A closer look at energy consumption in EVs

When it comes to factors that affect energy consumption in EVs, the big kahunas are weight and wind resistance (aka CdA), but there are other factors that can have a surprisingly outsized effect and that tend to be overlooked, such as the use of climate control (AC, of course, but especially heat). Conversely, one factor which does not seem to affect energy consumption all that much is the use of regenerative braking.

First, though, two terms that are confused or even used interchangeably way too often are power and energy. Power is a measure of the rate at which work can be done while energy is a measure of the amount of work done. Ignoring the effect of wind resistance (which would otherwise disprove what comes next), it will take the same amount of energy to drive a 2,000 kg vehicle a distance of 1 km whether it is going 1 kph or 2 kph or even 10 kph. Yes, the higher speed requires more power, but it is applied for an inversely lower amount of time, and energy is power * time.

Power

There are five primary factors that go into determining how much power is required to propel a vehicle: velocity (aka speed), mass (aka weight, at least as long as the vehicle remains on planet Earth), rolling resistance, wind resistance and the gradient of the road. The latter four components are used to determine the total drag force opposing the vehicle’s motion, and speed should be self-explanatory. The relevant physics equation that combines all these factors together is deceptively simple:

P = F * v

Where P is power (in watts, W), F is the total drag force acting on the vehicle (in Newtons, N), and v is the velocity (in meters per second, m/s). The components that make up the total drag force need to be evaluated for the above equation to be useful, however. Also note that the power required actually increases with the cube of the speed of the vehicle, because speed is present in the power equation above as well as speed squared in the equation for wind resistance. Speed really does kill…efficiency, anyway.

Drag forces

The easiest drag force to evaluate is rolling resistance, Fr, which is simply vehicle mass (in kilograms, kg) * gravitational acceleration of your particular planet (9.81 m/s² for Earth) * coefficient of friction, Cf (a dimensionless number, usually between 0.01 and 0.02 for most tires and roads):

Fr = m * 9.81 m/s² * Cf

For example, a 2,000 kg vehicle and a coefficient of friction between tires and road of 0.015 results in a drag force from rolling resistance of 294 N, or a mere 30 kg of force (1 N = 0.102 kg-f). This isn’t much force to overcome, though rolling resistance does increase dramatically if tires are underinflated. Conversely, overinflating the tires to reduce rolling resistance isn’t really worth the reduced tire life and increased risk of a blowout.

Next is the contribution from wind resistance, which is proportional to the square of speed, v (in m/s), air density, ρ (1.2 kg/m³ for air at 20° C at sea level), drag coefficient, Cd (typically in the range of 0.3 to 0.4), and the frontal area of the vehicle, A (in m²). The relevant equation to find the drag force from wind resistance is:

Fw = 0.5 * v² * ρ * Cd * A

For example, a vehicle traveling at 90 kph (25 m/s) with a Cd of 0.35 and a frontal area of 2.2 m² requires a force of 288.75 N to overcome wind resistance; at 120 kph that force increases to 513.33 N, or nearly double!

The last drag force is from a change in elevation, which is the only one which can actually assist the vehicle (aside from the unlikely scenario in which a tailwind is strong enough to propel the vehicle all on its own). This equation is a little less straightforward and requires some trigonometry. If the incline of the road is not given in degrees, then converting to such is the first step. In the US, grade is given as a percentage rise vs. a horizontal run, and these figures correspond to the opposite and adjacent sides of a right triangle (the vehicle itself drives along the hypotenuse) so to convert percentage grade into degrees first change percentage into decimal format (e.g., 10% = 0.1) then take the arctangent of the resulting number to get the slope in degrees (e.g., arctan(0.1) =  5.71°).

With the slope in degrees the following equation can be used to find the drag force from a change in elevation:

Fs = m * 9.81 m/s² * sin(Θ)

Where Fs is the drag force from a slope in N (Fs is a positive number if going up the slope and a negative number if going down), m is the vehicle mass in kg, 9.81 m/s² is the gravitational acceleration of Earth, and Θ is the slope in degrees. For example, a 2,000 kg vehicle going up a 10% grade experiences a drag force of 1,952 N (or 199 kg-f).

