<p>As
synchronous generators (SGs)
are extensively replaced by inverter-based
generators (IBGs), 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 IBGs, 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
an IBG-penetrated 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<a>,
which dramatically reduces the complexity of frequency analysis. </a>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. </p>