Wound Rotor Motor Resistor 2

[ArcsNSparks]

We have a 250 HP wound rotor motor that came with a salvaged rod mill that is going to be put back in service at another nine site. The nameplate has been lost. We have a consultant's interconnection diagram from the installation that shows a 4-stage resistor bank in connected to what I would call a tap changer which is drawn like it is manually operated. My understanding is that wound rotor motors are used with rod mills in the ore processing industry to achieve high starting torque.

We would like to buy a resistor bank for the drive, but don't know what rating to specify. I am thinking that if I measure the open circuit rotor voltage with the stator energized, and perhaps also the rotor current with the no resistance in the rotor circuit, I should be able to determine the needed resistance values.



I hope someone knows more about this than I do.

 

[waross]

Open circuit voltage will give you an indication of the turns ratio between the stator and the rotor. As a guess, I would select a first step resistor that will give a calculated 150% to 200% of full load current. Stator voltage over rotor voltage = rotor FLC over stator FLC. (More or less, at rest)
You may try using some scrap iron in a plastic barrel full of salted water as a liquid rheostat to try energizing the motor with a cheap resistor in the rotor circuit.
Stand by for other suggestions.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[edison123]

Provide the open circuit rotor voltage and the motor KW to any starter manufacturer and they will give you the right starter.

Muthu

http://www.edison.co.in

 

[ArcsNSparks]

I like the idea of a cheap liquid rheostat for testing. I was thinking we would have to buy a resistor bank and test it.

 

[ArcsNSparks]

I've been talking to vendors, but I think maybe I haven't phrased the question right. I will try some more. I'll let you know if it works.

 

[lectricwes]

The "tap changer" is probably step switches. Often, these switches are timed to drop out one after the other, varying the current draw and thus the torque. Four resistors would give you five steps.

 

[electricpete]

Bill's approach is similar to the approach described here:

http://www.postglover.ca/Literature/MC105-07_Wound_Rotor_Mtr_Res_Te_Sht.pdf

Rtot =SecondaryVoltage / (SecondaryCurrent x 1.713 x PercentageStartingTorque

Bill gives you a way to compute "secondary current" at full load. It should also be on the motor nameplate as per NEMA MG-1(2009) paragraph 10.40.2

The 1.71 converts your voltages to line-to-neutral, assuming your resistors are connected in wye.

The "Rtot" reminds you that after you do the calculation for total resistance Rtot, you have to subtract out the internal rotor resistance to get the external resistance. You can measure internal resistance from slip ring to slip ring (with brushes lifted) and divide by 2 to get the resistance per wye leg (assuming rotor is wye connected.)

The target torque mentioned in that reference is 150%-200% rated torque.. in same range as Bill mentioned.

I suspect if you used 150%, you would will probably get a resistance which is slightly higher than "optimal" in the sense that you're not starting with max torque. It's not the end of the world since you're also not starting with max current.... and it will be pretty good and seems to be an industry standard approach.

You could also try to get a little fancier to try to find a more exact optimal point of maximum torque at starting. It is pretty easy to begin to analyse using the motor equivalent circuit.

Tmech = Pmech / wm = [(1-s)*Pgap] / [(1-s)*wsync] = Pgap / wsync
where Tmech = mechanical torque, Pmech = mechanical power Pgap = airgap power, wm = mechanical speed, wsync = synchronous speed.

i.e, we just proved that we kind find mechanical torque from airgap power and synchronous speed:
Tmech = Pgap / wsync

Since wsync is a constant, the the conditions for maximizing Tmech are the same as the conditions for maximizing Pgap. We can figure that out from simple maximum power transfer principles. The maximum power transfer into the element R2tot/s (i.e. airgap power) occurs when the magnitude of the Thevinin impedance supplying R2tot/s is equal to R2/s. And we want torque max at starting s=1, so we want R2tot to match the Thevinin impedance of the motor... i.e:

R2tot = |Zthevinin|
R2ext + R2int = |Zthevinin|

There are a number of ways to estimate Zthevinin, depending on what you have available or what measurements you want to do. If you have a motor data sheet available, chances are it has enough data to get a very good estimate without any further measurements.

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[ArcsNSparks]

Yes, step switches. I couldn't think of the term. That's why I put tap changer in quotes. The way the diagram is drawn, it looks like it might have been manual, but regardless I think you are right. It should be timed.

