Mixed-integer LP model for volt/var control and energy losses minimization in distribution systems

- A convex optimization model for distribution systems is proposed.
- The model is based on a linearized model and considers distributed generation.
- The results were compared to the exhaustive enumeration using a nonlinear load flow.
- The solutions obtained applying the proposed model are of high quality.

This paper presents an optimization model for volt/var control and energy losses minimization in power distribution networks, considering the presence of distributed generation (DG); it can also be applied to obtain the optimal solution for the allocation of capacitor banks. Unlike usual approaches using nonlinear equations, the model uses a linear objective function and linear constraints, binary and continuous variables. Thus, the optimization problem can be represented as a mixed-integer linear programming (MILP) model, which can be solved through classical optimization techniques. The objective function considers the minimization of: (a) energy losses; (b) voltage violations; (c) acquisition, installation and maintenance costs of capacitors. The solution of the optimization problem provides the location and the rating of the capacitor banks; the solution also indicates the number of automatic capacitors to be connected for each load level, and the best operation point for DGs. The model is validated by comparing the results obtained for four test networks with those obtained through exhaustive enumeration technique and conventional load flow.