Systematic Current Measurement Error Due to Back-EMF in PMSM Drives Adopting Synchronous Sampling

Even though modern Permanent Magnet Synchronous Motor (PMSM) control techniques are digitally implemented, measurement of phase currents requires analogue domain sensing, sampling and conversion to a numerical form that is then fed to the digital controller as a feedback information. The piecewise linear approximation in synchronous sampling method enables the calculation of average value of stator current for a Pulse Width Modulation (PWM) cycle by sampling once at the middle of the modulation period. The stator currents of a PMSM drive change with the imbalance between the input supply voltage and the back-EMF. The PWM synthesized input voltage varies discretely over the control cycle, but back-EMF of the motor is continuously varying (sinewave), since the rotor moves continuously. The interaction of this discrete input voltage and continuous back-EMF causes non-linearity of the current waveform. Hence, the value of stator current sampled at middle of the modulation cycle deviates from the actual average value, causing the measurement error. In this paper, the current measurement error due to back-EMF in inverter-fed PMSMs with synchronous sampling is mathematically described for the first time. Improved analysis and understanding of this measurement error source is expected to contribute to the effective design and control of electric drive systems. The analytical model has been verified by means of simulations and experimental results.