A General Theory of Robust Multi-Period Scheduling Under Deep Uncertainty with Applications to Power Sector Operations in Nigeria

Power sector operations in Nigeria face profound deep uncertainty encompassing generation capacity availability, transmission line reliability, gas supply continuity, and demand variability, conditions under which the probability distributions required by conventional stochastic programming are themselves uncertain, necessitating more robust analytical frameworks. This dissertation develops a general theory of robust multi-period scheduling under deep uncertainty, making original contributions to robust optimization methodology with primary empirical application to Nigerian power sector operations. The theoretical framework is grounded in a formal characterization of deep uncertainty using imprecise probability theory, which subsumes classical probabilistic uncertainty as a special case. Original contributions include: the formulation and analysis of a minimax regret multi-period scheduling model under imprecise probability; theoretical results on the equivalence between certain imprecise probability formulations and distributionally robust optimization problems; and the development of a tractable reformulation hierarchy that generates increasingly tight approximations to the intractable exact minimax regret problem. Solution algorithms based on constraint generation and column generation exploit the reformulation hierarchy. Empirical application addresses the day-ahead unit commitment and economic dispatch problem for the Nigerian electricity grid, using operational data from the Transmission Company of Nigeria and Generation Companies covering 36 months. The robust scheduling policy reduces expected load shedding by 28 percent and eliminates the worst-case load shedding scenarios that the deterministic policy generates under adverse realization combinations. Recommendations include integrating the robust scheduling model into the Nigerian Electricity System Operator's day-ahead planning process. Keywords: robust optimization, power sector scheduling, deep uncertainty, Nigeria, unit commitment