Technology / Technical guide
Generator Inductance, Reactance & Impedance
Inductance, reactance and impedance are related but different quantities. Inductance describes an applicable flux-linkage relationship; reactance describes frequency-dependent AC behaviour; impedance combines resistive and reactive effects with phase information.
Frequency changes reactance without changing the unit of L.
A useful linear model preserves both magnitude and phase, while a real machine may require operating-dependent parameters.
01 / Inductance
Relate current change to flux linkage.
For a simple linear element, flux linkage can be written λ = Li, with inductance L in henries.
For a simple linear element, flux linkage can be written λ = Li, with inductance L in henries. With the passive voltage convention and constant L, the associated voltage is v = L di/dt.
A constant current does not produce that ideal inductive voltage drop, whereas changing current does. This does not make a real winding lossless or remove its generated EMF. The element relationship describes only one part of the machine.
02 / Reactance
Include the frequency of a sinusoidal condition.
For a linear ideal inductor in sinusoidal steady state, inductive reactance is XL = ωL = 2πfL, expressed in ohms.
For a linear ideal inductor in sinusoidal steady state, inductive reactance is XL = ωL = 2πfL, expressed in ohms. The same L gives a different XL when frequency changes.
In a hypothetical example, L = 10 mH at f = 50 Hz gives XL about 3.14 Ω; at 100 Hz it is about 6.28 Ω. These values illustrate the formula, not a MARSTON inductance or operating frequency.
03 / Complex impedance
Keep resistance and quadrature behaviour separate.
A simple series R–L branch has Z = R + jXL under the stated phasor convention.
A simple series R–L branch has Z = R + jXL under the stated phasor convention. Its magnitude is √(R² + XL²), rather than R + XL. OpenStax explains this quadrature combination in sinusoidal circuits.
The imaginary term represents phase-related behaviour, not a second dissipative resistance. In the ideal element model only R dissipates average resistive power; L stores and returns magnetic energy. Real core and winding losses require additional representation.
04 / Changing parameters
Avoid treating a measured L as universal.
Inductance can depend on magnetic bias, frequency, rotor position and the definition used in the model.
Inductance can depend on magnetic bias, frequency, rotor position and the definition used in the model. Incremental inductance around one operating point need not equal an overall linkage-to-current ratio.
Coilcraft’s magnetic-component discussion illustrates inductance changing with saturation. The saturation guide explains the cause. A single constant cannot automatically reproduce every current excursion of a nonlinear machine.
05 / Machine source
Keep induced EMF in the equivalent circuit.
A generator is not merely a passive R–L load.
A generator is not merely a passive R–L load. Its induced source and winding relationships participate together in the terminal behaviour. Internal EMF, terminal voltage and current therefore cannot be related by discarding the source and using only a passive impedance magnitude.
For a permanent-magnet sinusoidal model, electrical frequency follows rotor motion, so reactance can vary with speed even where L is approximated as fixed. Coupled phases and rotor-axis distinctions may require a model beyond one isolated branch.
06 / Model scope
Use each representation for its intended question.
The d–q guide explains another representation of coupled machine quantities.
The d–q guide explains another representation of coupled machine quantities. A steady-state phasor model does not automatically describe switching edges or rapidly changing operating conditions.
No actual MARSTON winding L, R, phase arrangement or impedance curve is assigned here. The confirmed FD14-50KW permanent-magnet machine provides product context, while this page remains an explanation of ideal and operating-dependent electrical quantities.
Continue the review with Generator Magnetic Saturation & Flux Density.
Continue the review with PMSG d–q Axes & the Rotating Reference Frame.
Continue the review with Copper Winding Resistance & Temperature Approximation.
General background: OpenStax: sinusoidal reactance and impedance combination · Coilcraft: operating-dependent inductance. 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 |
|---|---|---|
| Inductance | L in H | Flux-linkage/current relationship in its model. |
| Reactance | XL = 2πfL in Ω | Linear sinusoidal steady-state condition. |
| Resistance | R in Ω | Represents the stated dissipative path. |
| Impedance | Z = R + jXL | Preserves magnitude and phase. |
| Generated source | Internal induced EMF | Separate from the passive winding elements. |
Engineering questions.
Are inductance and reactance measured in the same unit?
No. L is in henries; XL is in ohms.
Does doubling frequency double XL?
For unchanged L in the stated linear sinusoidal model, yes.
Can R and XL magnitudes simply be added?
Not for the series R–L phasor magnitude; they combine in quadrature.
Is a generator only an R–L impedance?
No. Its induced source and coupled machine behaviour also matter.
Can saturation change the applicable inductance?
Yes. Incremental magnetic response can change with operating conditions.
Are actual winding parameter values provided?
No. The numerical L example is hypothetical.
Technical enquiry
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Inductance, reactance and impedance are related but different quantities. Share the model and applicable operating or design information for an engineering discussion.