Mathematical models and optimization techniques to support local electricity markets

The implementation of local electricity markets (LEMs) requires efficient tools that can provide solutions for the optimal management of distributed energy resources (DERs) considering economic and technical aspects. This chapter presents mathematical models for the formulation of optimization problems in LEMs including DERs (renewable distributed generation, energy storage devices, and electric vehicles) as well as control devices (capacitor banks and voltage regulators). Mathematical formulations based on mixed-integer linear programming (MILP), stochastic programming, and robust optimization are also discussed. Moreover, meta-heuristic and decomposition methods are presented as optimization techniques that contribute to tackle two critical aspects in the solution of complex optimization problems: finding good-quality solutions and reducing the computational effort. Those deterministic and approximate approaches form a stack of optimization techniques that can be adopted to solve optimization problems in LEMs such as feasible and economic operation, integration of DERs, and demand response.