Understanding price functions to control domestic electric water heaters for demand response

A well-known mechanism for demand response is sending price signals to customers a day ahead. Customers then postpone or advance their usage of electricity to minimize cost. Setting up price functions that adapt the customers' load to availability is a big challenge. This paper investigates the feasibility of finding day-ahead price functions to induce a desired load profile of domestic electric water heaters (DEWHs) minimizing their electricity cost for demand response. Bilevel optimization is applied for a single DEWH using a simplified linear model and full knowledge. This leads to a solvable bilevel problem and allows understanding optimality of price functions and resulting heating profiles. It is shown that with the resulting price functions the DEWH may select many significantly different heating profiles leading to the same cost. Thus the price does not uniquely induce the desired heating profile. The acquired knowledge forms the basis for a procedure to create price functions for controlling the load profile of many DEWHs.