My installer did a great job on sizing this system. Looked at our peak power usage as well as average for the day.
The highest peak I have seen was 12KW load, and what you need to remember is that even if it goes over 15KW it will then share the load between the panels and the batteries or grid through the inverter. Let's say it's 5pm and the solar generation sits at 4KW. If the yard is using 7KW at that time the other 3KW will then be supplied by the batteries or grid if batteries are empty. The system can handle 24KW total which will never happen.
Regarding the amount of panels. If our batteries are at 35-40% at 7am in the morning, which is where it usually sits on average, the panels are able to charge them to 100% at around 12:00. So currently I don't see the need to add more panels except if City of Cape Town starts giving me loads of cash for pushing power back into the grid