 

[electricpete]

Correction in bold: need a closing paranthesis as shown below:
Rtot =SecondaryVoltage / (SecondaryCurrent x 1.713 x PercentageStartingTorque)

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[rasevskii]

for ArcsNSparks:

Actually, in many Wound Rotor motor starters, the resistance steps are controlled by a current relay which measures stator current, allowing only the next resistance step to be cut out when the current falls below the setting of the relay. This is similar to an accelerator system used for DC motors whereby the current measured is the armature current, and the resistor group is in series with the armature circuit. A standard system used for subway trains when everything was electromechanical.

rasevskii

 

[electricpete]

I have 3 separate areas of discussion below
1 – Deriving Linear assumption torque vs current
2 – Optimal approach
3 - Questions
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1 - Deriving Linear assumption torque vs current
I was not familiar with the method described by Bill or that link. It seemed a little odd to me that we can draw a direct relationship between current and torque accross a wide range of speeds from starting to full load, so I studied it a little to come up with the explanation based on the equivalent circuit:
In the IM Eq Ckt, we can replace the leakage reactances and magnetizing reactance with a Thevinin equivalent impedance.

V1---Zth ---- R2tot'/s—ground

Where the prime (') in R2tot' implies that R2tot is expressed on a primary (stator) basis... We know the ratio between primary and secondary voltages is slip times a turns ratio. The turns ratio is equal to the voltage ratio at slip=1. Therefore it is V2/V1 where V2 is the open-circuit locked-rotor rotor voltage V2, given on the motor nameplate.

So we can express everything on the secondary (rotor) side as follows:
V2---Zth'' ---- R2tot/s—ground
where now Zth'' indicates that it is referred to the secondary side... and again V2 is open-circuit locked-rotor rotor voltage from nameplate.

Now we make a big assumption (*) that R2tot/s >>Zth'' over the range of interest from starting to full load. Under that assumption, we can rewrite the circuit as:
V2---- R2tot/s—ground

From which we can write:
I2 = V2/[R2tot/s] [eq 1]

Additionally, as per the post dated 25 Mar 11 14:11 above, we know
Torque = Pairgap/wsync
Under our assumption, Zth is negligible, so the circuit is resistive and
Pag = 3*V2*I2

Putting together the 2 equations above:
Torque = 3*V2*I2/wsync.

Since V2 and wsync are constant, we can simply say
Torque proportional to I2 (where I2 computed from eq1 above)

* The assumption R2/s>>Zth would not apply for SCIM during start since in that case Zth >> R2. But I believe it does apply pretty well for SCIM from start through full load.

By the way, conclusions based on equivalent circuit accross a range of conditions from start to run are much more reliable for WRIM than SCIM because WRIM does not have the deep bar effect.
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2 - optimal approach
New subject - I suspect I was wrong to suggest that the optimal solution involves an initial starting resistance that moves breakdown torque to s=0. (By the way I didn't invent that idea, I have read it several places). One reason that I think I'm wrong is that many industry sources suggest to use Bill's approach above shooting for initial torque of 1.5*rated using linear approach (1.5 is used by the link above and also by EASA). This puts will put the slip of breakdown torque far above 1.0 (for example 1.7 slip) for two reasons:
1 - actual breakdown torque is likely around 2.5, much higher than the 1.5 target
2 – the actual slip at breakdown torque is higher than we predict by this particular linear extrapolation method used. i.e. the linear extrapolation carries and error and direction of the error adds to error 1.

My initial thought was that we strive to maximize Torque/Current ratio, especially at low speeds. (The reason for emphasizing low speeds is that for constant acceleration rate, we have constant airgap power... kinetic energy varies with speed squared so that airgap power goes mostly into increasing kinetic energy of rotor at high speeds and mostly into rotor I^2*R at low speeds.) If that thought was correct, we should strive for breakdown torque at start, because breakdown torque is the highest torque to current ratio.

But Torque/Current ratio isn't the whole story. Let's assume unloaded start and we want to compute rotor I^2*R energy created during acceleration through a given speed range. It is I^2*R2internal*time. But time is inversely proportional to Torque. So it is I^2*R/Torque. Maximizing the ratio (Torque/I) doesn't minimize the heating amount. We want to maxmize (Torque/I^2).

