# Machine Learning-Based Relative Performance Analysis of Monocrystalline and Polycrystalline Grid-Tied PV Systems

Authors: Asfand Yar; Muhammad Yousaf Arshad; Faran Asghar; Waseem Amjad; Furqan Asghar; Muhammad Imtiaz Hussain; Gwi Hyun Lee; Faisal Mahmood
Journal: International Journal of Photoenergy
 (2022)

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## Abstract

In this research study, the design and performance evaluation of grid-tied photovoltaic systems has been carried out through experimentation, HelioScope simulation, and black-box machine learning methods for data-driven artificial intelligence system performance assessment and validation. The proposed systems are based on 15 kWp of monoperk and polyperk, which are separately installed in the industrial sector of Faisalabad, Pakistan. The experimental evaluation of the installed PV modules was performed from November 2020 to August 2021. The performance of the PV modules was evaluated by determining the annual average daily final yield (If), performance ratio (PR), and capacity factor (CF). The study showed that the annual average of daily final yield, performance ratio, and capacity factor for 15 kW polyperk was estimated to be 61.94 kWh, 84.17%, and 19.12, respectively. The annual average of daily final yield, performance ratio, and capacity factor for 15 kW monoperk was estimated to be 58.32 kWh, 81.42%, and 18.13, respectively. A comparison of final yield is obtained from simulation and real-time systems obtained from polyperk PV and monoperk. A significant mean error exists between the experimentation and simulation results which lie within the range of 1250 to 1470 kWh and 1600 to 1950 kWh, respectively. Substantial differences between both aforementioned results were initially tested and highlighted by statistical values; i.e., the standard error lies in-between 5 and 45% in polyperk crystalline and 5 and 25% in monocrystalline PV grid-connected module. Machine learning logistical regression evaluated that monoperk crystalline grid-connected system, experimental work was found to be more reliable with error difference reduces in off-peak months as compared to corresponding simulation study and vice versa for polyperk crystalline grid-connected system. Model accuracy after training and testing produced resulted up to 99.5% accuracy for either grid-connected experimentation or simulation outcomes with validation.


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## Body

## 1. Introduction

In any country, energy is one of the key factors for the smooth and faster upgradation of the socioeconomic activities, and it has become a universal fact now. One of the major drivers of economic growth is energy as identified by the government of Pakistan. Therefore, Pakistan requires adequate supplies of energy for the generation of healthy economic activities. The country currently is passing through the worst energy crisis in over 70 years. The energy crisis has led to the hindrance of socioeconomic progress below the level of critical sustainability and tolerance of the people. Pakistan has a land area of 881,913 km2 consisting of a population of 211.117 million [1]. In 2019, Pakistan’s electricity generation was recorded to be 87.3 TWh [1]. The energy mix of Pakistan’s energy scenario depicts that thermal energy is the widest energy resource upon which Pakistan has been relying in recent years. To warrant adequate, secure, and cheap energy supply to industries, transportation, domestic needs, and agriculture availing available resources in such a manner that it minimizes its losses should be the main objectives of the energy sector. For the proper growth of renewable energy sectors, they must be given the chance in the present energy mix.A photovoltaic system is not a new phenomenon as a plethora of literature is available on the topic. It has been in practice for the past few decades in our everyday life producing renewable energy, which is not only efficient, but it is carbon emission-free which is beneficial for the environment. Today, our technology has shifted to renewable resources, such as biomass, wind, and solar. In the development of countries, renewable energy plays a contentious role. Nowadays, the resource in trend is solar power. There are various kinds of photovoltaic (PV) power plants that can be integrated with existing power systems. PV energy plants generally use various types of PV engineering such as monocrystalline, polycrystalline, and amorphous silicon. They come as thin-film PV panels using copper indium di-selenide, copper indium gallium selenide, and cadmium telluride.Various studies have evaluated the performance parameters of installed PV power plants in different locations, with the varying climatic condition, such as Europe [2–5], tropical regions [6, 7], Malaysia [8, 9], Oman [10], and Asian countries, India, Korea [11–15], and China [16–22]. It was observed that the performance analysis is affected by system losses, module quality, inverters, shading effect, losses in wiring, array tilt angle, and type of grid connections. The effect of these factors was confirmed by literature where a 190 kWp grid-connected PV power plant in India was evaluated [16]. In another study, it was found that these factors played a crucial role in reducing the annual average daily final yield. The efficiency of the PV module, inverter, and system was found to be 14.9%, 89.2%, and 12.6%, respectively. The capacity factor and performance ratio were found to be 10.1% and 81.5%, respectively [2]. The impact of dust is one of the significant factors which reduces the efficiency of PV modules. As compared to previously mentioned factors, the effect of dust is inferior to the performance of the PV systems [20]. Research about the performance evaluation of PV systems installed in Serbia was carried out to investigate the effects of ambient temperature and compare it with similar studies around the world. The study reports an analysis of 2 kW monocrystalline silicon (mc-Si) PV power plant tied to the grid, which was built on the rooftop in Niš, Republic of Serbia. The values of PR and CF of the reported PV power plants were articulated to be 93.6% and 12.88%, respectively [23]. Performance evaluation of polycrystalline silicon- (p-Si-) based PV systems was carried out at various locations, namely, Singapore, Turkey, and Greece, with installed capacities of 142.5 kWp, 2.73 kWp, and 171.36 kWp, respectively. From these studies, it can be observed that local varying parameters such as CF, PR, and final yield affect the performance of PV systems. PV systems have also been installed to meet the energy demands of local office buildings in Singapore. The first zero-energy office building used a 142.5 kWp p-Si grid-connected system to meet its energy demands by using inverter factors such as efficiency and losses of heat. The first performance evaluation of the PV system was carried out over 18 months, which showed a good overall PR of 81% [24]. A similar study was published where performance analysis of a 2.73 kWp mc-Si PV power station located in the Muglia climatic conditions in Turkey was performed wherein winter thy efficiency of mono PV module is increased. According to a study carried out in Greece, a performance analysis of a fully monitored 171.36 kWp p-Si grid-connected PV system was done on an hourly, daily, and monthly basis [4].The claim regarding the change in the tilt angle of PV modules and the change in efficiency can be supported by a report coming from Italy. This article focused on the influence of climatic conditions on a 960 kWp mc-Si-based PV power plant. The installed systems were divided into two subfields with varying tilt angles and nominal powers (i.e., 606.6 kWp and 353.3 kWp). The results revealed that the performance ratio varied between 79% and 86.5% from March to October 2012 [24]. Another study from Italy (northern), articulated the functioning of two grid-tied PV systems (i.e., 17.94 kWp and 15.9 kWp) with the same factories but possessing varying PV technology, their rated power, and overall efficiency. The performance ratio was observed, over a year, to be 89.1% for the first mc-Si wafer-based PV system and 82.7% for the second mc-Si-based PV system [25].Although PV systems have been around for quite some time but there is no articulated study from this region that evaluates the performance of installed systems according to the region’s environmental conditions, to the best of our knowledge, there has not been a study conducted that takes advantage of machine learning algorithms for the difference in performance evaluation between installed and simulated PV systems. This study has been carried out to evaluate the performance of installed PV systems located in the outskirts of Faisalabad on the same rooftop of an industry. The objectives of this study were to investigate the difference between power obtained from installed PV systems and via simulation software. Further, a machine learning algorithm was applied to analyze the performance of installed systems for cost and timesaving in the future. The PV systems (15 kWp) have been analyzed over a time of seven months. The renewable systems were based on polyperk and monoperk types of PV modules. Moreover, to classify hyperparameter results of categorical division between experimental and simulation results, machine learning-based logistical regression has been introduced. Machine learning algorithm contains the error to a minimum and provides useful insight, corelation, and evaluation with class distinction according to subjective weather and time horizon.


