Technology / Technical guide
Generator Flux Linkage and Leakage: Define the Reference
Magnetic flux and winding flux linkage are related quantities with different references. Leakage describes a portion of flux relative to a chosen main path or coupling relationship. It does not mean magnetic flux disappears, and it is not automatically an equivalent amount of wasted electrical power.
A field line must be related to a surface, winding or coupling path.
Clarify what a magnetic quantity links before interpreting its role in an electrical machine model.
01 / Flux definition
A surface and orientation are part of the quantity.
Magnetic flux Φ is the surface integral of magnetic flux density B through a specified surface.
Magnetic flux Φ is the surface integral of magnetic flux density B through a specified surface. Flux has units of webers, while flux density has units of teslas. For a uniform field normal to a flat surface, Φ = BA; changing field angle changes the normal component.
A hypothetical uniform 0.2 T field through 0.01 m² normal area gives 0.002 Wb. This arithmetic isolates a flux definition. It is not a field value, geometric area or measurement for any MARSTON generator, and a local field value alone does not determine a winding’s complete linkage.
02 / Winding linkage
Turns do not always link identical flux.
Flux linkage λ sums the oriented flux linked by each winding turn.
Flux linkage λ sums the oriented flux linked by each winding turn. When N identical turns each link the same Φ, λ = NΦ. More complicated geometry requires the individual contributions or an equivalent winding description. Wb-turn is a common notation, with turn treated as a count.
In the hypothetical uniform example, 100 equally linking turns would give 0.2 Wb-turn. Different turn positions can change the linked portions even when a selected local B value remains unchanged. This is why visible winding size and an external magnetic photograph cannot supply a complete linkage result.
03 / Leakage reference
Identify what the flux does not share.
MathWorks’ transformer magnetic model distinguishes a main coupled path from leakage paths.
MathWorks’ transformer magnetic model distinguishes a main coupled path from leakage paths. This is a reference example for incomplete coupling, not evidence of a transformer inside a wind-generator package. A leakage contribution can link its producing winding without sharing the selected main path.
In a machine model, slot, end-region or other local paths may be represented separately from the useful air-gap contribution. The exact decomposition depends on the model. The word leakage is incomplete unless it identifies the winding, region or mutual interaction against which that path is classified.
04 / Inductive effect
A reactive contribution can exist without equivalent heating.
A leakage path can contribute to winding inductance.
A leakage path can contribute to winding inductance. In a constant linear lumped representation its changing linkage contributes an inductive voltage associated with current change. That term influences electrical behaviour even though an ideal inductance stores and returns energy rather than continuously dissipating it.
Real magnetic regions can also have resistive, eddy-current or hysteretic losses, but those require their own mechanisms and model terms. Treating every weber of leakage flux as a lost watt would mix a magnetic quantity with a power quantity and omit the time-dependent energy relationship.
05 / Coupled quantities
Self and mutual linkage describe different interactions.
In a reciprocal linear two-winding model, self-inductance describes a winding’s linkage response to its own current, while mutual inductance describes response to the other winding’s current.
In a reciprocal linear two-winding model, self-inductance describes a winding’s linkage response to its own current, while mutual inductance describes response to the other winding’s current. Orientation determines the mutual term’s sign. A reduced mutual contribution is not equivalent to eliminating every self-linked field.
The space-harmonic guide explains geometric weighting across different field components. The armature-reaction guide concerns loaded winding fields. Together these distinctions explain why main flux, total linkage and a local field map are not interchangeable measurements.
06 / Reading limits
A reference decomposition is not a product leakage rating.
An engineering description should retain its surface, winding orientation, linking turns and main-path definition.
An engineering description should retain its surface, winding orientation, linking turns and main-path definition. If two models split main and leakage contributions differently, compare the complete linkage or terminal response before treating the individual labels as contradictory.
FD14-50KW’s confirmed permanent-magnet direct-drive architecture establishes no leakage coefficient, inductance value or field distribution. This guide supplies magnetic reference concepts, rather than a claimed loss reduction or a field measurement procedure. Other current MARSTON generator architectures are not inferred from the 50 kW confirmation.
Related technical guides: Winding Space Harmonics: Position, Motion and Time Frequency · Generator Armature Reaction: How Load Current Changes the Field · Magnetic Energy and Coenergy: Fixed Variables in Torque.
General background: MathWorks: Main and Leakage Magnetic Paths · OpenStax: Magnetic Flux and Winding Reference. 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 |
|---|---|---|
| Flux density | B in T | Local vector field, not flux divided by turns. |
| Flux | Φ in Wb | Surface and normal orientation declared. |
| Linkage | λ = sum of turn-linked flux | λ = NΦ only for equally linking turns. |
| Leakage | Flux outside the selected shared path | Reference winding or interaction identified. |
| Power distinction | Magnetic quantity versus watts | Incomplete coupling alone is not a heating calculation. |
Engineering questions.
Does leakage flux disappear?
No. It follows a magnetic path outside the selected main coupling reference.
Is flux linkage always N times one local flux?
Only when every turn links the same oriented flux.
Can leakage contribute to inductance?
Yes. A self-linked leakage path can contribute to an inductive term.
Is leakage inductance itself a heating resistor?
No. Its ideal model stores energy; dissipation needs separate loss mechanisms.
Does the transformer example establish a MARSTON transformer?
No. It illustrates the reference distinction without claiming a product topology.
Can a photograph establish a leakage coefficient?
No. A defined magnetic model and relevant evidence would be needed.
Technical enquiry
Discuss the technical question.
Magnetic flux and winding flux linkage are related quantities with different references. Share the model and applicable operating or design information for an engineering discussion.