Joule heating estimation of photovoltaic module through cells temperature measurement

Received Jul 25, 2021 Revised Mar 25, 2022 Accepted Apr 10, 2022 Module temperature has a role in determining a PV module's performance. The purpose of this paper is to estimate the Joule heating in a photovoltaic (PV) module by comparing during PV-On (electricity generation) and PV-Off (without electricity generation). Joule heating was less evaluated due to simplifying formulation, which is easier to implement in experimental observation as proposed in this work. The experiment collected the temperature distributions of the PV module during PV-On and PV-Off. PV module temperature distribution follows the normal distribution curve as the irradiation uniformity pattern of the solar simulator has a slight ≤0.3 C difference between PV-On and PV-Off. Joule heating slightly increased the PV module temperature by 0.53 K/A, proportional to the irradiances. Joule heating has increased almost seven times from 2.65 W at 700 W/m to 18.07 W at 1000 W/m. Joule heating might slightly increase the overall thermal conductivity and slightly decrease the thermal resistances. It might affect the heat transfer. This research may improve the procedures prediction of PV or photovoltaic-thermal (PVT) collector temperature by considering Joule heating.


INTRODUCTION
The sun is an abundant source of energy available on earth. Based on the latest research, conversion of solar energy into electricity can reach 24% efficiency using mono-crystalline silicon (mc-Si) of photovoltaic (PV) modules [1] and into thermal energy by 70% efficiency using water-based flat-plate thermal collectors [2]. The rest of the unused solar energy is reflected or becomes heat lost by convection. Theoretically, PV module performance decreases with increasing module temperature or vice versa [3], [4]. For performance stability, converting heat into valuable energy can control the PV module temperature. That is one of the reasons for combining a PV module with a thermal collector into a hybrid photovoltaic-thermal (PVT) collector [5]. The conversion of solar energy is up to 80-90% [6]. The performance of the PV module and thermal collector influence the total performance of the PVT collector [7].
Here, PV temperature has a role in determining optimal performance. Many researchers evaluated the PV module or PVT collector performance for a long time. The actual measured PV temperature is the effect of irradiance and Joule heating simultaneously. Joule heating is the heat generated whenever a current passes through a resistive material [8]. The thermal performance of a hybrid PVT collector is also likely to be affected by Joule heating [9], [10]. Joule heating effect exists when the hybrid PVT collector generates electrical and thermal energy as PVT-mode [11]. PV module temperature is more determined through prediction. It used data from the manufacturer as environmental data (irradiation, ambient air temperature, wind speed). Moreover, the prediction data only used electrical parameters provided by the PV manufacturers [12]- [15]. If the prediction of PV module temperature is too low, then the actual efficiency of PV modules is often lower than the PV manufacturer data by standard test conditions (STC: 1000 W/m 2 , 25 °C, AM 1.5). There have been several methods and techniques in predicting PV temperature. Direct measurement by attaching a thermocouple to the solar cell from the back-sheet can accurately predict the PV temperature [16]. However, the temperature sensor insertion into a PV cell is quite challenging. The nominal operating cell temperature (NOCT) model is more accurate in predicting the PV temperature for the PVT system [17]. However, these models also depend on the accuracy of the environmental and operational data. Artificial intelligence (AI) techniques with artificial neural network (ANN) [18]- [20], modelling with various models [21]- [23] are satisfactory in estimating the PV module temperature. However, all these techniques have not demonstrated the physics interaction of input parameters, such as environmental and operational data. A model to estimate PV temperature involving wind speed effects gives quite reliable results [24]- [26]. However, the model is very dependent on the availability of wind speed data, in addition to data storage memory. Estimating the radiation and module temperature have used the algebra equation and non-linear parameter techniques [27]. The PV system must be on maximum power point tracking (MPPT). However, these methods require certainty data with quite complex calculations. In addition, Joule heating were not involved in the discussion.
