The photovoltaic panel

The photovoltaic panel is a device designed to convert energy emitted by the Sun, in the form of light (electromagnetic waves), into electrical energy. The main element of a solar or photovoltaic panel is the solar or photovoltaic cell.

Photovoltaic cell

A solar cell, also known as a photovoltaic cell, is an electronic device that directly converts solar light into electricity. The material used to make the solar cell is most often a semiconductor, with silicon crystal being the base. It is doped (impurities are added) to modify its electrical properties. The semiconductor is a PN junction where each layer is doped differently. At the top is the N layer, with excess electrons (which are negative charges), doped with phosphorus or arsenic, while the bottom layer is the P layer, with holes (which are positive charges), doped with boron or gallium.

Figure 1. Section of a photovoltaic cell ¹

Under the action of photons, corresponding to solar light radiation, a direct current will be generated as a result of the appearance of a potential difference. The absorbed photons will be captured by the electrons in the N layer, allowing them to overcome the potential barrier and thus generate a continuous electric current. To capture this electric current, grids with electrodes are placed on the two layers N and P. In addition, the upper electrode N will be treated in such a way as to maximize the absorption of photons from the sun.

Technologies for the production of solar cells from silicon

The most commonly used material for the production of solar/photovoltaic cells is silicon. From silicon, depending on how the crystals are associated, several types of photovoltaic cells can be produced, thus we encounter cells ², ³:

• Monocrystalline

Monocrystalline solar cells were the first to be produced, and they are made from so-called wafers, which represent a block of silicon from a single crystal. Due to the cylindrical shape of the silicon crystal, after processing and cutting, they have a round or pseudo-square shape.

It presents a higher efficiency compared to other silicon cells of approximately 12[%]-16[%], but also a higher price.

Figure 2. Monocrystalline Silicon ³

Figure 3. Monocrystalline Cell ³

• Multicrystalline

Multicrystalline cells, also known as polycrystalline cells, are made from a block of silicon where crystallization has occurred from multiple silicon crystals with different orientations. These can be made through a casting process and are therefore cheaper than monocrystalline ones.

They have a lower efficiency than monocrystalline ones, approximately 11[%]-13[%].

Figure 4. Polycrystalline Cell ³

• Amorphous

This type of cells is made on a glass or synthetic material substrate, onto which silicon vapor is deposited through a condensation process, and they are cheaper than cells made from crystals.

They have a lower efficiency, approximately 5[%]-10[%], compared to cells made from crystals, but they have the advantage of a lower price and good performance in low light, being most often used in electronic devices (watches, calculators, etc.).

Technology	Typical efficiency [%]	Theoretical efficiency [%]
Monocrystalline	12-16	24
Polycrystalline	11-13	18.6
Amorphous	5-10	12.7

Table 1. Efficiency of cells depending on technology ²

Construction of panels

The photovoltaic panel consists mainly of:

• Photovoltaic cells;
• Electrical conductors for collecting electrical energy from the cells;
• Schottky diode, for establishing the direction of current through the panel;
• The frame in which the photovoltaic cells are fixed.

For practical use, photovoltaic cells are connected together in modules called photovoltaic panels. Such a panel typically contains 36 cells, found in 12[V] systems, or 60 or 72 cells. The panels themselves have terminals/connections that end with connectors, making it easy to connect them in series.

Figure 5. Photovoltaic panel made with 60 cells

The technical characteristics of such a panel are:
\(P_{max}=245[W]\) – Maximum power;
\(U_{MPP}=29.9[V]\) – Voltage at maximum power;
\(U_{OC}=37.4[V]\) – Open-circuit voltage;
\(I_{MPP}=8.1[A]\) – Current at maximum power;
\(I_{sc}=9.7[A]\) – Short-circuit current;

The characteristics are valid for a standard solar irradiance of \(1000[W/m^2]\) and a panel temperature of \(25[^0C]\).

Figure 6. The technical characteristics of a panel made of 60 cells

The panel has its 60 cells divided into 3 groups. Each grouping made of 20 cells is connected in series with the next one, and each group is connected to a diode in an antiparallel configuration. The diodes used are Schottky type power diodes, which serve to prevent the group of 20 cells from becoming an energy consumer instead of an energy generator in case the panel is partially shaded. Blocking diodes are generally also Schottky power diodes, serving to block the reverse flow of current from the batteries to the panel during the evening ⁴.

.	Figure 7. The junction box with bypass diodes of the solar panel 4

Modeling for the simulation of a solar panel

Starting from the equivalent circuit of a solar cell, a model/library can be created for simulation and analysis in simulation programs like spice, in this case, LTspice.

