Series vs parallel
Series and Parallel have their own advantages. Series is where you wire each panel together in a long string, parallel is where you connect all the positives together and all the negatives together. Series results in high voltage and low amps, and Parallel results in low voltage and high amps.
Series is effected by shade much more, as shade on 1 panel takes out the whole string. However as series adds the voltage and keeps the amps the same its possible to have much larger arrays, as very high amps is much more expensive to deal with.
Parallel copes with shade much better, as shade on 1 panel only takes out that panel. However as the voltage stays the same and the amps go up this can be im-practical for a large system.
As large home systems have vastly different requirements and hardware compared to 12v systems, lets talk about each system separately.
12v
12v systems typically have 2 types of panels, "12v" panels typically produce about 20v max, and house panels unusually produce about 40v max.
For 12v systems theres basically 2 types of controllers
PWM - These controllers are outdated, they used to be a good option, however the price of PWM controllers have come down so much they should not be considered anymore.
MPPT controllers are whats used, theres 2 main specifications that you need to know about you're controller before you can pick solar panels and wiring.
Max voltage input. This makes the largest difference to what panels and wiring you can choose. As you can't exceed this rating, and many dual-purpose chargers have a very low max input voltage it often means you have to use "12v" panels only as house panels voltage is to high, and if you have multiple solar panels you need to wire them in parallel as it can not take a higher voltage, so you do not have a choice.
Max output current. This control's how much output amps the controller can put out. This mainly determines the total amount of charge it can put out, you can over-size the panels, it is not a hard limit. E.g. I have a Victron 100/30 which has a max output of 30 amps, at the bulk charge voltage of 13.7v, my 525w of solar puts out 38.3a this exceeds the max the charger can output, however as its not a hard limit it does not cause a problem. It also does not loose power at all, as in winter it rarely reaches max output, in summer it may only reach max output for a couple hours a day on sunny days, and you typically have more charge than is needed then anyway. So it doesn't make much sense to upgrade to a Victron 100/50 as its not going to make any meaningful difference.
The last thing you need to make sure you stay under is the max short circuit current, this is the maximum output all the solar panels can have combined (however they are wired). The max short circuit current is lower than the operating current, and on most controllers this is higher than the max output current. Which allows any reasonable amount of panels all wired in parallel wired to the controller, however this is not always the case, some controllers have a significantly lower short circuit rating which can limit the ability to wire panels in parallel.
If you have the option you should run your 12v panels in series, as the shading upside is much better than the downside of amps. Also when camping your solar panel array often gets partial shade from trees, especially if its mounted on your roof. Lets do an example to show how much benefit you can get from parallel panels.
Lets keep the numbers simple, so our system has 2 solar panels, 100w each and 1 of them has partial shade, dropping its output to 50w, the other one is in full sun. In a series setup both panels get effected by the shade on the 1 of them, so the total output is only 100w (50w from each panel). If the same panels were wired in Parallel then the shade only effects the 1 panel, so the total output is 150w, producing significantly more power than the series wiring.
The main downsides of parallel is the higher amps, and therefor larger cable needed to wire them together. However the significantly higher output under partial shade easily out-weighs the minor cost for slightly thicker cables. MC4 connectors used on most solar panels are also only rated for 30a, however this is on the solar side, so in my system even though the solar panels could charge at a max of 38a (if I had a larger controller), on the solar side its 20v, so its still only 26.3a max, under the 30a rating of MC4 plugs. This means for most 12v systems a simple branch or Y connector is all that is necessary, however if your amps exceed this you can always make a MC4 to Anderson cable to plug in all your panels to a thicker cable with a higher rating.
You can also wire panels up as both series and parallel, the minimum number of panels you need is 4, as each series string of panels need to have the same number of panels. This means it is fairly un-common for 12v systems, but may be the best option on a caravan or similar larger system. If you do wire up as both series and parallel try and make each string of series panels grouped in a way thats likely to get shaded together, so under partial shade only 1 string gets taken out. However due to the nature of portable systems this often is not possible, so maybe just set it up for what works best for you're favorite camp site and hope for the best elsewhere.
