1. Energy Conversion and Transport George G. Karady & Keith Holbert
EEE 360
Energy Conversion and Transport
George G. Karady & Keith Holbert
Chapter 6
Synchronous Machine
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360 Chapter 6 Synchronous Machine

2. 360 Chapter 6 Synchronous Machine
Lecture 15
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360 Chapter 6 Synchronous Machine

3. 360 Chapter 6 Synchronous Machine
Synchronous Machines
The DC excitation current in the rotor generates a flux.
The turbine drives the rotor and produces a rotating flux
The rotation cause flux changes in the windings
The rotating flux induce a ac three phase voltage in the stator winding.
This is the rotor induced voltage in the stator.
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360 Chapter 6 Synchronous Machine

4. 360 Chapter 6 Synchronous Machine
Synchronous Machines
The generator is loaded
The load current produces a rotating flux
This rotating flux induces a ac three phase voltage in the stator winding.
This voltage is
subtracted from the induced voltage.
represented by a voltage drop on the synchronous reactance
The equivalent circuit of a synchronous generator is a voltage source and a reactance connected in series
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360 Chapter 6 Synchronous Machine

5. 360 Chapter 6 Synchronous Machine
Synchronous Machines
6.3 Generator Application
Power angle: Angle between the dc excitation current generated induced voltage and the terminal voltage
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360 Chapter 6 Synchronous Machine

6. 360 Chapter 6 Synchronous Machine
Synchronous Machines
6.3 Generator Application
6.3.1 Loading: power is less than angle 90 deg
All generators in the system are connected in parallel
All generators rotates with the synchronous speed
The load can be increased by increasing the input mechanical power by regulating the turbine impute power
The speed does not change, the power angle increases
Maximum power angle is 90 degree, beyond that operation is unstable
6.3.2 Reactive power regulation
When the excitation is:
Increased, the generator reactive power also increases;
Decreased, the generator reactive power also decreases
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360 Chapter 6 Synchronous Machine

7. 360 Chapter 6 Synchronous Machine
Synchronous Machines
6.3.3 Synchronization
Verify that the phase sequences of the two systems are the same.
Adjust the machine speed with the turbine that drives the generator until the generator voltage frequency is nearly the same as the frequency of the network voltage.
Adjust the terminal voltage of the generator by changing the dc field (rotor) current until the generator terminal voltage is almost equal to the network voltage. Acceptable limit is 5%.
Adjust the phase angle of the generator terminal voltage by regulating the input power until it is nearly equal with the phase angle of the network voltage. Acceptable limits are about 15°.
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360 Chapter 6 Synchronous Machine

8. 360 Chapter 6 Synchronous Machine
Synchronous Machines
6.3.4 Static stability
Generator
Transmission line
Network
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360 Chapter 6 Synchronous Machine

9. 360 Chapter 6 Synchronous Machine
Synchronous Machines
Figure One-line diagram of a simple power system
Figure Single-phase equivalent circuit of the network in Figure
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360 Chapter 6 Synchronous Machine

10. 360 Chapter 6 Synchronous Machine
System Data
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360 Chapter 6 Synchronous Machine

11. 360 Chapter 6 Synchronous Machine
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360 Chapter 6 Synchronous Machine

12. 360 Chapter 6 Synchronous Machine
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360 Chapter 6 Synchronous Machine

13. 360 Chapter 6 Synchronous Machine
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360 Chapter 6 Synchronous Machine

14. The generator and network power vs power angle
Stable operation
Unstable operation
Maximum power
Operation point
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360 Chapter 6 Synchronous Machine

15. Maximum power transmitted
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16. 6.4 Induced Voltage Synchronous Reactance Calculation
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360 Chapter 6 Synchronous Machine

17. 360 Chapter 6 Synchronous Machine
Synchronous Machines
6.4 Induced Voltage and Synchronous Reactance Calculation
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18. 360 Chapter 6 Synchronous Machine
Synchronous Machines
Figure Rotor-generated magnetic field in the simplified generator.
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360 Chapter 6 Synchronous Machine

19. 360 Chapter 6 Synchronous Machine
Synchronous Machines
6.4.1 Induced Voltage
Ampere’s circuital law for this magnetic loop yields
If iron core is neglected
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360 Chapter 6 Synchronous Machine

20. 360 Chapter 6 Synchronous Machine
Synchronous Machines
6.4.1 Induced Voltage
Figure Rotor generated flux density distribution along the rotor surface
Square wave flux equation
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360 Chapter 6 Synchronous Machine

21. 360 Chapter 6 Synchronous Machine
Synchronous Machines
6.4.1 Induced Voltage
The base component is calculated using the Fourier series
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360 Chapter 6 Synchronous Machine

22. 360 Chapter 6 Synchronous Machine
Synchronous Machines
6.4.1 Induced Voltage
Substitution of current and flux density results in:
Flux integral
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360 Chapter 6 Synchronous Machine

23. 360 Chapter 6 Synchronous Machine
Synchronous Machines
6.4.1 Induced Voltage
Substitution of current and flux density results in:
Flux integral
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360 Chapter 6 Synchronous Machine

24. 360 Chapter 6 Synchronous Machine
Rotating Flux Generation
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25. 360 Chapter 6 Synchronous Machine
Synchronous Machines
Figure Arrangement for calculation of load current generated flux.
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26. 360 Chapter 6 Synchronous Machine
Synchronous Machines
Figure Phase A load current generated ac flux.
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27. 360 Chapter 6 Synchronous Machine
Synchronous Machines
Figure AC flux generated by the phase currents.
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28. 360 Chapter 6 Synchronous Machine
Synchronous Machines
Figure Rotating flux generated by the phase currents
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29. 360 Chapter 6 Synchronous Machine
Synchronous Machines
Figure Flux linkages with phase A.
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360 Chapter 6 Synchronous Machine

30. Exercises using MATCAD
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360 Chapter 6 Synchronous Machine

31. 360 Chapter 6 Synchronous Machine
Synchronous Machines
Figure One-line diagram of synchronous generator network
Figure 6.35 Single-phase equivalent circuit of synchronous generator network.
Figure Simplified single-phase equivalent circuit of synchronous generator network.
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360 Chapter 6 Synchronous Machine

32. 360 Chapter 6 Synchronous Machine
Synchronous Machines
Figure Power delivered to the network as a function of power angle.
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360 Chapter 6 Synchronous Machine