Impact of Reliability Formulations on the Optimal Planning and Operation of Power Systems

This paper develops an optimization model for longterm expansion planning and short-term operation of reliable power systems using a probabilistic reliability assessment. A state space method is used to represent various operational states by modeling component failures. The impact of additional generators for reliability improvement is taken into account in the probabilistic model. Generalized Disjunctive Programming (GDP), which integrates logical disjunctions and algebraic constraints, is introduced to develop the optimization model for the probabilistic model. Two expansion models, which use traditional reliability approaches, the reserve margin model and the N-k reliability model, are also modeled using GDP. The expansion planning model without reliability is also considered. The four different models are compared using a unified evaluation strategy that uses two key reliability criteria: loss of load expectation (LOLE), which represents the expected duration of power disruptions, and expected energy not served (EENS), which quantifies the total power shortage. The effectiveness of the proposed models is verified through two case studies: an illustrative example and a real-world application based on San Diego County. The results indicate that models with rigorous reliability assessments (e.g., probabilistic or N-k reliability) require higher investment and operational costs but achieve greater reliability compared to models using simplified reliability constraints. Computational results are also presented with problems with up to 200 buses.