In a typical example, with V=1, leakage reactance X is 0.2 in order to limit starting current to a value of 5 per unit. Breakdown torque is then equal to 2.5. If a starting torque

of 1.5 is required, the rotor cage must be designed to give R2 = 0.06. Taking stator resistance R1= 0.03 and Po (i.e. iron loss + mechanical losses) equal to 0.04, for illustrative purposes, motor losses at rated power are then: Stator I R1 = 0.03

Rotor I R2 = 0.06 Po = 0.04 Total losses = 0.13 Efficiency is approximately 0.87, or

87%, and power factor is typically also about 0.87 for a 4-pole motor. Induction motor with variable frequency supply If it can be assumed that, with variable frequency supply,  the motor will always be started with a low supply frequency then the breakdown torque is available at starting and the starting torque constraint is removed. Rotor resistance may then be designed to have a low value, thereby reducing the rotor losses and the slip at rated power. For example, if the above value of R2 is reduced to 0.03, the losses become:

Stator I R1 = 0.03

Rotor I R2 = 0.03

Po = 0.04

Total losses = 0.10

Efficiency is increased to

approximately 0.90 or 90%.

 

A physical example

Of course, it is necessary to demonstrate that the theoretical illustration can be realized in a practical design. A real example concerned an induction motor for a compressor drive which was required to deliver 50 hp (37.3 kW) at 1450 rev/min, 30hp (22.38 kW) at 1200 rev/min and 13hp (9.7 kW) at 900 rev/min. The original design had 3-phase, 400V, 50Hz supply and achieved the required output using variable voltage control and a high- resistance cage rotor with bronze bars and copper end rings. A revised design with variable frequency supply and copper bars gave much improved performance, as illustrated by the following figures at top speed.

Design Slip Losses Efficiency Power

% kW % factor

Original 3.8 4.60 89.0 0.85

Revised 0.83 2.36 94.1 0.90

 

Synchronous motor with permanent-magnet excitation

In contrast to an induction motor, a synchronous motor with permanent-magnet excitation as no rotor I R2 losses and can be designed to achieve approximately unity power factor at rated power. Stator current at rated power, being inversely proportional to the product of efficiency and power factor, is reduced to about (0.90/0.94)(0.87/1.0) = 0.833 times the previous induction motor's value. Its losses at rated power are then:

Stator I R1 = 0.02

P0 = 0.04

Total losses = 0.06

Efficiency is increased to approximately 0.94 or 94%. A

similar argument is applicable to brushless dc motors with

permanent-magnet excitation.

 

In a practical example of a 7.5kW, 3-phase, 50Hz, 4-pole motor, a rotor with buried permanent magnets was built and tested [1]. Its measured performance at rated output gave the following results in comparison with those of the standard line-start induction  motor using the same stator:

                                      Efficiency            Power

                                           %                    factor

  IInduction motor            86.3                   0.89

 P-m motor                       92.8                   0.99

These results fully demonstrate the validity of the simplified analysis.

Conclusion
The efficiency of a permanent-magnet synchronous motor is higher than that of an induction motor because:

• The starting torque restraint is removed
• The power factor can be close to unity so the stator current is reduced
• There are no rotor I R2 losses
• The power factor of the induction motor is further reduced by the presence of magnetizing current in the stator.

For more information vist. www.automotioninc.com

Reference
[1] B.J. Chalmers and S.K. Devgan: Comparative performances of 7.5kW permanent-magnet synchronous motors with SmCo5 and Nd-Fe-B magnets, Proc. International Conf. on Electrical Machines, Pisa, September 1988, III, pp. 41-43. 2