Optimal siting and sizing of battery energy storage systems in unbalanced distribution systems: A multi objective problem under uncertainty

In this paper the siting and sizing problem of battery energy storage systems in unbalanced active distribution systems is formulated as a mixed-integer, non-linear, constrained multi objective (MO) optimization problem under uncertainties. The problem is cumbersome from the computational point of view due to the presence of intertemporal constraints, a great number of state variables and the presence of uncertainties in the problem input data. A new approach based on the trade-off/risk analysis is proposed to obtain with acceptable computational efforts a solution that may not be the optimal solution but represents a reasonable and robust compromise. We use the trade-off/risk analysis, because it was specifically developed for power system planning problems in which we deal with a wide range of options, with possible conflicting objectives, and with uncertainty and risk. The proposed approach includes new procedures to select an adequate set of planning alternatives to be considered in the trade-off/risk analysis framework and to assist the planning engineer when difficulties arise in setting probabilities of the input data. Numerical applications to an IEEE unbalanced test system demonstrate the effectiveness of the proposed procedure and indicate the best alternatives of storage systems in the range from 450 kW to 600 kW globally installed in a reduced set of nodes.