Specific Yield Analysis of the Rooftop PV Systems Located in South-Eastern Poland

Abstract

In the last few years, Poland has experienced a significant increase in photovoltaic (PV) installations. A noticeable contribution to this dynamic growth belongs to the prosumers. This paper presents the energy efficiency analysis of nine prosumers’ PV installations located in South-Eastern Poland. Eight of the systems are grid-connected and one is a hybrid (PV with the energy storage). New technology modules with efficiencies between 19% and 21%, as well as various PV system configurations related to orientation and tilt, were taken into consideration. Final yields were found and a financial assessment was presented. The average annual specific yield of all analyzed PV systems was found to be 990.2 kWh/kWp. The highest ratio of yearly energy production was noted for the system of bifacial monocrystalline silicon modules with 20.3% efficiency (1102.9 kWh/kWp). Median and maximum yields obtained by this system for the best insolation month (June 2021) were 6.64 kWh/kWp and 7.88 kWh/kWp respectively. The annual specific yield of other systems ranged between 868.8 kWh/kWp and 1075.5 kWh/kWp in dependency on module efficiency, system orientation, or tilt angle. The amount of energy produced in the summer half-year was found to be significantly higher (between 76% and 83% depending on the system) than in the winter period. The self-consumption ratio of the energy produced by the PV system installed for company prosumers ranged from about 50% in the summer months to almost 97% in winter. The payback period was below 8 years with the levelized cost of electricity equal to 0.14 €/kWh.

1. Introduction

Nowadays about 77% of electric energy in Poland is produced from coal. This value should be successively decreased by the usage of renewable energy sources (RES) according to Regulation (EU) 2018/1999 of the European Parliament and of the Council of 11 December 2018 on the Governance of the Energy Union and Climate Action [1] as well as Poland’s National Energy and Climate Plan for the years 2021–2030 [2]. The objective is 21–23% of the RES share in gross final energy consumption by 2030 (total consumption including electricity, heating, cooling, and transport). The share of renewable energy sources in electricity production should increase to 32% in 2030 (28.4% share of RES in heating and cooling, 14% in transport). The reduction of greenhouse gas emissions in 2030 compared to 2005 (sectors not covered by the Emission Trading Scheme, ETS) is expected to be −7% [2].

Considering the goals for RES increase, significant growth of the photovoltaic (PV) market in Poland can be observed in the last few years. The latest data published by the Institute for Renewable Energy (September 2021) reveal that the total power capacity of the PV installations in Poland exceeds 6.3 GW [3]. It has to be noted that more than 70% of all systems belong to prosumers. In 2020 alone, the power capacity increase from new prosumers’ PV installations was 2.05 GW [4]. Such rapid growth in the prosumer’s PV market in the last two years was launched by the “My electricity” program dedicated to households in the first stage and then also for small companies. Information about this program in Poland can be found in [5,6].

It is assumed that the increase of photovoltaic installations in Poland will continue, achieving about 7.3 GW in 2030 and 16 GW in 2040 [4,6]. Bódis et al. analyzed the technical potential of the rooftop solar PV systems in each European Member State. The expected electricity output for fully covered available roofs in Poland is about 30,000 GWh/year, placing this country in the seventh position among all European Members [7]. Considering the fact that the total energy produced from photovoltaics in Poland in 2020 was 2374 GWh (prognosis in 2021 was 5280 GWh) [4], there is still space for increased rooftop PV systems.

One of the most important factors that should be taken into account in the development of photovoltaic installations is the system yield which depends on irradiation [8,9], module temperature [10,11], the technology of the PV modules [12], or tilt and azimuth angles of the PV system [13,14,15].

Many scientific papers have been published regarding the European sites with favorable solar resources where the PV market has been at a high level for a long time [16]. Detailed performance analysis of such systems including various locations, different sizes of the system, and technology of the modules can be found in the paper of Bansal et al. [17]. A review of rooftop systems was also proposed by Milosavliević et al. [18]. Micheli et al. presented the analysis of two PV systems located in northern Italy (latitude 45°38′ N) with a power capacity of 2.99 kWp and 11.7 kWp and efficiencies of the modules of 18.4% and 16.6%, respectively [19]. In the first system, the tilt angle was close to the optimal (30°). Modules of the second system were oriented 35° west and inclined at 10°. The annual specific yield was found to be 1400 kWh/kWp and 1277 kWh/kWp, respectively [19]. In the work of Žnidarec et al. [20], two 5 kWp rooftop PV systems with silicon monocrystalline (sc-Si) and polycrystalline (mc-Si) module technologies with efficiencies of 15.3% were analyzed. The location of the systems was Croatia (latitude 45°55′ N). The tilt angle of the PV array was 7°. The monthly specific yield ranged from 185 kWh/kWp in summer to 16 kWh/kWp in winter. The yearly yield of the sc-Si PV system was found to be 1116.3 kWh/kWp while for the mc-Si PV array it was 1065.3 kWh/kWp [20]. Due to favorable irradiation in the location of southern Italy (latitude 39°42′ N), a much higher value of yearly specific yield (1480 kWh/kWp) was found for the rooftop system analyzed in the paper of Ghiani et al. [21]. The module’s efficiency was relatively low (13.4%) compared to the present technology. The tilt angle was 11°.

