We have a detailed write up here.
The short answer?
In Australia, unless you have an export limited system, on-grid home energy storage does not reduce greenhouse gas emissions but instead contributes to them.
While battery storage will reduce emissions in the future when renewable penetration is so high that batteries are needed to add more renewables, we are a long way from that right now.
Battery systems installed now are almost certain to only contribute to global warming over their entire lifespan.
Early adopters would have helped rather than harm the environment if they had instead spent their money on installing larger solar systems or on improving energy efficiency.