Putting all the above together in another example should help solidify an understanding of the concepts:

Example: a 2,175 kg vehicle with 2.34 m² of frontal area and a Cd of 0.24 traveling at 110 kph on a road with a 5% grade:

Fr = 2,175 * 9.81 * 0.015 = 320.0 N

Fw = 0.5 * (110 / 3.6)² * 1.2 * 0.24 * 2.34 = 314.6 N

Fs = 2,175 * 9.81 * sin(2.86°) = 1,064.6 N

P = (320.0 + 314.6 + 1064.6) * (110 / 3.6) = 51,920 W

And if the road is flat? Now the power required is 19,390 W. Slope is no joke!

Weight

Weight also has a direct impact on the amount of energy it takes to change speed. It probably goes without saying, but the heavier the vehicle the more energy will be expended to increase its speed. The relevant formula for determining such is:

K = 0.5 * m * v²

Where K is energy (in Joules, J, aka W-s), m is mass (aka weight, in kg) and v is velocity (aka speed, in m/s). For example, to increase the speed of a 2,000 kg vehicle by 72 kph requires 400 kJ (or 0.111 kWh). That might not seem like much, but it can add up surprisingly quickly in stop-and-go traffic, and the ability of EVs to recapture some of this energy via regenerative braking is one reason why they deliver superior “fuel” efficiency in city driving compared to their ICE counterparts.

Regen

While regenerative braking can recapture some of every positive change in speed, keep in mind that energy must be fully converted twice when regen is used, so it incurs twice the losses.

Using the above equation for kinetic energy for a 1,000 kg vehicle decelerating from a speed of 100 kph gives a result of 384 kW-s (kilowatt-seconds). Divide by 3,600 to convert seconds to hours and that gives us a rather paltry 0.11 kWh of recovered energy – assuming 100% efficiency.

Multiply 0.11 kWh by the price for electricity ($0.11 per kWh) and the resulting savings is $0.0121. Still, you can’t make gasoline by braking in an ICE vehicle so any energy recaptured by regen is better than nothing.

It bears mentioning that along with regen, the two other reasons EVs excel in city driving are that they don’t need to idle their motor while stopped, nor do they need to use energy over and above what is required to deliver good acceleration performance. In the bad old days of carburetors and the first port fuel injection systems, there was a pump that literally sprayed a dollop of fuel every time the accelerator pedal was pressed, just to make sure the engine didn’t run too lean and stumble (of course, the engine could also stumble from running too rich).

Climate control

The final factor that can affect energy consumption – sometimes dramatically so – is cooling or heating the cabin. Many first-generation EVs used a conventional automotive AC system, except that the compressor was driven by its own electric motor, rather than by a belt to the traction motor. Using a dedicated motor is a more costly solution, but it is far superior, as the compressor always runs at its optimal speed, allowing it to be more efficient, and cooling isn’t lost every time the vehicle is stopped, since the traction motor doesn’t idle in an EV.

One huge disadvantage of the conventional automotive AC system is that it only pumps heat in one direction; there was no need for it to operate bidirectionally (i.e., as what is commonly thought of as a “heat pump”) because the ICE is a profligate producer of waste heat which comes at no additional burden to the engine or fuel economy. In contrast, the efficiency of the EV inverter and motor combination – the only potential sources of waste heat of any magnitude – is typically in the high 90s and the losses directly scale with power output, so you might get a reasonable amount of waste heat climbing hills all day, but very little driving the speed limit on any limited-access highway in the US.

So, heating the cabin in an EV requires an additional source of heat. Many early designs used resistance heating, as it is cheap, simple and 100% efficient at converting electricity into heat. That last spec sounds impressive, except that the typical compressor-type heat pump can move around 2 – 4 W of heat for every 1 W of electrical input power; the so-called “Coefficient of Performance” in refrigeration/HVAC parlance. This is also why switching from almost any kind of furnace to a heat pump tends to save quite a bit of money heating a home. Another bonus of the heat pump operating as a heater (rather than as an AC) is that waste heat produced by the compressor is useful, so the COP tends to be 1 higher in heating mode compared to cooling.

For a more concrete example, the average vehicle needs somewhere in the range of 4-8 kW of heating/cooling capacity, depending on interior volume, exposed glass area, insulation R value, outside temperature, etc. If heating is via electrical resistance then that will be a direct 4-8 kW of additional drain on the battery, whereas if it is supplied by a modern heat pump system with a COP of 4.0 in heating mode, then only 1-2 kW will be drawn (with 1.33-2.67 kW drawn in cooling mode, as COP will then be 3.0). Using the previously worked example for vehicle power demand, 19.4 kW was required to travel at 110 kph on the flat, so an additional draw of 2 kW for climate control would be equivalent to increasing the speed by nearly 6 kph or decreasing the range by 10%. Bumping the draw up to 8 kW for an electric resistance heater would be equivalent to increasing speed to 130 kph or cutting range by 40%!

