At a system's winter-peak risk hours

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

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

Problem

At a system's winter-peak risk hours, a

20\,\mathrm{GW}

wind fleet produces nothing for

30\%

of the hours and

10\,\mathrm{GW}

for the other

70\%

. Use the exponential loss-of-load model with

m = 1\,\mathrm{GW}

. ((a)) Find the fleet's mean output at those hours and its effective load carrying capability. ((b)) The fleet is enlarged so that its output in the windy hours becomes

X

, with the calm hours unchanged. Show that however large

X

becomes, the ELCC stays below

-m\ln p_0

, where

p_0

is the fraction of risk hours with zero output, and evaluate this ceiling. ((c)) Compare with a single

2\,\mathrm{GW}

firm unit available

95\%

of the time, independently of the weather: find its ELCC and say which is worth more to the system at the peak. ((d)) Find the largest fraction of calm risk hours a fleet could have and still reach an ELCC of

3\,\mathrm{GW}

at this

m

Browse the problem library