The Energy, Economic and Environmental Efficiency of a PV Installation Cooperating with a Heat Pump in the Central Part of Europe. Case study

The paper addresses an analysis of the efficiency and profitability of the operation of a photovoltaic installation located in the geometric centre of Europe (near Białystok, Poland), where the intensity of solar irradiation is not too high compared to other European countries. It is calculated that in that place average solar irradiation being lower even by approx. 26 kWh than that for the whole Europe, which results in a 26% drop in the economic potential of the utilisation of solar energy for its conversion. A case study and an economic analysis show that without minimum funding amounting to 50% of the investment costs paid for the modernisation of a central heating system assisted by PV cells, the time of return of pecuniary expenditures exceeds 7 years. Apart from the Simple Pay-Back Time SPBT, discount indicators determined in the paper also include the net present value NPV and the internal rate of return IRR. Moreover, a direct ecological effect has been determined for such an investment.


Introduction
When searching for efficient techniques increasing the energy potential related to the conversion of pure energy originating from the Sun [1] -a spectral type G star, attempts are made to utilise it both by means of direct -helioelectric, as well as indirect methods, related to heat transfer [2], meaning heliothermal. Due to this, the commissioning of installations with photovoltaic cells with increasingly larger areas and higher powers seems to be a reasonable trend [3]. Such an action also follows one of the main objectives of the amended EU directive related to the energy characteristics of buildings [4], meaning the reduction of the emission of greenhouse gases until 2050 by 80-95% compared to 1990. In the long term, it will enable conversion of existing buildings into buildings with an almost zero energy consumption -for which the ratio of demand for nonrenewable primary energy EP is close to 0 kWh/(m 2 year). A solution to this involves an increase in the scale of complex and deep thermal upgrading, as well as the construction of new facilities with a low emission of CO2 and particulate matter, PM.
The term deep thermal upgrading is to be understood as reaching such an energy standard of a building after thermal upgrading, which would fulfil requirements related to energy efficiency like those for new buildings, and, e.g. this standard for residential single-family and multi-family buildings expressed by the ratio of demand for nonrenewable primary energy for the needs of heating, ventilation and the preparation of warm utility water amounts to EPmax, H+w = 70 and 65 kWh/(m 2 year), respectively; educational buildings: EPmax, H+w = 190 kWh/(m 2 year) (status for Poland Materials (ASTM). Moreover, the following models are also known: Second Simulation of a Satellite Signal in the Solar Spectrum (6S) [12], SCIATRAN [13], SHARM [14], RT3 [15], RTMOM [16], RAY [17], STAR [18], Pstar2 [19], DISORT [20], along with computer programs which use them: MODTRAN [21], STREAMER [22] and SBDART [23], PV Lighthouse, SMART [24], SOLAR GIS, Solar CalQ 1.0 and others. The present paper analyses the energy, environmental and economic efficiency of a sample photovoltaic installation located in the geometric centre of Europe (near Białystok, Poland), where the intensity of solar irradiation is not too high compared to other European countries [25]. Currently, one of the basic requirements faced by buildings undergoing modernisation involves limitation in the emission of carbon dioxide even by over 90% compared to original values. In order to fulfil these criteria, it is necessary to use alternative solutions based on renewable energy sources. In here, photovoltaics constitutes a reasonable option and provides the possibility to achieve a high level of reduction in the emission of primary contaminants, such as CO2, SOx, NOx or solid particles.
European law [3][4][5]8] encourages the use of renewable energy sources, but an analysis of the profitability of their utilisation indicates the lack of feasibility, which is decided primarily by the location, as confirmed by economic efficiency indicators calculated for a sample investment, such as the Simple Pay-Back Time SPBT, the net present value NPV and the internal rate of return IRR.
Moreover, the paper presents a comparative analysis for the potential of utilising solar energy in European countries with extreme values of total average intensity of solar irradiation.

