Photovoltaic modules evaluation and dry-season energy yield prediction model for NEM in Malaysia

This study analyzes the performance of two PV modules, amorphous silicon (a-Si) and crystalline silicon (c-Si) and predicts energy yield, which can be seen as facilitation to achieve the target of 35% reduction of greenhouse gases emission by 2030. Malaysia Energy Commission recommends crystalline PV modules for net energy metering (NEM), but the climate regime is a concern for output power and efficiency. Based on rainfall and irradiance data, this study aims to categorize the climate of peninsular Malaysia into rainy and dry seasons; and then the performance of the two modules are evaluated under the dry season. A new mathematical model is developed to predict energy yield and the results are validated through experimental and systematic error analysis. The parameters are collected using a self-developed ZigBeePRO-based wireless system with the rate of 3 samples/min over a period of five days. The results unveil that efficiency is inversely proportional to the irradiance due to negative temperature coefficient for crystalline modules. For this phenomenon, efficiency of c-Si (9.8%) is found always higher than a-Si (3.5%). However, a-Si shows better shadow tolerance compared to c-Si, observed from a lesser decrease rate in efficiency of the former with the increase in irradiance. Due to better spectrum response and temperature coefficient, a-Si shows greater performance on output power efficiency (OPE), performance ratio (PR), and yield factor. From the regression analysis, it is found that the coefficient of determination (R2) is between 0.7179 and 0.9611. The energy from the proposed model indicates that a-Si yields 15.07% higher kWh than c-Si when luminance for recorded days is 70% medium and 30% high. This study is important to determine the highest percentage of energy yield and to get faster NEM payback period, where as of now, there is no such model to indicate seasonal energy yield in Malaysia.


Introduction
To lessen the effect on human life and emancipate environment from crippling by exhaling carbon and other greenhouse gases, solar energy is one of the major alternative energy harvesting systems for generating electricity [1,2]. Malaysia is one of the tropical countries comprising of two regions; Peninsular West and East Malaysia with tremendous solar potential (22-24 and 14-24 MJ/m 2 /day respectively for generating electricity [3]. This could meet its projected electricity peak-demand of 23.099 GW in 2019 which is reflecting 39.47% higher than the peak-demand in 2013 [4]. However, there are short and long term climate challenges in Peninsular West Malaysia that pose threat to electricity generation from solar [5]. Short term effects are intermittent cloud and supply disruption where long term effects are high ambient temperature, humidity, and Southeast Asian haze pollution, and extreme rainfall [6,7]. In the 10 th Malaysia plan, crystalline type PV modules were widely used due to their attractive efficiencies and it is promoted intensively in the 11 th plan (2016-2020) through NEM implementation [8]. The efficiencies of the PV modules are specified by the manufacturer in standard test condition (STC) defined as 1000 W m 2 incident irradiance, 25˚C module temperature, and 1.5 air mass. However, PV module efficiency in STC is not applicable for Malaysia climate condition since 33˚C ambient temperature can significantly affect the open circuit voltage by À 104 mV � C of the PV [9,10]. This can reduce 0.15% of FF and 0.4 * 0.5% of maximum output power, for every 1˚C increase in module temperature [11].
The performance of different PV modules varies from STC measurement and it depends on geographical position and climatic condition. Based on Malaysia's real climate variation, there should be an analysis on performance of Malaysian Energy Commission recommended PV modules and its energy yield modeling for the net energy metering (NEM, previously called FiT). Seasonal based performance and energy yield model of the recommended PV modules due to climate regime in Malaysia are still intangible. In this study, we have evaluated the electrical performance of the two PV modules, namely c-Si and a-Si for the case of peninsular Malaysia during the dry season. The performance parameters are module efficiency, output power efficiency (OPE), performance ratio (PR), fill factor (FF), energy yield, and yield factor. From the evaluation, we have developed a model which predicts the dry season's energy yield of the modules. The outcome of the research can be seen as a support of the 11 th Malaysia Plan (2016-20) development -accelerate renewable energy capacity in NEM as well as achieve target of 35% reduction of greenhouse gas emissions by 2030. The novelty of this study is that we have conducted regression analysis on a range of environmental and electrical parameters to investigate their degree of relationship under the dry season, while predicting the two modules' energy-yield as a part of payback investment in NEM.
