Shipping batteries is far more expensive and loses much energy than transmission lines.
The global electricity consumption is about 3 billion kW, that means we need 3 billion kWh per hour. A typical laptop battery might store something like 0.05 kWh. That means every hour we need to ship 60 billion batteries. If the shipping takes 10 days = 240 hours for a round-trip then we need an inventory of 60 billion * 240 = 14400 billion batteries. Worldwide production is maybe 1 billion per year. You can use other battery types but the problem doesn’t go away. We can’t produce that many batteries, and even if we could it would be far too expensive.
Even if we ignore how to get the batteries: At 50 grams per battery, our batteries have a total weight of 720 million tonnes. We need ~3000 of the largest oil tankers repurposed for battery transport. To match the energy carried by a single oil tanker we need ~40 battery tankers.
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