Mathematical modelling of district-heating and electricity loads

In recent years it has been more common to use linear or mixed-integer programming methods for finding optimal solutions to the complicated operating options in modern Combined Heat and Power (CHP) networks. Electricity may be bought from the national grid or it may be produced in ordinary condenser or CHP plants owned by the utility. In the same manner, district heat can be produced by the use of waste heat from industries or from a CHP plant. Other options are burning garbage in an incineration plant, using heat pumps in a sewage water plant or just burning fuels in an ordinary boiler. Combining these options and including the possibility of using conservation measures in industry or in the housing stock will result in a very complex situation if one tries to find the optimal solution characterized by the the lowest Life-Cycle Cost (LCC). Load management equipment, such as hot-water accumulators, will aggravate the problem even further. By the use of modern computers, complicated problems can be solved within a reasonable period of time. The bases for the mathematical models are the thermal and electrical loads. Splitting these loads into finer and finer segments will yield a model that will depict reality more closely. Two methods have been used frequently, one where the high and low unit price hours in each month have been lumped together, resulting in 24 segments plus one segment showing the influence of the maximum electricity demand. The other method tries to model the loads by lumping the energy demand in six electricity-tariff segments, but also using about 15 elements for a more versatile picture of the district-heating load. This paper describes the two methods using monitored data for 1990-1991 from Kalmar in the south of Sweden. It also discusses which of the methods is preferable or whether a combination must be elaborated upon in order to model reality closely enough for practical use.