Do they? I thought most fossil-fueled power plants use coal, which they burn to power a steam turbine. Natural gas plants often use gas turbines, but this is very different from the gas turbine used by a ship: the latter burns kerosene, not natural gas. (Natural gas is uneconomical to power a moving vessel; because it's a gas, you need space to store it, and that space can be orders of magnitude bigger than an equivalent energy-density of diesel fuel or kerosene.) Diesel engines or oil-powered gas turbines are very rare for power plants, outside of backup generators for hospitals etc.