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While conducting electrochemical experiments in 1838, Alexandre Edmond Becquerel, a French physicist, discovered the photoelectric phenomenon. He monitored the current flowing between two plated platinum electrodes in an electrolyte-filled container. Becquerel discovered that when exposed to light, the current’s strength alerted. The outside effect, in which electrons move out of a stationary substance when exposed to light was involved in this case.

Willough Smith and his assistant Joseph May in 1873 observed that when exposed to light, the semiconductor selenium’s resistance altered. They witnessed for the very first time the internal photo-effect significant to photovoltaics, where light breaks electrons from their bonds in the semiconductor and allows them to be available in the form of free charge carriers in the solid-state body.

After three years, William Adams and Richard Day discovered that when exposed to light, a selenium rod with platinum electrodes may generate electrical energy. This was the first time a solid body had shown the ability to convert light energy into electrical energy directly. In 1883, Charles Fritts, a New York inventor, created a small ‘Module’ with a surface area of 30 cm2 consisting of selenium cells that had nearly 1% efficiency. This was achieved by coating the selenium cells with a thin layer of the gold electrode. Fritts then sent a module to Werner von Siemens, a German inventor, to be evaluated. Siemens acknowledged the significance of the discovery and informed the Royal Academy of Prussia that the conversion of light into electricity had been exhibited.

In the years that followed, the physical background of the effect was better described. This was due to Albert Einstein and his light quantum theory presented in 1905 which received the Nobel Prize. There were also technological advancements occurring in 1916, where the AEG Company’s chemist Jan Czochralski developed the crystal formation process that made it possible to create semiconductor crystals of high quality as single crystals.

William B. Shockley, co-inventor of the transistor and American Nobel laureate, explained the mechanism of operation of the p-n junction in 1950 where he laid the theoretical basis for today’s solar cells. Using that theoretical foundation Bell Lab’s Daryl Chapin, Gerald Pearson, and Calvin Fuller built the first silicon solar cell that has an efficiency of up to 6% which was displayed to the public in 1954.

The photovoltaic research expanded rapidly in the late 1980s, specifically in Germany, Japan, and the USA. Moreover, studies have been conducted regarding the possibility of installing grid-coupled photovoltaic plants on single-family dwellings. From 1990 to 1995, Germany executed the ‘1000 Roof Program’ which provided with vital expertise on module reliability (Mertens, 2018).

## Solar Cell Operating Principle

The structure of a solar cell typically consists of a semiconductor known as a p-n junction where the positively charged p-type layer is located at the bottom and the negatively charged n-type layer at the top. The n-type accepts electrons while the p-type gives away electrons and gains holes as a result. When light enters the cell, it forms an electron-hole pair. There is an existing internal electric field where it forces these holes to separate. As a result, the electrons are transferred to the negative electrode and the hole to the positive creating an electrical current. A conducting strip known as a busbar typically made out of copper or aluminum, conducts the electric current generated by the cell. This process is known as the photovoltaic effect. (CITE)

## Modeling of PV Cell

To produce the required energy, solar cells are assembled in a series-parallel arrangement to size a PV array. Operational conditions and field factors such as irradiation levels, ambient temperature, and the sun’s geometric location all affect the amount of electric power generated by the PV array (Soto, 2006). An example of a current source model for a solar cell is illustrated below in Figure 3, where Iph known as photocurrent, is the produced current as a result of sunlight irradiation, Id is the diode reverse saturation current, Rsh is the intrinsic shunt of the cell and is usually a very large value, Rs is the series resistance of the cell and tends to have a much smaller value. Hence, the intrinsic shunt and the series resistance may be overlooked to simplify the analysis.

The I-V characteristic curve depicts a PV cell, module, or array’s voltage and current characteristics. It gives a detailed description of the solar energy conversion capacity and efficiency. Knowing these I-V characteristics is crucial as it determines the solar efficiency and output performance of the PV module. The following equation shows the typical I-V characteristic of a PV array (Singh, 2013):

I= NpIph-NpIdexpqVkTANs-1 #(1)Where the reverse saturation current is Id, the photocurrent is Iph, the PV output voltage is V, the electron charge is q, the Boltzmann constant is k, the PV output current is I, the cell temperature is T, the total number of cells in a series is Ns, the number of modules that are connected in parallel is Np, and the p-n junction ideality factor is A. The cell deviation from the typical p-n junction characteristic is governed by the factor A, which ranges from 1 to 5, where 1 is the ideal value.

