Tag: Prius Prime

Post #1656: The World Turned Upside-Down

 

Today my wife came across a thread on PriusChat in which a New Englander claimed that it now cost more to run his Prius Prime on electricity than on gasoline.

After I got done scoffing, I decided to look up the data.  Actually check the facts.  Just as a last resort.

And, in fact, that’s plausible.  With the recent declines in the price of gasoline, and sharp spikes in electricity prices in New England, it’s entirely possible that running a Prius Prime on gas is now cheaper than running it on electricity in that area.

Let me just chuck out a few numbers here, all based on the current EPA ratings of 4 miles per KWH and 54 miles per gallon for a Prius Prime.

First, it’s just math to figure out the break-even price of electricity, for any given cost of gasoline.  That is, the price at which it would cost you the same to power the car with electricity as with gasoline.  Because a gallon gets you 54 miles, and a KWH gets you 4 miles (per the U.S. EPA), just multiply the price of gas by (4/54 =~) 0.074.  So running the Prius Prime on $4/gallon gas costs the same as running it on electricity costing ($4 x 0.074  =) 30 cents per KWH.

Like so.  The “break-even” price of electricity just shadows the actual price of gas:

Source:  Gas price data from the St. Louis Fed FRED system.

Historically, at least in my area, that gasoline-equivalent cost was well above the actual price of electricity.  Hence, the fuel cost for electric-powered miles was well below the cost for gas-powered miles.

But now?  In, say, Boston?  Not so.  Take the red line off the prior graph — that’s your gasoline-break-even cost of electricity — and compare it to the actual cost of electricity in Boston and in the Washington DC area.

Source:  Electric rates via the St. Louis FRED system, e.g., DC electric rates.

And, sure enough, of late, the precipitous drop in gasoline prices, combined with the spike in New England electricity rates, has made it noticeably more expensive to run a Prius Prime on electricity, than on gasoline, in that area.  Although, as you can see from the very bottom line, it’s still cheaper to fill up on electricity than gasoline in the DC area.

Discussion

Apparently the spike in New England electric rates is due to a spike in U.S. natural gas prices, which, in turn, seems to be blamed on the war in Ukraine and the resulting spike in European gas prices.  The general idea being that the New England area is heavily dependent on natural gas for electricity production.

Either way, prices in the natural gas market now seem to be easing.

On the one hand, this raises an interesting advantage of having a true dual-fuel vehicle like the Prius Prime.  Within the limits of your battery capacity, your fuel cost can always be the lesser of the gas or electric per-mile rate.  You are protected from price spikes in either the gas or electric markets.

The question is, is the Prius Prime something of a special case, owing to its overall high efficiency? Or, does this have any strong implications for the per-mile cost advantages of electric vehicles in general?  I think the answer is, I think, the latter.

So, let me do the same calculation on a more typical U.S. vehicle.  Offhand, let me choose a PHEV Volvo, getting a pitiful 2 miles per KWH or equally pitiful 26 miles per gallon of gas.

Source:  2022 Volvo from Fueleconomy.gov

But the key here is “equally pitiful”.  The conversion factor from gas price per gallon, to the equivalent cost in electricity, is calculated just as it was for the Prius.  In this case, with 26 MPG and 2 miles per KWH, the conversion is (2 /26 = ) 0.077, virtually identical to what it was for the Prius.  And that’s because the Volvo uses just about twice as much gas, and twice as much electricity, as the Prius does.

Equally pitiful mileage on either gas or electric.  Which means that, as with Prius Prime drivers in New England, Volvo drivers in New England will also now find it cheaper to run on gas instead of electricity.  Sure, they’re paying twice as much per mile as Prius Prime drivers.  But that’s true whether they are burning gas or electricity.

I should probably do another one or two, to make sure that wasn’t an accidental cherry-pick.  But I’m guessing that what that sharp-eyed New Englander calculated for his Prius Prime applies to much of the dual-fuel gas-electric fleet.  With gas as cheap as it is now, there are spots in the U.S. where the fuel cost of gas is lower than the fuel cost of electricity.

