I would never have suspected you could
Power plants are something that improve efficiency the larger you make them, your small 'power plant' is far less efficient than a multi-megawatt one.
Obviously where it
CAN be generated cheaper is if you have a suitable continuous source of running water to generate hydro-electric power, when it's free apart from install and servicing costs.
Interestingly I delivered a washing machine to a house the other year (the address was 'Mill Farm Close' - so there was a clue in the name), and they had a small turbine fed from the water that fed the original mill, shared with their neighbour as the water feed came in dead on the dividing line between the two. It was only 3 or 4KW, but it was cheap to install and made appreciable savings on their energy bills. Apparently it wasn't worth selling any surplus back to the power company, so unused energy was send to electric heaters (presumably storage ones?) upstairs in the two houses.