3. How do hydroelectric power plants produce electricity with a frequency of 50Hz/6...

How do hydroelectric power plants produce electricity with a frequency of 50Hz/60Hz consistently?

1) Why 60 Hz? If I remember right ... You eye's "refresh rate" is a little over 20 Hz (24 hz?) and you will visually notices AC cycles less than twice that value. 50 Hz will do the job but mathematically speaking, it is easier to design a 3 phase system at 60 cycles per second with each phase spread 120 degrees apart on a 360 degree spinning machine. Otherwise, the synchronous load in the US has been designed to run at 60 Hz and deviations from 60 can cause serious damage (I think trips usually occour between 2-3 hz of deviation).

2) How does it stay consistently 60 Hz? The truth is is that it varies a little. Back in the day - commercial/residential clocks used to keep time based on the grid frequency and utilities would over produce or under produce to either speed up the frequency or slow it down to maintain time. Even though time is kept differenctly these days, NERC sets target deviation limits for each interconnection. And taking a step back - the analogy i like to use for how frequency is maintain is comparing it to cruise control. Power plants are set to operate at a certain speed (the ratio can change depending on the plant but a lot of them spin at 3600 rpm = 60 cycles per second [hz]) in what is called droop control. If the turb-gen assembly slows down too much, "cruise control" will kick in meaning fuel firing will increase / governor valve will open creating more torque (and effective more MWs to compensate for the increase load) and eventually more speed. The opposite will happen for overspeed. The overspeed isn't necessarily analogous to cruise control however, like cruise control, most Plants have a deadband before correction is applied. Some plants have no deadband specifically to chase frequency.

3) The part where its not modified during its trip is false. Transmission Owners have several tricks to try and keep phases, voltage, currents stable. If you looked at frequency in California and frequency in Montana - they may very well be the same at 60 Hz but do to transients across the grid there will be minor phase offsets. A lot of people use water to describe electricity - if you look up some youtube videos of FNETs visuals on black outs you can see electrical systems travel through a system like a wave. Facinating stuff.

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