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# Series Resistance

#### Series Resistance (Rs) and its factors

Three different factors cause series resistance  in solar cells: -The current movement through emitter and base of the solar cell -The contact resistance between the silicon and the metal contact -The resistance of rear and top metal contacts. The key effect of Rs is reducing the fill factor, even though extremely high values may  reduce the short circuit current as well. I=IL−I0 exp[q(V+IRS) / nkT] where:  I: the cell output current  IL: the light generated current V: voltage across cell terminals’ T: temperature n: the ideality factor  q & k: constants RS: series resistance of the cell.

#### Formulas for Series Resistance and FF

The formula resembles an implicit function based on the appearance of current (I), on the two sides of the equation and numerical methods are requires for solving it. It has no effect on solar cell at the open circuit voltage as the overall current flows through the solar cell, and as a result through the zero Rs. But, near open circuit voltage, the Rs strongly affects the IV curve. A clear method to estimate the Rs of a solar cell is by finding the IV curve slope at the point of open circuit voltage. An equation for the Fill Factor as a function of Rs can be represented with the notice that for normal values of series resistance, the maximum power can be approximated as power in series resistance absence minus the lost power in the series resistance. The equation the maximum power from a solar cell is:   P’MP ≈  VMPIMP – I2MP/Rs= VMPIMP ( 1 – ( IMP / VMP) Rs) = PMP (1 –( ISC/ VOC) Rs ) P’MP = PMP ( 1 – RS / RCH) While a normalized series resistance is defined as: rs = Rs / Rch   So the following equation approximates the effect of Rs on the solar cell output power as defined below: P’MP = PMP ( 1 – rS ) Using the assumption that open circuit voltage and short circuit current are both  unaffected by Rs, allows the Rs impact on FF to be : P’MP = PMP ( 1 – rS ) V’OCI’SCFF’= VOCISCFF(1– rs) FF’=FF (1– rS ) In the equation above the FF that doesn't change by series resistance is  FF0 and FF' is denoted by FFS. The equation then is: FFs=FF0 (1– rS )   A slightly more accurate empirical equation, for the relating both FF0 and FFS is then: FFs=FF0 (1–1.1 rS ) + rs2/ 5.4 This is valid for rs less than 0.4 and voc  greater than 10. Current levels in any solar cell have a huge impact on losses from series resistance.
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