Question

The phasor diagram of a synchronous machine connected to an infinite bus is shown in the figure below. The machine is acting as, 

• A. generator operating at leading p.f.
• B. generator operating at lagging p.f.
• C. motor operating at leading p.f.
• D. motor operating at lagging p.f.

Hint:

For synchronous machines connected to an infinite bus, remember: {E leading V indicates generator operation}, and {over-excitation corresponds to lagging power factor}.

Answer 1

The Correct Option is B

The relative position of \(E\) and \(V\) in the phasor diagram tells us the mode (generator or motor), and the size of \(E\) relative to \(V\) tells us the excitation level (leading or lagging).

1. Generator, leading p.f.: Would need under-excitation, i.e. a small lead of \(E\) over \(V\), not the large lead shown.
2. Generator, lagging p.f.: Matches: \(E\) leads \(V\) (generator), and the large lead angle signals over-excitation, which means supplying reactive power, i.e. lagging p.f.
3. Motor, leading p.f.: Would need \(E\) to lag \(V\), which is not what the diagram shows.
4. Motor, lagging p.f.: Also needs \(E\) lagging \(V\), again not matching.

So the machine is a generator operating at a lagging power factor.

Answer 2

A synchronous machine on an infinite bus can be placed in one of four operating regions depending on two independent facts: whether it delivers or absorbs real power (generator vs motor), and whether it delivers or absorbs reactive power (lagging vs leading, as seen by the bus). These two facts show up separately in the phasor diagram as the power angle between \(E\) and \(V\) (real power direction) and the size of \(E\) relative to \(V\) along with the angle of the current phasor (reactive power direction).

1. Generator operating at leading p.f.: This region corresponds to \(E\) leading \(V\) (generator) but with \(E\) only slightly bigger than \(V\) (under-excited). The diagram's large lead angle rules this out.
2. Generator operating at lagging p.f.: \(E\) leading \(V\) puts the machine in generator territory, and the pronounced lead of \(E\) in the diagram places it in the over-excited region, which corresponds to the machine pushing reactive power out onto the bus, i.e. a lagging power factor at its terminals.
3. Motor operating at leading p.f.: Motor operation requires \(E\) to lag \(V\), placing the power angle on the opposite side from what is shown.
4. Motor operating at lagging p.f.: This also requires \(E\) lagging \(V\), which again does not match the diagram.

Locating the diagram in this four-region picture places it squarely in the generator, over-excited, lagging power factor region.

Therefore, the correct answer is generator operating at lagging p.f.