Technology / Technical guide
PMSG Magnetic Flux, Flux Linkage & Induced EMF
A permanent magnet provides a magnetic field, but a winding’s induced voltage depends on how its linked flux changes with time. This distinction connects rotor motion to electrical voltage without turning a speed relationship into a complete loaded-generator model.
Voltage follows changing flux linkage.
Flux, flux density and flux linkage describe different quantities; the rate of linkage change produces the induced EMF.
01 / Magnetic flux
Distinguish a field density from flux through a surface.
Flux density B is expressed in teslas.
Flux density B is expressed in teslas. Magnetic flux Φ is the surface integral of the field component normal to a chosen area, expressed in webers. A strong local field and a large total flux are therefore different statements.
For a uniform field over a flat area, Φ = BA cos θ, where θ is between the field and the area normal. This simple geometry illustrates why orientation matters; an actual machine has a spatially varying field rather than one uniform patch.
02 / Flux linkage
Include the winding as well as the field.
Flux linkage λ accounts for flux linked by winding turns.
Flux linkage λ accounts for flux linked by winding turns. If every turn links the same flux, λ = NΦ. More generally it is the sum of the individual linkages. Its unit is commonly written Wb-turn, with turn a count.
Flux linkage can change as a permanent-magnet rotor moves relative to a stator winding, even if the magnet’s own field is steady in its rotating frame. The relative geometry changes what the stationary winding links.
03 / Induced EMF
Apply Faraday’s law with a stated orientation.
For a chosen winding orientation, induced EMF is e = −dλ/dt.
For a chosen winding orientation, induced EMF is e = −dλ/dt. OpenStax explains the flux rule and its directional sign. The minus sign expresses an orientation convention and the induction direction; it does not mean the magnitude is always negative.
For a sinusoidal idealisation λ = λpk cos(ωe t), the corresponding EMF is e = ωe λpk sin(ωe t). Larger electrical speed gives a larger amplitude when the same sinusoidal linkage amplitude is retained.
04 / Electrical speed
Separate pole cycles from mechanical rotation.
A synchronous machine with p pole pairs has electrical angular speed ωe = pωm.
A synchronous machine with p pole pairs has electrical angular speed ωe = pωm. One mechanical revolution can contain several electrical cycles. The maxon generator reference describes this speed-frequency distinction for its machines.
In a hypothetical mathematical example, λpk = 0.02 Wb-turn and ωe = 100 rad/s give a 2 V peak sinusoidal EMF, about 1.41 V RMS. These assumed values describe no MARSTON winding, speed or voltage constant.
05 / Loaded terminals
Keep the induced source separate from circuit drops.
Internal induced EMF is not automatically the measured terminal voltage when current flows.
Internal induced EMF is not automatically the measured terminal voltage when current flows. Winding resistance, inductive behaviour and the connected circuit affect that terminal quantity. A no-load relationship cannot determine every loaded operating point.
The term back EMF is common when the same induction opposes an applied motor drive. In generator discussion, induced or generated EMF makes the role clearer. Neither label alone establishes current, electrical power or conversion efficiency.
06 / Model scope
Use the principle without inventing machine parameters.
The speed-and-voltage guide discusses actual records; this page explains the physical relationship behind them.
The speed-and-voltage guide discusses actual records; this page explains the physical relationship behind them. A waveform that departs from the sinusoidal model requires its own flux-linkage and harmonic representation.
FD14-50KW is confirmed as a brushless permanent-magnet direct-drive generator. Its pole count, linkage amplitude and voltage constant are not specified here, and the other four current models’ generator types are not inferred from it.
Continue the review with Generator Inductance, Reactance & Impedance.
Continue the review with PMSG d–q Axes & the Rotating Reference Frame.
Continue the review with Generator Magnetic Saturation & Flux Density.
Extend the generator field review with armature reaction under load current, winding space harmonics, and flux linkage and leakage references.
Continue the electrical generator review with synchronous and induction generator principles and internal EMF and terminal voltage.
General background: OpenStax: magnetic flux and Faraday’s induced-EMF law · maxon: generator electrical frequency and mechanical speed. 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 | Magnetic flux per perpendicular area in the uniform-field model. |
| Flux | Φ in Wb | Field integrated through a defined surface. |
| Flux linkage | λ, commonly Wb-turn | Sum of winding-linked fluxes. |
| Induced EMF | e = −dλ/dt in V | Orientation and time variation matter. |
| Electrical speed | ωe = pωm in rad/s | p is the number of pole pairs. |
Engineering questions.
Does a permanent field mean zero generator voltage?
Not if linked flux changes as the rotor moves relative to the winding.
Are B and Φ interchangeable?
No. Flux density and surface-integrated flux have different meanings and units.
Is flux linkage always NΦ?
Only when the assumed turns link the same flux.
Is induced EMF identical to loaded terminal voltage?
Not generally; the winding and connected circuit affect terminal conditions.
Are the 2 V example values product data?
No. They are explicitly assumed values for the ideal mathematical relationship.
Does this explain all five models as PMSGs?
No. Permanent-magnet direct drive is confirmed here only for FD14-50KW.
Technical enquiry
Discuss the technical question.
A permanent magnet provides a magnetic field, but a winding’s induced voltage depends on how its linked flux changes with time. Share the model and applicable operating or design information for an engineering discussion.