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You would need a pretty big solar array to power a construction site with it. But you're headed in the right direction. Not only is it an option to use renewables to power battery-powered vehicles, but also pretty much any form of electricity generation increases in efficiency and decreases in emissions (per kilowatt generated) as it scales up. Even if you are burning the same fuel at the power plant, the emissions are going to be lower overall than the equivalent number of individual internal combustion engines because the efficiency of the power plant is much higher than an ICE. Vehicle engines are ridiculously inefficient overall and when you use a more efficient fuel like natural gas it is even more drastic of a difference.

It's also much easier to put stack controls on a power plant to capture or reduce emissions than it is to put emissions controls on all construction equipment individually. This has implications for carbon capture, which could happen right at the stack. However, there's a non-climate change benefit here as well which is that the local air quality would be greatly increased around construction sites. Currently most construction equipment does not have much in the way of emissions controls for other things like sulfur and nitrogen oxides or particulate emissions. Power plants have to meet emissions standards for all of these.