In prior posts, I already showed that recharging your car at typical commercial-charger rates already costs more than running it on gasoline.  So if you don’t have a home-recharge option, or can’t recharge for free, there are no fuel savings from converting to electricity.  This means a significant fraction of the U.S. market may have little financial incentive to go electric.  This latest analysis just shows that unless those electrical rates come down, entire geographic areas of the U.S. will be in the same fossil-fuel-powered boat.

Post #1624: 80 MPG?

 

Not quite.  But I think I’m finally figuring out how to drive my wife’s Prius Prime.

Above is the gas mileage on my wife’s Prius Prime, after a round trip from Vienna VA to Harper’s Ferry WV.  This is all after resetting the odometer once the battery was depleted.  So it’s straight-up gas mileage.

This trip contained a short section of high-speed driving, but was mostly hilly primary and secondary roads in western Virginia and West Virginia.  And I think I finally understand how I’m getting such great mileage.

The Prius Prime loves hilly roads.  It is an excellent car for a particular style of pulse-and-glide driving.

Continue reading Post #1624: 80 MPG?

Post 1621: Look ma, no battery!

 

Or, “why I truly don’t give a 💩 about high gasoline prices in the U.S.”, the sequel.

Back in June of this year, in Post #1454, I explained why I didn’t give a 💩 about the price of gas.  In a nutshell, I don’t use much.  I drive my wife’s Prius Prime.  The 30-mile battery range covers essentially all our local travel.  One we’ve run through that, the gas mileage is outstanding.

The genesis of the prior post was our annual trip to Ocean City, Maryland, where the car got 72 MPG on the highway.

I figured it was a fluke.  There were no hills to speak of.  We probably caught a tailwind.  Unlikely to be repeated.

Today we went leaf-peeping, driving from Vienna VA to Sperryville, VA and back.  There is just something about the autumn scenery in central Virginia that my wife and I both love.

(Best sign seen on the trip:  “God Allows U-Turns”.  This, at the exit of the parking lot of a little church in Sperryville where we were — yeah — making a U-turn.)

The trip was a combination of interstate highways, then primary and secondary highways traversing hilly terrain. It was a nice drive — once we got off the interstate.  I reset the odometer after the battery was depleted so that I could check the gas mileage.

Lo and behold, in round numbers, 72 MPG.  Straight-up gasoline-powered transport, no battery.  Completely different terrain, time of year, and driving conditions compared to last time.

So, no fluke.  I’m not drafting trucks. I’m not doing 35 in the right-hand lane.  I’m  just keeping up with traffic, and paying a bit of attention to instrumentation on the dashboard that offers guidance for best fuel economy.  (And it didn’t hurt that we didn’t need AC or heat for this trip.)

It’s odd how your expectations change.  These days, if I come in under 65 MPG for the gas portion of a trip, I’m disappointed.

This is not as clean as a pure EV of the same size.  At least, not as clean, at Virginia’s current electrical generating mix.  But it’s not bad for the latest refinement of a gasoline-based technology that Toyota put on the road more than two decades ago.  And the same drive train that gets us 72 on the highway allows us an effortless transition to electrical transport for all our around-town driving.

For us, this plug-in hybrid electric vehicle (PHEV) is absolutely the sweet spot in the spectrum of what’s on the market today.  After a year of driving this car, we have no regrets about buying it.

Post #1618: There ain’t no disputin’ Sir Isaac Newton: Efficient driving in an EV.



Driving an electric vehicle (EV) efficiently is forcing me to learn some new driving habits.  And, in particular, I have to un-learn some cherished techniques used for driving a gas-powered car efficiently.


When I look for advice on driving an EV efficiently, all I get is a rehash of standard advice for driving a gas car.  But the more I ponder it, and the more I pay attention to the instrumentation on my wife’s Prius Prime, the more I’m convinced that’s basically wrong.


