Analysis of Frequency and Voltage Strength in Power Electronics-Dominated Power Systems Based on Eigen-subsystems

The large-scale integration of inverter-based resources (IBRs) has deteriorated the frequency/voltage (F/V) responses of power systems, leading to a higher risk of instability. Consequently, evaluating the F/V strength has become an important task in power electronics (PE)-dominated power systems. Existing methods typically examine F/V strength separately, employing fundamentally different metrics, such as inertia (focusing on device dynamics) and short-circuit ratio (SCR, addressing network characteristics). These fragmented approaches have resulted in a lack of comprehensive understanding of the overall system strength, potentially overlooking critical aspects. To address this problem, this paper proposes a unified framework for analyzing F/V strength. First, a unified modeling of F/V regulations is introduced. Then, based on modal decoupling, the power systems are decomposed into several eigen-subsystems, where the F/V responses are both decomposed into common-mode (CM) and differential-mode (DM) components, namely, CM-F, DM-F, CM-V, and DM-V. The CM-F and CM-V represent the collective response of all devices to external active or reactive power disturbances, independent of the power network characteristics. In contrast, the DM-F and DM-V capture the redistribution of disturbance power within the system, which is strongly influenced by the network topology and the locations of devices. Notably, traditional strength analysis generally ignores the CM-V (global voltage response), which, as discovered in this paper, may also become unstable in PE-dominated power systems. Based on the proposed framework, new metrics are proposed to evaluate the strength of each modal component. Finally, the effectiveness of the proposed approach is validated through simulations.

💡 Research Summary

The paper addresses the growing concern that large‑scale integration of inverter‑based resources (IBRs) weakens both frequency and voltage (F/V) responses of modern power systems, increasing the risk of instability. Existing approaches treat frequency strength (typically characterized by inertia, damping, and droop gains) and voltage strength (usually quantified by short‑circuit ratio, SCR, and its extensions) as separate problems, using fundamentally different metrics. This fragmented view obscures a unified understanding of overall system strength, especially in power‑electronics‑dominated grids where the two phenomena interact.

To bridge this gap, the authors first propose a unified modeling framework that represents the frequency‑control loop (P‑θ) and the voltage‑control loop (Q‑V) of any grid‑connected device with a simple inertia‑damper‑spring analogy. In this representation, the device’s active‑power‑frequency dynamics are captured by an equivalent inertia (J), damping (D), and stiffness (K_P); the reactive‑power‑voltage dynamics are captured by a damping term (D_{QV}) and a stiffness term (K_{QV}). By scaling these nominal dynamics with relative support capacities (S_\theta) (frequency) and (S_V) (voltage), all devices can be expressed with the same transfer‑function structure, greatly simplifying system‑level analysis.

The power network is linearized around an operating point, yielding the classic Jacobian matrices (L) (active‑power‑angle) and (N) (reactive‑power‑voltage). The authors note that both (L) and (N) have a zero eigenvalue associated with the eigenvector of all ones, reflecting the invariance of total power flow under a uniform angle shift. By moving the steady‑state power matrices ((2P_e) and (2Q_e)) to the device side, the authors obtain symmetric expressions for frequency and voltage, enabling a unified treatment.

Next, the closed‑loop system equations are combined, and, under the reasonable assumption that cross‑coupling terms (H_{PV}(s)) and (H_{Q\theta}(s)) are small, the frequency and voltage dynamics are decoupled. The resulting simplified relations are:

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