Trying to figure out Power Curve

[DeaneG]

Can we move the utility rates to another thread ? Let me know what thread should I move it to ... (or a new thread).

Maybe since there are only ~30 california "pins" on the map so far, we should merge the SF Bay area San Diego / Los Angeles locale forums into a "California" forum, and put utility threads there. I think the critical mass will help.

Or like many other car forums, split it into Northern CA and Southern CA.

 

[TimeHorse]

Okay, here are my numbers for the function:

c1 = -0.000455444380434 hr-s per mi**2
c2 = 0.00000680056218 per mi
c3 = -0.000562935424884 hr per mi**2
c4 = 0.018817911169545 hr**2 per mi**3
c5 = 0.32216529899805 hr

(These constants incorporate the LEAF Battery Energy).

The nice thing is the c5 term, which is 0 when there is not A/C or Heater or the number given above when the A/C is used and c1 which when there is little to no change in speed (cruise control, chrome on everything, living large) c1 is also 0 so it reduces to the numbers I posted previously which I think are pretty dang close to the mark without taking wind speed, direction, or slope directly into account.

For example, I calculate at a constant speed of 69 mph and the A/C going, you could only go about 59 mi. Unfortunately, that's a little under my need (67 mi), so this may be bad news for me. But I think I'm pretty close. I want run my commute through that gMeter and then apply this function to that to see what my commute looks like with A/C (in the afternoon) and without (in the morning -- not very hot at 3am).

 

[evnow]

Maybe since there are only ~30 california "pins" on the map so far, we should merge the SF Bay area San Diego / Los Angeles locale forums into a "California" forum, and put utility threads there. I think the critical mass will help.

Or like many other car forums, split it into Northern CA and Southern CA.

Can you create the needed topic/s - and PM me what threads / posts should be moved.

 

[evnow]

Okay, here are my numbers for the function:

I thought you didn't have enough data ?

For example, I calculate at a constant speed of 69 mph and the A/C going, you could only go about 59 mi. Unfortunately, that's a little under my need (67 mi), so this may be bad news for me. But I think I'm pretty close. I want run my commute through that gMeter and then apply this function to that to see what my commute looks like with A/C (in the afternoon) and without (in the morning -- not very hot at 3am).

Get a charging source at work. Not only can you charge - you can condition before driving.

BTW, why are you using 69mph constant speed ?

 

[TimeHorse]

I thought you didn't have enough data ?

I decided to take 6, 7, 9 and 10, assuming that 9 and 10 have very little acceleration component; I assume 9 and 10 have very little acceleration component, essentially 0, and only apply the acceleration to the EPA LA4, where acceleration = change in velocity / 1 second for each sample and assuming no regenerative breaking since I have no idea what 'multiplier' I should use here. But I'm pretty confident with these numbers, not 100%, but I think range is probably with 5 miles of calculated, but I'm waving my hands to get that number; I really have no idea. I want to run this function against HWFET and US06 to see what that will get.

Get a charging source at work. Not only can you charge - you can condition before driving.

BTW, why are you using 69mph constant speed ?

Ah, well, my company is one of the biggest in the world and as such I do think I have a better than average chance of convincing them to give me charge time, at least at 110VAC; but as it is large, it also can be slow to move but I will have to get on the ball and start pushing A.S.A.P., won't I? As well as send out 500 or so letters to all the Commonwealth of Virginia House of Delegates, Senators and Governor containing the opened letter you can find on my blog. (I already sent something similar to my Delegate, but she never replied so I figure if I send it to everyone it may get a hearing in Richmond).

Anyway, in case you weren't bored yet with Virginia politics, it is convenient here to set ones cruise control to 69 because it's exactly 14 above the speed limit and cops don't generally ticket you until you hit 70. If you hit 75, they not only ticket you, they give you a criminal record with a Class 6 Misdemeanor! If you want to know what it's like to live in a totalitarian Highway System, you could do no better than the Commonwealth!

