Learning-Augmented Primal-Dual Control Design for Secondary Frequency Regulation

Abstract

Frequency stability is fundamental to the secure operation of power systems. With growing uncertainty and volatility introduced by renewable generation, secondary frequency regulation must now deliver enhanced performance not only in the steady state but also during transients. This paper presents a systematic framework to embed learning in the design of a primal-dual controller that provides provable (potentially exponential) stability and steady-state optimality, while simultaneously improving key transient metrics, including frequency nadir and control effort, in a data-driven manner. In particular, we employ the primal-dual dynamics of an optimization problem that encodes steady-state objectives to realize secondary frequency control with asymptotic stability guarantee. To augment transient performance of the controller via learning, a change of variables on control inputs, which will be deployed by neural networks, is proposed such that under mild conditions, stability and steady-state optimality are preserved. It further allows us to define a learning goal that accounts for the exponential convergence rate, frequency nadir and accumulated control effort, and use sample trajectories to enhance these metrics. Simulation results validate the theories and demonstrate superior transient performance of the learning-augmented primal-dual controller.