The model for the short term prognosis

For the projection of the current power progress it is necessary to design a mathematical model of the power progress. By extrapolation of the power progress of this model over the remaining time of the billing period, the expected power value at the end of the period is estimated.

Power trend

At the end of the period T the power P prog (T) is to calculate. In order to calculate the current power trend a linear function is used which is extrapolated to the end of the period.

P prog (T) = P const (t) + P trend (t) * ( T - t )

The mathematical polygon factors p0, p1 are named after their physical meaning in order to make it easier to understand.

Factor	Description
P prog	prognosticated power value
P const	Power constant (value of the last values)
P trend	Power trend (linear ascent(descent)
D	Point in time of the end of the measuring period
t	current time

Energy trend

Deducted from this the energy trend up to the end of the period E(T) can be calculated with the function

E prog (T) =P aver (t) * t + P const (t) * (T - t) + ½ * P trend (t) * (T - t)

Factor	Description
E prog	prognosticated energy value
P aver	average power value

The first addend describes the determined energy up to the time t. The energy can be either determined by the average power value as described in the formula or is is given as a direct calculated energy value E(t).

The second addend continues the present constant power to the end of the period and calculates the constant energy amount from that.

The third addend describes the additional influence of the trend.

Concerning the energy calculation for the actual billing a value is necessary which is set back exactly at the beginning of the measuring period. Therefore it is not possible to use externally filtered values.

From the formula mentioned above the average value at the end of the period is determinable.

P prog aver (T) = E prog (T) / T

Parameters	Description
P prog aver	prognosticated average power value