Optimal siting and sizing of energy storage devices considering energy generation and consumption uncertainties

Optimization plays a vital role in the operation and planning of electric power systems. From real-time to long-term planning, the most critical power system decisions are supported by a variety of different optimization problems. In dealing with the uncertainty that affects these decisions, today's power system operators usually exploit deterministic optimization models that aim to maintain the reliability of the system and minimize costs. While this approach is valid, it can be expected that the development of new techniques in the area of optimization under uncertainty could yield substantial benefits to this practice. This is the challenge that motivates this Thesis. More precisely, this Thesis proposes models and algorithms to address critical optimization problems in electric power system operations by considering uncertainty through an emerging technique such as Robust Optimization. OPF is a type of optimization problems where active and reactive power of devices connected to the electric grid can be optimized to minimize a cost function considering the physical constraint of the network. It is a suitable tool to model the operation and planning of distribution systems that contain active elements such as storage and demand response. Due to the high dimension of the distribution network characteristics, alternating current (AC) OPF is the most suitable method. In this thesis, convex relaxations have been chosen to guarantee a low calculation burden and globally optimal solutions. This thesis will emphasis on the development of operations and planning methods to incorporate new challenges in planning and operations for smart grids