Fundamental limitations on the control of lossless systems

TL;DR

This paper establishes fundamental limits on the control performance of lossless systems, highlighting how these constraints impact power systems with renewable integration and emphasizing the need for innovative control strategies.

Contribution

It derives theoretical bounds on $H_2$ and $H_ fty$ performance for lossless systems and applies these to power systems, revealing how performance scales with system parameters.

Findings

Performance limits scale inversely with harmonic mean of inertias

Power system performance degrades with increased renewable integration

Fundamental control constraints motivate new control solutions

Abstract

In this paper we derive fundamental limitations on the levels of $H_2$ and $H_\infty{}$ performance that can be achieved when controlling lossless systems. The results are applied to the swing equation power system model, where it is shown that the fundamental limit on the $H_2$ norm scales with the inverse of the harmonic mean of the inertias in the system. This indicates that power systems may see a degradation in performance as more renewables are integrated, further motivating the need for new control solutions to aid the energy transition.