Three-Year Exploitation Tests of a Photovoltaic Plant in a Zero-Energy Single-Family House under the Polish Conditions

The subject of the study is the analysis of the energy self-sufficiency of a single-family house, equipped with an on-grid photovoltaic plant and electric heating system. The study is based on 3-year tests of a real plant located in southwestern Poland. The main aim of the research was to determine the conditions for full balancing of the energy produced and returned from the grid in relation to the legal system in Poland. The climate conditions and trends of their changes at the location of the house, as well as the impact of the angle of inclination and orientation of the modules on energy yield were analyzed. The annual and monthly balances of energy produced, fed into the electricity grid and consumed during the period of 2017–2019, were presented. The monthly and annual variability of generated energy was subject to statistical evaluation. The payback time and the value of the avoided CO2 emissions were calculated. The final effect of the research was to determine the energy, economic and ecological profits of the analyzed installation. It was shown that in the “net-metering” system in force in Poland, it is possible to fully cover the energy demand just by using solar energy, and the reimbursement for a photovoltaic plant will take place after approx. 8 or 12 years, depending on the electricity tariff chosen.


INTRODUCTION
In the era of eliminating the energy based on fossil fuels and solid biomass due to the climate and smog threats, there seems to be no alternative to the zero-energy construction. The energy self-sufficiency effect of a single-family house can be achieved by using solar energy to power a heat pomp or electric heating. The latter case has been analyzed in this article. Considering the ever-increasing costs of grid electricity, the rapidly falling prices of solar plants, and the increasing number of sunny hours in Poland in recent years, photovoltaics has become the most promising direction for the development of distributed prosumer energetics under the Polish conditions. In Poland, in the years 1996-2016, the prices of photovoltaic modules dropped almost 10 times [Niechaj, 2016] and the installed capacity of photovoltaic plants as of 1.05.2020, according to the data from Polish Power Grids, amounted to 1833 MW, showing an increase of 181% y/y. Accumulation electric heating is distinguished by low investment costs and a practical lack of maintenance costs. In addition, it is characterized by moderate energy charges if it is accounted for under a dual-zone tariff-G12. It does not require a boiler or the construction of a heat distribution system, but only the purchase of the heating cables and their sinking in a slightly thicker than standard concrete underfloor screed, and/ or the purchase of relatively cheap free-standing accumulation furnaces. This study concerns such a heating system, which cooperates with an ongrid roof photovoltaic plant (hereinafter referred to as PV plant), i.e. releasing the surpluses of the produced energy to the electric grid, which are then retaken during the heating period. In addition, solar collectors are used to heat water. In accordance with the Polish Renewable Energy Act [Act, 2020], for the installations with an installed capacity ≤10 kW, to which this study relates, for 1 kWh fed into the electricity grid, 0.8 kWh can be retaken without any charge. The energy fed into the grid is billed not earlier than 12 months before the date of its introduction. The unused surplus can be used within the next 12 months, and if this does not happen, the seller has it for free.
Three years of operational experience of a typical single-family house located in south-west Poland (Fig. 1) showed that its energy self-sufficiency with the use of the energy and heat of solar radiation is possible -taking into account the legal conditions set out above.
The main aim of the study was to establish the conditions for achieving energy self-sufficiency, as well as to determine energy balances in relation to individual months and the years 2017-2019.

CLIMATIC CONDITIONS
The climate parameters affecting the efficiency of electricity production by a PV plant, in addition to insolation (Figs. 1-3, 5), include: • temperature (Fig. 6 Important arguments for the development of solar energy in Poland are: • the increase in insolation observed in recent years (Fig. 2); • the increase in the daily sunshine durationby over 1 h/d in 20 years (Fig. 3); • the decrease in the number of days with snowfall (Fig. 4).
The location of the analyzed building, due to the relatively high annual solar-radiation and moderate temperatures (Fig. 6), can be considered favorable from the point of view of photovoltaics. However, seasonal unevenness is a problem, because around 80% of total annual irradiation occurs between April and October (Fig. 5).
Other data affecting the energy yield in the area of the building location are collected in Table 1.

INFLUENCE OF THE ORIENTATION AND ANGLE OF INCLINATION OF MODULES ON THE EFFICIENCY OF A PHOTOVOLTAIC PLANT
The optimal direction of the module decline, regardless of latitude, is south, with an acceptable deviation to the east or west of ±45˚, which does not significantly affect the annual performance ( Fig. 7). According to Szymański [2013], with a 30˚ deviation from the south, the change in energy yield during a year is about 2%, and with a 60˚ deviation -about 8% 1 . For the angle of inclination of modules, this issue is less unequivocal. Due to the seasonal variation of the angle of incidence of sunlight, its optimum depends strictly on the geographical location. For Poland, in the case of the plants operating throughout the whole year, it is assumed that it should be in the range 1 Data for 30˚ module angle. of 30-40˚, with some authors pointing to an angle closer to the lower limit of the above range as more favorable [Baran, et al, 2013[Baran, et al, , Łotocki, 2013. For example, the authors [ Baran et al., 2013] indicate an angle of inclination of 27˚ as optimal for Wroclaw, i.e. ensuring the maximum energy yield per year. Similar values for southern Poland were obtained by Szymański [2013] -30-35˚ (Fig. 8). According to the author, for this range there is the highest percentage increase in energy yield in relation to the yield for the angle 0˚-113%. An additional aspect taken into account when choosing the slope of the modules may be their self-clearing, i.e. spontaneous sliding of the snow layer from the smooth surface of the module [Andrews et al., 2013]. However, in the era of global warming, this feature can be seen to be negligible for the considered location of the building (Fig. 3).