To rev-up 20% green energy by 2025, Malaysia Energy Commission has taken many initiatives and policies through establishing large scale solar generations [12]. Some of them are, namely 197 MW Quantum solar park and 65 MW Jasin solar plant. However, Malaysia is blessed with 62.3% of tropical forests containing rich flora of animal species [13]. The alteration of it by large solar plants would lead to the disturbance of the natural ecosystem. This would alter forests topology, crop yields, water supplies which might eventually lead to famine. Many plants and animal species would be threatened, and some would likely become extinct, for instance, Sumatran rhinoceros is one of the extreme rare species in Malaysia. Therefore, it would be irrational to alter the forest topology by the large solar generations.
For this mutual exclusive challenge in Malaysia perspective, one of the best alternatives could be the roof-top photovoltaic (PV) system that is also supported by the Malaysian government. The NEM has been rolled-out in Malaysia since December 2011 which obliges the distribution licensee in Peninsular West Malaysia, Tenaga Nasional Berhad to purchase from the approved applicants, the electricity produced from indigenous renewable resources at a fixed price and duration. Due to the encouragement of the Malaysian Government on NEM, recent trend shows increased number of total NEM generation, from 31.6 to 362.2 MW between 2012 and 2017 [2,12].
Considering the outdoor real weather condition, many researchers have conducted experiment to scrutinize the actual performance of different types of PV modules. The outcomes of the PV modules at different regions including Malaysia have been published in the literature, as shown in the synopsis in Table 1. In view of all that has been mentioned in the peerreviewed literature, there is no study on seasonal categorization from meteorological data analysis and energy yield model for the NEM payback in Malaysia. Previous studies in Malaysia are limited to performance analysis with seasonal categorization, regression analysis, energy modeling, and validation. Most of the researches conducted in Malaysia consider the climate as 'tropical' without any categorization. The data collected on specific days depict the performance of the PV based on that particular weather. Due to that, two researchers found different result in terms of module efficiency, such as c-Si and poly crystalline are found to be highest module by [15] and [16] respectively. A multiple regression model was predicted for output power by [7], however the key environmental parameter was the dust thickness on the PV surface due to the Southeast Asian haze in 2013. Some researchers have analyzed the performance of the modules for tracking system, finding optimum tilt angle, and cell design under desert climate [26], but these are not directly related to our NEM study. Researchers from other countries, such as Pakistan [19,21], Colombia [22], Australia [14], Southeast UK [18], Doha [17] etc. also conducted similar analysis of the different modules. In these studies, performance is also measured for their distinct environmental parameters, inter row spacing, and dust on the surface of the module.
As part of both the environmental and electrical data collection, most of the researchers have considered data logging methods, such as environmental sensors or pyranometer integration to computer via wired connection and digital multimeter or solar simulator [15,16,18,19,27]. However, few effective methods, such as real-time digital simulator-based novel system [28], high-speed four-channel digital oscilloscope [29], Façade technology [24] and automated measurement system [30] were considered by some researchers for performance test and analysing the PV.
In our study, electrical and environmental parameters are recorded using solar analyser and self-developed ZigBeePRO-based smart wireless communication system respectively. Prior to implement our system, a mathematical model is developed to ensure all the environmental data to be accommodated in to a 2GB memory for at least one experimental day. The latest ZigBeePRO with Waspmote microcontroller and smart metering board used in this study is convenient for sensor integration, longer coverage support, low power consumption, large number of child node integration, and better data encryption over Wi-Fi [2]. ZigBeePRO is recommended in this research as a wireless sensor network because it offers additional features over the other wireless transmission protocols as well as ZigBee. Commercially available ZigBeePRO range can go up to 7km, line of sight ( [31]), much higher than other wireless transmission protocols, such as WiFi (100m or more), Bluetooth (1-100m), and ZigBee (10-100m). It is also superior to other networks in terms of guaranteed data transmission capability and automatic detection of the addition or absence of nodes, without any manual intervention. In addition, ZigBeePRO protocol supports more than 65000 nodes with extended battery life compared to either WiFi (>1000 nodes) or Bluetooth (7 nodes). An extensive discussion on the most influential feature of ZigBeePRO for distributed solar energy monitoring as applied to the field of smart grid can be found in these authors' works [2,32,33].
