Diff for "EffectOfBatteries"

The red circle represents the total energy consumed over some time period.
The green circle represents the emissions free energy generated by PV panels over the same time.
The intersection of the circles represents energy both produced and consumed, that self consumption.
The remaining part of the red circle is energy bought from the grid. It adds to our emisions at a rate depending on the emissions intensity of the grid.
The remainder of the green circle represents energy generated but not consumed, that is the surplus that is exported to the grid. This reduces emissions from the grid by the same factor.
The size of both circles and the degree of overlap will all vary with time, weather etc. However we can neglect that by taking a long time interval, say 1 year.

Installing a battery does not change the energy consumed, the size of the red circle, nor the energy generated, the size of the green circle.
What it does change is the level of overlap. It increases self consumption by allowing some of what would otherwise have been exported, to be stored and used when instantaneous generation is less than consumption, e.g. at night.
This means that both export and import are reduced by the same amount.
Import and export have the same emissions intensity but different prices. Hence a battery saves money but not emissions.