A Methodological Framework for Studying the Tilt Angle of Solar Photovoltaic Panels
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
The current study present an attempt to experimentally test a PV system under various tilting angles. My main concern is related to the idea of the paper, tilting angle can be calculated for any longitude and latitude, so what is the added value of this study?
In addition, following Figures 9, and 10, the work demonstrate only a time interval of three months, where at least one year investigation is needed.
Author Response
Comment1: The current study present an attempt to experimentally test a PV system under various tilting angles. My main concern is related to the idea of the paper, tilting angle can be calculated for any longitude and latitude, so what is the added value of this study?
Response1:
The research was conducted under real-life conditions using solar panels installed at various tilt angles. Optimal tilting angle indeed can be calculated based on global irradiation, which consists of direct and diffused components. These can be modelled for any longitude and latitude. Diffused irradiation as a component of global solar irradiation begins to play important role in Northern regions with limited sun availability also due to weather conditions. According to open-meteo.com Historical Weather API on the experiment site 42% time was with at least 80% cloud cover in summer and 73% in autumn-winter season of year 2024. Diffused radiation depends on local atmospherics and geographic conditions. Current global irradiation model comparisons show dependencies from geographical area due to various tuned coefficients (https://doi.org/10.1016/j.rser.2021.111856). So cost-effective experimental measurement for local measurements would be beneficial. According to modeling data in some publications, a tilt angle of 33˚ to the horizontal is recommended for solar panel installation in Latvia. In our opinion, this does not correspond to the actual conditions. Moreover, the same angle is also recommended for many other countries that are geographically much closer to the equator (for example, North Macedonia). Although the cost of solar panels has significantly decreased over the past five years, installing large solar power stations on the ground at the correct angle can result in higher electricity output and reduce the land area required for the power station, thereby minimizing the ecological footprint and the need for land appropriation. The main idea of this research is to experimentally determine the effect of the solar panel tilt angle on the amount of generated energy through long-term studies. The data gathered may also help to improve and validate global irradiation models developed by other researchers by including diffused irradiation component in local measurements. Corrections have been made to the text.
Comment2: In addition, following Figures 9, and 10, the work demonstrate only a time interval of three months, where at least one year investigation is needed.
Response2: In the initial phase of the research, pilot measurements were carried out to confirm or refute the accuracy of the chosen methodological algorithm, as also reflected in the title of the publication “Development and Validation of a Methodology for Studying the Tilt Angle of Solar Photovoltaic Panels.” Improvements to the methodology are planned, including the elimination of data inaccuracies — for example, temperature correction, which can affect the measurement of solar panels output in short circuit measurement mode. Corrections have been made to the text.
Reviewer 2 Report
Comments and Suggestions for Authors
Reviews on manuscript Energies-3675173:
The manuscript presents an experimental study on determining the optimal tilt angle for solar photovoltaic (PV) panels in Latvia. While the topic is relevant, the study lacks significant novelty and fails to advance the current state of knowledge in the field. The methodology, though sound, is largely derivative, and the results do not offer substantial new insights compared to existing literature. Below are detailed comments supporting this assessment:
- Lack of novelty: the study replicates well-established methodologies for tilt angle optimization without introducing innovative approaches or addressing gaps in the literature. The authors acknowledge that most prior research focuses on latitudes below 40°, but their work does not sufficiently justify why Latvia (56° N) merits a standalone study, especially given the predictable seasonal behavior of solar irradiance at high latitudes. The conclusion that 40°–50° tilt angles are optimal aligns with known principles (e.g., tilt ≈ latitude ± seasonal adjustments). No counterintuitive findings or theoretical advancements are presented. The comparison to PVGIS data (shown in Figure 11) is superficial and does not resolve discrepancies (e.g., October–November underperformance), which are attributed vaguely to "shadowing" without rigorous analysis.
- Limitations in the methodology: the short-circuit current method, while cost-effective, introduces biases (e.g., panel overheating panel, no MPPT tracking) that are not adequately accounted for. The study also lacks validation against real-world PV systems with load connections. No comparison to standard IV curve measurements or power-output-based methods (e.g., [8, 20]).
- Incomplete data and seasonal assessment: the 6-month dataset (August–January) omits critical periods (spring/summer), undermining claims about annual optimality. The winter data, while useful, are overrepresented in conclusions. In fact, thee assertion that 40°–50° is optimal is based heavily on winter performance (low solar altitude), but summer tilt preferences may differ significantly.
