## Coordination of Resources Across Areas for the Integration of Renewable Generation: Operation, Sizing, and Siting of Storage Devices

An increased penetration of renewable energy into the electric power grid is desirable from an environmental standpoint as well as an economical one. However, renewable sources such as wind and solar energy are often variable and intermittent, and additionally, are non-dispatchable. Also, the locations with the highest amount of available wind or solar may be located in areas that are far from areas with high levels of demand, and these areas may be under the control of separate, individual entities. In this dissertation, a method that coordinates these areas, accounts for the variability and intermittency, reduces the impact of renewable energy forecast errors, and increases the overall social benefit in the system is developed. The approach for the purpose of integrating intermittent energy sources into the electric power grid is considered from both the planning and operations stages. In the planning stage, two-stage stochastic optimization is employed to find the optimal size and location for a storage device in a transmission system with the goal of reducing generation costs, increasing the penetration of wind energy, alleviating line congestions, and decreasing the impact of errors in wind forecasts. The size of this problem grows dramatically with respect to the number of variables and constraints considered. Thus, a scenario reduction approach is developed which makes this stochastic problem computationally feasible. This scenario reduction technique is derived from observations about the relationship between the variance of locational marginal prices corresponding to the power balance equations and the optimal storage size. Additionally, a probabilistic, or chance, constrained model predictive control (MPC) problem is formulated to take into account wind forecast errors in the optimal storage sizing problem. A probability distribution of wind forecast errors is formed and incorporated into the original storage sizing problem. An analytical form of this constraint is derived to directly solve the optimization problem without having to use Monte-Carlo simulations or other techniques that sample the probability distribution of forecast errors. In the operations stage, a MPC AC Optimal Power Flow problem is decomposed with respect to physical control areas. Each area performs an independent optimization and variable values on the border buses between areas are exchanged at each Newton-Raphson iteration. Two modifications to the Approximate Newton Directions (AND) method are presented and used to solve the distributed MPC optimization problem, both with the intention of improving the original AND method by improving upon the convergence rate. Methods are developed to account for numerical difficulties encountered by these formula- tions, specifically with regards to Jacobian singularities introduced due to the intertemporal constraints. Simulation results show convergence of the decomposed optimization problem to the centralized result, demonstrating the benefits of coordinating control areas in the IEEE 57- bus test system. The benefit of energy storage in MPC formulations is also demonstrated in the simulations, reducing the impact of the fluctuations in the power supply introduced by intermittent sources by coordinating resources across control areas. An overall reduction of generation costs and increase in renewable penetration in the system is observed, with promising results to effectively and efficiently integrate renewable resources into the electric power grid on a large scale.