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This paper proposes an adaptive mechanism for price signal generation using apiecewise linear approximation of a flexibility function with unknownparameters. In this adaptive approach, the price signal is parameterized andthe parameters are changed adaptively such that the output of the flexibilityfunction follows the reference demand signal provided by the involvedaggregator. This is guaranteed using the Lyapunov stability theorem. Theproposed method does not require an estimation algorithm for unknownparameters, that eliminates the need for persistency of excitation of signals,and consequently, simplifies offering the flexibility services. Furthermore,boundedness of the price signal is ensured using a projection algorithm in theadaptive system. We present simulation results that demonstrate the pricegeneration results using the proposed approaches.

Adaptive flexibility function in smart energy systems: A linearized price-demand mapping approach