Methodical approach to estimating the potential of thermal energy production by heat pump plants in case of their implementation in regional district heating systems

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Methodical approach to estimating the potential of thermal energy production by heat pump plants in case of their implementation in regional district heating systems The results of the estimation of the annual potential for thermal energy production using heat pumps (HPs) in district heating systems (DHS) for the regions of Ukraine and the country as a whole are given. This study is relevant due to the high level of DHS development in Ukraine, which reaches 52 %. Today, the outdated equipment of DHSs in Ukraine needs significant technological modernization. Also, in the near future, it will be necessary to restore DHSs destroyed as a result of the total destruction of the civil infrastructure by the russian aggressor. The post-war reconstruction of Ukrainian cities has a unique chance to radically update DHSs using renewable energy sources and innovative technologies, including HPs. The authors propose a new methodical approach for the regional determination of the forecast implementation scope of HPs in DHSs. Using this approach, the economically available energy potential of thermal energy production by HPs in DHSs from various lowpotential heat sources (LPHS) was determined, both for the regions of Ukraine and for the country as a whole. As of 2020, this energy potential for DHSs of Ukraine is 62.601 million Gcal/year (262.1 PJ/year): 22.2 % is provided by natural LPHS (heat of air (2.2 %), river water (16.9 %), ground and groundwater (3.1 %)) and 77.8 % is provided by anthropogenic LPHS (heat of ventilation emissions of buildings connected to the DHS (43.0%), sewage

Introduction
District heating systems are one of the effective and promising means for providing thermal energy to consumers. In Ukraine, the level of centralization of heating systems is quite high, although the demand for thermal energy from DHSs has been gradually decreasing since the mid-90s of the last century: from 146.6 million Gcal in 1997 to 49.8 million Gcal in 2015. Today, the main technical equipment of the DHSs of Ukraine needs significant modernization due to insufficient funding during the last 30 years [1], and it will also be necessary to build new DHSs in the areas where hostilities are currently taking place due to the total destruction of the civilian infrastructure. The post-war reconstruction of destroyed cities with their heating systems and new construction will result in densification of the existing buildings, which will cause an increase in the heat load density of the DHSs. As a result, their efficiency will improve and the level of competitiveness will increase. This will be a unique chance to radically update them with the use of renewable energy sources (RES) and innovative technologies, including heat pump plant (HPP). At the same time, the cost of thermal energy for the consumers of the DHSs will significantly decrease.
As shown by previous studies carried out by the authors [2], heat pumps are one of the heat-generating technologies that should be used in DHSs of Ukraine. The operation of heat pumps in the mode of daily regulation of the electrical load in energy systems is also economically beneficial.
According to the European project "Heat Roadmap Europe", in the future, up to 25 % of the energy from heat pumps (HP) may feed to the DHSs. It is assumed that thermal and electrical systems with low temperatures of supply and return water will be integrated in the 4th generation DHSs, and they will also interact with district cooling systems [22]. These problems are discussed also in detail in [14,23].
Currently, the 5th generation DHSs are already being developed, which will be integrated and smart controlled and will apply innovative technologies using various types of renewable and secondary energy sources, in particular LPHS, thermal and electric storage systems, etc. [24][25][26].
Today, HPPs are used in DHSs in many countries. For example [9,[27][28][29], in Germany, in the town of Bergheim, the heat of sump water from the mining pit is used by two HPs of 293 kW each in the first DHS and one HP of 865 kW in the second DHS. In Finland, the return line of the DHS is the heat source for the HP of 158 kW in the town and municipality of Mänttä-Vilppula, and waste heat from the data center is used for the HP of 3.6 MW in the city of Mäntsälä. In Denmark, waste heat from the local paper factory is used for the HP of 5.3 MW in the town of Skjern, and from a food industry enterprise in Lille-Skensved for the HP of 7-4 MW (winter/summer). In Norway, seawater heat is used for the 13.2 MW HP in the municipality of Drammen and two HP with the total heating capacity of 16 MW in Forne-bu/Rolfsbukta. In Lausanne (Switzerland) the heat source for the HP of 4.5 MW is the water of Lake Leman. In Budapest (Hungary) sewage energy is used for two HPs (heating capacity is 1.69 MW, cooling capacity is 1.748 MW) in heating system of district with more than 100,000 habitants. In Milan (Italy) the underground water is a heat source for two HPs of 850 kW each, and at the same time, the excessively high level of groundwater is reduced. In Great Britain, in London, 500 houses in the Islington district use waste heat from the subway (Bunhill 2 network) for district heating.

