How Many Wires Can You Fit in a Levitating Motor?
How higher phase orders (polyphase) would catapult linear induction motors (LIMs) in high-speed trains
I want to build a high-speed train/rail (HSR) or hyperloop! A HSR is a train that is fit to travel up to 250-1000km/h, a hyperloop can go beyond 1000 kph in Canada. First off I am starting with building a prototype linear induction motor (LIM) capable of going 700–900 km/h that is sustainable, cheap and efficient.
In this article, I’m going into the math about LIMs and how winding their coils in different ways can impact their performances.
So far I’ve done lots of research about Canada’s transit problems and simulated a few LIMs, check out my article below for over some efficiency challenges and more background for this project.
Generally, wires in everyday technologies are usually in groups of 3s, and we call them 3-phase circuits which are found in transmission cables and motors. Cooling systems use two wires called dual or 2-phase, but your house wiring only has 1 which is called single or 1-phase.
Higher-Phase Orders: Everything Above 4
Phases are lines of flowing electricity that happen at different times
First of all, a phase is sort of like different a lane or paths of flow for electricity, in a single-phase there’s one phase so one line of flow for electricity. Dual-phase has two lines of flow, 3-phase has three lines of flow, and so on.
In regular rotary motors, these lines of flow happen as coils of wires, and we show that phases happen at different “times” simultaneously.
This is because the electricity is still flowing through all the wires at the exact same time. What makes a 2 or 3-phase what they are depends on how far away each of the wires of electricity are from each other. In a 2-phase motor, the 2 lanes are separated from each other by 90 degrees, equal width. While in 3-phase rotational motors, all three lanes are split by 120 degrees equally.
This is similar for linear motors, except the entire motor is laid out flat and so are the coils instead of in a circle.
The 3-phase is the most common phase in any motor because it causes less vibrations so less energy is lost, but 3-phases are especially helpful in LIMs and this can be represented in the graphs:
Single-phase motors only work for tiny motors
The 1-phase, the graph is represented by cosine: cos(x + 60°) *cos(x)
Here 60 is just a random number that is representing frequency, it could literally be any number, it just has to be kept the same throughout all the phase equations.
Interestingly, if the frequency was exactly 0, the equations will look like this cos(x + 60°) *cos(x) which means we get cosine squared: cos²(x). The power output is always positive here and this is the characteristic of a circuit being purely resistive. This basically never happens in real life, because nothing in science is 100% pure.
But in this imaginary case, it cannot be negative cause resistors cannot supply power/store energy they only disipate energy by resisting electricity flow thus generating heat. So, the load consumes power instead of generating.
This blue graph represents the power output of a motor with 1-phase winding. All those ups and downs create power losses. Part of the time you are delivering lots of power to the motor, then delivering a little less, and other times you are delivering nothing at all and are actually removing some energy slowing it down.
So the motor does not turn smoothly at all.
The motor consistently gives and takes power, thus this would be very inefficient to use in large everyday motors so nearly all large motors today do not use this.
Dual-phases provide only a slight improvement to single-phase
The 2-phases are a slight improvement compared to single-phase, but again there are still some heavy ups and downs that reduce efficiency.
2-phases are separated by 90 degrees equal distances, so this time there are two equations that we call phase a and phase b.
a: cos(x -90°)
b: cos(x +90° +90°) or cos(x -90° -90°) — they are the same
This is probably the least common of all phase wiring because it provides no inherent benefit. It provides only a slightly better consistent power output. But it requires double the equipment because the more phases you have the more power sources and wires you will need. Thus, devices that would run on 2-phase simply end up running with 3-phase instead, the better, more consistent cousin.
But something interesting happens at the number three…
At 3-phases, when you add up all three of the equations below that describe 3-phases it actually produces a constant power output, a straight horizontal line on the graph!
This consistent power output reduces vibrations which makes motors run way more smoothly and with more uniform thrust and velocity forward.
You can’t get this with only 2-phases:
Only three’s can make consistent power
3-phases are the most common, single-phase is the second most common and dual-phase is just non-existent. So what about beyond 3-phases?
Weirdly, electricity tends to favour the powers of three: 3, 6, 9, 12, and so on. So phases beyond three that are not powers of three are not as efficient simply because they do not cancel out in the same way that 3 powers do to create a constant power output like in the example above.
If three phases create such efficient motors, what if we double it to six? Then 12?
