Inductance plays a crucial role in the performance of a Permanent Magnet synchronous Machine (PMSM) from various perspectives:
Machine Design Aspect
Torque Production: The reluctance torque production is influenced by the inductance differences in the d and q axes when saliency exists in a PMSM. Magnetic torque is more directly influenced by magnetic field strength of rotor and stator and their alignment. However, any factor that affects inductance is likely to influence torque as well.
Fault Tolerance: Higher machine inductance helps reduce short circuit current. A fault-tolerant PMSM can be realized by designing a machine with a short circuit current equal to lower than the rated current, using a high inductance design. However, this comes at the cost of reduced power factor and less available voltage, which could affect machine speed performance.
Control Aspect
Dynamic Behavior: Lower inductance can lead to faster current changes, enhancing the machine’s ability to respond quickly to control inputs. Conversely, higher inductance results in a smoother current waveform and reduces the harmonic components of the PWM current waveform.
Understanding Inductance in Electric Machines
Inductance measures the amount of magnetic flux produced or linked per unit of current. From an energy standpoint, it can also be defined as stored energy in the coil or phase windings divided by half the square of the current.
One caveat to the definition above, in terms of flux per unit of current, is that it describes the steady-state or apparent inductance, which is useful for machine design purposes. However, when considering inductance in a control context, dynamic or incremental inductance is required. This can be determined using the current/energy perturbation method.
Note: Calculating the incremental inductance is a post-processing step in Finite Element Methods. In this process, the permeability of the loaded model is applied to the current disturbance problem, ensuring that the incremental inductance calculation accounts for magnetic saturation. Apparent and incremental inductance values are associated with apparent and differential permeability values, respectively.
Self and Mutual Inductance in Polyphase Electric Machines
In a polyphase electric machine, phase windings exhibit self and mutual inductances.
Self-Inductance: This is the property of a single coil or phase winding to induce an electromotive force (EMF) in itself when the current flowing through it changes.
Mutual Inductance: This is the property of two coils or phase windings to induce an EMF in one coil or phase winding when the current in the other one changes. This occurs because the changing magnetic flux in one coil or phase winding induces a voltage in the adjacent one, proportional to the mutual magnetic coupling between them.
When calculating the self and mutual inductance values, magnetizing and leakage inductances are of interest. The magnetizing inductance is linked to the flux that crosses the air gap, and the leakage inductance is the summation of slot leakage inductance and the end winding inductance. Both the self and mutual inductance values include the magnetizing and leakage inductance values.