THREE PHASE MOTORS ON SINGLE PHASE SUPPLY: A MOCKERY OF INDUCTION

(This article was written by my friend, Laz. Thank you for writing this for my blog!)

hi i'm laz
Once again I have elected to write an alarmingly niche article about electrical equipment on a Diesel-focused blog.

Those aware of who I am regardless of from /where/ likely know that I have been working on a simulator, ever more complex than the last time I was "working on a simulator." Much like my prior article on an entirely unrelated bloggard, I have discovered dark and horrible things, and in the process perhaps disproved a "foamerism" - i.e. a myth that is typically incongruent with reality. More on that later.

Let's take a look at the kind of equipment in question here. 

 

Fig. 1: Norfolk and Western's L-C-1.

Fig. 2: Virginian's EL-1.

Fig. 3: PRR's FF-1.

A few things to note, beyond my obsession with jackshaft locomotives.
    - The motors themselves are massive, and jammed up into the frame
    - They're all boxcabs (Not relevant, but it's a sharp look)
    - They're all 1ϕ AC-collection, 3ϕ AC motor equipment.
    
    (hint: "ϕ" is your phase symbol)
    
That last item is where things get tricky. Equipment like the GG1 is, in the most technical of senses, AC drive; AC power is collected, where voltage is regulated via tap transfomer, and then in single phase format run through DC-style motors - usually referred to in documentation as "commutator motors". The upside of this format is the ridiculous simplicity. You lose some efficiency in exchange for not having to deal with some means of rectification (Especially in the 1930s, where the options are "Good luck" or "Lmao" if you don't have room for a massive motor-generator), or dealing with the quirks of DC distribution and collection (Further reading: Terrorizing M-G substation personnel on the MILW). The downside is you get all the downsides of DC and none of the upsides of AC, in terms of wheelslip control and motor performance. Single phase feed to true single phase induction motors is also a non-starter, as single phase induction motors tend to have issues with generating torque at 0 rpm and have other characteristics highly undesirable for railroad applications.

Fig. 4: The phase converter, as installed in the FF-1.

Fig. 5: The actual wiring diagram of the phase converter as installed
in the L-C-1. The actual operating theory is identical.

Fortunately (or not) in 1914 - when the N&W units were delivered - this was a solved problem with the recently invented Rotary Phase Converter. As far as concepts go, the device appears similar to a motor generator, except the "motor" part also contributes phaseulation to the actual traction circuts. This nets us true 3ϕ, though since it's not /actually/ a motor-generator set we cannot just vary excitation for load-side voltage control. Further, starting a locomotive by directly connecting the motors to knocked-down line voltage and frequency, and praying for the best through a (effectively) dead short connection at 0mph is, hopefully for obvious reasons, undesired. One has zero control over wheelslip or runout, and this leads to extremely poor train handling. This is a bit of a problem when you have hundreds of thousands of pounds of force available. There's a couple things we can do to mitigate this, fortunately. At least reversing the motors is simple enough - swap two leads, motor runs backwards. Simpler design than DC type setups. First off, the obvious one that gets brought up:

Fig. 6: Prints of the pole-changer device from the L-C-1. It's a two-position device that sets up connections from three-phase supply. Eight pole behaves like your low gear; four pole behaves like high gear.

Fig. 7: A diagram of motors #1 and #2 on same. Note the myraid of connections, feel free to match up letters with Fig 7. Worth noting that each married pair was not just a whole locomotive coupled; each set shared one phase converter.

All three locomotives above utilized pole-changing motors; note the connections halfway through each field. Using two different pole connections effectively gives you two "top speeds" - by changing the wiring configuration of the motors, you can select one of two top speeds on a fixed frequency. Both the N&W and VGN ran 14.3 and 28.6 mph, and the PRR unit ran 10.3 and 20.6. Above we see the Pole Changing Device (Each motor has one) and the motor itself, in a delta (Simulator namedrop? No way) wiring format. Two power notches, a top speed in the 10-28mph range depending on the exact configuration, we're getting better, but we still have untenable inrush current and a somewhat awkward motor force curve.

This answer was good enough for me for several years, but there's a better way. A more regulated way. A way with a secret, third handle: the actual throttle. 

 

Fig. 11: A diagrammatic top-down of the VGN EL-1 or 2 or 3 or whatever you like operating cab. Two handles for your brakes, then an Extra Surprise Handle for your viewing pleasure.

Fig. 10: The master controller from the FF-1. It was a miracle I got this photo and I wish I had it in higher quality; the upper handle is your "speed" handle. The lower - your accelerating handle. If you look closely you can see three positions in addition to the one the handle is presently at.

What could it /mean/?

