Model the solar cells first and then to perform simulations, writes Chandrika Ramiah
In this article the behavior of the solar cell with respect to solar irradiance has been studied. Solar cells have been modeled, simulated and analyzed through graphical interpretations. Three types of photovoltaic modules from different companies (50Wp monocrystalline, 50Wp polycrystalline and 50Wp amorphous silicon) have been modeled based on the one-diode model and their maximum power point has been simulated in PSpice AD. The performance of the solar modules has been evaluated in terms of their response variables namely short-circuit current, open-circuit voltage, maximum power point voltage and maximum power point current with respect to real weather data.
Solar cells represent a promising alternative to the increasing demand of energy supply and will ultimately replace the fossil fuel energy sources, which in the long run are deemed to become scarce. There is therefore a need to profoundly analyze and understand how the solar cell operates as an optimal system.
When compared to fossil fuels, the solar cell is a relatively untapped source of energy and as a result there remains a lot of work to be done to make solar cells as efficient and reliable as possible. One approach to understanding the solar cell is by modeling and simulation.
Two common types of solar cells which dominate the market are the crystalline and thin-film PV cells. It becomes necessary to test these cells up to their optimum operating points under real weather conditions. In this respect, practical tests are not the best solution, since the ability to work with the solar cells and to obtain the expected results in practice makes it difficult, time-consuming and costly. An alternative is therefore to model the solar cells first and then to perform simulations without actually building them. After successfully modeling and simulating solar cells, it is then possible to develop methods to optimize system operation.
Monocrystalline silicon (mono-Si) Solar Cells
Mono-Si or single-crystal Si solar cells were first developed in the year 1955. They can be manufactured using either the Czochralski (Cz) or Float-zone (Fz) methods . A Mono-Si cell has a uniform dark blue as shown in the above figure and is very efficient; however it is costly, wasteful during fabrication, requires a lot of maintenance  and is affected by light induced degradation .
Amorphous silicon (a-Si) Solar cells
The history of a-Si solar cells started over 30 years ago with the first demonstration of an a-Si device in 1976 . A-Si cells are made by depositing a thin layer of amorphous silicon onto a substrate, which is a simpler and cheaper manufacturing process. However, amorphous silicon solar cells are less efficient than c-Si solar cells, and therefore require more solar panels . Also they have a shorter lifespan . The above figure shows an amorphous silicon solar cell.
Polycrystalline silicon (Polysilicon) Solar cells
Polysilicon were explored in the mid-1970’s  to reduce the cost of fabrication of mono-Si solar cells. For Polysilicon, molten silicon is solidified into square blocks that can be cut into square wafers. They have a typical blue appearance as shown in figure 2.4. Benefits include less space being wasted in module, low cost, little light degradation ; Still the solar cells are less efficient than mono-Si yet more efficient than thin-films, have a bad performance in low light  and require large panels .
Behavior of solar cells
Solar cells consist of a p-n junction manufactured in a thin layer of semiconducting material. The semiconductor electrons are located either in the valence band or the conducting band. The amount of energy from sunlight, called photons, is absorbed by the solar cell providing the semiconductor electrons with enough energy to move from the valence band to the conduction band. The electrons in the conducting band start to move freely creating electricity. This phenomenon is known as the photovoltaic effect. Most solar cells are doped to reduce the amount of energy required for the electrons to leave the valence band . The photovoltaic effect is illustrated in figure 4.
Figure 4: The photovoltaic effect in solar cells 
Current-Voltage characteristic of the solar cell
The current-voltage characteristic of a solar cell is non-linear, which makes it difficult to determine the maximum power point. A typical I-V characteristic of a solar cell is shown in figure 5.
Figure 5: I-V characteristic curve of a solar cell 
As can be observed from figure 5, the solar cell is characterized by two key parameters – namely the short-circuit current denoted by ISC and the open-circuit voltage denoted by VOC. In order for the solar cell to reach its maximum power point, it must be operated at or very close to the point where the product of voltage and output current is highest. This point is referred to as the maximum power point (MPP) and is located around the “knee” of the I-V characteristic curve.
Basic model of the solar cell
To properly model a solar cell it is important to understand how it operates. Diode modeling is used in the approximate electrical representation of the solar cell. Diode modeling refers to the use of mathematical models to approximate the actual behavior of real diodes to allow calculations and analysis.
The current-voltage characterization of solar cells under environmental conditions (e.g. irradiance) is usually represented by an equivalent circuit of one-diode model or to an equivalent circuit of two-diode model. As depicted by its name, a one-diode model circuit will consist of only one diode while a two-diode model also called double-diode model will consist of two diodes, and may also include shunt and series resistors. The one-diode model and the two-diode model both provide the same accuracy in measurement when modeling solar panels. However, a double-diode model will have more unknown parameters as compared to one-diode model and consequently the calculations become more complex . The one-diode model has been used in this research.