Many analyses can be also found for the rooftop systems located at high latitudes in European countries leading photovoltaic technology and the market [22,23,24]. A comprehensive specific yield analysis in the period from 2012 to 2018 of several thousand PV rooftop installations located in Germany was presented by te Heesen et al. [22]. Annual yield ranged from 810 kWh/kWp to 1060 kWh/kWp depending on irradiation conditions and location. For the worst year, the average yield was found to be 901 kWh/kWp. During the best conditions year, the average yield was 1022 kWh/kWp [22].

Fewer reports can be found for sites located at high latitudes where the PV market is just developing. Studies carried out in the Netherlands (50°49′ latitude) by Ritzen et al. [25] revealed an annual yield of about 787 kWh/kWp with the efficiency of the modules equal to 14.8%. They observed that ventilation of rooftop systems led to 2.6% more electricity production than non-ventilated installations [25]. A relatively high value of annual yield (931.26 kWh/kWp) was measured by Adaramola et al. [26] for a system located in Northern Europe, Norway (59°65′ latitude). The efficiency of the PV modules ranged between 13.3% and 14.5%. One year of monitored results of a 1-kWp PV installation located in Poland (52°09′ latitude) was presented by Pietruszko [27]. The annual system yield was 830 kWh/kWp. The PV system was facing south and tilted at 30°. A PV rooftop system located in Poland was investigated by Zdyb et al. [28]. The PV modules with an efficiency of 15.2% were tilted at 14°. The annual specific yield was found to be 1098 kWh/kWp. This result was affected by a high sum of insolation during the studied period [28]. A comparison of energy production of experimental fixed and dual-axis tracking systems in a location in central Poland was presented by Frydrychowicz-Jastrzębska et al. [29]. The efficiency of the modules was 12.6%. Both systems were installed on the roof of a building. The specific yields of the systems varied between 16.45 kWh/kWp (fixed system) in December and 188.45 kWh/kWp in June (tracking system) [29].

With the dynamic development of the photovoltaic market in Poland [30], many households and companies have invested in photovoltaics. Some prosumers decided to install the PV systems despite unfavorable insolation conditions due to building orientation or roof slope. This paper focuses on the specific yield of various PV systems located in South-Eastern Poland to study the influence of azimuth and tilt angles, or the modules’ technology, on final energy production. The newest, monocrystalline silicon technology of the modules was considered. Most of the analyzed PV systems consisted of PERC (Passivated Emitter and Rear Cell), half-cut modules with efficiencies of about 20%, and the following system orientations: south, east-south, west-south, and east-west, were taken into consideration. To the best of the Authors’ knowledge, there are no analyses comparing specific yields under different working conditions of rooftop systems at a studied location available in the scientific literature when preparing this work. Thus, information about the specific yield of various prosumers’ rooftop PV systems at high latitude locations fills the gap in knowledge in this field.

2. Materials and Methods

2.1. Description of the PV Systems

Eight prosumers’ grid-connected PV systems and one hybrid were analyzed for specific yield. The self-consumption of the hybrid PV installation and the influence of energy storage on the systems’ functioning were also considered. All fields were installed in South-Eastern Poland. According to the Köeppen-Geiger classification, all of the analyzed installations were located on the border of two climates zones: Cfb (warm temperate, fully humid warm summer) and Dfb (snow, fully humid warm summer) [31]. According to Polish classification, the Lublin region is located in the third group, which is characterized by an average value of annual temperature equal to 7.6 °C [32,33] and average insolation of 1123 kWh/m²/year [5].

