## 3 Demand-Response Aggregator Frameworks in Future US Electricity Markets
### Uncertainty in Prosumer-Aggregator Game-Theoretic Frameworks  
A DR aggregator and prosumer framework can face several uncertainties depending on the level of implementation details. Some of the most common ones are clearing market price uncertainty, prosumer total and per-device demand uncertainty, and prosumer generation uncertainty [218]. In order to manage uncertainty in modeling, robust, stochastic, or RL-based approaches are usually proposed. In this paper [219], a robust optimization framework for DR aggregators in the DAM and RT markets was proposed, which takes into consideration prosumer demand uncertainty by forecasting the customer's baseline load. Their method includes a single optimization problem (no competition) where the DR aggregator makes all the decisions for the prosumers who have battery devices and shiftable and reducible loads, therefore allowing a degree of flexibility in the prosumers' device scheduling; however, this compromises prosumer privacy since the DR aggregator schedules all prosumer devices centrally, while solution scalability is not addressed. Robust optimization methods for DR aggregators have also been proposed within a game-theoretic context for the DAM [220], modeling the competition between DR aggregators as a Nash game but ignoring the competition with the prosumers. The main uncertainty considered is the market-clearing price, and hence, uncertainty sets are constructed. Since there are no explicit prosumer optimization problems, prosumer flexibility is not applicable, while privacy is not guaranteed if the DR aggregator is aware of some prosumer demand forecast. Scalability is not addressed theoretically or experimentally. Distributionally robust Stackelberg games have been proposed for the competition between DSO and DR aggregators, with some level of prosumer load type detail [221] provided specifically for HVAC and solar panels, which are part of the DR aggregator's model (no privacy). Uncertainties include renewable supply and outdoor temperatures that are distributions within this framework. Utilizing an MILP reformulation, the authors turn this into a tractable problem for a 33-bus system, but no larger simulations were performed to evaluate the scalability further. Lastly, another distributionally robust approach [222] proposed a robust Stackelberg game to model the competition between a microgrid operator (conceptually close to a DR aggregator) that includes battery systems. The microgrid operator competes with the prosumers (some level of flexibility due to load breakdown and EV battery), while the overall uncertainties are around market prices, uncontrollable load demand, and solar generation from each prosumer. The program generated is a MINLP, which is simplified after some linearizations and solved iteratively to protect prosumer privacy. Some examples in Bayesian or stochastic games for DR aggregators are found in the literature. These approaches assume that Bayesian or stochastic (distribution) uncertainties are present, with solutions optimized on average instead of the worst-case scenario (robust approaches), and they can be used when expected cost savings or performance is more important than guarding against extremes (risk level can be adjusted with CVaR). The DR aggregator game under demand uncertainty has been approached in [223] using Bayesian Stackelberg game theory, modeling only the game between multiple DR aggregators and ignoring the game between the prosumer and the DR aggregator (no competition). It is assumed that the DR aggregator has full control over the prosumer's load, with the customer's probability of opting out modeled (no privacy). An example of a stochastic game for the DR aggregator for the interested reader can be found in the context of microgrids participating in DR with DSO [224], solved by introducing the lower level KKT constraints to the upper level program, an approach that can lead to issues with privacy and scalability.