## 2. Designing of Solar Photovoltaic System

The PV systems are located at a latitude of 31.47° N, a longitude of 73.22° E, and an altitude of 186 m above sea level in the outskirts of Faisalabad city in Pakistan (Figure1). The monthly average daily values of solar radiation for the region range from 5.5 to 5.8 kWhm-2. Figure 2(a) displays the aerial view of the installed PV systems. The PV systems are installed on the rooftop of a switchgear manufacturing firm, where the top row is designed with monoperk PV modules, and the lower row is designed with polyperk PV modules as depicted in Figure 2(b). These PV plates are supported by a steel stand having tilt angles of 30°. To mitigate the effects of dust accumulation, it is necessary to regularly clean the plates at least once a week [12].Figure 1
Simulation of installed PV system (15 kWp).Figure 2
Overview of installed PV system (15 kWp): (a) location on map in Faisalabad; (b) real-time overview; (c) string diagram; (d) single line diagram (SLD).
(a)(b)(c)(d)


### 2.1. Types of PV Modules

The capacity of the installed grid-tied PV system is 15 kWp which is composed of two independent monocrystalline and polycrystalline segments. Each segment is installed in a series parallel and has a capacity of 15 kWp. The systems are installed facing south having an optimum monthly tilt angle to enhance their efficiency. In this study, thirty-eight monocrystalline modules (model CS3400WP) and thirty-four polycrystalline modules (model CS3400WP) of similar maximum power output and efficiency ratings are used. Properties of the installed modules are summarized in Table1. There are four mounting structures of galvanized steel frames holding six panels for each type of PV module. The design of the support structure is to keep a variable inclination with the horizontal plane with the reinforced concrete foundation to withstand the weight of modules and maximum wind speeds at the site as shown in Figure 2(b).Table 1
Electrical and mechanical parameters of the installed PV modules.
Electrical parameters of PV modulemc-Sip-SiMaximum power (Pmax)400 Wp440 WpModule efficiency (η)18.11%19.7%Maximum power point voltage (Vmpp)38.7 V40.3 VCurrent at maximum power point (Impp)10.34 A10.92 AOpen-circuit voltage (Voc)47.2 V48.7 VShort circuit current (Isc)10.9 A11.4 AModule temperature at NOCT (TNOCT)42+3°C41+3°CTemp. coefficient of short circuit current (μΙsc)0.05%/°C0.05%/°CTemp. coefficient of open-circuit voltage-0.29%/°C-0.28%/°CTemp. coefficient of maximum power-0.37%/°C-0.36%/°CMechanical properties of PV moduleNumber of cells144144Dimensions of cell2108∗1048∗40 mm2132∗1048∗30 mmOperating temperature-40~85°C-40~85°CWeight (kg)22.422.4The following formulae can be used for calculating parameters related to the designing of a PV system.Equations (1) and (2) can be used to calculate the required numbers of PV panels.
(1)PVMax=Le×IPHAvgηinvTcf,where PVmax is the peak power of PV array (kWp), Le is the electrical load (kWh/day), IP is the peak solar intensity, HAvg is the average available radiation in kWh/m2/d, and TCF is the temperature correction factor (0.4-0.5% °C for crystalline silicon) and the efficiency of inverter.
(2)PVN=PVMaxPm,where Pm is the rated power of the selected panel and PVN is the number of PV panels.
(3)Sizeofinverter=TotalLoad+1+AfIeVA,where Af is the additional further load expansion (20%), Ie is the efficiency of inverter, and VA is the volt-ampere.
(4)PM=VM×IM,where VM is the voltage at maximum power point, IM is the current at maximum power point, and PM is the maximum power.Soiling ratio:(5)SRatiomeasured=PmsoiledmodulePmcleanmodule∙kmismatch,where Pmsolidmodule is the measured maximum power of the solid module, PmCleanmodule is the measured maximum power of the clean module, kmismatch quantifies the disparity in Pm between the clean and the soiled modules, and SRatiomeasured compares the measured maximum power (Pm) of the soiled and the clean module.


### 2.2. Three-Phase Inverters

Since the PV modules are semiconductors in nature, they fundamentally generate direct current (DC). The transmission and distribution systems are designed for AC which is obtained by converting it from DC via inverters and feeds the utility of the electrical grid by synchronized frequency normally around 50 or 60 Hz. The selection of the inverter is based on the maximum output power from each type of PV module array. All inverters are of SolisMax, model Solis-15 K Max; the technical features of the inverters are provided in Table2.Table 2
Electrical datasheet of three-phase inverters.
Input (DC)Max. Dc power (cosθ=1)15 KVMax. input voltage1000 VMPP voltage range/rated input voltage200-800 VMin. input voltage/initial input voltage350 VMax. input current input A/input B18 A+18 AOutput (AC)Rated power (230 V, 50 Hz)15 kWMax. apparent AC power33 kVARated power frequency50/60 HzMax. output current21.7 APower factor at rated power0.8 (min.)Maximum efficiency97.5%General dataWeight30 KGOperating temperature range-26°C~60°CNoise emission (typical)<30 dBASelf-consumption (night)<1 watt (night)TopologyTransformer lessCooling conceptNatural convection


## 2.1. Types of PV Modules

The capacity of the installed grid-tied PV system is 15 kWp which is composed of two independent monocrystalline and polycrystalline segments. Each segment is installed in a series parallel and has a capacity of 15 kWp. The systems are installed facing south having an optimum monthly tilt angle to enhance their efficiency. In this study, thirty-eight monocrystalline modules (model CS3400WP) and thirty-four polycrystalline modules (model CS3400WP) of similar maximum power output and efficiency ratings are used. Properties of the installed modules are summarized in Table1. There are four mounting structures of galvanized steel frames holding six panels for each type of PV module. The design of the support structure is to keep a variable inclination with the horizontal plane with the reinforced concrete foundation to withstand the weight of modules and maximum wind speeds at the site as shown in Figure 2(b).Table 1
Electrical and mechanical parameters of the installed PV modules.
Electrical parameters of PV modulemc-Sip-SiMaximum power (Pmax)400 Wp440 WpModule efficiency (η)18.11%19.7%Maximum power point voltage (Vmpp)38.7 V40.3 VCurrent at maximum power point (Impp)10.34 A10.92 AOpen-circuit voltage (Voc)47.2 V48.7 VShort circuit current (Isc)10.9 A11.4 AModule temperature at NOCT (TNOCT)42+3°C41+3°CTemp. coefficient of short circuit current (μΙsc)0.05%/°C0.05%/°CTemp. coefficient of open-circuit voltage-0.29%/°C-0.28%/°CTemp. coefficient of maximum power-0.37%/°C-0.36%/°CMechanical properties of PV moduleNumber of cells144144Dimensions of cell2108∗1048∗40 mm2132∗1048∗30 mmOperating temperature-40~85°C-40~85°CWeight (kg)22.422.4The following formulae can be used for calculating parameters related to the designing of a PV system.Equations (1) and (2) can be used to calculate the required numbers of PV panels.
(1)PVMax=Le×IPHAvgηinvTcf,where PVmax is the peak power of PV array (kWp), Le is the electrical load (kWh/day), IP is the peak solar intensity, HAvg is the average available radiation in kWh/m2/d, and TCF is the temperature correction factor (0.4-0.5% °C for crystalline silicon) and the efficiency of inverter.
(2)PVN=PVMaxPm,where Pm is the rated power of the selected panel and PVN is the number of PV panels.
(3)Sizeofinverter=TotalLoad+1+AfIeVA,where Af is the additional further load expansion (20%), Ie is the efficiency of inverter, and VA is the volt-ampere.
(4)PM=VM×IM,where VM is the voltage at maximum power point, IM is the current at maximum power point, and PM is the maximum power.Soiling ratio:(5)SRatiomeasured=PmsoiledmodulePmcleanmodule∙kmismatch,where Pmsolidmodule is the measured maximum power of the solid module, PmCleanmodule is the measured maximum power of the clean module, kmismatch quantifies the disparity in Pm between the clean and the soiled modules, and SRatiomeasured compares the measured maximum power (Pm) of the soiled and the clean module.