Figure 6: One-diode model 
The ideal equivalent of the solar cell model comprises of a current source and a diode. It is the simplest model and is characterized by the one-diode model. The photocurrent generated when sunlight hits the solar cell is signified by the current source and the p-n junction of the solar cell is represented by the diode . The above figure shows the solar cell model based on the one-diode model.
A single solar cell produces an output voltage less than 1V, about 0.6 V for a crystalline silicon cell and around 0.5V for a thin-film solar cell. When the power generated by one cell is not enough to power for instance a street lamp or a building, then solar cells are connected either in parallel or in series or both to form a solar module and if more power is required, solar modules are connected to form solar arrays and likewise solar panels are built by connecting solar arrays . Most of the commercially available crystalline PV modules consist of 36 or 72 series-connected solar cells and are able to charge 12V and 24V batteries respectively. When solar cells are connected in series, the output current remains constant and the output voltage is the sum the voltage of each solar cell. When solar cells are parallel–connected, the output voltage remains constant while the current becomes additive. Figure 7 shows the effect of connecting solar cells in series.
Figure 7: Series-connected PV cells to make up a PV module 
Modeling of the solar cell
The modeling of a system over-simplifies practical difficulties and in this research there is no exception to this criticism. To further investigate the solar cell, it is useful to create a model which is electrically equivalent and is based on discrete electrical components whose behavior is well-known. The electrical model of the solar cell which is used in this project is shown in figure 6. Solar cells are primarily made of semiconductor material that when exposed to sunlight induce a short-circuit current, which is proportional to the level of solar irradiance . In order to implement this in PSpice, the value of Isc is assigned to a G-device which is a voltage-controlled current source.
Figure 8: (a) Cell_1.lib subcircuit of a solar cell and (b) block diagram 
From the electrical characteristics of the solar cell it can be observed that is it a non-linear device and one approach to tackle non-linear circuits in PSpice is by defining subcircuits for the main circuit blocks. Using subcircuits to model a solar cell is very useful, especially when there are several solar cells connected in parallel, series or both. The PSpice model of the solar cell characterized by the one-diode model is shown in figure 8(a) and the block diagram of the subcircuit of the solar cell is shown in figure 8(b). All the nodes of the subcircuit are labeled and the reference node is the ground node.
The short-circuit current, Isc,represented by “girrad” in figure 8(a), is given by:
Isc = Jsc 1000 × A × G (1.0)
Where A is the surface area of one solar cell in meter square (m2 )
G is the irradiance level in watt per meter square (W/m2 ).
And Jsc is the short-circuit density in Ampere per meter square (A/m2 ) provided by the Solar Cell’s manufacturer’s datasheet at standard (AM1.5G, 1000 W/m2 , T= 25°C) conditions.
Selection of solar modules
Information about each solar module has been gathered through different manufacturers’ datasheets and the selected monocrystalline solar module is the SC Origin SPM050-M solar cell , Sunmodule SW 50 poly RMA  for the polycrystalline solar module and Uni-Solar Solar Laminate PVL-68 module for the amorphous silicon thin-film solar module . The crystalline solar modules are able to output a maximum power of 50W while the thin-film module is able to output a maximum power of 68W. The table below provides more details about the solar modules.
Solar Module Type
Maximum Power, PM (W)
Maximum Power Voltage, VM (V)
Maximum Power Current, IM (A)
Short-Circuit Current , ISC (A)
Open-Circuit Voltage, VOC (V)
Dimension of one solar cell, A (mm)
125 x 125
62 x 156
356 x 239
Number of Solar cells
Table 1: Description on the solar modules using information from datasheets
Calculation of parameters
The open-circuit voltage, VOC is the voltage with zero current and is given by equation (1.1)
The total power dissipated is calculated by taking into account that the maximum power occurs at, it is possible to derive the maximum voltage VM and current IM as
The voltage at maximum power point, VM is obtained by solving for equation 1.2 using the mathematical tool Matlab which is a high-level language and interactive environment for numerical computation, visualization, and programming .
The current at maximum power point, IM is given by equation (1.3) which equals
And finally the maximum power has been calculated using the following equation
Manipulation of real-weather data
Most specifically the solar irradiance values obtained between 5am to 6pm on the 26th of November 2012 has been used in this project. The measurements were taken by a pyrometer. The month of November has been chosen because Mauritius is in the summer season during this period of the year and thus it is expected to have a greater amount of sunlight on this day. However the values for solar irradiance were provided with an interval of one minute and therefore an average over a time of three hundred seconds or the equivalent of five minutes has been calculated. Henceforth the behavior of the solar cells/modules with respect to every interval of five minutes over thirteen and a half hours is studied.
Validation of the solar cell model
A mono-Si, polysilicon and a-Si solar cell is modeled as described previously, using electrical characteristics from its respective manufacturers’ datasheet – namely SC Origin SPM050-M datasheet, Sunmodule SW 50 poly RMA and Uni-Solar Solar Laminate PVL-68 solar module datasheet. To be able to use the solar cell model further in the project, values obtained during simulation must closely match the ratings in the manufacturers’ datasheet.
