The change in the angle-specific Ross coefficient and the corresponding y-intercept were estimated and discussed. Normal Ross Coefficient model where dispersion data is covered from January 21, 2020 to February 2, 2020.
General Introduction
Therefore, there is a great interest in knowing the PV module's operating temperature in real time during an assessment of the performance of a PV plant. This project will find a way to more accurately estimate the temperature of the PV module.
Importance of the Study
Problem Statements
Aim and Objectives
Scope and Limitation of the Study
Sun’s Position
- Local Standard Time Zone Meridian
- Solar Time and Local Clock Time
- Equation of Time
- Hour Angle
- Declination Angle
- Sun Altitude and Azimuth Angle
The declination angle is determined as the angle between the horizontal line to the sun and the Earth's equatorial plane, as shown in Figure 2.2. The sun's azimuth angle is the angle measured clockwise on the horizontal plane from due north (north-pointing coordinate axis or true north) to the projection of the center of the sun's beam (Stine and Geyer, 2001).
Cosine Effect
Thus, the solar incidence angle is expressed in terms of solar altitude and azimuth angles and the orientation of the PV module. The vectors 𝑁⃗⃗⃗ and 𝑆⃗ can be derived using the spherical coordinate system instead of the rectangular coordinate system.
PV Module Temperature Models
- Ross Coefficient Model
- Time-Specific Ross Coefficient Model
- Sandia Model
- Faiman Model
- Ross and Smokler Model
During the period of the high operating temperature of a PV panel, the temperature of the PV panel is always underestimated by using the conventional Ross coefficient, because the coefficient of the model is assumed to be the same during a day or a year . Therefore, it was improved by Lai and Lim (2020) and a higher accuracy model called the time-specific Ross coefficients model was developed by them, taking into account the coefficient of sectioned time. Moreover, according to the research of Lai and Lim (2020), the y-intercept is significant during the estimation of PV panel temperature, and should be included in the conventional Ross coefficient model.
According to King, Boyson, and Kratochvill (2004), the Sandia model has yielded the estimated PV module temperature with an accuracy of . The value of the coefficients a and b depends on the chosen mounting type and the module construction and material. The Ross and Smokler model was developed using the nominal operating cell temperature (NOCT) with the relationship of the conventional Ross coefficient model as shown in Eq.
Liu and Jordan Isotropic Sky Model
𝐺𝑏= Direct solar radiation on the horizontal plane, (W/m2) 𝐺𝑑= Diffuse solar radiation on the horizontal plane, (W/m2) 𝐺𝜌𝑠 = Diffuse flux reflected from the ground, (W/m2) Geometric p. According to funding by Gracia and Huld (2013), the estimated total solar irradiance is not significantly improved by taking the diurnal variation and anisotropic albedo value into account.
Metric
Mean Squared Error (MSE)
The mean squared error (MSE) can be expressed as the average of the squared errors in a set of predicted data.
Root Mean Squared Error (RMSE)
General Flow of the Methodology
This modified version of the Ross coefficient model is known as an angle-specific Ross coefficient model. The last main part is the evaluation of the accuracy of the angle-specific Ross coefficient model. The angle specific Ross coefficient and other models were applied to a practical case study of estimating the module temperature during this stage.
Calculation and Data Processing
The difference between the peak (either positive or negative) in-plane solar irradiance and module temperature is the amount of time delay. Before calculating the angle of incidence of the sun, it is crucial to determine the position of the sun. Since we are only interested in the data between sunrise and sunset, since the PV module only gains energy during this interval, the purpose of assigning the value "NaN" to the altitude of the sun and the azimuth angle at night and before dawn is to facilitate the calculation of the angle of incidence of the sun and give a neat or better visualization of the set altitude and sun azimuth data.
The tilt angle of the PV module, in this project is equal to 10° as the tilt angle of the PV module for most of the installation in Malaysia is 5° to 10°. Since the meteorological and PV module temperature data were used for the year 2020, these three parameters were therefore calculated for every minute of the year 2020. Appendix A shows the python coding for calculating the parameters and generating the data sets.
Built Angle-specific Ross Coefficient Model
This is due to the degree of difference between the temperature of the module and the surroundings before and after noon, which is not the same or similar, since the incident angle of the sun has repeated itself after a long time (the difference between the two vertical black dotted lines in Figure 3.10). The reason is that the angle of incidence of the sun in this interval is repeated in a short time (the difference between the two vertical red dotted lines in Figure 3.10). The regression line shows the characteristics of the angle-specific Ross coefficient model, as shown in Figure 3.12.
The y-intercept of the linear regression line of the scatter plot will be zero if the temperature of the PV module immediately rises as soon as it receives solar radiation. In addition, the temperature of the PV module must reach thermal equilibrium with the ambient temperature when the PV module is not receiving solar radiation. In addition, the characteristics of the angle-specific Ross coefficient model were also determined by plotting a graph of the coefficient and y-intercept against the cosine angle of incidence.
