# Module Circuit Design

A bulk silicon PV module consists of multiple individual solar cells connected, nearly always in series, to increase the power and voltage above that from a single solar cell. The voltage of a PV module is usually chosen to be compatible with a 12V battery. An individual silicon solar cell has a voltage at the maximum power point around 0.5V under 25 °C and AM1.5 illumination. Taking into account an expected reduction in PV module voltage due to temperature and the fact that a battery may require voltages of 15V or more to charge, most modules contain 36 solar cells in series. This gives an open-circuit voltage of about 21V under standard test conditions, and an operating voltage at maximum power and operating temperature of about 17 or 18V. The remaining excess voltage is included to account for voltage drops caused by other elements of the PV system, including operation away from maximum power point and reductions in light intensity.

In a typical module, 36 cells are connected in series to produce a voltage sufficient to charge a 12V battery.

The voltage from the PV module is determined by the number of solar cells and the current from the module depends primarily on the size of the solar cells. At AM1.5 and under optimum tilt conditions, the current density from a commercial solar cell is approximately between 30 mA/cm2 to 36 mA/cm2. Single crystal solar cells are often 15.6 × 15.6 cm2, giving a total current of almost 9 – 10A from a module.

The table below shows the output of typical modules at STC. IMP and ISC do not change that much but VMP and VOC scale with the number of cells in the module.

Cells PMAX VMPP IMPP VOC ISC Efficiency
72 340 Wp 37.9 V 8.97 A 47.3 V 9.35 A 17.5%
60 280 Wp 31.4 V 8.91 A 39.3 V 9.38 A 17.1%
36 170 Wp 19.2 V 8.85 A 23.4 V 9.35 A 17%

If all the solar cells in a module have identical electrical characteristics, and they all experience the same insolation and temperature, then all the cells will be operating at exactly the same current and voltage. In this case, the IV curve of the PV module has the same shape as that of the individual cells, except that the voltage and current are increased. The equation for the circuit becomes:

where:
N is the number of cells in series;
M is the number of cells in parallel;
IT is the total current from the circuit;
VT is the total voltage from the circuit;
I0 is the saturation current from a single solar cell;
IL is the short-circuit current from a single solar cell;
n is the ideality factor of a single solar cell;
and q, k, and T are constants as given in the constants page.

The overall IV curve of a set of identical connected solar cells is shown below. The total current is simply the current of an individual cell multiplied by the number of cells in parallel. Such that: ISC total = ISC × M. The total voltage is the voltage of an individual cell multiplied but the number of cells in series. Such that:

$$I_{SC}(total) = I_{SC}(cell)\times M$$

$$I_{MP}(total) = I_{MP}(cell)\times M$$

$$V_{OC}(total) = V_{OC}(cell)\times N$$

$$V_{MP}(total) = V_{MP}(cell)\times N$$

If the cells are identical then the fill factor does not change when the cells are in parallel or series. However, there is usually mismatch in the cells so the fill factor is lower when the cells are combined. The cell mismatch may come from manufacturing or from differences in light on the cells where one cell has more light than another.

I-V curve for N cells in series x M cells in parallel.

X
130
X
15