Solar panel performance analysis under indonesian tropic climate using sandia PV array performance model and five parameter performance model

Evaluation and monitoring of solar panel are need to be done, primarily related to how much energy is produced. Energy production by a solar panel is affected by the characteristics of climate or weather of a particular location such as solar radiation and ambient temperature. This study aimed to compare two models of solar panel performance calculation, i.e., Sandia PV Array Model and Five Parameter Model by considering the tropical climate of Indonesia and see the effect of temperature and solar radiation changes on the results of the calculations of both methods through the I-V curve. The types of solar panels on monitored are a monocrystalline, polycrystalline, and thin film. The results show that the energy produced by Sandia PV Array Performance Model for the three types of solar panels are 54.36 Wdc, 51.57 Wdc, and 39.62 Wdc, respectively. Five Parameter Performance Model results are 56.58 Wdc, 52.7 Wdc, and 43.29, respectively. These results show that with a small amount of data, the Five Parameter Model is more optimal and efficient for the tropics compared to Sandia PV Array Model.


Introduction
Investments worth USD809 reported by Bloomberg for the construction of the power plant of the year 2010-2015 photovoltaic [1], Most of this investment was allocated for the purchase of solar panels that power the output values based on Standard Condition Test (STC) as radiation 1000 W/m2, solar panel temperature 25oC, wind speed 1 m/s and Air Mass (AM) 1.5 [2]. However, the advantage of this investment is not determined based on conditions of STC but rather determined by the energy produced by solar panels that are affected by environmental conditions [3]. The performance of a solar panel is rated based on the energy produced, reliability, and efficiency of its conversion [4], [5].
The production of energy by solar panels through the process of converting solar energy into electricity depends heavily on climate or environmental parameters of a particular region [2], [6], those parameters are solar radiation intensity, solar panel temperature, wind speed and humidity [7]- [9]. Solar panel performance testing studies are mostly conducted in sub-tropical regions, so the results do not necessarily represent the general tropical conditions, including Indonesia. Tropical environments have distinctive characteristics [7]- [10] : 1. Have a high-temperature range 18-40 o C that can cause a rise in temperature of the solar panel reach 90 o C so it can degrade the performance of the solar panel.
2. The high level of humidity, i.e., 35-85% with low wind speeds ranged from 0.2 m/s. 3. The trend of clouds and has high annual precipitation.
This condition causes the low index of brightness that has an impact on the performance of solar panels.
With these characteristics, the solar panels operating in tropical regions need to be evaluated to determine how much energy is produced for the benefit of the investment due to the tropical climate leads to a significant deviation from STC conditions [2]. Some research on evaluation and testing the performance of solar panels associated with a tropical climate have been carried out by several researchers. In Nigeria which is a tropical country, conducted a study to investigate the influence of environmental temperature on the solar panel [11]. The result shows the presence of correlation between the temperature of the environment with the power generated by the solar panels. At low temperatures, the power generated is high but on the contrary with the high temperatures the generated power is low. Furthermore, research that evaluates the efficiency of the solar panel power conversion related dust, humidity and air speed [12] report, the power conversion efficiency decline in some tropical countries. In the U.S. that reaches 1-4.7% for two months, in Saudi Arabia in the amount of 32-40% in a month, the 17-65% 6-8 in Kuwait for 38 days, and a decrease of 33.5-65.8% for six months in Egypt, and in Thailand reached 11%.
In Sinegal, Ababacar Ndiaye, et al [13] evaluates the degradation of short circuit current (Isc) and open-circuit voltage (Voc) associated with power. The results shown in the period of 10 years there is a decrease in Isc and Voc respectively by 13% and 11%. Furthermore, research was done in Singapore by Timothy M. Walsh et al [14] against commercial solar panels of various types, the results showed that some solar panels have a less good performance in Singapore's tropical climate.
The primary focus of the research is to compare two models calculation of the solar panels performance, i.e., Sandia PV Array Performance Model (SPAPM) and Five Parameters Performance Model (FPPM). These methods are chosen because in its calculation SPAPM method uses the results of climatology data processing directly to determine the value of solar panel output at its operating conditions, whereas in the FPPM method, the working principle of solar panels is modeled into a single diode equivalent circuit. The analysis of this circuit will yield five parameter values ie a, IL, Io, Rs, Rsh. These five parameters are components of a single diode equivalent circuit used to determine the value of solar panel output.

