So I did a brief search, and while I didn't dig enough to find a coal fired only plant I found this study that calculated well -to - wheel (includes everything from pulling petrol from the ground to burning it off in the engine) emissions for gas, diesel, and electric. What this shows is that for a clean grid BEV are around 36% in Netherlands where there is hefty use of renewable energy, and as low as 21% in Saudi Arabia where electric is produced largely with petroleum products. Gas ice cars are around 18%, making BEV better by a few points. I can't help but think if your specific elec plant is only coal fired that it would be a worse efficiency but alas id have to dig more to find a study on that. Interestingly, diesel ICE is around 25% which I did expect a higher number than gasoline but not by that much. Diesel is simply very energy dense. So tl;dr BEV are better in about every case. I can only imagine efficiency if using strictly renewables would be even greater than 36%! Here is study referenced in case interested - https://www.sciencedirect.com/science/article/abs/pii/S0967070X2600051X
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