Pricing Demand-Side Flexibility With Noisy Consumers: Mean-Variance Trade-Offs

We formulate and analyze a demand-side management framework in which an aggregator sets energy prices to flexible consumers who have a noisy demand. The aggregator strategizes between purchasing energy in the day-ahead market, and settling any possible mismatches due to demand variability in the real-time market. Because consumers are sensitive to volatility in their electricity bill, the aggregator sets an upper bound on the variance of the payments made by consumers. We derive the optimal strategies for the consumers and the aggregator in this problem, and show that the aggregator limits dynamic pricing for consumers with too large demand variance, so as to avoid large uncertainty in their payments. On the other hand, consumers with low enough demand variance are charged the same price that would emerge in a noise-free formulation. We also identify two instances of a mean-variance trade-off: one in the consumer payment, which can be made less uncertain at the expense of a higher mean value, and another one in the aggregator’s utility, which becomes less uncertain and lower on average as the consumer payment variance constraints become binding. We corroborate our analysis with a numerical case study.