PhD Thesis - Energy Systems Research Unit - University of Strathclyde

the course of a year. The end result of this normalisation process, are the columnspresent in the right hand side matrix in Figure 2.6, which represent the normalisedhourly consumption values.Once calculated, each column in the right hand side matrix was then used to find thecoefficients of the general trend described in equation (2.1) for each individualHour (ho) . Having been normalised all terms in equation (2.1) are dimensionless.- (2.1)Equation (2.1) describes the normalised electrical energy consumption,e App(z),Month(mo),Hour(ho) , for a specific domestic appliance App(z) during Hour (ho) ofMonth (mo) . As discussed by Stokes [27], this is made up of three parts. A constantψ ho ; a sinusoidally varying component with amplitude Amp ho and phase angle φ hoand a third part made up of a random ‘noise’ value. The constant ψ ho , amplitude A hoand phase angle φ ho for each individual Hour (ho) were obtained by applying asimplified curve fitting algorithm to the values contained in each individual columnpresent in the right hand matrix of Figure 2.6 (normalised values of each hour setHour (ho) ,Month (1) , Hour (ho) ,Month (2) ,…., Hour (ho) ,Month (12) etc.) [34], effectivelycalibrating equation (2.1) for each individual Hour (ho) . The random value added inthe third part of the equation was obtained by using a uniformly distributed selectionto select a value from a range comprising σ STDEVho and -σ STDEVho , the standarddeviation value calculated for the values contained in each column present in theright hand side matrix of Figure 2.6 (normalised values of each hour setHour (ho) ,Month (1) , Hour (ho) ,Month (2) ,…., Hour (ho) ,Month (12) etc.).Equation (2.1) differs from that proposed by Stokes in [27] in two ways. Firstly,given that the monitored data was only available as a profile representing one day ofeach month, the variations in appliance hourly electrical energy consumption werecalculated on a monthly basis (Stokes applies the calculation on a daily basis).46