Electrical Power Systems

Synchronous Machine: Steady State and Transient Operations 83
At no load (armature current is zero), the field mmf r produces the no-load generated emf
E and this voltage is proportional to the field current known as excitation voltage. It is worth
mentioning that in ig. 4.2 mmfs are space vectors whereas the emfs are time phasors.
When the synchronous generator is loaded, i.e., the armature is carrying balanced three
phase currents. The interaction of armature mmf and the field mmf, known as armature
reaction and produced resultant air gap mmf sr. sr is responsible for the resultant air gap flux
fsr which induces the generated emf on load Esr. s induces the emf Ear, known as the armature
reaction voltage. The voltage Ear leads the armature current Ia by 90° and thus can be represented
by a voltage drop across a reactance xar due to the current Ia. xar is known as armature reaction
reactance.
rom ig. 4.2,
E = Esr + jxar Ia ...(4.14)
Esr = V + raIa + j xl Ia ...(4.15)
rom eqns. (4.14) and (4.15), we get
E = V + {ra + j(xl + xar )}Ia \ E = V + {ra + jxs)Ia ...(4.16)
where xs = (xl + xar) is known as synchronous reactance.
The cosine of the angle between Ia and V represents the power factor (cos q) at the generator
terminals. The relative positions of r and sr dictates the action of the synchronous machine.
When r is ahead of sr by an angle dr, the machine is operating as a generator and when r falls
behind sr, the machine will act as a motor. igure 4.3 shows equivalent circuit of nonsalient
pole synchronous machine.
ig. 4.3: Synchronous machine equivalent circuit.
igure 4.4 shows the phasor diagram of the generator for lagging, unity and leading power
factors.
(a) Logging pf load (b) Leading pf load (c) Upf load
ig. 4.4: Phasor diagram of synchronous generator.
Voltage regulation of an alternator is defined as the percentage change in terminal voltage
from no load to rated load.
Voltage Regulation,