Mazen Elsaadany

Mazen Elsaadany, Mads R. Almassalkhi

Aggregated battery energy storage systems (BESS) enable large fleets of heterogeneous battery elements to participate in system-level optimization and electricity markets. Scheduling each element independently is computationally impractical at scale. While many aggregate battery models rely on convex relaxations, they often ignore element complementarity constraints, leading to dispatch solutions that may be infeasible when implemented on individual battery elements. This paper develops a realizable composite battery model for parameter-heterogeneous BESS fleets that guarantees feasibility at the element-level while preserving computational tractability. We derive simple linear conditions under which aggregate charging and discharging trajectories can be safely disaggregated while respecting individual power limits, energy limits, and complementarity constraints under a priority-based controller. Numerical experiments in a unit-commitment setting demonstrate that the proposed realizable composite battery formulation produces feasible dispatch solutions. Solve times are effectively independent of system size, unlike micro-model mixed-integer formulations. Solutions obtained from the proposed formulation converge to the optimal benchmark as control granularity is refined. Additional studies illustrate the robustness of the framework to moderate violations of key modeling assumptions, including heterogeneous power-to-energy ratios.

Mazen Elsaadany, Hamid R. Ossareh, Mads R. Almassalkhi

Aggregations of thermostatically controlled loads (TCLs), such as air conditioners, offer valuable flexibility to the power grid. The aggregate power consumption of a TCL fleet can be controlled by adjusting thermostat setpoints. An \textit{ex-ante} quantification of the flexibility that results from such setpoint change can inform grid operator decisions. This paper develops a rigorous, yet practical method to quantify flexibility in terms of the `reach-and-hold' set of TCL aggregations, which defines how much power can be shifted (reach) and for how long (hold). To quantify the reach-and-hold set, we employ a Markov-chain-based model of the TCL aggregation that captures second-order TCL dynamics, enabling accurate characterization of reach-and-hold sets. A tractable optimization problem is then formulated to numerically compute an inner approximation of these sets. Simulation results validate that our method accurately characterizes the fleet's flexibility and effectively controls its power consumption. Furthermore, a robustness analysis is carried out to investigate the effects of uncertainty in initial conditions and TCL parameters.