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Technology / Technical guide
PMSG Saliency: Directional Inductance and Reluctance Torque
Magnetic saliency means that a machine’s magnetic response depends on direction relative to the rotor. It describes a physical property, whereas d-q axes describe a coordinate system. A rotating reference frame can represent either a salient or an idealised nonsalient machine.
Changing coordinates does not create a different magnetic path.
Directional flux response explains what Ld and Lq represent and why their difference can contribute to electromagnetic torque.
01 / Physical direction
Distinguish rotor geometry from the chosen axes.
The d axis is commonly aligned with the permanent-magnet flux direction, and the q axis lies perpendicular to it in the electrical plane.
The d axis is commonly aligned with the permanent-magnet flux direction, and the q axis lies perpendicular to it in the electrical plane. Magnetic material, barriers and geometry can make the response to winding excitation differ along those directions. That response is the physical issue.
The d-q reference-frame guide explains coordinate rotation. Even an isotropic ideal model can use d-q variables. Naming two axes does not establish that the rotor contains buried magnets, flux barriers or any particular construction.
02 / Flux model
Define inductance through a stated linkage model.
In one linear, sinusoidal permanent-magnet model, λd = ψm + Ld id and λq = Lq iq.
In one linear, sinusoidal permanent-magnet model, λd = ψm + Ld id and λq = Lq iq. Here λ is winding flux linkage, ψm is the permanent-magnet linkage, current is in amperes and inductance is in henries. The rotor reference and scaling must accompany these expressions.
Under these assumptions Ld and Lq describe directional proportionality. With saturation or cross-coupling, linkage can depend on both current components, and local derivatives need not equal a constant catalogue inductance. The simple equations are an explanatory approximation, rather than a universal material law.
03 / Torque terms
State scaling and current direction before using a coefficient.
For balanced sinusoidal three-phase quantities in amplitude-preserving d-q coordinates, take d aligned with magnet linkage and q ahead by 90 electrical degrees.
For balanced sinusoidal three-phase quantities in amplitude-preserving d-q coordinates, take d aligned with magnet linkage and q ahead by 90 electrical degrees. With current positive into the machine under a motor convention, Te = (3/2)p[ψm iq + (Ld − Lq)id iq], where p counts pole pairs.
The first term comes from magnet linkage interacting with current. The second is the reluctance contribution in this model. Te is positive in the selected mechanical-angle direction; generating torque may therefore be negative. An output-positive generator current convention cannot be substituted without changing the sign definitions.
04 / Model comparison
An equal-inductance limit removes one contribution.
If Ld = Lq in the stated model, the reluctance term is zero while the magnet term remains.
If Ld = Lq in the stated model, the reluctance term is zero while the magnet term remains. MathWorks uses equal directional inductances for its ideal surface-magnet representation and unequal values for its interior-magnet representation. These are model descriptions, rather than guarantees for every physical machine.
As a hypothetical comparison, retain ψm, id and iq while changing only the assumed difference Ld − Lq. The reluctance term changes proportionally. This comparison isolates saliency mathematically; it does not show that changing a real rotor leaves magnet linkage, saturation, losses and mechanical constraints unchanged.
05 / Torque meaning
A contribution is not a complete performance result.
The sign of the reluctance term depends on both the inductance difference and the current components.
The sign of the reluctance term depends on both the inductance difference and the current components. A larger numerical difference alone does not establish greater useful generating torque, better efficiency or a preferred operating condition. Mechanical input, electrical power flow and loss need consistent boundaries.
Directional inductance also differs from geometric slotting effects and no-current cogging contributions. Those phenomena can coexist, but one cannot be calculated from this constant-inductance expression alone. The coenergy guide explains the energy derivative underlying electromagnetic torque.
06 / Product boundary
PMSG confirmation does not disclose rotor saliency.
FD14-50KW is confirmed as a brushless permanent-magnet direct-drive generator.
FD14-50KW is confirmed as a brushless permanent-magnet direct-drive generator. That statement does not identify its magnet placement, pole-pair count, Ld, Lq or implemented current-control method. The generator architectures of the other four current MARSTON models are not inferred from the 50 kW machine.
This guide explains the origin of a directional term. It supplies no current references, controller gains or operating commands. Comparing two technical models requires the same coordinate scaling, magnetic assumptions and current direction before their inductance and torque expressions can be compared meaningfully.
Related technical guides: Generator Armature Reaction: How Load Current Changes the Field · Magnetic Energy and Coenergy: Fixed Variables in Torque · Generator Flux Linkage and Leakage: Define the Reference.
General background: MathWorks: PMSM model and d-q torque conventions · MathWorks: PMSM Torque Equation and Parameter Scope. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Saliency | Directional magnetic response | A physical property, independent of naming axes. |
| Linkage | λd and λq in Wb-turn | Linear model and reference scaling declared. |
| Inductance | Ld and Lq in H | Constants only within the chosen approximation. |
| Reluctance term | (Ld − Lq)id iq | Torque coefficient needs scaling and pole pairs. |
| Torque sign | Motor-reference Te | Do not mix input-positive and output-positive currents. |
Engineering questions.
Does using d-q coordinates prove saliency?
No. Coordinates can represent either equal or unequal directional inductances.
Is p the total number of poles?
No. In the displayed torque expression p is the number of pole pairs.
Does Ld = Lq imply zero electromagnetic torque?
No. The magnet-linkage term remains when iq is nonzero.
Are these inductances constant in every operating condition?
No. Saturation and cross-coupling can require current-dependent linkage models.
Does saliency specify an efficient current setting?
No. The equation explains contributions without establishing an operating strategy.
Is the MARSTON 50 kW rotor identified as an interior-magnet design?
No. Its confirmed PMSG architecture does not disclose magnet placement or directional inductance.
Technical enquiry
Discuss the technical question.
Magnetic saliency means that a machine’s magnetic response depends on direction relative to the rotor. Share the model and applicable operating or design information for an engineering discussion.