Energy losses in a cable — due to resistance — are proportional to the current squared (I²). Thus if you double the current (by putting your panels in parallel) then you'll quadruple your losses ( (2I)² = 4I² ).
When panels are connected in series, the voltages add up but the current remains constant. Thus to minimise line losses, connect panels in series.
Another advantage of keeping current low is that you can minimise the thickness of the cable between your array and your charger. If the length of that run is long, the savings can really add up.
Your Renogy charger's open circuit voltage limit is 50V, so it should handle the voltage produced by your panels in series without a problem (2x22.7=45.4; 45.4 < 50). If you do end up with the occasional over-voltage condition, it will probably be due to transient cloud-edge effects.
If you want to play it really safe, size your cable for a parallel setup (2x2.84=5.68A) but then deploy it in series to start with. Since line losses are proportional to resistance, and resistance is inversely-proportional to cross-sectional area, a thicker cable will offer less resistance and reduce losses even further. If you do start experiencing over-voltage conditions due to cloud-edge effects, you'll be able to simply switch over to parallel without having to buy a new cable.
LShaver spotted that the Renogy Wanderer 10A is not in fact a MPPT charge controller, but actually a simpler/cheaper PWM charge controller, and checking the manual confirms that it does not feature voltage conversion.
What that means is that — regardless of array voltage — the maximum current that can exit the controller (to the battery) is equal to the current coming into the controller (from the array). Since the battery is 12V, that means that:
- a series setup, generating 2.84A, is limited to a bulk charge rate of about (12.6*2.84=) 36W
- a parallel setup, generating 5.68A, is limited to a bulk charge rate of about (12.6*5.68=) 72W
The PWM controller is clearly creating a bottleneck here. With (2*50=) 100W of panels, around 64% of the energy from a series configuration would be wasted. Even in a parallel configuration, around 28% of the energy would be wasted. Both of these figures far exceed the line losses discussed earlier.
If you have to stick with the PWM controller, then connecting the panels in parallel is clearly the way to go.
If controller losses of 28% are considered unacceptable, then there's little option but to replace the PWM controller with a MPPT controller. If you do that then connecting the panels in series (as discussed earlier) is the way to go.