Adaptive Flexibility Function in Smart Energy Systems: A Linearized Price-Demand Mapping Approach

The transactive control paradigm enables a flexible electricity-consuming asset to offer its flexibility upstream by simply adapting its consumption profile in response to pricing signals. A consumer's response to prices over time is modeled through a so-termed flexibility function. However, a consumer's flexibility function needs to be adaptive to account for changes to the consumer's internal dynamics over time. This paper proposes an adaptive mechanism for price signal generation using a piecewise linear approximation of a flexibility function with unknown parameters. In this adaptive approach, the price signal is parameterized and the parameters are changed adaptively such that the output of the flexibility function follows a reference demand signal. This is guaranteed using the Lyapunov stability theorem. The proposed method does not require an estimation algorithm for unknown parameters, which eliminates the need for persistency of excitation of signals, and consequently, simplifies practical adoption and deployment.