Four of the installations (PV1–PV4) were placed in the same location (latitude 51.29° N, longitude 22.74° E), which means they operated in the same solar radiation and temperature conditions. The total power capacity of the four systems was 49.96 kWp (136 modules). They were commissioned in October 2020. The next four systems (PV5–PV8) were selected from different locations in the area about 50 km from the city of Lublin (latitude was in the range between 51.24° N and 51.36° N). PV5 and PV6 systems were commissioned in November 2019. PV7 and PV8 were commissioned in February and March of 2020. The last analyzed installation, PV9, was located in the direction up to twenty kilometers from Lublin at 51.18° N latitude and 22.71° E longitude. This system was commissioned in 2019.

PV1 consisted of two subfields. The first one was composed of 22 series-connected PV modules, faced south-east and tilted at an angle of 10° (the tilt angle of the roof was 5°). The second PV field consisted of 18 series-connected PV modules, was oriented towards the south-west and tilted at an angle of 11° according to the roof tilt and orientation (azimuth angle was about 45°). PV2, PV3, and PV4 installations were composed of 32 series-connected PV modules (each system) faced south-east and tilted at an angle of 10°. Modules were fabricated in mono-PERC, half-cut technology characterized by high efficiency according to the manufacturer data. Additionally, the PV3 system consisted of bifacial PV modules. More details of the PV1–PV4 systems can be found in

Table 1. Main electrical parameters of the photovoltaic (PV) modules used in PV1–PV4 installations and system orientation details.

PV System	Modules’ Producer	Modules’ Power (Wp)	Efficiency (%)	Tilt Angle (°)	PV Power Capacity (kWp)
PV1: ES-WS	Canadian Solar CS3L-365MS	365	19.7	10–11	14.60
PV2: ES	Longi Solar LR4-60HPH-365M	365	20.0	10	11.68
PV3: ES BI	Longi Solar LR4-60HBD-370M Bifacial	370	20.3	10	11.84
PV4: ES	Longi Solar LR4-60HPH-370M	370	20.3	10	11.84
PV System	Inverter’s Producer	AC Power (kW)	Efficiency (%)
PV1-PV4	Solar Edge SE50K	50	98.3

and in the work of [34]. Every two adjacent modules were equipped with SolarEdge power optimizer P850 (68 devices in total) to raise the energy gain of the whole system. All systems were connected to a Solar Edge inverter SE50K (Figure A1). Data analysis was carried out using Solar Edge monitoring software.

A detailed description of the PV modules used in PV5–PV8 systems can be found in

Table 2. Main electrical parameters of the PV modules used in PV5–PV8 installations and system orientation details.

PV System	Module’s Producer	Modules’ Power (Wp)	Efficiency (%)	Tilt Angle (°)	PV Power Capacity (kWp)
PV5: EW	Longi Solar LR6-60PB 305M	305	18.7	30	3.66
PV6: ES 45°	Longi Solar LR6-60HPH 320M	320	19.3	30	6.40
PV7: S	Longi Solar LR6-60HPH 320M	320	19.3	20	40.0
PV8: WS 45°	LG355N1C-V5	355	20.7	30	8.165
PV System	Inverter’s Producer	AC Power (kW)	Efficiency (%)
PV5	Goodwe 3000D-NS-1F	3	97.8
PV6	Goodwe 6K-DT	6	98.2
PV7	Huawei sun 2000-36ktl-MO	36	98.8
PV8	Huawei sun 2000-8ktl-MO	7	98.0

. As can be seen, the tilt angles of the analyzed installations were close to the optimal (35° in Poland). The azimuth angle of the south-eastern system (PV6) was equal to 45°. The same angle was found in the case of a south-western system (PV8). PV5, the east-western installation, consisted of 12 series-connected PV modules of monocrystalline silicon (sc-Si) with half-cut technology. Six modules were oriented in the east direction, and the other 6 towards the west. The system was connected to a 3000 W inverter. PV6 consisted of 20 series-connected PV modules (sc-Si, half-cut) and it was connected to an inverter of 6000 W. PV7, a south-oriented installation, consisted of 125 PV devices fabricated in silicon monocrystalline, half-cut technology. A 36 kW inverter was used. The PV8 system consisted of 23 PV Si monocrystalline PV modules and a 7 kW inverter (Figure A2). More details can be found in [35].

The south-east oriented PV9 system consisted of 104 PV modules in three series-connected strings with 36, 34, and 34 PV generators in each. Every two modules were equipped with SolarEdge power optimizer P600. All strings were connected to the Solar Edge inverter SE 25K (Figure A3). Another inverter was used for energy storage purposes (Solar Edge SE 3500K) together with the battery (LG Chem RESU). The main parameters of the system can be found in

Table 3. Main parameters of the hybrid PV system (PV9).

