non-inferior solutions, such as weighted sum method, evolutionary programming-based interactive fuzzy satisfying method, differential evolution, particle swarm optimization and hybrid multi-objective cultural algorithm.