Solar Radiation
The distance between the center of the earth and the sun is estimated as far as 1.495x10 11 m, and solar radiation reaches the Earth's surface through a process called radiation. Solar radiation outside the Earth's atmosphere is called the solar constant (Gsc) of 1.367 W/m 2 [15].

The Geometric Solar Radiation to Earth's Surfaces
The geometric relationship between the beam radiation and the earth's surface is shown in Fig.1 [15].  is Slope Angel i.e. the angle between the surface plane and the horizontal plane (0 o ≤   180 o ).  is Surface Azimuth Angel i.e. the projection deviation on a horizontal plane from normal to the surface of the local meridian. While s is solar azimuth angle that is the angular displacement from the southern beam radiation projection on the horizontal plane. Zenith angle (z) is the angle between the vertical surface and the line to the sun, i.e. the angle of incident beam radiation on a horizontal surface. s or solar altitude angle is the angle between the horizontal surface and the line to the sun, or the complement angle of zenith.

Solar Time
Solar Time is the time of movement of the sun's angle visible in the sky with solar noon as the sun passes the observer's longitude or is the relative position of the sun to the observation point [15]. Solar time depends on the time of observation and the day of observation in a year [16].
Substitution of equation (2) into (1) then the obtained value of the EoT. Thus the solar time can be calculated using the equation: Equation 4 is the hour angle that is a representation of the solar time in the form of the value of the degrees from the movement of the sun at all times.

Sun Declination
Sun declination angle () is the angle between the line of the equator the Earth with a straight line that connects the center of Earth to the center of the Sun. This angle determines the position of the Sun towards the Earth at a given day within a year. The angle of declination varies every season because of the tilt of the Earth on the axis of its rotation and the rotation of the earth around the Sun [17]. The magnitude of the angle of declination is calculated with the equation: = sin −1 ( sin 23.45) sin( 360 365 ( − 81))) (5)

Sun Elevation
Sun elevation angle (h) is the height of the Sun in the sky angle measured from the horizontal line (ground level) or in other words the angle formed between the direction of the oncoming sunlight with the soil surface. The elevation angle is 0 o at the time of sunrise and sunset, and 90 o valued when the Sun is exactly above head [18]. The elevation angle is calculated using the equation: ℎ = sin −1 ( sin sin + cos cos cos ℎ ) Zenith angle (z) is the complement of the angle of elevation or angle formed between the direction of the oncoming sunlight with a vertical line. The magnitude of the zenith angle: = 90 − ℎ (7) or = cos −1 (sin sin + cos cos cos ℎ ) (8)

Sun Azimuth Angle
Sun azimuth angle denoted by s is the direction of the compass from which sunlight comes. As in the compass direction the azimuth angle will be 0 o when the sun is to the north of the observation point and will be 180° when the sun is on the south [19]. The azimuth angle is calculated by the equation: = sin −1 ( − sin ℎ cos cos ) (9)

Angle of Incidence
Angle of Incidence (AOI) is the angle between the direction of the coming of the light from the Sun to the surface of the solar panel and the line normal to the surface of the solar panel. The value is determined by the angle of the AOI formation especially solar panel tilt angle (tilt angle) the effect on solar radiation absorbed by the solar panels. The greater the value of the AOI then solar radiation absorbed progressively reduced so that the output of solar panels to decrease. This happens when AOI worth 65 o or more [20]. The value of AOI is determined by the equation: = cos −1 ( cos cos + sin sin cos( − ) (10)

