Inertia in Power Systems
1. Definition: Kinetic energy stored in the rotational masses of generators and motors synchronously connected to a power system.
2. Inertial Response: The kinetic energy is exchanged with the power systems (either released or absorbed) whenever there is an instantaneous imbalance between generation and load.
The rotational inertia/kinetic energy (KE) and inertia constant (H) are given by,
J is the moment of inertia in kg.m2
ω = 2πf = angular frequency in rad/s.
f is the nominal frequency in Hz.
Sn is nominal apparent power of the machine in VA.
H is the inertia constant in s.
KE is the rotational inertia/kinetic energy in MWs.
3. Relation between Inertia and System Frequency
When load > generation, kinetic energy from inertia supplies the energy deficit, but the rotating machine slow down, i.e., system frequency declines.
When generation > load, the excess generation is converted to kinetic energy and the rotating machine speed-up, i.e., system frequency rises.
When generation = load, there is no inertial exchange and system frequency is stable.
The relation between Inertia and system frequency can be arrived from the swing equation and using equations (1) & (2) as given below,
RoCoF is the Rate of Change of Frequency and it depends on the power balance and acceleration time constant (2H).
Δ P = Pm - Pe = Generation load imbalance.
References
Julius Susanto, Frequency Control in Low Inertia Power Systems Tutorial, 2020.
entso-e, Inertia and Rate of Change of Frequency (RoCoF), 2020.
Tamrakar, Ujjwol, et al, Virtual inertia: Current trends and future directions, Applied sciences, 2017.