Under the linear assumption Torque ~ I, maximinizing (Torque/I^2) means we want to minimize current... as long as we meet our other constraints. Another new constraint we should probably impose is that motor torque remains above 100% throughout the start so that the motor will not stall even if 100% load torque is applied. So this leads to the logic of choosing some target only sightly above 100% (like 150%), and then switching to the next lower resistance step before torque would be expected to decrease to 100%.
================
3 - Questions
1 – Does anyone have any comments on my discussion of justification for "optimum" strategy for selecting rotor resistors
2 – Does anyone have alternate discussion of optimum strategy?
3 - I see Mark E's site says:

http://www.lmphotonics.com/slipring.htm

"2. Determine the short circuit current of the rotor from the motor nameplate."
I thought the nameplate shows the locked-rotor open-circuit rotor voltage and the full load rotor current (not short circuit current). Are there some motors that show short circuit current?


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[electricpete]

Correction in bold:
that moves breakdown torque to s=0
should've been:
that moves breakdown torque to s=1

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[electricpete]

There is a detailed discussion of wound rotor motor rotor resistance selection below. It is the same approach as described by Bill, but very detailed:

http://books.google.com/books?id=V1...ure to calculate the rotor resistance&f=false

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[electricpete]

Below is an attempt to develop a rough optimum approach, considering the effects of load torque which were not previously included.

We assume that the objective is to minimize the total I^2*R energy generated in the rotor over the course of the start. This is equivalent to minimizing final rotor temperature if we don’t take any credit for heat dissipated during the start. This also roughly minimizes the stator heating and temperuture.

We further assume linear relationship between rotor current and torque as discussed above.

We initially assume that Rext is continuously variable over time to provide the exact optimum current and torque at each time increment and speed increment. At the end we will relax this assumption.

Symbols:
E = (joules) = total rotor heating over the duration of the start
I2 = rotor current
I2FL = Full load Rotor Current
TFL = Full Load torque
Te = motor Electrical torque
Tm = load Mechanical torque
Tm(s) = load Mechanical torque as a function of slip
R2int = rotor winding INTernal resistance
R2ext = rotor winding EXTernal resistance
R2tot = TOTal... R2tot = R2int + R2ext
w = radian speed
delta_w = small speed increment
delta_t = Time to accelerate through speed range delta_w
O = Objective function
dO/dTe = Derivative of Objective function with respect to Te
d^2O/dTe^2 = 2ndDerivative of Objective function with respect to Te

E is defined as total I2^2*R2 loss energy during accelerationg through a given speed range delta_w. If we minimize loss energy during each interval delta_w (by means of our continuously adjustable Rext), then we also minimize the total loss energy during the entire start
Minimize: E

E = (I^2*R Power) * Time = (I2^2*R2int) * delta_t

Substitute delta_t = delta_w *J/ (Te – Tm) :
E = I2^2*R2int delta_w * J/ (Te – Tm)

Minimize E => Minimize: I2^2*Rint delta_w * J/ (Te – Tm)

Remove constants which don’t affect minimization (delta_w, J, Rint)
Minimize: I2^2/ (Te – Tm)

Express in terms of torques:
Minimize: Te^2 * (I2FL / TeFL)^2 / (Te- Tm)

Again remove constants which don’t affect minimization (I2FL, TEFL)
Minimize: Te^2 / (Te- Tm)

Divide top and bottom by Te^2:
Minimize: 1 / (1/Te – Tm / Te^2)

Invert:
Maximize: O = (1/Te – Tm / Te^2)
(where O stands for Objective function)

Take derivative and set to 0 to find local extremum
dO/dTe = -1/Te^2 + 2*Tm / Te^3
Set dO/dTe = 0
-1/Te^2 + 2*Tm / Te^3 = 0
Multiply by Te^2...
-1 + 2*Tm / Te = 0
2*Tm / Te = 1
Te = 2*Tm


Examine 2nd derivative to see if extremum is a relative max or minimum:
d^2O/dTe^2 = 2/Te^3 – 6*Tm / Te^4
Substitute Te = 2*Tm
d^2O/dTe^2 = 2/(2*Tm)^3 – 6*Tm / (2*Tm)^4
d^2O/dTe^2 = 2/(2*Tm)^3 – 6 / (2^4*Tm^3)
d^2O/dTe^2 = (1/Tm^3) * [1/4 – 3/8]
d^2O/dTe^2 <0
=> Te = 2*Tm is a Relative maximum of Objective function
=> Te = 2*Tm is a Relative minimum of Energy as desired.

