Modeling and Optimization Techniques for Sizing and Scheduling Applications in Power and Energy

Optimization techniques were applied to solve critical power system problems. We first studied the sizing and scheduling of stand-alone loads and generators for optimal energy utilization. The main application of this work is water treatment or desalination plants which are powered by stand-alone solar farms in off-grid setup. The techniques can also be applied to large loads operating in island modes - such as motors or pumps, steel manufacturing, and data centers. Mixed integer linear programming was used for sizing and scheduling the loads. Historical solar data was also used to optimally schedule the available resources in a selected location. Static and dynamic loads types were simulated. The second portion of this thesis focuses on methods to mitigating macrogrid power outages by utilizing available Distributed Energy Resources (DER) to supply load locally, but across several customers. Real household data was analyzed. The algorithm schedules load and demand to meet certain objective functions such as minimizing power losses or maximizing solar energy utilization and is implemented in the framework of mixed integer linear programming. Reliability metrics increased significantly through power sharing. Finally, optimization methods are applied to size a Battery Energy Storage Systems (BESS) from an economic perspective. As BESS can mitigate effects of intermittent energy production from renewable energy sources they play a critical role in peak shaving and demand charge management. The trade-off between BESS investment costs, lifetime, and revenue from utility bill savings along with microgrid ancillary services are taken into account to determine the optimal size of a BESS. The optimal size of a BESS is solved via a stochastic optimization problem considering wholesale market pricing. A stochastic model is used to schedule arbitrage services for energy storage based on the forecasted energy market pricing while accounting for BESS cost trends, the variability of renewable energy resources, and demand prediction. The approach is illustrated with an application to various realistic case studies based on pricing and demand data from the California Independent System Operator (CAISO). The case study results give insight in optimal BESS sizing from a cost perspective, based on both long-term installation schedules and daily BESS operation