Efficient methods for solving power system operation scheduling challenges: the thermal unit commitment problem with staircase cost and the very short-term load forecasting problem - Lezama Lope, Uriel Iram (2023)
This dissertation addresses two crucial power system operational scheduling aspects: the thermal unit commitment problem and real-time load demand forecasting. These two are important challenges that need the development of models and efficient algorithms. To tackle the generator scheduling problem, we propose and develop five matheuristic methods, including four variations of local branching (LB) and one using kernel search (KS). Additionally, we have introduced a novel constructive approach named HARDUC, which effectively generates high-quality initial solutions for the matheuristic methods. To assess the effectiveness of the proposed matheuristic algorithms, tests were con ducted on instances simulating scenarios where an analyst must deliver a generation sched ule within one or two hours. A comparison with CPLEX, an off-the-shelf solver, under two scenarios (i) using the solver from scratch and (ii) using the solver with an initial feasible solution from the heuristic, revealed interesting insights. For small instances, the off-the-shelf solver outperformed the matheuristic methods. However, in medium-sized instances, the solver sometimes struggled to find a feasible solution. When solutions were found, there were no significant differences in performance between the solver and the methods. However, the proposed methods excelled and achieved remarkable results for large instances where the solver left many instances unsolved. Furthermore, we tested the proposed constructive method by comparing it with the best UCP constructive method from the literature. The results, supported by statistical tests, indicate the superiority of our proposed method. Our implementation of the KS algo rithm outperformed both the solver and the LB method in terms of relative optimality gap, especially in challenging instances. This discovery is significant as it reveals tremendous potential in utilizing KS for solving the UCP, paving the way for further research. As expected, as complexity increased, matheuristic methods outperformed the solver, delivering quicker, more e↵ective solutions. Matheuristics have a proven track record and are incorporated into commercial solvers for efficient solutions in mixed-integer linear programming problems. In our research, we customized matheuristics for the termal UCP by identifying dominant variables and addressing implementation challenges of the KS method, improving its efficacy. In addition, we introduced a novel method called the Analogue with Moving Av erage (AnMA) approach in very short-term load demand forecasting. AnMA exploits the seasonal characteristics of load demand time series by selecting the most correlated days. Its adaptability to real-time data positions it as an ideal choice for accommodating new demand patterns, rectifying biases, and enhancing accuracy. AnMA was compared against other methods recognized for their efficency and precision in the literature. The results showcased AnMA’s superiority, outperforming naive algorithms and exponential smoothing methods in accuracy, computational speed, and cost-e↵ectiveness. Addition ally, AnMA achieved comparable accuracy to ARIMA models while requiring significantly fewer computational resources and less time. Our research addresses critical challenges in power system operational scheduling, highlighting the e↵ectiveness of tailored methods that align with problem-specific char acteristics. These findings hold practical significance for the electricity industry, as our approach leverages a profound understanding of problem characteristics to improve opera tional scheduling. The success of our methods could potentially guide the development of future hybrid heuristic approaches combining mixed-integer programming or matheuris tics alongside analogy-based forecasting techniques, o↵ering substantial practical advance ments in the electricity sector.