So, if we had a continuosly variable Rext, we would adjust Rext such that:
Te = 2*Tm(s) where Tm(s) denotes that Tm is a function of s

How does this tranlate to I2 and R2ext:
I2 = Te *I2FL/TFL = 2*(Tm(s)/TFL)* I2FL

Using our equivalent circuit:
R2tot/s = V2 / I2 = V2 / [2*(Tm(s)/TFL)* I2FL]
R2tot = s * V2 / I2 = V2 / [2*(Tm(s)/TFL)* I2FL]
R2ext = s * V2 / I2 = V2 / [2*(Tm(s)/TFL)* I2FL] – Rint

So assuming we have function Tm(s), we have “optimum” function R2 which will give optimum I2 and Te functions as above.

Translating this to practical implementation requires some more work. A few thoughts about that:
1 – We dont’ have continuously variable R2ext, but rather stepwise variable. Thus during start, the resistance, current and torque are zig-zag type functions similar to shown in the link above. First simplest approach would be to zig-zag equally above and below the optimum target. However, we have to leave room for error and the consequences of torque too low are probably more severe than consequences of torque too high. This suggest zig-zag path where the optimum path above forms the maximum R2ext, minimum I2, minimum Te. In other words R2ext will be <= optimimum and I2 and Te >= optimum.
2 – Where Tm is very small near 0, the above approach suggests R2ext =very large near Infinity. What it is telling us is that the optimal approach to accelerate low/no-torque-load under these assumptions is to accelerate it very slowly at low torque and current. (which is the same as had concluded in earlier post dated 27 Mar 11 15:09 that did not consider load torque). That sounds somewhat counterintuitive, does anyone have any opinion if this conclusion is correct?

At any rate, it seems reasonable to at least shoot for minimum of full load current and full load torque during startup since we know that will not likely pose a big thermal challenge. Accordingly we could revise our target to:

Te = max{2*Tm, TFL} (whichever is higher)
(This also gives corresponding revisions to the expressions for R2ext, I2)

We can see the target Te is always above 100% and never above 200% (assuming load torque remains below 100%). So it ends up not too much different than what was described in Bill’s approach and the other references. If there is any new insight from all this, it is only that the target motor torque should be roughly twice the load torque.


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[electricpete]

A small correction in bold:
R2tot = s * V2 / I2 = V2 / [2*(Tm(s)/TFL)* I2FL]
R2ext = s * V2 / I2 = V2 / [2*(Tm(s)/TFL)* I2FL] – Rint
should’ve been
R2tot = s * V2 / I2 = s* V2 / [2*(Tm(s)/TFL)* I2FL]
R2ext = s * V2 / I2 = s*V2 / [2*(Tm(s)/TFL)* I2FL] – Rint


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[electricpete]

Attached is a graphical demonstration that the minimum of this particular energy function (E~Te^2/[Te-Tm]) occurs at Te = 2*Tm.

Perhaps that makes the discussion above easier to follow, without the need for a lot of algebra and derivatives.


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[ArcsNSparks]

I think if I measure the open circuit voltage on the rotor circuit and I study the equations that have been sent in I will have my answer. Thanks for the input.

Some to the responses talk about using the nameplate data. Probelm is there is no nameplate. I don't know how old this motor is. The installation drawings for the previous installation of this mill are dated 1975, but I don't if that was the first place it was installed. It's probably older. I'm sure it had a nameplate at one time, but I'm equally sure I will never see it.

 

[electricpete]

I apologize... I lost track of your question and was just taking the opportunity to try to talk through / understand for myself the general strategy for selecting steps. I didn't realize your question wasn't yet answered.

Edison suggested contacting a starter manufacturer with the info you have... that sounds like a good start to me (fwiw.. I haven't worked much with WRIMs).

This link below talks about collecting some data when nameplate is lost. It could be that the data they mention is useful data for someone trying to provide you a starter. I imagine they'd want to know about your load as well.

http://benshaw.cwfc.com/download/lvs-637.pdf

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