 

[evnow]

There is something wrong with those numbers. Is this what it is supposed to be ? With a as zero (constant speed) I get basically 0 range for all speeds above 10 mph.

range = 24/(c1 * a + c2 + c3 * v + c4 * v**2 + c5 / v)

c1 = -0.000455444380434 hr-s per mi**2
c2 = 0.00000680056218 per mi
c3 = -0.000562935424884 hr per mi**2
c4 = 0.018817911169545 hr**2 per mi**3
c5 = 0.32216529899805 hr

 

[TimeHorse]

There is something wrong with those numbers. Is this what it is supposed to be ? With a as zero (constant speed) I get basically 0 range for all speeds above 10 mph.

range = 24/(c1 * a + c2 + c3 * v + c4 * v**2 + c5 / v)

c1 = -0.000455444380434 hr-s per mi**2
c2 = 0.00000680056218 per mi
c3 = -0.000562935424884 hr per mi**2
c4 = 0.018817911169545 hr**2 per mi**3
c5 = 0.32216529899805 hr

I think I have c2 and c4 mixed up; c2 is the smaller so I'm pretty sure that's the v**2 term otherwise it doesn't make sense. You don't need the 24; the charge is already compensated for. So it should be:

range = 1/(c1 * a + c2 * v**2 + c3 * v + c4 + (<using A/C> ? c5 / v : 0))

I.e. only include the c5 term if you want to assume with A/C.

(Actually, I had the values of c2 and c4 mixed up, but let's just say the names are and leave it at the equation above.)

 

[TimeHorse]

So, following on from the 1/range function, we can now get at a Power function:

P(a, v) = v * E * (c1 * a + c2 * v**2 + c3 * v + c4 + (<Using A/C> ? c5/v : 0))

And if you take a series of samples at 1 Hz, you should be able to simply sum P(a, v) for all samples to get the total Energy used, in Joules. Multiply this by 3600000 to convert to kWh. Then you know how much of your energy, and thus how much of your battery life, you've expended. Further, if you know how far you went in that trial, you can extrapolate how far you could go if you continue it repeatedly until you're out of charge.

So, if my numbers are correct, here's what I get for EPA US06, the Aggressive Driving Schedule:

2.09889538223213 kWh consumed.
The course is 8.00797222222222 mi
Average Speed is 48.1280467445743 mph
So your total range would be 91.5678480024772 mi.

About 92 mi under US06. Hmm. I expected a lot worse than that. I mean, that's only 8 miles less than EPA LA4. Mind you, if you use the A/C, I compute a bit over 5.8 kWh drain and thus only 33 or so mile range! I hope that's wrong too!

I wish I could get an account on TheEEStory, but the registration link is broken; I'd really like to discuss this with Student. After all, he made his calculations by actually plugging in numbers where as I did it by curve matching and making some gross assumptions about the magazine data.

 

[Bicster]

I don't see how it's possible the A/C could draw 5.8kW except maybe on startup.

I have a mini split system in my house that draws 1.7kW peak for 8,500 btu. (It's rated for 14.5 amps with the indoor and outdoor unit combined, at 120 volts.)

An automotive system should be around 20,000 btu. That would be around 4kW... and again, that should be peak, not average, and should drop much lower once the cabin cools off.

 

[evnow]

About 92 mi under US06. Hmm. I expected a lot worse than that. I mean, that's only 8 miles less than EPA LA4. Mind you, if you use the A/C, I compute a bit over 5.8 kWh drain and thus only 33 or so mile range! I hope that's wrong too!

A/C can't have so much drain. Moreover, the AC will be variable - depending on the desired cabin temperature and outside temperature (may be also Sunshine ?).

I think the scenarios with A/C (1,3,5,8&9) are all using some average speed. Only 6 (or 7) & 10 are cruise speeds. What happens if you take only these and the LA4 cycle to calculate the constants, ignoring the AC component.

I'd expect the AC to be max 2KW continuous. That should make not more than 8 to 10 miles of difference in range at high speeds and may be 15-20 miles at medium speeds.

 

[TimeHorse]

I don't see how it's possible the A/C could draw 5.8kW except maybe on startup.

I have a mini split system in my house that draws 1.7kW peak for 8,500 btu. (It's rated for 14.5 amps with the indoor and outdoor unit combined, at 120 volts.)

An automotive system should be around 20,000 btu. That would be around 4kW... and again, that should be peak, not average, and should drop much lower once the cabin cools off.