Basic material
As you can see from the given examples, it is possible to use HPPs of different types in the DHSs, depending on the available LPHS. LPHSs can be of natural or anthropogenic origin. LPHS of natural origin is external air, surface waters of reservoirs (rivers, seas, lakes), underground waters, ground and rocks of the upper layer of the Earth, and solar energy; LPHS of anthropogenic origin is discharge (waste) water, air from heating and ventilation systems, flue gases, heated air and heated water or other liquids of cooling systems of technological processes, etc.
In European countries, large HPs use seven main types of LPHS [30,31], the features of which are given in the table 1. Generalized characteristics of heat pump technologies that use the mentioned above LPHSs are given in [31].
The use of LPHSs of anthropogenic origin for the operation of HPPs makes it possible to solve two tasks at the same time: reducing the negative impact on the environment and improving the energy efficiency of heat and cold production. This approach corresponds to the EU Strategy 2020 [32], which provides for the development of low-temperature DHSs, connecting local demand with RES and LPHS of anthropogenic origin, as well as with electricity and gas networks.
In [33], it is shown that it is advisable to use the heat of LPHS of both anthropogenic and natural origin for the DHSs of Ukraine. An estimate of the thermal potential of the above-mentioned sources for the HPPs of the DHSs is given in [34].
A new methodical approach was developed to estimate the potential of thermal energy production by HPPs in regional DHSs, which differs from the existing ones in that it takes into account the coverage of the region by DHSs and the possibilities of HPPs to access LPHS. According to this approach, a calculation model (formula (1)) was created. This model enables to determine the current and forecast economically achievable output of thermal energy ( ) τ Q by HPPs in DHSs for cities of the country: where n = 1,..., N is the sequence number and the total number of regions in the country; m = 1,..., M is the sequence number and the total number of cities with district heating systems in the region n; j = 1,..., J is the sequence number and total number of LPHS types; ( ) 0 τ jnm SPF is the (average annual) seasonal performance factor of energy trans formation in the city m, region n, LPHS of type j ( ) τ ac nm k is the access ratio in the city m of the region n to LPHS of the type j in the year τ; tr j k is the conversion factor of the HPP heat exchanger from LPHS of the type j; ϕ p jnm is the economically feasible energy potential of LPHS of the type j in the city m of the region n in the year τ, Gcal/year. It should be given some explanations about the estimated average seasonal performance factor 0 SPF . Thus, Article 10 of the Law of Ukraine "On Alternative Energy Sources" [35] contains the general conditions for classifying heat pumps as renewable energy equipment: "Aerothermal, geothermal, and hydrothermal energy obtained with heat pumps should be considered as obtained from renewable sources, provided that the final energy output significantly exceeds the consumption of primary energy, which is necessary to drive heat pumps". The Directive (EU) 2018/2001 [36] establishes the criterion for classifying HPP as renewable energy equipment -it is the minimum acceptable value of 0 SPF , which is equal to: where η is the efficiency factor of the energy system for electricity production, which means the "the ratio between total gross production of electricity and the primary energy consumption for the production of electricity and shall be calculated as an EU average based on Eurostat data" (Directive (EU) 2018/2001, ANNEX VII [36]). Calculations of the electrical efficiency of the energy system of Ukraine according to the Eurostat methodology given in [37] and in accordance with the data of the State Statistics Service of Ukraine regarding the energy balance of the country for 2010 [38] provide the 0 SPF of 3.2 [39]. Based on the mentioned above and taking into account the information given in [40] and [41], the value of 0 SPF was calculated for different LPHSs, and assumptions were made regarding the access factors for LPHSs and transfer coefficients of HPPs heat exchangers. The results are shown in the table 2.
The coverage coefficient ( cav nm k ) by DHS for the region was determined according to [42].
Economically feasible potentials of LPHS are Note. * It is assumed that HPPs air-water and HPPs ventilation emissions-water will operate together during the heating period, therefore the air will be diluted by ventilation emissions of buildings and its temperature will rise. In the non-heating period, ventilation emissions will not be used, but only air. τ nm is the duration of the heating period in the city m of the region n, days; n is the rate of air circulation in apartments, once per hour; 24 is the number of hours in a day. The thermal energy potential of air was determined by the formula [34]: where ϕ p е is the economically feasible air potential in the region n; ϕ p t is the technically achievable air potential in the region n; ϕ t c , ϕ e c is the technically achievable and economically feasible air potentials in the country, respectively [43,44].
