The Western Power/Synergy table above explained.

Many people aren't sure whether their home has single phase power or three phase.
If you can see three fuses under (or over) your meter and your 'Main Switch' is 3 poles wide
as shown in the picture below, then you have 3 phase supply. If not, it's single phase.


Single phase
The largest solar inverter you are allowed is 5kW.
Unlike the Eastern States, we are not allowed to have a 10kW inverter and 'export limit' it to 5kW.
(I add that because it is the most common question I am asked).

The 5kW inverter can be a 'solar only' inverter or a 'solar & battery' (hybrid) inverter.
A hybrid inverter doesn't normally include a battery, just the capability to add one when you want to.

In addition to the 5kW solar inverter allowance, you can have a 5kW 'battery only' inverter.
That additional inverter cannot have the capability to connect solar panels.
It must be 'battery only', like the one inside a Tesla Powerwall (there are others).

There is an export limit of 5kW, which is a bit of a silly rule, because there's no way to export
more than 5kW if you are restricted to a 5kW inverter.
New single phase solar installations are all eligible for DEBs, the payment made for any surplus power you
export back to the grid. It's all done automatically.

Three phase
You are allowed 15kW of solar inverter(s).
Any combination of three phase 'solar only' and 'solar & battery (hybrid) inverter is permitted up to 15kW.
In addition you can have a further 15kW of 'battery only' inverters.
Those additional inverters cannot have the capability to connect solar panels.
It must be 'battery only', like the one inside a Tesla Powerwall 2 (but not Powerwall 3).

You can also install 5kW single phase inverters on three phase, so long as they have a DC Coupled battery connected.

If your solar inverter total capacity is 5kW or less you are eligible for DEBs payments for surplus power.

If your solar inverter total capacity is over 5kW then:-
1. You must export limit your solar to no more than 1.5kW in TOTAL, not per phase.
1a. You can export limit to zero if you wish.

Here is a link to a Youtube video showing export limiting in action.

2. You must purchase whatever device the inverters require to perform export limiting.
2a. This 'device' is usually at least one 3 phase 'consumption meter' costing around $600.

Summary
Single phase, 5kW inverter for solar, plus you can add a 5kW inverter to run a battery only (no solar capability).
Three phase, 15kW inverter(s) for solar, plus you can add 15kW of inverters to run batteries only (no solar capability).

Single phase gets the DEBs feed in tariff as does three phase if the solar inverter total size is 5kW.
Three phase must buy a 'consumption meter' and export limit to <= 1.5kW if inverter capacity is greater than 5kW.
Three phase gets no feed in tariff if inverter capacity is over 5kW