**5. Educational application**

The model shown in Section 4 can be used for the formation of PV system. In particular, us‐ ing subcircuit for an attractive presentation for the student, [10]. In addition to evaluating the effects of: association series and parallel, potential losses, weather conditions, non-ideali‐ ty of photovoltaic cells and effect of partial shadow. Figure 7 shows steps for modelling by subcircuits of a PV cell and module, first represented a equivalent circuit and include pa‐ rameters gets of datasheet, second create a symbol to represented a PV cell, third the subcir‐ cuit used to external variables for irradiance (*G*) and cell temperature (*Tc*), fourth associate cells to build a PV module, and finally create a symbol to represented a PV module.

To create a subcircuit needs connection for output PV cell, after to select all component of equivalent circuit (figure 3) the output connection of PV cell (in series with *Rs* for positive con‐ nection) connects used insert port (figure 8). Once finish equivalent circuit can be edit repre‐ sentation of subcircuit pressing *F9*, for edit representation can be used painting library, [13].

Model for PV module can be create using PV cell subcircuit and connection in series and parallel, for example a PV module for 12V nominal voltage can be formed by 36 PV cells connects in series, in figure 9 shows connections of PV module with 2 pass diodes and exter‐ nal ports connections (positive for *P1* and negative for *P2*). Representation used for PV cell and module shows on figure 7, after can be used subcircuit of PV cell or module on different practices.

**Figure 7.** Steps modeling subcircuit

Further, if changes value *Tamb* variable on eqn2 (figure3), change ambient temperature and therefore the cell temperature condition based on equations 1*0 and* 11. For example on figure 6 shows *IV curve* to different values of cell temperature at the same value of irradiance

The model shown in Section 4 can be used for the formation of PV system. In particular, us‐ ing subcircuit for an attractive presentation for the student, [10]. In addition to evaluating the effects of: association series and parallel, potential losses, weather conditions, non-ideali‐ ty of photovoltaic cells and effect of partial shadow. Figure 7 shows steps for modelling by subcircuits of a PV cell and module, first represented a equivalent circuit and include pa‐ rameters gets of datasheet, second create a symbol to represented a PV cell, third the subcir‐ cuit used to external variables for irradiance (*G*) and cell temperature (*Tc*), fourth associate

To create a subcircuit needs connection for output PV cell, after to select all component of equivalent circuit (figure 3) the output connection of PV cell (in series with *Rs* for positive con‐ nection) connects used insert port (figure 8). Once finish equivalent circuit can be edit repre‐ sentation of subcircuit pressing *F9*, for edit representation can be used painting library, [13].

Model for PV module can be create using PV cell subcircuit and connection in series and parallel, for example a PV module for 12V nominal voltage can be formed by 36 PV cells connects in series, in figure 9 shows connections of PV module with 2 pass diodes and exter‐ nal ports connections (positive for *P1* and negative for *P2*). Representation used for PV cell

cells to build a PV module, and finally create a symbol to represented a PV module.

): *50ºC* (*T\_50*), *25ºC* (*T\_25*) and *0ºC* (*T\_0*). Then, combining the two variables can

(*1000W/m2*

adjust weather conditions.

128 New Developments in Renewable Energy

**Figure 6.** IV Curve for different values of cell temperature

**5. Educational application**

**Figure 8.** Insert connection to subcircuit

Practiques Descriptions

Effect of irradiance and temperature on PV cell

Partial and total shadowing

Using bypass diodes and losses from partial shading on PV

Voltage drop in PV cells

connection

effect

module

Obtaining IV Curve This practice consists in the practical realization of obtaining an IV curve, connecting a

Modeling of Photovoltaic Cell Using Free Software Application for Training and Design Circuit in Photovoltaic...

Connecting PV cells In this practice the student performed tests: vacuum, short circuit and load. Also,

practice can be extent compare with a real measurement.

photovoltaic cell.

practice of PV module.

shadow problem on PV cell.

compare results.