D'Oh! There was a bug in my formula! I forgot to multiply the c5 term by the 1/v term and in fact I needed to re-arrange that term because from a Power point of view, you get v/v and when v = 0 this should be 1 so I moved it out of the v*E*(...) and made it:

P = E*(v*(...) + (<Using A/C> ? c5 : 0))

Also, I made a mistake in the units for c5: that should be 0.32216529899805 per hour, so that when it's multiplied by Energy in kWh it comes out to 322 Watts or so, which is what was measured in test 9, assuming test 9 was fairly constant speed, which I think we've established it is (also note that by reversing c2 and c4, their units also reverse -- the thing to remember is since c2 is smallest, it should be applied to the v**2 term and is hr**2 per mi**3).

So, in fact, I estimate a 3.389 704 346 884 32 kWh draw under US06 with the A/C running at a capacity similar to Test 9 (about 1.3 kWh used just for the A/C for the 10-minute cycle) for a total estimate range of 56.698 553 521 338 2 mi. I think this is more accurate since we know A/C is the bane of all electric vehicles. That's down from a bit less than 92 miles without A/C. Certainly, I may be able to make due if I usually drive to work without A/C and only only turn it on when driving home; the main problem I'll have is remembering to turn it off in the evening, though I suppose with all the vehicle smarts, when it's charging it could do that automatically.

All this said, I have to admit I too am dubious of the idea that the A/C alone would draw c5*E = 7.731 967 175 953 19 kW of power! There's got to be more to test 9 than meets the eye. We really need a cruise + A/C test. I'm pretty sure the linear algebra is right, but I'll check my numbers to be sure.

 

[TimeHorse]

Also, another cruise or dynometer-rated test would allow me to break out a worrying 6th variable: the Regenerative Breaking factor, which currently is assumed 0%.

 

[TimeHorse]

Not to be at all negative, but he appears to be using averages as opposed to following the actual cycle. I have several thousand cells of data (source and derived). I think around 25k cells of data for the UDDS and HWFET cycles. I used the actual cycles as opposed to approximation.

:roll: The proper way to analyze EPA cycles is to sum the partials and average. I don't take v<ave>**2 to get the velocity squared, I take sum(v[n]**2)/samples. In effect, I'm assuming a discrete sample to calculate energy used: E<total> = sum(P<instant> <for all> samples) / <sample rate>. The power function I gave is assumed to be P<instant> and you need to take each sample velocity, its square, the instantaneous acceleration (?v * <sample rate>; 1 Hz for LA4, 10 Hz for HWFET), and apply the constants to get the interim result. I'll be happy to show my EPA charts to anyone who cares to see them, though they're rather messy but believe me there is a bundle of data I'm not showing to keep from boring you on the specifics of the LA4 cycle.

Effectively, what I'm doing is taking the sums of all the equations components (sum a, sum v, sum v**2, sum 1/v) and then dividing by the number of samples to get the average power used in a second; I then apply the same calculation to the cruise speeds and end up with a series of unknowns which I solve for for each test run using linear algebra.

I will not comment further on TimeHorse's approach unless he brings it up in this thread.

he said from behind a locked door. :roll: So, does anyone else get redirected to the home page of TheEEStory when they click on the register link: http://www.theeestory.com/register

 

[sjfotos]

Not to be at all negative, but he appears to be using averages as opposed to following the actual cycle. I have several thousand cells of data (source and derived). I think around 25k cells of data for the UDDS and HWFET cycles. I used the actual cycles as opposed to approximation.

:roll: The proper way to analyze EPA cycles is to sum the partials and average. I don't take v<ave>**2 to get the velocity squared, I take sum(v[n]**2)/samples. In effect, I'm assuming a discrete sample to calculate energy used: E<total> = sum(P<instant> <for all> samples) / <sample rate>. The power function I gave is assumed to be P<instant> and you need to take each sample velocity, its square, the instantaneous acceleration (?v * <sample rate>; 1 Hz for LA4, 10 Hz for HWFET), and apply the constants to get the interim result. I'll be happy to show my EPA charts to anyone who cares to see them, though they're rather messy but believe me there is a bundle of data I'm not showing to keep from boring you on the specifics of the LA4 cycle.

Effectively, what I'm doing is taking the sums of all the equations components (sum a, sum v, sum v**2, sum 1/v) and then dividing by the number of samples to get the average power used in a second; I then apply the same calculation to the cruise speeds and end up with a series of unknowns which I solve for for each test run using linear algebra.