Beam Radiation
Beam Radiation (Eb) Beam Radiation (Eb) is the solar radiation received directly without the occurrence of scattered by the earth's atmosphere [15]. Beam Radiation is the multiplication of Direct Normal Irradiance (DNI) with Angle of Incidence (AOI) written as [21]: = cos (11)

Diffuse and Ground Reflected Radiation
Ed or diffuse radiation is solar radiation received after scattering occurs which is caused by the Earth's atmosphere so that the direction of the radiation is turned or deflected [15]. Ed is calculated using equation [22] : While the ground reflected radiation (Eg) that is leaning on the surface radiation reflected from the ground, and formulated as [23] = 1− cos

Total Radiation (Plane of Array Irradiance)
Total Radiation or Plane of Array Irradiance (Epoa) is the summation of the beam radiation, diffuse radiation and ground reflected radiation [24]. Written mathematically as :

Air Mass
Air Mass is the length of the path traversed by the light rays through the atmosphere normalized to the along the path with the shortest possible. Air mass quantifies the reduction in strength of the light when passing through the atmosphere and is absorbed by air and dust [25]. The air mass is calculated based on the equation: The air mass is calculated based on the equation [26]: Furthermore, to calculate the air mass in the form of a function of a polynomial of the air mass absolute or referred to as the air mass modifier (MAM) used equation [27]: Value of ao, a1, a2, a3, a4 are the coefficient vektor whose value is determined while testing the solar panel.

Methodology
In this study, the selected location is Halim Perdanakusuma area in East Jakarta (-6.264451 N and 106.895859 E). Data required such as solar radiation climatology, environment temperature, air mass, albedo, and wind speed. The data obtained by use of the software of Meteonorm. As for the data is as follows:  The temperature of the solar panel is one of the parameters is calculated in this study based on equation [27]: The value a dan b on the equations (19) and (20) are parameters that depend on the material of construction, as well as the configuration of the installation of the solar panels specified [28] as shown in the table below:

Sandia Photovoltaic Array Performance Model
Sandia Photovoltaic Array Performance Model (SPAPM) is one of the solar panel performance calculation models developed by David L. King et al. [27] at Sandia National Laboratories. The basic equations used to describe the electrical performance of individual solar panels, but can also be used in array configurations. The equations used in this model are: Where, To form a more precise I-V curve with this model two more equations are added when Ix is V = 0.5 VOC and Ixx when V = 0.5 (VOC + Vmp), the equation is:

Five Parameter Performance Model
Five Parameter Performance Model (FPPM) is a method that is also used to calculate the performance of solar panels. This model was developed by W.De Soto et al [20]. Unlike the SPAPM model, FPPM requires fewer data in its calculations. The required data are the initial parameter values found in nameplate solar panels Isc0, Voc0, Imp0, Vmp0 and climatological data in the form of total solar radiation and ambient temperature and the curve of solar panel characteristics at STC. The FPPM method modeled a solar panel into a single diode equivalent circuit shown in Fig.4.

Climatology data process
Climatological data in  (4). The amount of declination angle on the 296th day of -12.19 o is calculated using equation (5). Next is to determine the magnitude of zenith angle (z) with local latitude equal to -6,25 (table 1), based on equation (8) than z is 6,298 o . This zenith angle value is used to determine s or sun azimuth angle, based on equation (9) the value of s is -2,079 o .
Based on the zenith and azimuth angle, Angle of Incidence (AOI), Air Mass (AM) dan Air Mas Absolut (AMa) values can be calculated using equations respectively (10), (16) and (17). With the equation we get the value of AOI (38,71o), AM (1.006) and AMa (1.0025). The next step is to determine the total value of solar radiation absorbed by the surface of the solar panel or Plane of Array Irradiance (Epoa). However, to determine Epoa, we first determine the value of Beam Radiation (Eb), Diffuse Radiation (Ed) and Ground Reflected Radiation (Eg) using equations (11), (12) and (13). From the three equations Eb (74,13 W/m 2 ), Ed (360,2 W/m 2 ), dan Eg (15,11W/m 2 ). Based on these values, the magnitude of Plane of Array Irradiance (Epoa) shown in equation (15) are : = 74,13 + 360,2 + 15,11 = 449,45 W/m 2 The final part of this calculation is to determine the temperature of the module (Tm) and cell temperature (Tc). Tm and Tc are determined based on the material configuration and the type of mounting of the associated solar panels values of coefficients a, b and T. In this study using three types of solar panels are polycrystalline, monocrystalline, and thin film. The related information specifications of the three types of solar panels as well as the coefficients a, b and T are presented in table 2 and  table 3. The calculations of Tm dan Tc are done using equations (19) and (20), as for the values are as follows: Tm and Tc in this study are considered the same for all three types of solar panels because they have the same material configuration and mounting type.

