Many energy-related problems are dynamic in nature with uncertain parameters, e.g., multi-period power generation and distribution control with uncertain demand in future periods. The focus of this project is on designing smart power grids that are robust to uncertainty in energy demand, and efficiently controlling these grids in a decentralized manner while respecting data privacy requirements of each grid node. To achieve these goals, the principal investigator will develop distributed computational methods that leverage existing grid hardware capable of only simple local computation and communication with neighboring devices. With the help of distributed methods, the grid will operate as a decentralized system exploiting computational resources, e.g., smart-meters and smart-thermostats, to optimize power flow throughout the network. These goals will be realized more economically as compared to traditional central computing infrastructure that is expensive and lacks scalability. The research will contribute to reliable, robust, and privacy-enabled operation of a stable grid through the development of scalable computational tools for optimization. This research has multi-disciplinary nature: requiring techniques from optimization theory, computational mathematics, and electrical engineering. The PI will engage in this research undergraduate and graduate students from underrepresented groups in engineering and mathematics.
The PI will investigate the optimal placement of capacitor banks on the distribution system to make it robust to changes in the uncertain load-profile by formulating the underlying problem as a (distributionally) robust offline optimization problem. Next, given the locations of capacitor banks and a short-term demand forecast engine, the PI will consider the optimal reactive power injection from capacitor banks into the grid to minimize the generation cost. This is a large-scale dynamic problem, and can be addressed through distributed optimization algorithms that will regulate power generation and distribution while respecting privacy, and contending with dynamic uncertain load. Moreover, to account for errors in demand forecasts, a decentralized sample average approximation scheme will be developed. Due to communication, memory, and computational overhead, these distributed optimization methods are practically limited to use first-order information only. Exploiting the specific structure in optimal power flow problems, the research is expected to make contributions to the development of new first-order primal-dual methods to solve consensus optimization problems over a network of computing nodes when there are node-specific private constraints. If successful, this project will result in the creation of new mathematical models, analyses, and algorithms for decision-making related to energy production and distribution.
