Abstract
This paper uses classical probability theory to derive expressions for the expected (or mean) value of quantities such as the irradiation on inclined surfaces, collector output, and net gain through windows. The random variables are the clearness index k t and the diffuse fraction k, whose means are k t and k , respectively. The probability function for k t is assumed to depend only upon k t and is represented by a simple function chosen so that its corresponding distribution function is a close fit to the one originally graphed by Liu and Jordan. The probability function for k is represented, for a given k t , by an impulse function centred at the k observed at that k t ; the Orgill-Hollands functional form is used for the function k(k t) . A general purpose integral expression is presented for the expected value of any quantity which can be expressed as a functionof k, k t and time of day. The integral is evaluated for several such quantities: the solar irradiation on an inclined surface, the output of both flat plate and concentrating collectors, and the net heat gain through a window with an automatic shutter. Example calculations are included.
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