In Chapter 6 we worked a simple example with only four consumers and seven
pipe segments. The example illustrated the use of our method and also showed how
the branch-and-bound technique can be used to quickly eliminate candidate de-
signs. A method is also demonstrated for further refinement of the pipe network to
eliminate excessive throttling losses in the consumer's control valves.
CONCLUSIONS
The method developed here should be feasible for designing the piping networks
for district heating systems of moderate size, and in particular the systems used on
military facilities or college campuses, which tend to be smaller and less complex
than those of large cities. For very large systems, the branch-and-bound method
used for finding the discrete diameters may become cumbersome and
computationally too expensive. However, this remains to be shown and it may be
that, with the commercially available software and the enormous power of today's
computers, this perceived problem is quite manageable.
The major advantage of the method developed here is its flexibility to accommo-
date any set of economic and physical parameters and operating strategy. In
addition, the approximations, where used, are much more suitable than some made
in the past: for instance, linearization of the equations, neglecting heat losses, and
oversimplification of the effect of varying load. It is felt that a significant contribu-
tion has been made by the derivation of mathematical expressions for all of the major
constraints. Perhaps the most significant contribution of this work has been the
analysis of constraint activity and the development of a method to exploit that
knowledge to arrive at a solution. In addition, we have shown what bounds can be
put on the solution such that the designer can be reasonably assured of whether or
not further significant cost reduction is possible. This not only gives the designer
some comfort in knowing what possible improvement remains, but it also avoids
excessive calculations that often result when no such knowledge is available.
Another possible use of the methodology developed here is for studies of the
relative merits of various operating strategies and what effect they have on the
design of the system. The general form of the cost coefficients can be useful for such
studies and can not only be used to develop designs based on the methods presented
here, but they may also be used to evaluate the effect of economic or physical
parameter changes, including operating strategy changes, on existing designs.
With many systems already in use in Europe, the issue of optimal design is of
lesser importance there. Currently, however, the interest in optimal operation of
district heating systems is significant in Europe, as evidenced by several recent
conferences devoted almost entirely to this topic alone (Nordic Council of Ministers
1989, 1994). Most of the efforts seem to be centered on real-time simulations of
operation and subsequent forecasting of short-term operating strategy. It seems that
a method such as the one developed here would be useful for studies at a higher level
to determine optimal overall operating strategies for the yearly load cycle.
RECOMMENDATIONS
It is recommended that the methodology developed here be field tested on the
design of a moderately sized system, such as would be found on a military base or
college campus. The design should be compared with a completely independent
design, as would be achieved by methods normally used by the district heating
design profession.
Under the assumption that the results of the field test were positive, it is
recommended that the method be coded for computer execution to the maximum
extent possible. The resulting CAD program could then be incorporated into one or
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