The contribution of this research can be summarized in three folds:  (40) • a-Si produces 15% (summer) and 8% (winter) more energy compared with c-Si. • CIS module is higher energy producer (between 9-13%) than c-Si due to its higher temperature coefficient.
• Performance analysis of 6 types of modules • Average ambient temperature is 16. • Analysis of 63 years meteorological rainfall data in peninsular Malaysia where the dry season is chosen for conducting the performance analysis of the PV modules (c-Si and a-Si). The effectiveness of environmental data collection is ensured by a self-developed ZigBeePRObased smart wireless communication system in an aim of obtaining the data at higher frequency of 3 samples/minute.
• The prediction of the PV modules' performance in terms of energy yield in kWh, that is, the deviation from the STC stated by the modules' manufacturers, is modelled in a manner analogous to the NEM system for the dry climate condition.
• The performance of PV modules is modeled by regression relationship between the environmental and electrical parameters with stochastic analysis. The relationship is evaluated by determining significant statistical indicators, namely, coefficient of correlation (r), coefficient of determination (R 2 ), mean bias error (MBE), root mean square error (RMSE), mean absolute percentage error (MAPE), and symmetric mean absolute percentage error (SMAPE).
The organization of this paper is as follows. Section 1 presents the analysis of meteorological data for categorizing peninsular west Malaysia climate. It also highlights vernal and solstice factors for positioning solar module. Then in section 2, hardware setup for electrical parameters using the ZigBeePRO-based smart wireless communication system is explained. Section 3 shows the a-Si and c-Si modules' performance evaluation in three different perspectives. Then regression and statistical analysis on the modules' performance and its validation have been included in this section. This section also explains the estimation model for energy yield in NEM with validation. Finally, section 4 concludes the overall outcome of this research.

Overview of Peninsular Malaysia climate
In Peninsular Malaysia, the average day-time ambient temperature is 33˚C, humidity of 80-90% other than dry season, average cloud-covered factor of 6.5 [1], and average 135.285-366.985 mm rainfall [34]. According to the Malaysian Meteorological department data between 1951 and 2018, three main types of seasonal variation are observed in peninsular west Malaysia: maximum rainfall, secondary maximum rainfall, and the dry season (shown in Fig  1) [35,36]. In this peninsular, maximum rainfall occurs in the months of October, November, December, and January; however, southwest region of the peninsular has recorded extreme rainfall during October and November (e.g., the heaviest rainfall 9-11 December 2004, 600 mm day [34,37,38]). The secondary maximum rainfall is recorded in April and May. The trend of rainfall since 1951 in the southwest peninsular is linearly increasing by year, rainfall (mm) = 7.0458 × year + 2036.1 [35]. According to the standardized precipitation index or SPI, the prolonged dry months are June and July where the least rainfall is observed, for example, total rainfall received in June 2015 is less than 100 mm. Another category is indefinite rainfall within 200-300 mm in the months of March, August, and September. The highest solar radiation is achieved within the period of February-March [35]. Furthermore, peninsular Malaysia sky is mostly cloudy, 80% of days in a year, thus plummets substantial solar irradiance [1]. However, the sky is generally clearer in the mornings and cloudy in the afternoons. During the rainy seasons, rainfalls are experienced between 14:45 and 18:00, averagely. This means, the harvested solar irradiance during afternoon time should be significantly less than the irradiance during morning time, with the same angular position of the sun. On the other hand, no or fewer rainfall days are generally observed during the dry season. Based on observations from the meteorological data, each seasonal category is consisting of similar indices, such as solar irradiance, rain/no-rain, cloud factor, and humid level. Our observation is also supported by all the previous researchers where they state the climate of Malaysia as predictable weather, hot and humid all year round, and no large variation in temperature [12,15]. A research from the analysis of 10 years meteorological data shows that average solar irradiance of June and July is approximately same. It also describes very mere difference in ambient temperature in June (28˚C) and July (27.7˚C) [39]. Similarly, another research describes Malaysia as 'mere distinctive season country and its climate is hot and humid' [40]. Due to the similar indices, we considered 5 days' of dry climate data to estimate seasonal-based energy yield for peninsular Malaysia.