Solar Irradiation Density in Europe.
It turns out that, according to the calculations of Szymon Antonii Sobiekrajski of 1775, the geometric centre of Europe is located in north-eastern Poland, in Suchowola near Białystok. According to statistical data originating from a weather station in this area, developed based on full 30-year measurement cycles used for energy balances of buildings, the sum of total intensity of solar irradiation incident on a horizontal plane amounts to ITHav,year = 897.14 kWh/m 2 (the monthly average is ITHav,month= 74.76 kWh/m2) [26], while this value for Poland and Europe is estimated (based on interpolation and modelling of 580 meteorological measurements constituting a database for a period of 1981-1990) at 1012 kWh/m 2 (ITHav,month = 84.33 kWh/m2) and 1205 kWh/m2 (ITHav,month = 100.42 kWh/m 2 ), respectively [27,28]. The highest and lowest values of total intensity ITHav,year are recorded in Malta and Finland and they amount to 1766 kWh/m 2 and 841 kWh/m 2 , respectively. The distribution of direct average annual solar irradiation in Poland and European countries is mapped and updated in the Solar GIS base in an ongoing manner [29]. The Solar GIS database has been validated at 200+ locations globally. A long historical archive of solar irradiation data is available for any location between latitudes of 60N and 45S. Figure 2 presents a general map of the distribution of total annual average solar irradiation for Poland and for European countries. Graph 3 presents the monthly distribution of total solar irradiation intensity for the geometric centre of Europe -a spot near Białystok, which indicates that the monthly average solar irradiation intensity for the geometric centre of Europe is lower by approx. 26 kWh than the European average, which results in a 26% reduction in the economic potential of utilisation of solar energy for the purpose of its conversion. Compared to conditions in the country, this amounts to 11%.
Additionally, Figure 4 shows a climograph representing countries with extreme values of the dry-bulb temperature, MDBT, which is compared to the ITH value for the geometric centre of Europe.   Graph 5 in turn presents average ITH values recorded by the Photovoltaic Geographical Information System (PVGIS) for European Communities in the years 2001 -2019, which indicate that Poland is rated twentieth in terms of the conditions of insolation, and the ITH in here is lower by 16% and 43% than European average and the maximum average for Malta, respectively, and higher by 17% than the minimum average recorded for Finland. For the highest possible utilisation of the energy potential of PV panels, it is suggested to optimise their tilt angle, or additionally to commission a tracking installation [30,31]; the 18-year average optimal angle of the position of photovoltaic panels for Poland amounts to approx. 36 o , with 32 o for Malta and even 45 o for Finland (see Figure 6).    Simulations were performed for the central part of Europe -an area near Białystok (Poland), the capitals of Malta -Valletta and Finland -Helsinki, for which the respective values of total average intensity of solar irradiation on the horizontal plane were the highest and the lowest. Special attention should be paid to Finland, for which, due to locational aspects, the conditions of insolation were also estimated in the city of Rovaniemi, situated in the Arctic Circle. The input data and sample results of the performed simulations of spectral irradiance (extraterrestrial, direct, diffuse, global) vs wavelength incident on the module, horizontal and perpendicular, are listed in Table 1 and on x -y graphs. The tilt angle varying among countries results from the optimisation of the positioning of solar panels aimed at the utilisation of their maximum capacity (see Figure 6).  8,9,10,13 Power density (perpendicular and into module location) (W/m2): see Figure 14 Photon current (perpendicular and into module location) (mA/cm2): see Figure  15 Atmospheric transmission vs wavelength: see Figure Figure 12 Power density (perpendicular and into module location) (W/m 2 ): see Figure 16 Photon current (perpendicular and into module location) (mA/cm 2 ): see Figure  17   In addition, for the geometric centre of Europe -Białystok, Figure. 11 presents sample atmospheric transmission vs wavelength, taking into account variables implemented into a computational algorithm, which include: Rayleigh scattering, aerosol scattering, water vapour absorption, ozone absorption and unmixed gas absorption.    As can be seen based on Figures 14 and 15, the middle of summer, which is considered to occur on the 15th of July, does not exhibit high variances in insolation in each one of the analysed cases. The difference between the values of power density and photon current for Poland, Malta and Finland does not exceed 3.5% both for solar rays with perpendicular incidence and those with an average optimal angle for a given country, amounting to 36, 32 and 45 o , respectively.
However, considering the data on insolation for January, in which the average respective numbers of sunshine hours recorded for Poland and Malta amount to 31 [34] and 169 [35] (meaning 5.5 times more solar energy in Malta in January and 33% more annually), the modelled values of power density and photon current exhibit considerable variability. Therefore, between the central point of Europe -Białystok (Poland), the capitals of Malta -Valletta and Finland -Helsinki, the respective differences in power density amount to 37 and 36% for direct, 37 and 50% for scattered, 41 and 37% for total solar irradiation directed perpendicular to the plane, as well as 60 and 34% for direct, 26 and 27% for scattered, 54 and 33% for total solar irradiation directed at an average optimal angle for a given location (see Figure 16). As regards the estimated difference between the potential utilisation of electrical energy from solar photons, the relationships are comparable. Thus, the photon current amounts to 29 and 30% for direct, 69 and 49% for scattered, 32 and 31% for total solar irradiation directed perpendicular to the plane, as well as 50 and 28% for direct, 18 and 17% for scattered, 46 and 27% for total solar irradiation directed at an average optimal angle for a given location, respectively (see Fig. 17). However, when the above values are related to the city of Rovaniemi (Finland), located in the Arctic Circle, the respective estimated differences in power density and the energy of photons will each time amount to approx. ~98 and 97% (see Figures. 18 and 19).    The presented optimization could be also conducted using SMARTS software. It seems to be a slightly more complicated and complex tool, being used by scientists and engineers to test the capacity of devices such as spectroradiometers or spectrophotometers, and to verify broadband irradiance beam models, determine the reference spectra (e.g. ASTM G-173 and ASTM G-177) used by the American Society of Testing and Materials (ASTM), the deterioration of materials (e.g. in photovoltaics) subjected to long solar exposure; the software calculates, for a specific wavelength, the impact of the changing composition of Earth's atmosphere on the distribution of solar irradiation energy or photon energy.
The program is written in the FORTRAN language; an implemented algorithm enables presenting the relationship between atmospheric attenuation, as a function of changing albedo, and optical depth. The proposed spectral resolution varies depending on irradiation wavelength, and thus for a UV range of 280 -400 nm it amounts to 0.5 nm, for a 400 -1750 nm range it is 1 nm, and for 1750 -4000 nm it amounts to 10 nm. However, on our part, we believe that the software is highly unstable and it often displays errors or crashes without any reason.

