Why power factor is used in power plant? why generators ralated engine sound noise depends on load?

actually, the power factor means how much energy you get from what you entered, so that's what it's very important and vital at least economically.

for the noise you ask about: always remember that any change in any machine would bring up unstable condition, I mean in loading or unloading the machine passes through unstable moment so the machine trying to step out of this it will used more (or less) effort to come back to be stable once again.

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The Active power used by a machine is given by V * I *power factor. When the pf is low the machine will take more current at constant voltage as compared to good pf. In power plants we transmit power at high pf as possible as unity. When we transmit power at lower pf we have to transmit high current through the transmission line, it's lead to more losses in power system. It is uneconomical to the system.So we use pf meter in power plants.