A mill (“un moulin”) for producing flour (“farine”) is driven by a hydraulic turbine and a synchronous machine connected to the grid. Turbine, synchronous machine and millstone are in the same axis.The power required for proper operation of the mill is 80 kW. The mechanical power supplied by the turbine varies between 0 and 170 kW depending on the water flow in the feed line. The figure below gives an overview of the system:
We neglect all losses and friction.
1- Knowing that the machine is connected directly to the grid, justify the use of a synchronous machine for such application.
2- To compensate for the reactive power consumption of the entire system, the synchronous machine must provide to the grid a reactive power Q=36 kVAR.
a) Calculate the active power to be absorbed from the grid by the machine when the turbine does not give power.
b) Calculate the active power that should return the machine to the grid when the turbine gives 100% of its power. Deduce the apparent power of the synchronous machine.
3- Installed machine has a minimum apparent power of 97 kVA. It is coupled on star with a 50Hz 380V grid. Its cyclical reactance at 50 Hz (Behn Eschenbourg reactance)
is Lsω = 1.95Ω . Resistances are neglected. It is hexapole (p = 3). When turbine provides 170 kW,
a) Calculate the current I absorbed by a phase of the machine.
b) Calculate the phase shift φ between the voltage across a winding of the machine and the phase current. (Receptor convention: cosφ< 0 and sinφ<0 ).
c) Draw as accurately as possible the Behn Eschenbourg diagram (vector diagram)
d) Graphically assess the emf at no load E required for this operating point.
e) Check (verify) by calculating the value of the emf E.