Mathematical model for predicting the performance of photovoltaic system with delayed solar irradiance

In Malaysia, solar energy is the primary renewable energy source due to its proximity to the equator. In comparison to fossil fuels, solar technology is the fastest-growing, most cost-effective, and least harmful to the environment. Photovoltaic systems convert solar irradiance into electricity. Due to some factors, the amount of solar irradiance arriving at the solar photovoltaic collector at a specific location varies. The goal of this study was to develop a mathematical model for predicting the performance of a photovoltaic system, which depends on the amount of solar irradiance. A novel model for solar irradiance in the form of a delay differential equation is introduced by including the factor of delayed solar irradiance, hour angle and the sun's motion. The simulation study is carried out for the three scenarios of weather conditions: a clear day, a slightly cloudy day, and a heavily overcast day. The numerical solution is obtained by adopting the Runge Kutta method coupled with a parameter fitting technique, the Nelder Mead algorithm, which is implemented by using MATLAB software. The data from a solar plant in Pahang, Malaysia, was used for model validation and it is found that the prediction profile for solar irradiance aligns well with the intermediate and decay phases, but deviates slightly during the growth phase. The output current and power for the solar photovoltaic panel were treated as time-dependent functions. As the solar irradiance increases, the output current and power of the solar panel will increase. The result showed that the maximum output current and output power of STP250S-20/Wd Crystalline Solar Module decreased by 42% and 76% , respectively, during slightly cloudy and heavily overcast conditions when compared to clear days. In other words, the performance of a photovoltaic module is better on clear days compared to cloudy days and heavily overcast. These findings highlight the relationship between delayed solar irradiance and the performance of the solar photovoltaic system

Mathematical modelling for predicting the performance of photovoltaic module

The demand for photovoltaic (PV) system is growing rapidly driven by technological development and awareness of green environment. A photovoltaic system converts the energy of light into electricity without emission of harmful by-product. A complete PV system consists of a solar panel (which combination of few solar cells), Pulse Width Modular (PWM) and a battery. Eight photovoltaic parameters are used to characterized the quality and efficiency of a PV module i.e (i) short circuit current (ISC), (ii) open circuit voltage (VOC), (iii) Theoretical Power (PT), (iv) maximum power (PMAX), (v) voltage at PMAX (VMPP) , (vi) current at PMAX (IMPP), (vii) fill factor (FF) and (viii) efficiency (). The PV parameters of laboratory scale solar cell could be determined based on current-voltage (I-V) and power voltage (P-V) curves which could be plotted using a combination of solar simulator and a potentiostat instruments. Two additional PV parameters i.e (i) reverse saturation current of diode (IRC) and (ii) photocurrent (IPV) have been studied intensively as input of mathematical models to simulate and determine the quality and efficiency of solar cells. However, reproduceable results and robust mathematical models are yet to be established. A mathematical model employing the IRC, IPV and diode ideality factor (a) – which received lack of focus by previous researchers; is proposed. We have validated the mathematical model by comparing the calculation I-V and P-V curves results with the specifications established by the manufacturer. We have conducted three studies based on different specification of silicon based solar module i.e (i) 300W, (ii) 265W and (iii) 250W to obtain temperature distributions and average solar irradiance at selected locations. Through a comparative analysis, the theoretical calculation results and the manufacturers’ specifications are in good agreemen

Mathematical Modelling for Predicting the Performance of Photovoltaic Modul

The demand for photovoltaic (PV) system is growing rapidly driven by technological development and awareness of green environment. A photovoltaic system converts the energy of light into electricity without emission of harmful by-product. A complete PV system consists of a solar panel (which combination of few solar cells), Pulse Width Modular (PWM) and a battery. Eight photovoltaic parameters are used to characterized the quality and efficiency of a PV module i.e (i) short circuit current (ISC), (ii) open circuit voltage (VOC), (iii) Theoretical Power (PT), (iv) maximum power (PMAX), (v) voltage at PMAX (VMPP) , (vi) current at PMAX (IMPP), (vii) fill factor (FF) and (viii) efficiency (). The PV parameters of laboratory scale solar cell could be determined based on current-voltage (I-V) and power-voltage (P-V) curves which could be plotted using a combination of solar simulator and a potentiostat instruments. Two additional PV parameters i.e (i) reverse saturation current of diode (IRC) and (ii) photocurrent (IPV) have been studied intensively as input of mathematical models to simulate and determine the quality and efficiency of solar cells. However, reproduceable results and robust mathematical models are yet to be established. A mathematical model employing the IRC, IPV and diode ideality factor (a) – which received lack of focus by previous researchers; is proposed. We have validated the mathematical model by comparing the calculation I-V and P-V curves results with the specifications established by the manufacturer. We have conducted three studies based on different specification of silicon based solar module i.e (i) 300W, (ii) 265W and (iii) 250W to obtain temperature distributions and average solar irradiance at selected locations. Through a comparative analysis, the theoretical calculation results and the manufacturers’ specifications are in good agreement

Pembangunan dan penilaian video pengajaran penaakulan statistic untuk pelajar pasca siswazah pendidikan

Statistics is a set of mathematical procedures used to compile, make inferences and interpret information (Gravetter & Wallnau, 2011). While education is a combination of statistics between two different disciplines of mathematics education and the field of statistics. The goal now is to foster education statistics and developing statistical reasoning skills in the classroom (Delmass, 2004). Although learning of statistics begins from pre school to professional level but still many students do not master in statistical reasoning. The studies were done by Thomas Jaki and Melanie Autin (2009), Bilgin & Crowe. S (2008) and Arinah et al (2012) have shown that social science postgraduate students do not dominate the statistics with good reasoning skills. Therefore Statistical Reasoning Learning Environment model (Statistical Reasoning Learning Environment, SRLE) was introduced. SRLE model was developed based on the six principles of instructional design described by Cobb and McClain (2004). Process-oriented teaching and learning will help improve understanding SRLE next statistic can develop statistical reasoning skills. Statistical reasoning instructional video (VPPS) was produced to test the effectiveness of the student. The results showed student were improving their understanding of statistics and they can accept this video as teaching aids and reference when doing research. Teaching aids based on technology-oriented and using principles of SRLE will facilitate students preparing for exams and referrals without the boundaries of time and plac

Parameter estimation in mathematical modelling for photovoltaic panel

The demand for solar photovoltaic (PV) system is growing rapidly driven by new technology and strong economies of scale. PV systems directly convert solar energy into electricity without release any pollution into the environment and deplete natural resources. PV technology has matured and its reliability keeps improving. However, PV system is more expensive to produce than conventional sources of energy due in part to the cost of manufacturing PV devices and in part to the conversion efficiencies of the equipment. Besides, important attention in designing, developing and installing the PV systems is time-consuming. In this paper, we propose a mathematical model to predict the PV systems behaviour and performance by considering the plausible factors. The factors accept in this model are solar irradiance and manufacturers' information for the type of PV panel. A case study at the eastern part of Peninsular Malaysia was conducted to examine the effect of factors on the performance of PV. Through the comparative analysis, the results have a good agreement