@TECHREPORT\{IMM2000-01042,
    author       = "H. A. Nielsen and H. Madsen",
    title        = "Predicting the Heat Consumption in District Heating Systems using Meteorological Forecasts",
    year         = "2000",
    keywords     = "greybox modelling, forecasting",
    number       = "",
    series       = "",
    institution  = "Informatics and Mathematical Modelling, Technical University of Denmark, {DTU}",
    address      = "Richard Petersens Plads, Building 321, {DK-}2800 Kgs. Lyngby",
    type         = "",
    url          = "http://www.imm.dtu.dk/~han/pub/efp98.pdf",
    abstract     = "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."
}