Calculating inductance -- Mystery units?

[Jamie1234]

TL;DR Summary

Corroborating the output of a trivial equation

Hello.
I would like to replicate the plot (a figure) provided in an example. The example is presented in a journal paper and shows the calculation for the inductance of a motor with known torque and angular speed.
Below is the figure, and the table of parameters provided in the paper

Border 2 in the above figure is given by equation 10, below:

Calculating the inductance for the values of magnetic flux 0.24:0.05:0.260 as shown in the Figure, we obtain the values:
La_10 = 0.0000 + 0.0115i, 0.0000 + 0.0118i, 0.0000 + 0.0120i, 0.0000 + 0.0123i and 0.0000 + 0.0126i
Am I going mad?? :/ .

Code snippet:
N_a = 1500 % Speed [RPM]
Ta = 10 % Torque [Nm]
I_am = 20 % Armature current limit [A]
V_om = 100 % induced voltage limit [V]
V_lim = 160 % Voltage limit of inverter [V]
Flux_PM = [0.240:0.005:0.260]
La_10 = 1 / I_am * sqrt((V_om/N_a)^2 - Flux_PM.^2)
plot(Flux_PM, La)

 

[Jamie1234]

For those interested in the paper:
https://www.jstage.jst.go.jp/article/ieejjia/6/6/6_409/_pdf

 

[Baluncore]

Welcome to PF.

Am I going mad?? :/ .

You have imaginary inductance values, so it may drive you mad.

I suspect the subtraction within the square root is doing that to you. You will need to check the absolute values of those variables before subtraction, one or both of them would appear to be wrong. Is one dependent on the other, and you are not evaluating that deeper dependency ?

 

[Jamie1234]

Hi Bluncore. Thanks for your reply. Yes, mad as a hatter.

Yes, it's the subtraction in the square root as you mention. What gives me pause / confuses me; the paper was peer reviewed and published, the figure was constructed, and the results validated (in the paper). So it must be I that is mad..?

However; looking at the figure and table.
If we take a value on the x axis (flux linkage), say.. psi_a = 0.240, and from the table (and equation) we have, omega_base = Na = 1500 [RPM], and v_om = 100 [V], we obtain:
sqrt( ( v_om / omega_base)^2 - 0.240^2) = sqrt( (100 / 1500)^2 - 0.240^2) = sqrt( 0.0044 - 0.0576).

And yet, in the figure, for psi_a = 0.240 we have a value for the inductance of ~ 10.5 e-3 (shown in the figure to be the first point of boundary 2).

So who's crazy? and how has this magical value been obtained I wonder.