## 2 State of the Art
Let us give a brief description of the DHS generations:  
* The first generation (1 GDH) is characterized by steam heating with a steam temperature of 100-200 \({}^{\circ}\)C and high thermal energy losses exceeding 30%. It is mainly used in steam boilers operating on solid fuels (coal, peat, etc.). * The second generation (2 GDH) is characterized by water heating with a network water temperature above 100 \({}^{\circ}\)C at high pressure and high thermal energy losses (up to 30%). These DHSs mainly focus on providing heat to industrial consumers, while the surplus thermal energy is used to meet the needs of household consumers. They can include heat and electricity cogeneration plants operating mainly on solid fuels. * The third generation (3 GDH) is characterized by water heating with a network water temperature of 70-100 \({}^{\circ}\)C for heat supply to domestic consumers. Energy saving measures are implemented to reduce thermal energy losses during the coolant transfer from the source to consumers (up to 18%) and to control harmful emissions from the combustion of hydrocarbon fuels. Thermal energy sources use solid and gaseous fuels [44]. Cogeneration technologies are widely used to generate heat and electricity. There is an insignificant share of generation (up to 10%) using renewable energy resources [45]. * The fourth generation (4 GDH) is characterized by a network water temperature of 50-70 \({}^{\circ}\)C, while heat losses do not exceed 6%. Secondary and renewable energy resources are massively used; heat storage, automation, and digitalization systems are introduced into the processes of thermal energy production and distribution [46; 47]. Along with efficient cogeneration technologies, heat pumps, solar collectors, and other plants based on renewable energy resources are used to produce thermal energy. Figure 2: Projected growth of the global district heating market from 2022 to 2028 (billion USD). Trigeneration technologies are utilized for the air conditioning of buildings, enhancing the capabilities of district heating systems. * The fifth generation (5 GDHC) is characterized by a coolant temperature from 5 to 25 \({}^{\circ}\)C, while heat losses do not exceed 5%. Highly efficient thermal energy sources are utilized that make use of secondary energy resources such as solid industrial, agricultural, and domestic waste to minimize CO2 emissions. These district heating systems employ integrated automation systems as the basis for intelligent control systems to be created [48]. In [41; 42; 49], 5 GDHC systems do not relate to the evolutionary development of the previous four generations of heating systems, because there are significant disparities in the structure and composition of sources, where electric heat plays a major role. The latter creates additional loads on electrical networks and increases the risks of power supply disruption. The use of low-power cogeneration plants in close proximity to heat sources using electricity, however, makes it possible to eliminate this problem. Therefore, we believe that the 5 GDHC systems can be considered as a stage in the evolutionary development of DHS. Figure 3 shows the process of district heating evolution, which reflects the key differences in all five generations of district heating systems. The higher the district heating generation, the more diverse the set of energy resources used by heat sources. Modern district heating systems use heat sources focused on the use of primary energy resources, which can be divided into three groups:  
* Hydrocarbon fuels, industrial, agricultural, and domestic solid waste (boilers, combined heat and power plants (CHPPs));
* Renewable energy resources (heat pumps, solar collectors, etc. );
* Electricity (electric boiler rooms, individual electric boilers) [50]. When choosing the direction of DHS development, special attention is paid to enhancing their reliability and reducing heat transmission losses. Since 1986, no major accidents have been registered in the Danish DHS (4 GDH) [51; 52].