## 2.2. Three-Phase Inverters

Since the PV modules are semiconductors in nature, they fundamentally generate direct current (DC). The transmission and distribution systems are designed for AC which is obtained by converting it from DC via inverters and feeds the utility of the electrical grid by synchronized frequency normally around 50 or 60 Hz. The selection of the inverter is based on the maximum output power from each type of PV module array. All inverters are of SolisMax, model Solis-15 K Max; the technical features of the inverters are provided in Table2.Table 2
Electrical datasheet of three-phase inverters.
Input (DC)Max. Dc power (cosθ=1)15 KVMax. input voltage1000 VMPP voltage range/rated input voltage200-800 VMin. input voltage/initial input voltage350 VMax. input current input A/input B18 A+18 AOutput (AC)Rated power (230 V, 50 Hz)15 kWMax. apparent AC power33 kVARated power frequency50/60 HzMax. output current21.7 APower factor at rated power0.8 (min.)Maximum efficiency97.5%General dataWeight30 KGOperating temperature range-26°C~60°CNoise emission (typical)<30 dBASelf-consumption (night)<1 watt (night)TopologyTransformer lessCooling conceptNatural convection


## 3. Parameters Considered for the Performance Analysis of Installed PV Systems

Effective and credible assessment of any system’s performance is crucial for the designing of an efficient power system. The PV performance is a vital indicator to analyze the quality of its design and reliable combination of PV equipment. According to the International Electrotechnical Commission (IEC) standard 61724, the standard performance parameters for PV-based power systems play a crucial role in the efficiency of a system.


### 3.1. Final Yield

The definition of the final yield revolves around the portion of total energy generated (EEA) by the whole PV power plant to the rated output power (PPV) per kilowatt of installed PV array during a specified period (i.e., day, month, or year). It can be calculated by
(6)FinalYield=EACPPV,Rated,where EAC is the total energy generated and PPV is the rated output power.


### 3.2. Reference Yield

Referenced yield can be defined as the total irradiance (Ht) divided by irradiance (GSTC), which, primarily, is 1 kW/m2 (Equation (7)). This constitutes the solar energy that is available for a specifically mentioned time frame at any place where the PV power system has been deployed. It constitutes the hours per day that are necessary to obtain solar radiation to be at reference irradiance level to produce the same incident energy as received by the sun [25].
(7)Referenceyield=HtGstc,where Ht is the total irradiance and Gstc is the irradiance.


### 3.3. Performance Ratio

Performance ratio (PR) is a significant parameter that depends on the PV power plant’s geographical location. It is represented by the ratio of energy outputs obtained actually and theoretically over the time of a month or a year as depicted by Equation (8). A high PR value for a grid-connected PV is an indication that the system is efficient and reliable. The overall losses from various factors such as inverter losses, module mismatch, wiring, temperature, and dust or snow on the rated output power are less. The overall efficiency of the solar photovoltaic power system is closely related to the value of the performance ratio, i.e., closer to 100% [25].
(8)Performanceratio=YfYr,where Yf is the actual energy output and Yr is the theoretical energy output.


### 3.4. Capacity Factor

The capacity factor is mainly the ratio of produced electricity capacity factor. Geothermal energy and biomass among the clean and renewable energies perform at higher capacity factors compared to intermittent renewable sources which tend to have lower capacity factors. For PV plants, the capacity factor ranges from 10% to 30%, as their outputs fluctuate resulting from weather conditions [25]. It can be calculated by using
(9)Capacityfactor=Yfhours,where Yf is the actual energy output.


### 3.5. Meteorological Data

To examine the performance of the PV system, it is required to study the weather data recorded by the weather station. This may include data set comprising temperature and wind speed. The ambient and module temperature fluctuated during the nominated period from November 2020 to August 2021 individually. Undesirable module temperature was usually observed during nighttime. During the measured period, wind velocity varied from 1 ms_1 in January and 2 ms_1 in June on average, whereas relative humidity reached almost 87% level during the monsoon season (i.e., July and August), and the maximum value of global-tilt solar irradiation of 1225 Wm-2 was recorded for Faisalabad. It has been observed that on any sunny day, the module performance is affected by three meteorological parameters. These factors include temperature, solar irradiation, and wind speed, whereas other parameters are shown in Table 3.Table 3
Meteorological data for Faisalabad.
Parameter measuredValue obtainedMeasuring range0.0-1400.0Wm-2Resolution<1Wm-2Spectral range300-2800nmSensitivity range5-20μv/Wm-2Operating temperature rate-40°C to+80°CMaximum operational irradiance2000Wm-2Relative humidity range4.35-17.4 PsiRelative humidity accuracy±2%RHAir temperature range-50°C to +60°CAir temperature accuracy0.5°CWind speed range0.8-40m-2Wind speed measuring accuracy±0.5%


## 3.1. Final Yield

The definition of the final yield revolves around the portion of total energy generated (EEA) by the whole PV power plant to the rated output power (PPV) per kilowatt of installed PV array during a specified period (i.e., day, month, or year). It can be calculated by
(6)FinalYield=EACPPV,Rated,where EAC is the total energy generated and PPV is the rated output power.


## 3.2. Reference Yield

Referenced yield can be defined as the total irradiance (Ht) divided by irradiance (GSTC), which, primarily, is 1 kW/m2 (Equation (7)). This constitutes the solar energy that is available for a specifically mentioned time frame at any place where the PV power system has been deployed. It constitutes the hours per day that are necessary to obtain solar radiation to be at reference irradiance level to produce the same incident energy as received by the sun [25].
(7)Referenceyield=HtGstc,where Ht is the total irradiance and Gstc is the irradiance.


## 3.3. Performance Ratio

Performance ratio (PR) is a significant parameter that depends on the PV power plant’s geographical location. It is represented by the ratio of energy outputs obtained actually and theoretically over the time of a month or a year as depicted by Equation (8). A high PR value for a grid-connected PV is an indication that the system is efficient and reliable. The overall losses from various factors such as inverter losses, module mismatch, wiring, temperature, and dust or snow on the rated output power are less. The overall efficiency of the solar photovoltaic power system is closely related to the value of the performance ratio, i.e., closer to 100% [25].
(8)Performanceratio=YfYr,where Yf is the actual energy output and Yr is the theoretical energy output.


## 3.4. Capacity Factor

The capacity factor is mainly the ratio of produced electricity capacity factor. Geothermal energy and biomass among the clean and renewable energies perform at higher capacity factors compared to intermittent renewable sources which tend to have lower capacity factors. For PV plants, the capacity factor ranges from 10% to 30%, as their outputs fluctuate resulting from weather conditions [25]. It can be calculated by using
(9)Capacityfactor=Yfhours,where Yf is the actual energy output.


