**2. Methods**

water and lakes. Minor quantities of biogas and gas from ironworks are used but fossil fuels now produce less than 15% of the district heating (Fig. 2). The fossil carbon-dioxide emis‐ sions from district heating have been reduced significantly during the past decades because fossil fuels have produced a decreasing fraction of the heat. This transition has been facilitat‐

ed by an early introduction of a carbon-dioxide tax and other policy measures [5].

4 Sustainable Energy - Recent Studies

**Figure 2.** Fuels etc. used for district-heating production in Sweden (TWh/year)

vest in infrastructure and reduce dependency on imported fossil fuels.

Oil and coal use decreased during the 1980s (Fig. 2) due to increasing taxes. There has been a carbon-dioxide tax in Sweden since 1991, which now is 100 euro/ton. An energy tax was in‐ troduced even earlier. There is natural gas only in south-west Sweden. The use of electric boilers for district-heating production increased when nuclear power expanded during the 1980s but decreased when the electricity was taxed in the 1990s. Use of biomass (e.g., wood‐ chips) was first promoted by the taxes on fossil fuels and later also by green electricity certif‐ icates and higher electricity prices that make biomass-fired CHP plants more profitable. Waste incineration increases (Fig. 2) because it is prohibited to dispose combustible fuel on a dump and district heating companies collect revenues for taking care of the waste. There have also been investment subsidies to some selected projects using local energy sources. The district-heating increase during the last decades reflects a political commitment to in‐

Favourable comprehensive solutions can be elucidated through system analysis and optimi‐ sation models. These methods can show the best way to use resources to satisfy aims. Com‐ mon aims are low costs and low environmental impact, which often can be conflicting. The essential features of an issue under study for a system can be represented in a model. Mod‐ els often help system understanding and reveal relations among components, such as be‐ tween district-heating production, solar energy extraction and wall insulation. The best solution according to a criterion and under certain conditions can be shown by an optimisa‐ tion model. For energy issues, an energy system optimisation model can be used to find the best design and operation of a system. In such models, many technical components can be described [6].

Examples of energy system optimisation models are MARKAL (e.g., [7]) and TIMES (e.g., [8]). These models were primarily developed for national energy-system analyses, whereas the model MODEST was originally made for optimising district-heating supply under con‐ sideration of heat-demand fluctuations.

MODEST is an energy system optimisation model, which uses the optimisation method line‐ ar programming to find the minimum cost for satisfying energy demand and presents the system design and operation that achieves the lowest cost. A large number of options for energy supply and conservation can be considered with this model framework. The user can make a comprehensive representation of the energy system under study with chosen level of detail. Many different energy systems can be analysed as long as the important properties of the system can be described by linear relations. An almost arbitrary set of parameter val‐ ues may be attributed to each component and energy flow in a system. A flexible time divi‐ sion makes it possible to reflect diurnal, weekly, monthly, seasonal and long-term variations of, for example, costs, capacities and demand. The modelling result presents the optimal in‐ vestments and the optimal operation of existing and new units as well as emissions and costs [6].

MODEST has been most used for optimisation of electricity and district-heating production. MODEST has been applied to more than 50 district-heating systems, some regional energy systems and a few national power systems. Studied issues include introduction of waste in‐ cineration and combined heat and power production and connections between industrial and municipal energy systems [6], for example, how large CHP plant should be built, is waste or biomass the best fuel and should industrial surplus heat be utilised? The model has been used a lot to study impact of energy prices and policy instruments on investments and operations in energy conversion, for example, how emissions allowances influence com‐ bined heat and power production.