I will not comment further on TimeHorse's approach unless he brings it up in this thread.

he said from behind a locked door. :roll: So, does anyone else get redirected to the home page of TheEEStory when they click on the register link: http://www.theeestory.com/register

I end up here:

http://www.theeestory.com/

 

[evnow]

So, in fact, I estimate a 3.389 704 346 884 32 kWh draw under US06 with the A/C running at a capacity similar to Test 9 (about 1.3 kWh used just for the A/C for the 10-minute cycle) for a total estimate range of 56.698 553 521 338 2 mi. I think this is more accurate since we know A/C is the bane of all electric vehicles.

That doesn't look right. We can't be spending so much energy to cool such a small space. I don't think test 9 is constant speed either.

 

[MikeD]

TimeHorse, how good of a curve fit can you get on the Tesla "Range vs (Constant) Speed" graph shown previously using a function of the form "R(v) = v / (av^4 + bv^3 + cv^2 + dv + e)" where a thru e are constants? As you've indicated before this should take 5 points, but you have plenty to choose from that graph. It may also be of interest to discover where it is best to pick those 5 points in order to get the "best (looking?) fit". In order to get as good a fit as you require I suppose you can go to higher degree in v (and required data points) in the denominator, but for the sake of simplicity ultimately limit the degree (or maybe find a better model function than I have suggested).

 

[TimeHorse]

TimeHorse, how good of a curve fit can you get on the Tesla "Range vs (Constant) Speed" graph shown previously using a function of the form "R(v) = v / (av^4 + bv^3 + cv^2 + dv + e)" where a thru e are constants? As you've indicated before this should take 5 points, but you have plenty to choose from that graph. It may also be of interest to discover where it is best to pick those 5 points in order to get the "best (looking?) fit". In order to get as good a fit as you require I suppose you can go to higher degree in v (and required data points) in the denominator, but for the sake of simplicity ultimately limit the degree (or maybe find a better model function than I have suggested).

Actually, the function would use only the constants c2 - c4 since c1 assumes acceleration, of which there is none and c5 is the constant power drain one finds at idle and all speeds beyond. In essence, since P = dE/dt, if you compute Energy you end up with c2*v**2 + c3*v + c4, a quadratic. Also, we don't need a quartic term. Let's stick with this:

R(v) = 1/(c2*v**2 + c3*v + c4)

Here, I've dropped the c5/v term because it is a bad measure of the draw of an A/C.

So, if we are to do this, can someone do me a favor and pick 3 points on the Tesla graph and post them here:

velocity (in mph), distance (in mi)
..., ...
..., ...
..., ...

Then I will run my linear algebra to calculate c2, c3 and c4 and then predict some new velocity-distance numbers for you which you can verify against the graph at your leisure. How does that sound?

 

[TimeHorse]

Finally, here is my estimate of HWFET, which is dubious IMHO in both the no-A/C case and in the A/C case because what effectively it is saying is that the LEAF is more efficient on the highway! Ungh! But anyway, this time I'm going to show you my calculations so that if Student ever criticizes me again in that forum that prevents new members from joining, you can send him this link to show him I know what I'm doing -- even if the numbers are wrong.

HWFET Schedule at 10 Hz

Anyway, what I calculate for HWFET is 125.113 505 143 643 mi and with A/C at 67.8734849570356 mi.

Well, 125 mi doesn't contradict much some of those real-world tests but the biggest issue is that I've always heard EVs do better the slower you go. After all, the Tesla seems to get the most range at 17 mph. But here, we're seeing 25 miles more range when focusing most of ones driving on Highway. Hmmm.

 

[TimeHorse]

Okay, I've fixed the linear algebra so the stages of it are easier to follow: zero out the first column, then the second, etc. No new numbers yet and I haven't split the acceleration from the deceleration to figure out the regenerative breaking factor but it should make it easier to modify when the new numbers come in.

Updated spreadsheet; Nissan Leaf in Blue

 

[evnow]

Anyway, what I calculate for HWFET is 125.113 505 143 643 mi and with A/C at 67.8734849570356 mi.

That sounds somewhat dubious. Anyway, one thing I noted in the other thread is how much of a difference apparently AC makes. All non/AC figures from Nissan are above 100 miles and AC/heat are below 80.

BTW, when you post can you just use round numbers for range - it makes it more readable.