Tidal power plants taps into the energy in the motion of the oceans due to the gravitational interaction between the earth and the moon, so much is clear to me. This question is about where would this energy be if it were not exploited by humans. Does it actually make a difference in the orbit of the moon, or would the same energy just become heat in the ocean though friction anyway? To rephrase, are we just redirecting the flow of energy going from the earth-moon orbit into the heating of the earth, or are we actually pulling on the moon to extract energy?
The chosen answer here is simple on how the energy in the tides comes from the slowing of the rotation of the earth due to the tides induced by the moon.So this will happen whether one uses that energy or not .
If it is not used in a power station it will become part of the energy feeding the weather and climate. It will not affect the mathematical tidal description of the earth moon system.