## 3.5. Meteorological Data

To examine the performance of the PV system, it is required to study the weather data recorded by the weather station. This may include data set comprising temperature and wind speed. The ambient and module temperature fluctuated during the nominated period from November 2020 to August 2021 individually. Undesirable module temperature was usually observed during nighttime. During the measured period, wind velocity varied from 1 ms_1 in January and 2 ms_1 in June on average, whereas relative humidity reached almost 87% level during the monsoon season (i.e., July and August), and the maximum value of global-tilt solar irradiation of 1225 Wm-2 was recorded for Faisalabad. It has been observed that on any sunny day, the module performance is affected by three meteorological parameters. These factors include temperature, solar irradiation, and wind speed, whereas other parameters are shown in Table 3.Table 3
Meteorological data for Faisalabad.
Parameter measuredValue obtainedMeasuring range0.0-1400.0Wm-2Resolution<1Wm-2Spectral range300-2800nmSensitivity range5-20μv/Wm-2Operating temperature rate-40°C to+80°CMaximum operational irradiance2000Wm-2Relative humidity range4.35-17.4 PsiRelative humidity accuracy±2%RHAir temperature range-50°C to +60°CAir temperature accuracy0.5°CWind speed range0.8-40m-2Wind speed measuring accuracy±0.5%


## 4. Performance Analysis and Result Discussion

This comparative study visualizes that in winter, the efficiency of monoperk is better as compared to other types of modules. In summer, polyperk performed with better efficiency because it is highly efficient in the high-temperature range. The maximum production of kWh in winters was more than 2,100 kWh for polyperk. The data obtained displayed that the annual average of daily final yield, performance ratio, and capacity factor for 15 kW polyperk was estimated to be 61.94 kWh, 84.17%, and 19.12, respectively. The annual average of daily final yield, performance ratio, and capacity factor for 15 kW monoperk was estimated to be 58.32 kWh, 81.42%, and 18.13, respectively. The reported results are comparatively better than a similar study conducted in Iran [26].On the other hand, a maximum yield of around 1,700 kWh was obtained from monoperk as summer ambient temperature is high leading to reduced efficiency. At the start of November, the ambient temperature began to decrease, and thus, the efficiency of monoperk also increased, whereas the efficiency of polyperk started decreasing till December as the highest temperature of the season was monitored this month. In March, the yield of monoperk plummeted, whereas for the polyperk modules, the yield improved. In April, May, June, and July, the ambient temperature stayed at a peak level. Therefore, the efficiency of polyperk increased, and consequently, the efficiency of monoperk decreased. In August, temperature variation was observed due to the monsoon season. On warm days, the efficiency of polyperk increased whereas, on the other hand, the efficiency of monoperk increased on relatively cool days as depicted by simulation results in Figure3(b). So, it can be concluded that polyperk modules outperform monoperk type modules when the ambient temperature increases. The common material used in solar cells, crystalline silicon, does not help to prevent them from getting hot either. As a great conductor of heat, silicon actually speeds up the heat building up in solar cells on hot summer days. Mono PV modules are made from a single crystal of silicon whereas poly is made from several fragments of silicon melted together which prevents it from heating up.Figure 3
Comparison of yield obtained from simulation and real-time systems: (a) yield obtained from polyperk PV modules; (b) yield obtained from monoperk PV modules.
(a)(b)As it can be seen in Figure3(a), HelioScope-based system generated higher power in comparison to a real-time system as the software considers ideal conditions and ignores various factors that affect the real system output performance such as dust losses and shadow factor.Scatter plot in Figure4 displays two hotspots and distinct regions highlighted by two circles. The upper-end circle has a wide range of experimental mono- and polycrystalline systems and polyperk simulation yield results. The lower circle has a keen distribution of yield results in experimental monocrystalline systems and polyperk simulated systems. Only peculiar results in raw data for the distinctive monocrystalline solar energy material produce oblique and relatively lesser in midseason.Figure 4
Comparison of hotspots generated by mono- and polyperk on monthly basis using real-time installed systems and simulations.Quantified data and behavior in tail line circles need to be categorized using learning, training, and testing data sets for relative comparison, which is a new theme in solar energy system classification; further details are defined in Section4.Ideal conditions and real-time working systems classify two different data sets and elucidated graphs. Statistical graphs show the relatively higher difference in total yield over the time scale length in real time due to undistinguished and random errors in calculations and measurement. Figure4 shows the hotspot regions using the estimated data varying from lower tail to high end. Figures 5 and 6 depict raw data sets in peak slope form. Figures 4 and 5 show distinct groups and variations in estimated and calculated values. In polyperk system experimentation, Figure 6 shows the error doping in mean values for polyperk crystalline modules (simulation and experiment result comparison). A greater mean error exists in the experimentation results with the range lying in 1250 to 1470 kWh in comparison to simulation results with the least mean error in the upper bound of 1950 kWh. Significance of new advance predictive and artificial intelligence tools in the realm of statistical-based machine learning produces a counterproductive approach using both real-time and ideal simulation patterns and data sets for classification and decision-making for applied applications while using monoperk and polyperk solar systems. The apparent results are statistically plotted for heat mapping to understand the relationship between the distinctive classes of monoperk and polyperk crystalline modules of simulation and experimental data sets.Figure 5
Peak form data of experimental and simulation results for polycrystalline material energy systems (1, simulation; 0, experimentation).Figure 6
Mean error-box plot using Seaborn library of experimental and simulation result data for mono- and polycrystalline material energy systems.Figures7 and 8 display futuristic parameters that are independent and dependent in nature on each other. Plasma-type heat map of monoperk crystalline modules shows maximum nonlinearity in the experimental and simulation results up to -0.86. The corresponding increase in module yield is inferred from the heat map but linearity is minimum in experimental and simulation results with values as low as 0.14 and 0.16. In polyperk crystalline modules, greater amount of synergy is accounted for in the experimental and simulation results. The corresponding results are accounted for and validated with heat map-linearity values greater than monoperk crystalline modules up to ~0.98. However, in relationship with months and method classes, a reverse effect has been observed with negative values of as low as -0.061 and -0.96 for experimental and simulation data sets.Figure 7
Heat map between each independent and dependent variable in case of monoperk crystalline modules.Figure 8
Heat map between each independent and dependent variable in the case of polyperk crystalline modules.Heat maps in Figures7 and 8 depict the statistical difference with nonlinearity and class distinction. An efficient technique must be applied for validating results, consolidating decisions for which type of crystalline modules and which method needs to be implemented for desirable calculation of yield measurement according to our requirements. Machine learning algorithms are statistically powerful algorithms that over the period of using artificial intelligence learning update their sets and make the logical decision of either using experimental means or simulation for time and cost-saving.


### 4.1. Machine Learning-Based Relative Performance Investigation of Mono- and Polyperk Modules

As previously defined, the nonlinearity and class distinction in the available raw data sets are classically classified into the categorical division between experimental and simulation results. Parametric results of machine learning-based logistical regression have been introduced as a strategic machine learning algorithm due to its robust nature and easiness with mixed data set performance. Using this technique, the algorithm will evaluate the reasons behind the performance gap between simulation and real-time system outputs as shown in Figure3 and help to contain the error to a minimum; it also provides useful insight, corelation, and evaluation with class distinction according to subjective weather and time horizon.


