Photovoltaic Panel Simulation User's Guide

Photovoltaic system

Photovoltaics is the art of converting sunlight directly into electricity using solar cells.
Solar cells are manufactured from semiconductor material, that is, material which acts as an insulator at low temperatures, but as a conductor when energy or heat is available. At present most solar cells are silicon based, since this is the most mature technology.
A silicon solar cell is a diode formed by joining p-type (typically boron doped) and n-type (typically phosphorous doped) silicon.
Light shining on such a cell can behave in a number of ways as illustrated in fig. 1. To maximize the power rating of a solar cell, it must be designed so as to maximize desired absorption (3) and absorption after reflection (5).

Fig. 1. Behavior of light shining on solar cell:
1. Reflection and absorption at top contact;
2. Reflection at cell surface;
3. Desired absorption;
4. Reflection from rear out of cell-weakly absorbed light only;
5. Absorption after reflection;
6. Absorption in rear contact.

A typical representation of an IV curve for a photovoltaic cell, showing short circuit current (Isc) and open circuit voltage (Voc) points, as well as the maximum power (Vmp Imp) is shown in Fig. 2.

Fig. 2. IV curve.

The two limiting parameters used to characterize the output of solar cells for given irradiance, operating temperature and area are:

Short-circuit current, Isc, the maximum current, at zero voltage. Note that Isc is directly proportional to the available sunlight.

Open-circuit voltage, Voc, the maximum voltage at zero current. Voc increases logarithmically with increased sunlight. This characteristic makes solar cells ideally suited to battery charging.

For each point on the IV curve, the product of the current and voltage represents the power output for that operating condition. A solar cell can also be characterized by its maximum power point, when the product Vmp Imp is at its maximum value. The maximum power output of a cell is graphically given by the largest rectangle that can be filled under the IV curve.

Effect of temperature

The operating temperature of solar cells is determined by the ambient air temperature, by the characteristics of the module in which it is encapsulated, by the intensity of sunlight falling on the module, and by other variables such as wind velocity.
The main effect of increasing temperature for silicon solar cells is a reduction in Voc and hence the cell output as shown in Fig. 3.

Fig. 3. The effect of temperature on the IV characteristics of a solar cell.

PV cell interconnection and module design

Solar cells are rarely used individually. Rather, cells with similar characteristics are connected and encapsulated to form modules (arrays) which, in turn, are the basic building blocks of solar arrays.
As maximum voltage from a single silicon cell is only about 600 mV, cells are connected in series to obtain the desired voltage. Usually about 36 cells are used for a nominal 12 V charging system.
Under peak sunlight (1 W/m^2) the maximum current delivered by a cell is approximately 30 mA/cm^2. Cells are therefore paralleled to obtain the desired current.

Fig. 4. Cells in series and in parallel.

A typical 36 cell module based on screen printed silicon cell technology has the cells series connected to suit the charging of 12 volt battery.

The typical characteristics for each cell would be:
Voc = 600 mV (25 C)
Isc = 3.0 Amps
Vmp = 500 mV (25 C)
Area = 100 cm^2

Therefore 36 cells in series give:
Voc = 21.6 Volts (25 C)
Isc = 3.0 Amps
Vmp = 18 Volts (25 C)
Imp = 2.7 Amps

Arrays structures

1) Fixed arrays.
Fixed arrays are the most commonly used. The modules are placed on a support structure, facing north in the southern hemisphere and south in the northern hemisphere, at an angle determined by the latitude. The angle chosen depends upon the seasonal power requirement. For example, for the most constant output over the year, an angle of latitude plus 23 degrees is used, which places the array at right angles to the Sun's rays midwinter.

2) Seasonally adjusted tilting.
The array angle can be changed manually, for example, monthly or seasonally, to allow for the changing solar elevation at noon. This is a relatively simple way of increasing output and does not add significantly to the cost. Flexibility in tilt angles for seasonal changes is marginally economical for small systems. For midlatitude locations, adjustment to the tilt angles every 3 months increases the annual energy production by less than 5%.

3) One axis tracking.
The array can be tilted automatically every hour, along a single axis, to follow the Sun from east to west. Output can be increased by about 20% compared to a fixed array.

4) Two axis tracking.
Power output can be increased by 40% compared to fixed array, by tracking the Sun along the north-south and the east-west axes.

5) Concentrator arrays
Concentrator array use optical lenses and mirrors to focus sunlight onto small areas of high efficiency cells.

Thermal considerations

It is desirable for modules to operate at as low a temperature as possible, since:

1) cell output is increased at lower temperatures;
2) thermal cycles and stress are reduced;
3) degradation rates approximately double for each 10 degrees C increase in temperature.

The modules and the solar array must therefore take full advantage of radiative, conductive and convective cooling and absorb the minimum of unused radiation.
Different encapsulation types, giving vastly different thermal properties, have been utilized by manufacturers to meet different market needs.

Equation to calculate the output power

To calculate the output power generated by a photovoltaic panel the program uses the following equation:

power = n_modules_series * (Vmp - Vtc * (working_temp - standard_temp)) * n_modules_parallel * Imp * irrad;

where:
n_modules_series is the number of modules in series;
Vmp is the voltage at maximum power point (Volts);
Vtc is the voltage temperature coefficient (Volts/ deg C);
working_temp is the working temperature (deg C);
standard_temp is the standard temperature (deg C);
n_modules_parallel is the number of modules in parallel;
Imp is the current at maximum power point (Amps);
irrad is the normalized irradiations, it means that if the irradiations are measured in Watth/m^2 you have to divide that one per 1.000 Watth/m^2, istead if it is measured in kWatth/m^2day you have to divide that one per 1 kWatth/m^2day.

Photovoltaic panel simulation applet's buttons

In the photovoltaic panel simulation applet you can navigate in time and space.
You can move in time using the buttons situated on the bottom of the picture. You can stop, play forward or play back the simulation.
You can move in space using the buttons situated on the right of the simulation picture to rotate and to tilt the Earth, it is also possible zoom in and zoom out the simulation picture using the corresponding buttons.
You can set the simulation type, the month, the day and the hour by pushing the mouse button down on the simulation type button, it's possible to select a different location and to input a new location by the location button. It is also possible to configure the main characteristics for the photovoltaic panel, like: number of modules in series, number of modules in parallel, voltage at maximum power point and current at maximum power point.