A national system with nominal frequency has synchronised kinetic energy

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 national system with nominal frequency

f_0=50\,\mathrm{Hz}

has synchronised kinetic energy

E_k=120\,\mathrm{GW\,s}

. It suddenly loses its largest single infeed,

\Delta P=1.2\,\mathrm{GW}

, and frequency response ramps in linearly over

T_r=5\,\mathrm{s}

. ((a)) Estimate the frequency nadir, using

\Delta f_{\rm nadir}=f_0\Delta PT_r/(4E_k)

. ((b)) Three generating units of rated real power

500\,\mathrm{MW}

800\,\mathrm{MW}

and

1200\,\mathrm{MW}

all have droop

R=0.05

. Using the frequency fall found in part (a) as the drop each unit responds to, estimate the extra power each supplies, from

\Delta P_i/P_{{\rm rated},i}=-(\Delta f/f_0)/R

. ((c)) On the same evening, the system must also carry a new electrified winter peak from

8

million homes needing

5\,\mathrm{kW}

of heat each at the design outdoor temperature (heat-pump coefficient of performance

2.4

there, all homes heating at once) and

5

million electric cars charging at

7\,\mathrm{kW}

each with a coincidence factor of

0.3

. Estimate the total added peak power from these two electrified loads.

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