Technology / Technical guide
Winding Space Harmonics: Position, Motion and Time Frequency
A space harmonic describes variation across position. A time harmonic describes variation as time passes at a specified observation point. Winding distributions can create spatial field components, and relative motion can turn those components into time variation without making the two descriptions interchangeable.
Always ask which coordinate is varying.
A spatial order, an electrical angle and an observer’s motion are required before a time frequency can be assigned.
01 / Position dependence
A field pattern can contain several spatial orders.
An idealised winding-produced magnetomotive force can be represented as a function of position around an air gap.
An idealised winding-produced magnetomotive force can be represented as a function of position around an air gap. The fundamental is one spatial component; higher orders have shorter repeating patterns in the same declared coordinate. They describe the distribution of the source, rather than a time-current spectrum by themselves.
MIT’s winding-inductance notes treat space harmonics of winding magnetomotive force within a narrow-air-gap model. The introductory scope excludes several additional reactance contributions. A drawing of evenly spaced slots is therefore not sufficient to infer an actual harmonic spectrum or a complete inductance model.
02 / Coordinate choice
Mechanical and electrical angles need a conversion.
Let θm be a mechanical position angle and p the assumed pole-pair count.
Let θm be a mechanical position angle and p the assumed pole-pair count. For the fundamental magnetic periodicity, θe = pθm. A spatial component written cos(hθe) has order h in electrical angle, corresponding to hp repetitions around a complete mechanical revolution.
A hypothetical model with two pole pairs and spatial order three therefore has six repeating periods around the mechanical circumference. These counts are invented to explain the coordinate conversion. They specify no MARSTON pole count, winding harmonic or measured air-gap pattern.
03 / Motion mapping
Time frequency depends on relative motion.
Consider a pattern fixed in one reference frame, F(θe) = Ah cos(hθe + φh).
Consider a pattern fixed in one reference frame, F(θe) = Ah cos(hθe + φh). If an observer passes through it with constant electrical angular speed Ωe relative to that pattern, the observed angular frequency magnitude is |hΩe|. The phase offset changes timing, rather than that magnitude.
If pattern and observer move together, this relative-motion contribution can become constant at that observer. Another observer can see a different time variation. The frequency statement requires both reference frames; multiplying an order by shaft speed without defining the pattern’s motion can give the wrong interpretation.
04 / Winding factors
Turn placement weights individual spatial contributions.
Distributed turns do not necessarily link each field component with the same proportion.
Distributed turns do not necessarily link each field component with the same proportion. Contributions can add or cancel according to their spatial phase. A winding factor associated with the fundamental therefore does not automatically describe every higher-order component.
The source notes explicitly distinguish harmonic winding factors. This is a geometric weighting concept, separate from resistance or insulation material. Changing a hypothetical turn distribution may change several weighting factors simultaneously; it does not establish a universal method for improving every torque or loss characteristic.
05 / Physical outcomes
A harmonic is a contributor, not a complete diagnosis.
Spatial field components can interact with other fields, motion and material response.
Spatial field components can interact with other fields, motion and material response. Their effects may appear in induced waveforms, electromagnetic force or losses, depending on the model. A spatial order alone does not determine the amplitude of any of those outcomes.
The loaded torque-ripple guide discusses torque as an outcome with several possible contributors. The THD guide concerns a time waveform at an electrical measurement boundary. Neither quantity is simply the winding’s space-harmonic index.
06 / Reading scope
Keep the field model and observation point visible.
A meaningful spatial description identifies position, angle convention, order, amplitude and the frame in which the pattern is fixed.
A meaningful spatial description identifies position, angle convention, order, amplitude and the frame in which the pattern is fixed. A corresponding time description additionally identifies observer motion and any time dependence already present in the excitation. This prevents one spectrum from being relabelled as another.
FD14-50KW’s confirmed PMSG architecture does not disclose slot count, pole count, winding distribution or harmonic amplitudes. This guide presents a coordinate and mechanism explanation. It establishes no measured harmonic reduction, winding optimisation or converter waveform performance for any MARSTON model.
Related technical guides: Generator Armature Reaction: How Load Current Changes the Field · Generator Flux Linkage and Leakage: Define the Reference · Two-Inertia Torsional Vibration in Wind Generators.
General background: MIT OpenCourseWare: Winding Inductances and Space Harmonics. 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 |
|---|---|---|
| Spatial variable | θm or θe | State whether the angle is mechanical or electrical. |
| Pole pairs | θe = pθm | Applies to the defined fundamental periodicity. |
| Spatial order | h in cos(hθe + φh) | An index of positional repetition. |
| Relative motion | Ωe in rad/s | Observer motion relative to the stated pattern. |
| Time frequency | |hΩe|/(2π) in Hz | Constant relative speed and a frame-fixed pattern. |
Engineering questions.
Is a space harmonic a distorted time-current waveform?
Not by definition. It describes positional variation; time variation needs an observer and motion.
Does third spatial order mean three repetitions per mechanical revolution?
Only if the angle is mechanical; electrical-angle order also involves pole pairs.
Can a moving pattern look constant?
Yes, to an observer moving with that pattern when there is no additional excitation variation.
Does one winding factor apply to every order?
No. Different spatial orders can have different geometric weighting.
Can THD identify a complete spatial field distribution?
No. THD concerns a specified time waveform and does not uniquely reconstruct the spatial field.
Does the example specify a MARSTON winding?
No. Its assumed order and pole-pair count are mathematical examples.
Technical enquiry
Discuss the technical question.
A space harmonic describes variation across position. Share the model and applicable operating or design information for an engineering discussion.