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.

In modern power systems, the randomness and uncertainty of the generation and loads greatly increase the balance discrepancy between the power supply and demand, which introduces major potential security hazards to the stable operation of power systems. In particular, out-of-bounds frequencies emerge. To control the system frequencies, a frequency control method based on the state space model for power systems under small, uncertain disturbances is proposed in this paper. Considering the general model of the power system frequency response with the aim of improving the input‒output finite-time stability of the system, the frequency deviation of the power system is controlled in a closed loop. The Monte Carlo simulation of different systems shows that the proposed method can effectively control the frequency deviation of the power system. When the closed-loop system is disturbed by uncertain power fluctuations, its frequency will always remain within the allowable range to ensure the secure and stable operation of the power system.

In modern power systems, the impact of random power sources and loads on power systems is increasing, resulting in threatened system frequency security. However, traditional methods are often not comprehensive in modelling randomness, and there is no analytical method to assess the frequency response of power systems under uncertain power disturbances. In this paper, the power disturbance in a power system is regarded as an interval random quantity. Based on a general model of the system frequency response (SFR-G) and the theory of stochastic processes, an analytical prediction method of the power system frequency deviation under uncertain power disturbance is proposed. Through further deduction, the allowable range of power disturbance under the premise of secure frequency deviation can also be defined, which provides a reference for frequency security and accident prevention in power systems. Numerical simulations demonstrate that the proposed analytical method can delimit the response interval of system frequency deviation well, and the backstepping calculation can also delimit the allowable range of power disturbance to ensure the secure operation of the system.