Phasor Diagram of a Brushless PM SNW or BLPB Synchronous Motor

PHASOR DIAGRAM OF A BRUSHLESS PM SNW OR BLPB SYNCHRONOUS MOTOR:

Consider a BLPM SNW motor, the stator carries a balanced 3ϕ winding .this winding is connected to a dc supply through an electronic commutator whose switching action is influenced by the signal obtained from the rotor position sensor.

Under steady state operating condition, the voltage available at the input terminals of the armature winding is assumed to be sinusoidally varying three phase balanced voltage. The electronic commutator acts as an ideal inverter whose frequency is influenced by the rotor speed. Under this condition a revolving magnetic field is set up in the air gap which is sinusoidally distributed in space, having a number of poles is equal to the rotor. It rotates in air gap in the same direction as that of rotor and a speed eq1ual to the aped of the rotor

Rotor carries a permanent magnet. Its flux density is sine distributed. It also revolved in the air gap with as particular apreed

It is assumed that the motor acts as a balanced 3ϕ system. Therefore it is sufficient to draw the phasor diagram for only one phase. The armature winding circuit is influenced by the following emfs.

1.  V  - supply voltage per phase across each winding of the armature .

The magnitude of this voltage depends upon dc voltage and switching techniques adopted .

2.     E_f -   emf induced in the armature winding per phase due to sinusoidally varying

permanent magnetic field flux. Magnitude of E_f=4.44ϕ_mfK_w1T_ph=Ӏ E_fӀ

As per Faradays law of electromagnetic induction, this emf lags behind ϕ_mf-permanent magnet flux enclosed by armature phase winding by 90°.

3.     E_a - emf induced in the armature phase winding due to the flux ϕ_a set up by resultant armature mmf ϕ∞I_a

Further the current I phasor is resolved into two components Id and Iq 

Id set up mmf along the direct axis (or axis of the permanent magnet)

Iq sets up mmf along quadrature axis (i,e) axis perpendicular to the axis of permanent magnet.

Note:

In case of salient pole rotors the electromagnetic torque developed from the electrical power. From eqn. (5.43)