Someone argues: "A wind fleet

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

Someone argues: "A

60\,\mathrm{GW}

wind fleet, at a typical winter capacity factor of about

32\%

, has a mean output near

19\,\mathrm{GW}

during winter-peak hours. So it is worth about

19\,\mathrm{GW}

of firm capacity, and the system can retire nearly

20\,\mathrm{GW}

of gas plant." The winter-peak-hour output of this fleet takes four levels over a representative sample of peak hours:

0\,\mathrm{GW}

for

15\%

of the hours

6\,\mathrm{GW}

for

25\%

of the hours

18\,\mathrm{GW}

for

35\%

of the hours

45\,\mathrm{GW}

for the remaining

25\%

of the hours ((a)) Confirm that the mean output over these hours is close to the

19\,\mathrm{GW}

claimed. ((b)) Using the exponential loss-of-load approximation,

\mathrm{ELCC} = -m\ln\langle e^{-P_{\rm v}/m}\rangle

, with system constant

m = 1\,\mathrm{GW}

, compute the fleet's effective load carrying capability from the stated distribution. ((c)) Find the error in the argument.

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