A couple of ways to generate electricity without moving parts (other than solar panels, piezoelectric and thermoelectric generations mentioned in other comments)
There’re MHD generators, where plasma (i.e. hot ionized gas) as a conductor moves through magnetic field instead of copper coil. These generators work without moving parts (plazma is not considered as a part of generator). They’re usually added as additional cycle of generation to extract more energy from the steam that rotates turbines, but MHD can be used on their own.
There’re fuel cells which are somewhat similar to batteries, with two electrodes and catalyst that helps to split fuel to ions. Catalyst in hydrogen fuel cells splits an electron from hydrogen atom. Remaining positively charged ion of hydrogen joins oxygen and produces water, while eletron produces eletrical current.
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