One of the key points of harvesting maximum solar irradiance is when the panels are perpendicular to the sun rays. For the best performance, solar tracker can enhance the PV efficiency by a factor of 40-48% [41]. However, installation of solar tracker in NEM system is neither cost effective nor feasible for small scale capacity. Another key point is the position of the sun that varies throughout the year. It makes an angle of up to 23.5˚with respect to the equator towards the north in one half of the year, whereas this angle is tilted towards the south in the other half (described in Fig 2) [42]. Therefore, for one sided PV panel installation on the roof top under NEM system, it is not possible for the panels to achieve the maximum output in a year. To overcome this problem, both northern and southern sided-panel can be installed on the roof top in order to harvest maximum solar irradiance.

Hardware setup for electrical parameter acquisition
Efficiency, OPE, PR, FF, and yield factor are essential key indices to evaluate the performance of a PV module. These key indices can be obtained from the model equations where the variables are electrical and environmental parameters. The electrical parameters (V max , V oc , I max , I sc ) are measured using solar analyser (Prova 200) and environmental parameters (solar irradiance, module and ambient temperature, humidity, and wind speed) are acquired by self-developed ZigBeePRO-based smart wireless communication system. The required model equations are explained as follows.
The other parameter indices, such as OPE and PR are obtained by Eqs (2) and (3) respectively.
FF can be determined by considering maximum power, short circuit current, and open circuit voltage of a PV module, shown in Eq (4).
Yield factor can be determined by Eq 5.
where P a is the measured actual power (W); P max,STC is the maximum power in STC (W); I a is the measured actual current (A); I max is the maximum current (A); V a is the measured actual voltage (V); V max is the maximum voltage (V); V oc is the open circuit voltage (V); I sc is the short circuit current (A); Z STC is the solar irradiance in STC ( W m 2 ); Z a is the measured actual solar irradiance ( W m 2 ); and A M is the area of the module (m 2 ). We have considered two popular commercially available PV modules (c-Si and a-Si) where the specification in STC is given in Table 2. The cost of PV modules is region-specific and varies greatly depending on the market; however, it has been declined gradually in recent years. For the world market, the up-to-date PV module price is US$0.736/Wp [44]. In this study, the cost of the PV modules is US$3.5/W (c-Si) and US$1.75/W (a-Si) according to the supplier price quotation. During the dry months (Jun-Jul), no rain was observed at Klang valley region, southwest peninsular Malaysia where experimental data was collected. The days considered for the experiment were 12 th , 15 th , 16 th , 19 th , and 20 th of July corresponding to day1 to day5, respectively. Both modules were installed on fixed roof closed-rack at tilt angle of 15˚(In Malaysia, 15o ptimum tilt angle is found by [45]) without considering any sun tracker. Fig 3 shows the outdoor experimental setup located at UPM solar farm, coordinate 2.945˚North and 101.75E ast.
The ZigBeePRO-based smart wireless communication system is illustrated in Fig 4. The technique has been adopted from the previous works of these authors [2,32,46]. Here in brief, temperature, humidity, and luminosity sensors were interfaced with smart metering and microcontroller board (combining embedded board) with ZigBeePRO communication radio. The temperature sensor MCP9700A is connected to pin6 of the smart metering board for reading analog temperature of the PV module. The other three parameters, such as ambient temperature, humidity, and solar irradiance are measured using identical temperature sensor (MCP9700A), humidity sensor (808H5V5), and luminosity sensor (TSL2561). The sensors specifications are shown in Table 3, Appendix. For simplicity, an approximate conversion of 0:0079 W m 2 per Lux is considered. All the sensors are accommodated within the smart metering board which is interfaced with Waspmote microcontroller board. All the sensors are manufacturer-calibrated. Additionally, a 2 GB micro SD card for data recording and a ZigBeePRO radio are interfaced to the embedded board for transferring data to the control centre through the ZigBeePRO gateway.
