Predicting central station demand and output

For relatively long-term predictions of central station demand and output, of the order of one year or more, the use of constant (or approximately constant) yearly percentages of growth is common and well understood. This method is frequently applied by straight, or nearly straight, line projection of the plot of past data on semi-logarithmic paper. When the term of the prediction is less than one year, or when detailed estimates are required throughout any year, this method fails on account of the seasonal variations. In this paper is investigated the nature of the seasonal variations in the daily load curve of the company with which the author is connected, as they affect the output and the peak demand. The variation of the kilowatt-hour output is first analyzed: and it is found that, in a year fairly free from abnormal business conditions, a plot of the “normal mid-week day” outputs on semi-logarithmic paper can well be rationalized to a curve whose components are an inclined straight line and a single-frequency sine curve. This curve is represented analytically by the following equation: $y = J e^{kr} [1 + L cos (0.986 , r - M)^{0}]$ In this equation, e is the base of the natural system of logarithms: r, the number of days (positive or negative as the case may be) counted from a given zero date: and J, k, L and M are parameters to be determined for each curve. Factors are included for determining the output on holidays, Sundays, Mondays and Saturdays, as compared with adjacent “normal” mid-week days.” For short-term peak demand predictions, the method employed is to separate into three components that portion of the daily load curve beginning at 2.30 P. M. and ending one and one-half hours after sunset. These three components are a constant “base load,” an “afternoon block” and an “evening block.” In the formula; $z = A F , (t) + B , f (t) + C$\n\n\t\t