Stochastic modelling of temperatures affecting the in situ performance of a solar-assisted heat pump: The univariate approach

Abstract

Univariate stochastic modelling, using Box-Jenkins methods, is carried out for three air temperatures which can influence the performance of a solar-assisted heat pump system. In this system, external ambient air (the low grade source) is pre-heated by the conventional tiled roof of an occupied domestic residence. The air then crosses the evaporator of an electrically driven split heat pump which is situated in the roof space. Autocorrelation coefficients are presented for time series of the following dry-bulb temperatures: the external air, the residence internal (lounge) air, and the air in the roofspace after pre-heating but prior to crossing the heat pump evaporator. Hourly data relating to a two-week period in the heating season was utilised, providing a 336-h dataset. Univariate models fitted to the first 300 observations were validated by forecasting ahead for the remaining 36 h in steps of 1 h. Comparison of forecasted and measured values showed good agreement, except for a 4-h period in which the intensity of solar radiation exceeded that which prevailed during the modelled period. It is concluded that the Box-Jenkins approach can be used to develop univariate mathematical models which adequately describe building and climate thermal behaviour, and that the importance of solar radiation in this respect should not be overlooked.