Efficiency

Last to be considered is the question of how changes in the efficiency of some of the major drivetrain components affect energy consumption. The inverter seems to receive a lot of the focus here, but there really isn’t much room for improvement – 98% is already achievable using state-of-the-art 600 V IGBTs, and to get to 99%, say, would require cutting losses in half…good luck with that. The traction motor is a juicier target as it typically operates with an efficiency in the 80-90% range, but improving motor efficiency invariably results in a bigger (and costlier) motor. Still, higher efficiency in both these components can have positive effects in other areas, such as reduced cooling complexity/cost and, of course, even a small efficiency boost can add up to significant energy savings over the life of the EV.

Using the same example as above, if the average efficiency of the motor is improved from 90% to 95% (easy to achieve for an industrial motor operating at a fixed load; a rather more heroic achievement for a traction motor in an EV), then the power would drop from 21.56 kW to 20.42 kW (assuming 19.4 kW required at 100% efficiency), which works out to a savings of around $0.125 per hour if energy costs $0.11 per kWh. Guesstimating a 5,000 hour operational life for the EV (e.g., 300,000 km at an average speed of 60 kph), that works out to a lifetime savings of $625, minus whatever it cost to achieve the efficiency improvement (a figure which may very well exceed the savings). 

 

This article originally appeared in Charged Issue 35 – January/February 2018 – Subscribe now.

  • rg michel

    I am not sure where this article took me. I already knew that a heavier car, with resistive heating for winter climate control, and high wind resistance is not good, while regen is good and electric motors and inverters are already efficient. I suppose I need more convincing about the regen part of the article. There are many who intuitively argue that putting an electric car in neutral down a hill and regaining the energy on the uphill is better than regen, so this article will tend to fuel that discussion with little in it for rebuttal. I ignore that argument and keep my Chevy Bolt EV in one-pedal/regen driving and love to see the energy meter go backwards on a downhill.

  • Brandon

    There is one thing that I consider is missing from the list. It is ambient temperature, but not as related to climate system but related to battery heating and increased battery IR and corresponding reduced capacity. I drive both a Tesla and a Bolt; I live in Minnesota and we’ve had a very cold winter.
    For Tesla is comes down to battery heaters. When the car is stored overnight in very cold temperatures the battery heaters engage when first starting the car. If the car is connected to charger it will pull from power, but once you disconnect and start driving it uses a lot of battery capacity to run the battery heating system. Even if I’m on a short drive there is no way to control this. See the image which shows the equivalent Wh per mile at 581 for a 15 mile stretch. The range is greatly affected by the battery heaters.
    With Bolt I think it is slightly different. It seems the battery chemistry causes a loss in capacity through reduced battery performance. I get a monthly report sent to me from OnStar that showed my consumption go from an average of 270Wh/mile to 500Wh/mile running the same route, driving the same way. Some of the loss is climate system, but the bigger portion is battery performance in cold.
    In general, this is a massive hit to vehicle performance that doesn’t seem to be talked about all that much and I feel is missed in this article. https://uploads.disquscdn.com/images/cf127299b13976fa8fda14fbcc511e848f25b1bbc9772b04d7735638d40b56f2.jpg https://uploads.disquscdn.com/images/c2ee69d36523d4bc68912ffdc307530f6170c3822143072584724bed808eb148.jpg

  • Jon

    On two occasions, I tested how much energy could be recovered by regen. in my 2017 Volt when going down a mountain using L and the paddle. The mountains were Mt. Equinox in VT and Mt. Washington in NH, using the paved toll roads. I first noted the decrease in battery range driving up the mountains and then the range recovery going back down at about the same speed, circa 25 mph. Insignificant brake or accelerator pedal usage was needed going down – just a little brake use on tight switchbacks, mostly on Mt. Equinox. In both cases, the range recovered about 60%.

    • rg michel

      That gels with my experience. That is not insignificant, and beats being copped for speeding while chasing kinetic energy.

  • ZeeDan

    Really great article, I love how you broke everything down. Particularly the conclusion that speed is the big deal in energy use, the one thing a person can control.

