Power quality and networks
Rate of change of frequency after a loss of infeed
- where
- initial rate of change of frequency (Hz/s)
- power imbalance (MW)
- nominal frequency (Hz)
- inertia constant (s)
- rating of synchronised plant (MVA)
- time to reach the deviation with no response (s)
- frequency deviation of interest (Hz)
Explain this equation
Gives the initial rate of change of frequency when a block of generation or load is lost. Use it to check RoCoF loss-of-mains settings or the inertia needed to ride through the largest infeed loss.
H × S is the kinetic energy stored in the rotating masses, in MW·s. ΔP is the sudden mismatch between generation and demand, which is drawn from that stored energy.
It comes from the swing equation. Kinetic energy is proportional to speed squared, so for small changes the rate of energy loss ΔP equals 2HS/f0 times df/dt. Rearranging gives the expression shown.
Sense check: losing 1.8 GW from a system with 90 GW·s of inertia gives 0.5 Hz/s. Halving the inertia doubles the RoCoF.
Watch out: this is the value at the instant of the loss. Governors and load damping reduce it within seconds, while local oscillations can make measured RoCoF higher near the event.
Initial rate of change of frequency from the swing equation when a block of generation or load is lost, for checking RoCoF protection settings and inertia requirements.
Enter your values to see the result.
Good to know
H × S is the system stored energy; GB transmission figures are quoted in GW·s. Typical H: 2–9 s for synchronous generators on their own rating; inverter-based plant contributes none unless it provides synthetic inertia. EREC G99 requires loss-of-mains RoCoF protection, where used, to be set at 1 Hz/s with a 500 ms delay, and generation to ride through RoCoF up to 1 Hz/s.
Common mistake
Mixing ratings: H must be on the same MVA base as S. Also treating the initial RoCoF as constant; governor and load damping reduce it within a second or two.
Limits
Initial (t = 0+) value of a single-machine equivalent; ignores load damping, primary response and the local oscillations that make measured RoCoF higher near the disturbance.
Sources
- Badesa L., Teng F., Strbac G., Importance of linking inertia and frequency response procurement: the Great Britain case (RoCoF constraint from the swing equation), arXiv:2010.07161
- ENA Engineering Recommendation G99 Issue 1 Amendment 9 (2022): Requirements for the connection of generation equipment in parallel with public distribution networks
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.