Can over-excited synchronus motor operate on lagging power factor?

Question

All of the Electric Machines literature I'm using states that over-excited (back emf E> supply voltage V) synchronus motor will operate on leading power factor (one of them states that it may also operate on unity power factor for some value of back emf E). But my calculations shows that it may even operate at lagging power factors if E is not that much greater than V. Specifically, motor will operate at lagging pf if cosine of load angle is less than V/E . This will cause resultant emf to lead V by less than 90 and thus, neglecting armature resistance, I has to lag V. However as most of (standard) literature are not verifying this, I am having quite doubt on myself if I am doing something wrong😅. So please let me know if I'm right..

Bonus question : What may be nature of armature reaction if machine is operating on lagging pf while being over excited.

PS: I know that even if I'm right, in most of cases, over exciting will mean increasing E much above V so that we'd have leading pf but still, I thought atleast books must've included this possibility...

Answer 1

I believe that a synchronous motor that is operating at a leading power factor is over-excited by definition and under-excited by definition if it is operating at a lagging power factor. If V > E, it seems to me that the motor must be acting as a generator and the definitions are reversed. The actual field current required to maintain unity power factor varies with load, so a given value of field current could be either over or under excitation depending on load.

Answer 2

You are talking about the "load angle". Synchronous machines used for phase shifting are used without load. An unexcited motor would just be a large inductivity. As you increase excitement, more rotational energy is put into and taken out of the rotation in one AC cycle (so actually you don't want the machine to be rotating "without load" but put something with the quality of a flywheel on in order to store energy better than just in the axle: but the usual synchronous machine equations just assume stationary speed and don't tell you about that kind of torsional vibration).