Calculation of Cross-Coupling Inductance and Electromagnetic Torque in Wound-Rotor Synchronous Starter/Generator

Abstract

In this paper, the cross-coupling phenomenon in the wound-rotor synchronous starter/generator system is studied. Due to the armature reaction, the excitation field is dragged away from the d-axis by the armature magnetic field and the cross-coupling inductance L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</sub> exists. What is more, the cross-coupling phenomenon also occurs in the excitation field, it means not only the mutual inductance M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">df</sub> between the d-axis and excitation field exists, but also mutual inductance M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">qf</sub> between the q-axis and excitation field exists. If this M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">qf</sub> component is ignored, this will result in a torque calculated error, especially facing an intense armature reaction, the error can be more than 20%. The mathematical expressions of cross-coupling inductance L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</sub> , M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">qf</sub> are derived. Based on these expressions, a more accurate torque equation is proposed. The validity of the proposed analysis is proved by showing the agreement with experimental results and maximum torque per ampere (MTPA) loci.