A synchronised power system with nominal frequency suddenly loses of generation

PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · Energy systems, storage and demand · Energy systems, storage and demand

Energy from Physics, Ch The grid with variable renewables: power flow, inertia, adequacy and electrification

Problem

A synchronised power system with nominal frequency f0=50 Hzf_0=50\,\mathrm{Hz} suddenly loses 2.4 GW2.4\,\mathrm{GW} of generation. Before frequency response acts, the initial rate of fall of frequency is set by the swing equation summed over the system, −df/dt=f0ΔP/(2Ek)-\mathrm{d}f/\mathrm{d}t=f_0\Delta P/(2E_k), with ΔP\Delta P the size of the loss. ((a)) Find the initial rate of fall of frequency if the system's stored kinetic energy is Ek=180 GW sE_k=180\,\mathrm{GW\,s}. ((b)) Find the initial rate of fall if the same loss occurs when only half that kinetic energy, 90 GW s90\,\mathrm{GW\,s}, is synchronised (for example, with more converter-connected generation running and fewer spinning machines).

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