I have seen several people with questions about this, so I will try to explain the details.
In your case, you said 4500 watts for 10 panels, that is not enough information to figure this out. You need the VOC, VMP, ISC, and IMP and the voltage temp coefficient also helps. 450 watt panels are most likely 72 cell units. But they still vary a bit from there. And some companies are also making 96 cell panels. I just looked up a Canadian Solar brand 72 cell panel at just 390 watts, and it has a VOC of 46.8 volts at 25C. This may be a problem.
MPPT charge controllers use a DC to DC buck converter to match the solar panel voltage to the battery voltage. This can cause some confusion about the input and output relationship.
When choosing a charge controller and solar panels, you want to ensure that the voltage from the solar panels will never exceed the maximum input voltage of the charge controller. You have to use the VOC voltage, and then add to that if the temperature can get cold. A safe rule of thumb is allow 20% over the 25C VOC voltage. If the panels are rated at 40 volts VOC, and you have a 100 volt controller, you can run 2 panels in series for 80 volts, and have room to spare. If you are in an area that gets very cold, you may have to do the math on the panels to be sure you are safe. My panels have a temp coefficient of 0.38 % per degree C. You can find this number of the spec sheet. If the temperature gets down to -15C that is 40C colder than the spec VOC voltage. 40 x .38 = 15.2% voltage increase. 40 x 1.152 = 46.08 volts. 2 panels in series is then 92.16, so still safe on the 100 volt controller. But a 72 cell panel at 46.8 volts at 25C is already closer at the base temperature. If it gains even 10% in the cold, 2 in series goes over 100 volts and could fry the charge controller. That 10% increase pushes a pair of panels to 102.96 volts.
On the current, side, the limit is usually on the output. As the buck converter lowers the voltage to the battery, the current increases. The 20 amp controller into a 48 volt battery bank will only be able to charge at about 1,000 watts. 50 volts x 20 amps. My "48 volt" battery voltage ranges from 50 to 57 volts.
Most charge controllers can handle more panel on the input, but it just won't be able to use it. Some are limited to 50% or 100% over rated output watts. So 2,000 watts of panels can go on a 1,000 watt charge controller. It will max out at only putting 1,000 watts into the battery bank, but there is still some benefit to over paneling. It will start charging earlier, hit the maximum 1,000 watts much sooner, flat line at the charge controller limit for a couple hours, and keep charging longer. If you have a limited charge current, this is a way to still get more power into the batteries by having it work a longer time. You can also put panels aimed a bit east and panels aimed a bit west in parallel. This will extend the time even longer.
With 4,500 watts of panels, you will want more charge controller capacity. 75 to 100 amps into the battery would be good. But you have to watch to make sure the battery can handle all the charge current. While many lithium batteries can take 1C charge rate, most lead acid types are 0.2C or less. A typical RV/Marine deep cycle battery can only take 0.1C
On the input side, it is more about the watts because of the higher voltage. That 100/20 controller will only pull about 10 amps max while charging a 48 volt battery at 20 amps. Because of how MPPT searching works, it will occasionally pull more current to find the maximum power point. So they don't want way too much current available from the solar panels. About 1.5 to 2 times the output wattage is typically safe. But again, check the spec sheet. Many charge controller will list the maximum input power, and it will be different for 12/24/48 volt systems. In the case of 48 volts on a 20 amp controller, the input power limit is probably about 2,000 watts.
