### 2.1 Quoted Values

PV cells are connected in series to produce PC panels. These usually contain 36 or 72 cells to match 12 and 24V systems respectively. 36 cells in series will produce a panel rated at about 75W and 72 cells will produce a panel that is rated at about 160W. Panels must be able to produce a voltage higher than that of the battery bank (the nominal system voltage) otherwise the batteries will not charge, panels for a 12V system normally have V_{OC} in the region of about 17V. Values of I_{SC} for panels will vary from make to make but will be approximately the same for a single cell, 36 cells or 72 cells. The I-V curve for a panel therefore looks the same as that for a single cell, only the voltages are larger (figure 6).

P_{Max} is the preferred point of operation however, if the temperature is too high this may not be possible. If a voltage below P_{Max}, in the linear section of the I-V curve (figure 6), is acceptable the effect of temperature can be eliminated and the output current is dependent only on irradiance. Some modern charge controllers have maximum power point tracking that will alter the voltage across the panel to find the maximum power output for any given conditions. Other charge controllers rely on a charging voltage being set manually (e.g. 15V for a 12V battery bank) and you will have to take whatever current is available at that voltage.

Manufactures provide data for I_{SC}, V_{OC} and P_{Max}, also the characteristic I-V curve can usually be obtained. These figures are quoted for standard conditions: and irradiance of 1kW/m^{2}, spectral distribution of AM1.5 and a cell temperature of 25°C. Panels are never used under perfect standard conditions and the manufactures’ data must be altered to find the true power output under relevant conditions. Figure 6 illustrates how a PV panel’s output changes with temperature and irradiance, this curve if for a typical panel from a 12V system.

### 2.2 Fine Tuning Manufactures’ Data

#### 2.2.1 Voltage

V_{OC} must be calculated for the operating temperature (T_{C}), for each cell it drops by about 2.3mV for each °C over 25°C. For a panel with n cells connected in series:

Specification sheets may quote a value for the Temperature Coefficient of Voltage for particular makes, for example for a BP 585 panel it is -80±10mV per °C. Note that this is almost exactly the same as -2.3mV when multiplied by 36 cells.

The voltage at the maximum power point (VM) does not vary much with irradiance and can be estimated as 80% of V_{OC} under standard conditions.

#### 2.2.2 Current

I_{SC }is directly proportional to irradiance (G). Therefore the short circuit current at the given irradiance (I_{SC}(G)) is given by:

I_{SC} does not vary much with temperature and this effect is normally ignored. However, manufactures’ specification sheets often provide a Temperature Coefficient of I_{SC}, for example this is 0.064±0.015% per °C for a BP 585 panel; this is about 3.25mA for a 36 cell panel.

#### 2.2.3 Cell Temperature

The cell temperature will normally be higher than the air temperature because they are black and sitting in the sun. The cell temperature under different conditions can be estimated using the Normal Operating Cell Temperature (NOCT), which is defined as the cell temperature under the following conditions: irradiance of 0.8kW/m^{2}, spectral distribution AM1.5, ambient temperature 20°C and a wind speed < 1m/s. NOTC is normally in the region of 42 to 46°C.

The following equation can be used to calculate the difference between the cell temperature T_{C} and the ambient temperature T_{A} (ambient temperature is the air temperature measured in the shade):

#### 2.2.4 Maximum Power Point (P_{Max})

We can calculate PMax if we know the current at P_{Max} (I_{M}) and the voltage at P_{Max} (V_{M}) since:

However, manufactures’ usually only provide us with I_{SC} and V_{OC}, also even if we did know I_{M} and V_{M}under standard conditions they will change for different conditions. A scaling factor called the Fill Factor (FF) is used, once calculated it can be used to scale the modified values of I_{SC} and V_{OC} to find P_{Max} for the true operating conditions (this makes the assumption that FF does not change with temperature or irradiance).

Figure 7 shows an I-V curve, P_{Max} can be found by maximising the area of the rectangle I_{M}P_{Max}V_{M}0.

The following equation is used to find FF from the manufacturers’ data, which can then be used to find P_{Max} under non-standard conditions.

#### 2.2.5 Example

Determine the parameters of a panel formed from 34 cells in series, under the operating conditions G = 700W/m and T_{A} = 34°C. The manufacturer’s values under standard conditions are: I_{SC} = 3A, V_{OC} = 20.4V, P_{Max} = 45.9W, NOCT = 43°C.

a. Short circuit current:

b. Soar cell temperature:

c. Open circuit voltage (n=number of cells that make up the panel):

d. If it is assumed that the fill factor is independent of temperature and irradiance:

Note that this is 62% of the manufacturer’s P_{Max} value.

#### 2.2.6 Other Reductions

The manufacturing process is not perfect and some PV panels will be rated slightly higher than others so that the total power of an array of panels will be slightly less than the down rated power of a panel multiplied by the number of panels. This phenomena is known as mismatch and the array output should be down rated by the manufacturing tolerances; normally in the region of 2-4%. Another 2 to 6% can be subtracted for a further mismatch caused by dirt and dust on the panels.