The increasing penetration of inverter-based resources (IBRs) in power systems has raised many concerns in terms of frequency stability. However, prior art analytical models for system frequency generally cannot precisely account for the impact of voltage dynamics, leading to potentially incorrect results. The main challenge lies in understanding system frequency in the case of non-constant bus voltages, and integrating the voltage dynamics of generation devices at different bus locations into the system frequency model. To address this issue, this article defines the voltage-influenced common-mode frequency (VCMF), serving as a system frequency analysis model considering voltage dynamics. The VCMF is derived through the decomposition of bus frequency responses, leveraging the connection between the consistent part of bus frequencies and the rotational invariance of power flow. The decomposition process introduces voltage dynamics into the system frequency response, represented as a global term that interconnects all devices through the power network. To address the complexity of this global term, an algebraic graph theory-based network partitioning method is introduced. This method effectively divides the globally coupled term into several locally coupled components, making the analysis of the VCMF more manageable. Finally, simulations are provided to validate the proposed methods.

Inertia assessment is an important step for frequency stability analysis in power systems. Typically, the total inertia of all devices in the system is summed up to obtain the system inertia. However, such method may be optimistic when there are a considerable number of converter-interfaced generations (CIGs). Particularly, if the CIGs saturate under large disturbances, their inertia to be provided will be significantly reduced. To this end, this letter proposes a method to assess the system inertia considering the power limits. Then, the distribution of system inertia under uncertain power limits is also analyzed. Simulations are conducted to validate the analysis.

As synchronous generators (SGs) are extensively replaced by converter-based generators (CBGs), modern power systems are facing complicated frequency stability problems. Conventionally, the frequency nadir and the rate of change of frequency (RoCoF) are the two main factors concerned by power system operators. However, these two factors heavily rely on simulations or experiments, especially in a power system with high-penetration CBGs, which offer limited theoretical insight into how the frequency response characteristics are affected by the devices. This paper aims at filling this gap. Firstly, we derive a formulation of the global frequency for a CBG-integrated power system, referred to as common-mode frequency (CMF). The derived CMF is demonstrated to be more accurate than existing frequency definitions, e.g., the average system frequency (ASF). Then, a unified transfer function structure (UTFS) is proposed to approximate the frequency responses of different types of devices by focusing on three key parameters, which dramatically reduces the complexity of frequency analysis. On this basis, we introduce two evaluation indices, i.e., frequency drop depth coefficient (FDDC) and frequency drop slope coefficient (FDSC), to theoretically quantify the frequency nadir and the average RoCoF, respectively. Instead of relying on simulations or experiments, our method rigorously links the system’s frequency characteristics to the characteristics of heterogeneous devices, which enables an in-depth understanding regarding how devices affect the system frequency. Finally, the proposed indices are verified through simulations on a modified IEEE 39-bus test system.