New Algorithm to Solve Mixed Integer Quadratically Constrained Quadratic Programming Problems Using Piecewise Linear Approximation

A Two-Stage Approach to Locate and Size PV Sources in Distribution Networks for Annual Grid Operative Costs Minimization

This paper contributes with a new two-stage optimization methodology to solve the problem of the optimal placement and sizing of solar photovoltaic (PV) generation units in medium-voltage distribution networks. The optimization problem is formulated with a mixed-integer nonlinear programming (MINLP) model, where it combines binary variables regarding the nodes where the PV generators will be located and continuous variables associated with the power flow solution. To solve the MINLP model a decoupled methodology is used where the binary problem is firstly solved with mixed-integer quadratic approximation; and once the nodes where the PV sources will be located are known, the dimensioning problem of the PV generators is secondly solved through an interior point method applied to the classical multi-period power flow formulation. Numerical results in the IEEE 33-bus and IEEE 85-bus systems demonstrate that the proposed approach improves the current literature results reached with combinatorial methods such as the Chu and Beasley genetic algorithm, the vortex search algorithm, the Newton-metaheuristic algorithm as well as the exact solution of the MINLP model with the GAMS software and the BONMIN solver. All the numerical simulations are implemented in the MATLAB programming environment and the convex equivalent models are solved with the CVX tool.