PV Modules
Module’s producer	Penta ASM6610M Series
PV power (Wp)	290
Efficiency (%)	17.7
Tilt angle (°)	25
System capacity (kWp)	30.16
Inverter
Producer	Solar Edge SE 25K
Max. efficiency (%)	98.3
AC power (kW)	25
Producer	Solar Edge SE 3500K
Max. efficiency (%)	97.6
AC power (kW)	3.5
Battery
Producer	LG Chem RESU10H
Capacity (kWh)	9.8

. More details can be found in [36].

2.2. Calculated Parameters for Energy and Economic Analysis

The energy output was calculated as the amount of AC (alternating current) power produced by the system over a given period of time [13,26]:

$$E_{AC,d}={\displaystyle \sum }_{k=1}^L{P}_{AC,k}·{\tau }_k$$

(1)

$$E_{AC,m}={\displaystyle \sum }_{d=1}^N{E}_{AC,d}$$

(2)

where $E_{AC,d}$ and $E_{AC,m}$ are AC energy output during the day (d) and month (m) respectively, $P_{AC,k}$ is the k-th recorded output AC power,${\tau }_k$ is the duration of k-th interval, L is the number of registered data points during the day, N is the number of days in a month, and d is the day number.

Specific yield (final yield), Y_f (kWh/kWp), was calculated from energy output E_AC (daily, monthly or yearly) divided by the rated power output $P_{PV,rated} \left(Wp\right)$of the PV system [13,26,37].

$$Y_f=\frac{E_{AC}}{P_{PV,rated}}$$

(3)

The self-consumption ratio (SC), defined as the amount of energy consumed locally, was calculated using Equation (4) [38,39].

$$SC=\frac{E_C}{E_C+E_E}$$

(4)

where E_C is the amount of energy consumption from PV and E_E is the amount of energy exported to the grid.

The self-sufficiency ratio (SS), defined as the amount of consumption delivered by the local production from the PV system, was calculated from Equation (5) [38,39].

$$SS=\frac{E_C}{E_C+E_I}$$

(5)

where E_I is the amount of energy imported from the grid for a remaining load.

The cost of a unit of electricity in EUR/kWh of various PV systems can be compared using the levelized cost of electricity (LCOE) parameter [7,17]. LCOE was calculated following the method proposed by the National Renewable Energy Laboratory (NREL) [40].

$$LCOE=\frac{{{\displaystyle \sum }}_{n=0}^{ns}\frac{c_n}{{\left(1+d_r\right)}^n}}{{{\displaystyle \sum }}_{n=0}^{ns}\frac{e_n}{{\left(1+d_r\right)}^n}}$$

(6)

where $c_n$ is the PV system cost (EUR/kWp) in year n (for n = 0 the initial cost of the system was considered, for n > 0 the annual operation and maintenance O&M costs were included), n_s is the system lifetime in years, $d_r$ is the discount rate (%), $e_n$ (kWh/kWp) is the energy produced in the year n including systems’ annual degradation rate R_d (%), according to the Equation (7)

$$e_n=\{\begin{array}{cc}0& n=0\\ e_0\left(1-R_d\left(n-0.5\right)\right)& n>0\end{array}$$

(7)

where $e_0$ is the initial, undegraded energy yield (kWh/kWp). LCOE is in units of EUR/kWh.

For LCOE computations, the following parameters were considered according to the analysis of Bódis et al. [7]. The cost of the initial investment was assumed as 1100 EUR/kWp. The annual O&M costs were estimated as 3% of the initial capital investment (33 EUR/kWp/year). A time horizon (n_s) of 20 years was considered. The discount rate ($d_r$) was assumed as 8.7%. The yearly degradation rate was 0.7%. The initial energy of the systems was assumed as the energy produced during the analyzed year (all of the analyzed systems were commissioned in a similar period).

The return of the investment was calculated using a simple payback period ratio (SPP) [38] using Equation (8) according to the assumptions of the “My electricity” program [32].

$$SPP=\frac{Investment cost \left(EUR/kWp\right)}{Annual profit \left(\frac{EUR}{kWp}/year\right)}$$

(8)

The energy price of 0.15 EUR/kWh was assumed according to the data provided by Eurostat [41].

The code for analysis was designed using Matlab software.

3. Results

Figure 1 shows the results of the monthly specific yield (final yield, Yf) obtained by the PV1–PV4 systems during one year of operation. A seasonal trend with very low energy production in winter and much higher production in the summer period was observed in the previous works related to PV system performance [42,43]. Additionally, the average profile of irradiation (2005–2015) was computed using PVGIS [44] to compare with the seasonal trend of energy production.

Annual energy production ranged from 1041.8 kWh/kWp for the PV2 system to 1102.9 kWh/kWp for the PV3 bifacial system (specific yields of the PV1 and PV4 systems were 1071.7 kWh/kWp and 1075.5 kWh/kWp, respectively). Similarly, high values (1010 kWh/kWp–1046 kWh/kWp) were observed by Sarniak [45] in central Poland for the south-oriented system with a tilt angle of 22° and module efficiency of 16.5%. The mean annual yield of all PV fields was 1072.9 kWh/kWp. Almost 80% of the total energy was produced in the summer half-year. It should be pointed out that the presented results are for systems installed at the same location. Thus, not only irradiance but also temperature conditions were the same. Moreover, modules of very similar efficiencies were installed (Table 1). This led to the conclusion that the bifacial modules of the PV3 installation were characterized by a higher ratio of energy production compared to the monofacial devices. This is shown in Figure 1 for the summer months. In June, the difference in the final yield between PV2 and PV3 was the highest (over 3%). Lower values were observed for July and August (about 2.5%). Similarly, higher energy gains for a bifacial installation in Poland were observed by Olczak et al. [46]. In terms of high insolation conditions, the double-sided modules produced 10% more energy compared to the monofacial devices. The ground-mounted system was oriented towards the south and inclined at an angle of 45° [46]. These favorable conditions explain a relatively high ratio of energy production by the bifacial system. However, even for the suboptimal conditions forced by the roof angle and orientation (as in this case), the bifacial PV3 system exhibited a significant increase in energy production. This effect is shown in Figure 2. In the case of high irradiation days of summer month (June 2021), the PV3 system produced more energy (Figure 2a) with a median yield of 6.64 kWh/kWp (Figure 2b). The maximum yield was found to be 7.88 kWh/kWp. The median yield of the PV1, PV2, and PV4 systems ranged between 6.32 kWh/kWp and 6.44 kWh/kWp and the maximum yield was in the range of 7.65–7.66 kWh/kWp. Similarly, in a location in Poland on high insolation days (in June), Olczak et al. [46] observed daily specific yields of 6.08 and 6.39 kWh/kWp for a rooftop system and up to 7.03 kWh/kWp for bifacial modules. However, in the second case, it was not a rooftop system. Studies on a bifacial system (not a rooftop) under Polish climate conditions are also presented in [47].

Figure 3 presents the distribution of the daily specific yield of the PV1–PV4 systems in the selected month of spring (April) and autumn (November). In both cases, the interquartile range was higher compared to the summer month (Figure 2b), which means higher variability of energy production during the analyzed months. In the case of April, the specific yield varied from about 0.1 kWh/kWp to 7.28 kWh/kWp which proved the presence of not only fully covered, cloudy days but also clear sky days with high irradiance conditions.

The median yield was found on a similar level, between 4.57 kWh/kWp and 4.68 kWh/kWp in April and between 0.64 kWh/kWp and 0.67 kWh/kWp in November. With such a low amount of energy yield under the studied climate conditions, November can be also considered a winter month together with December and January. Similar observations related to November were revealed by te Hessen et al. [22]. Again, the maximum median results were observed for the bifacial PV3 system.

It should be emphasized that the specific energy production of the PV1 system (south-east and south-west oriented) is very close to the energy production of the south-eastern systems (PV2 and PV4) consisting of modules of the same monofacial sc-Si technology. Details of the daily average energy production in each month is summarized in

Table 4. Summary of daily specific yield obtained by the analyzed systems.

Month/Year	Daily Specific Yield (kWh/kWp)								Average Yield (kWh/kWp)
	PV1	PV2	PV3	PV4	PV5	PV6	PV7	PV8
11/2020	0.85	0.80	0.83	0.82	0.62	0.78	0.72	0.54	0.75
12/2020	0.47	0.43	0.45	0.45	0.35	0.45	0.36	0.24	0.40
01/2021	0.32	0.27	0.29	0.28	0.25	0.41	0.27	0.17	0.28
02/2021	0.97	0.38	1.29	1.31	0.92	1.52	0.79	1.02	1.03
03/2021	2.65	2.50	2.69	2.63	2.09	2.57	2.40	2.33	2.48
04/2021	4.02	4.00	4.11	4.02	3.23	3.50	3.00	3.39	3.66
05/2021	5.03	5.04	5.18	5.04	4.18	4.11	4.84	4.36	4.72
06/2021	6.05	6.11	6.31	6.06	5.03	4.49	5.69	5.31	5.63
07/2021	5.27	5.20	5.40	5.23	4.34	4.12	5.01	4.58	4.89
08/2021	3.73	3.72	3.83	3.73	3.14	3.10	3.60	3.31	3.52
09/2021	3.24	3.21	3.29	3.24	2.60	2.85	2.93	2.78	3.02
10/2021	2.51	2.43	2.50	2.47	1.83	1.61	2.16	1.93	2.18

.

Figure 4 depicts the results of the monthly yields (Yf) obtained by the PV5–PV8 rooftop installations located in various places within a radius of 50 km from the city of Lublin. It should be noted that the systems experienced slightly different (local) weather conditions. The total yearly specific yields were as follows: 868.8 kWh/kWp (PV5), 895.7 kWh/kWp (PV6), 966.8 kWh/kWp (PV7), and 910.7 kWh/kWp (PV8). The highest value was found for PV7, a south-oriented PV system with a tilt angle of 20° (close to optimal for this location). Other research carried out for this location in Poland revealed specific yields of 1098 kWh/kWp [28] and 830 kWh/kWp (system commissioned in 2000) [27] for roof-top south-oriented systems, and 853 kWh/kWp [46] for a south-western orientation.

Similar to the previous analysis, about 80% of the energy was produced in the summer half-year and only 20% in the winter half-year. The exception was the PV6 system which produced 222.3 kWh/kWp (25%) in the winter months (energy production of PV5, PV7, and PV8 in the winter period ranged between 184.6 kWh/kWp and 204.6 kWh/kWp).

As can be seen in Figure 4, from November 2020 to April 2021, the PV6 system exhibited higher energy gains due probably to the preferable orientation of the PV modules. This can be a matter of interest to all investors who want to increase energy production in the winter half-year (thus, increasing the self-consumption ratio of PV energy). Figure 5a shows a boxplot of average daily yield in February where the energy production of the south-eastern oriented PV6 is much higher (with a median of 1.3 kWh/kWp) compared to the rest of the installations (medians below 0.65 kWh/kWp). this was confirmed by the clear sky day energy profile shown in Figure 5b. Each point represents the energy output in 15 min. As can be seen, during almost the whole day, the energy production of PV6 exceeded the energy gains of PV5, PV7, and PV8. The total energy output of PV6 on this day equaled 4.0 kWh/kWp. The other systems produced 2.5 kWh/kWp (PV5), 3.0 kWh/kWp (PV7), and 2.8 kWh/kWp (PV8).

Considering annual yield maximization, the south-oriented system (PV7) was the most profitable. As Figure 4 shows, this installation resulted in the highest specific yield in high insolation months (from May to August) than other systems in the period under study. Figure 6 presents the daily final yield together with the daily profile obtained in selected summer months (July and August 2021). As can be seen from Figure 6a, the highest median value was found for PV7 (5.3 kWh/kWp). The maximum yield was found to be 7.0 kWh/kWp. The median yields of the PV5, PV6, and PV8 systems ranged between 4.47 kWh/kWp and 4.89 kWh/kWp and the maximum yields were in the range of 5.3–6.7 kWh/kWp. Similar to the observation for the previous group of roof installations, the energy yield scatter during July was relatively low (below 2 kWh/kWp). A much larger interquartile range was observed for spring, e.g., for April 2021, the value ranged between 2 kWh/kWp and 4 kWh/kWp (all systems). The median specific yield in April was about 3.5 kWh/kWp and was found to be similar independent of the installation.

Figure 6b presents the energy production observed for all installations under clear sky conditions on a summer day (August 2021). Plots reveal the differences in orientation between each PV system. On the presented day, the south-oriented (PV7) system produced the highest energy (6.0 kWh/kWp), however, the local maxima belonged to south-eastern PV6 and south-western PV8 systems with specific yields of 5.3 kWh/kWp and 5.9 kWh/kWp, respectively. Shifting the maximum energy production to the left or right from noon is of high importance to increase the PV energy self-consumption ratio in different parts of the day. Considerably higher energy gains in the morning and afternoon hours of the day were noticed for the east-west oriented PV5 system, as can be seen in Figure 6b. The final yield, in this case, was equal to 5.4 kWh/kWp.

The following roof installation (PV9), equipped with small energy storage was analyzed including not only energy output but also energy balance (energy demand, energy exported to and imported from the grid). To keep coherence with the findings presented above, the specific yield of the system was computed (Figure 7).

