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# Motor torque oscillations during DOL start

## Motor torque oscillations during DOL start

(OP)
http://home.comcast.net/~electricpete/eng-tips/NewOscSummaryR4.ppt

In the thread below, we discussed various strange predictions from the induction motor transient model, including torque oscillations during start
thread237-248895: quiz - can a DOL-start unloaded induction motor "overshoot" sync speed

In the following thread, side discussions led again to the same topic of torque oscillations

Milovan pointed out some interesting features of the locked rotor torque oscillations... namely that they persist much longer than the obvious dc in the currents.  It raises a question where these torque oscillations really come from.

I have attempted to answer that question and several other questions about model results, by referring back to the model (explaining torques in terms of currents, explaning currents in terms of the equivalent circuit).

The reasons for this torque can be traced to very small remaining dc components which produce a torque that seems far out of proportion to their magnitude (explained slide 19).  The locked rotor condition actually provides a simpler analysis since the rotor=stator reference frame d and q circuits become uncoupled so we can study the dc current behavior very simply in the d-axis circuit.

Translating these results conclusions to a normal (vs locked rotor) start is a little tougher.   We can no longer uncoupled the q and d circuits.  It is no longer a simple dc, but something like a rotating dc... I have not fully explored the reasons... only provided simulation outputs.

I have included a lot of the discussion in "question and answer" format.  The questions usually identify things that didn't seem immediately obvious (to me), but can be explained.