According to the following equation, the reverse saturation current is Id fluctuates with temperature (Singh, 2013):

Id=Ic[TTc]3expqEgKA1Tc-1T (2)

Where Tc is the cell’s temperature of reference, the reverse saturation current at Tc is Ic, and the band gap energy of the semiconductor is Eg. Similarly, the photocurrent Iph is governed by the cell temperature and radiation from the sun, this can be expressed in the following equation (Singh, 2013):

Iph=Iscr KiT-TcS100#(3)Where at reference temperature and radiation Iscr is the cell short circuit current, the current temperature coefficient in a short circuit is Ki, and S is the sun radiation measured in milliwatts per square meter (mWcm2). Moreover, the power of a PV array can be estimated using the following (Singh,2013):

P=I-VP=NPIphV-NpIdVexpqVKTANs-1#(4)Setting (dPdV) = 0 yields the maximum power point voltage Vmax at the maximum power operating point (MPOP) as shown in equation 5:

expqVmaxKTANsqVmaxKTANs 1=Iph IdId #(5)The photocurrent acts as a function of the PV cell output voltage and is influenced by the load current concerning the levels of solar irradiation during operating conditions, this can be expressed in the following equation:

V=AKTqlnIph Id-IId-RsI (6)

The PV array’s I-V characteristics can be simulated by varying the solar radiation S and cell temperature T in equations 1 to 5. A PV panel ideally would usually operate at a voltage that maximizes the power output. This operation has been made possible through the usage of a maximum power point tracker (MPPT). Kuo et al. (2001) elaborate on the development of a novel MPPT controller for PV energy conversion systems. Additionally, Hua et al. (1998), presented a simple way of tracking these maximum power points where the systems are forced to operate near these points. The large and small signal models as well as the transfer function, are obtained through the energy conversion concept; the authors have validated the simulation results. In the absence of an MPPT, the PV panel runs at a position on the cell I-V curve that also corresponds to the load’s I-V characteristic. Five independent pieces of data are required to evaluate the variables in the previous equations. These variables are known to be the functions of the solar energy impinging on the cell and its temperature. For a given set of operating and field conditions, reference values of these variables are determined. The short circuit current, the open circuit voltage, and the voltage and current at maximum power point are three current voltage pairs that are typically available from the manufacturer’s standard rating conditions (SRC). The derivative of the power at the maximum power point can be set to zero to yield a fourth piece of data (Soto, 2006):

dIVdV=Imp-VmpdIdV=0 #(7)Where, dIdV is:

dIdV=-IdAeVmp ImpRsA-1Rsh1 IdRsAeVmp ImpRsA RsRsh #(8)Additionally, the open circuit voltage temperature coefficient is as follows:

Î¼Voc=dIdV=Voc,ref-Voc, TTc-T#(9)It is required to know Voc, T which is the open circuit voltage near the reference temperature at some cell temperature, to evaluate Î¼Voc numerically. For this purpose, the cell temperature is not of significance because T values between 1 and 10 K higher or lower than Tc produce essentially the same outcome (Soto, 2006).

Nguyen and Lehman (2006) focused on studying the influence of non-uniform changing shadows caused by passing clouds. They have suggested a modeling and computing approach (algorithm) to simulate that scenario and see its effects on the power output of a PV array. They found that the model they have developed can predict the power losses in individual solar cells, detect hotspots in shaded PV modules, and the power output. Their model is also capable of simulating solar PV arrays in a variety of topologies, including or excluding bypass diodes which function as a hotspot eliminator. Using the circuit equations of PV cells and effects of temperature variations and solar irradiation as a basis, Atlas and Ashraf (2007) designed a PV array simulation model to be utilized in MATLAB Simulink GUI environment. Gonzalez (2005) was interested in examining the behavior of PV cells at different temperatures and irradiance levels. He developed a circuit-based simulation and compared his results to that of the manufacturer’s published curve. Chowdhury et al. (2008) published a MATLAB Simulink model of a polycrystalline PV array with a DC voltage source. They discussed the model’s performance under different loads and weather circumstances, as well as how they used it to build a load-shedding strategy for a standalone PV system. The authors have also stated that the laboratory-based cell characterization work can be used to construct simpler low-burden mathematical models for numerous types of PV arrays. This will be extremely useful when simulating and studying distributed power systems and microgrids in the future. Chang et al. (2010) introduced a performance monitoring system of a model-based PV in LabVIEW with an online diagnosis capability. The data obtained was compared to estimated values derived from a single-diode practical PV system. Jiang et al. (2010) developed a better MATLAB Simulink simulation model for PV cells. The results of this newly developed model have been compared to that of current models. Additionally, the authors have also proved the model’s capacity to precisely simulate the I-V characteristics of an actual PV module. This newly suggested model can be used to build and simulate solar PV systems with various MPPT control approaches and power circuit topologies.

There have been some notable conclusions and trends based on the several studies mentioned previously on PV system modeling and analysis:

- The accuracy of the PV cell mathematical model and analysis can be enhanced by integrating diode saturation current, temperature dependency of photocurrent, and series and shunt resistance
- The model and analysis can be made more accurate by adding two parallel diodes with different saturation currents or by making the diode quality factor a configurable parameter
- The relationship between the photocurrent and temperature is linear
- In cases of high daily irradiation variability, energy output vs irradiation might help compare different modules
- The maximum power falls as the diode quality factor increases
- With an increase in atmospheric height, the direct normal irradiance’s absolute value rises
- As the temperature of the cell rises, the open circuit voltage decreases linearly, resulting in a loss in cell efficiency
- The value of series resistance should be kept as low as possible to extract the maximum power from the solar cell
- With increasing the environmental irradiation, the open circuit voltage rises logarithmically
- The power output of solar cells is determined by the irradiance distribution and temperature

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