Since the solar panels will be recharging your caravan battery all of the loads you mention, fridge, lights, tv will need to be driven from that battery, and the daylight charge capacity of the solar panel must equal or exceed the day and nighttime load on the battery.
Solar panel charge capacity is generally given in Watts because this gives a falsely optimistic impression of the actual useful capacity of the panel array.
How does that happen? The best-case power capacity of panel is calculated from the maximum output voltage (usually about 19V) multiplied by the maximum current produced at that voltage. For example an average panel will drive a 4.5A current at 19,5V. Multiply that out and you get 87,75W. Very impressive, but totally false.
Why? because when that panel is connected to you battery (through a regulator please) that current won’t increase above 4,5A just because the opposing voltage in the battery is only 12,6 to 13,8V depending on the state of charge of the battery. Read the short-circuit current specified on the sticker and you’ll see some thing like 4,7A. So you will never get more than 4,7A charging your battery, think 4,6A at absolute max, and when you multiply that out you get 4,6A x 13,8V = 63,5W. Not so impressive anymore.
Where your calculation should in reality start is with how much power are you going to suck out of your battery in a 24 hour period so you can figure out how to put that back during the following daylight period.
First the fridge. Many caravans are equipped with absorption fridges, the kind with a heater and no compressor. Absorption fridges work by heating a water solution of ammonia which drives off the gas which is cooled and later re-absorbed into the water. No moving parts but quite energy inefficient. If you do the arithmetic you find that the energy contained in LP gas (46MJ per kg @ R20/kg) work out much the same as municipal electricity (1 unit = 3,6MJ @ R1,80 per unit = R23 for 46MJ), and a lot less than solar power (over low-frequency use), so you’re better off running your absorption fridge on gas. If you have a compressor fridge disregard the above.
Most tv sets require mains power. Dstv decoders can be driven from 12V or mains power. Lights are always driven from 12V, or should be. Mains power must be supplied by an inverter which is powered from 12V.
To know how all of these loads add up over a 24 hour period is not difficult, but must be known in Amperes and not in Watts, since the Amperes x hours going out must be at least matched by Amperes x hours going back in. Of course the ‘back in’ time is shorter than the ‘going out’ time.
The lights are the easiest – add all the wattages together and divide the total by 12. If you run an average of 20W of lights for 4 hours every night that works out to 1.6A x 4 = 6,6 Ampere/hours. Round that up to 8 for safety.
The fridge is running on gas and we won’t count the lamp inside the fridge if that is 12V, and it won’t be working if it’s not. If you have a compressor fridge you need to multiply its current requirement (usually about 3A) by its duty cycle (think 50%), so an average of 1,5A x 24hours or 36Ampere/hours
The tv and decoder take about 25W each – 50W total. They are going to be driven from an inverter which is about 85% efficient, so the total draw is 59W, call it 60. Divide that by 12 and you get 5A. Running them for 5 hours will eat 25Amp/hours.
So now (excluding the compressor fridge) you have to replace 33Ampere/hours during the daylight hours of what? 6 hours at max charging current? To generate 33A/hours in just 6 hours requires 33/4,6 = 7,1 hours, so that single panel will not quite cut the mustard. However if you accurately track the sun to get maximum efficiency you might just make it.
If you have a compressor fridge then you’re getting ready to write a cheque for a second panel just about now.
You have here everything you need to know to make you own calculations. Always add a little to be on the generous side since there’s parasitic losses all over the place.
And you see how useless the Wattage specification of the panel is, it’s all about the current.