The data collection was conducted through remote data monitoring system saving environmental parameters to the SD card and simultaneously sending the data to the control centre using ZigBeePRO communication in every 20 second. The 20 seconds interval ensures that all the data is accommodated for at least one experimental day into the 2 GB SD card by the mathematical relationship in Eq (6).
Here, N is the total number of packet during 9 hours experimental time of a day (without any delay). Based on the ZigBeePRO specification [31], the parameters of Eq (6) can be set: packet size = 1280 bits with header and checksum  S a = 1.83 GB = 1.83 × 10 9 Bytes = 10.83 × 8 × 10 9 bits where S a is the actual SD card size. data rate = 15 kbps = 15000 bit/s (manufacturer provided which is practically achievable). This yield (N × packetsize) < S a when no delay is considered. Therefore, 20 seconds interval is sufficient for accommodating all the data into the 2 GB SD card. Also, the received data (i.e., SD card saved data) is monitored from the control centre through a LabVIEW system. This ensures more reliability and capability for detecting any power failure or other unusual faults of the remote ZigBeePRO-based node. For instance, battery charging status and remaining SD card size are sent with the packet to the control centre. After completion of the data collection, Python program is used for further analysis.

Result analysis
Stochastic analysis is employed for analysing the result considering 15min averaged-data of both environmental and electrical parameters between 8:30-17:30, which are then evaluated for obtaining linear models. The accuracy and pertinence of the models are determined considering few common but significant statistical indicators, such as r, R 2 , MBE, RMSE, MAPE, and SMAPE. The dimensionless r-value has determined the strength of linear relation between environmental and electrical parameters or two environmental parameters in the range of ±1. Another statistical term, R 2 has defined the predictive power of the model in connection with the independent parameter. The error terms compute the dispersion of the model's validation results. It is observed that MAPE may cause distortion to the error rate due to the presence of zero or nearly zero data. In such condition, SMAPE performs better measurement than MAPE. The computational formulas of these statistical indicators are shown in Eqs (14)- (16) and (19), Appendix.

Solar irradiance and temperature
Based on individual day data analysis, the lowest irradiance was attained on day1; however, last four hours of the afternoon session of day3 gained less than 200 W m 2 (the least gain among the five days). Therefore, day1 and day3 can be considered as medium luminance days. Then, average maximum solar irradiance was noticed on day2 (560 W m 2 ), day4 (672:94 W m 2 ), and day5 (663:11 W m 2 ); so, these three days can be considered as high luminance days. Hourly average (mean) and median solar irradiance data of the five individual days are statistically extracted, analysed and plotted as box-plot in Fig 5. Statistical analysis of the five days has shown that variation of solar irradiance at 8:30 and 17:30 is small. However, the variation is high within this period. The highest variation occurred at 13:30 which is ideally expected to harvest the maximum solar irradiance; however, it did not happen due to the cloudy nature of the days. Hence, considering the statistical hourly median and mean values, the approximate hourly variations of irradiation within the days are shown in the subsequent sections. Fig 6 shows five days relative humidity with solar irradiance from 8:30 to 17:30. It can be observed that solar irradiance is inversely proportional to relative humidity. From the recorded data, the calculated average peak sun-hour per day is 4.69 hours which corresponds to 16.88 MJ direct solar radiation harvested on average per day. Moreover, the optimum formula for humidity can be obtained in Eq (7). The equation is based on the regression analysis in Fig 6. H avg ¼ À 0:04 � Z avg þ 69:59 Where, H avg is the average humidity, and Z avg is the measured solar irradiance. The slope, -0.04 indicates negative correlation between the solar irradiation and humidity. Further by extracting dZ avg dH avg from Eq (7), the approximate mathematical model can also be obtained as in Eq (8).
Eq (8) states that for every 1% increase in humidity, the solar irradiance drops by 25 W m 2 (the least gain among the five days).
