Renewable energy is the path for a sustainable future. The development in this field is progressing rapidly and solar energy is at the heart of this development. The performance and efficiency limitations are the main obstacles preventing solar energy from fulfilling its potential. This research intends to improve the performance of solar panels by identifying and optimizing the affecting factors. For this purpose, a mechanical system was developed to hold and control the tilt and orientation of the photovoltaic panel. A data acquisition system and electrical system were built to measure and store performance data of the photovoltaic panels. A design of experiments and Response Surface Methodology were used to investigate the impact of these factors on the yield response as well as the output optimization. The findings of the experiment showed an optimum result with a tilt of 60° from the horizon, an azimuth angel of 45° from the south, and a clean panel condition. The wind factor showed insignificant impact within the specified range.
The relation between man and the sun is ancient. The sun has played a massive role in the history of mankind. Some old civilizations even had spiritual belief in the power of the sun. According to Hsieh (1986), the sun is a giant nuclear reaction that transforms four million tons of hydrogen into helium per second. The earth will receive only a tiny amount of the sun generated energy [
The fossil fuels used today were formed over the course of thousands of years, but they are consumed rapidly. In 2009, the world consumed 11,164.3 million tons of oil equivalent. Comparing this consumption with the amount of received solar radiation during the same year, one will find that the input of solar radiation was 11,300 times greater than the world’s total primary energy consumption [
Solar energy is now estimated for one-third of the United States new generating capacity in 2014, surpassing both wind energy and coal for the second year in a row [ The manufacturing and material specifications where the maximum theoretical efficiency is limited Improving the power conversion for the PV panels systems, where the conversion from the generated DC into AC causes losses in efficiency Environmental factors (e.g., temperature, wind) Status of the PV panels (e.g., orientation, tilting)
Many PV system optimization efforts have utilized these factors from performance and economic perspectives [
Suitable infrastructure to conduct this research has been developed. The infrastructure includes a mechanical system (Figure
The specification of the monocrystalline photovoltaic panel.
Open circuit voltage | 44.9 V |
Optimum operation voltage ( | 37.08 V |
Short circuit current ( | 5.55 A |
Optimum operating current ( | 5.15 A |
Maximum power at standard conditions ( | 190 W |
Cell efficiency | 17.04% |
Operating temperature | −40°C to 85°C |
Maximum system voltage | 1000 V |
Pressure resistance | 227 g steel ball falls down from 1 m height under 60 m/s wind |
The mechanical system design, manufacturing, and assembly.
The wiring diagram of the system used in the research.
The experiment was designed using Response Surface Methodology (RSM). The selection of the method was based on both the objective of the experiment and the number of factors and levels. RSM can be defined as a combination of mathematical and statistical techniques effective for establishing, refining, and optimizing processes. It can be also used for the design and creation of new products as well as improving current ones [
Variables (
An experiment, as described by Montgomery (1997), is a test or sequence of tests where deliberate adjustments are made to the input variables of a system so that we may detect and distinguish the causes of the changes in the output response. Designed experiments are used in many disciplines and their impacts can be seen in almost every aspect of our lives. They help to build our knowledge about certain processes and systems, which give us insight to enhance and improve performance. Engineering fields are one of the biggest venues where design of experiment is used. Lower costs, new ideas, new processes, new products, and new systems are invented due to the practice of design of experiments.
The first stage of the Response Surface Methodology is to identify the important factors and their levels. They should have significant impact on the yield response. In this experiment independent variables with multilevels are identified with a goal to study their effect on the response yield and to find the optimum setting of the factors’ levels. A model of typical process is applied with input, independent variables, uncontrollable factors, and output. The photovoltaic effect is considered as the process. Two PV panels are used as the input materials. The irradiance is considered another input to the process. The date, time, and location were also considered as inputs to the process. The temperature of the PV panels and the ambient temperature, though measured, were considered as uncontrollable factors. General weather conditions were considered as uncontrollable factors including the clouds and humidity. Tilt angle, azimuth angle, wind intensity, and solar panel cleanness were considered as the controllable factors.
