Optimal Sizing of Photovoltaic Generation in Radial Distribution Systems Using Lagrange Multipliers

José Adriano Da Costa,Max Chianca Pimentel Filho,Manoel Firmino De Medeiros Júnior,David Alves Castelo Branco,Neilton Fidelis Da Silva

doi:10.3390/en12091728

Abstract

The integration of renewable distributed generation into distribution systems has been studied comprehensively, due to the potential benefits, such as the reduction of energy losses and mitigation of the environmental impacts resulting from power generation. The problem of minimizing energy losses in distribution systems and the methods used for optimal integration of the renewable distributed generation have been the subject of recent studies. The present study proposes an analytical method which addresses the problem of sizing the nominal power of photovoltaic generation, connected to the nodes of a radial distribution feeder. The goal of this method is to minimize the total energy losses during the daily insolation period, with an optimization constraint consisting in the energy flow in the slack bus, conditioned to the energetic independence of the feeder. The sizing is achieved from the photovoltaic generation capacity and load factors, calculated in time intervals defined in the typical production curve of a photovoltaic unit connected to the distribution system. The analytical method has its foundations on Lagrange multipliers and relies on the Gauss-Jacobi method to make the resulting equation system solution feasible. This optimization method was evaluated on the IEEE 37-bus test system, from which the scenarios of generation integration were considered. The obtained results display the optimal sizing as well as the energy losses related to additional power and the location of the photovoltaic generation in distributed generation integration scenarios.

Highlights

The smart grid concept has as premise the stimulus of the adoption of more efficient technologies which should contribute to the reduction of technical losses and the mitigation of negative environmental impacts derived from the operation of the current electrical system [1], for example, greenhouse gas emission (GGE) mitigation, for the energy input in the distribution system
It is important to highlight that when accounting for the energy losses, environmental impacts related to distribution systems cannot be neglected, since they contribute to total GGE, adding to the electric power generation and transmission segments [3]
The present study proposes an analytical method that addresses the problem of the sizing of nominal powers of multiple photovoltaic generation (PV) generation units connected to a radial distribution feeder, in order to minimize total energy losses during the daily insolation period

Summary

Introduction

The smart grid concept has as premise the stimulus of the adoption of more efficient technologies which should contribute to the reduction of technical losses and the mitigation of negative environmental impacts derived from the operation of the current electrical system [1], for example, greenhouse gas emission (GGE) mitigation, for the energy input in the distribution system. In this context, distributed generation (DG) plays a leading role in boosting the adoption of renewable energy sources in the system, such as photovoltaic generation (PV). In order to achieve a higher level of benefits from the integration of DG into the power grid, proper optimization techniques must be applied in order to better size the generation, handling problems that may contain multiple objectives and present specific constraints

Methods

Results

Discussion

Conclusion