CHARACTERISTICS OF THE ANALYZED HOUSE
The tests were carried out for a detached single-family house with a usable attic (Fig. 9). The building has a roof with a slope of 32˚ and a direction of decline -SW (227˚). It is made in a brick technology from silicate blocks insulated with mineral wool. The roof was covered with black cement tiles. The living room with glazing was placed on the SW side and the utility rooms-on the NE side. The design data of the building, relevant from the point of view of heat balance, are collected in Table 2.
Electric heating was installed as the primary heat source. Accumulation floor heating was used on the ground floor, and accumulation electric stoves in the attic. The water is heated using solar collectors. The parameters of the heating installations are collected in Table 3, and the basic data of the PV plant -in Table 4.

ENERGY EFFECTS AND STATISTICAL ANALYSIS OF THEIR VARIABILITY
The results of the electricity balance calculations, averaged over 3 years, are presented in Table 5, the comparison of balances for individual years from 2017-2019 -in Fig. 10, and balances for individual months and years -in Fig. 11 and 12.
Electricity production in individual years can be considered stable and consistent with the value forecast by the SolarGIS model for the local conditions (maximum deviation of 10%). The variability of annual electricity production is a simple function of the variability of insolation in individual years (according to Fig. 3).    Figure 11 shows the characteristic mismatch between the electricity production maxima and the electricity consumption maxima per year. In the non-heating periods, the distribution network mainly serves as an energy accumulator.
The surpluses of the produced energy over consumed energy occur from April to October, when 80% of the total annual energy is generated. In the remaining months, the energy consumed definitely exceeds the production. The deficit is compensated by the energy "accumulated" in the distribution grid.
The distribution of electricity generated in relation to the average monthly values in the years 2017-2019 (Table 6) was assessed using a relative deviation from the average value (Table 7): (1) Fig. 9. View of the analyzed house from the SW side  The mean value of absolute deviations from the average value (D abs ) was also determined: where: i -subsequent months, E avi -the average value of energy produced in month "i" in a period of 2017-2019, E ri -the real value of energy produced in the month "i" of the year.
It is a frequently used measure of data set variability, illustrating the concentration of real values around an average value. The smallest absolute deviation from the monthly average was recorded in June 2017 -4.6 kWh, which is 0.3% of the average for this month, and the highest in April 2017 -252.7 kWh, which is 22% of the average ( Table 8).
Annual deviation of the energy production value from the average annual value for the years mentioned above can be assessed as insignificant. It amounted to -6.2%, 4.8% and 1.3%, respectively.
The results of the statistical evaluation showed the stability of annual energy production, despite significant deviations in some months, especially in XII, I, II - Table 7 (e.g. up to approx. 40% in January 2017).

ENVIRONMENTAL EFFECT
The environmental effect of the PV plant was estimated on the example of the avoided CO 2 emissions by the end user of electricity in Poland. According to [KOBiZE, 2019], the CO 2 emission factor for such users, according to the data for 2018, is 765 kg/MWh. It takes into account all electricity produced, regardless of the type of plant, i.e. installations for the combustion of fossil fuels and RES, as well as the losses during the distribution of electricity. The avoided emissions in 2017-2019 averaged about 7.7 Mg CO 2 /y.

FINANCIAL EFFECT
In order to assess the profitability of the PV plant, the PBT (Pay Back Time) indicator was used. This indicator specifies the time needed to recover the investment costs: where: K -gross PV plant cost, 14640 EUR 2 ; P -donation, 1100 EUR (acc. to the current Polish government program "My electricity"); E P , E F -according to Table 5; E P -E F -average annual amount of electricity produced and directly consumed, 1173 kWh/y; 0.8 -"return" factor (for 1 kWh fed into the network, the prosumer can retake 0.8 kWh -in accordance with [Act, 2020]); k -gross unit price of electricity, including distribution costs for individual customers in 2017, for the G11 tariff -0.12 EUR/kWh and for the G12 tariff (night zone / day zone: 70/30%) -0.09 EUR/ kWh; j -subsequent year of operation.
An annual increase in the electricity and distribution prices of 3%, and a 25 year lifetime of the plant were adopted. The assessment was carried out for 1-zone (G11) and 2-zone (G12) tariffs, assuming in the second case that 70% of energy is consumed in the reduced "night" zone. The costs of the energy drawn from the grid by the inverter (self-consumption at night -1 W) and the costs of cleaning the panels (in the analyzed period there was no need to wash the panels) were omitted.
On the basis of the PBT indicator defined above and the adopted assumptions, it can be predicted that the investment will pay back after 8.6 years for the G11 tariff, and after 12.1 years for the G12 tariff.
Taking into account the "return ratio" of 0.8 [Act, 2020], an annual energy balance close to zero was obtained, which allowed the charges for grid electricity to be minimized (or their practical absence in 2019, apart from minor distribution fees -approx. 3 EUR/mth).