# Synchronous generator mechanical characteristic

Why does the synchronous generator produce a torque just in correspondence of the synchronous speed, that is why is he mechanical characteristic just a straight vertical line in $\omega = \omega_S$ and $T(\omega) = 0$, for $\omega \neq \omega_S$?

If the rotor is connected to a turbine, I cannot understand the reason why it cannot produce a torque for whichever speed; until it is not connected to the bus bar system it has no relation with the mains frequency (and the rotation speed).

• Well it isn't right T=0, but the mean value is 0. When the rotor bounces skipping poles it produces +/-max torque, not really nice situation where you can get magnets out of it. The engineers in some power plant would avoid such situation at all cost. – Marko Buršič May 10 '16 at 17:47
• Then there is a transient with a zero average torque but the rotor is continuously pushed and pulled, with a torque that alternatively changes sign. When it is positive, is the machine seen by the line as a passive load (motor functioning)? What happens really inside the air gap when the two fields are not synchronized? Which is the danger for the stability of the network? – Vexx23 May 10 '16 at 17:55

First, the unloaded generator can not make any torque (we neglect dissipation friction etc). It simply has no place to send the energy while not connected to bus bars.

Second, assume this generator is connected to AC system and its rotation frequency differs from that of AC system. Then the magnetic field created by rotor "jumps over" the poles of unmovable part (typically connected to AC line). Therefore the torque varies periodically in time with fundamental frequency equal to difference between rotation frequency and AC frequency.

The average torque is just zero in this case.

So it is better to say that the generator does not create average torque in this case. It can not make any useful power.

• Thanks for the answer. Then the turbine can force a torque at a working speed different from the one related to the mains frequency so that the magnetic field created by the rotor rotates asynchronously with respect to the rotating field produced by the three phase in the stator. I would like to ask you if this transient with a non zero torque (with zero average torque) somehow is destined to finish in a natural way, by obtaining for example that the rotor rotates at the same velocity of the AC line (since it is by far more stronger) or it brings to damages for the machine and why. – Vexx23 May 10 '16 at 17:49
• I have read that, when connected to the line, within a safe limit, whatever action performed by the mechanical motor on the shaft cannot modify the speed and the machine tracks always the mains frequency with a proportional speed $n =\frac{60f}{p}$ with $p$ number of pole pairs and $f$ the mains frequency (50Hz in Europe e.g.); but from where does this tracking capability derive? Thank you – Vexx23 May 10 '16 at 18:04
• @Vexx23 Practicaly that would cause a short circuit like behaviour that would blow the fuses, but before that a turbine would be possibly smashed due to high accelerations and decelerations, the minimal damage could also be just a ball bearing or nothing. – Marko Buršič May 10 '16 at 18:04
• Why is the mismatch condition seen as a short circuit by the mains? Why does the generator behave as a passive load sinking active power? – Vexx23 May 11 '16 at 12:50

A synchronous generator can be operated over some range of speeds. The torque characteristic would be a vertical line at the driven speed. The maximum continuous torque would change somewhat depending on the limits for voltage and power. The excitation control would need to be designed to accommodate the desired speed range.

It is usual to concentrate on fixed frequency operation when studying generator fundamentals. When studying generators for use with wind turbines, the variable-speed characteristics are considered.

The fundamentals of connecting two AC sources to the same network should explain why they need to be synchronized in the required manner. Texts have sections covering the connection of a synchronous generator to an infinite bus and connecting two generators to each other. Vector diagrams, equivalent circuits and example calculations are provided. The material explains what needs to be done to assure that the generators are operated only with their rated parameters. There may not be much material available that studies in detail what would happen inside a generator if operation outside of the rated parameters is attempted. It is possible that some technical papers have been written on the subject. Google scholar may be able to find something.

Quote from a technical paper:

When an off-line generator is energized while on turning gear or coasting to a stop, it behaves as an induction motor and can be damaged within a few seconds. During three-phase energization at a standstill, a rotating flux at synchronous frequency is induced in the generator rotor. The resulting rotor current is forced into paths in the rotor body, similar to those rotor current paths for negative-sequence stator currents during generator single-phasing. Rapid rotor heating, and damage to the rotor will occur. The machine impedance during this high-slip interval is equivalent to the generator negative-sequence reactance.

C. J. Mozina, "Lessons learned from generator tripping events at industrial facilities," 2008 55th IEEE Petroleum and Chemical Industry Technical Conference, Cincinnati, OH, 2008, pp. 1-8.

• Thanks, I would like to understand the electromagnetic interaction when the generator rotating at an arbitrary speed is connected in parallel to the bus bar system, the way it is synchronized and the dangers related to this interface. – Vexx23 May 10 '16 at 17:51
• It seems like the comments by @Marko_Buršič may be directed to the above comment. Prior to connecting to a bus system supplied by other sources, a generator must be adjusted for a close frequency, phase angle and voltage match. Mismatch would cause current and torque transients that would have catastrophic results. – Charles Cowie May 10 '16 at 19:32
• I know the canonical procedure to be followed before closing the switches for the parallel connection to the mains, now i want to understand the physical phenomena inside the air gap when the two magnetic fields are not synchronized. – Vexx23 May 11 '16 at 12:48
• You need to study the theory of synchronous machines in text books and tutorial presentations that can be found on the internet. By asking questions here, you may be able to get answers for specific questions, but not detailed explanations of complex concepts. I don't have a strong enough background in this subject to provide a detailed explanation. – Charles Cowie May 11 '16 at 23:33
• I have already studied all the theory regarding the synchronous machines used as power generators in a wide range of textbooks and also on my lecture notes, but no book has been able to provide me information about this specific issue. If you can suggest one to me I would thank you. – Vexx23 May 17 '16 at 14:34