=========CONTENTS =======
SLIDE 1 – Brief TOC
========Notation/Conventions etc.=====
SLIDE 2 Krause's equivalent circuit for transient analysis of SCIM.
SLIDE 3 transformation between d-q and stationary a/b/c
SLIDE 4 Transferring d-q variables between reference frames
SLIDE 5 Various ways to describe the same set of balanced forward rotating voltages (or currents).
SLIDE 6 Notation
SLIDE 7 Example Motor Parameters used for the simulation (Milovan's motor )
========LOCKED ROTOR SIMULATION RESULTS/ANALYSIS=====
SLIDE 8 Locked rotor torque vs time. Has small dc component approx 2500 N-m and large LF frequency oscillating component of 18,000 N-m. The ac component decays away with time constant of approx -1*(2.5)/LN(0.3/0.9)=2.3 sec... will explain this time constant later
SLIDE 9 Locked rotor torque zoom-in 0-1 seconds. There is a torque oscillation buildup period from t=0-0.15 and then a torque oscillation decay period from 0.15 sec on.
SLIDE 10 Locked rotor q-axis currents in rotor (or stator) ref frame. No dc or other distortion evident.
SLIDE 11 LR d-axis currents in rotor (or stator) ref frame. Similar to q axis, except we now have decaying dc component decaying with approximately time constant Tsc. QUESTION:There appears to be nothing blatantly unusual past 0.1 seconds, so where does torque oscillation come from?
SLIDE 12 Locked rotor stator currents I1A/B/C is s or r ref frame. Similar to the d-axis currents we see rapid decay at time constant Tsc decay, but nothing else obvious remains after 0.1 seconds
SLIDE 13 Question 1:  WHERE DOES THE TORQUE OSCILLATION COME FROM
SLIDE 14 Answer: Look again at the stator/rotor frame currents. We can see the magnetizing (which is sum of stator and rotor) has a very very small dc offset. There is also dc present in the stator and rotor branches, more details in next slide.
SLIDE 15 Red = d-axis magnetizing current. Has DC component with rapid initial decay (~Tsc) followed by slower decay (~Toc). This dc component includes large dc component from I2dr (green) and smaller dc component from
I1dr (blue). No dc offset is present in the q axis component in this scenario. The magnitude of this dc offset (200A @ 1 sec) is small compared to LRC. This small dc current interacts with the LF ac to cause the 1*LF oscillations in torque.
SLIDE 16 Study the current during the "torque buildup period"
SLIDE 17 Study the current path for circulating current during the "torque oscillation decay period" and find associated
time constant.
SLIDE 18 Question: Why does torque increase during the torque buildup period even though dc currents are decreasing • Answer: Torque can be expressed as cross product of stator current and magnetizing current. The peak of the torque occurs at the peak of the magnetizing current (Idmr). This peak in magnetizing current occurs when the rotor dc current passes from positive (during the torque
build upperiod) through zero (at torque peak) to negative (during the torque decay period). During the torque buildup period, the Idmr =I1dr
+ I2dr is decreasing because I2dr is opposite polarity to I1dr and decreasing faster than I1dr.
SLIDE 19 Question – How does the miniscule dc current cause such large torque oscillations?
• Answer: We will examine how the currents interact to create these torquest in next several slides... The bottom line is that the large 12,500A pk stator and
rotor LF currents are practically in-phase, so their cross product (which creates the dc=average torque) is relatively low (the LF current is inefficient at
creating torque due to phase angle). In contrast, the space phase angle of the LF currents continuously changes with respect to the DC and passes
through the worst case 90° spatial relationship to dc twice per cycle, resulting in maximum torque (cross product is maximum when arguments are 90
degrees apart).
SLIDE 21 Sync Ref Frame currents – we can see I1q*I2d ~ I1d*I2q -> cross product is very small and dc component of torque is very small in relation to currents. Need to look at magnetizing component (next slide) for better estimate
SLIDE 22 ** [LR_J=1E6] Sync Ref Frame Estimate average component of torque. Imqe~0. I1qe~0.06*20000=1200. I1de~0.02*20000=400.
Tq = (3/2)*(Poles/2)*(Lm) * (I1q*Imd-Iqd*Imq) ~ (3/2)*(6/2)*(0.0015) * (1200*400-Iqd*0)=3200N-m. Not too far from the value that we eyeballed from torque graph (2500.)
SLIDE 23 Look at sync ref frame currents and they tell the same story LF reverse rotating current in sync frame correspond to our previously-seen dc in the stator/rotor ref frame. At approx 0.15 seconds where oscillating T envelope is near max, the oscillating components of rotor current pass through a zero and reverses phase (corresponding to reverseal of dc direction in stationary ref
frame). We can see that the magnetizing LF remains perfectly steady during this period, suggesting the magnetizing branch dc is relatively constant, it is just shifting paths.
SLIDE 24 Question: if LF in sync frame is associated with dc in stationary frame, and dc in stationary frame is limited to d axis, then why do we see LF in the q axis in previous (sync) slide?
• Answer:There is not 1:1 correspondence between stationary/rotor frame d value and sync frame d value.... instead we transform the (d,q) pair from
====NORMAL-INERTIA DOL START SIMULATION RESULTS====
SLIDE 25 [LR_J=1E6] Boost magnitudes of magnetizing components in sync ref frame. We see that the LF portion is decaying in this sync
ref frame.. that corresponds to slow decay of dc in the stator/rotor ref frame.
SLIDE 26 [Normal start: J=104] Torque. Torque oscillations reaches same peak, but decay away much faster than
they did during locked rotor start
SLIDE 27 [NormJ=104] I1qe & I1de. DC + s*LF. q leads d -> s*LF rotates backwards
28 [NormJ=104] I1qr and I1dr. Osc dc + s*LF. d leads q => s*LF rotates forward. Cannot ascertain lead/lag of the slowly varying dc.
SLIDE 29 [NormJ=104] I1qs and I1ds. Oscillating DC + LF. LF d leads q -> LF rotates fwd. Oscillating d leads q ->
slow dc rotates forward
SLIDE 30 I2qs and I2ds. Both LF and slow DC rotate fwd in this ref frame
SLIDE 31 Norm. I2qr and I2DR
SLIDE 32 Question: Slowly oscillating DC is larger fraction of current for DOL start than dc was for LR... how come does not result in even
larger oscillating torques?
• Answer: Not sure. Perhaps look at magnetizing current and phase relationships.
SLIDE 33 [NormJ=104] I1A/B/Cs – Oscillating dc + LF. A leads B leads C -> LF rotates fwd
SLIDE 34 [NormJ=104] I2qe and I2de. DC plus s*LF. For s*LF portion, q leads d => s*LF rotates backwards.
SLIDE 35 [NormJ=104] I2qr and I2dr. Decay/osc dc plus s*LF. d leads q-> s*LF rotates forward. Not clear how the dc
rotates
SLIDE 36 [NormJ=104] I2qs and I2ds. Decay/osc dc plus LF. d leads q-> LF rotates forward. Also the slow osc dc
rotates fwd
SLIDE 37 [NormJ=104] Rotor frame d axis current
SLIDE 38 * Stator frame mag currents (0-3sec). DC shows a fwd rot pattern.
SLIDE 39 Norm: I1qr, I2qr, Imqr. Like locked rotor start, there is no initial dc present. But unlike locked rotor start,
there is oscillating dc showing up in q-axis
SLIDE 40 [Norm J=104]: I1dr, I2dr, Imdr. Like locked rotor start, the high initial dc shows up in the d axis. Later
pattern is different
SLIDE 41 * Rotor frame mag currents: (0-3 sec). Osc has possible slight backward rot. Q: Why does it tail off to dc? A: At no- load SS, rotor current goes to 0 and stator
current is left... AND rotor ref frame eventually becomes sync ref frame where stator current is dc
SLIDE 42 Question
• Q – What reference frame does Torque = 1.5*Poles/2* Lm * I2 x I1 apply in?
• A – Any reference frame, as long as I2 and I1 are both expressed in the same ref frame.
• Q –But if I change between reference frames, that changes the values of I2 and I1 , so wouldn't the computed torque change?
• A –In going from one ref frame to another ref frame at some given time t, the I2 and I1 angles would change, but both by the same amount,
so the angle between them will remain the same, their cross product remains the same, and the torque remains the same.
SLIDE 43 Q&A
• Q: Why put the d coordinate first in the cross product?
• A: d leads q corresponds to forward rotation of an ABC sequence system (just like the x coordinate cos leads y coordinate sin in CCW
rotation in the x-y plane).
• Q – I thought d component corresponds to reactive current and q corresponds to real current. In that case shouldnt' q lead d?
• A – Indeed in the sync ref frame with angle of Va defined as 0: d does correspond to reactive current and q corresponds to real current.
However these components are dc, so there is no "leading" behavior evident in the sync ref frame. When we transform to any other
forward rotating reference frame, d leads q. It is noteworthy that the transformation involves 2 coordinates at a time, not 1. So we don't
individually transform I1qe to I1qs and I1de to I1ds, we transform the pair (I1de,I1qe) to (I1ds,I1qs).
• Q Is the starting LF torque oscillation similar to torque oscillation from the steady state oscillation expected for single-phase motors or
unbalanced 3-phase motors?
• A No. One big difference is the frequency: single-phase or unbalanced 3-phase motors have 2*LF torque oscillation. This is s*LF torque
oscillation.
• Q - Explain the nature of the slowly oscillating DC during DOL start.
• A - Beats me. But it causes the torque oscillations in similar manner to Locked rotor start.

