Series Resistance
Series resistance in a solar cell has three causes: firstly, the movement of current through the emitter and base of the solar cell; secondly, the contact resistance between the metal contact and the silicon; and finally the resistance of the top and rear metal contacts. The main impact of series resistance is to reduce the fill factor, although excessively high values may also reduce the short-circuit current.
Schematic of a solar cell with series resistance.
where: I is the cell output current, IL is the light generated current, V is the voltage across the cell terminals, T is the temperature, q and k are constants, n is the ideality factor, and RS is the cell series resistance. The formula is an example of an implicit function due to the appearance of the current, I, on both sides of the equation and requires numerical methods to solve.
The effect of the series resistance on the IV curve is shown below.
The effect of series resistance on fill factor. The area of the solar cell is 1 cm2.
Series resistance does not affect the solar cell at open-circuit voltage since the overall current flow through the solar cell, and therefore through the series resistance is zero. However, near the open-circuit voltage, the IV curve is strongly effected by the series resistance. A straight-forward method of estimating the series resistance from a solar cell is to find the slope of the IV curve at the open-circuit voltage point.
An equation for the FF as a function of series resistance can be determined by noting that for moderate values of series resistance, the maximum power may be approximated as the power in the absence of series resistance minus the power lost in the series resistance. The equation for the maximum power from a solar cell then becomes:
defining a normalized series resistance as;
gives the following equation which approximates the effect of series resistance on the output power of a solar cell;
Assuming that the open-circuit voltage and short-circuit current are not affected by the series resistance allows the impact of series resistance on FF to be determined;
In the above equation the fill factor which is not affected by series resistance is denoted by FF0 and FF' is called FFS. The equation then becomes;
An empirical equation, which is slightly more accurate for the relationship between FF0 and FFS is;
which is valid for rs < 0.4 and voc > 10.
The following calculator determines the effect of Rs on the solar cell fill factor. Typical values for area-normalized series resistance are between 0.5 Ωcm2 for laboratory type solar cells and up to 1.3 0.5 Ωcm2 for commercial solar cells. The current levels in the solar cell have a major impact on the losses due to series resistance and in the following calculator, examine the impact raising the current has on the FF.
Comments
Series Resistance
Series Resistance
by stuartb » Wed Jul 14, 2010 11:10 pm
Reason: Edit
- stuartb
- Registered User
- Posts: 28
- Joined: Sun Jul 24, 2011 6:42 pm
Re: Series Resistance
by palok » Sun Jul 17, 2011 2:42 pm
- palok
- Registered User
- Posts: 1
- Joined: Sun Jul 17, 2011 2:28 pm
Re: Series Resistance
by stuart » Sun Jul 24, 2011 7:07 pm
palok wrote:how do I use the calculator? How can I estimate the FFo when n becomes 2 (for instance)?
The calculator is broken. I'll look at fixing it.
- stuart
- Site Admin
- Posts: 49
- Joined: Sat Jul 17, 2010 4:13 am
- stuart
- Site Admin
- Posts: 49
- Joined: Sat Jul 17, 2010 4:13 am
Re: Series Resistance
by virus26280 » Sat Aug 13, 2011 5:17 pm
- virus26280
- Registered User
- Posts: 1
- Joined: Sat Aug 13, 2011 5:10 pm
Re: Series Resistance
by stuartb » Tue Aug 30, 2011 5:02 am
virus26280 wrote:I think that the calculator is still broken. Rs is always zero!
Rs is an input, Change it and you will see the FFs go down
- stuartb
- Registered User
- Posts: 28
- Joined: Sun Jul 24, 2011 6:42 pm
Re: Series Resistance
by pritesh_vh » Wed Nov 02, 2011 12:03 am
I think one of the equations here may have a typo. On the first long equation of the derivation, is the last part really Isc and Voc or should it be Imp and Vmp?
Thanks.
- pritesh_vh
- Registered User
- Posts: 1
- Joined: Wed Nov 02, 2011 12:01 am
Re: Series Resistance
by stuartb » Sat Nov 05, 2011 4:29 pm
pritesh_vh wrote:Hello,
I think one of the equations here may have a typo. On the first long equation of the derivation, is the last part really Isc and Voc or should it be Imp and Vmp?
Thanks.
We are using the approximation from this page:
http://www.pveducation.org/pvcdrom/sola ... resistance
I admit is just shows up without explanation. I'll add one.
- stuartb
- Registered User
- Posts: 28
- Joined: Sun Jul 24, 2011 6:42 pm
- huropenz
- Registered User
- Posts: 1
- Joined: Sun Dec 04, 2011 2:10 pm
- Location: USA
- abogallod
- Registered User
- Posts: 8
- Joined: Thu Dec 29, 2011 5:44 am