Conic-sector-based analysis and control synthesis for linear parameter varying systems

TL;DR

This paper extends the conic sector theorem to LPV systems that are conic on average, enabling less conservative control design and improved stability in systems like power grids with renewable energy.

Contribution

It introduces an average conic sector theorem for LPV systems and develops conic controllers that operate effectively in nonconic parameter regions.

Findings

Successfully stabilizes a power grid with high renewable penetration

Reduces conservativeness compared to traditional conic controllers

Demonstrates effectiveness through simulation results

Abstract

We present a conic sector theorem for linear parameter varying (LPV) systems in which the traditional definition of conicity is violated for certain values of the parameter. We show that such LPV systems can be defined to be conic in an average sense if the parameter trajectories are restricted so that the system operates with such values of the parameter sufficiently rarely. We then show that such an average definition of conicity is useful in analyzing the stability of the system when it is connected in feedback with a conic system with appropriate conic properties. This can be regarded as an extension of the classical conic sector theorem. Based on this modified conic sector theorem, we design conic controllers that allow the closed-loop system to operate in nonconic parameter regions for brief periods of time. Due to this extra degree of freedom, these controllers lead to less conservative performance than traditional designs, in which the controller parameters are chosen based on the largest cone that the plant dynamics are contained in. We demonstrate the effectiveness of the proposed design in stabilizing a power grid with very high penetration of renewable energy while minimizing power transmission losses.