#### 4.1.1. Machine Learning-Based Logistic Regression Modeling

Machine learning- (ML-) based regressions are keenly a new method for inference of error and hyperparameter deduction. For efficient future predictive system installation, result synchronization, and error reduction between the simulation model and real-time system, machine learning-based logistic regression modeling has been performed in this section. ML classification has been done on the following three algorithms:(1)
Supervised learning(2)
Unsupervised learning(3)
Reinforcement learningFlowchart classification of machine classes, input and output data set nature, and algorithms are presented in Figure9.Figure 9
Machine learning algorithms and flow chart.The categorical data in ML lies mainly in the domain of logistic regression. Linear and polynomial regressions are commonly used for conventional regressive weight parameters and their corelations based onp values. ML differentiates logistical regression from linear regression based on the continuous and descriptive data set, respectively. The regular fit in linear regression mainly highlights continuous values in a data set. Logistic regression predicts whether something is either true or false, yes or no, and 1 or 0, instead of predicting the weight or performance based on the mean absolute, R2, etc., values. Due to significant differences between the simulation results and experimental results performed earlier and as highlighted by statistical values, i.e., the standard error lies in-between 5 and 45% for polyperk crystalline and 5 and 25% for Monocrystalline PV grid-connected module. ML-based logistic regression modeling has been carried out. A pair plot drawn in Python using the Seaborn library assimilates the finest set of attributes and features for a relative explanation of relationships between two and more variables. The plot displays clusters and separation of offset data points along with hyperparameters that results in decision-making and classification of either supervised or unsupervised algorithm for machine learning. Pair plots in Figures 10 and 11 show class representations in monoperk and polyperk module data sets with bar plots showing energy yield produced over a time series.Figure 10
Pair plot of monoperk module data sets in grid-connected formation for correlation between each independent and dependent variable.Figure 11
Pair plot of polyperk module data sets in grid-connected formation for correlation between each independent and dependent variable.Monoperk crystalline grid-connected system shows the sigmoidal plot and two hotspot regions mainly featuring yield and timeline variable, i.e., month. Figures10 and 11 also depict method validity for the experimentation and simulation results. The pair plot of monoperk has data sets more aligned statistically for simulation data and interpretations, while the polyperk features data more viable within experimentation data points. The pair plot consists of scatter plots and bar plots. Experimentation data points in the pair plot depict a higher yield for polyperk as compared to the monoperk crystalline grid-connected system.The under discussion ML-based case study for monoperk and polyperk crystalline module-based grid-tied systems is being conducted first time as no previous literature is available regarding the AI-based performance analysis. This method highlights the significance of implications between simulated and experimental methods with error reduction, consolidation, and the performance evaluation of grid-tied PV solar modules.Anaconda-Python 3.8 libraries including NumPy, Matplotlib, Seaborn, pandas, and scikit-learn have been utilized for data analysis and machine learning-based decision modeling between experimental and simulation results. The initial case study for the polyperk crystalline module data set shows a higher error doping in mean values during experimental evaluation in comparison to simulation results as shown in Figure5.Figure5 displays the comparison based on error occurrence between simulation and experimental results in the polyperk crystalline module where class 0 represents experimental and class 1 represents simulation results. In both simulated and experimental environments, per month yield maximum output has been calculated. The descriptive statistics of the polyperk and monoperk crystalline PV module performance can be seen in Tables 4 and 5.Table 4
Statistics (extracted features) based on performance analysis of polyperk modules.
FeaturesExperimental valuesSimulated valuesMean1842.981733.76Standard error196.6675112.8729366Median2152.851909.65Standard deviation621.9171356.9355659Sample variance386780.9127402.9982Kurtosis-1.78782-1.825932887Skewness-0.51473-0.450257756Range1537.4879.6Minimum900.81243Maximum2438.22122.6Sum18429.817337.6Count1010Largest (1)2438.22122.6Smallest (1)900.81243Confidence level (95.0%)444.8927255.3363221Table 5
Statistics (extracted features) based on performance analysis of monoperk modules.
FeaturesExperimental valuesSimulated valuesMean1265.671849.62Standard error108.0271232122.1181821Median1328.62037.5Standard deviation341.6117584386.1715992Sample variance116698.5934149128.504Kurtosis-2.063216661-1.835603662Skewness-0.155217059-0.435316653Range827.7957.9Minimum834.61317.3Maximum1662.32275.2Sum12656.718496.2Count1010Largest (1)1662.32275.2Smallest (1)834.61317.3Confidence level (95.0%)244.3743305276.2505204It can be seen from the extracted features represented in Tables4 and 5 that there is a significant difference between simulation and experimental data. This difference is due to the ideal scenario of the software as there is no consideration of temperature variance and its effect on the system performance as well as other factors such as dust factor and shadow factor. Based on the abovementioned features, a machine learning algorithm has been used to signify the error reduction and predictability module.


#### 4.1.2. Logistical Regression Mathematical Representation

Logistical regression is generally used for two-class problems and can be extended for implications in the multiclass problems but becomes highly unstable in calculations when classes are well separated; the working diagram is represented in Figure12. The baseline for the mathematical formulation of logistical regression is simple linear regression.
(10)y=bo+b1x,where y is the continuous output result while the bo is the intercept of the line, b1 is the slope of the line, and x is the input or independent variable. In continuous data, we can utilize linear regression, but in distinct classes, we cannot draw the best-fit curve. We introduce a classifier for whether an action/event shall occur or not. Figure 13 shows that the output in logistical regression is binomial. LR has a sigmoid function based on the probability of an event (P) and ranges from 0 to 1 and is given as
(11)P=11+e−y.Figure 12
Working diagram of the testing and training in logistical machine learning regression modeling.Figure 13
Sigmoid function behavior at a discrete event time scale length.IntroducingP in the LR equation and computing at the natural log scale gives the following mathematical expression:
(12)lnP1−P=bo+b1x.Weighted output is in the range of either 0 or 1; if the output is <0.5, then it corresponds to 0th class if not then 1st class. For training and testing data sets after incorporation into machine learning the module, accuracy is defined by(13)Accuracy%=CorrrectPredictionsTotalPredictions×100%.The accuracy of a system based on the prediction of classification problems is either correct or can be incorrect so a matrix, namely, a confusion matrix, is formed for a relational summary of actual and predicted values of classification problems.


#### 4.1.3. Performance Analysis of Mono- and Polyperk Crystalline Modules

The total reading count of simulation and experimental work is divided into 80% training and 20% testing data as shown in Figure14. The classifier is introduced for encoding purposes to have the binary distinction between greater probability events. The timeline horizon consists of 10 months; no data was conceived for the month of September and October.
(14)logp=lnp1−p1−p,where P is the probability of a discrete event defined earlier.Figure 14
Working data sets of monoperk and polyperk modules using logistic regression: (a) training set of monoperk module; (b) testing set of monoperk module; (c) training set of polyperk module; (d) training set of polyperk module.
(a)(b)(c)(d)The training data set selects a total of 80% values from raw data. The algorithm reads the pattern according to the problem statement and improves the probability values. In each run, a class check is run for appointing the new red and green distribution as highlighted in Figure14. An increase in the iterations increases the width of class boundaries. Based on the extracted features and training/testing of both modules, the data set collected from simulation and experimental work of mono- and polyperk crystalline module for a one-year cycle (except September and October) can be seen in Tables 6 and 7 which depict the difference between them ranging from 1% to 60.5% in monoperk and 6% to 27% in polyperk crystalline.Table 6
Data set of monoperk crystalline module in simulation and experimental work.
MonthMonoperk experimental resultsMonoperk simulation resultsMethod/class max. yield outputDifferenceError percentageJanuary1629.513290300.518.44123964February159115610301.885606537March1456.52003.5154727.30222111April1200.72110.7191043.11365898May1000.22275.21127556.03902954June899.12254.11135560.11268355July865.52071.51120658.21868211August834.62111.61127760.47546884November1662.31462.3020012.03152259December1517.31317.3020013.1813089Table 7
Data set of polyperk crystalline module in simulation and experimental work.
MonthExperimental polyperk resultsPolyperk simulation resultsMethod/class max. yield outputDifferenceError percentageJanuary900.81245.8134527.69304864February1371.21471.211006.797172376March2007.11881.101266.277714115April2311.11976.1033514.495262May2298.62122.601767.656834595June2405.62105.6030012.47090123July2438.21938.2050020.50693134August2377.51977.5040016.82439537November1276.51376.511007.264802034December1043.212431199.816.07401448In logistical regression training, the data set values determine the probable event in advance. The most likelihood and unlikelihood are distinguished for experimental and simulation results. For the monoperk crystalline grid-connected system in the experimental scenario, readings are likelihood, and the probability after training and testing the data set lies about 99% accuracy. The confusion matrix produces an absolute validated summary result for the method and material to be incorporated in each particular scenario. A 20% test data set values in most actual and predicted values are in harmony with each other using the ML module. In further classification, as shown in the heat map and pair plot in Figures8–11, the class distinction reflects that those major values classified in the experimental work are authentic.To determine the evaluation of the monoperk crystalline grid-connected system, experimental work is more reliable than compared to a simulation study. The error difference reduces in off-peak months of the data cycle, i.e., January, February, and March, whereas in peak months, the evaluation results are likely the same and coherent. In the case of polyperk crystalline grid-connected studies, a greater significance and accuracy lies within the simulation and experimental studies, and the likelihood of probability is significant as seen in Tables6 and 7. Model accuracy after training and testing produces results of up to 99.5%. Simulation results are likely most favorable in predicting the performance evaluation of maximum yield in grid-connected systems. During off-peak (i.e., winter season), the error difference increases due to various factors such as module angle, line losses, cell dimension, and temperature invariability.


