For an optimal operation of grids and cogeneration plants good prognoses of the expected loads (electric and thermal) and feed-in of fluctuating generation are essential. For this we suggest a statistic method with empiric formulas to fit the load. In several projects we tested an algorithm based on the method of multiple linear regression [4],[7]. The scheme of this algorithm is shown in Fig. 4.

Basis for this method is a database with a time horizon of at least one year, which contains the profile of the value y[t] to be predicted together with other data {z1[t], .., Zn[t]} that might correlate with y. These are calendar data (e. g. day of year) and weather data (e. g. temperature, global radiation). To keep the database as up-to-date as possible it is continuously actualised with the newest measurements

before the actual prognosis calculation. The method of multiple linear regression [8] estimates the given depended variable y[t] by a linear function y[t] = co + ci Xi[t] + c2 X2[t] + … + cn Xn[t] + e[t]

of the given independent variables {x1 [t], .., xn[t]}, where the factors {c0, .,cn} are unknown and e[t] gives the error for each time step.

The error is minimised with a least square estimation, which has got the advantage that it can be solved analytical with a linear set of equations. From experience we know, that the thermal load will not depend linear on the input variables. To integrate also nonlinear relations the variables xi[t] are introduced. They are defined as a function of the input data in the database {z1[t], .., zn[t]}:

xi[t] = f (zi[t],…,zJt]) (4)

In a pre-analysis we tested, which combination of input variables fits the load best and got for each hour a model equation. The regression analysis results in a specific formula for each hour of the day, e. g. hour = 13:

Pioad. iih = Cl + C2 • Sunday + c3 ■ doy2 + c4 ■ doy4

r, ump ■ r,,-hmp — r — limp’ <ч limp’ (5)

+C9 • sunrise + C10 • sunset

For the prognosis the multiple linear regression routine calculates the coefficients {c1, …, cn} for the chosen equation by use of the updated database. The resulting model is used together with weather forecasts from a commercial meteorological service. Fig. 5 shows the curve of a thermal load of a real district heating system and the prognosis which was predicted one day ahead.