- Weak comparative analysis: the literature review cites global studies but does not contextualize Latvia’s unique conditions (e.g., cloud cover, albedo from snow) to explain deviations from expected trends. In effect, the 30% irradiance deficit in winter (Figure 7) is attributed to "clouds" without quantitative meteorological data, whilst, no discussion of how Latvia’s diffuse-light climate (e.g., frequent overcast skies) affects tilt-angle sensitivity.
Author Response
Comment1: Lack of novelty: the study replicates well-established methodologies for tilt angle optimization without introducing innovative approaches or addressing gaps in the literature. The authors acknowledge that most prior research focuses on latitudes below 40°, but their work does not sufficiently justify why Latvia (56° N) merits a standalone study, especially given the predictable seasonal behavior of solar irradiance at high latitudes. The conclusion that 40°–50° tilt angles are optimal aligns with known principles (e.g., tilt ≈ latitude ± seasonal adjustments). No counterintuitive findings or theoretical advancements are presented. The comparison to PVGIS data (shown in Figure 11) is superficial and does not resolve discrepancies (e.g., October–November underperformance), which are attributed vaguely to "shadowing" without rigorous analysis.
Response1: It is known from literature (e.g., DOI:10.1016/j.renene.2018.12.057), that ratio of diffuse to direct solar radiation is not constant over time and geographical locations. Due to diffused component annual (seasons, weather changes etc.) global irradiation cannot be evaluated accurately by existing theoretical models as they also use location specific coefficients (DOI: 10.1016/j.rser.2021.111856). Diffuse radiation becomes very important during cloudy days (according to open-meteo.com Historical Weather API on the experiment site 42% time was with at least 80% cloud cover in summer and 73% in autumn-winter season of year 2024). In current stage of the study as a main novelty we evaluate a cost-effective methodology for finding tilt angle effect on total output of typical of-the-shelf panels in local conditions trying to avoid influence of possible common irradiation model inacuracies and effect of PV controller algorithm for maximum power tracking. We agree that, as this primary study is more oriented towards validation of the methodology, the conclusion on the optimum angle of installation of the solar panels is only relevant for a study period of 6 months. We agree with the reviewer that this study cannot serve as a recommendation to install solar panels at 40˚-50˚ at this scale. A correction to the conclusions has been made. Authors admit, that discrepancies in Fig. 11 can be analysed in more detail with a help of larger data set. It was also noted in original version of the manuscript.
Comment2: Limitations in the methodology: the short-circuit current method, while cost-effective, introduces biases (e.g., panel overheating panel, no MPPT tracking) that are not adequately accounted for. The study also lacks validation against real-world PV systems with load connections. No comparison to standard IV curve measurements or power-output-based methods (e.g., [8, 20]).
Response2: The main interest in this study was effect of tilt angle. One of reasons was that in recent years there are huge investments in solar energy (installed power increase from 100 MW in 2022 to 660 MW in 2024), but in a lot of situations non-optimal angle was used. Therefore the idea was to demonstrate angle effect on typical solar panels by possibly excluding other factors. This is why trackers were not used, IV curve also was not relevant as current measurement was used. In this case in our opinion load connection (as it would be for real-world production PV systems) is also factor not relevant for tilt angle study. Authors agree, that temperature bias in short-circuit measurement mode is taking place as panels at different angles will heat up differently and this will also be further affected by self-heating due to photocurrent. Installation of temperature sensors is planned on the second stage of the research. Conclusions on prospective studies are corrected.
Comment3: Incomplete data and seasonal assessment: the 6-month dataset (August–January) omits critical periods (spring/summer), undermining claims about annual optimality. The winter data, while useful, are overrepresented in conclusions. In fact, thee assertion that 40°–50° is optimal is based heavily on winter performance (low solar altitude), but summer tilt preferences may differ significantly.
Response3: In the initial phase of the research, measurements were conducted that may confirm or refute the accuracy of the chosen methodology. Following the refinement of the methodology, the research is planned to be carried out over a period of at least 1 to 3 years, depending on the results of interim analyses—this initial phase can also be considered part of that process. We fully agree with the reviewer that the analyzed phase of solar energy reception at the geographical latitude of Latvia does not provide particularly precise insights into the overall trends and the choice of angles. Based on this short research period, the evaluation of the optimal tilt angle for solar panel installation may be inaccurate. However, the methodology—emphasized in the article title “Development and Validation of a Methodology for Studying the Tilt Angle of Solar Photovoltaic Panels”—after refinement, could serve as a foundation for a broader and longer-term research program. We also fully agree that the current conclusions, based on data obtained during the winter season, cannot serve as the main criterion for determining the optimal installation angle, as the proportion of sunny days in Latvia during the summer is significantly higher, and the amount of energy generated during this period exceeds winter production several times over. Detailed conclusions about the study, including analysis over a longer period and of the produced capacity, will be developed in the next stages of the research, which are planned to cover at least 1–3 years. Conclusions are corrected.
