consider a hydroturibine as an example. suppose it is rotating at X rpm at a given load.Suppose load changed the new equilibrium speed(mass flow rate of working fluid changes wrt load) will be X or different.
This depends on the load (generator) and more particularly on how it is controlled. I suppose for generators directly attached to the grid, the frequency should be fixed and therefore, controllers will maintain constant rotation speed.
Gas turbines can be operated with variable speed to get better efficiency at part-load. If they drive the generator, then the constant current frequency is obtained electronically.
If the control is done using control valves in the steam inlet. Normally after a transient the speed will be generally the same. If the power is reduced in the first instant the turbine will increase the speed, the control valves will close and the normal speed will be recovered. If the load is increased, at the first instant the turbine wil reduce the speed but the control valve will open and the speed will be recovered.
Ordinarily, the answer would have been yes to your question but there are steps that have been advanced and used to cushion the effect of variable load on shaft. Some have been listed and explained. Mechanically, flywheel is also used to cushion the effect of load variation on shaft, abrupt load chande
Simplified function of a steam turbine not connected to the network:
rpm = A - B times load,
where the constants A and B depend on the position of the inlet valve. If the turbogenerator is connected to the network, rpm is determined by the network, (i. therefore the load distribution among the turbines is done by modifying the position of the inlet valve.
Simplified function of a steam turbine not connected to the network:
rpm = A - B times load,
where the constants A and B depend on the position of the inlet valve. This valve is used to automatic control the rpm in case of change of load.
If the turbogenerator is connected to a network, rpm is determined by the network, (it is constant, because the loads of the turbogenerators summing up, so the value of B of the network is practically zero) therefore the load distribution among the turbines is done by modifying the position of the inlet valve, and not the controlling rpm.
(Sorry for hitting the submit key before finishing the above text.)
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