For four independent variables three levels in the feasible ranges were identified:
The two PV panels used in the experiment were identical. One panel was placed on the dual axis mechanical system while the other was flat on the ground. The rheostats loads that were used in the electrical system were identical. To overcome the minor discrepancy of the initial output power of the two PV panels, a small calibration was applied to them with
The four uncoded factors with their three levels.
level | | | | |
---|---|---|---|---|
Low | 0 | | 0 | 0 |
Mid | 30 | 0 | 5.5 | 20 |
High | 60 | 45 | 10 | 40 |
Experimental design has been implemented to characterize the process in terms of how input parameters affect the power output. The main two kinds of designs of Response Surface are Central Composite designs and Box-Behnken designs. The selection of the type of Response Surface design is the second stage. In this experiment Box-Behnken was used. The advantages of using Box-Behnken designs are to have less design points than Central Composite designs, which will make it less costly. High efficiency is needed to estimate the first- and second-order model coefficients. The disadvantages are the incapability to use runs from a factorial experiments, the limitation of three levels per factor while the Central Composite can have up to five, and finally they cannot have runs with the extreme value of the factors.
The software is used for the design of experiment and to analyze the result is Minitab. The setting included the selection of three replications and randomization to reduce the bias. The software generated the following 81 uncoded runs.
The experiment was conducted on 17th and the 18th of December 2015. The readings were collected from the data acquisition system and were inputted to the runs’ charts. These runs were later compared to the data saved in the system to guarantee the accuracy.
The next stage of the RSM is to analyze the data and find the RSM coefficients. Minitab is used to perform the aforementioned tasks. The confidence level used during the analysis was 95%, and it was two-sided.
The normal probability plot on Figure
Four-in-one residual plot generated by Minitab.
The calculated
The final equation is as follows.
The optimization of the response was determined by Minitab. The software generated the optimum settings of the factors to maximize the yield response. Table
Multiple Response Prediction.
Variable | Setting |
---|---|
A | 60 |
B | 45 |
C | 0 |
D | 0 |
The optimization graph generated by Minitab. The four factors and their optimum setting are shown in red.
The Minitab calculations show the optimum settings to maximize the power difference are achieved when the tilt of the PV panel is 60° and the PV panel is oriented toward the west and there is no wind and dirt on the surface of the panel.
The PV panel was subjected to the founded optimum levels of treatments on the 26th of February. A sample of the data was collected from 27th record and results were close to the predicted value in the model (119 W) (Table
Validation sample of data. A sample of data from the 27th of February 2016 with the optimum settings of 60° and 45° from the south, 0 wind and 0 talc.
Date and time | Power 1 | Power 2 | Power difference | Irradiance 1 | Irradiance 2 |
---|---|---|---|---|---|
Feb 27 | 169.8 W | 60.5 W | 109.31 W | 1000.8 W | 394.25 W |
Based on the results from validation experiments, power difference for two PVs was 109.31 Watts.
For similar setting (Table
Therefore, the model predicted the power difference with about 8% error.
Model versus validation difference =
One element, which was ignored during the study and optimization process, is the fact that sun’s position was changing during the data collection of the experimental runs. It is obvious the optimum positon for tilt and azimuth is when PV is pointed exactly toward the sun (continuous sun tracking). However, for the fixed level settings and since conducting experiments may take several hours, assuming a fixed position for the sun is inaccurate (Figure
Optimum versus main effect inconsistency for factor
Further investigation of the data showed that the optimum point for the tilt angle changes simply by changing the time of the day when the runs were conducted. To show this effect, in this study, the experiment was conducted during two consecutive days, the 17th and 18th of December. Midday on these two days was around 12:28 PM. The runs were divided into two groups, before and after midday. The runs before midday were 22 runs with the following run orders [1 to 5; 42 to 58] and after midday were 59 runs with the following run orders [6 to 41; 59 to 81]. The main effect plots were generated using Minitab for each group. The maximum power differences for the runs before midday were achieved with the PV panel oriented toward the east. The maximum power differences for the runs after midday were achieved with the PV panel toward the west. This shows the significant importance of tracking the sun for the PV panel (Figures
The main effect for the runs before midday. The highest achieved response is when the PV panel is pointed toward the east (a) and the main effect plot for the runs in the afternoon. The highest achieved response is when the PV panel is pointed toward the west (b).
The research used design of experiments and Response Surface Methodology to plan, analyze, and optimize the experiments. The three out of four factors investigated in this research to optimize the performance of the PV panels have significant impacts on the power output. In addition to these factors, other variables such as the date/time and the location of the PV panels affect the performance of the PV panels as well.
Sponsors are not responsible for the content and accuracy of this article. This article is a portion of a Master of Science thesis by Almusaied reported in [
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work has been completed with funding from the US Department of Education MSEIP program (Grant no. P120A140065). The authors would like to thank the US Department of Education and Texas State University for providing funding and access to infrastructure and laboratories.