For silicon PV modules, the efficiency is logarithmically dependent on irradiance. Due to that the efficiency was observed almost constant between 200-1000 W m 2 . Also, temperature efficiency coefficient is negative, thus efficiency of the both modules goes down with higher irradiance in this outdoor experiment . Fig 7(a)-7(d) shows the effects of module temperature (T M ) and solar irradiance (Z) on the efficiency (η) of the a-Si and c-Si modules. It is observed between 11:30 to 13:30 of the day, module efficiency is inversely proportional to the solar irradiance. During this time, hourly average efficiency of c-Si and a-Si are 9.8% and 3.5% respectively at 200-800 W m 2 solar irradiance. c-Si is renowned for higher efficiency and it showed the highest efficiency on both medium and high luminous days compared to the a-Si module. Fig 8 shows five days' average ambient and module temperature. The module temperature of c-Si is about 2.26% higher than a-Si until 11:30 but slightly different (a-Si is 8.1% higher) in the afternoon. However, overall pattern of the module temperature are the same which also reported by [19]. On average, both modules' temperature remained below 58˚C (maximum temperature of a-Si and c-Si is 62.9˚C and 59.9˚C respectively). Comparatively, lower module temperature trend was observed after 13:00 due to continuous 3:88 m s average wind speed (maximum 5:83 m s and minimum 0:79 m s ) from east to west direction that cools modules' heat. The five days' ambient temperature was between 28.9-34.9˚C.
The approximate trend lines of solar irradiance and OPE with corresponding module temperature are shown in Fig 9(a) and 9(b) respectively. Results show that there is a positive correlation among modules temperature, solar irradiance, and OPE. Also, the slope of c-Si is more fitted than a-Si. However, OPE of a-Si is better than c-Si when both modules' temperature is between 30-43˚C and solar irradiance is below 500 W m 2 ). In contrast, solar irradiance above 500 W m 2 and module temperature of 45-53˚C, comparatively c-Si performs better. Similar result was found by two researchers on a-Si performance below 400 W m 2 [19] and 600 W m 2 [16]. With this, Fig 10 illustrates the statistical analysis of the five days' efficiencies of a-Si and c-Si modules. A positive correlation is found between the two modules' temperature and the efficiency. However, temperature dependence on the efficiency of a-Si (Fig 10(a)) is not as significant as of c-Si (Fig 10(b)). Fig 10(c) shows that the efficiency of c-Si is almost 50% higher than a-Si at below 48˚C module temperature. The rate drops to 36.05% above 48˚C.

Module efficiency
The comparison between the effiency of a-Si and c-Si (hourly average) on individual days and five-day average corresponding to daytime is shown in Fig 11. During the high luminance  days (day4 and day5), similar trend of efficiency is observed for both modules. The least efficiency was recorded on day3 (medium luminance day); however, a-Si achieved higher efficiency (38.17%) than c-Si (29.92%) as in the manufacturer-rated specification. In Malaysia climate condition, a-Si achieve better efficiency at low irradiance, supported by [15].
Based on the five-day average data, Fig 12 shows that the module efficiency is generally inversely proportional to the solar irradiance. This result is also supported by [19,47]. The changing rate of solar irradiance shown in Fig 12 explains that the fluctuation of a-Si efficiency is lesser than c-Si efficiency. This is because, a-Si has better shadow tolerance and is less affected by the direction of sunlight. To this extent, 1 W m 2 increase in solar irradiance may cause about 0.013% and 0.004% decrease in efficiencies of c-Si and a-Si respectively.

Output Power Efficiency (OPE) and Performance Ratio (PR)
Even though the relationship between OPE and solar irradiance with respect to R 2 value is not strong, the R 2 value is more significant than a-Si (Fig 13). This is because of the inconsistent distribution of data points for both modules on medium luminance days (day1 and day3). In contrast, PR of a-Si is better than that of c-Si and both modules' PR are inversely proportional to the solar irradiance (Fig 14). The PR is decreased by 14.68% (c-Si) and 24.8% (a-Si) between 8:30-12:30 for 298% increase in solar irradiance. This trend is also supported by [19] where the PR was found to be decreased by 5.68% (c-Si) and 22.6% (a-Si) for 175% increase in solar irradiance. The average PR for c-Si and a-Si are 1.02 and 1.21 respectively indicating a-Si for better light absorbing capability during cloudy condition.