## 4.1. Machine Learning-Based Relative Performance Investigation of Mono- and Polyperk Modules

As previously defined, the nonlinearity and class distinction in the available raw data sets are classically classified into the categorical division between experimental and simulation results. Parametric results of machine learning-based logistical regression have been introduced as a strategic machine learning algorithm due to its robust nature and easiness with mixed data set performance. Using this technique, the algorithm will evaluate the reasons behind the performance gap between simulation and real-time system outputs as shown in Figure3 and help to contain the error to a minimum; it also provides useful insight, corelation, and evaluation with class distinction according to subjective weather and time horizon.


### 4.1.1. Machine Learning-Based Logistic Regression Modeling

Machine learning- (ML-) based regressions are keenly a new method for inference of error and hyperparameter deduction. For efficient future predictive system installation, result synchronization, and error reduction between the simulation model and real-time system, machine learning-based logistic regression modeling has been performed in this section. ML classification has been done on the following three algorithms:(1)
Supervised learning(2)
Unsupervised learning(3)
Reinforcement learningFlowchart classification of machine classes, input and output data set nature, and algorithms are presented in Figure9.Figure 9
Machine learning algorithms and flow chart.The categorical data in ML lies mainly in the domain of logistic regression. Linear and polynomial regressions are commonly used for conventional regressive weight parameters and their corelations based onp values. ML differentiates logistical regression from linear regression based on the continuous and descriptive data set, respectively. The regular fit in linear regression mainly highlights continuous values in a data set. Logistic regression predicts whether something is either true or false, yes or no, and 1 or 0, instead of predicting the weight or performance based on the mean absolute, R2, etc., values. Due to significant differences between the simulation results and experimental results performed earlier and as highlighted by statistical values, i.e., the standard error lies in-between 5 and 45% for polyperk crystalline and 5 and 25% for Monocrystalline PV grid-connected module. ML-based logistic regression modeling has been carried out. A pair plot drawn in Python using the Seaborn library assimilates the finest set of attributes and features for a relative explanation of relationships between two and more variables. The plot displays clusters and separation of offset data points along with hyperparameters that results in decision-making and classification of either supervised or unsupervised algorithm for machine learning. Pair plots in Figures 10 and 11 show class representations in monoperk and polyperk module data sets with bar plots showing energy yield produced over a time series.Figure 10
Pair plot of monoperk module data sets in grid-connected formation for correlation between each independent and dependent variable.Figure 11
Pair plot of polyperk module data sets in grid-connected formation for correlation between each independent and dependent variable.Monoperk crystalline grid-connected system shows the sigmoidal plot and two hotspot regions mainly featuring yield and timeline variable, i.e., month. Figures10 and 11 also depict method validity for the experimentation and simulation results. The pair plot of monoperk has data sets more aligned statistically for simulation data and interpretations, while the polyperk features data more viable within experimentation data points. The pair plot consists of scatter plots and bar plots. Experimentation data points in the pair plot depict a higher yield for polyperk as compared to the monoperk crystalline grid-connected system.The under discussion ML-based case study for monoperk and polyperk crystalline module-based grid-tied systems is being conducted first time as no previous literature is available regarding the AI-based performance analysis. This method highlights the significance of implications between simulated and experimental methods with error reduction, consolidation, and the performance evaluation of grid-tied PV solar modules.Anaconda-Python 3.8 libraries including NumPy, Matplotlib, Seaborn, pandas, and scikit-learn have been utilized for data analysis and machine learning-based decision modeling between experimental and simulation results. The initial case study for the polyperk crystalline module data set shows a higher error doping in mean values during experimental evaluation in comparison to simulation results as shown in Figure5.Figure5 displays the comparison based on error occurrence between simulation and experimental results in the polyperk crystalline module where class 0 represents experimental and class 1 represents simulation results. In both simulated and experimental environments, per month yield maximum output has been calculated. The descriptive statistics of the polyperk and monoperk crystalline PV module performance can be seen in Tables 4 and 5.Table 4
Statistics (extracted features) based on performance analysis of polyperk modules.
FeaturesExperimental valuesSimulated valuesMean1842.981733.76Standard error196.6675112.8729366Median2152.851909.65Standard deviation621.9171356.9355659Sample variance386780.9127402.9982Kurtosis-1.78782-1.825932887Skewness-0.51473-0.450257756Range1537.4879.6Minimum900.81243Maximum2438.22122.6Sum18429.817337.6Count1010Largest (1)2438.22122.6Smallest (1)900.81243Confidence level (95.0%)444.8927255.3363221Table 5
Statistics (extracted features) based on performance analysis of monoperk modules.
FeaturesExperimental valuesSimulated valuesMean1265.671849.62Standard error108.0271232122.1181821Median1328.62037.5Standard deviation341.6117584386.1715992Sample variance116698.5934149128.504Kurtosis-2.063216661-1.835603662Skewness-0.155217059-0.435316653Range827.7957.9Minimum834.61317.3Maximum1662.32275.2Sum12656.718496.2Count1010Largest (1)1662.32275.2Smallest (1)834.61317.3Confidence level (95.0%)244.3743305276.2505204It can be seen from the extracted features represented in Tables4 and 5 that there is a significant difference between simulation and experimental data. This difference is due to the ideal scenario of the software as there is no consideration of temperature variance and its effect on the system performance as well as other factors such as dust factor and shadow factor. Based on the abovementioned features, a machine learning algorithm has been used to signify the error reduction and predictability module.


### 4.1.2. Logistical Regression Mathematical Representation

Logistical regression is generally used for two-class problems and can be extended for implications in the multiclass problems but becomes highly unstable in calculations when classes are well separated; the working diagram is represented in Figure12. The baseline for the mathematical formulation of logistical regression is simple linear regression.
(10)y=bo+b1x,where y is the continuous output result while the bo is the intercept of the line, b1 is the slope of the line, and x is the input or independent variable. In continuous data, we can utilize linear regression, but in distinct classes, we cannot draw the best-fit curve. We introduce a classifier for whether an action/event shall occur or not. Figure 13 shows that the output in logistical regression is binomial. LR has a sigmoid function based on the probability of an event (P) and ranges from 0 to 1 and is given as
(11)P=11+e−y.Figure 12
Working diagram of the testing and training in logistical machine learning regression modeling.Figure 13
Sigmoid function behavior at a discrete event time scale length.IntroducingP in the LR equation and computing at the natural log scale gives the following mathematical expression:
(12)lnP1−P=bo+b1x.Weighted output is in the range of either 0 or 1; if the output is <0.5, then it corresponds to 0th class if not then 1st class. For training and testing data sets after incorporation into machine learning the module, accuracy is defined by(13)Accuracy%=CorrrectPredictionsTotalPredictions×100%.The accuracy of a system based on the prediction of classification problems is either correct or can be incorrect so a matrix, namely, a confusion matrix, is formed for a relational summary of actual and predicted values of classification problems.