The following figure shows the simulation result of the I-V characteristic of a SC Origin SPM050-M solar cell for irradiance values of 600, 800 and 1000 W/M2. The mono-Si module consists of thirty-six solar cells connected in series and therefore the short-circuit current of one cell is the same as that of the module and is equal to 2.86A while the voltage of one cell is about 55mV using the related equation. As it can be observed from the plot the short-circuit current, ISC, when the irradiance level is highest is equal to 2.86A and the open-circuit voltage, VOC is around the 550mV which clearly corresponds to the rated value on the manufacturer’s datasheet. The simulation has been repeated for the polysilicon and amorphous-silicon solar cells model.
Figure 9: I-V plots for an SC Origin SPM050-M solar cell
Simulation of Solar modules in PSpice AD
The strategy of modeling a PV module is no different from modeling a PV cell. It uses the same PV cell model. The parameters are all the same except for a voltage parameter (such as open-circuit voltage) which is different and must be divided by the number of cells. In this project both the crystalline modules and the amorphous module are made up of series-connected solar cells. As mentioned in chapter two, when solar cells are connected in series the current remains constant and the voltage of each solar cell adds up.
Figure 10: Schematic for an association of two series-connected solar cells 
The schematic illustrating the circuit representation of the series connection of two solar cells is shown in figure 10. It can be observed that the use of subcircuits simplifies the development, analysis and correction of the solar cell model rather than having a single circuit block which represents the module.
Simulation of the maximum power point
The maximum power point of the SC Origin SPM050-M, Sunmodule SW 50 poly RMA and Uni-Solar Solar Laminate PVL-68 solar models is simulated in PSpice based on the concepts covered so far. The mono-Si and polysilicon solar module are both rated at fifty Watt-Peak (50Wp) and consist of thirty-six cells connected in series and the a-Si solar module is rated at sixty-eight (68Wp) and consists of eleven series-connected solar cells. The PV modules will therefore comprise of an equal number of subcircuit files as the solar cells present in the modules. The subcircuit netlist constitutes values of the time period over which solar irradiance has been considered along with the voltage and current at maximum power point. The circuit netlist which is the main building block of the solar module includes the subcircuit files and commands about the type of analysis that is performed. The simulations of IM and VM for the solar modules are performed and the maximum power point attained by the modules with respect to the solar irradiance is obtained by the product of the current and voltage at MPP. The following figures show the results obtained for the simulation of the MPP for the solar modules
- The following figure illustrates the PSpice plots generated for the mono-crystalline solar module where the maximum power is about 51.461 Watts and is given by the blue line. The trace for the power is obtained by the product of the current to the summation of the maximum power point voltage because of the series-connected PV cells. The current and voltage at maximum power point are given by the red and green line correspondingly.
Figure 11: PSpice plot for the maximum power point of the mono-si solar module, PM including IM and VM
- The simulated maximum power point obtained for the polysilicon solar module is 53.167 Watts.
- The following figure illustrates the PSpice plots generated for the amorphous silicon thin-film solar module where the maximum power is about 78.354 Watts.
- As can be shown in the above figures, the current at maximum power point attain peak values at different instants. This is because the current, IM occurs under short-circuit conditions and is directly affected by fluctuations in the irradiance level as shown by equation 3.1. Therefore when irradiance level increases especially during peak hours of sunlight, IM reaches peak values and when irradiance decreases so does the current .
- The effect of irradiance on the voltage, VM is demonstrated by the green line on the PSpice plots. It can be observed that the voltage remains more or less constant. This is because of the logarithmic relation between the irradiance and the output voltage .
- As noted for PM, as irradiance increases, it also rises. This is because the power is directly proportional to the modules’ current and voltage where current is greatly affected by irradiance and voltage is only slightly altered.
- It can also be observed that the simulated value for the peak power differs from the rated value provided by the manufacturers’ datasheet. For instance the simulated value for the mono-Si solar module is about 51.461 Watts and that of the polysilicon solar module is nearly 53.167 Watts instead of 50 Watts each and likewise for the a-Si PV module the simulated peak value is about 78.354 Watts instead of 68 Watts. These differences can occur when the Standard Test conditions (STC) are no longer respected. As mentioned earlier the values of the maximum power point current and voltage are both derived from the two key parameters namely short-circuit current, ISC and open-circuit voltage, VOC which originate from the manufacturer’s datasheet at standard test conditions(STC): irradiance of 1000 W/m2, air mass 1.5 and cell temperature 25ºC. However the operation of a module outside STC affects VOC and ISC and consequently affecting VM, IM as well as PM. In this project the values obtained for the irradiance level at various time intervals exceed 1000 W/m2 and subsequently affecting the simulated values.
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