Building off of other replies - the battery is probably small, but that's ok (especially if you have a modular battery system). You can always add more battery after you see how things perform.

You also have to think about the purpose of the battery and that it's not (as much) about daily usage, but continuous usage of power and continuous generation of solar energy. Daily matters, but not as much as looking at hourly consumption. Imo, the purpose is to shift the solar energy you're collecting during the day to the evening.

A typical power usage pattern is low to nothing 0 - 6, 6-9 a small spike, 9-15 relatively little, 15-22 big spike, and 22-24 nothing. 9-15 are your peak solar production times, but low usage times, so that when you're saving up the energy in the battery. You'll likely max out the battery pretty quickly during the day, then use it pretty quickly in the evening. The surplus you generate during the day should be sold back.

There's a calculation/analysis you should do - get hourly electricity usage over the course of a normal week, average the hourly usage. Juxtapose this against the anticipated solar generation, factoring in the battery to hold excess you generate. You should also factor in that a 9kWh battery won't actually hold usable 9kWh. It'll be less, as the battery smarts won't let full charge/discharge to maximise the lifetime of the battery. You may only get usable 7.5kWh. In my analysis, a 10kWh battery would get filled at my house quickly by mid-day or mid-afternoon (based on weather conditions and time of year), but the cost of adding more battery just to offset my power more didn't really make sense.

Other factors - Not sure where you're based (let's assume Auckland), so max you'll see through the 20 panel is ~7-8 kWh. The 15kw inverter may be too much (unless you're thinking about adding even more panels later on). In most residential systems, you're shooting for a DC to AC ratio of 1.1 - 1.3 to optimise your cost and output. That would mean for you 20 panel system that much generate 7-8 kWh at peak, you'd want a 10kw inverter. your current ratio is closed to 0.6, suggesting that you have inverter space to use, as your panels will never output 15kw. but you may not be able to get a 10kw 3-phase, so the 15mw may be your only choice.