    Not sure that I totally agree with cabin heating. Dropping the temperature a degree or two doesn’t have much of an impact on energy use, unlike dropping a MPH or two.

    You didn’t mention battery temperature control (granted Nissan sidestepped that issue). Heating a battery that has cooled off below 43 degrees uses a ton of energy. Far more than heating the cabin. The problem doesn’t go away even when you warm the battery with shore power – when the temperature drops outside, the car will work hard to keep that battery warm.

    The issue around cabin temperature depends more on how much air leaks into the cabin. That’s a little different from R value. With a car built as an electric, leakage is less of a problem. Cars that start as an ICE pose a really big problem – there are just way too many holes in the firewall, and tons of cold air gets in the car (when you have all kinds of free heat with an ICE, sealing the car isn’t terribly important).

    I totally agree with your point about finding a better way to heat things in the winter – there has to be a better way. Even though it seems all wrong, a propane heating system sure would be nice. Not unlike those old kerosene heaters for Volkswagen Beetles.

    • rg michel

      I am not sure I agree that speed is a big deal. The article simply talks about the weight of the vehicle and how it relates to speed. We drive at the speeds dictated by the road or highway or traffic, not to improve efficiency. My Bolt’s efficiency drops by at least 25% by turning the heater on in the winter. That’s the main problem. in the summer the A/C is much less of a problem.

      Its also interesting that my bolt draws a few kWh every eight hours or so just sitting in my garage, in order to keep the batteries warm. This does not show up in the efficiency of the car, which is measured only by kWh expended while driving.

      Yes, resistance heating is not good. A heat exchange system would be much better, and hopefully that will happen in future models of the Bolt.

      • ZeeDan

        Thanks for reminding me the purpose of this article, it is intended for designers, people in the EV Industry. This isn’t necessarily a consumer publication.

        As such, weight is important, from a design standpoint. If a company is being good to their customers, it will design the lightest car it can, along with the lowest Cd possible. That will translate into greater range for a given battery size.

        From a consumer standpoint, you are mistaken about speed. It is the biggest single factor in the energy equation, there are no bigger factors. It is also the single factor you can do something about. You can’t change the Cd or the weight of the car – you can change the way you drive.

        The day you drive your Bolt on a long trip, or someplace where you are range limited – as in the charging station is pretty darn close to what your predicted range says – you will understand and learn how to conserve energy with speed and wind resistance.

        On a highway there are at least two choices for speed – there isn’t one single answer. Frequently there are three. And when you are in a situation of making it or not making it to a charging station, you will make the efficient choice.

        You might want to revisit the thought that while parked and plugged in the car is warming the battery every eight hours. That would be a massive waste of electricity – there is no reason to keep the battery warm long term while parked. Either the car is doing something other than warming the battery (possibly topping of the charge), or there is a setting that is off (it thinks you want to drive the car and is pre-conditioning the battery and interior).

        • rg michel

          I agree. Once you have actually driven an electric car, such as my Bolt EV, you realize that none of the discussed factors matter. The only thing that matters is the range. All the other factors are fixed by the car. The range is what it is.

          If you plan your charging stops properly, including a back-up charger, there is never any doubt about whether or not you will make it to a particular charging stop. I have never had to spin out the efficiency of my driving to make sure I reach a charging stop, as its all much more solid predictable than that. Speed and cabin conditioning is totally unimportant unless your planning is incorrect. By this I mean that you need to leave a planning margin that accounts for variability in speed, heater and a/c use. My experience in long-distance driving is such that a margin of 30-60 miles is plenty adequate. Of course, if you plan to work on a margin of say 10-15 miles, then you will be in for a bit of nail-biting because you are then within the variability of speed and cabin conditioning use. Speed and cabin conditioning is unimportant except for those who are not able to plan for one reason or another.

          To further enlarge, it is quite trivial to understand what your range is likely to be, because the car will tell you what it is. In the winter, it will give you a different number than in the summer, but you will know for sure what it is. The range on the dashboard varies with your driving style and it can be relied upon. The Chevy Bolt has this down cold….

          Further, of course, if you insist on trying to obtain maximum efficiency at all times, and going the maximum distance between chargers, then its not going to be much fun. Its the same thing with a gasoline car. You can spin out your driving technique to squeeze out a few extra miles per gallon, but what is the point of doing that except for bragging rights? Who deliberately avoids going to a gas station until the very last minute in order to maximize the range between gas stations?