Deep Koopman Controller Synthesis for Cyber-Resilient Market-Based Frequency Regulation

Abstract

This paper investigates a data-driven countermeasure for price spoofing in the context of cyber security and market-based frequency regulation. Market-based control of transmission power networks relies on cyber-physical infrastructure, which raises questions of system vulnerability in relation to cyber-security. In this paper, we consider the challenge of engineering a robust data-driven controller in the presence of price spoofing, i.e. where hacking mechanisms adjust price signals in an ex-post market. We extend a recently developed algorithm called deep dynamic mode decomposition to learn Koopman operators of nonlinear systems with affine inputs. Based on the learned input-Koopman operator model, a design algorithm for nonlinear controller synthesis is devised to compute optimal dynamic pricing policies that restore the nominal frequency and recover economic efficiency in the presence of price spoofing. The efficacy of the proposed data-driven Koopman controller synthesis approach is validated through tests on a IEEE 39-bus benchmark.