Joule heating has difficulty observing outdoors for a long measurement. Joule heating requires the ideal conditions such as; high irradiation, long duration of the steady conditions and slight temperature differences between inlet water and ambient air. The system must be in a steady state to be more controlled for getting an accurate result. While most of the indoor ones only used a small PV cell, it was not easy to detect and measure Joule heating. Thus, several studies have examined Joule heating by simulation rather than experimentation. A finite element model using COMSOL Multiphysics simulated the PV module temperature and Joule heating [28]. The PV module temperature was corrected using simulation for a constant current density. However, Joule heating was neglected for more complex simulations reasoning less contribution comparing irradiances and memory concerns. The comprehensive energy distribution model [29], the novel thermal model [30] also the electrical loss prediction of modules (ELMO), and the outdoor measurement method [31] investigated the electrical and thermal performance of PV modules including the series resistance loss from Joule heating. The model determined the amount of incident solar energy lost. However, there was no detailed discussion regarding Joule heating. The heat transfer model was developed based on the ambient condition [32]. It can implicitly involve the Joule heating in the simulation. Unfortunately, Joule heating has not been the main focus to examine in more detail. Finally, Joule heating did not involve in the model development. The 1D numerical model predicted the cell efficiency and temperature during operation [33]. This model encompassed every heat mechanism occurring in a solar cell.
Research on the system performance of PV or PVT modules through module temperature is still quite interesting especially involving Joule heating. From previous studies, it seems that there have been some researches that specifically discuss the behaviour of PV or PVT module temperature as an effect of Joule heating. Although all studies have examined the PV module temperature, electrical and thermal efficiency; however, Joule heating has not been explicitly discussed [32]. The experiments could observe Joule heating but neglected it due to simplifying formulation. For continuing the previous study [34], the present work is to validate the Joule heating experimentally by investigating the thermal distribution of PV cells under PV-On or generating electricity and PV-Off or without generating electricity. The current study purposes in estimating the value of Joule heating which affected the PV module temperature during PV-On.

METHOD 2.1. Experimental setup
Since the ideal conditions are hardly difficult to achieve outdoors, the experiments have been done indoors. Figure 1 shows the indoor experimental configuration using a halogen solar simulator. The halogen solar simulator can control the significant parameters properly. The comprehensive dimensions, designs, and characteristics of the simulator were previously discussed [35]. Before the experiment, the irradiance level was adjusted by the sliding regulator (Matsunaga, SD-1310) to the simulator and measured by a pyranometer (MS-42, Eko) at the midpoint of the PV module mounting surface (mc-Si, GT434 type, KIS Solar Japan). Then, the PV module changed the pyranometer position, connected to the simulator [35], sliding variable resistor (Berco, Rheostats), and analogue-digital-converter (ADC). The sliding variable resistor adjusted the MPPT [36], [37].   Figure 2 shows the detailed measurement position of the PV module. Figure 2(a) shows the PV cells coordinate at the rear surface to measure the temperature of each cell. As shown, there are four rows, each row with eight cells. The outer dimension of the PV module is 380x350 mm, giving the total area is 0.133 m 2 . The PV module had 17 cells with 35×160 mm for each cell. Each cell gave an effective area of about 0.0054 m 2 . The total area of the PV cells was 0.091 m 2 or approximately 69% of the total area of the PV module . Figure 2(b) describes the coordinate position of the halogen light sources. As a reference, the lower-left corner was the centre (0.0). The previous studies have discussed the detailed dimensions, construction, and characteristics of the solar simulator and the PV module [27]- [29]. Table 1 shows the specific measurement positions.