Obtaining Others Model
- Conventional Ross Coefficient Model
- Time-specific Ross Coefficient Model
- Sandia Model
- Faiman Model
A scatterplot of the change in temperature (Tmod – Tamb) versus the corresponding GTI was plotted to obtain the Ross coefficient, k (Ross, 1976). The coefficients for the time-specific Ross coefficient model were obtained by plotting the temperature change (Tmod - Tamb) against the corresponding GTI according to its time interval (Lai and Lim, 2020). 2.16, the gradient of the regression line is the ross coefficient, k while the y-intercept of the regression line is the model y-intercept of the time-specific ross coefficient, c.
The coefficients of the Sandia Model were obtained by plotting a graph of ln(𝑇𝑚𝑜𝑑− 𝑇𝑎𝑚𝑏 . 𝐺𝑇𝐼 ) against the corresponding wind speed (King, Boyson and Kratochvill, 2004). Comparing these two equations, the coefficients a and b are the y-intercept and gradient of the regression line, respectively. The coefficients, 𝑈0′ 𝑎𝑛𝑑 𝑈1′ were determined by the y-intercept and gradient of the regression line respectively (Faiman, 2008).
Evaluation of the Accuracy of the Angle-specific Ross Coefficient Model
Derive the cosine solar incidence angel Calculate the sun's position and solar incidence angle Generate data sets of time at 1-minute interval at. Preparation of progress report and presentation All the interested data filtered and compiled Identify the most suitable cos and time interval Arrange the temperature data according to its cosq and. Draw graph of module temperature against solar radiation for cos and time interval Identify the modified model's characteristic by analyzing.
Use the modified model and other models to estimate the module temperature for a practical case study Compare them with the practical measured module.
Introduction
Conventional Ross Coefficient Model
This value shows agreement with the study conducted by Lai and Lim (2020) on the roof of UTAR Sg.Long campus. The percentage difference of the measured conventional Ross coefficient between this project and Lai and Lim (2020) is 6%.
Time-Specific Ross Coefficient Model
The Ross coefficient increases significantly in the early morning, begins to decrease in the afternoon, and increases slightly as sunset approaches. As a result, the Ross coefficient increased rapidly as the module temperature gradually increased over this period. Therefore, the Ross coefficient during this period was lower than that in the morning.
The trend of the time-specific Ross coefficient and y-intercept obtained in this project is compared with that of Lai and Lim (2020). This indicates that the time-specific Ross coefficient model obtained in this project is acceptable for estimating the module temperature. 4.2, while Table 4.1 shows the time intervals of the time-specific Ross coefficient model with the corresponding site Ross coefficient and y-intercept.
Sandia Model
The magnitude of coefficient b for the metal deck mounting type PV system is small compared to other mounting types listed in Table 2.2. The reason may be that the air ventilation of the metal deck mounting type is poor.
Outlier removal For 400, where the scattered data spanned from January 21, 2020 to February 2, 2020. We can see that the gradient and y-intercept of the linear regression line change after outlier removal, as shown in Figures 4.6 to 4.9. . This indicated that deviations will significantly affect the linear regression line and cause estimation errors.
The Faiman model with the coefficients listed in Table 4.2 was used to estimate the module temperature using data on February 13, 2020 to determine its accuracy. The RMSE and MSE of the Faiman model after removing the deviation above 400 are the lowest.
Angle-specific Ross Coefficient Model
The increase in the angle of incidence of the cosine sun occurs only before noon, indicating that the sun rises and moves towards the highest point of the sky. The angle-specific Ross coefficient increases slightly as the sun rises, followed by a significant decrease towards the range of 0.8 to 1 and a small increase as one approaches sunset. As the air mass decreases when the sun rises, solar radiation increases drastically during this period.
Nevertheless, the angle-specific Ross coefficient increases slightly when the sun starts to fall since the heat dissipation from the metal deck is slow. The general equation of the angle-specific Ross coefficient model can be written as the equation given in Eq. 5, while Table 4.3 shows the cosine solar incidence angle and time interval and the corresponding site's Ross coefficient and Y-intercept.
Comparison of Module Temperature Estimation
The time-specific Ross coefficient model produces almost the same error as the in-estimation Ross coefficient model. It can be seen that the angle-specific Ross coefficient model has the highest accuracy, followed by the time-specific Ross coefficient model, the conventional Ross coefficient model, the Sandia model, and the Faiman model. The accuracy of the angle-specific Ross coefficient model is slightly higher than that of the time-specific Ross coefficient model, as shown in Figure 4.16.
The time-specific Ross coefficient model is ineffective in regions near the South or North Pole. This is due to the primary consideration during the section of the angle-specific Ross coefficient, where k is the position of the sun rather than time. Therefore, the angle-specific Ross coefficient will be more effective in estimating the modulus temperature in these regions.
Conclusions
Recommendations for future work
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