Methods for on-line prediction of heat consumption in district heating systems hour by hour for horizons up to 72 hours are considered in this report. Data from the district heating system Vestegnens Kraftvarmeselskab I/S is used in the investigation. During the development it has been assumed that meteorological forecasts are available on-line. Such a service has recently been introduced by the Danish Meteorological Institute. However, actual meteorological forecasts has not been available for the work described here. Assuming the climate to be known the mean absolute relative prediction error for 72 hour predictions is 3.8% for data in November, 1995 (17% when no climate information is used). However, at some occasions large deviations occur and in January 1996 a value of 5.5% is obtained. The relative prediction error tends to increase with decreasing heat consumption. Approaches to implementation are suggested in a separate chapter of the report. The methods of prediction applied are based on adaptive estimation, whereby the methods adapt to slow changes in the system. This approach is also used to track the transition from e.g. warm to cold periods. Due to different preferences of the households to which the heat is supplied this transition is smooth. By simulation, combined with theory known from the literature, it is shown that it is crucial to use the actual meteorological forecasts and not the observations of climate when estimating the parameters of the model. To our knowledge, this is somewhat contrary to practice. The work presented is a demonstration of the value of the so called gray box approach where theoretical knowledge about the system under consideration is combined with information from measurements performed on the system in order to obtain a mathematical description of the system. Furthermore it is also demonstrated that it is important to select the estimation method depending on the particular application. Maximum likelihood estimates are often considered optimal, but here they prove to be inferior to output error estimates for long-term prediction. This is because the optimality of the maximum likelihood estimates are related to the properties of the estimates, whereas for prediction purposes the properties of the prediction errors should be in focus.
- greybox modelling