The expression for Y(f) is a valid math model for AC component of a DC motor but at f=0 does not represent the processes in a DC motor.
For a DC motor if I remember it correctly
the formulae is:
U = I*R - E
E - electromotive induction voltage in the rotor circuit
I - DC current
U - DC voltage

In other words DC current at given DC voltage depends mainly on mechanical load. AC current depends on Urms and R-L at given f.

The assumption that I have made is that a dc motor at a given load acts like an R-L circuit. The R would be an equivalent circuit parameter which depends on the load. (it does not represent the physcial resistance of the windings). R would be considered constant over time for a given load level. Whether it is a valid assumption is certainly worthy of question and discussion.

To argue in favor of your point (that it is not a valid model), we could think about the fact that the motor torque speed curve varies with voltage. So as terminal voltage varies, torque varies, the power input to the motor varies. This represents a change to the real power supplied to the motor as voltage changes. But a resistor would also change real power drawn when the voltage changes. Whether the change is in the same proportions for these two cases (change in real power drawn by motor as voltage oscillates and change in real power drawn by R-L circuit as voltage oscillates), I'm not sure. A quasi-static analysis (applying steady state dc motor model to time-varying input voltage) suggests that the motor real power variation in response to voltage would exceed that of a resistor, but it's not clear a quasi-static analysis is appropriate.

The following passage from NEMA MG-1 does lead me to believe the dc motor at a given load can be modeled as an R-L circuit:

quote:

NEMA MG-1 2003
14.62 ARMATURE CURRENT RIPPLE [Small and medium DC machines]
Peak-to-peak armature current ripple is defined as the difference between the maximum value of the current waveform and the minimum value. The peak-to-peak armature current ripple may be expressed as a percent of the average armature current. The peak-to-peak armature current ripple is best measured on an oscilloscope incorporating capability for reading both direct-current and alternating-current values. An alternative method is to use a peak-to-peak-reading voltmeter, reading the voltage drop across a noninductive resistance in series with the armature circuit.

The rms value of the ripple current cannot be derived from peak-to-peak values with any degree of accuracy because of variations in current waveform, and the converse relationship of deriving peak-topeak values from rms values is at least equally inaccurate.

Armature current ripple of a motor-rectifier circuit may be estimated by calculation. For this purpose, the inductance of the motor armature circuit must be known or estimated, including the inductance of any components in the power supply which are in series with the motor armature. The value of the motor inductance will depend upon the horsepower, speed and voltage rating and the enclosure of the motor and must be obtained from the motor manufacturer. The method of calculation of the armature current ripple should take into account the parameters of the circuit, such as the number of phases, the firing angle, half-wave, with or without back rectifier, etc., and whether or not the current is continuous or discontinuous. Some methods of calculation are described in the following references:
“Characteristics of Phase-controlled Bridge Rectifiers with DC Shunt Motor Load” by R.W. Pfaff, AIEE Paper 58-40, AIEE Transactions, Vol. 77, Part II, pp. 49-53.
“The Armature Current Form Factor of a DC Motor Connected to a Controlled Rectifier” by E.F. Kubler,
AIEE Paper 59-128, AIEE Transactions, Vol. 78, Part IIIA, pp. 764-770.

If there were going to be more complex calculations involving torque oscilation, they would have been interested in the motor armature resistance, flux density and other motor parameters. The fact that they identify the inductance as the main variable of interest for the motor (in addition to the obvious power supply parameters and load level needed to solve the R-L circuit simulation) leads me to believe they will model the motor as a simple R-L circuit.

I would feel more sure if I had those papers referenced or some other info. But it seems very logical to me that they intend to treat it as an R-L circuit.

===============================================

For me it is important to step back and look at why we are talking about this (relationship between voltage ripple and current ripple). For me it was to resolve an apparent contradiction:

• #1 - The current waveform bears a strong resemblance to the voltage waveform of a 3-phase full-wave diode unregulated supply, seems to suggest the machines are fed from this type of supply.
  
• #2 - A 3-phase full-wave diode bridge has very low ripple - much lower than seen on the current
  
• #3 - I believe the current ripple (and form factor) should be less than or equal to the voltage ripple and form factor.

