This will be quick page put together to present simulation results for ford F250 truck towing 10,000 lb. trailer and equipped with a single motor Siemens AC drive system.

Vehicle gearing, inverter's PI controller, moments of inertia of rotating parts, battery interconnects and chemistry specifics (Peukert effect, polarization, etc.) were all modeled and believed to reflect real objects with enough accuracy, typically the goal is 1% error margin. I was staying on very conservative side on the rolling resistance, allowing it to be 0.015 for empty truck and 0.02 for one with loaded trailer. Inflating the tires hard will help significantly, especially driving uphill. Please note, the incline is given as geometry angle in degrees, not %. I asked a few people, but was unale to get clear definition of US % grade - some say it's vertical drop (feet) divided by the distance vehicle actually roll (100 feet on the odometer), while others said it's the vertical drop divided by 100 feet distance on the map, i.e. horizontally. At large angles the two become very different.

Simulation was done in Matlab R12 environment. Siemens AC drive system and Optima battery models were developed a while ago as a university graduation project. So far there were no complains about prediction accuracy. To give an idea of what the model look like, this is top level model consisting of sub-models of various complexity:

Back to the ford truck. First, the result for an unloaded truck. Traction motor is 45 kW rated 78 kW max induction motor type 1PV5135WS14, power inverter is Simovert 6SV-1. A battery consists of two parallel strings of 28 YT Optimas D950S. So, the first round:

Vehicle data fed into simulation program
===============================
Vehicle drag coefficient:    0.4400
Vehicle frontal area, m^2:    3.5665
Gear ratios
1st:    5.7200
2nd:    2.9400
3rd:    1.6100
4th:    1
5th:    0.7600
Final diff.:    4.1000
Wheel diameter, m:    0.7764
Rolling resistance:    0.015 unloaded or 0.02 loaded
Moment of inertia of all 4 wheels, kgm^2:    3.5000
Moment of inertia of rotor and clutch (if retained), kgm^2: 0.1100
Average efficiency of the gear box: 0.9500
Environment and constants
Road incline, deg.    0
Air density, kg/m^3    1.25
Gravimetric acceleration, m/s^2:    9.8
Motor RPM switch to lower gear    2000
Motor RPM switch to taller gear    7000
Motor and inverter combined efficiency 0.8600
Max motor torque (N*m) is    190
Vehicle weight without battery, kg    2223
Battery type - Optima D950S   
Battery weight, kg    1120
Driver and payload mass, kg:    100 unloaded and 4,545 kg loaded
Total vehicle weight including driver and pay load, kg:    3443 unloaded and 7943 kg loaded

I performed 2 types of simulation - max performance (wide open throttle), basically demonstrating rather drive train capabilities, and real world standardized driving cycle,  reflecting, in addition, battery performance.

To satisfy curiosity of a tradability, empty truck simulation was done for flat surface, and loaded one - also for 1º,  2º and 3º incline.

The results for the max incline an empty truck will handle are as follows:

1st gear - 18.98º
2nd gear - 9.198º
3rd gear - 4.632º
4th gear - 2.549º
5th gear - 1.731º

Now, max performance simulation results (single motor):

The acceleration time to 50 km/h (31 MPH) is about 8 seconds, to 80 km/h (50 MPH) - about 16 seconds, to 120 km/h (75 mph) - 41 seconds. Maximum obtainable speed is 143 km/h (89.4 MPH) and it takes a bit more than 120 seconds to get there. The peaks on RPM curve represent the points where gears are switched (7000 RPM).

Let's look at system current and voltage:

My apology, the title of the plot has to be changed (the plotting script was modified numerous times and this was overlooked; there is no SOC on this plot).

The battery current is limited to 282A; the motor current raise with RPM (to overcome back EMF and sustain constant torque) and when the motor hits certain RPM limit (in this case 4400 RPM), tapers down representing constant power mode (product of the motor current and RPM is constant). The voltage sags to about 361V right from the start and peaks only for short time allowed to switch gears (no current consumption at these moments).

