## 2 State of the Art  
The structure of thermal energy consumers largely determines the strand of development for heating systems. Figure 1 shows an enlarged structure of thermal energy consumers in the heating systems of some countries. The investigations presented in [27; 28] indicate that in countries and regions located above 45\({}^{\circ}\) north latitudes, the prevailing consumers of thermal energy are domestic households. This is due to the harsh climate and the significant role of heating systems in ensuring the life of the population and the functioning of service companies. There are two ways to organize heat supply to the population, including household consumers: individual and centralized [29; 30]. Their main function is the heating of public and residential buildings and premises during low-temperature periods. The performance of heating systems is assessed by the level of reliability, efficiency, and environmental friendliness of heat production [31; 32]. The current state of heating systems and future trajectory of their development are largely affected by historical features, traditions, the social structure of society, and other factors. In European countries, where the heating period is about 100 days a year, the focus is on individual heating systems and home boilers. The countries where this method of heating and hot water supply dominates in the domestic sector include England, France, Germany, Italy, the USA, and other countries in Europe and North America. This is usually due to the lack of inexpensive hydrocarbon fuel in these countries, which requires the population to limit their consumption of expensive thermal energy. District heating systems are widely used in densely populated urban or industrial areas of regions and countries with a sharply continental climate. There are about 80 thousand of them in the world. The main proportion of DHSs is in Scandinavian countries, since the heating period in them lasts more than 200 days a year. In Australia, China, Mongolia, Poland, Russia, Belarus, and other countries, the energy policy is aimed at the development of district heating systems [33; 34; 35]. The process of urbanization in developing countries drives the advancement of DHSs that supply thermal energy to household consumers. Orientation towards DHSs is normally accompanied by the improvement in market mechanisms that determine the rules and procedures for the production and consumption of thermal energy. According to statistics, the global district heating market in 2022 was estimated at $49.96 billion, and according to preliminary estimates, its value will be $56.05 billion by 2028 [36] (Figure 2). Figure 1: Structure of thermal energy consumers in some countries. To streamline the process of thermal energy production and consumption, it was necessary to develop and implement modern systems for metering thermal energy. To increase energy saving, measures are taken to improve market mechanisms and methods of technical regulation [37; 38]. Improvement in market mechanisms and technical requirements is aimed at  
* Stimulating the reduction in thermal pollution during thermal energy transmission and consumption;
* Boosting the DHS controllability to reduce harmful emissions into the environment from the thermal energy production. The progressive development of DHSs in European countries is the result of implementing an integrated approach [39]. For example, the values of heat pipeline transmission losses achieved in the EU countries are at the level of 1-7%, against 35-40% in some other countries [40; 41]. Existing DHSs are usually referred to one of five generations that differ in the level of energy efficiency [42; 43]. About 50 years elapsed between the first and second generation of DHSs. With the advancement of technological progress, the rate of change in generations of heating systems has almost doubled.