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Using the energy equation for a flowing fluid, by doing a lot of assumptions on the flow behavior, (incompressible fluid, stationary flow, ideal flow...) and applying it to the inlet and outlet of a turbine, you get: $$\dot{W}=\Delta P Q$$ Which means that power generated is proportional to the volumetric flow rate and the pressure drop. I'd like to know if in a real plant these two variable are continuously modified in order to obtain a constant power output or if instead their are let naturally evolve in time.

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  • $\begingroup$ The power of the turbine depends on the angular velocity of rotation. The rotation speed is kept constant, therefore the consumer has an alternating current in the electric network with a frequency of 50 or 60 Hz. $\endgroup$ – Alex Trounev Feb 29 at 14:32
  • $\begingroup$ Ok, so are there control valves and systems to keep the rotational speed always at the same value? @AlexTrounev $\endgroup$ – Landau Feb 29 at 16:50
  • $\begingroup$ Yes, a frequency of 50 or 60 Hz is supported with great accuracy (different standards are used in different countries), since all equipment is tuned to this frequency. $\endgroup$ – Alex Trounev Feb 29 at 20:20
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In a hydro installation, the important control variable is generator speed, because the generator must be locked in on the 60Hz AC present in the power grid to which it is connected.

There are several ways to maintain constant AC frequency from a hydro turbine system, as the load seen by the generator changes and as the height of water behind the dam changes.

First, the inlet gates carrying water to the turbine can be opened or closed slightly to vary the flow rate of water through the turbine.

Second, in the case of a generator which uses an externally applied excitation current to generate the field through which the armature rotates, the excitation current can be electronically trimmed so as to maintain constant armature speed.

It is also possible to maintain speed lock by adjusting the pitch of the turbine blades themselves but this is a complex and expensive method.

Finally, it is common practice to have more than just one turbine in a hydro generation system. When electrical power demand goes up, the gates are opened to a second turbine whose generator then comes on-line and establishes frequency lock with the first one.

Note also that in installations where there is always more water flowing downstream than the system needs, you can design a spillway that keeps the height of water behind the dam more or less constant at the system's design point. This makes the rest of the system easier to control.

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  • $\begingroup$ In many countries they generate 50 Hz AC - see en.wikipedia.org/wiki/Mains_electricity_by_country . $\endgroup$ – Alex Trounev Feb 29 at 20:15
  • $\begingroup$ But I know that also variable speed turbines exist. These turbines won't generate always voltage at the same frequency since their speed will change. Are used power electronics devices to turn into 60 Hz the voltage? $\endgroup$ – Landau Mar 1 at 18:23
  • $\begingroup$ Nope, the big generators are all 50/60hz synchronous AC machines that operate directly at tens of thousands of volts. For a family of synchronous generators all connected to the same load network, there is a natural tendency for all of them to quickly achieve frequency lock. regarding variable speed turbines, of course they exist but for power grid generation purposes you want constant speed all the time. $\endgroup$ – niels nielsen Mar 1 at 20:38

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