An off-grid settlement has a flat electrical demand of all year

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

An off-grid settlement has a flat electrical demand of

L = 2.0\,\mathrm{MW}

all year. It is supplied by a solar field and a wind fleet, backed by a hydrogen store for the seasonal mismatch. The solar field has area

A = 40\,000\,\mathrm{m^2}

, mean plane-of-array irradiance outside one winter month

\bar F = 220\,\mathrm{W\,m^{-2}}

, module efficiency

\eta = 19\%

and performance ratio

\mathrm{PR} = 0.82

, so that its mean output is

P_{\rm pv} = A\bar F\eta\,\mathrm{PR}

. The wind fleet is rated at

3.0\,\mathrm{MW}

and, from a Weibull analysis of the site's wind speed record, has a capacity factor of

38\%

outside that month. Outside that month the combined mean output of the two sources is as computed from these figures; during the winter month itself, of

30

days, the combined mean output falls to

0.85\,\mathrm{MW}

. Surplus electricity is stored as hydrogen and returned through a fuel cell at a round-trip efficiency of

35\%

(electricity to electricity). ((a)) Find the solar field's mean output, the wind fleet's mean output, and hence the combined mean output for the eleven non-winter months. ((b)) Find the energy shortfall against demand during the winter month. ((c)) Find the electrical energy that must be diverted from the surplus, through the hydrogen store, to cover that shortfall. ((d)) Find the surplus electrical energy generated over the rest of the year, and state whether it is enough to cover the requirement found in part (c).

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