## 3 Materials and Methods  
The more electricity generated by CHPPs, the greater their energy efficiency tends to be. Modern CHPPs have a high fuel utilization factor, which, when the consumed fuel is distributed in proportion to the generated volumes of electrical and thermal energy, makes them the most efficient sources of electricity. As a source of thermal energy, CHPPs are inferior to modern boiler plants, which have a fuel utilization factor of about 92-95%, since they require more fuel to produce the same volume of thermal energy. When boiler plants  
Figure 7: Scheme of a DHS with various sources of thermal energy. function as a backup source of thermal energy and as a source to meet peak thermal loads, their role changes. Efficient electric boiler systems can reduce and even eliminate the need for boiler facilities that leave a significant carbon footprint. The main reduction in fuel consumption when using CHPPs occurs due to the displacement of outdated thermal power plants from the balance of electrical energy and power with steam power units (SPUs) running on hydrocarbon fuel. The advantages of CHPPs over SPUs with electrical efficiency no higher than 35% are obvious. The magnitude of the fuel effect depends on the amount of electricity generated by CHPPs, the electrical efficiency of which depends on the thermal load, which varies throughout the year. Given that the fuel and environmental effects depend on the volume of electricity produced by CHPPs, to increase the efficiency and capacity factor, it is advisable to implement measures aimed at increasing the heat cogeneration [99]. The main characteristic of DHSs is the annual heat load curve, known as the load duration curve (Rossander graph). It can be built for any region or country as a whole, considering their climatic characteristics. The Rossander graph allows selecting a mix of thermal power and energy sources, as well as the degree of their participation in supplying the heat load. By utilizing this method, it becomes possible to assess the capacity factor of thermal energy sources and, knowing the level of their efficiency, calculate the quantity of energy resources required to produce the needed volume of thermal energy [100]. For example, gas reciprocating CHPPs have a direct relationship between the production of electrical (\(P^{G}\), \(E_{G}\)) and thermal (\(Q^{G}\), \(W_{G}\)) power and energy, which is reflected by cogeneration factor (\(k\)):  
\[Q^{G}=P^{G}\cdot k, \tag{1}\]  
\[W_{G}=E_{G}\cdot k. \tag{2}\]  
The thermal energy generated by gas reciprocating plants and gas turbine units is a by-product of electricity production, which, however, affects their economic efficiency. The efficiency of CHPPs depends on the use of generated thermal energy in the DHS. The greater the share of cogenerated thermal energy, the lower the fuel component in the cost structure of electricity generated by the CHPP. Knowing the calorific value of gas (\(q\)) used in the gas reciprocating plant, the fuel utilization factor (\(\eta^{G}\)), and the capacity factor (\(T_{G}\)), we can calculate the volume of the fuel used:  
\[B^{G}=(P^{G}+Q^{G})\cdot T_{G}\ /\ (\eta^{G}\cdot q). \tag{3}\]  
When using all the thermal energy generated by the gas reciprocating plant in the DHS, the fuel consumption (\(B^{G}\)) should be distributed in proportion to the thermal and electrical energy produced from the CHPP:  
\[B^{Q}/B^{P}=k, \tag{4}\]  
In this case, we obtain:  
\[B^{Q}=B^{G}\cdot k/(k+1), \tag{5}\]  
\[B^{P}=B^{G}/(k+1). \tag{6}\]  
Based on expressions (4)-(6), with a proportional distribution of fuel for the production of thermal and electrical energy, the calculated values of electrical and thermal efficiency will be equal to the fuel utilization factor of the gas reciprocating plant:  
\[\eta^{Q}=\eta^{G}=\eta^{P}, \tag{7}\]  
Based on this conclusion, an objective function can be formulated as follows: maximize electricity generation, provided that all cogenerated thermal energy is supplied to the DHS.