### 4.1.3. Performance Analysis of Mono- and Polyperk Crystalline Modules

The total reading count of simulation and experimental work is divided into 80% training and 20% testing data as shown in Figure14. The classifier is introduced for encoding purposes to have the binary distinction between greater probability events. The timeline horizon consists of 10 months; no data was conceived for the month of September and October.
(14)logp=lnp1−p1−p,where P is the probability of a discrete event defined earlier.Figure 14
Working data sets of monoperk and polyperk modules using logistic regression: (a) training set of monoperk module; (b) testing set of monoperk module; (c) training set of polyperk module; (d) training set of polyperk module.
(a)(b)(c)(d)The training data set selects a total of 80% values from raw data. The algorithm reads the pattern according to the problem statement and improves the probability values. In each run, a class check is run for appointing the new red and green distribution as highlighted in Figure14. An increase in the iterations increases the width of class boundaries. Based on the extracted features and training/testing of both modules, the data set collected from simulation and experimental work of mono- and polyperk crystalline module for a one-year cycle (except September and October) can be seen in Tables 6 and 7 which depict the difference between them ranging from 1% to 60.5% in monoperk and 6% to 27% in polyperk crystalline.Table 6
Data set of monoperk crystalline module in simulation and experimental work.
MonthMonoperk experimental resultsMonoperk simulation resultsMethod/class max. yield outputDifferenceError percentageJanuary1629.513290300.518.44123964February159115610301.885606537March1456.52003.5154727.30222111April1200.72110.7191043.11365898May1000.22275.21127556.03902954June899.12254.11135560.11268355July865.52071.51120658.21868211August834.62111.61127760.47546884November1662.31462.3020012.03152259December1517.31317.3020013.1813089Table 7
Data set of polyperk crystalline module in simulation and experimental work.
MonthExperimental polyperk resultsPolyperk simulation resultsMethod/class max. yield outputDifferenceError percentageJanuary900.81245.8134527.69304864February1371.21471.211006.797172376March2007.11881.101266.277714115April2311.11976.1033514.495262May2298.62122.601767.656834595June2405.62105.6030012.47090123July2438.21938.2050020.50693134August2377.51977.5040016.82439537November1276.51376.511007.264802034December1043.212431199.816.07401448In logistical regression training, the data set values determine the probable event in advance. The most likelihood and unlikelihood are distinguished for experimental and simulation results. For the monoperk crystalline grid-connected system in the experimental scenario, readings are likelihood, and the probability after training and testing the data set lies about 99% accuracy. The confusion matrix produces an absolute validated summary result for the method and material to be incorporated in each particular scenario. A 20% test data set values in most actual and predicted values are in harmony with each other using the ML module. In further classification, as shown in the heat map and pair plot in Figures8–11, the class distinction reflects that those major values classified in the experimental work are authentic.To determine the evaluation of the monoperk crystalline grid-connected system, experimental work is more reliable than compared to a simulation study. The error difference reduces in off-peak months of the data cycle, i.e., January, February, and March, whereas in peak months, the evaluation results are likely the same and coherent. In the case of polyperk crystalline grid-connected studies, a greater significance and accuracy lies within the simulation and experimental studies, and the likelihood of probability is significant as seen in Tables6 and 7. Model accuracy after training and testing produces results of up to 99.5%. Simulation results are likely most favorable in predicting the performance evaluation of maximum yield in grid-connected systems. During off-peak (i.e., winter season), the error difference increases due to various factors such as module angle, line losses, cell dimension, and temperature invariability.


## 4.1.1. Machine Learning-Based Logistic Regression Modeling

Machine learning- (ML-) based regressions are keenly a new method for inference of error and hyperparameter deduction. For efficient future predictive system installation, result synchronization, and error reduction between the simulation model and real-time system, machine learning-based logistic regression modeling has been performed in this section. ML classification has been done on the following three algorithms:(1)
Supervised learning(2)
Unsupervised learning(3)
Reinforcement learningFlowchart classification of machine classes, input and output data set nature, and algorithms are presented in Figure9.Figure 9
Machine learning algorithms and flow chart.The categorical data in ML lies mainly in the domain of logistic regression. Linear and polynomial regressions are commonly used for conventional regressive weight parameters and their corelations based onp values. ML differentiates logistical regression from linear regression based on the continuous and descriptive data set, respectively. The regular fit in linear regression mainly highlights continuous values in a data set. Logistic regression predicts whether something is either true or false, yes or no, and 1 or 0, instead of predicting the weight or performance based on the mean absolute, R2, etc., values. Due to significant differences between the simulation results and experimental results performed earlier and as highlighted by statistical values, i.e., the standard error lies in-between 5 and 45% for polyperk crystalline and 5 and 25% for Monocrystalline PV grid-connected module. ML-based logistic regression modeling has been carried out. A pair plot drawn in Python using the Seaborn library assimilates the finest set of attributes and features for a relative explanation of relationships between two and more variables. The plot displays clusters and separation of offset data points along with hyperparameters that results in decision-making and classification of either supervised or unsupervised algorithm for machine learning. Pair plots in Figures 10 and 11 show class representations in monoperk and polyperk module data sets with bar plots showing energy yield produced over a time series.Figure 10
Pair plot of monoperk module data sets in grid-connected formation for correlation between each independent and dependent variable.Figure 11
Pair plot of polyperk module data sets in grid-connected formation for correlation between each independent and dependent variable.Monoperk crystalline grid-connected system shows the sigmoidal plot and two hotspot regions mainly featuring yield and timeline variable, i.e., month. Figures10 and 11 also depict method validity for the experimentation and simulation results. The pair plot of monoperk has data sets more aligned statistically for simulation data and interpretations, while the polyperk features data more viable within experimentation data points. The pair plot consists of scatter plots and bar plots. Experimentation data points in the pair plot depict a higher yield for polyperk as compared to the monoperk crystalline grid-connected system.The under discussion ML-based case study for monoperk and polyperk crystalline module-based grid-tied systems is being conducted first time as no previous literature is available regarding the AI-based performance analysis. This method highlights the significance of implications between simulated and experimental methods with error reduction, consolidation, and the performance evaluation of grid-tied PV solar modules.Anaconda-Python 3.8 libraries including NumPy, Matplotlib, Seaborn, pandas, and scikit-learn have been utilized for data analysis and machine learning-based decision modeling between experimental and simulation results. The initial case study for the polyperk crystalline module data set shows a higher error doping in mean values during experimental evaluation in comparison to simulation results as shown in Figure5.Figure5 displays the comparison based on error occurrence between simulation and experimental results in the polyperk crystalline module where class 0 represents experimental and class 1 represents simulation results. In both simulated and experimental environments, per month yield maximum output has been calculated. The descriptive statistics of the polyperk and monoperk crystalline PV module performance can be seen in Tables 4 and 5.Table 4
Statistics (extracted features) based on performance analysis of polyperk modules.
FeaturesExperimental valuesSimulated valuesMean1842.981733.76Standard error196.6675112.8729366Median2152.851909.65Standard deviation621.9171356.9355659Sample variance386780.9127402.9982Kurtosis-1.78782-1.825932887Skewness-0.51473-0.450257756Range1537.4879.6Minimum900.81243Maximum2438.22122.6Sum18429.817337.6Count1010Largest (1)2438.22122.6Smallest (1)900.81243Confidence level (95.0%)444.8927255.3363221Table 5
Statistics (extracted features) based on performance analysis of monoperk modules.
FeaturesExperimental valuesSimulated valuesMean1265.671849.62Standard error108.0271232122.1181821Median1328.62037.5Standard deviation341.6117584386.1715992Sample variance116698.5934149128.504Kurtosis-2.063216661-1.835603662Skewness-0.155217059-0.435316653Range827.7957.9Minimum834.61317.3Maximum1662.32275.2Sum12656.718496.2Count1010Largest (1)1662.32275.2Smallest (1)834.61317.3Confidence level (95.0%)244.3743305276.2505204It can be seen from the extracted features represented in Tables4 and 5 that there is a significant difference between simulation and experimental data. This difference is due to the ideal scenario of the software as there is no consideration of temperature variance and its effect on the system performance as well as other factors such as dust factor and shadow factor. Based on the abovementioned features, a machine learning algorithm has been used to signify the error reduction and predictability module.


