Disjunctive optimization model and algorithm for long-term capacity expansion planning of reliable power generation systems

This paper proposes a new optimization model and algorithm for long-term capacity expansion planning of reliable power generation systems. The model optimizes both investment decisions (e.g., size, location, and time to install, retire and decommission facilities) and hourly operation decisions (e.g., on/off status, operating capacity, and expected power output). It is also able to optimize both the main generation capacity and reserve capacity to improve power system reliability. The impact of operational strategies of generators (i.e., participating in electricity production vs. remaining as idle units during operation) on power system reliability is considered. Probability of equipment failures and capacity failure states are used to rigorously estimate the power system reliability depending on design and operation strategies. The optimization model is firstly formulated with Generalized Disjunctive Programming (GDP), which is then reformulated as a mixed-integer linear programming (MILP) model using the Hull relaxation. Two reliability-related penalties, such as downtime penalty and unmet demand (or load shedding) penalty, are included in the objective function to maximize reliability while minimizing the total net present cost. Furthermore, a bilevel decomposition with tailored cuts is developed to reduce computational times of the multi-scale optimization model. The effectiveness of the proposed model is shown by comparing it with the expansion planning model without explicitly considering reliability. We also show that the proposed bilevel decomposition is computationally efficient for solving large-scale problems with millions of variables and constraints through 5-years and 10-years planning case studies.