PLOS ONE
Dry-season energy yield prediction model for NEM Table 4 shows the regression analysis for the models obtained from the plotted figures. The analysis is also validated by calculating statistical and systematic error terms. The high value of r (0.8168-0.9803) implies that there is a significant relationship between the considered parameters and environmental factor. The accuracy of the models can be further demonstrated by the R 2 value outstandingly in Fig 10 compared with the models from Figs 6 and 9(a-Si), which are moderate. Least value of MBE is desirable and it is achieved with acceptable estimation for all the models. Further analysis shows similar observations considering the other error terms, such as RMSE, MAPE, and SMAPE. Besides these indicators, the accuracy of the data can be considered satisfactory based on the calculated t-statistic (t s ) which also validate the models' estimation in this analysis. For the validation, critical t-statistic (t c ) is determined from the standard statistical table considering (b − 1) degree of freedom at 5% significance level with two-tailed test. Here, b is the number of collected data points at every 15 minutes interval from 08:30 to 17:30; therefore, b = (total number of hours × 4 + 1) per day. This b is determined to be 37 for all the models. To ensure the models' estimation with statistical significance, the notation ft s 2 RjÀ t c ⩽ t s ⩽ t c g has to be true. According to the standard statistical table, the T c value can be obtained based on b = 37 which confirms the models' validation.

Statistical analysis
A thorough study from the validation results shows that a-Si or c-Si module efficiency has strong relationship with the module temperature (Fig 10). On the other hand, OPE has strong  relationship with the modules temperature (Fig 9). The relation between humidity and solar irradiance is not strong (Fig 6), which means that other factors, such as degree of cloud cover, ambient temperature, atmospheric dust, and water vapour density weaken the relationship. The validation results are evident for the similar climate characteristic during dry season in Malaysia.
In Table 5, a set of PV measurement parameters are considered for comparing STC, experimental results and other researchers' outcome. We have observed that the environmental parameter, such as average ambient temperature is similar to the research [15], which leads to approximately similar outcome in FF, module efficiency, PR, and yield factor; however, OPE is varied. The result is also closely matched with that of [19] in terms of FF, OPE, PR, and yield factor. Since both researches did not have peak sun-hour data, we obtained their yield factor by considering similar peak sun-hour of this study, 4.69 h day . The yield factors of this study for c-Si and a-Si are found to be 2.33 and 2.73 kWh kWp respectively, which are also within 2.6 ±0.15 kWh kWp , referred by [48]. In case of efficiency, the researcher, found higher outcome than this study due to variance in ambient temperature [19]. The average maximum powers for a-Si and c-Si achieved in this study are 1.63 W and 17.45 W respectively and are found to be 4.12% (a-Si) and 12.75% (c-Si) less than STC rated values. In comparison with the average module efficiency, c-Si and a-Si attained 49.6% and 59.75% respectively of their STC rated-value. Moreover, a-Si shows better performance over c-Si in the case of the other three parameters, OPE PR, and yield factor.

Estimation of energy yield for NEM
Based on the experimental analysis on medium and high luminance days, the total energy yield in kWh during dry season can be estimated. For the estimation, a 1 kW capacity of c-Si and a-Si PV modules are assumed for modeling purpose in accordance with Malaysia's NEM application. The modeling equation for estimating the total energy yield, E in the unit of kWh, during dry season is derived as in Eq (9). where, and Here, α and β are probability of medium and high luminance days respectively. Therefore, α + β = 1 and 0 � (α, β)�1. In Eqs (10) and (11), P i and P j denote total output power in αD and βD days respectively. Sh i and Sh j are sun-hour, and D denotes the total number of days in dry season.
To validate the estimated model, we have considered other models from [49] and [50] shown in Eqs (12) and (13) respectively.
In Eqs (12) and (13), the value of temperature coefficient, � 1 is taken from c-Si and a-Si module datasheet specified as 0.0045˚C −1 and 0.0020˚C −1 respectively. � 2 is also considered 0.0044˚C −1 (c-Si) and 0.0026˚C −1 (a-Si) by [50]. The module area (A M ) for 1 kW capacity is calculated as 7.765 m 2 for c-Si and 24.41 m 2 for a-Si. Finally, the energy yields are shown in Table 6. The data is normalized for comparison based on the experimental output power in kWh when the capacities of both modules are 1 kW and sizes are 7.765 m 2 (c-Si) and 24.41 m 2 (a-Si).