Comment4: Weak comparative analysis: the literature review cites global studies but does not contextualize Latvia’s unique conditions (e.g., cloud cover, albedo from snow) to explain deviations from expected trends. In effect, the 30% irradiance deficit in winter (Figure 7) is attributed to "clouds" without quantitative meteorological data, whilst, no discussion of how Latvia’s diffuse-light climate (e.g., frequent overcast skies) affects tilt-angle sensitivity.
Response4: The analysis of Latvia's specific climatic conditions, which confirms the need for experimental studies, is included in the analytical review.
Reviewer 3 Report
Comments and Suggestions for Authors
1. The novelty of the paper needs to be justified and clearly defined. It includes the clear difference with the available literature and previous works. The authors are asked to provide the limitations of the previous correlated works and then linked those limitations to the current ideas and contributions of the current work. There are many works that have been done for this kind of prediction and optimization problems. You need to emphasize the research gap in your study.
2. In the abstract and highlights, please also include the quantitative results, not only qualitative explanation. Therefore, the readers can understand accurately the contents of the work.
3. Several references are lumped together without providing sufficient description for each of them. It gives nothing to the readers. Please provide a short description or descriptor for each used references, hence, the readers can understand the content of each used references.
4. The English must be improved significantly. There are several grammatical errors and unclear sentences throughout the manuscript.
5. How can you validate and compare your results with any other methods and application (validity)? This is very important, you need to compare the results wih any data-driven method which usually has much higher accuracy.
Author Response
Comment1. The novelty of the paper needs to be justified and clearly defined. It includes the clear difference with the available literature and previous works. The authors are asked to provide the limitations of the previous correlated works and then linked those limitations to the current ideas and contributions of the current work. There are many works that have been done for this kind of prediction and optimization problems. You need to emphasize the research gap in your study.
Reply1. It is known from literature (e.g., DOI:10.1016/j.renene.2018.12.057), that ratio of diffuse to direct solar radiation is not constant over time and geographical locations. Due to diffused component annual (seasons, weather changes etc.) global irradiation cannot be evaluated accurately by existing theoretical models as they also use location specific coefficients (DOI: 10.1016/j.rser.2021.111856). Diffuse radiation becomes very important during cloudy days (according to open-meteo.com Historical Weather API on the experiment site 42% time was with at least 80% cloud cover in summer and 73% in autumn-winter season of year 2024). In current stage of the study as a main novelty we evaluate a cost-effective methodology for finding tilt angle effect on total output of typical of-the-shelf panels in local conditions trying to avoid influence of possible common irradiation model inacuracies and effect of PV controller algorithm for maximum power tracking.
Comment2. In the abstract and highlights, please also include the quantitative results, not only qualitative explanation. Therefore, the readers can understand accurately the contents of the work.
Reply2. The main objective of this research is to develop and validate a methodology for determining the optimal angle of solar panel placement, therefore the amount of quantitative data is limited during the study period (6 months). The quantitative data from the primary experiments are included in the abstract.
Comment3. Several references are lumped together without providing sufficient description for each of them. It gives nothing to the readers. Please provide a short description or descriptor for each used references, hence, the readers can understand the content of each used references.
Reply3. The introduction analyses each source of literature separately with sufficient precision.
Comment4. The English must be improved significantly. There are several grammatical errors and unclear sentences throughout the manuscript.
Reply4. The English language was significantly improved, with corrections noted.
Comment5. How can you validate and compare your results with any other methods and application (validity)? This is very important, you need to compare the results wih any data-driven method which usually has much higher accuracy.
Reply5. The results of the initial experiments demonstrate that the developed methodology is functional for obtaining results. We have compared the results from data obtained so far with PVGIS, PVGIS-SARAH3 database (see Fig. 11). It is free to use database based on data calculated from sattelite images. To conduct comprehensive experiments, some adjustments are necessary—for example, installing precise temperature sensors on each group of solar panels and carrying out the experiments over a period of at least 1–3 years to include all seasonal variations. Experimental research is generally more representative of real-world conditions, as modeling cannot accurately capture all specific factors, such as diffuse and reflected radiation. Corrections have been made.
Reviewer 4 Report
Comments and Suggestions for Authors
The review report of the manuscript # energies-3675173, Titled "Development and Validation of a Methodology for Studying the Tilt Angle of Solar Photovoltaic Panels ".
The following improvements are suggested:
- The study lacks uncertainty analysis or error margins, which are essential in experimental energy research.
