- Synchronous Motor Definition: A synchronous motor is defined as an AC motor where the shaft rotation matches the frequency of the supply current.
- Synchronous Motor Circuit Diagram: The synchronous motor circuit diagram includes terminal voltage, effective resistance, leakage reactance, fictitious reactance, and synchronous reactance.
- Counter EMF: Counter EMF is the voltage induced in the stator winding due to the rotating magnetic field, which opposes the applied voltage.
- Zero Power Factor Method: This method involves plotting the armature terminal voltage against the field current at zero lagging power factor to measure synchronous reactance.
- Potier Triangle: A graphical representation used to determine synchronous reactance by forming a triangle that represents different voltage drops.
The model diagram of a synchronous motor is the per-phase equivalent circuit that relates terminal voltage, counter EMF and the stator voltage drops.
V = Terminal voltage
Re = Effective resistance
XL = Leakage reactance
Xa = Fictitious reactance
Xs = Synchronous reactance
E = Counter emf
In a synchronous motor the rotor field is supplied by direct current (DC). The stator sees that DC field moving at synchronous speed and also sees the stator’s own revolving MMF. Those two effects induce a voltage in the stator winding. The model diagram puts that induced voltage and the stator impedance drops on one phasor circuit.
The induced voltage is the counter EMF (E). On the phasor diagram it opposes the applied stator voltage (V). Its magnitude rises with field excitation current. The stator circuit then uses two reactances: leakage reactance and a fictitious reactance that stands in for armature reaction.
Armature reaction is replaced by a fictitious reactance (Xa). Add that to armature leakage reactance to get synchronous reactance (Xs). Combine this reactance with the armature effective resistance (Re) to get the synchronous impedance (Zs).
Zero Power Factor Method or Potier Triangle
The Potier triangle is read from the zero-power-factor characteristic. For an alternator the ZPFC plots armature terminal voltage per phase against field current while armature current stays at its rated value, speed is synchronous and the power factor is zero lagging.
A zero-power-factor load can be an under-excited synchronous motor or a variable reactor. The ZPFC then has the same general shape as the open-circuit characteristic (OCC) but sits below it and to the right.
The phasor diagram is shown below –
Here,
Y = Terminal voltage
Ia = Armature current
Ra = Armature resistance
XL = Leakage reactance
Eg = Generated voltage per phase
Fa = Armature reaction mmf
Ff = Field mmf
Fr = Resultant emf
If armature resistance is neglected the phasor is as follows-
Taking the reference terminal voltage at zero p.f. lagging, the armature current lags the voltage by 90o. Here IaRa parallel to Ia, IaXL perpendicular to Ia.
Then we can say that from first phasor diagram
From the second phasor diagram we can say that terminal voltage (V), the reactance voltage drop (IaXL), and the generated voltage (Eg) are in phase.
Arithmetically :
The three MMF phasors are in phase, so :
If we convert this equation into the equivalent field current by dividing its both sides by Tf which is the effective number of turns per pole on the rotor field.
Where,
If = Field current
Ir = Resultant current
Ia = Armature current
Take point b on the zero p.f. curve at rated terminal voltage (v) and field current
The armature current
Resultant current
Field current OL would produce generated
The vertical distance AC must then equal the leakage-reactance voltage drop (IaXL)
The triangle formed by the vertices a, b, c is the Potier triangle.