**Table 2.** Examples of practical using modeling and GPL application

and irradiance (variable *G* in *W/m2*

measurement of short circuit current.

diode. After the student compare results.

Connection blocking diodes This practice is to see the effect and necessity of blocking diodes. Must connect a

Mismatch losses in PV Module This practice is to see effects to use different PV cells to manufacturing PV module,

resistor to photovoltaic cell, how it is done in laboratory, the student modify the values of resistance load and take measurements of voltage and current generate by

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131

performed measurements with various connections: serial, parallel and mixed. This

This practice is to see the effects on curve IV by changing irradiance and temperature. Simulation can be used by scanning parameter to be directly represents the curve IV and only change the values of irradiance and cell temperature. Can use the same

This practice associated series and parallel solar cells and see the effects for partial shadowing about currentand voltage generate by PV cell. After can repeat practice for total shadowing effect. After, the student can extract conclusion about the

This practice is to see the utility about bypass diodes in the manufacturing on PV module. Must create two models about PV module, one with diode and other without

circuit PV cell and battery between blocking diode, after remove blocking diode and

must create two models about PV module, one with ideal PV cells and other with

This practice is to see the losses associated with wiring to connect photovoltaic devices. Can show the effect of using one or another section, and the length between the module and circuit regulator. It creates a new subcircuit corresponding to the

) cell, see the effects of partial shading on the association

different values of short current. After the student compare results.

calculation of the resistance of the wiring with copper conductors.

Figure 10 shows several examples for use subcircuits model for educational, and are directly applicable to any practices described. As parameters such as temperature (variable *Tc* in *ºC*)

of cells and the use of bypass diodes in the manufacture of photovoltaic modules, and the

**Figure 9.** Model of PV module based on subcircuit PV cell

Then, student works directly with subcicuits independently of equivalent circuit model, be‐ cause student can be used the same representation for different PV cells. The material used will consist of a compressed file, which contains a project *QUCS* (for example *practices\_so‐ lar\_prj.rar*), this file contains a number of files to be need for practical work (files used on *QUCS* use extension *sch* and a project contains all files on *QUCS* directory). The practices developed show in table 2, for study for photovoltaic training on stage generation, after can be complete with model of all components on photovoltaic system (battery, regulator or in‐ verter) and can be used on renewable energy training. Practices on table 2 can be complete with a previous work: select values for equivalent circuit and introduction of *QUCS*.

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**Table 2.** Examples of practical using modeling and GPL application

**Figure 9.** Model of PV module based on subcircuit PV cell

130 New Developments in Renewable Energy

Then, student works directly with subcicuits independently of equivalent circuit model, be‐ cause student can be used the same representation for different PV cells. The material used will consist of a compressed file, which contains a project *QUCS* (for example *practices\_so‐ lar\_prj.rar*), this file contains a number of files to be need for practical work (files used on *QUCS* use extension *sch* and a project contains all files on *QUCS* directory). The practices developed show in table 2, for study for photovoltaic training on stage generation, after can be complete with model of all components on photovoltaic system (battery, regulator or in‐ verter) and can be used on renewable energy training. Practices on table 2 can be complete

with a previous work: select values for equivalent circuit and introduction of *QUCS*.

Figure 10 shows several examples for use subcircuits model for educational, and are directly applicable to any practices described. As parameters such as temperature (variable *Tc* in *ºC*) and irradiance (variable *G* in *W/m2* ) cell, see the effects of partial shading on the association of cells and the use of bypass diodes in the manufacture of photovoltaic modules, and the measurement of short circuit current.

**Figure 11.** Component library for QUCS

Other application, its predict power generation from PV cells and modules, using a variable parameter for irradiance and ambient temperature. In addition, can be include partial shad‐ ow for same object (for example: tree or building) in PV grid connection or stand-alone.

