Datong P. Zhou

Datong P. Zhou, Mardavij Roozbehani, Munther A. Dahleh et al.

This paper analyzes stability conditions for wholesale electricity markets under real-time retail pricing and realistic consumption models with memory, which explicitly take into account previous electricity prices and consumption levels. By passing on the current retail price of electricity from supplier to consumer and feeding the observed consumption back to the supplier, a closed-loop dynamical system for electricity prices and consumption arises whose stability is to be investigated. Under mild assumptions on the generation cost of electricity and consumers' backlog disutility functions, we show that, for consumer models with price memory only, market stability is achieved if the ratio between the consumers' marginal backlog disutility and the suppliers' marginal cost of supply remains below a fixed threshold. Further, consumer models with price and consumption memory can result in greater stability regions and faster convergence to the equilibrium compared to models with price memory alone, if consumption deviations from nominal demand are adequately penalized.

Datong P. Zhou, Munther A. Dahleh, Claire J. Tomlin

Load-serving entities which procure electricity from the wholesale electricity market to service end-users face significant quantity and price risks due to the volatile nature of electricity demand and quasi-fixed residential tariffs at which electricity is sold. This paper investigates strategies for load serving entities to hedge against such price risks. Specifically, we compute profit-maximizing portfolios of forward contract and call options as a function of the uncertain aggregate user demand. We compare the profit to the case of Demand Response, where users are offered monetary incentives to temporarily reduce their consumption during periods of supply shortages. Using smart meter data of residential customers in California, we simulate optimal portfolios and derive conditions under which Demand Response outperforms call options and forward contracts.

Datong P. Zhou, Maximilian Balandat, Claire J. Tomlin

We evaluate the causal effect of hour-ahead price interventions on the reduction in residential electricity consumption using a data set from a large-scale experiment on 7,000 households in California. By estimating user-level counterfactuals using time-series prediction, we estimate an average treatment effect of ~0.10 kWh (11%) per intervention and household. Next, we leverage causal decision trees to detect treatment effect heterogeneity across users by incorporating census data. These decision trees depart from classification and regression trees, as we intend to estimate a causal effect between treated and control units rather than perform outcome regression. We compare the performance of causal decision trees with a simpler, yet more inaccurate k-means clustering approach that naively detects heterogeneity in the feature space, confirming the superiority of causal decision trees. Lastly, we comment on how our methods to detect heterogeneity can be used for targeting households to improve cost efficiency.

Datong P. Zhou, Claire J. Tomlin

We study the multi-armed bandit problem with multiple plays and a budget constraint for both the stochastic and the adversarial setting. At each round, exactly $K$ out of $N$ possible arms have to be played (with $1\leq K \leq N$). In addition to observing the individual rewards for each arm played, the player also learns a vector of costs which has to be covered with an a-priori defined budget $B$. The game ends when the sum of current costs associated with the played arms exceeds the remaining budget. Firstly, we analyze this setting for the stochastic case, for which we assume each arm to have an underlying cost and reward distribution with support $[c_{\min}, 1]$ and $[0, 1]$, respectively. We derive an Upper Confidence Bound (UCB) algorithm which achieves $O(NK^4 \log B)$ regret. Secondly, for the adversarial case in which the entire sequence of rewards and costs is fixed in advance, we derive an upper bound on the regret of order $O(\sqrt{NB\log(N/K)})$ utilizing an extension of the well-known $\texttt{Exp3}$ algorithm. We also provide upper bounds that hold with high probability and a lower bound of order $Ω((1 - K/N)^2 \sqrt{NB/K})$.