Statistically, if 70% and 30% of days during dry season are considered as medium and high luminance day respectively, the total energy output of a-Si (125.23 kWh) is higher than that of c-Si (108.85 kWh) based on our estimation model, Eq (9). Similar energy output can be noticed for the models Eqs (12) and (13). The percentage difference between our model (Eq (9)) and that of Eq (12) is 6.55% (c-Si) and 17.01% (a-Si) respectively. On the other hand, the difference is 6.19% (c-Si) and 18.18% (a-Si) considering model Eq (13). This insignificant difference validates our model, deemed appropriate for the NEM.
Based on the real data and model analysis, it is observed that total energy output of a-Si is 15.07% higher than c-Si, which is optimum between these recommended two modules during dry season in Malaysia.

Conclusion
In this study, performance evaluation of a-Si and c-Si PV modules and their dry-season energy yield prediction model are developed for NEM in Malaysia. The evidence from this study confirms that 4.69 h of average peak sun-hour, minimum humidity value of 25.7%, and maximum solar irradiance of 1100 W m 2 are achievable at Klang valley of peninsular Malaysia during the dry season. However, the environmental data monitored by self-developed wireless smart system shows that 38:9 W m 2 solar irradiance can be dropped with 1% increase in humidity. Module temperatures of both the modules do not exceed 58˚C due to the blowing wind at 3:88 m s , on average. From the evaluation of electrical parameters of the modules, it is observed that the average efficiencies attained about 49.6% (c-Si) and 59.75% (a-Si) of the manufacturer rated efficiency. This attainment has occurred due to module temperature significant to c-Si which causes 13.95% less efficient when the module temperature exceeded 48˚C. Also, a-Si has achieved better OPE than c-Si at < 500 W m 2 solar irradiance and between 30-43˚C module temperature, whereas opposite performance is noticed above 500 W m 2 solar irradiance. Due to better light absorbing capability during cloudy condition, the average PR of a-Si (1.21) is higher than c-Si (1.02). The PR is found to be inversely proportional to the solar irradiance and thus, decreased by 14.68% (c-Si) and 24.8% (a-Si) with 298% increase in solar irradiance. In addition, the yield factor of a-Si (2.73 kWh kWp ) is found to be higher than c-Si (2.33 kWh kWp ). The regression analysis validates most of the obtained models based on electrical and environmental parameters by confirming the statistical and systematic error terms. The strongest (module efficiency versus module temperature) and the weakest (OPE versus module temperature)  (12) and (13) (12) and (13). This comparison analysis validates our estimation model. relations are determined by calculating r = 0.9803, R 2 = 0.9611 and r = 0.8168, R 2 = 0.6672 from the respective models. Based on the results of the evaluation, the proposed model estimated total energy yield in kWh during the dry season for the NEM monthly reimbursement. The model projects that if 70% is medium and 30% is high luminance days of the dry season, a-Si produces 15.07% more energy than c-Si. The overall information suggests promoting a-Si module due to its higher energy yield, PR, OPE, yield factor, and cost over c-Si when the size of the module is compromised. Future research should therefore focus on the investigation of better-performed PV module during the secondary maximum and maximum rainfall seasons. Thus, it can determine the total energy yield in kWh of all the seasons in order to come up to a decision about feasibility, right choices of modules, and the fastest payback of NEM investment in Malaysia.

r ð18Þ
where, b is the number of collected data at every 15 minutes interval from 08:30 to 17:30; therefore b = (total hours � 4 + 1) per day. � e i and � a i represent estimated and actual data respectively. While comparing the X with Y axis actual data samples, correlation coefficient (r) is evaluated by using the following expression (19): i¼0 Y i Þ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi b The value of r is −1 � r � + 1 and closest to −1 or + 1 indicates perfect negative or positive fit respectively. The negative (−) or positive (+) sign denotes relationship between X i and Y i such that by increasing X i , Y i decreases or increasing X i , Y i also increases, i.e. r > 0 refers to positive linear relationship between X i and Y i . r < 0 refers to negative linear relationship between X i and Y i . r = 0 refers to weak or no linear relationship between X i and Y i .