(125c) Demand Response Aggregation Under Customer Response Uncertainty

Demand response (DR), where electricity consumers adjust their consumption profiles in response to price signals from the electricity market, is considered a crucial strategy for maintaining a stable power grid and achieving a sustainable energy system with net-zero carbon emissions [1]. In the context of DR, smaller loads are often combined such they can collectively participate in the wholesale electricity market. This aggregation of DR resources is typically coordinated by DR aggregators that serve as intermediaries between the electricity consumers and the market or grid operator.

In this work, we take the perspective of a DR aggregator that operates in the ancillary services market to provide interruptible load to the grid using their customers' aggregated load. Interruptible load refers to load reduction capacity that the grid operator can call upon during contingency events when power demand exceeds supply in the grid [2]. In such an event, electricity consumers providing interruptible load can be requested to reduce their load up to an agreed maximum amount. Here, the DR aggregator decides how much interruptible load to sell to the market while ensuring that this required load reduction can be provided by their customers, i.e. the electricity consumers, when requested. A major challenge is due to the fact that the DR aggregator typically cannot force their customers to reduce their load but instead needs to offer a payment to incentivize load reduction. However, while the likelihood of a customer accepting the payment and performing the corresponding load reduction increases with the offered price, we do not know in advance how high this price has to be [3, 4].

We address this problem of DR aggregation under customer response uncertainty, where the amount of load reduction that each customer is willing to provide is an uncertain parameter, using a robust optimization approach. The uncertainty set is decision-dependent as it changes as a function of the price offered by the DR aggregator; the resulting robust optimization problem is known to be very difficult to solve [5]. However, it turns out that in this case, the uncertainty set has a specific structure that can be exploited. Specifically, it allows us to develop a tailored column-and-constraint generation algorithm that involves the generation of cuts parametrized by the decisions affecting the uncertainty. Each cut represents a possible realization of the uncertainty, which in turn corresponds to a vertex of the polyhedral uncertainty set; hence, we can parametrize it using the set of active constraints at that vertex. Results from our computational experiments show that the proposed algorithm significantly outperforms the traditional reformulation method [6] in larger instances. In our case study, we also demonstrate the advantage of the robust optimization approach over a deterministic approach that ignores the uncertainty in an out-of-sample analysis.

References

1. IEA. Tracking clean energy progress 2023. Technical report, International Energy Agency, 2023. URL https://www.iea.org/energy-system/energy-efficiency-and-demand/demand-r….

2. Jnana Sai Jagana, Satyajith Amaran, and Qi Zhang. Multistage robust mixed-integer optimization for industrial demand response with interruptible load. Computers & Chemical Engineering, 194:108974, 2025.

3. Xiaoxing Lu, Xinxin Ge, Kangping Li, Fei Wang, Hongtao Shen, Peng Tao, Junjie Hu, Jingang Lai, Zhao Zhen, Miadreza Shafie-khah, et al. Optimal bidding strategy of demand response aggregator based on customers’ responsiveness behaviors modeling under different incentives. IEEE Transactions on Industry Applications, 57(4):3329–3340, 2021.

4. Fei Wang, Xinxin Ge, Peng Yang, Kangping Li, Zengqiang Mi, Pierluigi Siano, and Neven Dui´c. Day-ahead optimal bidding and scheduling strategies for der aggregator considering responsive uncertainty under real-time pricing. Energy, 213:118765, 2020.

5. Nikolaos H Lappas and Chrysanthos E Gounaris. Robust optimization for decision-making under endogenous uncertainty. Computers & Chemical Engineering, 111:252–266, 2018.

6. Qi Zhang and Wei Feng. A unified framework for adjustable robust optimization with endogenous uncertainty. AIChe journal, 66(12):e17047, 2020.