=====================================
(2B)+(2B)'  ?

### RE: Motor torque oscillations during DOL start

(OP)
Aside from discussion of how/why the model creates these torque oscillations, I meant to ask a question:

QUESTION: Has anyone seen evidence of large s*LF torque oscillations (starting at line frequency and decreasing in frequency as speed increases) during DOL start of an induction motor?

You can see this feature shown in many simulations posted in textbooks and IEEE articles, but I haven't seen anyone ever mention any problem created by these torque oscillations.  In contrast, there are a few articles addressing sync motors where torque oscillations during startup occasionally excite a torsional resonant frequency. I realize there are some different mechanisms at work in a sync machine (like reluctance variations due to salient poles), but I'd still think that since the induction motor predicted torque oscillations are so large (breakdown torque or more), and induction motors are so common, if there really was a torque oscillation present someone would have seen some effects from it.

=====================================
(2B)+(2B)'  ?

### RE: Motor torque oscillations during DOL start

Probably just relevant enough to annoy you:

A FHP PSC motor built into a single diaphragm air compressor mounted on soft rubber isolators inside a medical instrument managed to fill a doctor's office with smoke over the course of a weekend.  ISTR we were asked to repaint the office and replace the carpet, in addition to repairing the instrument.

We were able to duplicate the failure in our lab.  Because an unloader valve failed to open, the compressor was trying to start against reservoir pressure.  It couldn't quite make it through the first half rotation, and fell back from just before TDC down to somewhere near BDC. ... and kept doing it indefinitely.  The motor was developing enough back emf to keep it from blowing the fuse, while heating up enough to cause the paint on the windings and shell to smoke and char.  In the lab, the entire compressor was rotating nicely, maybe 1/4 turn, in resonance with the crank.  We couldn't make it happen when the compressor was tied down with rigid mounts; the fuse blew quickly then.  But we needed the acoustic isolation, so we changed the unloader valve.

Mike Halloran
Pembroke Pines, FL, USA

### RE: Motor torque oscillations during DOL start

(OP)
That's a weird one Mike.

If it were a 3-phase motor, I'd have a hard time believing it.

It is maybe a hair more believable for single phase motor, since apparently PSC can have low starting current below 200% of FLA.
http://www.clrwtr.com/Single-Phase-Electric-Motors-Characteristics-Applications.htm

#### Quote:

SC motors have low starting currents, usually less than 200% of rated load current
That means if the  fuse is set to provide steady state trip somewhere above FLA (like 140%), it is not too far below LRC (at least not as far below as it would be for 3 phase motor).

Still tough to imagine that that small movement less than 1 turn could reduce the current significantly below LRC. But you never know...

=====================================
(2B)+(2B)'  ?

### RE: Motor torque oscillations during DOL start

electricpete,

Excellent work. So final conclusion is that Krause was right. I will read this carefully.

Milovan Milosevic

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