A cold Prius engine initially operates in a open-loop mode because the O{2} sensors are too cold to measure the oxygen level. During this time, the car tries to maximize use of battery traction power and this results in two distinct fuel consumption rates:
- 0.30 gal/hr - "N" or unloaded
- 0.60 gal/hr - in "D" or loaded
The car can accelerate without burning more than 0.60 gal/hr. Exploiting this limited EV mode can improve cold engine operation by roughly +5 MPG.
This afternoon I created an excel model based upon these assumptions:
- weight: 3,000 lbs
- electric motive power: 2, 4, 6, 8, ... 18 hp (746 W/hp)
- electric overhead: 450 W
- nominal traction battery volts: 272 V
This model estimates the traction battery motive power vs. amps including
overhead:
hp - A
2 - 7.1
4 - 12.6
6 - 18.1
8 - 23.6
10 - 29.1
12 - 34.6
14 - 40.1
16 - 45.5
18 - 51.0
As a practical matter, we know the traction battery voltage sags during discharge but my NHW11 is not standard. Last November I upgraded it to NHW20 modules that have significantly lower internal resistance. Still, traction battery modeling remains difficult.
The 'extended EV mode' ends with going closed-loop, mixture control once the O{2} sensors reach operational temperature which takes about ~45 seconds. My wife's ZVW30 seems to go ~200 seconds in some cases, further than just closed-loop control. Some of Ken@Japan's data suggests the NHW20 may also have ~200 second interval in this mode BUT I do not have one to test with.
It will take a week or so to get Graham scanner data so the model helps identify boundary conditions. Still, the model is consistent with my memory of ScanGauge observations.
The model use an energy analysis, specifically the vehicle kinetic energy and the traction battery energy draw. The model calculates one second intervals that are crude but reasonably accurate representations of vehicle state from
second-to-second. I also used Ken@Japan's drag formula:
DRAG = 190 + 0.42*(V**2) :: in Newtons
The tricky part was calculating the next interval velocity using an energy model. So I used the following:
dK - change in kinetic energy, watts = traction battery energy
m - vehicle mass kg
v2 - next velocity m/s
v1 - previous velocity m/s
** - power function
dK = (1/2)*m*(v2**2) - (1/2)*m*(v1**2) :: change in kinetic energy
(2/m)*dK = (v2**2) - (v1**2)
((2/m)*dK)+(v1**2) = (v2**2)
( ((2/m)*dK)+(v1**2) )**.5 = v2
The only problem with this crude model is Zeno's paradox of the tortoise and
Achilles shows up in the acceleration chart. With these assumptions, this is
what the NHW11 velocity looks like as a function of motive, electrical energy,
over 50 seconds:
My typical experience is I can accelerate reliably to 35 mph during the extended EV mode while keeping the fuel consumption at ~0.60 gal/hr. This roughly corresponds to ~10-12 hp of electric power. But earlier this week and one other occasion, I achieved in excess of 40 mph much to my surprise.
Now as I accelerate, monitoring the instantaneous MPG, I've seen under power, MPGs as high as ~50+ MPG. Sure enough, the model shows similar, instantaneous MPGs in the 10-12 hp range:
But of course this level can not be sustained as the O{2} sensors will kick-in and the engine resume normal warm-up behavior and higher fuel consumption rates during acceleration. However, shifting into "N" puts the engine whether in open or closed-loop mixture control into 0.30 gal/hr mode. The result is these MPGs as a function of speed when shifted into "N":
Now the vehicle speed will decay and Ken@Japan's formula does a good job of predicting NHW11 speed fall off. I've not tried to model the coast-down behavior. In the real world, road grades, stop lights, and traffic are going to limit how far the car can coast in "N." But careful route selection can maximize this desirable MPG interval. I also use shifting into "N" until the coolant reaches 70C and normal, hybrid engine-off operation begins.
In practical terms, more aggressive acceleration in extended EV mode to a higher speed and longer coasting in "N" during close-loop engine operation is a good strategy. The inertial energy debt paid by the traction battery will have to be repaid but once moving, it is a modest 'tax'.
My wife's ZVW30 has some slight differences in that the extended EV seems to have two periods:
A) During open-loop operation before O{2} enabled:
- "D" runs about 0.60 gal/hr
- "N" runs about 0.45 gal/hr
B) During close-loop operation the remaining ~200 seconds (*):
- "D" runs about 0.60 gal/hr
- "N" runs about 0.30 gal/hr
* - I have distinct memory of the 200 second interval but it failed to show up this afternoon when I ran the dogs over to the dog-park.
I don't have an NHW20 for testing but I would expect it's behavior to be
somewhere between the NHW11 and ZVW30.
Questions?
Bob Wilson
Today
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