Optimization of Off-grid Photovoltaic Systems

Abstract

Among various renewable energy sources, solar energy is considered one of the most effective solutions because it is abundant, eco-friendly, sustainable energy resources to address the energy shortage of the present and future. Electricity generation by an off-grid photovoltaic (PV) system is particularly effective in isolated areas where there is no access to any other source of electricity. However, it makes difficult to estimate the cost-effective capacity of an off-grid energy system under the inherent nature of solar irradiance, unexpected climate changes and energy demand uncertainty. The objective of the dissertation is to develop mathematical optimization models that assist and improve the decision-making process in designing the optimal capacity of a residential off-grid PV-battery system under uncertainties. In the first chapter, a mathematical model for energy consumption scheduling of an off-grid PV-battery system problem is proposed. It is a mixed-integer programming problem that considers energy consumption patterns and appliance priorities. The model pre-schedules appliance operation that maximizes the operation of higher priority appliances given the forecasted solar irradiance. It is represented how it can be solved on case studies based on region and season. The results demonstrate that the proposed model provides optimal schedules for operating the higher-priority appliances. In the second chapter, an off-grid PV system design approach that considers energy consumption scheduling and system operation under solar irradiance uncertainty is developed. The solution method combined the Nelder-Mead algorithm, mixed-integer programming, and Monte Carlo simulation. The day-ahead schedule obtained by the energy consumption scheduling model is executed on a Monte Carlo simulation that considers the uncertainty of solar irradiance. The performance of the algorithm is tested using solar irradiance data at two locations in the USA. Based on the simulation results, the algorithm finds the cost-efficient capacity of the energy system at a minimum annual equivalent cost (AEC). Finally, in the third chapter, a stochastic optimization model that simultaneously considers scenarios to represent the uncertainty of solar irradiance and energy consumption scheduling is studied. The resulting model is a complicated multi-objective mixed integer programming problem. The model aims to determine the optimal PV array and battery capacity to supply the energy demand at minimum AEC of the energy system in variation of solar irradiance occurrences. Experimental results confirm that the stochastic optimization model better estimates the energy system capacity at minimum AEC than the non-optimized deterministic model. Moreover, 20-scenario model is more effective than less-scenario models since the solution obtained by 20-scenario model satisfies energy demand under all number of scenarios considered.