Scenario-Based Multi-Objective Optimisation for Rural Electrification Under Carbon, Economic, and Equity Constraints

Rural electrification in Sub-Saharan Africa faces a trilemma: cutting carbon emissions, making it economically viable, and achieving fair access to energy for all. This paper develops a multi-objective framework that optimises carbon revenue, net present value (NPV), total energy supply, cooking fuel (firewood and LPG), health costs, and benefit to society. The model uses continuous decision variables: daily energy allocation among four sources (solar, generator, firewood, LPG) to three population groups (men, women, children). The case study is a rural community of 7000 people in Nigeria (Tier 1 energy consumers). Six policy scenarios are considered: baseline, high carbon price, low carbon price, microfinance, government subsidy and community cooperative. This study compared algorithms and identified a hybrid Non-dominated Sorting Genetic Algorithm and Particle Swarm Optimisation II as the most suitable algorithm for solving the formulated optimisation problem. It was found that NPV and unit cost of energy would increase to $175,500 and 26.4 ¢/kWh, respectively, by increasing the price of carbon from $8/ton to $12/ton. Firewood generates health savings and carbon revenue in the range of $4100–$12,270/year. Prices below $8/ton do not induce optimal reconfigurations in the system. The best energy supply (2825 kWh/day) and the lowest unsatisfied demand occur in the government subsidy scenario with the greatest disparity index, displaying an equity-efficiency trade-off. The framework shows that sustainable access to energy can be unlocked using strategic integration of carbon finance, valuation of health benefits and equity constraints.