Calculation process of SPAPM
The SPAPM calculation process is done based on the flowchart shown in Figure 3. The data used are solar electrical specification data and the results of data processing climatology. Calculations will be made on solar panels with the type of monocrystalline, but the results of the three types of solar panels will be displayed.
The first step of this process is to do the calculation of f1 that is the value of Air Mass Modifier (MAM) using equation (18) and produce f1 (AMa) is 0.982. While f2 is the value of the Angle of Incidence Modifier (MAOI) and the calculation uses the equation:  (21) is used to determine the value of Isc under its operating conditions. This Isc value is influenced by the level of solar radiation absorbed by the solar panel. Through the equation (21) the resulting Isc value is 1.87 A. The next is to determine the effective radiation value (Ee), this value is determined by the ratio of the short circuit current value at the operating condition and at the STC condition. Based on equation (27) the value of Ee produced is 0.425 (unitless) Imp, Voc, and Vmp under operating conditions are determined using equations (22), (23) and (24). The coefficient contained in the equation can be seen in Table  2 The results of the calculations for the three types of solar panels using SPAPM are shown in the table below:

Calculation process of FPPM
Calculation of the performance of solar panels using FPPM is done following the flowchart is shown in Figure  5. The data used are solar panel specification data on STC condition, total radiation absorbed by a solar panel, and cell temperature The first step of the calculation is to determine the value of reference or aref ideality factor with equation ( In some cases the value of Rs,ref produced by equation (41) is sometimes negative. This problem is solved by removing Rs and Rsh components in equivalent circuits and replacing them with photovoltaic resistance or Rpv [29]. Thus the single diode equivalent circuit in figure. 4 becomes: Fig. 6. Equivalent circuit diagram for the effective solar cell characteristic [29] The equation model generated according to the equivalent circuit in Fig. 6 is: The determination of the value of Rs requires the value of the second parameter resulting from the total radiation different from the fixed cell temperature, resulting in the value of the equation: The values of V1 and V2 are given by equation (45), while V1 and V2 are: Index 2 represents a parameter with a characteristic value with a lower short-circuit current. The value of I is determined by the equation: From equation (55) and (56)   Based on the calculation in Table 5, the curve of I-V under operating conditions is shown in the following figure:

Fig. 7. I-V Curve of Solar Panel under Operating Condition
In the calculation of solar panel performance with five parameters method, the value of solar panel output parameters can be known from the calculation of the current for each voltage value and characteristic curve. The calculation results for the three types of solar panels using five parameters are shown in the table below: The results of this study show that FPPM method is more efficient and optimal in assessing the performance of solar panel compared with SPAPM method. This occurs because the FPPM method requires only a small amount of data but can provide the results of solar panel output parameters that approximate the results obtained by the PAPM method. In addition to these two methods, solar panels with thin film types have smaller Pmp values of 39.62 W (SPAPM) and 43.29 (FPPM), this occurs because theoretically thin film has a smaller efficiency than the other two types.
The Authors would like to thank this work supported by "Hibah Penelitian Kerjasama Antar Perguruan Tinggi" Kemenristek Dikti. The Authors would like to thank for all member in Tropical Renewable Energy Centre (TREC) Universitas Indonesia.

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