Error analysis of calculating average d-q current components using regular sampling and Park transformation in FOC drives

In electric drives using voltage source inverters, motor currents contain ripple component resulting from pulse-width modulated (PWM) voltage. The frequency range of the ripples is much higher than the bandwidth of current control. Therefore the control is performed on the basis of a fundamental current component, i.e. average value with the averaging time being the PWM period. In majority of cases the average current is measured without low-pass filtering, with the use of Regular Sampling method. The method enables extraction of the current fundamental component by sampling current instantaneous value once in a PWM period, synchronously with peaks or valleys of PWM carrier signal. Regular Sampling is widely used in industry in combination with field-oriented motor control algorithms. In such a case motor flux and torque are controlled by current components expressed in a rotating reference frame d-q. The feedback signals for current controllers are calculated on the basis of sampled motor phase currents, with the use of Clarke and Park transformations. However, transforming samples of average phase currents into the rotating reference frame does not result in exact values of average d- and q- current components. This influences motor torque and flux. The error reaches considerable values in high-speed drives operating at relatively low PWM frequency. The value of the error was derived analytically, followed by simulation verification.