Equivalent Circuit and Phasor Diagram of Synchronous Motor

EQUIVALENT CIRCUIT AND PHASOR DIAGRAM OF SYNCHRONOUS MOTOR

Equivalent Circuit of a synchronous motor:

Figure 3.60 shows the equivalent circuit model for one armature phase of cylindrical rotor synchronous motor.

It is seen from figure, that the applied voltage V is the vector sum of reversed back emf ie. -E_b and the impedance drop I_a Z_s. In other words, V = -E_b + I_aZ_s. The angle δ between the phasors V and E_b is called the load angle or power angle of the synchronous motor.

Except for very small machines, the armature resistance of a synchronous motor is negligible as compared to its synchronous reactance. Hence the equivalent circuit for the motor becomes as shown in figure 3.61.

From the phasor diagram figure,

AB = E_b sinδ and Eb

cosϕ = AB/ I_a X_s

So AB = I_a X_s cosϕ

E_b sin δ = I_aX_s cos ϕ⇒ I_a cos ϕ = E_b sin δ/X_s

P = VI_a cos ϕ

P = VE_b sin δ/X_s

P_in = 3E_bV/ X_s sin δ for 3-phases

Since stator copper loss has been neglected, P_in also represents the gross mechanical power (P_in) developed by the motor.

P_m = 3E_bV/X_s sin δ

Gross torque developed by the motor

T = P_m/ω_m

ω_m =2πN/60

T = 9.55 P_m N_m/N