People tend to use the inertia H constant (MW*s/MVA) when it comes to describing the amount of inertia that grid forming inverters and batteries can provide. Sometimes the units are simplified to seconds, which makes it easier to understand how many seconds it could provide rated power for this specific function.

Active inertia or synthetic inertia do vary power when frequency changes but the key is the dynamic behavior. They typically do so by emulating a synchronous machine by implementing something like the swing equation in the active power control (see REGFM_B1 [1]). They essentially emulate the inertia, which makes them have some damping in changing the phase angle and frequency of their voltage waveform just like a spinning synchronous generator would when resisting frequency changes due to physical inertia, resulting in an inertial active power response. This makes it easier for people to analyze because they understand the swing equation from synchronous generators.

[1] https://docs.nrel.gov/docs/fy24osti/90260.pdf

Thanks for the reply and the link.

A machine with infinite inertia would resist any frequency change and instantly go to maximum or minimum power upon any grid frequency deviation.

A 25s inertia constant is impressive. The hydro units I work on are anywhere from 1s for newer units to 7s for older ones intended to run isolated networks. And then the ease of frequency regulation on the unit is dictated by the inertia of the water in the water conveyance system “water starting time”

So 25s inertia constant would appear to be a response to frequency change much faster and greater than the typical 5% droop implemented by the governors controlling mechanical power applied to the shaft.

Wild stuff!