The method of assessing the effectiveness of air-water heat pumps for heating individual buildings

This paper provides a justification for the assessment of the effectiveness of the use of air-water heat pumps in the heating systems of individual residential buildings in conjunction with the water boiler. The criterion for the cost-effectiveness of the heating system with a combined heat source is the relative cost of equipment and operation of the system, given to the duration of the heating period. Cost components are presented in the form of a system of equations reflecting the dependence of the price parameters of heating system equipment on thermal characteristics. The proposed method of assessing the benefits of renewable energy is applicable to different climatic areas.


Introduction
In the practice of applying heat pumps in the heat-consuming systems of buildings, there is a lot of experience [1][2][3][4][5][6]. Having a large range of models and sizes of these industrial products allows you to choose the most suitable device for a particular object. However, it should be noted that heat pumps have been most prevalent in areas with moderately temperate "heat" climates, and in colder areas the use of heat pumps is stimulated by economic measures [7,8]. This is due to a decrease in the amount of heat extracted from the environment when its temperature is lowered, which affects the profitability of the system [9]. This is especially true for objects using air-water heat pumps. But on the other hand, these "heat generators" are the most environmentally friendly, easy to operate and install, do not require highly skilled and expensive maintenance, which makes them the most attractive for use in individual residential buildings.
The peculiarity of heating systems with heat pumps is the divergence in the production and need of thermal energy with a decrease in the temperature of the outside air. This leads to the need to use either a heat pump with notoriously high thermal power, sufficient to compensate for the heat residues of the building in the calculated conditions and excess in the rest of the period, or to apply a less powerful pump in conjunction with the traditional heat generator, connected to work only during the peak period of heat consumption.
Both solutions are associated with an increase in the cost of the system and may seem unjustified compared to systems with a traditional heat generator (carbon boilers on hydrocarbon or electric fuel) that can change performance in proportion to the needs of the object. But it should be borne in mind that the possibility of using a renewable energy source contributes to the savings of fossil resources is in itself useful and self-sufficient (without regard to economic feasibility), and the profitability of this method in heating systems can be increased by the appropriate design solution, based on taking into account as many factors as possible affecting technical and operational performance.

Materials and methods
This paper presents a method of evaluating options for building heating systems with air-water pumps in changing heat and heat-producing environments. The technique is based on the use of mathematical models of technical devices and statistical models of outdoor air parameters in different climatic areas of the country.

Results
The criterion of the cost-effectiveness of the heating system with a combined heat source (heat pump and boiler) will accept relative costs со C for the equipment and operation of the heating period: where is КТ С and ТН С -cost of boiler and heat pump, ruble respectively. rub; КТ k and ТН k -self-sufficiency ratio, respectively, boiler and heat pump, year -1 ; -corrective coefficients that take into account the cost of installing the boiler and heat pump respectively, rub.
The cost of thermal equipment usually depends on its power and can be represented by the following equations determining statistical distribution by different brands, models and manufacturers: -for heat pumps with minimum prices [10]: where is Operating costs will be expressed through the cost of heating the heat in the heating system in the respective devices.
In a water heater with an electric heater: where is эл с -electricity tariff, rub./W* hour; where is КТ  -heat generator useful factor; Accordingly, the formula (4) will take the form: where is . .
-coefficient, taking into account the standing period -the power of the heat pump, at the current temperature of the heat-containing environment, W.
For the temperature of the coolant in the heating system С t w   55 the power spent is determined from the expression [10]: where is The amount of heat transferred by the heat pump to the heating system during the period Т , determined through the transformation factor Qt k and the energy spent on the pump ТН W :   (13) Required nominal pump thermal power 0 . ТН Q to cover the thermal needs of the heating system and determine the cost of the device, accordingly, will be determined from the expression: where is -the need for thermal energy of the heating system is provided by the heat pump to the temperature of the outdoor air, corresponding to the equality of thermal power of the heating system and the power generated by the heat pump (bivalent temperature), and then the current heat load of the system is covered only by the boiler: