A Methodological Framework for Studying the Tilt Angle of Solar Photovoltaic Panels

Abstract

With the development of alternative energy technologies, energy production from renewable sources is gaining wide application. One of the types of renewable energy sources is solar power. In the past 5 years, solar cells have become very popular for both private electricity microgeneration and large power plants. There are two main options for installing solar photovoltaic panels: on the roof of a house or the ground; on specially made frames. When installing solar cells on the roof, it is not always possible to choose a tilt angle that is appropriate for all seasons, since the angle is mainly adjusted to the plane of the roof. When installing solar cells on the ground, it is usually possible to choose both the orientation relative to the cardinal points and the tilt angle relative to the ground. There are various theories about the best tilt angle of solar cells for producing the most amount of energy during the year. Therefore, the aim of the present research study is to develop an original research methodology for determining an optimal tilt angle for solar cells. The research study examined six different tilt angles of solar cells, 0°, 30°, 35° 40° 45° and 50°, orienting the cells towards the south. The research study used 18 identical monocrystalline solar panels with a power of 20 W. Three solar panels were set at each angle. This way, the experiment had three replications at each angle of the solar cells. The measurements were recorded by a GWL840 data logger with an interval of 10 s. The experiment was conducted by placing all solar cell modules on the roof of the building at Lat. 56.66181° and Long. 23.75238°. During the experimental period, the highest efficiency was found for the solar panels set at 50° and 40°, reaching the total solar irradiation of 266.61 Wm⁻² and 266.27 Wm⁻², respectively.

1. Introduction

An optimum tilt angle for solar cells is an important parameter that depends on the geographical location of the solar plant. Other characteristics, e.g., the amount of clouds, surrounding objects, precipitation, snow cover, etc., can also affect the choice of the tilt angle of solar cells for the best performance. There are a number of options for placing solar cells. In urban areas the most obvious choice is the roof. There are two main types of roofs where solar cells can be placed: horizontal (or nearly horizontal) roofs and sloped roofs. Sloped roofs usually have a tilt angle of 20–50°. Although sloped roofs might be the most convenient for solar cells, they are not always oriented towards an optimal azimuth. In the hot season, solar panels placed on the roof have higher temperatures due to limited cooling and heat radiated by the roof surface, which greatly reduces their efficiency. For horizontal roof-mounted solar plants, the panels could be oriented towards the south and installed at a different angle than the roof, yet such structures require additional costs for construction and fastening them to the roof to make them wind resistant. Problems with solar cell installation also arise if the building is not oriented exactly to the south (for Northern hemisphere); construction allowing the precise orientation of solar panels limits the number of panels for the same roof area and reduces the capacity of the solar power plant. This problem has also been researched by A. Barbón and others, who analysed the solutions for PV panel installation on roofs in urban areas, as well as mechanisms to maximise the amount of energy generated. The researchers concluded that even if oriented south, PV systems can lose up to 20%. In Spain, the best tilt angle for solar panels oriented south, according to analytical research studies, is 14–15° [1].

Solar panels should be placed on the ground if there is more space available or if there is not a suitable roof. In this case, it is possible to achieve a more accurate azimuth of solar panels. In Latvia, solar panel installers are not generally guided by the criterion of the highest yearly energy output when placing solar panels on ground structures. The choice of the tilt angle often depends on the available frame construction (with a fixed tilt angle), which is not always made to suit a specific geographical location in the specific country. An important criterion for solar panel installers is also labour intensity of the installation process. Frames with lower labour intensity are preferred, not taking into account the fact that more energy could be generated at a different angle. If there is a sufficiently large free area and there is a need to generate as much electricity as possible at a limited maximum power (e.g., 11 kW for 0.4 kV distribution grid in Latvia), the azimuth of solar panels could be set with the aim to maximise the output for certain hours of days, seasonally or yearly. For example, more energy can be generated in the morning and evening using solar panels oriented to the southeast and southwest. In such cases, the optimum tilt angle as a rule will differ from the south-facing panels, as the sun is lower above the horizon in the morning and evening.

An optimum angle of solar cells relative to the sun could be achieved by setting up a tracking system, with the solar cells precisely tracking both the height and position of the sun in respect of the azimuth. In the current circumstances, with the price of solar cells falling significantly (according to the World Energy Outlook 2024 [2], prices of PV panels decreased by almost 64% from 2015 to 2023), it is mostly not economically reasonable to install solar tracking systems at large power plants as well as at small-scale plants, especially in urban areas. Therefore, the choice of a fixed tilt angle in different situations and using scenarios nowadays (e.g., available area for installation, maximisation of the profit on the energy market or yearly energy output, or achieving autonomy) is a very interesting subject.

M. Jacobson and V. Jadhav employed computer modelling to identify an optimum stationary angle of solar panels. Data for the modelling were obtained from the nearest meteorological station to the particular geographical point. The researchers proposed optimal angles of solar panels for several countries around the world [3]. An optimum angle for Latvia was found to be 33° (55.5° N), which was practically the same as for Uzbekistan, 32° (41° N). The similarity of solar panel positions in the significantly different geographical locations examined is questionable.

A. Gharakhani Siraki and P. Pillay proposed a calculation algorithm to be used for identifying the angle of solar panels placed on roofs in urban areas. The authors made the principles of solar panel installation clearer: if the solar plant is located closer to the equator, it is recommended that the angle of solar panels be equal to the latitude, but if closer to the north, the angle should be less than the latitude [4].

E. Abdeen et al. experimentally investigated tilt angles for solar panels in a desert environment in Egypt, where the amount of energy generated can be significantly affected by dust. Their research presented a detailed analysis of photovoltaic (PV) system performance under a desert environment to maximise the energy captured by the PV system. The experiment showed that if the effect of dust is taken into account, the PV panels should be set at an angle of 30° in winter and 15° in summer and the autumn [5]. Similar simulations have also been performed in Pakistan [6]. In Latvia, based on the principle of analogy, the practical application of such experiments could be appropriate for snowy winter conditions when solar panels are covered by snow.

In Portugal, stationary solar panel systems have been simulated, compared with one- and two-axis solar tracking systems. The mathematical model also considered the effect of dust, which reduces the efficiency of solar panels. It was concluded that more energy could be recovered using a tracking system, but such systems were more expensive and had lower operational reliability. An assessment of the economic effect of different systems was also performed by the researchers [7].

An optimum tilt angle of solar panels is one of the crucial variables for the efficient installation and operation of PV systems, as defined by A. K. Yadav et al. for Indian conditions. The researchers performed a simulation using a machine learning method for the selection of optimum parameters for the installation of solar panels [8].

In their research, M. A. Danandeh and S. M. Mousavi G. investigated and evaluated solar panel position angle calculation models for major Iranian cities. Their models also considered the effect of diffuse irradiation on energy generation [9].

In China, L. Xu et al. employed computer modelling to identify the specifics of establishing solar farms in mountainous areas with high solar irradiance and a low cloud cover. The terrain has a significant impact on the amount of energy generated when solar irradiation is not directed to the solar plant due to the shadow falling from the mountains. By optimising the angle of solar panels, which takes into account the shading effect, it is possible to significantly increase the annual energy output [10].

Hassan Z. Al Garni et al. simulated the amount of energy generated in Saudi Arabia, taking into account the irradiation intensity and temperature. They identified the potential amount of energy generated depending on the temperature in various months of the year and the amount of energy generated depending on the tilt angles of solar panels [11,12].

J. Kafka and M. A. Miller have conducted research on the efficiency of solar panels at large-scale solar power plants, setting the solar panels at two different angles. As the price of solar panels decreases significantly, more solar panels are used to generate more energy. The authors performed simulations and identified how the cost of energy generated in the US would change if the price of land on which the solar plant would be built is considered. By setting solar panels at two angles, more use can be obtained from both direct and diffuse solar irradiation [13].

A research study of tilt angles for solar panels in Turkey performed simulations and found that an average solar panel angle of 31.2° to 33.2° could result in the highest energy output [14].

In countries located on the equator, the effect of temperature on the amount of energy generated is a major problem for solar energy production. Computer simulations have been performed for solar panel angles ranging from 0° to 40° and for different positions in respect of the azimuth. The system was also simulated for the case of a hybrid power plant combined with a diesel generator [15].

A. A. Babatunde et al. conducted research in Cyprus, examining the effects of temperature, tilt angles and dust for solar plants located in various regions, by experiments and simulation. The most energy, according to their experimental data, was generated by setting the solar panels at an angle of 25°, yielding 5.6–17% more energy over the year. Cleaning the solar panels of dust resulted in 2.5% more energy per year. A comparison of the simulated and experimental data found a difference of 4.5% [16].

Experiments with solar panels set at different angles were conducted in Bangladesh, located at a latitude of 23.7°. The experiments were performed with 18 identical solar panels positioned at 0°, 10°, 20°, 30°, 60° and 90°. The groups of solar panels were cleaned for dust once a day, once a week and once a month. The best tilt angle for solar panels, if not changed throughout the year, was experimentally found to be 20°. The scientists found that a single-axis solar tracking system can only generate 2.17% more revenue than a fixed system [17].

M. Arslan and M. Çunkas have experimentally investigated the effect of solar panel tilt angles on the amount of energy generated in Turkey, identifying optimal solar panel angles for winter, summer and the autumn. If the tilt angle was not changed, it was 32°. The experiments were conducted at solar panel tilt angles of 15°, 30°, 32°, 30°, 45° and 60° [18].

M. Nfaoui and K. El-Hami conducted research on the effect of solar panel tilt angles on the amount of energy generated in Morocco (latitude 32°). Calculations were performed using the Matlab Simulink programme, simulating both the tilt angle and the azimuth for solar panels. In Morocco, the optimum tilt angle ranged from 28° to 32°, depending on the geographical location [19].

M. A. A. Mamun et al. conducted their research in Malaysia. An experiment was carried out with two modules: the first module with a variable tilt angle from 0° to 80° (5° change step) and at a constant irradiance of 750 Wm⁻², the second module with variable solar irradiation and an optimum constant tilt angle set to 15° for Malaysian conditions. The experiment showed that an increase in solar irradiation of 100 Wm⁻² resulted in an average temperature increase of 5.7 °C [20].

Hasan N. Muslim conducted research on optimising the tilt angle of solar panels by using the Matlab simulation programme. Optimal angles were identified by month for California (USA) and Iraq, ranging from 0 to 30° in summer months and from 30 to 60° in winter months [21].

The computer modelling method was also applied by Hungarian researchers who considered the experience of determining an optimum angle in several countries on the Eurasian continent [22].

R. Abdallah et al. simulated optimisation of the tilt angle of solar panels in Palestine. The simulation results show that a seasonal adjustment of the solar panel angle (ideally 12 times per year, but recommended at least 2 times per year) can lead to a 15% increase in the amount of the energy generated. If solar panels are placed on a horizontal surface, or at an optimum angle of 29°, the amount of the energy generated increases by 10% in Palestine [23].

M. K. Sharma et al. have conducted experimental research on the roof of a building in India. Solar panels were placed at different angles: 10°, 20°, 25°, 30° and 40°. According to the research study, the optimum angle of the solar panels was 26–28°. It is recommended to adjust the angle of solar panels four times during the year, changing the angle from 15° to 37° [24]. M. Benghanem, from Saudi Arabia, also proposes seasonal changes in the angle of solar panels four times a year between 12 and 37° for maximum energy generation [25].

Although in countries near the equator, e.g., Nigeria, the sun is high above the horizon, scientists have conducted experimental research focusing on different angles of solar panels. The research has resulted in identifying an optimum angle of 16.8° for solar panels [26].

M. Masili and L. Ventura have researched tilt angles for solar panels in Brazil, most of which are located in the Southern hemisphere. Simulation was performed for latitudes between 0° and 55°. The research found that the standard method of installing solar panels, which was based on a latitude coordinate as the tilt angle, was not accurate. Adjusting the tilt angle results in 14% more energy output, compared with the standard method [27].

J. I. Laveyne et al. have conducted analytical research into tilt angles for solar panels in Belgium. One of the problems with solar panels is that the optimally oriented solar panels in the middle of the day (34.5° in Belgium) generate an amount of energy that exceeds the consumption of the house. By setting solar panels at other angles to the azimuth and to the horizon, the amount of energy generated can be levelled out over the whole day [28].

The use of solar energy has also been researched in Latvia [29]. A research study was conducted on polycrystalline (200 W) and monocrystalline (270 W) solar panels installed on buildings in the botanical garden in Riga, the capital of Latvia. The solar panels were set at a 13° tilt angle and oriented towards the east, west and south. This angle has been chosen in case the solar panels are placed on flat roofs. The solar panels were also set at 40° and 90° and oriented south. The 90° tilt angle was chosen in case the solar panels are placed on a fence or a building wall. It is difficult to understand why the results for June revealed that the solar panels set at 40° generated less energy than those set at 13° and oriented south and east. The research study concluded that the amount of energy generated in various months was impacted by clouds and the solar panel orientation, without giving accurate quantitative comparisons of the data for different settings. It is therefore difficult to understand which solar panel orientation option was the best.

Most of the research studies on tilt angles for solar cells are based on theoretical research and simulation. Parameters for simulation are obtained from various sources, such as meteorological stations and other observational databases. Most of the research studies analysed focus on countries close to the equator, with latitude coordinates not exceeding 35–40°. In this case, the angle of incidence of solar irradiation has a different character than in latitude regions above 50°. The geographical distribution of research studies is similar for experimental studies, which are more oriented towards countries closer to the equator. According to preliminary observations, since the angle of solar cells in the Baltic region is generally not selected based on scientific experiments and might differ significantly from the optimum angle in terms of maximum energy output, such experiments are worthwhile. The aim of the present research study is to develop an original research methodology for determining an optimal tilt angle for solar cells over a long period in the Baltic States. The main benefits of the research involve identifying scientifically based tilt angles for solar cells, considering the specific geographical and meteorological conditions, aimed at generating more electricity and tailoring a PV setup for different energy consumption scenarios ranging from the energy market to isolated power systems.

In the past 3 years, a lot of solar power plants have been built on the ground in Latvia, but according to preliminary studies, the angles of their location to the horizon are often chosen according to the cheapest available installation structures, e.g., 30° to the horizon. Such an inappropriate geographic setting can reduce the total amount of electricity generated and contribute to the alienation of areas, which increases the ecological footprint.

Latvia has specific climatic conditions, especially in the autumn and winter, which can be different from the countries closer to the equator. The autumn and winter periods are usually associated with very low sun angles above the horizon, when solar panels in populated areas may be shaded by neighbouring houses (in late December the sun is only 10° above the horizon). In winter, there may be weather conditions with snow covering the solar panels, requiring cleaning. Snow can also be a positive factor as it can have the positive effect of reflecting solar radiation, increasing the amount of energy produced from the reflected radiation, especially if double-sided solar panels are used. In the autumn, but especially in spring, there are a large number of different types of clouds that can provide reflected radiation, which is very difficult to include in modelling and demonstrates the benefits of experimental studies.

2. Materials and Methods

The research involves developing a methodology to investigate the tilt angle of solar cells. The ultimate goal is to determine the optimal tilt angle for solar panels, orienting the solar cells exactly to the south for cases when changing the tilt angle is not possible. Such research studies require at least one year of data recording, as the optimum tilt of solar panels for a particular month of the year might vary. In total 18 identical photovoltaic panels of low-power monocrystalline technology selected for the experiment are summarised in

Table 1. Key parameters of Victron Energy Blue Power photovoltaic panels (model SPM040201200) used by the research.

Characteristic	Parameter Value
Rated maximum power	20 W
Tolerance	0–3%
Voltage at Pmax	18.46 V
Current at Pmax	1.09 A
Open-circuit voltage	22.61 V
Short-circuit current	1.19 A
Nominal operating cell temperature	47 ± 2 °C
Maximum system voltage	1000 VDC
Maximum series fuse rating	10 A
Dimensions	440 × 350 × 25 mm

below.

A pyranometer Apogee SP-510-SS was employed to measure the solar intensity. It is a blackbody thermopile pyranometer with voltage output intended to measure shortwave radiation from the sky at a planar surface where the radiation emanates from all angles of a hemisphere. A sensor was installed alongside experimental panels and levelled to the surface at 0° (see Figure 1a).

The tilt angles of solar panels to the horizon in the experiment were 50°; 45°; 40°; 35°; 30° and 0°. The 0° angle was set to identify the energy production parameters on a horizontal surface and to be able to quantify the potential energy generation at different tilt angles of solar panels. This angle was also appropriate for stationary solar panels placed on various mobile equipment, such as solar-powered vehicles and watercraft. The other angles were representative of the angles most commonly used for solar panels in Latvia.

Due to the fact that each solar cell of the same batch might also have different individual energy generation parameters, three identical solar cells were used at the same tilt angle. The three solar cells were arranged in a single row according to the set tilt angle. One experimental module used solar cells mounted at two different tilt angles (see Figure 1). The solar modules were mounted on special concrete footings with levelling screws.

The experiment was conducted with all the modules placed on the roof of a building at Lat. 56.66181° and Long. 23.75238°. The roof of the building was flat with bitumen coating. The building was selected among several possible options so that the surrounding buildings, trees and other tall objects could not create a shadow, especially during the experiment in winter conditions when the angle of incidence of sunlight at noon in the geographical conditions of Latvia does not exceed 12°. After placing the solar modules on the roof, they were accurately oriented to the south. The orientation to the south was performed using the sunlight incidence method at the moment when the sun was at its highest point during the day. After adjusting the orientation, the modules were levelled exactly horizontal to the ground surface to ensure correct tilt angle for each panel group. The experimental solar battery modules placed on the roof are shown in Figure 2 and Figure 3.

During the current phase of the experiment, the output of all solar panels and the pyranometer were recorded. The GL840 data logger (manufactured by Graphtec Corporation, Yokohama, Japan, country of origin: Japan) with 20 input channels is used as the main data-gathering and storage instrument. The data logger and signal conditioning board are placed indoors in an electrical cabinet (see Figure 4).

For the needs of the current research, the forward-bias photocurrent measurement approach was used. According to a well-known semiconductor photodiode equation, the photocurrent is directly proportional to the intensity of radiation at a given wavelength:

$$I_{ph}=R_{\lambda }P,$$

(1)

where

I_ph—photocurrent, A;

R_λ—photodiode responsivity, A·W⁻¹;

P—incident light power, W.

Responsivity changes at different wavelengths if the sun’s position and the ratio of direct to diffuse irradiation changes. Assuming that all the panels in the experiment are in the same conditions, except for tilt angles, the photocurrent can be used to compare the performance of panels at different inclinations. The parallel-to-surface (0°) panel is used as a reference and the output of all other panels with different tilt angles is expressed as a ratio of the output of selected panel to the panel with zero degrees. This ratio is denoted as K_d in this research:

$$K_d={\displaystyle \frac{{\overline{I}}_{ph\_d}}{{\overline{I}}_{ph\_0}}},$$

(2)

where

d—identificator of the panel inclination angle: 0, 10, 20, 30 and 50°;

Ī_ph—average photocurrent for a panel group at given angle, A.

The equation is used for instantaneous current measurements as well as for sums of currents for time intervals of interest. The ratio K_d was also used to estimate solar irradiation falling to tilted panels:

$$W_d={\displaystyle \frac{R_0{K}_d}{360000}},$$

(3)

where

W_d—irradiation for a panel at the angle d for a period of time, kWh·m⁻²;

R₀—irradiation at the angle 0°, measured by the pyranometer, 10 s average, W·m⁻².

In contrast to a number of various research studies, e.g., [18], this approach simplifies the experimental setup by minimising the number of components and allows for the focus to be on the research problem. There is no need for a dedicated MPPT and dump load for each panel. The main drawback of this approach is the increased heating of the panels, as technically they are in a short circuit, and all solar energy is converted into heat with no electric power generated outside the panel. This might affect the photocurrent output and is a matter for further investigation.

The signal conditioning circuit (shown in Figure 5) consists of a shunt resistor, 0.012 Ω nominal, and an NCS199A3R (manufactured by ON Semiconductor, Scottsdale, AZ, USA, country of origin: Malaysia) current sense amplifier. Photocurrent from each panel is converted to voltage and measured by the GL840 data logger input. The input range was set to 5 V. The nominal static transfer function is given by the following equation:

$$U_o=I_{ph}{R}_{s}A,$$

(4)

where

U_o—voltage at the GL840 input, V;

R_s—shunt resistor, nominal 0.012 Ω;

A—fixed amplification of the NCS199A3R circuit—200.

Figure 5. Conceptual measurement circuit identical for all 18 current channels.

Figure 5. Conceptual measurement circuit identical for all 18 current channels.

Signal conditioning circuits for all 18 current measurement channels were implemented on a single PCB with the same filtered power supply. To increase the measurement accuracy, each current measurement channel was calibrated using a 34465A bench multimeter (manufactured by Keysight, Santa Rosa, CA, USA, country of origin: Malaysia). The calibration procedure for each channel included the following steps:

• Setting constant current to the measurement loop input using MX180Tp laboratory PSU (manufactured by Aim-TTi, Huntingdon, United Kingdom, country of origin: United Kingdom).
• Reading the current value from the bench multimeter and respective voltage from the GL840 input.
• Setting a conversion coefficient for a respective analogue input.

Maximum error was calculated for current measurements by taking into account the GL840 input uncertainty of 0.1% of the full scale (5 V) and the NCS199A3R gain error of 1.5%. Adding positive and negative errors in Equation (5), we obtain a maximum error of –5.5% to +3.5% in the range of 0.1 to 2 A.

$$I_{ph}={\displaystyle \frac{U_o\pm e_{\mathrm{GL}840}}{R_s\left(A\pm e_{\mathrm{NCS}199\mathrm{A}3\mathrm{R}}\right)}}$$

(5)

The short-circuit current of a silicon solar cell is affected by temperature. The relation is positive: with an increase in temperature, there is a slight increase in short-circuit current, but open circuit voltage is decreased at the same time, resulting in a decrease in output power. According to experimental research performed on Si solar cells, changes in short-circuit currents in the range of 295–320 K were 8 and 10 mA for two tested cells, which resulted in a 0.058% and 0.081% per K degree change in relation to the nominal short-circuit current for the AM1.5 spectrum at a 100 mW·cm⁻² intensity [30]. The relation at this range was close to linear. The temperature effect in the surveyed range is comparable with current measurement uncertainty. Short-term preliminary temperature measurements during a cloudless day showed a temperature difference between panels less than 25 K. However, as the temperature effect is positive, it is planned to take it into account in the next stage of the research by adding temperature probes for panels at all angles.

An additional analogue voltage channel of GL840 was used to measure the pyranometer output. The data logging interval was set to 10 s.

The data were organised by a PostgreSQL database and processed using Python 3.12 pandas 2.2.1, matplotlib 3.8.3 and pvlib 0.11.2 libraries. The data processing procedure included the following:

• Generating time series charts for graphical analysis.
• Adding theoretical solar irradiation on a flat surface for a comparison of the 0° inclination panel and pyranometer output. A Python pvlib.clearsky.ineichen module implementing the Ineichen and Perez clear sky model for global horizontal irradiance (GHI) [31] was used.
• Summarising tables of 0° to different inclinations and panel outputs.

3. Results and Discussion

Currently, the data were collected for the period from 22 August 2024 to 20 January 2025. An analysis of days and seasons of various solar intensities was performed for this period (Figure 6, Figure 7 and Figure 8), and the potential amount of energy generated over 6 months was calculated (see Figure 9 and Figure 10). A comparison to PVGIS datasets [32] is provided in Figure 11. Photocurrents given in all charts are average values for simultaneous samples for three panels in each angle group. The solar intensity (GHI) graph shows both the theoretical solar intensity (red line) and the practical measurements from the pyranometer (blue line).

On 24 August 2024, there were variable amounts of clouds at the beginning of the day (Figure 6), yet at 12:30 the clouds dissipated, and the solar intensity from 12:30 to 14:00 was on average 6.5–7.5% lower than the theoretical intensity. The characteristic difference in solar intensity between the measurements and the theoretical curve for the sun’s position from 14:00 to 17:00 ranged from 8.9% to 11.1%. On this day, the solar altitude reached 44.21° at noon at the measurement site. As the comparison was made with the theoretical solar intensity, the deviations could be due to various reasons, e.g., increased temperature due to heat build-up on the roof, atmospheric saturation with optical filter elements, dust, etc. An analysis of the current revealed that the curve characteristics of solar panels placed at different angles were similar to those of the solar intensity curve. An analysis of the current values obtained at noon showed that the lowest current value was for solar panels placed at 0° and reached 0.83 A. The highest values were found for solar panels placed at 30°, 40° and 50° tilt angles, reaching a current of 1.15 A, which was 38.5% higher than for a horizontal solar panel. It was interesting that the difference in short-circuit current between the 30°, 40° and 50° panels was less than 2%. A similar percentage was found at other periods of the day. Figure 5 clearly shows the impact of clouds in the morning, e.g., at 9:45. Since diffuse irradiation was stronger in that period, the current was very similar for panels placed at any tilt angle. On that day, the results were also strongly affected by the ambient temperature, which could significantly reduce the amount of the energy generated.

A significantly different trend was observed on 31 December 2024 when the sun rose at midday to only 10.38° (Figure 7). The theoretical maximum solar intensity at midday was only 120.6 Wm⁻², yet the real value measured was 84.4 Wm⁻², which was 30% less than the maximum. This significant difference was due to the specificity of the measurement, as the real cloud cover could differ significantly from that calculated theoretically. The air temperature during this period was around 0°, which could not reduce the efficiency of the solar panels. The day length was significantly shorter in this period than in summer, reaching only 6 h 56 min on the experimental day. In the middle of the experiment, between 11:00 and 13:00, the highest values of the short-circuit current were found for the solar panels with a 50° tilt angle, which could be explained by the low position of the sun above the horizon.

The current values established at 12:00 for the solar panels positioned at 40° and 50° were 0.21 A, which was 5.5 times lower than on a summer sunny day. The lowest value of 0.07 A was found for the solar panels at 0° and 10° tilt angles because they had very different tilt angles (different by 70° and 80° at midday). At 14:30 when the solar altitude was less than 6°, the capacities of almost all solar panels were very similar, with reflected solar radiation accounting for the largest proportion.

On a sunny winter day, 18 January 2025, when the maximum solar altitude was 10.3°, the pyranometer readings were very close to the theoretical ones and did not differ by more than 4–5% when there were no clouds (Figure 8). Due to the low maximum altitude of the sun above the horizon, the tilt angles of the solar panels had a very significant impact on the efficiency.

The following analysis was performed for the current measurements at 11:30. The highest current values were found at a 50° tilt angle (0.79 A), while the lowest values were at 0°, reaching 0.2 A, which was 74.7% less. Proportionally, the situation was also the same for the other solar panels placed at smaller tilt angles. Compared with 50° solar panels, 40° solar panels generated 11.4% lower current output, 30° solar panels 24% lower, 20° solar panels 41.7% lower and 10° solar panels 68.2% lower current output. Due to the low solar altitude above the horizon, at 12:35 a shadow was cast on 50° solar panels and at 13:30 a shadow was cast on the other solar panels. During winter, it is difficult to position solar panels, especially on the ground, so that they are exposed to solar radiation throughout the day, as surrounding buildings and trees might interfere.

Figure 9 shows a comparison of solar panels set at different tilt angles during the measurement period, assuming 100% for those installed at 0°. In mid-August (15 August) at the measurement site, the solar altitude at noon was 47.2°. In August, the highest efficiency was found for 40° solar panels, which was 31.7% higher than for horizontal solar panels. The efficiency of 40° solar panels was only 0.7% higher than that of 30° and 2.6% higher than that of 50° solar panels.

In September, the average solar altitude was 36.11°. The highest efficiency was found for 50° solar panels, as they were better oriented towards the low solar altitude, reaching 44.8% compared to horizontally positioned ones, while 40° solar panels had only 0.5% lower efficiency than 50° solar panels.

In October, the average solar altitude above the horizon was 24.6°. The highest efficiency was for 50° positioned panels, which is 74.5% higher than for horizontally positioned panels. These panels already have an efficiency in October 4.8% higher than the 40° positioned panels.

In November, the average height of the sun above the horizon was 14.7°. The highest efficiency during this month was found for 40° solar panels, reaching 51.2% compared to horizontal solar panels; 50° solar panels had a 6.2% lower efficiency. It is likely that reflected solar radiation was the major contributor during this period. For the solar panels set at other angles, the efficiency was significantly lower.

In December, the average solar altitude at the measurement site was only 10.12°. Similarly as in November, the efficiency was highest for solar panels set at 40°, reaching 16.4%. The efficiency was slightly lower, i.e., 5.4%, for 50° solar panels than for the horizontal ones. Given the low solar intensity, the changes could be considered as minor.

In January, the average solar altitude above the horizon reached 12.34°; 50° solar panels showed the highest efficiency, 39.6%, followed by 40° solar panels, reaching a 35.7% efficiency. For the solar panels placed at other angles, the efficiency was low.

The results given in Figure 10 were calculated by multiplying the measured GHI by the output ratio of a solar panel group to the 0° solar panel group. Note, that August and January are not completely surveyed, and one week in December was dropped due to technical issues of the measurement system.

The energy generated in December and January was very low for almost all the experimental solar panels. During the experimental period, the highest efficiency was found for the solar panels set at 50° and 40°, reaching a total solar irradiation of 266.61 Wm⁻² and 266.27 Wm⁻², respectively. The results were practically the same. The next-best performance was found for the 30° solar panel group, with a total solar irradiation of 4.6%; the 20° group had 12.5%, the 10° group 21.1% and the 0° group had 31.9% lower total solar irradiation than the 50° group.

Compared to the simulation results, which suggest a 33° tilt angle of the solar panels relative to the horizontal [3], our initial experimental studies have yielded angles exceeding 40°. These angles will be refined upon inclusion of full-season research data.

Results were also compared to the PVGIS data [32] monthly averages for years 2005 to 2023 (Figure 11).

The comparison included three fully covered months. Although there are only slight differences for GHI at 0°, the comparison for 50° panels shows a decrease in the measured output for October and November. A preliminary explanation could be the effect of shadowing; however, in order to create a justified solution, more data is needed.

4. Study Limitations

At the current stage of the study, a methodological framework for cost-effective study of optimal tilt angle using off-the-shelf industry tools has been developed and evaluated. The data-logging interval currently is six months for the autumn–winter season and does not allow to conclude about annually optimal tilt angle configuration.

The positive temperature effect on silicon solar cell short-circuit current value used in measurements is not currently taken into account, but is planned to be included in the next stage of the study by adding temperature probes on solar panels being tested. The short-circuit current and temperature dependence is well-studied in the literature and is close to linear at the typical working temperature range of solar panels, and can be easily added as a bias to experimental data.

In the next phases of the research, when study is conducted over a period of at least 12 months, it will be possible to evaluate the optimal tilt angle of solar panels to achieve higher electricity production.

5. Conclusions

• An original research methodology for determining the efficiency of solar panels set at different tilt angles has been developed and validated, with the aim of identifying the best tilt angle if solar panels are installed in a fixed position; the choice of a tilt angle is technically possible.
• The solar panel output comparison at different tilt angles by short-circuit current measurements is a simple and cost-effective method allowing performing experiments with larger groups of panels to improve statistics and increase the reliability of conclusions.
• In contrast to the majority of research projects, where only a single panel per scenario (azimuth, angle) was used, the use of three panels per group allowed us to compare the outputs between individual panels, thus providing a possibility to reliably identify shading events, dirt build-ups (e.g., bird droppings) and malfunctions on individual panels. It should be noted that during the experiment period, no failures were detected on panels.
• Based on the experimental methodology found in the literature, in future research studies, in experiments snow should be cleared off the solar panels immediately after the snowfall has stopped. It is also planned to clean dust and plant pollen off the solar panels at least once every 2 weeks during the dry season of the year. Dust can have a significant impact on the energy output of the solar panels.
• A careful examination of the data obtained on winter days when the maximum altitude of the sun did not exceed 10–12° revealed that the solar panels were shaded by objects slightly higher than the solar panels and located at a distance of 80–100 metres. Given that the proportion of solar energy generated in winter is low in Latvia, shadows will not significantly affect the research results. In winter at high-capacity, for solar power plants with multiple rows of solar panels, the solar panels are likely to be shadowed by parallel rows of solar panels.
• Just like at real solar power plants with solar panels installed on horizontal bitumen roofs, the temperature could affect the experimental results, which was higher on sunny summer days due to the black roof colour than on other kinds of roofs or on the ground. To identify the impact, it would be advisable to conduct other research on the performance of solar panels on different surfaces with regard to the temperature.
• The amount of the energy generated (Wm⁻²) in months when measurements were not taken during the whole month represent only rough estimates. Not taking measurements throughout the month might give a misleading impression that the efficiency of solar panels was higher in October, which is not the case. For a more accurate interpretation of the data, the average energy generated per day during a month could be calculated, which would give more easily perceivable data. This comparative data representation is intended to be used in the next phases of the research.
• Further studies are planned for at least 1–3 years, covering different weather conditions, cloud cover, sunny days and other specific conditions. It is also planned to install accurate temperature sensors on each group of solar panels and to record the temperature, as the panels used in the short-circuit experiments will experience higher temperatures in summer compared to the grid-connected solar panels. The experimental data will be corrected according to the temperature of the solar panels.