Measurement and data collection
For the study purpose, an experiment on the PV module temperature had conducted during PV-On and PV-Off. That is to determine the difference in temperature distribution between PV-On and PV-Off due to the Joule heating on the PV module. The measurement of each cell temperature took the rear surface of the PV module. This method allowed the light to reach the PV cell surface without being blocked by thermocouples. As a benchmark, measurement took 32 points. The steady-state measurements were made during MPPT with ≈ 30; 33; 37; 41 Ω for the fixed irradiances =1000; 900; 800; 700 W/m 2 , respectively. Due to the limited data-logger ports (only ten ports), measurements were made row by row, with the same conditions and treatment for each row. An experiment used eight ports to measure the temperature of each cell, the remaining two more ports for voltage and power of the PV module. The experiment started from row A with I = 1000 W/m 2 . For measurement stability and accuracy, each endpoint of the T-thermocouple was given a speck of wax and affixed to the measurement point, then covered with a thin transparent tape. First, turn on the simulator. Then, connected the circuit for PV-On. After 30-40 minutes, the system reached the steady-state. With 1-minute intervals, measuring 3 data were taken for stability. Then, the circuit was cut off for PV-Off without turning off the simulator lights and left for about 10 minutes before repeating the same measurement. The same treatment and conditions repeated the experiments for rows B, C, D during PV-On and PV-Off for =900; 800; 700 W/m 2 . Table 2 shows the summaries of measurement and data collections.
where;  ,  and  are the mean, the constant number, and the standard deviation of the PV cell temperatures distribution, respectively, while subscript n is cells 1 to 32. The NPDF can be proceeded using the Excel syntax function: NORMDIST (x, mean, standard_dev, false) [39].
The electrical efficiency as the dependent of the PV temperature is expressed in [3], [4]: where; is the efficiency of the PV module (STC). For every 1 o C increase of at STC as in (2), then e  will decrease by 0.0045. It is due to increased recombination losses of PV cells [29]. Practically, the electrical efficiency is also given [40] [32]. Joule heating as internal heating ℎ [W] linearly dependent on the internal series resistance [Ω], but dependence quadratically on the current-induced [29]; ℎ = 2 (4) Figure 3 shows the Joule heating conduction model from layer to layer. For simplification, assume; a). The system was in a steady-state with heat transfer only affected by Joule heating [41]. b). Silicon layer as a source of Joule heating [32], c). No Joule heating absorbed by the frame due to silicon packing, d). No loss by convection for Joule heating, e). PV layer temperature was the same for each point. As shown in Figure 3 where; and are the mass [g] and specific heat [J/g. o C] of the individual layer. The subscript gl, eva, si, tpt are the glass, eva (ethylene vinyl acetate), silicon, and tedlar/polyester/tedlar, respectively, as shown in Table 3. Then, [ o C] is the temperature difference between PV-On and PV-Off. From (5) and Figure 3, Joule heating ih Q can be formulated as (6) Figure 3 (b).    Figure 4 demonstrates the PV surface temperature and electrical efficiency from starting to reach a steady-state. As shown, the room temperature was relatively stable with an average of 25.3 o C. Each irradiance had a different increased, where an increase in gave a faster rise. The fastest rise occurred in the collection-state (0-15 minutes) when the mass begins to collect heat, then enters the transitionstate (15-30 minutes) starting to slow down and eventually flattens out into a steady-state (after 30 minutes). The effect of increasing causing a decrease in (2). In the collection-state, decreased faster with higher , due to higher . After reaching a steady-state, has tended to be stable. Figure 5 shows the bell-shaped curves normal distribution of during steady-state for PV-On and PV-Off. The curves are constructed based on each cell temperature with fixed irradiance I in (1), Figures 5(a) to 5(d) represent =1000, 900, 800, 700 W/m 2 , respectively. As shown in Figures 5(a) to 5(d), the mean increased with increasing . The graphs show that the difference in the temperature distribution of each cell decreased with decreasing . As shown, the distribution got closer to the mean temperature. The normal distribution curve will be higher. However, the difference between for PV-On and PV-Off diminished as decreased. 1125 Figure 6 shows the thermal and electrical performance during steady-state. The relationship between PV surface temperature and irradiance I under PV-On and PV-Off conditions is given in Figure 6 (a). As shown, the increased with increasing I or vice versa. The difference between for PV-On and PV-Off was greater with increasing irradiance, and close to zero for ≈620 W/m 2 . Figure 6 (b) shows the relationship between electrical efficiency for PV-On with PV module temperature . As shown, the decreased with increasing , or vice versa. From the graph, the temperature efficiency coefficient =-0.0049/ o C is quite reasonable compared to the previous studies [3], [42], [43].

