1. Measured data from motor start
Measured data from motor start. Unusual wiggle in power factor with minimum in power factor occuring at same time as minimum in current envelope.

2. Motor Data

3. Motor Curves. Note values are close but not exactly same as data sheet

4. My Fitted Model Parameters. (used data sheet as target)
The Rectangular Deep bar correction that I used can be seen as equations 3 thru 5 here:
They can also be seen in Kliman’s “Handbook of Electric Motors” linked below, but there is a typo in the definition of skin depth eqn (entire expression should go inside sqrt), and another typo in (should have a - instead of + between terms in the denominator). These typo correctionscan be verified by plotting the functions to match the supplied figure:
I used two independent rectangular bar depth parameters: one for R and one for L. The reason is that the bar is not rectangular, so we cannot force a rectangular fit on both parameters R2 and L2. Providing two independent parameters allows more flexibility to match the actual target LRT and LRC. Note this correction is approximately linear variation with slip. Many references uses “cage” factor which applies simple exact linear correction vs slip... and they use independent cage factors for R2 and L2. The advantage of using rectangular bar is that the model can be forced (thru weighting factors) to make the bar depths for R2 and L2 match in those individual caes when it is known that the bar is in fact rectangular (not this case)

5. Performance of Model Parameters against target (S.I. units)

6. Model Output using steady state equivalent circuit calcs
Model Output using steady state equivalent circuit calcs. Note does not recreate the dip in torque between LRT and BDT. Also note Tq and Current are normalized by their full-load S.I. values

7. Simulation output when driving high inertia load (10 kg
Simulation output when driving high inertia load (10 kg*m^2), plotted vs speed on same scale as previous slide.... results are virtually identical, which verifies the transient simulation conforms to the equivalent circuit model.
Speed

8. Current Speed P.F. Torque Speed zoom-in
Simulated start 100% Load. Speed overshoots final speed, and minimum of current and power factor occurs at the same time as the overshoot
Current
Speed
P.F.
Torque
Speed zoom-in

9. Simulated start 75% Load. Similar to 100%, with more oscillation
Current
Speed
P.F.
Torque
Speed zoom-in

10. Current Speed P.F. Torque Speed zoom-in
Simulated start 50% Load. Even more oscillation. At this load level, the speed overshoots not just the final speed, but also the sync speed (when the red curve exceeds 1.0)
Current
Speed
P.F.
Torque
Speed zoom-in

11. Current Speed Speed zoom-in Torque P.F.
Simulated start 25% Load. Even more oscillation. This time we see the torque and power factor drop below zero
Current
Speed
Speed zoom-in
Torque
P.F.

12. Current Speed Speed zoom-in Torque P.F.
Simulated start No-Load. Most oscillation. Large overshoot of sync speed (by 0.56 hz!), accompanied by substantial negative torque from motor.
Current
Speed
Speed zoom-in
Torque
P.F.

13. Miscellaneous notes (conclusions in red)
Load was approx 75% during the actual start
Inertia of pump/motor combination is not readily available. Adjusted inertia to 0.7 kg*m^2 so the 75%-load simulation match the actual measured time to start at in the observed waveform. This was the only item in the model that was “fudged” to match the observed waveform, but seems justified since inertia is not well known for this machine and torque-speed characteristic of the model was verified against data sheet pretty carefully (if torque is right, the only other determinant of start time is inertia)
In all simulation cases above 50% load, the minimum in power factor occurs at the same time as a minimum of current. This is the same behavior as was seen in the actual waveform. In all simulation cases, the minimum in power factor corresponds to the maximum overshoot in speed (can’t confirm this for actual start because speed was not measured during the actual start)
The 75% simulation is reasonably close to the actual measured waveform... except the wiggle in power factor is not as large in the simulation as the actual. For lower load level of 50%, the magnitude of the wiggle is comparable to the actual, (but the final power factor and current ends up too low.
We can say the model is not an exact recreation. But it suggests to me that the speed did overshoot the final steady state speed during this start, as predicted by the transient model and evidenced by the minimum in power factor occurring at the same time as minimum in current.
It is acknowledged there may be other factors at work... for example burping and churning of the fluid system during start.
During the first half-second after start, the current calculated from instantaneous Id and Iq wiggles at 60hz. If convert to phase quantities and average over one cycle, I suspect the wiggle would not show up (because of the averaging period)
Speed vs time looks almost like a striaght line, which would correspond to constant accelerating torque. This is a function of the motor torque speed curve which increases very slowly from LRT. If you hold a straight-edge against the no-load curve, you can see it is not a straight line, but instead has increasing slope. As load increases, the line becomes straighter because contribution from speed-squared load torque makes the accelerating torque relatively constant.