Stochastic Optimization for Renewable Energy System Design and Operation

In this dissertation, we present novel stochastic optimization models and solution methods for the optimization of renewable energy systems. Specifically, the focus is on bioenergy supply chains and operations in the presence of uncertainty. Overall, our applications highlight the breadth in which stochastic programming models can be applied in the energy sector. We first study the impact of biomass blending practice on reducing the cost of producing biofuels. In detail, we consider a biomass supply chain problem where the goal is to identify purchase quantities of different biomass feedstocks from possible suppliers in order to meet the quality requirements of the biomass conversion process. The model incorporates the quality requirements using chance constraints that take into account the stochastic nature of biomass quality. There are two problem settings in this study, a centralized and a decentralized supply chain. Proposed is a mixed-integer linear program that models the blending problem in the centralized setting and the bilevel program models the blending problem in the decentralized setting. We use the sample average approximation (SAA) method to approximate the chance constraints and propose solution algorithms to solve this approximation. The case study developed for South Carolina using the Billion Ton Study data provides an environment to conduct numerical experiments. Numerical results demonstrate that the blends identified and the suppliers selected by both models are different, and the cost of the centralized supply chain is 2 to 6\% lower. The implications of these results are two-fold. First, these results could lead to improved collaborations in the supply chain. Second, these results provide an estimate of the approximation error from assuming centralized decision-making in the supply chain. In addition, we provide managerial insights based on the identified biomass blends. We next study the optimization of biorefinery operations under stochastic biomass characteristics and stochastic equipment failure. Variations of physical and chemical characteristics of biomass lead to an uneven flow of biomass in a biorefinery, which reduces equipment utilization and increases operational costs. Uncertainty of biomass supply and high processing costs increase the risk of investing in the U.S.\u27s cellulosic biofuel industry. We propose a stochastic programming model to streamline processes within a biorefinery. A chance constraint models the system\u27s reliability requirement that the reactor is operating at a high utilization rate given uncertain biomass moisture content, particle size distribution, and equipment failure. The model identifies operating conditions of equipment and inventory levels to maintain a continuous biomass flow to the reactor. The Sample Average Approximation method approximates the chance constraint, and a bisection search-based heuristic solves this approximation. A case study is developed using real data collected at Idaho National Laboratory\u27s biomass processing facility. An extensive computational analysis indicates that sequencing of biomass bales based on moisture level, increasing storage capacity, and managing particle size distribution {increases} utilization of the reactor and reduces operational costs. Finally, we extend the previous work on optimizing biorefinery operations to integrate the sequential information flow from moisture sensors into the decision-making process. Integrating the sensory data into the operational decisions in biomass processing will increase its responsiveness to the changing biomass conditions. We propose a multi-stage stochastic programming model that minimizes the expected operational costs by identifying the initial inventory level and creating an operational decision policy for equipment speed settings. These policies take the sensory data and the current biomass inventory level as inputs to dynamically adjust inventory levels and equipment settings according to changes in the biomass\u27 characteristics. We ensure that a prescribed utilization target of the reactor is consistently achieved by penalizing the violation of the target reactor feeding rate. A case study is developed using data collected at Idaho National Laboratory\u27s biomass processing facility. We show the value of multi-stage stochastic programming from an extensive computational experiment. Our sensitivity analysis indicates that, by updating the infeed rate of the system, the processing speed of equipment and bale sequencing based on moisture level of biomass improves the processing rate of the reactor and reduces operating costs