## 103 – Efficiency Analysis of a Permanent Magnet Synchronous Motor

### Overview A permanent magnet synchronous motor rotates by converting electric energy to mechanical energy.
The important thing when converting energy is efficiency indicated by the power factor for the amount of current effectively used, as well as the percentage of output versus input.
Evaluating the power factor and input/output characteristics that account for efficiency is necessary to design a highly efficient motor.
This example presents the use of a magnetic field analysis to evaluate the efficiency of a permanent magnet synchronous motor.

### Voltage Waveform / Current Waveform The voltage waveform and current waveform for the U-phase are indicated in fig. 1. The displacement between the phase voltage and phase current can be seen in the figure. θ=7.4 deg can be obtained for the phase difference θ, called the “power factor angle.” The power factor of this motor is 0.99 because the power factor is expressed as cosθ.

### Effective Power Waveform / Power Vector Plot

The U-phase active power waveform is shown in fig. 2, and the power vector plot is shown in fig. 3. The U-phase average active power is 10.7 W as indicated in fig. 2. The apparent power and reactive power can be obtained from the average active power and power factor of the three phases and displayed in a vector plot as in fig. 3.  ### Output Characteristics

The torque waveform is indicated in fig. 4, and the output characteristics are indicated in table 1. An average torque of 0.15 Nm can be obtained from fig. 4. The mechanical output is calculated from the obtained torque and rotation speed, resulting in 28.1 W for this motor. The efficiency is calculated from the active power, mechanical output, and iron loss, resulting in 82.6 % for this motor. The copper loss consumed in the coil is 4.0 W.  