The available thermal energy potential of river water a m E (GJ/year) is calculated according to the formula [34]: where w C is the specific heat capacity of water, 4190 J /(kg•°Ñ) at 15 °Ñ; p is the water density, 998 kg/m 3 at 15 °C; ∆t is the change of the river water temperature in the heat pump condenser, 2 °Ñ is accepted; r W is the annual flow (volume) of river water, km 3 /year.
The potential of waste heat of boiler houses and combined heat power plants (CHPPs) is The economically feasible potential of waste water, ground and groundwater, and thermal secondary energy resources in industry was determined according to [21,45,46], respectively.
The economically feasible potential of seas is limited only by the presence near the DHS, accessibility, technical and financial capabilities of the heat supply company.
Information on the production of product types in the regions is presented by the State Statistical Service of Ukraine as confidential, therefore the potential of thermal secondary energy resources (TSER) was determined for the country as a whole. The total annual energy potential of TSER will be 32,075.8 thousand GJ, or 7,660.8 thousand Gcal. The access factor is taken as 0.3, and the heat exchanger conversion factor is 0.7, 0 SPF = 4.2. Then the amount of thermal energy produced by HPP in DHS will be 6756.8 thousand Gcal/year. Using this model, the above-mentioned potential was calculated for Ukraine as a whole (Fig. 1) Figure 1. The total energy potential of thermal energy production of HPPs in DHSs of Ukraine and distribution by its components: 1 -Air -Water; 2 -Ventilation emissions -Water; 3 -Flue gas -Water; 4 -Process heat -Water; 5 -Sewage water -Water; 6 -Rivers, reservoirs -Water; 7 -Ground and groundwater -Water. and at the level of its regions (Fig. 2) for 2020. Fig. 1 shows that, as of 2020, the total potential of thermal energy production by HPP in DHS of Ukraine may reach 62.601 million Gcal/year, which is equivalent to 8.9 million tons of standard coal per year. The distribution of the energy potential of thermal energy production from LPHSs of various origins is: from natural LPHSs  LPHS is greater than in regions with agrarian industry (Fig. 2).
Undoubtedly, it will be impossible to fully realize such thermal potential in the DHSs because of the following reasons: -in the process of DHSs development, in addition to HPPs, other thermal energy generation technologies will be used -solar collectors, CHPPs, biofuel boilers, electric boilers. Accordingly, these technologies will compete with each other, and it is not a fact that HPPs will occupy the entire thermal energy market; -processes of decentralization will continue, especially in the field of hot water supply due to mass installation of individual water heaters (boilers); -the efficiency of production, transportation, and consumption of thermal energy will increase; -the population of Ukraine will decrease; -global climate change (warming) will occur. As a result of these and other reasons, as it is shown in [2], the demand for thermal energy of the DHSs will steadily fall and will reach the level of 35 million Gcal/year in 2050 (28 % less than in 2020), and thermal energy production will be 38.8 million Gcal/year. At the same time, the share of HPPs will be about 38.7 % (about 15 million Gcal) [48]. In fact, this is the predictive potential that will be used.
As a result of the financial analysis of the projects of the use of HPPs in the DHSs with various LPHSs, a profitability index was determined and used as a measure for their ranking. The profitability index was calculated by the formula: where i PI is the profitability index of the project i, i NPV , i IC are the net present value and initial cost of the project j, respectively.
The ranking results are given in the table 3. Of course, it is advisable to implement projects with the best financial indicators in the first place. According to the table 3, they are HPPs, which use waste heat of boiler houses and CHPPs, technological processes, and ventilation systems as LPHS. An additional advantage of these LPHSs is that they are anthropogenic. It is also advisable to include projects for the implementation of HPPs, which use the heat of sewage water, in the list of priority implementation, despite the fact that they are less effective than projects with natural LPHS (heat of the sea and rivers). This is due to their convenient location (in every quarter of the city), high heat and temperature potential, heat flow stability, accessibility, and a decrease in their impact on the environment. The priority of implementing HPPs, which use low-potential heat from sources of anthropogenic origin, is also explained by the direct proximity to the DHS, greater specific heat capacity and relatively greater temperature potential (15 °Ñ to 45 °Ñ). Whereas sources of natural origin have a lower temperature potential (5 °Ñ to 20 °Ñ, and for outdoor air in winter and below -10 °Ñ). Open reservoirs are not always located within the settlements with DHS, and the air and topsoil have a low specific heat capacity, which requires the use of significant volumes of air and land areas to extract the necessary heat capacity from these sources.