- No correction for temperature coefficients, which can alter photocurrent output.
- The use of a single pyranometer at 0° introduces bias when comparing to panels at other inclinations. Ideally, a pyranometer per angle group or angular correction factor should be applied.
- The literature review is comprehensive and appropriately cites global studies across various climatic zones. However, it would benefit from a clearer critical analysis, especially:
- Differentiating between simulation vs. experimental studies.
- Highlighting the unique challenges of diffuse-dominated irradiance at higher latitudes.
- The manuscript is generally well-written, but there are noticeable grammatical issues:
- Misuse of terms like "choose of tilt angle" instead of "choice".
- Repetition and awkward sentence structures in several paragraphs.
- The conclusion section could be more concise and clearly enumerate implications and future directions.
Author Response
Comment1: The study lacks uncertainty analysis or error margins, which are essential in experimental energy research. No correction for temperature coefficients, which can alter photocurrent output.
Response1: Based on current research findings and reviewers’ recommendations, methodological adjustments are planned for the implementation of prospective long-term measurements. In the initial phase of the study, temperature sensors with low accuracy were used, which did not allow for precise correction of the generated power depending on the temperature of the solar panels in relation to their installation angle. Due to the inaccuracies of the sensors, their data was not analyzed in the article. Currently, efforts are underway to acquire and replace them with high-quality temperature sensors, so that temperature variations can be accounted for and used to correct the potential output of the solar panels depending on the installation angle. Corrections have been made to the conclusions. Measurement error calculation has been added in methods section. Authors agree, that temperature bias in short-circuit measurement mode is taking place as panels at different angles will heat up differently and this will also be further affected by self-heating due to photocurrent. Installation of temperature sensors is planned on the second stage of the research.
Comment2: The use of a single pyranometer at 0° introduces bias when comparing to panels at other inclinations. Ideally, a pyranometer per angle group or angular correction factor should be applied.
Response2: We agree that the experiments would be more accurate if a separate pyranometer were used for each investigated angle. However, due to limited funding for the experiment, the methodology validation was carried out using a single pyranometer and power measurements from solar panels positioned at a 0° angle. These solar panels serve as a reference point for power correction at other angles, which are recalculated using geometric trigonometric relationships. An explanation is included in the methodology: “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.”
Comment3: The literature review is comprehensive and appropriately cites global studies across various climatic zones. However, it would benefit from a clearer critical analysis, especially:
Differentiating between simulation vs. experimental studies.
Highlighting the unique challenges of diffuse-dominated irradiance at higher latitudes.
Response3: An analysis has been carried out on the differences between the simulation and experimental studies, as well as on the significance of diffuse or reflected radiation in the context of Latvian conditions. The additions and corrections are included in the Analytical Review.
Comment4: Misuse of terms like "choose of tilt angle" instead of "choice".
Repetition and awkward sentence structures in several paragraphs.
The conclusion section could be more concise and clearly enumerate implications and future directions.
Response4: Revisions have been made to address the identified grammatical inaccuracies in the text. Conclusions supplemented with directions for further research.
Round 2
Reviewer 2 Report
Comments and Suggestions for Authors
- Detailed analysis was not elaborated due to the la k of big data base.
- The methodology was limited and further investigation and optimization due to the biases induced by the short-circuit current method, the consideration of this critical concern is unfortunately projected in the upcoming stages of the related research of this work..
Author Response
Comment1: Detailed analysis was not elaborated due to the la k of big data base.
Response1: Regarding amount of experimental data authors have already pointed out this issue in the manuscript and during discussion on preliminary results; and paper is aimed to show methodology of the study.
Comment2: The methodology was limited and further investigation and optimization due to the biases induced by the short-circuit current method, the consideration of this critical concern is unfortunately projected in the upcoming stages of the related research of this work..
Response2: Methods section has been updated with temperature effect analysis, additionally a reference has been added. To summarize: Isc dependence on temperature obtained in experimental research presented in literature for temperature ranges in this study (temperature difference of panels at different tilt angles) is less than measurement error. But taking into consideration that temperature coefficient is positive this bias (in percent of Isc in normal conditions) will added to the measurements after enough temperature data will be gathered.
Reviewer 3 Report
Comments and Suggestions for Authors
Accept
Author Response
Some minor changes in text were added, analysis of short circuit bias was added. Thank You for helping to improve our paper!
Reviewer 4 Report
Comments and Suggestions for Authors
The paper is significantly improved, no further comments are required.
Author Response
Some minor changes in text were added, analysis of short circuit bias was added. Thank You for helping to improve our paper!
