Somebody check my math, please

[Gigi]

Somebody check my math and see if I am figuring this correctly.  My wife got antsy and filled up the tank when it was only down to about a quarter of a tank.

8.92 gallons of gas went into the tank @ $3.099 = $27.64.
798 miles were driven.
Over the 21days since the last fill-up, I think that we charged the car 40 times.  (I should keep better track.)
6.93 kWh to charge x 8.9¢ per kWh = 61.7¢ per charge.

40 charges x 61.7¢ per charge = $24.68 of electricity
$27.64 gas + $24.68 electricity = $52.32 total cost for 798 miles.
$52.32 total cost ÷ $3.099 (the cost of gas at the pump today) = the equivalent of 16.88 gallons of gas.
798 miles ÷ 16.88 gallon equivalents = 47.27 miles per gallon equivalent (MPGe).

I am thinking 47.27 is my MPGe for this tank of gas at today’s gas and electric prices.  Do I have this figured correctly?  Am I missing anything?

[Gigi]

As I continue thinking about this, the days when I added a second charge to the car, often, this was not a full charge.  If I lower my estimate to 30 full charges over 21 days (averaging in a guess at the number and amount of several partial charges), that would give me an MPGe of 53.59, which sounds a little more respectable.  I am going to need to keep track of charging time between fill-ups to come up with a better estimate of how much electricity is going into the car.

[larryh]

MPGe is computed using equivalent gallons of gasoline.  Divide the total number of kWh of electricity by 33.705, i.e. 6.93*40/33.705 = 8.22 equivalent gallons of gasoline.  So MPGe is then

 

798 / (8.92 + 8.22) = 46.6 MPGe. 

 

A more accurate way of computing the electricity consumed is to reset one of the trip odometers each time you fill with gas.  The odometers record the total kWh of plug-in energy used.  However, this reflects the amount of electricity that was drawn from the battery.  To compute MPGe accurately, you need the amount of electricity drawn from the wall outlet.   The car generally reports that it drew about 5.7 kWh from a fully depleted HVB.  The amount of electricity required to charge a fully depleted HVB using a 240 V charger is about 7 kWh.  Thus you would need to multiply the plug-in energy displayed by the car's trip odometer by 7 / 5.7 = 1.23 to get a more accurate estimate of plug-in energy consumed.  For the 120 V charger, it takes about 8 kWh, so you would multiply by 1.39 instead.  This method is only semi accurate.  The actual factor that you need to use varies with temperature.  In addition, if you precondition the car, the car will not record the amount of electricity that was used. 

 

I have a separately metered circuit for the charger, so I can always look at the meter to determine how much electricity was used. 

Edited January 6, 2014 at 10:09 AM by larryh

[Gigi]

Thanks, Larryh

 

I feel better now.  Rather than go with my faulty memory of how many times I charged the car, I took your suggestion and looked back at the trip odometer, which I reset at each fill-up.

 

145kWh were used. 145kWh ÷ .80 charging efficiency = 181.25 ÷ 33.705 = 5.38 gallon equivalents

 

8.92 gallons of gas + 5.38 electricity gallon equivalents = 14.3 gallon equivalents

 

798 ÷ 14.3 = 55.8 MPGe

 

That's more like it.

 

What values are assumed to arrive at the 33.705 figure?

 

Which is more nearly accurate, to divide by .8 for charging efficiency or to multiply by 1.23 as you suggest?

[JATR4]

I bought this Kill-A-Watt electricity monitor at Home Depot.  Not a stock item but free pickup at the store.  Gives an accurate measure of the electricity used to charge the car.

 

Only drawback is it loses its settings if there is a power outage.

http://www.homedepot.com/p/Unbranded-Kill-A-Watt-Electricity-Monitor-P4400/202196386#.UsrLBrSsT0k

[Gigi]

I think I may have a more nearly accurate number now:

 

145kWh used for 798 miles.

145kWh ÷ .80 charging efficiency = 181.25

181.25kWh x 8.865¢ per kWh = $16.07 of electricity used for charging

$27.64 for 8.92 gallons of gas + $16.07 for electricity = $43.71 total cost for 794 miles

$43.71 ÷ $3.099 (the cost of a gallon the day I filled up) = 14.10 gallon equivalents

798 miles ÷ 14.10 gallon equivalents at today's electric rate and today's gas prices = 56.6 MPGe

 

I am assuming that the 145kWh shown on the trip odometer is the actual kWh used by the vehicle and that charging efficiency is 80%.  Or is there another number that should be included to account for efficiency in cold weather?  I realize that I am not including preconditioning.  Is that included in the 145kWh?

 

The 33.705 figure used by the EPA to arrive at gallon equivalents is pretty accurate considering my electric rate at this time of year.  It will be a little low come summer rates.

 

If I understand this correctly, when gas prices go up, MPGe goes up.

When May 1 arrives and battery charging goes up to 12.885¢ per kWh, MPGe will go down. 

 

It will be interesting to see how this all figures come summer with better electric range, perhaps higher gas prices, but also higher charging cost.

 

My bottom line from figuring this up: I think that 56.6 MPGe is well worth the small amount of effort it takes to plug in.

Edited January 6, 2014 at 06:09 PM by Gigi

[shaggy314]

I wait for the car to bug me about being low on gas (<50 miles to empty), even then it takes right at 2 months per tank. :)

 

I can tell the extra weight I'm hauling around in gas on a full tank... (6.25 # per USG).

[larryh]

The post with 55.8 MPGe is correct.  The price of gasoline or electricity does not affect MPGe.  The 33.705 kWh is the energy released by burning 1 gallon of gas.  So 33.705 kWh electricity and 1 gallon of gas provide the same amount of energy. 

 

The electricity used for preconditioning is not shown by the car's odometer.  The amount of electricity consumed for preconditioning can be significant.  Today, it took 3 kWh of electricity to precondition the car.  The temperature in the garage was 1 F.  The temperature in the car after preconditioning was not all that warm. 

 

The factor 1.23 is only a estimate.  The true value can vary greatly depending on temperature and various other factors. 

Edited January 6, 2014 at 09:43 PM by larryh