So a funny thing: the "speed handle" is perhaps counterintuitively not a throttle at all. It is functionally a selector, with three major positions, and mechanically five positions. For the N&W and VGN equipment above, positions are: OFF, 8P, 8P-14MPH, 4P, 4P-28MPH; "P" designating "Pole", and typically referred to by railroads as a specific speed connection. In the OFF position, the pantographs cannot be raised and several other functions do not receive power, such as the sanders. By and large, intended operation is to operate the whole route in one speed connection as there's no disconnect logic for the pole changeover switch. So if you can't use the speed handle for anything other than what today's maximum speed will be, what's the third handle actually /do?/

Fig. 9: All three drums pictured - each device here is physically linked to a handle.

Essentially, it controls the acceleration selection drum. It's a four position handle in and of itself - RAISE, HOLD, LOWER and OFF. This acceleration drum drives a rheostatic control group, which drives a notching relay, which serves as a regulator for raising or lowering the effective fluid immersion for the liquid rheostats. It's like a nuclear reactor, except you bring the reactor to the fuel rods.

Fig. 12: Another cross section from the FF-1, illustrating the Liquid Rheostat tanks and arrangement. The spindly thingies - one per motor - in the orange are the actual conductors. The blue electrolyte is pumped up, and a higher level gives lower resistance; this gives a fail-safe, where any failure causes electrolyte to fall back to the holding tank and the resistors to return to an "open line" state.

 
Why use air-cooled multi-notched resistor banks (A la most DC equipment of this vintage) when you can have your resistor itself be the coolant, plus infinitely variable? Add more saltwater and you lower the resistance. Reduce, or raise the electrode out, and you raise the resistance. Obsolete now, but a very popular device up through the 1980s and capable of very high loads and high-capacity softstarts without a means for burnout, provided the liquid doesn't boil. The only real challenge is corrosion control. All three classes of locomotive above use the same design: speed handle is set-and-forget top speed plus power on or not, accelerating handle varies the rheostat immersion which, mind you, occupy a significant portion of carbody, which then allow you to vary line voltage supply to -

Wait, hang on.

Fig. 8: God Bless Wikimedia Commons. A diagram illustrating the somewhat unfavorable torque curve for a given supply frequency-amperage; note that as the motor accelerates, torque actually /drops/ before picking back up. If this sounds wonky and uncomfortable and Difficult To Handle, it's because it is.

So, first. Induction motors, in their typical "squirrel cage" format, have a rotor with coils shorted together - current, and consequently torque, is induced as the rotor then tries to chase the field to the limit of frequency. The actual force equation requires some big brain math much smarter people than me can explain, and which is outside the scope of this article. For the most part, though, to have any reasonable control over an induction motor you need to vary frequency with supply voltage, as induction motors are extremely sensitive to supply voltage changes. So what are these rheostats actually doing?

Fig. 13: Something's Wrong I Can Feel It. Typical "squirrel cage" induction motors have their coils shorted together - yet these are not only /not/ shorted, but all six rotor connections run out of the motor through slip rings, outways. What.

So, back to the motors themselves - these /are/ induction motors. Current is induced in the rotor, to net torque. Those connections back out of the motor require (several!) slip rings, which are another wear item - something you don't put in without a good reason. Another note about induction motors: If the rotor connections are open, rather than shorted, the rotor develops no torque even with a fully excited field. There's another effect - as you add resistance to the rotor coils, the maximum torque-speed (aka "breakdown torque") of the motor slides back to 0rpm - pretend the peak of the chart above moves leftways, and then moves past zero until eventually the line slides down to (0,0). If you have good control over this resistace, you not only have a soft starter, but actual graduated torque control without frequency or voltage manipulation. This here is what those rheostat banks vary, and don't "see" full line voltage at any point. The motor design in practice is what's known as a wound-rotor motor. By varying the resistance across the rotor coils, fine load control is accomplished.

Fig. 14: Here's a very rough and approximate chart I made up in desmos. Each axis is normalized to 0-1. X axis is RPM as a function of selected top speed (1 being 100%), Y axis is a function of your motor's absolute maximum torque (0-1, 100% being, well, full torque). The dotted red line is your "fully-on" torque-speed characteristic. Blue is marginal resistance, black is somewhat more, red is more, purple is more, orange is Even More - you can see how the line gets flatter and any given speed has less and less torque for more resistance.

 

So that's about all there is to it. Big Liz was not simply a three notch throttle, with Off/Half Go/All Go. The reputation for ripping cars in half is almost certainly undeserved; fine control over starting loads was possible which speaks more to poor handling than design flaw, and compared to her contemporaries isn't necessairly that overpowered. The VGN and N&W units often operated in three unit sets, netting /massively/ higher drawbar forces - and 50% more horsepower nominal - than the orphaned PRR example, and all three classes enjoyed long service lives of >20 years.