I always lean heavily on what’s been done by other teams, for a couple of reasons. The biggest one is I don’t have much in the way of math skills.
Seriously, I joke about this, but the gods-honest is my eyes start rolling back in my head when people start tossing numbers around, and I blame a girl who shall only be known as “Sharon” from my Algebra class back in High School, when I came to the conclusion that she was infinitely more fascinating than what Mr. Stanley was yabbering on about in the front of the room. Once you fall that far behind, that early on, it’s hard to catch up. And it drives me particularly crazy because there are a whole lot of tools that can save you a whole lot of time and expense, rather than the trial-and-error methods I’m forced to use.
Enter a Mr. Andrew Rivers, The First Esteemed CBRe Team Member (Systems and Performance Modeling for an Electric Superbike utilizing the GNU Octave Electric Motorcycle Simulation program) and Master of All that is Maths. Andrew offered to work up some modeling for the CBRe, based on the Emrax 268, the Rinehart controller, and a few choices of battery chemistries. This isn’t a small task, but it’s a work in progress he’s been chipping away at for over a month now, with some pretty impressive results. (Don’t forget, click on the small images for the full-sized charts.)
Here’s the explanation from Andrew:
I worked off of the dyno plot from EMRAX for the HV268. The torque constant for the HV (high voltage) version is 2 while the MV (medium voltage) version is 1.4 (note that this is only valid below base speed for determining peak torque). So based on that, to get the 400Nm shown in the EMRAX plot they had about 200A motor side up until the base speed of about 1684rpm (measured by pixel count).
Once I had that, I could determine everything up to base speed, torque from the new constant of 1.4 and base speed based on peak voltage (it is close to linear). Above base speed, I took more pixel measurements to get an idea of the decay rate of torque. Once that was measured, I made it dynamic so it would compress and expand as the peak rpm varied with total power.
The maximum speed is a function of total input, so initially 400v and 200A gave 3778rpm max. With that known it was possible to adjust it based on the new voltage and peak current from the Rinehart. That gave me the torque plot in Figure 1. Note that peak torque is around 490Nm, which is 350A*1.4Nm/A. Power is easily calculated from torque and speed by the equation: P = rpm*torque*pi/30, so using that gave the power plot in Figure 2. Peak power is initially 110kw (it will be corrected for battery parameters later).
Now the fun part. So far everything is motor side, current, power and all that, but to test the battery model I of course needed battery side current and power. To get that I derived a second order equation to convert between the two. It isn’t perfect, but typical error is only 1%. Figure 3 shows the result.
Much to my delight, it is pretty much exactly what you would expect, beginning with a constant current region then a near linear current slope(constant torque) and then tapering off above base speed (constant power). After the error in the current calculation is accounted for, the peak motor power is reduced to around 108.6kW, still very respectable.
And that brings us to Figure 4, a simulated dyno plot of your setup with LEAF cells (just because I had to choose one). Maximum rpm is around 4627.
So these curves are dynamic with Battery voltage, Battery resistance, and Peak controller current. There may be one or two more little things I can account for, but those are the major variables.
Remarkable work, and I can say honestly that even I, math challenged as I am, am starting to think I understand this a little more.
Here’s a little more about Andrew, from his LinkedIn page:
I am a recent graduate from the University of Memphis with a B.S. in Electrical Engineering concentrating in Signals and Systems.
This experience combined with my studies in electrical engineering at the University of Memphis has helped me focus my career path and allowed me to combine my passion for motorcycles with my fascination with electric vehicle technology.
And, can I add, his skills with the MATHS? Oh, by the way, Zero? Harley? Polaris? Are you paying attention? Read on:
With over four years of independent electric vehicle research and more than two years focused on a custom electric motorcycle project, I am seeking a position in the motorcycle industry which will allow me to work with electric vehicles.
Want to get in touch with Andrew directly? You can send him an email here.
This is the update I just got, so stay tuned. There’s more:
I have made some big improvements to the battery models as well as added one for the 60Ah GBS cells, just for the sake of comparison. I also have been refining the outputs to give the most valuable information, like the SOC before peak current needs to be limited and the output power just before, as well as average voltage levels under load.
I am also looking into making models for all of the vehicles tested by the INL, more or less because I want to. If you are interested in the results to write a battery comparison article I would be happy to share the results. That would be a comparison between the LEAF, Volt, Smart EV, Focus, Fustion, Cmax and the Prius PHEV in addition to the A123 RC lipo and GBS.