I now have what I consider a resolution to the contradiction. #1 is not true - based on examination of Aditya's voltage waveform, it is not a diode type (unregulated) supply, but it is in instead a regulated SCR type supply ("line frequency phase controlled rectifier"). The fact that the waveform has such a similar appearance (neglecting magnitude of the ripple) is somewhat of a coincidence and a result of the low-pass filtering effect or some other characteristic of the motor as an electrical load. Aditya's voltage and current waveforms are also consistent with item #3. Presumably similar current waveforms from David and Jan also originated from similar regulated SCR type supplies.

fwiw, I will try to do a simulation of Aditya's voltage waveform fed into an L/R circuit with the L and R parameters tuned to match the magnitude and general shape. If it results in a current waveform resembling Aditya's current waveform very closely, then it will support what I said above. If not, then it would suggests there may be more to the story of modeling the terminal characteristics of a dc motor terminal than just a simple R/L circuit.

This message has been edited. Last edited by: electricpete,

After further review, I agree with you David. The model as a simple R-L circuit was flawed and the conclusion that I drew from that model (item #3 above) could be wrong.

"Power Electronics & Motor Drives – Advances and Trends" states: “the load can be R, RL, RC, or RL with CEMF (such as a dc motor)”

They are implying a dc motor can be modeled as a series circuit of equivalent R, L and DC source. And they also seem to present this model in the context of determining current as suggested in the attached figure of a single-phase LF- Phase-regulated SCR supply feeding a dc motor.

You could take that R/L/DCvoltage model of the motor and combine DC voltage portion with the original voltage source part over to the source to get a new equivalent voltage source. The new equivalent source has a lower dc compared to the original and the same ac as the orignial. So the new equivalent soruce has a higher ratio of ac rms to dc (and higher form factor) than the original voltage source. Now when you apply that equivalent source to an R/L circuit, if the L is very small (and therefore low-pass filtering effect is small), this certainly could result in the acrms/dc of the current bearing higher than the acrms/dc of the original voltage source.

I am still going to try to recreate Aditya's voltage and current waveforms to see if I can create that current shape from that regulated SCR supply voltage shape.

MotorAsR_L_DC.ppt (167 Kb, 13 downloads)

Attached I have simulated a dc motor (R / L / DC circuit) fed from a "line-frequency phase-controlled rectifier".

The final results are shown in the graphs on the last page. It shows one period of the repeating waveform (1/6 of one cycle of 50hz). So if you use your imagination and add exactly repeating waveforms before and after this, you can see a similar shape as was shown for Aditya's motor 35kw. The voltage takes an abrupt step at t=0, t=0.00333, t=0.00666 etc and slowly drops between. The current looks something like the trajectory of a bouncing ball returning to the ground at t=0, t=0.00333, t=0.00666 etc. One noticeable difference is that my current waveform slopes a little to the left - not sure why that is. I could manipulate the R / L / DC values of the motor to make it symmetrical, but then I couldn't match the magnitudes. Perhaps if I experimented more I could have found some true R / L / DC parameters that more closely recreated his results.

So what does it prove? Not much. Except I am very sure of the type of supply (LF phase-controlled rectifier). And the sharp voltage waveform is transformed into a smoother current waveform by something similar to a low-pass filter action of the motor.

LFPCR.pdf (41 Kb, 7 downloads)

Looking at Aditya's 435kw motor voltage waveform, there is an interesting feature of a little "glitch" in the middle of the vertical step-increase of voltage (as shown in slide 1).

Review of "Power Electronics" by Mohan etc suggests this is the commutation period when two of the input phases are temporarily paralleled. It occurs when there is series inductance on the ac input. The diode which is shifting off cannot have it's input current immediately go to 0 due to that inductance, which results in the commutation period during which these are paralleled. This is shown in slide 2 for a single-phase line frequency phase-controlled rectifier and you can see the familiar glitch in the veritcal section. It is shown in slide 3 for a 3-phase line frequency phase-controlled rectifier. This particular plot has a different format where the positive bus voltage curve shown on top and the negative bus voltage curve shown on botoom, and the dc voltage is the vertical distance between these two curves. There are 6 switching operations per ac cycle, 3 on the positive bus and 3 on the negative bus (alternating).

What does this prove? Not a whole lot, except we can understand why the voltage looks the way it does.

There are some other features of Aditya's voltage waveform of slide 1 that I don't quite understand. A lot of higher-frequency "ringing" on every other switching operation, which would correspond to perhaps the positive bus (or if not, then the negative bus). I'm not sure why that is... maybe there is some capacitance which results in ringing LRC circuit (?)

CommutationPeriod.ppt (468 Kb, 5 downloads)