Mathematical Modelling of an Autonomous Photovoltaic Standalone System

Abstract

Autonomous stand-alone Photovoltaic power systems are an essential element in providing power in Nigeria looking forward. In order to effectively exploit this technology while avoiding the pitfalls of the past, it is essential to establish a well-structured and formal framework for the design, maintenance and operations. This paper presents the mathematical model for the study and possibly design of such systems by solving the dynamical equations that describe the system during sunshine and dark periods. Both periods can be represented by nonlinear differential equations which are solved numerically and used to develop scenarios. The results of the studies indicate that under circumstances similar to those encountered during the rainy season when insolation can be markedly reduced, create conditions whereby for specific systems, the loading may have to be markedly decreased. Tests with larger battery capacities indicate that the batteries may fail to charge fully and subsequently the system fails unless an external intervention is made to augment the PV power.