Motor connected to generator

I've recently made a test in our laboratory at the University.

We have a 3 phase synchronous generator connected to a synchronous motor.

The generator has its exciter coil connected to an external power supply.

Our professor says that in this case, when there is no load connected at the output of the generator, the mechanical power consumed $P$ is:

$$P = P_\text{loss, mechanic} + I_0^2 R_0 + P_\text{loss, iron}$$

I understand that the generator has losses due the friction.

I also understand that the generator has some losses due the magnetization of the stator.

The problem is that I cannot understand why the losses in the exciter coil affects the mechanical power drained from the motor.

I think, this power loss affects the external power supply connected to the exciter coil.

Is that right?

If not, can somebody explain me this effect?

If the exciter coil is connected to an external power supply, then the entire power input to that supply is part of the system losses. The exciter losses are only taken from the mechanical input when there is a separate exciter generator that is driven by the mechanical input. Even then, there may be external power used to control the excitation.

$$P = P_\text{loss, mechanic} + I_0^2 R_0 + P_\text{loss, iron}$$

That is the general equation, but with no output, I = 0, so the second term is zero. The magnetization of the rotor by the exciter is DC, so there is no rotor iron loss caused by excitation. There is only I^2 R loss. Even without stator current, there would be iron loss in the stator due to the rotor field moving through it.

If the rotor excitation is supplied through slip-rings, it would need to be initially supplied from an external source, but would be probably be supplied by the stator once generation is established. However, this is a laboratory test set-up, so there would be not reason to do that.

• The exciting voltage is DC, that's true. But it is rotating, so the stator iron sees AC magnetization, not DC. – Marko Buršič Aug 26 '16 at 20:46
• @Marko Buršič Revised answer to say no rotor iron loss caused by excitation – Charles Cowie Aug 26 '16 at 20:59

The problem is that I cannot understand why the losses in the exciter coil affects the mechanical power drained from the motor.

Well, that energy has to come from anywhere! Since (I assume) the exciter coil is fed from the same generator, the power lost to ohmic losses needs to get generated.

I would say: $P = P_\text{loss, mechanic}$ The exciter energy loss has no effect on input mechanical power. In a qd-model of PMSM only the q-component is responsible for torque generation, in this case you only have d-component which is excitation. It is quite the same looking at DC brushed generator/motor with separate excitement.