A horizontal

PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · Energy resources and conversion · Energy resources and conversion

Energy from Physics, Ch How efficient a solar cell can be: detailed balance, tandems and the field

Problem

A horizontal,

1\,\mathrm{kWp}

array of silicon modules (rated at

1000\,\mathrm{W\,m^{-2}}

25^\circ\mathrm{C}

) sits at latitude

\phi = 52^\circ

. Using the daily extraterrestrial insolation formula

\begin{aligned} H_0 &= \frac{24}{\pi}S_0\left[\omega_s\sin\phi\sin\delta + \cos\phi\cos\delta\sin\omega_s\right], \\ \omega_s &= \arccos(-\tan\phi\tan\delta), \end{aligned}

with the solar constant

S_0 = 1361\,\mathrm{W\,m^{-2}}

and chapter 1's orbital factor

(\bar d/d)^2

set to one, take the summer solstice (

\delta = +23.4^\circ

) and the winter solstice (

\delta = -23.4^\circ

). Assume a clearness index

K_T = 0.45

on both days, so

H = K_TH_0

arrives at the ground on the horizontal plane, and ignore all other atmospheric and array losses except cell temperature. The module's power falls by

0.40\%

per kelvin of cell temperature above

25^\circ\mathrm{C}

. Take the mean daylight cell temperature to run

20\,\mathrm K

above the mean daylight ambient temperature, which is

18^\circ\mathrm{C}

in summer and

5^\circ\mathrm{C}

in winter, and assume this mean temperature derate applies throughout each day and that output otherwise scales linearly with irradiance. ((a)) Estimate the electrical energy generated per

\mathrm{kWp}

on the summer solstice. ((b)) Estimate the electrical energy generated per

\mathrm{kWp}

on the winter solstice.

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