An electric motor is fundamentally different from a gas engine.  With an electric motor, you want to avoid turning your electricity into heat, rather than motion.  That boils down to avoiding “ohmic heating”, also known as I-squared-R losses.


To minimize those heating losses, you want to accomplish any given task using or generating constant power.  That task might be getting up to speed after stopping at a red light, or coming to a stop for a red light, in some given length of roadway.


Here’s the weird thing.  Assuming I have that right — assuming that an efficient EV driving style focuses on providing or generating constant power over the course of an acceleration or deceleration — that implies a completely different driving style, compared to what is recommended for efficient driving of a gas-powered vehicle.


In particular, the standard advice for gas cars boils down to accelerating and decelerating with constant force.  When you take off from a stop light, aim for a constant moderate rate of acceleration.  When you are coming to a stop, aim for a steady rate of deceleration.  Constant acceleration or deceleration boils down to constant force on the wheels, courtesy of Sir Isaac Newton’s F = MA (force is mass times acceleration).


But power is not force.  As I show briefly, in the next section.  In a car, power depends on speed.  Constant force on the brake pedal (and so, on the brake rotors in a traditional car) generates far more power at high speed than at low speed.  Similarly, a constant rate of acceleration consumes more power at high speed than at low speed.


And so, there seems to be a fundamental conflict between the way I was taught to drive a gas car efficiently, and what seems to be the right way to drive an EV efficiently.


In a nutshell, to drive an EV efficiently, you should be more of a lead-footed driver at low speeds.  And taper off as the car speeds up.   Conversely, hit the brakes lightly at high speed.  And press the brakes harder as the car slows.


That’s the driving style that aims for production and consumption of power at a constant rate, over the length of each acceleration or deceleration. And that’s completely contrary to the way I was taught to drive a gas vehicle.


Think of it this way.  Suppose you apply a certain level of force to the brake pedal of a traditional car.  The resulting friction between brake pads and rotors will generate heat.  That rate of heat production is, by definition, power, as physicists define it.  You’re going to generate a lot more heat per second at 80 MPH than you are at 4 MPH.  (In fact, 20 times as much.)  Restated, for a given level of force, you are bleeding a lot more power off the car’s momentum at 80 MPH than at 4 MPH.  And those big differences in power, over the course of an acceleration or deceleration, are exactly what you want to avoid in an EV with regenerative braking, in order to avoid I-squared-R losses.


 




Force and power:  A brief bit of physics and algebra




1:  Two definitions or laws of physics


Work = Force x Distance


Power = Work/Time


2:  A bit of algebra


Substitute for the definition of work:


Power = (Force x Distance) / Time.


Re-arrange the terms:


Power = Force x (Distance/Time)


Distance/time = speed (definition)


Power = Force x speed.


For a constant level of force applied to or removed from the wheels, the rate of power consumption (or production) is proportional to the speed.


Upshot:  To accelerate or decelerate at constant power, the slower you are going, the heavier your foot should be.  The faster your are going, the lighter your foot should be.  For the gas pedal and the brake pedal.




Ohmic heating:  Why a long, hard acceleration trashes your battery reserve.




Anyone who drives a PHEV — with a relatively small battery — will eventually notice that one long, hard acceleration will consume a big chunk of your battery capacity.  On a drive where you might lose one percent of battery charge every few minutes, you can knock several percent off in ten seconds if you floor it.


Another way to say that is that getting from A to B by flooring it, then coasting, consumes much more electricity than just gradually getting the car up to speed.


I’m not exactly sure why that is.  But I am sure that it is universally attributed to I-squared-R or ohmic heating losses in the motors, batteries, and cables.


Any time you pass electric current through a wire or other substance, it heats it up.  From the standpoint of moving your car, that heating is a loss of efficiency.  The more current you pass, the more it heats up the wire.  And that heating is non-linear.  Watts of heat loss are proportional to I-squared-R, in the argot.  They go up with the square of the current that you pass through that wire.