## 4.1.2. Logistical Regression Mathematical Representation

Logistical regression is generally used for two-class problems and can be extended for implications in the multiclass problems but becomes highly unstable in calculations when classes are well separated; the working diagram is represented in Figure12. The baseline for the mathematical formulation of logistical regression is simple linear regression.
(10)y=bo+b1x,where y is the continuous output result while the bo is the intercept of the line, b1 is the slope of the line, and x is the input or independent variable. In continuous data, we can utilize linear regression, but in distinct classes, we cannot draw the best-fit curve. We introduce a classifier for whether an action/event shall occur or not. Figure 13 shows that the output in logistical regression is binomial. LR has a sigmoid function based on the probability of an event (P) and ranges from 0 to 1 and is given as
(11)P=11+e−y.Figure 12
Working diagram of the testing and training in logistical machine learning regression modeling.Figure 13
Sigmoid function behavior at a discrete event time scale length.IntroducingP in the LR equation and computing at the natural log scale gives the following mathematical expression:
(12)lnP1−P=bo+b1x.Weighted output is in the range of either 0 or 1; if the output is <0.5, then it corresponds to 0th class if not then 1st class. For training and testing data sets after incorporation into machine learning the module, accuracy is defined by(13)Accuracy%=CorrrectPredictionsTotalPredictions×100%.The accuracy of a system based on the prediction of classification problems is either correct or can be incorrect so a matrix, namely, a confusion matrix, is formed for a relational summary of actual and predicted values of classification problems.


## 4.1.3. Performance Analysis of Mono- and Polyperk Crystalline Modules

The total reading count of simulation and experimental work is divided into 80% training and 20% testing data as shown in Figure14. The classifier is introduced for encoding purposes to have the binary distinction between greater probability events. The timeline horizon consists of 10 months; no data was conceived for the month of September and October.
(14)logp=lnp1−p1−p,where P is the probability of a discrete event defined earlier.Figure 14
Working data sets of monoperk and polyperk modules using logistic regression: (a) training set of monoperk module; (b) testing set of monoperk module; (c) training set of polyperk module; (d) training set of polyperk module.
(a)(b)(c)(d)The training data set selects a total of 80% values from raw data. The algorithm reads the pattern according to the problem statement and improves the probability values. In each run, a class check is run for appointing the new red and green distribution as highlighted in Figure14. An increase in the iterations increases the width of class boundaries. Based on the extracted features and training/testing of both modules, the data set collected from simulation and experimental work of mono- and polyperk crystalline module for a one-year cycle (except September and October) can be seen in Tables 6 and 7 which depict the difference between them ranging from 1% to 60.5% in monoperk and 6% to 27% in polyperk crystalline.Table 6
Data set of monoperk crystalline module in simulation and experimental work.
MonthMonoperk experimental resultsMonoperk simulation resultsMethod/class max. yield outputDifferenceError percentageJanuary1629.513290300.518.44123964February159115610301.885606537March1456.52003.5154727.30222111April1200.72110.7191043.11365898May1000.22275.21127556.03902954June899.12254.11135560.11268355July865.52071.51120658.21868211August834.62111.61127760.47546884November1662.31462.3020012.03152259December1517.31317.3020013.1813089Table 7
Data set of polyperk crystalline module in simulation and experimental work.
MonthExperimental polyperk resultsPolyperk simulation resultsMethod/class max. yield outputDifferenceError percentageJanuary900.81245.8134527.69304864February1371.21471.211006.797172376March2007.11881.101266.277714115April2311.11976.1033514.495262May2298.62122.601767.656834595June2405.62105.6030012.47090123July2438.21938.2050020.50693134August2377.51977.5040016.82439537November1276.51376.511007.264802034December1043.212431199.816.07401448In logistical regression training, the data set values determine the probable event in advance. The most likelihood and unlikelihood are distinguished for experimental and simulation results. For the monoperk crystalline grid-connected system in the experimental scenario, readings are likelihood, and the probability after training and testing the data set lies about 99% accuracy. The confusion matrix produces an absolute validated summary result for the method and material to be incorporated in each particular scenario. A 20% test data set values in most actual and predicted values are in harmony with each other using the ML module. In further classification, as shown in the heat map and pair plot in Figures8–11, the class distinction reflects that those major values classified in the experimental work are authentic.To determine the evaluation of the monoperk crystalline grid-connected system, experimental work is more reliable than compared to a simulation study. The error difference reduces in off-peak months of the data cycle, i.e., January, February, and March, whereas in peak months, the evaluation results are likely the same and coherent. In the case of polyperk crystalline grid-connected studies, a greater significance and accuracy lies within the simulation and experimental studies, and the likelihood of probability is significant as seen in Tables6 and 7. Model accuracy after training and testing produces results of up to 99.5%. Simulation results are likely most favorable in predicting the performance evaluation of maximum yield in grid-connected systems. During off-peak (i.e., winter season), the error difference increases due to various factors such as module angle, line losses, cell dimension, and temperature invariability.


## 5. Conclusions

In this research, a comparative study was conducted for two solar systems of 15 kW. The systems primarily included monoperk and polyperk crystalline. From the study, it was observed that maximum yield was produced, in winters, by monoperk, while during summers, polyperk displayed enhanced efficiency. In Faisalabad, polyperk has proven to be efficient considering the high rates of temperature whereas monoperk, consequently, reduced the efficiency of the solar system. The annual average of daily final yield, performance ratio, and capacity factor for 15 kW polyperk was estimated to be 61.94 kWh, 84.17%, and 19.12, respectively. The annual average of daily final yield, performance ratio, and capacity factor for 15 kW monoperk was estimated to be 58.32 kWh, 81.42%, and 18.13, respectively. The efficiency can also be attributed to the quality of the system. For example, good quality inverter requires quality plates for enhanced efficiency. Additionally, the production of a 430-watt panel was noted as 400 watts. Furthermore, according to the applied machine learning module, a significant difference was observed in the considered PV module types (i.e., mono- and polyperk). A machine learning modeling study using logistical regression was applied to determine the greater significance of experimentation results in monoperk crystalline with an accuracy of 99.5%, while the results in polyperk using simulation studies are more accurate and recommended in the evaluation of PV-connected grid. Depending upon observed parameters and frequency period, the model elucidated a better understanding of the performed real-time analysis leading to both cost and time saving for the installation of similar projects in the region. Furthermore, better performance can be achieved from installed systems if factors such as dust, tilt angle, and shadow effects are considered before the installation of PV systems.



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*Source: 3186378-2022-08-12.xml*