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133

For example, in figure 12a shows curve of irradiation variation of irradiance (*G*) around day. Value used can be extracted to Photovoltaic Geographical Information Systems (*PVGIS*) [18] mean values per moths. After connection a constant resistor to photovoltaic cell and get out‐ puts: power, voltage and current (figure 12b). After can complete modifying load connected. Also, can included ambient temperature around day using variable *TC*. The PV cell charac‐

Other example shows on figure 13 to use PV cell model for simulate a circuit control to obtain the maximum power point to PV cell. In figure 13a show a subcircuit connect to dc converter, and figure 13b show output voltage and control signal, the output is controlled modify duty cycle, then the duty cycle decrease when the output voltage arrive to maximum power voltage

teristics used on figure 12 is: *3,27A* for *ISC* and *0,6V* for *VOC* on *SCM*.

**Figure 12.** Variation Irradiance (G) around day with a constant load

**Figure 10.** Examples for subcircuit model

### **6. Design circuit application**

The availability of the model described in section 4, allows design circuits power manage‐ ment when energy source are PV cells or modules. For example, in power supply of sensor nodes, [14], to design efficient harvesting energy control, because *QUCS* dispose different electronic components for simulation by means of changing parameters to adjust to real component. *QUCS* has generic devices electronic *on non lineal* library and adjust parameter on properties menu to adjust real component, or use component library (selected on *Tools* menu or *Ctrl+5*) for used component with properties adjusted to real device (figure 11).

Also, working in selection PV cells to power supplies performing a comparative commercial device to adapted for applications at climatologic conditions of system localization, for ex‐ ample to study PV cell to weather station [15] or irrigation actuator [16]. Further, to test reg‐ ulator circuit using in stand-alone PV system and control circuit to obtain maximum power point tracker, [17].

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**Figure 11.** Component library for QUCS

**Figure 10.** Examples for subcircuit model

132 New Developments in Renewable Energy

**6. Design circuit application**

point tracker, [17].

The availability of the model described in section 4, allows design circuits power manage‐ ment when energy source are PV cells or modules. For example, in power supply of sensor nodes, [14], to design efficient harvesting energy control, because *QUCS* dispose different electronic components for simulation by means of changing parameters to adjust to real component. *QUCS* has generic devices electronic *on non lineal* library and adjust parameter on properties menu to adjust real component, or use component library (selected on *Tools* menu or *Ctrl+5*) for used component with properties adjusted to real device (figure 11).

Also, working in selection PV cells to power supplies performing a comparative commercial device to adapted for applications at climatologic conditions of system localization, for ex‐ ample to study PV cell to weather station [15] or irrigation actuator [16]. Further, to test reg‐ ulator circuit using in stand-alone PV system and control circuit to obtain maximum power Other application, its predict power generation from PV cells and modules, using a variable parameter for irradiance and ambient temperature. In addition, can be include partial shad‐ ow for same object (for example: tree or building) in PV grid connection or stand-alone.

For example, in figure 12a shows curve of irradiation variation of irradiance (*G*) around day. Value used can be extracted to Photovoltaic Geographical Information Systems (*PVGIS*) [18] mean values per moths. After connection a constant resistor to photovoltaic cell and get out‐ puts: power, voltage and current (figure 12b). After can complete modifying load connected. Also, can included ambient temperature around day using variable *TC*. The PV cell charac‐ teristics used on figure 12 is: *3,27A* for *ISC* and *0,6V* for *VOC* on *SCM*.

**Figure 12.** Variation Irradiance (G) around day with a constant load

Other example shows on figure 13 to use PV cell model for simulate a circuit control to obtain the maximum power point to PV cell. In figure 13a show a subcircuit connect to dc converter, and figure 13b show output voltage and control signal, the output is controlled modify duty cycle, then the duty cycle decrease when the output voltage arrive to maximum power voltage and increase when output voltage away from maximum power voltage. The PV cell character‐ istics used on figure 13 is: *150mA* for *ISC* and *0,62V* for *VOC* on *SCM*.