The annual specific yield was found to be 978.1 kWh/kWp. A value of 816 kWh/kWp was produced in the summer half-year and 162 kWh/kWp in the winter half-year. The most profitable month was also June 2021.

The yearly average daily values of specific yields computed for eight grid-connected analyzed systems are summarized in Table 4. As can be seen, the worst month for PV energy production was January 2021 with daily specific yields ranging from 0.17 kWh/kWp to 0.32 kWh/kWp. The best PV conditions were found for June 2021 with specific yields ranging between 5.03 kWh/kWp and 6.31 kWh/kWp in dependency on the PV system.

Table 5. Financial assessment of the analyzed systems.

Parameter	PV System
	PV1	PV2	PV3	PV4	PV5	PV6	PV7	PV8	PV9
LCOE (€/kWh )	0.15	0.15	0.14	0.15	0.18	0.18	0.16	0.17	0.16
SPP(y)	8.1	8.4	7.9	8.1	10.0	9.7	9.0	9.6	8.3

shows the results of a financial assessment of the analyzed PV systems. As can be seen, the levelized cost of electricity (LCOE) is approximately on a similar level, ranging from 14 to 18 EURcent/kWh. These results are in accordance with the calculations made by Bódis et al. [7] for EU countries. The lowest value of LCOE was found to be 6.2 EURcent/kWh for high insolated countries (e.g., Cyprus). Countries with low irradiation levels were characterized by the value of LCOE up to 32 EURcent/kWh [7].

In this study, the lowest value of LCOE was observed for the PV system of bifacial modules, which produced the highest amount of energy per kWp. High production also led to the shortest payback period, equaling less than eight years. It should be noted that the presented analysis did not include the initial co-financing of the system [6], which would lead to a further decrease in the SPP ratio. The presented results of SPP are in accordance with the modeling research carried by Krawczak [32] in the location of Warsaw with the “My electricity” program included.

For the needs of energy balance presentation, the total energy output of the PV9 system was used in the following results (without dividing by the rated power of the PV system). Figure 8a presents the monthly energy balance of the PV9 system obtained in the studied period. The daily energy balance for July 2020 is shown in Figure 8b. It should be noted that the PV9 roof installation was designed for a company characterized by daily working hours, which is crucial for increasing the self-consumption ratio of the system. The yearly energy demand was 49 MWh.

The annual solar energy production was about 29.5 MWh. As can be seen in Figure 8a, for higher insolation months from May to August, total energy production from PV exceeded the energy demand (from 22% in August to 33% in June). Despite this fact, some energy had to be imported from the grid, mostly due to cloudy or partly cloudy days or low production near the end of the day (Figure 9). Total energy imported from the grid was about 31.2 MWh with the greatest component (about 80%) imported during the winter half-year. Energy exported was approximately 11.7 MWh, with 90% of this energy from the summer half-year. Figure 8b displays the energy balance obtained for July 2020. PV energy production ranged from 52.1 kWh to 207.6 kWh and, in most cases, exceeded the demand. Median daily production was about 162.8 kWh (4.82 kWh/kWp). The median daily energy demand was 111.1 kWh. Considering the daily working time of the company, the self-consumption ratio of PV energy output was also at a relatively high level compared to the typical household. In July 2020, the self-consumption ratio ranged between 10% and 88% with a median value of 59%. This can be seen in Figure 8b in the case of days with high PV production and high energy demand levels (e.g., 7th, 8th, 9th day). Energy exported these days was at a low level due to direct consumption. Indeed, for the days with low energy demands and high PV production (weekends, e.g., 4th, 5th day), much higher peaks of exported energy were found. The self-consumption ratio was found between 10% and 16%. However, even on such days, a small amount of energy was imported from the grid. Median daily energy imported from the grid and exported to the grid were 22.7 kWh and 63.2 kWh, respectively.

Figure 9 presents the energy balance profiles obtained for a sunny and a partly cloudy day in July 2020. With the low energy demand (83.6 kWh) and high PV energy output, depicted in Figure 9a, most parts of the energy produced were exported to the grid (PV output was 207.6 kWh while energy exported was 137.1 kWh). Only about 13.1 kWh of energy was imported from the grid due to a lack of PV production at the beginning of the day. In the case of a partly cloudy day with a high ratio of PV production and energy demand (Figure 9a), energy was imported not only at the beginning of the day but also in the middle (PV production was not sufficient). Lower energy export was also observed. PV energy output, energy demand, energy export, and import were as follows: 169.8 kWh, 161.7 kWh, 40.5 kWh, and 32.4 kWh. The self-consumption ratio for this day was found to be 73%.