Let see what the power consumption is:

This plot has battery SOC so the title must be fixed. Anyway, we can see how much energy is consumed in the first 120 seconds (3.25 kWh), how far did we get (4 km or 2.5 miles) and how the battery is doing (SOC is down from 1 to 0.896).

Now, vehicle efficiency plot. This represents vehicle shape and rolling resistance and does not depend on the mass directly (until mass, increasing the size of the tire patch contacting the road, affects rolling resistance. This is ignored here).

Unlike previous plots, this one shows power and energy as the function of the speed. You can see how much battery power is needed to move at certain speed (kW/km/h) and it's derivative - energy per km at certain speed (kWh/km/h). Power represents air drag (thus is 0 at zero speed) and energy represents the rolling resistance multiplied by power divided by time. In this case, for instance it will take 27 kW to run at constant speed of 80 km/h (50 MPH) and you consume 335 Wh/km (536 Wh/mile) at that speed. This can be taken as an estimate of the range - with about 23 kWh on board (35 useable Ah per Optima, 70 Ah per pair, * 327V average voltage = 22,890 Wh) the range will be 22,890/536=42.7 miles @ 50 MPH. This number is just for reference - no one in real life drives at 50  MPH until the pack is dead (10.5V/battery under load).

Therefore I did this over again for US06 driving cycles - typical highway use. It takes total of 10 minutes for some stop-and-go to get to the highway, run some distance and after getting off, run on the streets again to the destination point (see http://www.metricmind.com/cycles.htm for definitions). Then the cycle gets repeated until the battery is at 20% SOC, at which point the total distance is more realistic real life range.

The results are here:

Motor and speed. It will take about 2220 sec (37 min) to drain the pack to 20% SOC.

By then, 47.5 miles will be covered and almost 24 kWh used. Note, the range is slightly better and available battery capacity is a little greater than our estimations for 50 MPH steady speed. Why? Thanks to Peukert effect; while max speed for US06 cycle reach 128 km/h (80 mph), average is less than 50 mph, so available capacity each optima will have, die to lower average current, is slightly greater than 35 Ah.

OK, let see how tough is Siemens AC induction motor and inverter. We're hooking up a 10,000 lb. trailer to the truck. The total weight becomes 7,943 kg (17,475 lb.). One assumption: a trailer would probably affect air drag C_d value. Since depending on its shape it can actually improve it as well as spoil it more, I left it unchanged - 0.44. Also rolling resistance is increased to 0.02.

Can the single 45 kW rated motor handle it now, at least on the flat? Let see for the wide open throttle:

Acceleration now is noticeable slower, but far from being a slug holding up the traffic: 0-50 km/h (31 mph) is 15 sec, 0-80 km/h (50 mph) is 39 seconds. The max speed it will reach, is a tad greater than 120 km/h (70 MPH), but it will take 180 sec (3 min) to get there. Still impressive. What about tradability? How it can handle:

1st gear - 7.612º
2nd gear - 3.485º
3rd gear - 1.519º
4th gear - 0.8178º
5th gear - 0.2631º

So getting on the flat freeway is no problem. What about the motor and battery current?

Now, even on the first gear the motor current reaches 282A rms limit. Otherwise, the plot is similar to the one for non-loaded truck.

Let see how's energy being spent:

Well, now after max speed of 70 mph is reached, SOC is down to 0.84, total distance is 4.8 km (3 miles) and 4.8 kWh is spent to do that. So far so good. What about "fuel" economy?:

As expected, power and energy consumption are greater now. To move at 50 MPH it will demand 45 kW of battery power and spend 650 Wh/km or 1,040 Wh/mile. Don't plan to go very far, you have about 30Ah Optimas now, or 19,620 Wh on board, so you better stop and recharge after 19,620/1040=18.8 miles. This, however, is pure limitation of the battery, not the drive system. Overall it is still 85% efficient.

Let's put it on the 1º incline, and repeat:

A little above one minute to reach 50 MPH. The max speed now is 53 MPH, but eventually the motor thermal reserve will limit it to the lower value, see comment under Vehicle efficiency plot below.

