Optimization Models and Algorithms for Infrastructure Planning of Reliable and Resilient Power Systems

This thesis develops optimization models and algorithms for infrastructure planning of reliable and resilient power systems. Chapter 1 presents an introduction with a basic review of the main concepts used in the thesis, as well as providing a general overview of the chapters of the thesis. Chapter 2 first provides a review of key concepts in the planning of generation and transmission expansion. The computational challenges of expansion planning models and several simplification strategies to tackle the issues are also reviewed, including spatial aggregation, temporal aggregation, and decomposition techniques.

Chapter 3 proposes a reliability-constrained expansion planning model for power generation systems using the probabilistic reliability approach. The model optimizes long-term investment decisions (e.g., size, location, timing of generator installation and retirement) for both main and the reserve (or backup) systems, and short-term operational decisions (e.g., unit commitment and economic dispatch)under the consideration of failure probabilities. The model is formulated using Generalized Disjunctive Programming(GDP).The model can capture the impact of dual role of back up generators on power system reliability, which can serve either as reserves or actively contribute to electricity production. To solve large scale problems, a bilevel decomposition algorithm is proposed, which separately solves an investment master problem and operational reliability subproblems. Logic-based tailored cuts are developed for convergence, including capacity pruning cut, timing pruning cut, and capacity and timing fixing cut. Through comparative case studies, the proposed model is shown to significantly enhance reliability while remaining computationally tractable, even for multi-year planning problems with millions of decision variables.

Chapter 4 focuses on evaluating the impact of different reliability formulations on the optimal design and operation of power systems. Four models are developed: a baseline model without reliability constraints, a deterministic model using reserve margin, a deterministic model using N–k reliability, and a probabilistic model based on equipment failure probabilities. Specifically, the probabilistic model used in this chapter is a simplified version of the model described in chapter 3. A unified evaluation framework is proposed to compare these models with different objective functions, which uses loss of load expectation (LOLE) and expected energy not served (EENS) as reliability metrics. Although rigorous reliability models such as N-k reliability and the probabilistic models require higher investment costs, they result in more robust and reliable system designs. Moreover, it is identified that the probabilistic model, which is developed primarily in this thesis and is not commonly used in power system planning, can provide a more reliable solution than conventional reliability methods, such as reserve margin or N-k reliability.

Chapter 5 extends the generation-focused reliability framework proposed in chapter 3 to a more comprehensive model that includes transmission planning and environmental constraints, such as CO2 emissions reduction and renewable generation target. To manage computational complexity, a simplification strategy is developed, which identifies critical nodes and generators whose failure can significantly impact the system. A three-step solution algorithm is also proposed: it first solves a base expansion planning model without reliability, then identifies critical nodes and generators, and finally solves a reliability-constrained model. The model is applied to the San Diego County, and several cases are generated based on California’s energy policy. It is identified that larger reserve capacity is required with larger capacity of dispatchable generators due to their relatively higher
failure rates. On the other hand, as renewable penetration increases, the additional capacity needed for reliability decreases due to the inherently low failure rates of renewable technologies.

Chapter 6 proposes a two-stage stochastic Generalized Disjunctive Programming (GDP) model for proactive planning and reactive operation of power systems under disruptions. Specifically, the proposed model can make both proactive planning (e.g., line hardening, distributed resource deployment) and reactive operational decisions (e.g., generator redispatch, line switching) under a range of disruption scenarios. The model accounts for uncertainty by generating disruption scenarios based on the probabilities of failure of transmission lines. To solve large-scale stochastic optimization problems, a topology-based method is selected to identify critical transmission lines. A scenario reduction-based decomposition algorithm is also proposed, which iteratively solves a master problem with a reduced set for disruption scenarios and a sub-problem that evaluates solutions across the full set for disruption scenarios. The proposed two-stage stochastic programming model demonstrates how probabilistic disruptions should be incorporated into long-term infrastructure planning to improve system resilience and minimize losses during extreme events.