Lq

Lq is a symbol used in the rotating dq0 (or d–q) model of alternating-current electric machines, representing the quadrature-axis inductance. In this modeling framework, stator currents are decomposed into two components, id along the direct axis and iq along the quadrature axis, as seen from a reference frame rotating with the machine’s rotor. Inductances Ld and Lq describe how the machine’s magnetic circuit resists changes in those axis currents.

In machines with symmetric rotors, such as non-salient machines, Ld and Lq are approximately equal. In salient-pole machines, where the rotor’s magnetic reluctance differs along the two axes, Ld and Lq diverge. This difference is a measure of saliency and has implications for torque production, dynamic response, and control performance. Lq specifically governs the current response and voltage behavior associated with the q-axis current, iq, and thus plays a key role in how torque is generated and how the machine reacts to fast changes in operation.

Lq is an essential parameter in the modeling, simulation, and control of electric machines, including permanent magnet synchronous motors and reluctance motors. It is used in control strategies such as field-oriented control and model-based observers to predict and regulate torque and speed. Lq, along with Ld, can be determined from design data or identified experimentally, and it may vary with operating conditions due to magnetic saturation and rotor position.

See also: Ld, dq0 transformation, synchronous motor, electromagnetic torque.