Virtual Reduced-Order Model-Based Back EMF Estimation and Speed Sensorless Control for $LC$-Filtered PMSM Drives

The installment of the $LC$ filter at the inverter output side reshapes the sinusoidal input voltage for the motor terminal, thus, extending a longer motor lifetime. Despite this, achieving speed sensorless control remains essential for enhanced reliability and saved costs. Currently, there is limited research on the development of a speed sensorless control tailored to high-order drive scenarios due to the increased complexity and strong coupling of the system modeling, and the unaltered adoption of the prevailing general observer methodology demands a considerably large dimensional gain matrix to guarantee observability. To fill this important research gap, this article proposes a novel back-electromotive force (EMF) modeling for the permanent magnet synchronous machine drives based on the weighted current between the filter inductor current and motor stator current. This new approach converts the third-order $LCL$ model to the first-order $L$ case (virtual reduced-order modeling), which enables the estimation of back EMF without relying on voltage sensors. In addition, the observer designed based on the proposed virtual model not only removes the dependency on capacitor parameters but also reduces the size of the gain matrix. This further enhances the robustness of the back EMF estimation and simultaneously simplifies the design and computation of the observation algorithm. A Kalman filter observer for back EMF estimation is implemented as a case study to verify the proposed modeling. The efficacy of the proposed speed sensorless control is also evaluated under scenarios involving variations in filter and motor inductance.