System Frequency Response Calculator

ROCOF is calculated as the power imbalance divided by twice H times total generation, so H sits in the denominator — a higher inertia constant means more stored rotational energy is available to absorb the sudden imbalance, which slows the initial rate of frequency decline. This is why grid operators worry about retiring synchronous generators (which supply real physical inertia) in favor of inverter-based renewables that typically don't, since it shrinks the effective H and steepens ROCOF for the same size of disturbance.

Steady-State Frequency is where the grid settles once governors have fully responded to the imbalance, calculated as nominal frequency minus the steady-state deviation. Frequency Nadir is the lowest point frequency actually reaches on the way down before recovering, and it always dips further than the steady-state value — this calculator approximates it as 1.5 times the steady-state deviation, reflecting the typical overshoot seen before governor response and load damping arrest the decline.

Both act as forms of resistance to frequency change: droop measures how much generators ramp output per unit of frequency drop, and load damping measures how much load naturally falls off as frequency sags (motors slow down, drawing less power). The calculator adds the regulation effect from droop (the inverse of the droop setting) to the load damping percentage to get a combined effective damping figure, then divides the per-unit imbalance by that sum — so increasing either input reduces the resulting steady-state deviation.

Time to Nadir here is a simplified estimate — the projected overshoot (1.5x steady-state deviation) divided by the initial ROCOF — that assumes a roughly linear frequency decline and ignores governor dead-bands, response delays, and any nonlinear system dynamics. Real systems can reach nadir earlier or later depending on how quickly primary response actually kicks in, so this figure is meant for order-of-magnitude reserve planning, not for calibrating under-frequency load-shedding or protection relay trip times.