## Page content – 2.2.1. The Surface Area of the Photovoltaic Array

### 2.2.1. The Surface Area of the Photovoltaic Array

The insolation duration of the PV array that designed for the PV power plants can be defined based on the solar radiations that reach to the array in one day, at the optimum angle;

where;
t = the insolation (sunshine) duration of the panel(h)
φ = optimum angle (˚)
Es = solar radiation energy (Wh/m2)

The maximum power that can be obtained from the photovoltaic array can be determined by depending on the highest current and the battery voltage that produced of the array at the temperature of 25 ℃. This can be expressed as:

where;
PPV = maximum power amount that can be obtained from the array (W)
IP(max) = maximum current amount that produced by the array (A)
VB = the voltage value of the battery (V)

The energy amount that can be obtained from photovoltaic array on a daily basis depends on insolation duration of the array and the maximum available power;

where;
EPV = the amount of electricity that can be gained from the array (Wh)

The amount of energy that can be obtained from a photovoltaic array reduces depending on the efficiency of the equipment in the PV system is;

where;
ηe = the efficiency of the equipment
ηi = the efficiency of the inverter
ηccd = the efficiency charging control device
ηB = the efficiency of the battery
ηca = the efficiency of the cable

The efficiency of the photovoltaic array varies depending on the temperature of the cell. Catalog data relating to the efficiency of photovoltaic cells are determined based on measured values at a constant temperature of 25 ℃ in laboratory conditions. Therefore, in case of a change of the outside temperature, the efficiency of the PV array also changes. During the experiments that carried out in laboratory, the temperature of a PV cell is called as the nominal operating temperature of a PV cell (TPVn). It is accepted that the temperature of the array is 22 ℃ higher than outdoor temperature. In the different the ambient temperatures, the operating temperature of photovoltaic array can be calculated with equation (5). While the voltage of photovoltaic array increases due to the increase of the array’s temperature, the current of photovoltaic array decreases due to the increase of the array’s temperature. The changes with the temperature difference of the voltage and current values that can be obtained from the photovoltaic array are given in the following equations;

where;
TP = panel temperature (℃)
Ta = the ambient temperature (℃)
TPVn = nominal operating temperature of PV cells (℃)
Vocv = open-circuit voltage (V)
Iscc = short circuit current (A)

The efficiency of photovoltaic array (ηPVarray) can be determined by following equation:

The photovoltaic arrays are placed at the optimum angle, but the solar radiation comes on the array from different angles during the day, therefore photovoltaic efficiency of the system decreases. The change of angle is 15˚ when photovoltaic arrays are placed at the optimum angle. The decrease of the efficiency is taken as 5% for the angle change of 15˚ difference. The total efficiency of the photovoltaic system is determined as follows:

where;
ηte = total efficiency of PV system
ηea = the efficiency of the angle inclination

When determining required number of PV modules, the maximum amount of energy must be taken into account. To meet the energy requirements in such systems, the required number of solar PV modules can be calculated as follows;

where;
nPV = the number of solar PV modules
Er = the amount of required energy (Wh)
EPV = the amount of electricity that can be gained from the PV array (Wh)

Photovoltaic arrays are very sensitive to shading. Therefore, it should be paid much importance not to be in the shade during the installation of PV arrays. The solar module is comprised of a number of photovoltaic cells connected in series with a metallic material to get usable voltage. If the power of a PV cell falls because of shading, other cells will be forced to fall to the same degree of the power with this PV cell. In other words, there is no difference being shaded between a half of a cell and a half of a PV module. The soiling of the PV array is similar to the shading effect, which causes the losses, around the level of 3%.

To get the highest levels of solar radiation for PV arrays during a year, they must be placed in the right direction, which in the tilt of the angle that equal to the latitude of the area by inclining to the south. Generally, to optimize the performance of PV panels in the winter, they must be tilted up from horizontal at an angle 15° greater than the latitude. In an opposite manner, if a PV system is going to be used in summer, the most advantageous way to optimize the performance of the PV panels for summer, the PV panels must be tilted 15° less than the latitude.