Again, I’m not completely sure here, but my takeaway is that your heating losses, at very high power, are hugely disproportionate to your losses at low power.  At constant voltage, I believe those losses increase with the square of the power being produced by the electric motors.  In other words, ten times the power produced to move the car creates 100 times the ohmic heating losses.


And that’s how ten seconds of pedal-to-the-metal can use up as much electricity as 10 minutes of moderate driving.


That said, I have to admit that I’m relying on “what everybody says” for this.  For sure, hard acceleration seems to trash your battery capacity far in excess of the distance that you travel at that rate of acceleration.   Whether the root cause for that is I-squared-R losses, or something else about the car, I couldn’t say.


Either way, my takeaway is that if losses are proportional to the square of power consumed or generated, then to accomplish any given task (any fixed acceleration or deceleration episode), your aim should be to do that at constant power.  Because that’s what will minimize the overall energy loss from that acceleration or deceleration episode.




Drive like you are pressing on an egg — that was a real thing.  EV drivers should chuck the egg.




Source:  Duke University Libraries, via Internet Archive.


Those of us who grew up during the 1970s Energy Crisis will probably recall public service announcements that asked you to drive as if there were a raw egg between your foot and the gas pedal.  I managed to find a Texaco ad of roughly that era, laying out that egg-on-gas-pedal meme.  The picture above is from that video.


As kids, that was pretty much beaten into us.  Responsible driving means no jackrabbit starts, no tire-smoking stops.  Easy does it.  We’re in the middle of a prolonged gasoline shortage, after all.


So now I come to the part that is absolute heresy for someone of my generation.  If you’ve absorbed the prior two sections, you realize that this advice probably isn’t correct for an EV.  Why?  To consume power at a constant rate over the course of an acceleration, you should start off with a brisk rate of acceleration, then diminish that as the car speeds up.


In other words, if you drive an EV, drive with a lead foot.  Not all the time.  But at the start of every acceleration.  And the end of every deceleration.


If you drive an EV, chuck the egg.




The Prius Prime Eco display




Source:  Underlying picture is from Priuschat.


With that understanding in hand, I’m finally starting to make some sense of the “eco” display on my wife’s Prius Prime.


In theory, this little gauge is giving you guidance on how to drive the car most efficiently.  In practice, I could never make head or tail out of it, except that it seemed to be telling me to drive with a lead foot.


Which, I now understand, it was.


On this display, if you put your foot on the gas, it will show you your actual throttle (gas pedal) position, and the gas pedal position that will, in theory, give you greatest efficiency.


By contrast, when you put your foot on the brake, it doesn’t show you the brake pedal position.  Near as I can tell, it shows you the amount of power than you are generating.  That is, a constant brake pedal position will lead to a shrinking bar, as the car slows down and less energy is generated.


Watch what happens if I try to accelerate gently:




It’s possible that all the meter is actually telling me is that a very lightly-loaded electric motor will operate inefficiently.  I don’t think the Prius eco monitor is actually trying to get me to drive at constant power.


Edit 3/11/2024:  After driving around with a ScanGauge III, my conclusion is that accelerating at constant power is exactly what the eco-meter is trying to get you to do.  It wants you to start off with a heavy foot, and then, as you accelerate, it wants you to back off.  Near as I can tell, that bar is set up to keep you at around 23 HP of power output, or 50 amps of discharge current, or a “2 C” rate of discharge, for this battery.


In particular, my diagram above is labeled wrong. The two red arrows should be labeled “desired power output” and “actual power output”.  You will notice that if you don’t move the gas pedal, the “actual power output” line will creep up as you speed up.  The only way to keep that line in the same place is to back off the gas as your speed increases.  So that line isn’t the throttle position, it’s the power output (power = force x speed).


But no matter how I arrive at it — from theory, or from finally paying full attention to the Prius eco meter — the whole drive-like-there’s-an-egg-between-foot-and-gas-pedal is clearly obsolete.  Gentle acceleration may get you your best mileage in a gas-powered vehicle.  But it’s not the correct way to drive an EV.