The use of the LPHSs discussed above for the mass implementation of HPPs in the DHSs will enables make their projects typical and carry out wholesale purchases of equipment, which will reduce investment costs. The use of natural LPHS (heat of the sea, rivers, ground and groundwater) will be limited and has a single character.
An ideal place for HPP location is a place close to LPHS and DHS networks. CHPPs meet these When the heat output of CHPP changes, its electric output proportionally changes, and this can be used to provide auxiliary (system) services to power systems. To do this, HPP should be installed on the CHPP territory. When the heat output of CHPP changes, the heat balance in the DHS will be maintained by the HPP and, if necessary, by gas boilers. HPPs can also be implemented in district and quarterly boiler houses. In this case, it is attractive that: -the majority of boiler houses are located in the center of heat loads; -there are no problems with heat accumulators, because main heat networks can be used as them; -near the boiler houses, as a rule, sewer collectors are located, which can be used as LPHS for HPP; -according to statistical data, boiler houses have a significant excess of installed capacity, and, accordingly, boiler units. Therefore, there are no problems with the HPP placement, they can be placed on the sites of dismantled outmoded and worn-out boilers; -an increase in the electrical load of boiler houses in the case of HPP introduction is not problematic.
In addition to the LPHSs mentioned above, the heat of cooling and condensation of steam of flue gases from boilers and the outside air can be used as a LPHS for HPPs.
HPPs can be located on the roofs of residential, public, and administrative buildings, which are connected to the DHS. Ventilation emissions of these buildings and ambient air can be used as LPHS.
Another variant of HPPs implementation is in heat distribution systems. This option provides for the installation of HPPs in central heating points, heat distribution stations (heat substation). During the heating period, the technology can be used for heating and/or hot water supply. The heat produced by the HPPs can replace the energy produced by the boilers in the boiler house or be accumulated in the main return line. The heat of sewage, the collectors of which are located in every residential area of large cities, and air (if there are no others nearby) can be used as LPHS.
Taking into account the significant unevenness of hot water consumption, the use of this technology in the non-heating period is possible only if a heat accumulator is installed in the heat substation, or a branch of the main network connected to the heat substation is used as an accumulator.
The technology of using HPPs in heat distribution systems can be used to increase the heat load of the existing DHS (in case of new consumers). Let's consider it on the example of Kharkiv CHPP-5. According to the project, it was supposed to supply heat to the city through three main pipelines, but only two of them were built. Therefore, part of the installed heat capacities turned out to be actually "closed" due to the insufficient transmission capacity of the existing heating networks. As a way out of this situation, there is installation of HPP, which will obtain heat from the return lines of existing networks, on the consumer side in the heat distribution systems. In this case, the heat carrier flow rate will not change, and its temperature in the return lines will decrease that indicates the release of additional heat. Thus, funds for the laying of additional pipelines will be saved. HPP installed in heat distribution systems can be used to control the load of energy systems. The algorithm of operation is as follows. At low load in the power system (night-time valley), HPPs operate with maximum productivity, and at high load -with minimum productivity, up to their complete shutdown. In this case, the heat balance in the DHS of the residential area is provided with the heat of the main pipelines. In this technology, both electric heaters and HPP can be used. LPHS for HPP can

Conclusions
A new methodical approach is proposed for the regional determination of the forecast implementation scope of heat pump technologies in the DHSs. During the period of post-war renewal of Ukraine, this approach enables to estimate the economically available energy potential of HPPs in the case of using different LPHS in each region, taking into account the consequences of Russia's military invasion of Ukraine. This methodical approach takes into account the regional features of the use of heat pump technologies with different types of LPHS and their changes over time for perspective forecasting: seasonal (average annual) calculated coefficient of energy transformation from the LPHS, coverage of the DHS region; access to LPHS; heat transfer efficiency of the HPP heat exchanger from the LPHS; economically feasible energy potential of the LPHS.
The total achievable potential of heat production by HPPs in the regional DHSs of Ukraine was calculated: 62,601 thousand Gcal/year, which is almost twice the annual release of these DHSs in 2020.
The post-war reconstruction of destroyed cities with their heating systems and new housing const-ruction will result in densification of the existing buildings, which will cause an increase in the heat load density of the DHSs. As a result, DHS's efficiency will improve and their level of competitiveness will increase. This will be a unique chance to radically update DHSs using RES and innovative technologies, including HPPs. At the same time, the cost of thermal energy for the consumers of the DHSs will significantly decrease.