Tesla and Motor Metrics


This fall showed some interesting teardowns of the Model 3 and competing motors. The conclusion indicated the Tesla motor cost was around $754.

The standard Model 3 (RWD) motor is rated around 211 kW peak. The Model S standard motor was rated at 270 kW. These peak ratings are important to understand, because they are far in excess of what the motor would ever be able to produce for an extended period. Short bursts, yes, but probably on the order of seconds rather than minutes. A Model S cruising on flat ground at 80 MPH would be pulling around 28 KW from the pack, and a Model 3 cruising on flat ground at 80 MPH would be around 22 kW. A Model S will supposedly run into thermal limiting at extended periods of operation at 100 MPH or so, which is about 45 kW (that limit could be motor or it could be battery. It’s not clear precisely). But make no mistake, these peak power levels are used to accelerate hard, and hard acceleration only occurs for a seconds at a time.

In any case, the specified motor ratings are clearly peak, not continuous. And if the continuous rating is around 45 or 50 kW for the Model S then the peak rating is about 5.5X the sustained rating. That gap is enormous. And it’s definitely not achieved by over-sizing the motor. When you do that, you tend to operate in a compromised region of efficiency, which means you need to make up range with the battery. And adding range with the battery is usually a lot more expensive than adding range via motor efficiency. Plus, look at the weight of the Tesla motor compared to BMW. They weigh a bit less and deliver substantially more power.

Putting the teardown figures in a table for the Model 3, i3 and Bolt we get the following


Above we see that at the estimated cost of $754 for 211 kW peak we get around $3.6/kW. That figure of merit is hugely important to the success of electrics. And it’s one of the reasons the various governmental agencies are so focused on this metric: The more the industry succeeds at driving that number down, the sooner the public will appreciate the value of electric over ICE. And Tesla is killing it.

It’s interesting to look back at DoE data from 2014 and at their predictions of what would be reasonable for the 2020 time frame. Below, they break down both the power electronics (inverter) and motor cost for a 55 kW peak/30 kW continuous motor. Their assumptions appear to be considering peak power, based on the fact that the Tesla Model S (page 3 in the ppt) was considered a 270 kW drive for $5,400, yielding $20/kW system cost.


In any case, Tesla’s Model 3 motor at $3.6/kW peak has handily beat the DoE predictions for 2020, which hoped for $4.7. And Tesla achieved this almost two years ahead of the DoE’s expectations.

One very interesting thing to consider in the DoE estimates is that the DoE viewed the ratio between continuous and peak as being just under 2:1—a pretty typical and conservative figure for that time. If we assume the Bolt and i3 are needing around 40 kW at their top-end speeds, then both the Bolt and i3 are a ways below Tesla’s 5.5:1 ratio. But still well beyond the sub 2:1 historically used.

The usual limiting factor in peak to average is that the peak is usually limited by the magnetic field reaching a point of saturation and thus further increases in motor current no longer produce the expected rise in field strength. And once you’ve hit that point, the motor efficiency quickly drops. Doubling the current no longer gives you twice as much torque. And the efficiency figures you might expect at the mid-band of 95% can fall to 90% or worse. Still seems pretty good, yes, but that means 10% of your ~200kW is lost as heat inside the motor—that’s 20 kW. That’s a lot.

You can really see how EV motor’s have evolved in the efficiency maps below (from ppt located here). On the left is a motor from a 2005 Accord Hybrid and on the right is a Model S motor. What you see on the left is a classic motor efficiency map. Note the deep red indicating peak efficiency—it’s localized to a fairly narrow region of operation. As you get out to the higher RPMs you are stuck with poor efficiency at any torque output. Contrast that with the map on the right and notice how elongated the peak efficiency (>96%) region is. The white dot indicates a swag at where on the efficiency map you’d sit for 80 MPH cruise on flat ground (assumptions are 80 MPH = 9200 RPM * 29 Nm gives 28 kW).


So, in the end, Tesla seems to have really pushed the peak to average ratio hard and benefited enormously by doing so. And I’m not sure the folks at BMW and Chevy quite understand how they did it yet.

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