House Systems
House Systems are very different to 12v systems and usually can't be wired in parallel at all, however they typically have multiple strings, which is similar to wiring the panels in a hybrid setup of both series and parallel, however as each string uses its own MPPT controller you have much more flexibility as each string can have a different amount of panels. There may be some controllers that can handle parallel panels, however I have not seen any. Most home inverters have 2 strings, however there are quite a few that have 3 strings, which can be a significant advantage under certain circumstances.
Solar sales people often just cram as many panels onto a roof as possible, and leave it up to a sparky to wire it up in a way that will work, which they can do without a problem, but the way it is wired up can have a massive impact on real-world performance, since in a string shade on 1 part of it may as well be shade on all of it. Because of that when designing you're system make sure to get a good wiring layout agreed upon, and make sure its followed when installed.
In general you should have 1 string for each direction you have some panels facing, so if you want to have east/west array you will need 2 strings, but if you want all north panels you may be able to get away with a single string.
Each string has a minimum and maximum number of panels, this is determined by the voltage range of the MPPT. A solar panel on a house typically operates at about 40v, and the range of the MPPT is usually 120v-550v, meaning you need 3-14 panels in each string, however this varies with each panel and controller, so changing panels or controllers may mean certain layouts do/don't work, or at least work well.
For the following examples lets assume were doing a 5kw inverter with 6.6kw of 370w panels, giving us 18 panels in total. Lets also assume each string can have 3-15 panels.
- Lets say we want all 18 panels facing north. Thats to many for 1 string, however we can easily divide it up into 2 strings with any inverter. How you divide up the strings is going to come down to shade. If you have shade that goes across your roof from east to west, then you want your 2 strings to be divided up into east and west. However if you have shade that approaches from the north and only just touches some panels, then diving up lower and higher panels may make more sense.
- This time we have 15 panels facing north and just 3 facing west, didn't quite have enough room for them all to be north. This causes a bit of a problem if you have a 2 string inverter, as the 15 north facing panels do not fit into a single string, so we would have to have 1 north string, and 1 string thats both north and west. The divided string is not going to perform great, however by just choosing a different inverter that has 3 strings means we can do 2 north strings, and 1 west string.
- The solar I have on my home has 6 panels east and 12 panels west, arranged as 2 rows of 6 panels. This may seam super simple we can just have 1 east string and 1 west string and were all good! And that is the case, however like most houses I do get some shade, I have 2 sources of shade on my west array my own roof shades the lower row in winter, when the shadows get stretched in the afternoon. I also have large trees to the west, so the shade creeps up the roof as the sun goes down. Because of this I went with a 3 string inverter, separating the top and bottom rows of west panels to their own strings. So now in the afternoon as the shade from the trees come over the top row gets the full sunny output for a bit longer each day, as well as when the shade from my own roof hits the panels on the bottom row. This small change in wiring has resulted in quite a substantial increase in output over the year, it may only be an extra hour or so each day, but thats every day, it really does add up.
Once you have figured out your panel layout, and how its all going to be wired up, you need to make sure that its actually done that way. Even though I had requested a 3 string inverter, to do the above string configuration it was actually wired up as just 2 strings east/west. After explaining why I wanted them wired up like that, as well as showing them the sales person had agreed (in writing, because I suspected this may happen) they were "happy" to re-do the string wiring. In my case it was very easy to see it was not wired up properly as there was only 2 pairs of MC4 connectors plugged into the inverter. If you have a harder to check wiring requirement, like in the first example there is still an easy way to check. Every modern inverter has some form of app or website where you can check the inverter output, these typically also show you (even though it may be hidden in the menus) the output, or voltage for each individual string. In our first example, if we had east/west shade so east/west strings of the north facing panels, you just have to wait for the shade to be on the east panels one morning (or whatever partial shading you have), and check the app and make sure the 2 strings are performing very differently, if they are both performing the same, when they shouldn't be theres a good chance they wired them up in a way that was easier, instead of the way you requested for efficiency.