Analysis Approach for Line-Start PM Synchronous Motors

Synchronous motors use a three-phase sinusoidal voltage source to induce a rotating magnetic field in the stator. Applying this three-phase sinusoidal voltage source to the stator winding of a synchronous motor yields the rotational magnetic field in the air gap. The permanent magnet poles mounted on the rotor try to align in this rotating field, producing a synchronous torque on the rotor. Upon starting, the damping winding on the rotor generates the asynchronous starting torque, creating a self-starting feature.

The phasor diagram for the line-start permanent-magnet synchronous motor (LSSM) in the frequency domain is shown in Figure 6.

In Figure 6, R₁, X_d, and X_q are armature resistance, d-axis synchronous reactance, and q-axis synchronous reactance, respectively. X_d is the sum of leakage reactance, X₁ and d-axis armature reactance X_ad, and X_q is the sum of X₁ and q-axis armature reactance X_aq:

For a given torque angle q, the angle that E₀ lags U:

Solving for I_d and I_q yields

The angle that I legs E₀ is

The power factor angle (or torque angle) that I legs U, is

The input power (electric power) can now be computed from voltage and current as

The output power (mechanical power) is

where P_fw, P_Cu, and P_Fe are frictional and wind loss, armature copper loss, and iron-core loss, respectively.

The output mechanical power (torque) T₂ is

where w is the synchronous speed in rad/s.

The efficiency is computed by

The motor is started the same way as for an induction motor, by using a squirrel-cage-type winding – called a damper winding in this case – that is mounted on the rotor, producing the starting torque.