article · IEEE Transactions on Industry Applications
Synchronous reluctance motors rely on direct-axis and quadrature-axis inductances that vary nonlinearly with currents and rotor position. Determining the necessary level of model detail is critical for accurately predicting dynamic behaviour and stability limits, particularly during scalar control without position sensors. An investigation evaluated three modelling approaches: full dependence on currents and rotor position, current dependence averaged across rotor position, and constant inductance values. The findings demonstrate that averaging out the rotor position introduces negligible error into the dynamic motor model. In contrast, incorporating magnetic saturation and cross-saturation is essential. Assuming constant inductances causes significant errors when predicting torque capability relative to actual motor behaviour. Furthermore, embedding magnetic saturation within closed-loop motor control enables the system to achieve maximum torque per ampere. These modelling and control approaches were verified using experimental measurements.
Synchronous reluctance motors are increasingly sought after as efficient, rare-earth-free electric drives. Simulating their performance accurately without excessive mathematical complexity helps engineers design better motor controllers. Demonstrating that position-averaged models capture dynamic performance without loss of accuracy allows engineers to simplify simulations while still ensuring motors deliver optimal torque and remain stable without costly position sensors.
This work directly benefits electric motor drive manufacturers and control system engineers developing algorithms for synchronous reluctance motors, including sensorless drives. By identifying which magnetic parameters must be modelled and which can be simplified, it enables more efficient controller designs targeting maximum torque per ampere. Because the modelling method has been validated on experimental hardware, the approach represents applied research ready for integration into industrial motor drive software.
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In synchronous reluctance motors (SynRMs), the d- and q-axis inductances (L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> ) are nonlinear functions of d- and q-axis currents (i <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> and i <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> ) and rotor position (θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ). The main research question for dynamic studies of SynRMs in this paper is how accurate should the inductance model be to have a reliable computation of dynamic behavior and stability limits? The stability limits are important in the case of V/f control without position feedback. To answer the question, we consider three cases: 1) inductances are function of id, i <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> , and θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ; 2) inductances are function of i <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> and i <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> , averaged over the position θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ; and 3) inductances are constant values, with properly chosen values. The cases 1 and 2 include saturation and cross saturation, while case 3 does not. It is found that averaging the rotor position θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> is almost not jeopardizing accuracy of the SynRM model. However, including magnetic saturation is crucial: it is observed that using constants L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> to represent the SynRM modeling leads to a large deviation in the prediction of the torque capability compared to the practical motor. In addition, including the magnetic saturation effect in the closed-loop control of SynRMs is necessary. Then, maximum torque per ampere can be achieved. Finally, the proposed method of including the magnetic saturation and the rotor position effects in the SynRM modeling has been validated by experimental measurements.
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DOI: 10.1109/tia.2016.2614954
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