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.