Optimisation of the Size of a PV Installation Cooperating with a Heat Pump
In order to determine the size and estimated costs of a photovoltaic installation (supporting the operation of a heat pump), as well as static and dynamic pay-back time indicators for investment expenses, necessary auditing calculations were performed for a sample educational building (with an area with adjusted temperature of Af = 1324.29 m 2 ) located in Białystok -near the geometrical centre of Europe. Table 2 presents basic and necessary input data for further analysis. In the current '0' status, the building is heated by means of a boiler fired with type E methane-rich natural gas; an electric brinewater heat pump supported by a PV installation has been proposed for use after thermal upgrading. Upon thermal upgrading, also encompassing the enhancement of heat insulation, the design heat load and usable energy decreased by 30%. Calculations of the annual amounts of carbon dioxide emitted into the atmosphere and its ecological effect are based on emission indicators listed in table 3 [36]. In order to establish the direct ecological effect of the investment [37], the first step involves determining the emission of CO2 from a natural gas boiler station, for option '0' (formulas 1-3), the next one focusing on a boiler station based on a system of heat pumps (formulas 4-5); the combined results and the achieved reduction in CO2 are presented in tables 4 and 5. Annual emission of CO2 from a natural gas boiler: Annual emission of CO2 from electrical energy for powering the boiler assembly: Total annual emission of CO2 for the boiler station: Annual emission of CO2 from electrical energy for powering the heat pumps: Combined annual emission of CO2 for a system based on heat pumps: Resulting reduction in CO2 for a system based on heat pumps: 1) except for CO2, the ratios of unit emissions are specified based on [36]; negative values represent an increase in emissions, with positive ones for reduction The next step involved determining the required minimum power of PV cells amounting to Pmin= 36.43 kW (relationship (7)) and their number nPV = 182, in order to achieve a minimum reduction in CO2 emission of 90% relative to the current status.
The required number of PV panels: . ≅ In order to select the minimum number of PV cells, it was assumed that the estimated average daily time of harvesting energy by photovoltaic cells for the winter period is 7.5 h, the surface area of a single photovoltaic panel -1.6 m 2 , and the recovery of electrical power from a single panel is 0.2 kW.