A power company in the early 1900s actually tested the idea out in real life to see what would happen!
Power Technologies Inc. (PTI) Built 6 and 12-phase Transmission Towers
No power company with money in mind would attempt to build 6 and 12-phase transmission towers and lines! But PTI did it and it turned out to be not very surprising, but a pretty interesting concept.
In traditional transmission lines, the industry standard was, and still is, 3-phase power. The inside of the wires as a cross-section essentially looked like a triangle with each of the three wires separated equally. If we duplicate this triangle and turn it 60 degrees so it is upside down compared to the original and place it in between the original we get 6-phases.
As you’d imagine the power output very nearly doubles with double the phases. In practice, when PTI tested it out they did get nearly double the power output!
At 6-phases there are twice the amount of wires going in and out carrying electricity, but this means you also need more equipment to process all this power since Just as the phase number tells you how many equations you will have. 1-phase had one equation and one coil, 2-phases had 2 equations and 2 coils, 3-phases had 3 equations and 3 coils and so on. This leads to more complexity but yields higher efficiency too.
Still, it is possible to go on and double 6-phases to get 12-phases, by duplicating the last circle of wires turning it about 30 degrees and putting it inside the original 6-phases. Phases beyond 3-phases are called higher-order phases, or polyphases.
Theoretically, you could continue this process infinitely and end up with a tube where the inside is electrically conductive and the outside is not, this is an example of an anisotropic tube.
Being an anisotropic tube means that the material is NOT uniform in all directions, so it will show different characteristics depending on the direction you look at or measure. Some everyday examples are wood and crystals, the wood grains are not uniform throughout often a bit random and same with crystals so the properies in different places very close up on these materials will be different.
Currently, I’m doing the calculations to describe infinite phases mathematically!
Beyond Three and Six, Power Goes Downhill
Lionel Barthold, the founder of PTI, was the one who proposed they test out this idea, and in the end, they found out that beyond 6-phases the power no longer doubles.
So, at 12-phases, even though it is quadrupled the 3-phases doesn't output four times the power, instead, it creates a diminishing return since you would need more equipment and machinery for each added phase which economically is pretty bad.
Can Six-Phases Apply to High-Speed Train Motors?
If 6-phase doubles the power output from 3-phase, wouldn’t this make them massively more useful in motors that have to travel at crazy speeds, like in HSR?
Overall 6-phase LIMs are not common in real life simply because they are more complex than 3-phases. They require more components, more intricate wiring, and so on. However, many research papers have been written about 6-phases in LIMs describing that 6-phase LIMs are feasible and effective to run.
6-phases could improve overall efficiency by a lot
One of the major advantages is more precise control of the motor which is SUPER important as they begin traveling at crazy high speeds. Another advantage is creating more even magnetic fields around motors, which reduces all the problems associated with uneven fields like when fields are leaking where some stray, spread out too far or get too close to each other resulting in energy losses.
Also, similar to how 3-phases reduce vibrations and make power and motor movement more uniform compared to 2-phases, 6-phases do even more compared to 3-phases. In other words, it reduces torque ripple or in the case of LIMs linear force ripple which basically means reducing the variations in thrust outputs of a motor as it operates. We want this to be as low as possible to get smoother motion, instead of large jolts of force.
With more complexity comes more cost
The obvious drawback with 6-phases in LIMs is the cost. 6-phases are more complex than 3-phases so they would make motor control systems more complicated, impacting cost and practicality, especially in applications where 3-phase motors are already doing their job well.
After the math, I’m going to build one
Going forward, after I figure out how to describe what infinite phases would look like and how they would look and work in a LIM, I will do the same for 6-phases.
Then with this theoretical data, I will build a small-scale prototype of a 6-phase LIM. Once I’ve built a small working prototype, showing that these concepts actually do translate effectively in the real world, I’m going to design and build a LIM that is capable of travelling at 700–900 km/h, that uses 6-phases, and it fully feasible to build multiple times and use in a high-speed train.
I hope you were inspired by the future of what we can do to make more efficient high-speed trains!
Hey! I’m Julia, thanks so much for reading my article, if you enjoyed it add a clap and follow on Medium for more on green energy and transportation.
Right now, I’m curious about exploring energy & transportation solutions, synthetic biology, and nanotech’s role in it all. For more from me, you can connect with me on LinkedIn and subscribe to my monthly newsletter!
