Multi-Objective Dispatch of PV Plants in Monopolar DC Grids Using a Weighted-Based Iterative Convex Solution Methodology

Abstract

The design of an efficient energy management system (EMS) for monopolar DC networks with high penetration of photovoltaic generation plants is addressed in this research through a convex optimization point of view. The EMS is formulated as a multi-objective optimization problem that involves economic, technical, and environmental objective functions subject to typical constraints regarding power balance equilibrium, thermal conductor capabilities, generation source capacities, and voltage regulation constraints, among others, using a nonlinear programming (NLP) model. The main characteristic of this NLP formulation of the EMS for PV plants is that it is a nonconvex optimization problem owing to the product of variables in the power balance constraint. To ensure an effective solution to this NLP problem, a linear approximation of the power balance constraints using the McCormick equivalent for the product of two variables is proposed. In addition, to eliminate the error introduced by the linearization method, an iterative solution methodology (ISM) is proposed. To solve the multi-objective optimization problem, the weighted optimization method is implemented for each pair of objective functions in conflict, with the main advantage that in this extreme the Pareto front has the optimal global solution for the single-objective function optimization approach. Numerical results in the monopolar version of the IEEE 33-bus grid demonstrated that the proposed ISM reaches the optimal global solution for each one of the objective functions under analysis. It demonstrated that the convex optimization theory is more effective in the EMS design when compared with multiple combinatorial optimization methods.

A Robust Conic Programming Approximation to Design an EMS in Monopolar DC Networks with a High Penetration of PV Plants

“…where γ ∈ {0, 1} defines the set of uncertainties; ppv kh and ppv kh are the power available from the PV generator and its deviation, respectively; pd kh is the power consumption of the load, and pd kh is its deviation. Note that in (34) and (35), only the values in the following intervals are considered:…”