Development of a Mathematical and Heuristic Model for the Techno-Economic Design of Renewable Energy Systems Ensuring a Convex and Directly Optimizable Objective Function

Abstract

This paper presents a techno-economic optimization framework for the design and sizing of a hybrid renewable energy system (HRES) integrating photovoltaic generation, wind energy, and battery storage for isolated and weak-grid coastal communities. The proposed methodology aims to minimize the annualized life cycle cost, also referred to as the equivalent annual total cost (CAET), while explicitly incorporating system reliability through the Value of Lost Load (VOLL), a concept widely adopted in power system planning and regulatory studies.

The optimization problem is formulated using an hourly energy balance over a full annual horizon of 8760 hours, allowing the explicit representation of load variability, renewable resource intermittency, and battery charge-discharge dynamics. Capital investment costs are annualized using the capital recovery factor based on established engineering economics principles, while operational costs and the economic valuation of unserved energy are jointly considered in the objective function. By embedding reliability costs directly into the cost formulation, the proposed approach modifies the mathematical structure of the optimization problem, leading to a convex cost behavior within the feasible design space.

The framework is applied to a real-world case study corresponding to the coastal community of Chérrepe, Peru, using site-specific solar irradiation, wind resource, and demand data. Simulation results demonstrate that the explicit inclusion of reliability valuation significantly influences optimal system sizing, discouraging undersized configurations with excessive unmet demand as well as oversized configurations with unnecessarily high capital costs. The resulting optimal design achieves a balanced and economically consistent trade-off between investment cost and supply reliability.

The results confirm that integrating reliability valuation directly into the techno-economic optimization process provides a transparent, robust, and replicable approach for the planning of hybrid renewable energy systems in isolated contexts. The proposed methodology can be readily adapted to other locations and technology combinations, offering a practical decision-support tool for distributed generation and alternative energy planning.