Whether you have a single phase or 3 phase power system in place, the outcome will be the same for load balancing.
The power generated by any solar and battery system installed with a utility meter is directed to the household need initially and any excess generation is exported back to the grid. When the generation is lower than the demand, the grid supplies the difference. This means, you only pay for the electricity you actually use, and profit from the energy you export back to the grid.
With 3 phase power systems your utility meter takes into consideration the power flow from each phase and adds them together to create a single value before it goes back to the grid.
So, your battery which is separate from your utility meter will examine the overall power consumed, the solar power generated and regardless of the energy balance between each phase. With just one overall power value (even with a 3-phase system) for the battery to read, it will either charge or discharge the power in the battery to help you make the most of your solar and battery system.