Power production estimation for grid-connected, tracking and off-grid systems.
The simulation performed using the Photovoltaic Geographical Information System (PVGIS) application [38] allowed comparing the production of energy in a photovoltaic system PV for three cases: 1. on-grid, 2. in a tracking system, 3. off-grid The calculations were performed for the same locations which are analysed above: Białystokthe geometrical centre of Europe, the capital of Malta -Valletta, and the city of Rovaniemi situated in the Arctic Circle, in Finland. The results of the simulation are presented on graphs 25-27 and exemplary simulation inputs and outputs are provided below:

Simple and discounted indicators of economic efficiency
For the options of thermal upgrading analysed in an energy audit (improvement groups), at least the following simple and discounted indicators of economic efficiency are calculated: •  Table 7 were made in order to estimate the static indicator of profitability, which is the SPBT. Moreover, assuming a discount rate of R = 4%, the indicator determined based on relationship (8) is NPV < 0 and it amounts to -1070259.69, which also negates the feasibility of the investment.
The investment does not turn out to be undeniably feasible until reaching 70% of fundingpossible to acquire via contests organised periodically with the participation of the European Union's capital, e.g. Norwegian Funds 2020. Therefore, when taking advantage of the funding, in this case SPBT = 6.6 years, which is a value lower than the maximum threshold value for which the investment is considered profitable, meaning 7 years. Interestingly, already with 50% of funding, the dynamic indicator of economic efficiency, which is the NPV, deemed more credible than the SPBT, takes on values higher than '0'. To be clear, the relationship between the NPV indicator and the discount rate was determined as well, as shown in Figure 28.  Figure 28. NPV for an investment as a function of the discount rate, R Figure 28 indicates that the internal rate of return IRR (for which the net present value of the evaluated option equals zero, NPV = 0 -see relationship (9)) is between 4% and 5%, and it is higher than the discount rate effective in the calculation period R = 4% Table 8 lists the basic indicators of economic efficiency of an investment implemented in an education centre, near the geometrical centre of Europe, involving the modernisation of a gas boiler station and the assembly of a renewable heat source -a ground heat pump with a vertical heat exchanger supported by photovoltaic cells (the total costs include the purchase of a heat source, the drilling of boreholes, the assembly of PV cells along with gel batteries). On the one hand, and for good reason, calculations are performed involving the pay-back time for expenses paid for investments related to the installation and use of renewable energy sources, which include, e.g. photovoltaic cells, often pointing at very significant savings in operating costs, as well as a reduction in harmful substances emitted into Earth's atmosphere -especially carbon dioxide and particulate matter PM -compared to the conventional manner of producing this energy.
However, these values should be related to the life cycle of a given installation, taking into account the energy, the costs and emissions associated with its components [39].

Conclusions
An analysis of the energy and economic efficiency and the ecological effect of the commissioning of a photovoltaic installation located in the geometrical centre of Europe (near Białystok, Poland) supporting a modernised central heating system based on heat pumps with a vertical ground exchanger proves that: • in order to achieve a minimum reduction in CO2 emission of 90% (a level required to be granted funding) relative to the existing status, it is necessary to install PV cells in a number of 182, which generates high investment costs; • the economic potential of the utilisation of solar energy for the purpose of its conversion may reach even up to 26%; • the Simple Pay-Back Time of expenses paid for the investment SPBT = 22 years, which in the practice of investment economics is considered infeasible; • it is not until reaching 50% of funding that the dynamic indicator of economic efficiency NPV would take on values higher than '0'; • an investment is entirely profitable with 70% of funding, at which SPBT < 7 years, although NPV > 0; IRR is lower than the effective and adopted rate of return amounting to 4%.