Technology / Technical guide
Permanent-Magnet Operating Point: Curves and Load Lines
A permanent magnet does not operate at one fixed flux density simply because its material has a stated remanence. Its magnetic state also depends on the surrounding magnetic circuit. A load-line construction makes that distinction visible under a declared simplified model.
Material response and magnetic-circuit constraint meet at an operating point.
Keep the normal demagnetisation curve, external magnetic path and temperature reference separate before interpreting their intersection.
01 / Curve coordinates
Normal and intrinsic curves describe different quantities.
A normal demagnetisation curve uses magnetic flux density B against magnetic field strength H.
A normal demagnetisation curve uses magnetic flux density B against magnetic field strength H. In SI units, magnetic polarisation J is related by B = µ0H + J. An intrinsic curve using J therefore is not interchangeable with the normal B curve on the same H axis.
Remanence describes the curve at zero applied H under its specified magnetic history. It is not automatically the flux density present at every working point. A material-curve intercept and the field delivered through a complete machine’s air gap describe different boundaries.
02 / Circuit constraint
The external path introduces another relationship.
In a simple fixed-geometry magnetic circuit without externally applied magnetising excitation, the magnet and its return path must satisfy a common flux and magnetomotive-force balance.
In a simple fixed-geometry magnetic circuit without externally applied magnetising excitation, the magnet and its return path must satisfy a common flux and magnetomotive-force balance. With idealised linear external reluctance, that balance can be represented by a descending line on B-H axes.
Arnold’s magnet reference illustrates the normal-curve intersection and the load-line slope convention. The positive reported permeance coefficient represents a slope magnitude under its declared units or normalisation. An unlabelled number cannot be compared across B-H axis systems without checking those conventions.
03 / Intersection
Neither the curve nor the line alone sets the state.
The operating point in this simplified picture is where the material’s normal curve and the magnetic-circuit constraint intersect.
The operating point in this simplified picture is where the material’s normal curve and the magnetic-circuit constraint intersect. Holding the material curve fixed while changing the external path can move the intersection. Holding the path fixed while changing the curve can also move it.
These are two different hypothetical comparisons. A narrower return path, an altered air region or another geometric change cannot be treated as a temperature coefficient. Likewise, a temperature-dependent material curve cannot be analysed solely by relabelling the geometry-derived line.
04 / Loaded excitation
A current-produced field changes the constraint.
Additional winding excitation can reinforce or oppose the magnet’s field in the relevant direction.
Additional winding excitation can reinforce or oppose the magnet’s field in the relevant direction. The simple no-external-excitation load line then needs modification to represent that contribution. A full machine can also contain nonuniform paths, leakage and local saturation beyond a single-line approximation.
The armature-reaction guide explains current-produced field interaction. It does not imply that every opposing component causes lasting demagnetisation. Operating position, magnetic history and the material’s response must remain part of that interpretation.
05 / Curve excursions
Returning along a recoil path differs from retracing everything.
A limited change can move the magnetic state along a recoil relationship.
A limited change can move the magnetic state along a recoil relationship. A larger excursion into an unfavourable region can result in a different state after the original external conditions return. Distinguishing those behaviours requires the applicable curve family, rather than one attractive intercept number.
The temperature and demagnetisation guide separates reversible and irreversible changes. This page instead explains how a circuit constraint locates the working point. Neither approach alone supplies a universal temperature limit or acceptable reverse-field threshold.
06 / Model scope
An operating-point diagram is not a magnet specification.
A readable diagram identifies B or J, H, units, temperature, magnetic history and the external-circuit assumptions.
A readable diagram identifies B or J, H, units, temperature, magnetic history and the external-circuit assumptions. A point drawn on an unspecified curve establishes little about an actual assembly. The gap field also requires the relationship between magnet flux and the selected air-gap region.
FD14-50KW is confirmed as a permanent-magnet direct-drive generator, but no magnet grade, load-line coefficient or allowable operating-point region is specified here. The explanatory construction supplies no magnet selection, geometry modification or demagnetisation test procedure for that machine or any other MARSTON model.
Related technical guides: Generator Armature Reaction: How Load Current Changes the Field · Magnetic Energy and Coenergy: Fixed Variables in Torque · PMSG Saliency: Directional Inductance and Reluctance Torque.
General background: Arnold Magnetic Technologies: Magnet Curves and Operating Load Line. 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 |
|---|---|---|
| Normal curve | B versus H | Flux density and field strength use distinct units. |
| Intrinsic curve | J = B − µ0H | Do not substitute J for B without conversion. |
| Load line | External magnetic-circuit constraint | Geometry, excitation and units are declared. |
| Operating point | Curve-line intersection | Same temperature and model reference. |
| Recoil behaviour | Return after a field excursion | Depends on magnetic history and applicable curve. |
Engineering questions.
Is remanence the working air-gap flux density?
No. It is a material-curve quantity at a specified reference condition.
Can normal and intrinsic curves be interchanged?
No. Their vertical quantities differ by µ0H in SI.
Does the load line come only from the magnet material?
No. It expresses a constraint associated with the surrounding magnetic circuit.
Is a permeance coefficient always written with identical units?
No. Axis units and normalisation must accompany the reported value.
Does an opposing field always leave permanent loss?
No. The excursion and applicable magnetic response determine whether the change is reversible.
Does MARSTON publish a magnet grade in this explanation?
No. PMSG confirmation does not establish a particular magnet material or working-point boundary.
Technical enquiry
Discuss the technical question.
A permanent magnet does not operate at one fixed flux density simply because its material has a stated remanence. Share the model and applicable operating or design information for an engineering discussion.