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How big a solar battery do I need to store all my home's electricity?

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I have a modest set of solar panels on an entirely ordinary house in suburban London.

On average they generate about 3,800kWh per year. We also use about 3,800kWh of electricity each year. Obviously, we can't use all the power produced over summer and we need to buy power in winter. So here's my question:

How big a battery would we need in order to be completely self-sufficient?

Let's take a look at a typical summer's day. The graph is a little complex, so I'll explain it.

The yellow line shows solar production. It starts shortly after sunrise, peaks at midday, and gradually drops until sunset.

The red line shows how much electricity our home is using. As you can see, there's a large peak about 19:00 when we cook dinner.

The blue line shows how much electricity we draw or export from the grid. From midnight until sunrise we import because the sun isn't shining. Once the sun has risen we're able to power our house and export to our neighbours. When we cook, we draw from the grid and our battery - which is why the evening grid peak is lower than the household use dip.

The CSV of the data looks something like this:

Local_time Household_(W) Solar_(W) 2025-08-25T08:25:00.000+01:00 -187.76 1166.77 2025-08-25T08:30:00.000+01:00 -227.04 1193.25 2025-08-25T08:35:00.000+01:00 -253.06 1222.84 2025-08-25T08:40:00.000+01:00 -266.87 1245.18 2025-08-25T08:45:00.000+01:00 -450.8 1268.66 2025-08-25T08:50:00.000+01:00 -251.84 1281.79 2025-08-25T08:55:00.000+01:00 -1426.26 1306.93 2025-08-25T09:00:00.000+01:00 -206.78 1341.37 2025-08-25T09:05:00.000+01:00 -215.52 1390.9 2025-08-25T09:10:00.000+01:00 -242.6 1426.19 2025-08-25T09:15:00.000+01:00 -246.84 1473

It's fairly trivial to sum both columns and subtract one from the other. That shows either the excess or deficit in solar power for the household.

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