Integrating renewable energy into the power grid is challenging due to the intermittent, variable, and non-dispatchable characteristics of renewable energy generation. From behind-the-meter (BTM) to transmission settings, this thesis employs stochastic optimization methods to account for uncertainty in renewable energy generation and addresses computational challenges of including grid-connected energy storage systems (ESSs) models in optimization problems.
For a BTM setting, a stochastic model predictive control (MPC)-based residential energy management system (EMS) algorithm is proposed to optimally coordinate residential electricity usage, controllable appliances, and customer-owned energy sources (e.g., rooftop photovoltaic (PV) panels and an ESS). Instead of computationally limiting sampling-based stochastic optimization approaches, chance constraints are used to ensure both a demand response (DR) event and indoor thermal comfort are satisfied with a high probability given uncertainty in PV generation and weather forecasts. Case study results highlight the residential EMS algorithm performance from both customer and utility perspectives.
For large-scale wind power integration in a transmission setting, a two-stage stochastic flexible line capacity rating algorithm is proposed to determine economic conventional generator dispatch while minimizing the amount of curtailed wind power across probable wind power generation scenarios. Flexible line ratings are incorporated into the model using a sample average approximation of an integer chance constraint, limiting the probability of non-nominal line capacity rating violations. Case study results demonstrate the flexible line capacity rating algorithm can reduce total average wind power curtailment by 40\% compared to the static line rating case.
From BTM to transmission settings, grid-connected ESSs are often coupled with renewable energy sources in optimization models for many applications in power systems. Theoretical analysis is provided that guarantees a relaxed convex ESS model will produce a physically realizable optimal control strategy with non-simultaneous ESS charging and discharging. The relaxed convex ESS model omits the non-convex complementarity constraint that explicitly ensures non-simultaneous ESS charging and discharging, avoiding computationally limiting non-convex or mixed-integer optimization solvers. Case studies with the relaxed convex ESS model show the optimal solutions satisfy the omitted complementarity constraint, result in significantly faster computation times, and the penalty-based approach has a negligible impact on the optimal solution.</p
