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What does Toyota see in "Fool" Cells?

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If you assume you start with natural gas, hydrogen cars can be more efficient than BEVs. A natural gas power plant is at best around 55% efficient, whereas steam reformation of natural gas into hydrogen is around 80% efficient. With a 90% efficient drivetrain in a BEV and 85% efficient charging compared to a 65% efficient drivetrain in a hydrogen car, you can arrive at an efficiency of around 44% for a BEV and an efficiency of around 52% for a hydrogen car.
If it were efficient to produce electricity out of natural gas by steam reformation into Hydrogen, then the big natural gas power plants would do that and their stationary fuel cells would be no less efficient than the light weight fuel cells in your car.
Similarly, it's hard to imagine that hydrogen distribution could be more efficient than electricity distribution.

natural gas -> hydrogen -> mobile fuel cell -> electricity -> can't be more efficient than natural gas -> electricity at a power plant, so the only way the system could be more efficient with hydrogen is if batteries are inefficient. and they're really not.
 
It may be a bit more efficient to steam reform the gas into hydrogen, and run a fuel cell, and capture the waste heat of both as well. But a fuel cell in a car isn't going to be able to match the efficiency of the fuel cell in a power plant, unless you can perform a miracle or three.