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

TL;DR

This paper addresses damping inter-area oscillations in weakly-connected, high-renewable power networks by extending COI-based frequency shaping with a root-locus based pole-placement framework. It reduces the oscillation damping problem to the analysis of a scalar subsystem through modal decomposition and derives closed-form expressions for the minimum damping ratio and decay rate under FS, linking these metrics to network eigenvalues. The authors provide foolproof FS tuning guidelines that simultaneously achieve COI Nadir elimination and specified oscillatory stability, and demonstrate through WSCC-like simulations that FS outperforms virtual inertia in both convergence speed and control effort. The work offers a practical, visualization-assisted approach that exposes the influence of the network spectrum on oscillatory performance and enables robust, scalable tuning for inverter-based control in weak grids.

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.

Figures (15)

• Figure 1: Block diagram of power network.
• Figure 2: Diagram of $9$-bus $3$-generator WSCC test case.
• Figure 3: Frequency deviations of the WSCC system without inverters when a $-0.2\pu$ step power change is introduced to bus $1$.
• Figure 4: Frequency deviations of the WSCC system under VI and FS control with Nadir elimination tuning when a $-0.2\pu$ step power change is introduced to bus $1$.
• Figure 5: Region $\mathcal{S}_{\alpha,\psi}$.

Theorems & Definitions (14)

• Definition 1: $(\alpha, \psi)$-stability
• Theorem 1: Poles of $\hat{z}_{k}(s)$ residing on root locus of $\mathcal{F}(\hat{z}_{1}(s)/s,\lambda)$
• proof
• Lemma 1: Root locus associated with $\hat{L}_{\mathrm{fs}}(s)$
• proof
• Theorem 2: Minimum damping ratio and decay rate under FS
• proof
• Proposition 1: Frequency convergence rate under FS
• proof
• Remark 1: Discrepancy between pole-specific and system-level damping ratios in second-order systems