This dissertation comprises three main essays that share a common theme: developing methods to promote sustainable and renewable energy from both the supply and demand sides, from an application perspective.

The first essay (Chapter 2) addresses demand response (DR) scheduling using dynamic programming (DP) and customer classification. The goal is to analyze and cluster residential households into homogeneous groups based on their electricity load. This allows retail electric providers (REPs) to reduce energy use and financial risks during peak demand periods. Compared to a business-as-usual heuristic, the proposed approach has an average 2.3% improvement in profitability and runs approximately 70 times faster by avoiding the need to run the DR dynamic programming separately for each household.

The second essay in Chapter 3 analyzes the integration of renewable energy sources and battery storage in energy systems. It develops a stochastic mixed complementarity problem (MCP) for analyzing oligopolistic generation with battery storage, taking into account both conventional and variable renewable energy supplies. This contribution is novel because it considers multi-stage stochastic MCPs with recourse decisions. The sensitivity analysis shows that increasing battery capacity can reduce price volatility and variance of power generation. However, it has a small impact on carbon emissions reduction. Using a stochastic MCP approach can increase power producers' profits by almost 20 percent, as proposed by the value of stochastic equilibrium solutions. Higher battery storage capacity reduces the uncertainty of the system in all cases related to average delivered prices. Nevertheless, investing in enlarging battery storage has diminishing returns to producers' profits at a certain point restricted by market limitations such as demand and supply or pricing structure.

The third essay (Chapter 4) proposes a new practical application of the stochastic dual dynamic programming (SDDP) algorithm that considers uncertainties in the electricity market, such as electricity prices, residential photovoltaic (PV) generation, and loads. The SDDP model optimizes the scheduling of battery storage usage for sequential decision-making over a planning horizon by considering predicted uncertainty scenarios and their associated probabilities. After examining the benefits of shared battery storage in housing companies, the results show that the SDDP model improves the average objective function values (i.e., costs) by approximately 32% compared to a model without it. The results also indicate that the mean objective function values at the end of the first stage of the proposed SDDP model with battery storage and the deterministic LP model equivalent (with perfect foresight) with battery storage differ by less than 30%.

The models and insights developed in this dissertation are valuable for facilitating energy policy-making in a rapidly evolving industry. Furthermore, these contributions can advance computational techniques, encourage the use and development of renewable energy sources, and increase public education on energy efficiency and environmental awareness.