Ibrahim S. Madugu, Abubakar Abdulkarim, B. J. Olufeagba, Yinusa A. Adediran, Mutiu Shola Bakare
The increasing global demand for renewable energy requires an efficient and cost-effective microgrid design. This study proposes a novel optimisation technique for autonomous solar PV–battery microgrids, tailored for Kano, Nigeria, that integrates forecast-based modelling with advanced nonlinear system simulation. Unlike traditional trial-and-error or simplified sizing approaches, the proposed framework uses an autoregressive moving average (ARMA) model to forecast sunshine hours, providing statistically reliable reference values for system design. The battery charging process is formulated as a nonlinear differential equation and solved using Picard’s iterative method, ensuring accurate modelling of charge–discharge dynamics. Simulation models of PV arrays, batteries, inverters, and charge controllers were developed and tested under multiple operating scenarios. Key findings demonstrate that the modal sunshine duration of 6 h accounts for ~ 50% of long-term predictions, making it a robust reference for system design. Sensitivity analysis reveals that a 5% improvement in battery discharge efficiency reduces the required capacity by nearly 100 Ah, while economic evaluation shows that inflation impacts system costs more significantly than interest rates (a 50% reduction in inflation led to a 45.37% cost decrease, compared to only 6.08% for interest rate reduction). Additionally, the developed framework identifies suboptimal but cost-efficient configurations that balance system reliability with affordability for both small- and medium-scale facilities.