Optimizing stand-alone microgrids with lagrange multiplier technique: A cost-effective and sustainable solution for rural electrification

This paper addresses the challenge of optimally sizing and planning stand-alone microgrids in remote areas, focusing on generating sources using a novel algorithm based on the Lagrange multiplier optimization technique. The study centers on the Gulf of Aqaba, Egypt, where five configurations of PV and wind micro plants with diesel generation are evaluated. Detailed cost analysis includes wind turbines, PV modules, and diesel generators. Motivated by the need for cost-effective, reliable, and environmentally friendly microgrids, the proposed algorithm is benchmarked against the widely used Hybrid Optimization Model for Energy Renewable HOMER software. Key criteria for analysis include economic benefits, environmental impacts, and system reliability. Results highlight the superior performance of the proposed optimization technique. It achieves up to 22% lower net present costs (NPC) and up to 13% lower cost of electricity (COE) compared to HOMER. Additionally, the algorithm demonstrates significant environmental benefits, with emissions reductions of up to 25% for carbon dioxide and substantial decreases in carbon monoxide and nitrogen oxides. Reliability is also enhanced, with the proposed schemes showing higher excess energy and renewable energy contributions. The study justifies the use of the Lagrange multiplier optimization technique as a superior approach for planning and sizing stand-alone microgrids, offering significant economic and environmental advantages. This work provides a comprehensive framework for developing sustainable energy solutions in isolated regions.