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The EU has a goal of reducing greenhouse gas emissions and energy consumption by 20% by 2020, by 40% in 2030 and by 80% in 2050 compared to 1990-levels, and Denmark has set the even more ambitious goal of being completely fossil-fuel-free by 2050. On the way to this goal, the aim is that the energy-supply mix for buildings including heating and electricity should be free of fossil fuels as early as 2035 including heating and electricity. Urgent action is therefore needed to meet these requirements for the future energy system. A balance needs to be found between saving energy in buildings and supplying energy from district heating based on renewable energy resources and waste incineration. This research took a new approach combining heat savings in buildings with heat supply from district heating and seeing them as two segments that reinforce each other, instead of seeing them as two separate competitive instances. The question was to what extent we should supply renewable energy and to what extent we should save energy in buildings to optimise the costs and energy at a societal level. Calculations showed that the socioeconomic cost of reducing heating consumption in buildings by 30-65% is similar to the socioeconomic cost of supplying the same amount of district heating using renewable energy sources. For the district heating system in the Copenhagen area, socioeconomic calculations indicate that it is slightly more cost-beneficial to invest in energy renovations from 2013, so that we can reduce the heat demand, before investing in new renewable energy supply technologies. However, the results from the socioeconomic calculations are very sensitive to the discount rate assumed. The higher the discount rate is, the more beneficial it will be to postpone large investments, i.e. the energy renovations. However, the conclusion is that it does not make a great difference which scenario is chosen from a socioeconomic point of view. The costs for supplying heat and saving heat are at comparable levels. But investing in energy renovation from today will reduce the investment costs for new supply capacity significantly and result in more competitive heat prices. Recently, there has been a lot of focus on 4th generation district heating, i.e. low-temperature district heating with a supply temperature of 55°C. This research looked at the possibility of supplying low-temperature district heating to old existing multi-storey buildings when the buildings undergo various levels of renovation. The investigation aimed at keeping the existing heating system and the existing district heating distribution network. Theoretical investigations showed that low-temperature district heating can be supplied to existing buildings most of the year if they have been energy-renovated to moderate levels, without replacing the existing heating system in the buildings and without replacing the existing district heating distribution network. However, the supply temperature will have to be increased to 60-70°C during cold periods corresponding to approximately 5% of the year. Furthermore, the lower the level of energy renovation, the longer the period required with this increased supply temperature. To be able to renovate old heritage buildings to high energy performance standards we need to find robust solutions. The solutions on the market today for heritage-valued buildings have still not been documented to the extent needed for the building sector to take responsibility for applying them on a large scale. While old heritage buildings have similar constructional trends, each is unique in its specific design, so solutions are difficult to standardize. Yet we need to find standard solutions that are both technically and economically feasible for the energy renovation of this segment of buildings. One solution to save energy is to use internal insulation, since exterior façade insulation is clearly not an option due to the need to preserve the building’s appearance. This research investigated the application of internal insulation with regard to the risk of moisture problems behind the insulation and in the wooden beam construction embedded in the brick wall. The approach was to find a balance between energy savings and moisture safety, so the focus was firstly to ensure moisture safety and secondly to achieve energy savings. Two solutions were investigated; (i) with a gap in the insulation above the floor construction, and (ii) with a gap in the insulation above and below the floor/ceiling. Due to the uncertainty of the actual rain exposure on the façade, it is difficult to draw conclusions from the results. However, if the façade is exposed to low amounts of driven rain and the façade is orientated towards west, the solution with a gap above and below the floor/ceiling could be moisture safe. But further research is needed to draw final conclusions. It is recommended not to apply 80mm insulation, but only a maximum of 40mm (with λ=0.019 W/mK). Moreover, based on the results from this investigation, it not recommended to apply internal insulation on a north-orientated wall with a thickness of 1.5 and 2 bricks, and caution should be exercised if it is applied on a west-orientated wall. Investigations were only carried out for 1.5 and 2-brick walls and wall orientations towards north, west and southwest. Internal insulation applied on thicker walls (2.5-3.5 bricks) and/or other wall orientations might show different results.