Frequency Shaping Control for Oscillation Damping in Weakly-Connected Power Network: A Root Locus Method

TL;DR

This paper introduces a root locus-based method for frequency shaping control in weak power grids, enabling simultaneous frequency security and inter-area oscillation damping through systematic tuning rules.

Contribution

It develops a systematic, root locus-based analysis and tuning guidelines for frequency shaping control that improve oscillation damping and frequency response in weak power networks.

Findings

Proposes closed-form expressions for damping ratio and decay rate of inter-area oscillations.

Provides simple tuning guidelines for frequency shaping control.

Demonstrates FS's superiority over virtual inertia in simulations.

Abstract

Frequency control following a contingency event is of vital concern in power system operations. Leveraging inverter-based resources, it is not hard to shape the center of inertia (COI) frequency nicely. However, under weak grid conditions, it becomes insufficient to solely shape the COI frequency since this aggregate signal fails to reveal the inter-area oscillations. In this manuscript, we advocate for foolproof fine-tuning rules for \emph{frequency shaping control} (FS) based on a systematic analysis of damping ratio and decay rate of inter-area oscillations to simultaneously meet specified metrics for frequency security and oscillatory stability. To this end, building on a modal decomposition, we simplify the oscillation damping problem into a pole-placement task for a set of scalar subsystems, which can be efficiently solved by only investigating the root locus of a scalar subsystem associated with the main mode, while FS inherently guarantees a Nadir-less COI frequency response. Through our proposed root-locus-based oscillatory stability analysis, we derive closed-form expressions for the minimum damping ratio and decay rate among inter-area oscillations in terms of networked system and control parameters under FS. Moreover, we propose useful tuning guidelines for FS which need only simple calculations or visualized tuning to not only shape the COI frequency into a first-order response that converges to a steady-state value within the allowed range but also ensure a satisfactory damping ratio and decay rate of inter-area oscillations following disturbances. As for the common virtual inertia control (VI), although similar oscillatory stability analysis becomes intractable, one can still glean some insights via the root locus method. Numerical simulations validate the proposed tuning for FS as well as the superiority of FS over VI in exponential convergence rate.