Figure 10 shows the energy balance taking into account self-consumption and consumption from the battery. The annual period of operation (Figure 10a), as well as an example of a summer month (Figure 10b) are shown.

It should be noted that the battery capacity used was about 7% of the average daily energy demand. Despite this low value, the influence of energy storage on the increase in self-consumption of the PV energy output is visible in Figure 10, especially during high-insolation days. The amount of energy cumulated in the battery depends on the month and varied from 17.9 kWh in January (winter) to 383 kWh in July (summer). The yearly amount of energy used from the battery was about 2.3 MWh. Consumption in the summer period was 1.9 MWh while in winter a value of 0.4 MWh was noted. Noteworthy results were obtained in terms of mean and median consumptions from the battery in July, i.e., 12.4 kWh and 13.1 kWh, respectively. Values higher than the battery capacity of 9.8 kWh show that during partly cloudy days, the battery was charged and discharged more than once.

This lead to the conclusion that even a small energy magazine installed for the PV system can effectively increase its self-sufficiency.

Table 6. Summary of self-consumption and self-sufficiency obtained by the PV9 system.

Month/Year	Self-Consumption Ratio (%)	Self-Sufficiency Ratio (%)
07/2020	49.2	70.6
08/2020	48.8	64.1
09/2020	54.7	53.1
10/2020	76.2	23.8
11/2020	90.6	13.8
12/2020	92.9	6.9
01/2021	96.9	4.9
02/2021	52.8	6.4
03/2021	70.6	28.0
04/2021	67.1	46.7
05/2021	57.5	62.5
06/2021	49.4	70.4

summarizes the self-consumption ratio and the self-sufficiency ratio of the PV9 system calculated according to the work of Alrawi et al. [39]. As can be seen from Table 6, the ratio of PV production consumed locally varied from almost 50% in summer months to 97% in winter (January). High self-sufficiency values were found for the summer half-year.

To summarize, the annual average specific year of nine analyzed systems was found to be 990.2 kWh/kWp. This value could be considered as an assumption of specific yield for roof-top systems located in Poland taking into account the variety of installation conditions forced by roof orientation and tilt angle. Taking into consideration specific yields analyzed for different location roof systems, this average value lies between the higher yields observed for lower latitudes [18,20,48] and lower yields characterized by higher latitude locations [25,26,49]. The annual yield analysis from a big data perspective of The Netherlands presented by Moraitis et al. [50] revealed similar average values ranging between 919 kWh/kWp and 970 kWh/kWp depending on the year. Another interesting big-scale PV data result was presented by Kausika et al. [51] for (among others) countries with similar latitudes to Poland: Germany, The Netherlands, and Belgium. In most of the analyzed cases, the median specific yield ranged between 900 kWh/kWp and 1000 kWh/kWp.

4. Conclusions

Nine PV installations located in South-Eastern Poland were analyzed in terms of a specific yield. New technology modules of high efficiency, as well as, different system configurations with various tilt angles and orientations (south, south-west, south-east, east-west) were taken into account.

The total average energy production of all systems during one year of operation was 990.2 kWh/kWp. The annual specific yield varied from 868.8 kWh/kWp to 1102.9 kWh/kWp, depending on the system. The highest ratio of specific yield was noted for the system consisting of bifacial modules. Thus, the levelized cost of electricity, as well as the payback period, were also the lowest for this system. About 80% of the total energy production fell in the summer half-year. The best months for PV production in the studied period were June and July, with a median daily yield up to 6.6 kWh/kWp. The highest energy production was noted for the system consisting of bifacial monocrystalline silicon modules with 20.3% efficiency. The worst months for photovoltaics in the location under study were November, December, and January, with a median daily yield much below 1 kWh/kWp.

From the analysis of the PV system installed for a company prosumer, the winter half-year was found as the period with the highest energy import from the grid (about 80%). About 90% of the energy was exported to the grid during the summer half-year. Due to the daily working time of the company, the self-consumption ratio of PV energy output was found to be relatively high compared to the typical household. For high irradiation months (summer), the auto-consumption reached 50%. In winter, the self-consumption ratio was much higher but mostly due to very low specific yields during this period. It was shown that the usage of even small battery storage in the PV system led to a noticeable increase in PV energy consumption locally.

It should be emphasized that publishing the final yields was not a matter of competition. The intention was to deliver the energy production data of PV systems working under various operating conditions at high latitude locations. It is believed to be useful for scientists and anyone who plans to design a PV rooftop system.