QUESTION:
I performed an AC analysis using a 2D axisymmetric model of a coil wrapped around a permeable core. I calculated coil inductance L by two ways: magnetic energy (W) computation that gives L by W=1/2Li2, and flux computation (F) that gives L by F=Li (i is the coil current). The two values obtaines for L do not match. Why ?
ANSWER:
The inconsistency you see probably stems from the way you are post processing AC results. In your input file, the SENERGY macro is used to extract AC stored magnetic energy, which is a "time averaged" value for a complete cycle of operation. There are no electrically conductive parts in your model, so results are pure real. In this special case, AC energy is exactly half the DC energy associated with the real part of the results, and an energy based assessment of inductance may be accomplished 2 ways:
1) Use SENERGY,,1 to extract time averaged stored magnetic energy W_ac. Evaluate energy-based inductance L_energy using W_ac = 1/2*L_energy*i_rms^2, where i_rms is the root mean square of the amplitude of the coil current i, i.e., i_rms = i/sqrt(2)
2) Use SENERGY,,0 to extract the instantaneous stored magnetic energy associated with the real part of the solution, W_dc, which prevails when the electrical angle is zero. Evaluate energy-based inductance L_energy using W_dc = 1/2*L_energy*i^2, where i is the amplitude of the coil current
You have used the time averaged AC energy with the amplitude of the coil current rather than the rms current, which leads to an incorrect result.
Attached a modified version of your input file that evaluates energy-based inductance both ways. Results are identical:
L_energy = 5.064e-7 H
Next, your flux-based evaluation of inductance considers flux passing through the coil at a section halfway along its length. If I plot fluxlines, I see significant flux leakage between the midspan and the ends of the coil. I therefore used 2 paths: one to evaluate flux at the coil midspan and an
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QUESTION: I performed an AC analysis using a 2D axisymmetric model of a coil wrapped around a permeable core. I calculated coil inductance L by two ways: magnetic energy (W) computation that gives L by W=1/2Li2, and flux computation (F) that gives L by F=Li (i is the coil current). The two values obtaines for L do not match. Why ? ANSWER: The inconsistency you see probably stems from the way you are post processing AC results. In your input file, the SENERGY macro is used to extract AC stored magnetic energy, which is a "time averaged" value for a complete cycle of operation. There are no electrically conductive parts in your model, so results are pure real. In this special case, AC energy is exactly half the DC energy associated with the real part of the results, and an energy based assessment of inductance may be accomplished 2 ways: 1) Use SENERGY,,1 to extract time averaged stored magnetic energy W_ac. Evaluate energy-based inductance L_energy using W_ac = 1/2*L_energy*i_rms^2, where i_rms is the root mean square of the amplitude of the coil current i, i.e., i_rms = i/sqrt(2) 2) Use SENERGY,,0 to extract the instantaneous stored magnetic energy associated with the real part of the solution, W_dc, which prevails when the electrical angle is zero. Evaluate energy-based inductance L_energy using W_dc = 1/2*L_energy*i^2, where i is the amplitude of the coil current You have used the time averaged AC energy with the amplitude of the coil current rather than the rms current, which leads to an incorrect result. Attached a modified version of your input file that evaluates energy-based inductance both ways. Results are identical: L_energy = 5.064e-7 H Next, your flux-based evaluation of inductance considers flux passing through the coil at a section halfway along its length. If I plot fluxlines, I see significant flux leakage between the midspan and the ends of the coil. I therefore used 2 paths: one to evaluate flux at the coil midspan and another to determine flux at the end. I arithmetically averaged these 2 very different values to get a more representative value for use in a lumped parameter assessment of flux-based inductance using L_flux = Flux_ave/i The resulting value is: L_flux = 4.174e-7 H Discrepancy between the energy and flux based evaluations of inductance is still quite high, but much better than the 2 numbers you originally calculated. I suspect that if you create more paths along the length ofthe coil and possibly additional paths extending to the coil OD to determine an average coil flux, the flux based assessment of inductance will converge to that determined by the energy method. |
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