**7. PV cells of module**

inside module.

ies on a string.

allel with 1 diode pass.

Some case has available information of PV module on *SCM* to emulate PV module (figure 15), then needs calculate values for PV cells: division between module open voltage (*VOC\_MODULE*) and number PV cells series (*NCELLS\_SERIES*) to obtein open voltage of cell (*VOC\_CELL*), division between module current short (*ISC\_MODULE*) and number of strings cells connection (*NCELLS\_STRINGS*) to obtain current short of cell (*ISC\_CELL*), and repeat by module maximum val‐ ues of voltage (*VMAX\_MODULE*) and current (*VMAX\_MODULE*) to obtain maximum values of voltage

Modeling of Photovoltaic Cell Using Free Software Application for Training and Design Circuit in Photovoltaic...

\_

\_

\_ *SC MODULE*

\_

\_

Values obtained on equations 1*3 and* 14 used to obtain: *voc*, *RS*, *IL*, and *I0*, on *equa‐ tions*: *6*, *8*, *9* and *10*. The values obtained on equations 13 to *16* used to obtain *FF* on equation 7. This approximation is based on a PV module is union of PV cells connect‐ ed in series and parallel strings. Model of PV module included connections cells loss

On figure 15 shows an example for PV module based on subcircuit on PV cells, char‐ acteristic of PV module on *SCM* is: *150W* to *PMAX*, *22,6V* to *VOC*, *8,7A* to *ISC*, *18,5V* to *VMAX* and *8,12A* for *IMAX*. The module used in figure 15 used 36 cells connected in ser‐

Advantage to use model PV cells on model PV module is that change parameter of ir‐ radiation and temperature by cell (figure 7), and so study effects: partial shading, num‐ ber pass diode, different connections of pass diode, hot cells, etc. Also can be study effect on mismatch on module used PV cell with different electrical characteristics. For example on figure 16 show effects of partial shading on module using 2 diodes pass (figure 9): figure 16a without shadow, figure 16b shadow affect to same number of cell connects on parallel by diode and figure 16c shadow affect only to cells connects on par‐

\_ *MAX MODULE*

*CELLS STRINGS*

\_ *MAX MODULE*

*CELLS SERIES*

*CELLS STRINGS*

*V*

*I*

*V*

*I*

\_ *OC MODULE*

*CELLS SERIES*

*<sup>N</sup>*<sup>=</sup> (13)

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135

*<sup>N</sup>*<sup>=</sup> (14)

*<sup>N</sup>* <sup>=</sup> (15)

*<sup>N</sup>*<sup>=</sup> (16)

(*VMAX\_CELL*) and current (*VMAX\_CELL*) of cell; equations 13 to *16* respectively.

\_

\_

*SC CELL*

\_

*MAX CELL*

\_

*MAX CELL*

*V*

*I*

*V*

*I*

*OC CELL*

**Figure 13.** Used model to study circuit control of PV cell

Also, model PV cell can be used to study number of PV cells need to supply energy to the system, for example figure 14 show *16 PV cells* for simple circuit supply of *5V* source formed by: block diode (*D1*) and a regulator circuit (*LM140*).Then, change number of PV cells and configure climatic conditions (Irradiance and temperature) can see if has enough or need more PV cells, too if has more PV cells that is need. On figure 14 show: output voltage (*V\_load.V*), output current (*I\_load.I*) and voltage cells (*V\_cells.V*), to different values of irradi‐ ation, therefore study irradiance needs to obtain *5V* on load resistor. Conclusions on figure 14 is than needs *16 PV cells* on series and irradiance value around *500-550 W/m2* or higher to obtain *5V* and *0,5A* output (on load). The PV cell characteristics used on figure 14 is: *1A* for *ISC* and *0,6V* for *VOC* on *SCM*.

**Figure 14.** Study irradiation for simple regulator circuit