RESULTS AND DISCUSSION
The complete results for PV surface temperature , standard deviation  , root mean square error ϵ and Joule heating ℎ are summarized in Table 4. As shown, the irradiance decreased so that , , ϵ, ℎ also decreased. Table 5 compares the present and previous results [32], such as thermal resistance and temperature rise due to current (Joule heating) / . The lower thermal resistance in the current result compared to the previous result was probably due to the different PV module construction. However, the temperature rise due to the current / was not much different.  From the results with the condition of PV-On and PV-Off, such as; normal distribution, mean of , , thermal and electrical performance, and so on, three things can be discussed. First, related to the thermal distribution from Figure 5. The reason why the distribution of PV module temperature follows the normal curve is that follows the irradiance uniformity pattern of the simulator [35]. The detailed overlap coordinate position between halogen light sources and the PV module has shown in Figure 2. There was a slight ≤0.3 °C of the temperature difference between PV-On and PV-Off. The small may be caused by the small generated by the small . For =1000 W/m 2 , the difference in the middle and at the edge was 2 °C. The temperature rise due to the current / was 0.53 K/A. Those are close to the glass to back sheet (GB) module [32]. Implicitly, it might be due to irradiance as well as Joule heating [9], [10].
Second, related to the thermal and electrical performance of the PV module as shown in Figure 6. The temperature uniformity of PV cells is one of the main factors affecting electrical efficiency. With a more uniform temperature distribution, the electrical efficiency will be higher (2). The output power will be even greater. Conversely, the PV module temperature increases, the power output will decrease. As a result, the fill factor (FF) decreased, which mean the electrical efficiency of PV also decreases [44].
Third, related to the overall thermal conductivity and thermal resistance . Referring to Figure 3(a), Figure 3(b) at steady-state and constant ambient air temperature , the changes with load variations . With fixed and , when increases, causing to increase, then ℎ also increases. In this case, the Joule heating might slightly increase and also slightly decrease (from glass cover to back sheet) which affect the heat transfer [32]. The difference in operational temperature of each PV cell results in different performance. The PV module accuracy decreases from low-temperature toward the hightemperature range [45].
Finally, the effect of Joule heating has been proved and estimated, with the results positively correlated to the irradiances increase from 700-1000 W/m 2 . For more accurate results, further experiments use more precise and sophisticated instrumentation. This study tries to estimate the effect of Joule heating in a PV module as a reference analysis for PV and PVT performances. The current study contributes to improving the procedure of predicting PV module temperature by considering the Joule heating. In practical application, Joule heating optimises the electrical efficiency of PV modules. Joule heating also increases the thermal and electrical performance of the PVT system as additional heat [9], [10], [15]. By involving the temperature distribution of each PV cell, the performance prediction and calculation of PV or PVT module temperature will be more accurate. For future research, the performance of a large PV or PVT system should consider Joule heating as a complement by improving the performance modelling tools, system design and development [46]- [48].

CONCLUSION
The existence of Joule heating has been investigated indoors by comparing the PV surface temperature of each cell with the higher irradiances of 700-1000 W/m 2 during PV-On and PV-Off in steady-state. The PV module temperature distribution follows the curve as the irradiation uniformity pattern of the solar simulator with a slight ≤0.3 °C difference between PV-On and PV-Off. Joule heating slightly increased the PV module temperature of 0.53 °C/A, which is proportional to the irradiances. Joule heating has increased almost seven times from 2.65 W at 700 W/m 2 to 18.07 W at 1000 W/m 2 . Joule heating might slightly increase the overall thermal conductivity and also slightly decrease the thermal resistance. Joule heating affects heat transfer. For more accurate results, further experiments use more precise and sophisticated instrumentation. This research may improve the procedure in predicting the PV module temperature by considering the Joule heating during the PV-On and also PVT-mode. Joule heating increases the electrical efficiency of the PV module and the thermal efficiency of the PVT collector. For future research, consider Joule heating in the thermal and electrical performance of a large PV module or PVT collector by improving the modelling and control systems.