Figure 8. Equivalent electrical circuit of a solar cell ⁵

The above figure presents the elements and connections of the main components of a photovoltaic cell. The PN junction is represented by the diode, the electrical connections, and the conductors that add electrical resistance are represented by \(R_s\), while the resistance \(R_{sh}\) in parallel with the diode represents a parasitic resistance. From the circuit analysis, we find that an ideal cell will have a resistance \(R_s\) of zero value, while the resistance \(R_{sh}\) will have an infinite value.

In LTspice, the electrical schematic of a cell, presented above, will be transposed, and to account for the number of cells associated with a photovoltaic panel, we will create a parameter n that will multiply the number of cells associated with the panel by the voltage at the output of the panel.

Figure 9. The electrical schema, in LTspice, of a solar panel model

The netlist file of the above circuit is as follows:

* C:\Users\Florin\Master_RCC\Disertatie\PV-Spice_files\Fotovoltaic\Model_panou_solar.asc
D Isc 0 Dcelula
Rsh Isc 0 {Rsh}
Rs cell Isc {Rs}
Fcelula 0 celula Eps 1
Eps Vps+ Vps- celula 0 {n}
.model D D
.lib C:\Users\Florin\Documents\LTspiceXVII\lib\cmp\standard.dio
.model Dcelula D IS={IS}
.param Rs=0.005
.param Rsh=100
.param IS=1.5nA
.param n=60
* Isc reprezinta\ncurentul de scurtcircuit\nal panoului si este direct\nproportional cu iradierea\nsoarelui
* Tensiunea de ieșire\ndin panoul fotovoltaic
.backanno
.end

The circuit has been designed parametrically so that in the future the spice command .step, related to a parameter, can be easily used to analyze its influence on the results.

The parameter \(Rs\) represents the series resistance (\(R_s\)), while \(R{sh}\) represents the shunt resistance (\(R_{sh}\)) mounted in parallel with the diode, and \(n\) is the number of cells, which is related to \(E{ps}\) (Voltage dependent voltage). \(E{ps}\) will output a voltage that will depend on the input voltage multiplied by the parameter \(n\). \(F{cell}\) (Current dependent current) will generate a current that will be equal to a multiple (in this case it is 1) of the current through the voltage source \(E{ps}\).

Using the circuit above, a model will be created in a library, using the command from the menu Hierarchy->Open this Sheet’s Symbol. The library thus created will be used in future simulations.

To verify the created model, the following presents the circuit used for simulating the created library, in order to test the characteristics of the solar panel with 60 cells that will supply a load/battery composed of a series resistance \(R{sarc}\) of 10[mΩ] and a source \(Vps\) of 24[V].

Figure 10. The electrical schema of the simulation using the model created earlier

The plotted characteristics represent the power and current at the output of the panel under different sunlight illuminations. The current source \(Isc\) will generate a current that is proportional to solar irradiation. In this case, \(Isc\) is the value of the short-circuit current of the panel above.

The netlist file of the simulation is as follows:

* C:\Users\Florin\Master_RCC\Disertatie\PV-Spice_files\Fotovoltaic\TesPanou.asc
XX1 N002 ps 0 model_panou_solar
Isc 0 N002 9.7
Rsarc N001 ps 0.01
Vps N001 0 24
* block symbol definitions
.subckt model_panou_solar Isc Vps+ Vps-
D Isc 0 Dcelula
Rsh Isc 0 {Rsh}
Rs cell Isc {Rs}
Fcelula 0 cell Eps 1
Eps Vps+ Vps- cell 0 {n}
.model Dcelula D IS={IS}
.param Rs=0.005
.param Rsh=100
.param IS=1.5nA
.param n=60
.ends model_panou_solar
.model D D
.lib C:\Users\Florin\Documents\LTspiceXVII\lib\cmp\standard.dio
.dc Vps 0 40 0.01 Isc 1 9.7 1
.backanno
.end

The technical parameters of photovoltaic panels are listed by manufacturers for a standard irradiation of \(1000 [W/m^2]\), and after 25 years of use, they still retain 70[%]-80[%] of their initial characteristics. If the location has higher irradiation and the panel will correspondingly output a higher power, proportional to the irradiation.

	Figure 11. The solar energy maps of Romania6

From the charts above, we can observe that for the location of Suceava, we have an irradiation of approximately \(1200[W/m^2]\), which will result in an approximate increase of 20[%] in the power generated by the photovoltaic panels.