Temporal Decomposition for Multi-Interval Optimization in Power Systems

Large optimization problems are frequently solved for power systems operation and analysis of electricity markets. Many of these problems are multi-interval optimization with intertemporal constraints. The size of optimization problems depends on the size of the system and the length of the considered scheduling horizon. Growing the length of the scheduling horizon increases the computational burden significantly and might make solving the problem in a required time span impossible. Many simplifications and approximation techniques are applied to reduce the computational complexity of multi-interval scheduling problems and make them solvable in a reasonable time span. Geographical decomposition is presented in the literature to divide optimization problems according to the power system geographical regions and solve them faster than centralized methods. These decompositions, however, do not relieve the computational complexity originated from intertemporal constraints. In this dissertation, temporal decomposition strategies are proposed to decompose the overall scheduling horizon into several smaller subhorizons. The proposed strategies, which can be combined with geographical decomposition, relieve the computational complexities of the multi-interval scheduling problems originated from intertemporal constraints, such as ramp up/down limits and minimum on/off time of thermal generation units and storage systems energy balance constraints. An optimization subproblem is formulated for each subhorizon with respect to local variables and constraints inside that subhorizon and intertemporal connectivities between consecutive subhorizons. Several distributed optimization algorithms are developed to coordinate subproblems in a parallel manner and find a feasible solution that is also optimal from the perspective of the whole scheduling horizon. These coordination algorithms are based on analytical target cascading and auxiliary problem principles. Since the number of subhorizons affects the solution time, a machine learning-based approach is proposed to decompose the scheduling horizon optimally with the goal of obtaining the most time-saving. The proposed approach, which uses XGBoost as a multi-class classifier, reads the load profile and determines the best temporal decomposition pattern