Now it will consume 82 kW from the battery to move at 50 MPH and spend 1,63 kWh each mile. Since the motor is rated at 45 kW, after about 3 minutes we have to limit the battery power to 45/0.85 (system efficiency) = 53 kW. This limits max speed to about 55 km/h, or 34.4 MPH. You can improve that by increasing the water flow to greater than 8 l/min, but I wouldn't advise to push it.

Well, let's do 2º now:

OK, 69 km/h (43 MPH) max on the second gear, never switch to third. But we already know, we have the power, just after 3 min must reduce speed to 34 MPH.

Well, since we can only reach 69 km/h (43 MPH) die to the motor torque limit, let see how much battery power it will require at that speed. Guess what?Inverter reached its 100 kW limit too, even if you freeze it (IGBTs current limit).

FINALLY, tough test: 3º incline. Single 45 kW motor and over 17,000 lb. vehicle. Well, we know that it will handle 7.612º on the first gear, so it WILL be able to ACCELERATE on the 3º uphill, but how quickly? Drums please...:

As soon as you switch from the first to second gear (at 42 km/h=26.25 MPH) you stop accelerating,so you better keep going on the first gear. As we will see later, this can be fixed by inflating the tires hard and reducing rolling coeff from 0.02 to 0.015. Then, the truck will keep accelerating eventually reaching 52 km/h. Well, let see if inverter power will allow that though.

This is the most informative plot, let see what limits performance: the motor or the inverter. From the speed plot above, we know that the motor has guts to accelerate the vehicle to 52 km/h (32.5 MPH). From above, we can see that it would take about 90 kW of power, so the inverter is not at its current limit, but very close. Ditto to Siemens engineers for making the two match so well - ideally you don't want to reach a limitation of one while way underpower the other - this means you wasted resources (weight, space and money) on something you can't take advantage of.

So, the question was, can you reasonably quickly get on the 5.234 % steep California freeway, accelerating  from still in the Ford F250 towing 10,000 lb. trailer, equipped with single 45 kW rated 1PV5135WS14 motor?

The answer is - yes as long as you keep critical properties like rolling resistance in check Inflate your tires hard. As expected, your limitation is THE BATTERY.

For fun to get you hooked and make your F250 a scilent head turner: what happens if we use dual AC setup? Needless to mention, with dual AC motors setup, F250 will well outperform stock model. First the max gradeability ... Oh my God, keep your hat on and pants dry:

1st gear - 41.71º  (is it close to 100% US grade?)
2nd gear - 19.55º
3rd gear - 10.17º
4th gear - 5.966º
5th gear - 4.324º

Now, racing:

0-50 km/h (31 MPH) - under 5 seconds
0-80 km/h (50 MPH) - 7.4 seconds
0-120 km/h (70 MPH) - 17.5seconds
0-160 km/h (100 MPH) - 38 seconds
Max speed - 180 km/h (112.5 MPH).

Battery current now hits 2 inverters limit - 560A, but the motors didn't even sweat - 280A limit.

Now, the price for the fun - enerfy consumption:

Well, how dual setup improves 3 degrees uphill performance of fully loaded truck? Here:

You accelerate uphill and reach 80 km/h (50 MPH) in 40 seconds, reaching max speed of 85 km/h (53.1 MPH).

I want to mention, that in this application performance of a single motor is limited by its thermal reserve and cooling effectiveness rather than raw power. If you can sustain 45 kW for long time and stay on the first gear (thanks to 7000-8000 RPM), I'd much prefer that than 100 kW motor which delivers this peak power but on the long ramp overheats in 30 seconds so you have to stop (on the ramp...) to cool it off. This is the reason that I believe water cooled AC induction motors are better suited for heavy duty application like this than higher peak power air cooled DC motors, which rather will excel in drag racing where the burst of max power is required only for few seconds, so the cooling is not that much of a concern. I'd love to see and compare these simulation results with ones for any type of common air cooled DC motor(s).

To see the Siemens AC motors page, please go here: http://www.metricmind.com/motor.htm

Victor Tikhonov,
1991 ACRX