April 11 2008

Initial Estimations

Overall measurements around the vehicle yield this:

Overall measurements Measurements around stock Audi A6 Avant.

Searching internet revealed few more numbers needed for initial performance simulation necessary to select gearing to achieve desired goals. Along with measurements, the numbers are:

Frontal area 2.4 m2  
Air Drag coefficient, Cd 0.31  
Vehicle total mass 1782 kg = 57% / 43% front/rear
Front on scales 1009 kg = 57% of total
Rear on scales 773 kg = 43% of total
Left side on scales 891 kg = 50% of total
Right side on scales 891 kg = 50% of total
Riding height, front 676 mm to the fender wheel arc top
Riding height, rear 683 mm to the fender wheel arc top

It pays to do the home work and calculate as much ahead of time as possible. This avoids unnecessary trial and error, wasting time material and effort leading to dead solutions. Unfortunately I can't suggest good alternatives to the experience and "feel" gained by just doing conversions and see what works and what doesn't. There is information and there are software tools out there to help you design and predict the outcome, but these are only useful tools; they won't do the work for you. Sort of like a fancy calculator - it can do a lot, but you're the one who will push its buttons and making sense of the numbers you get. Most of precise performance predictions will be done in Matlab environment using software vehicle model. The model consists of separate inter-linked models of major components - gear box, motor, battery, wheels with their associated parameters. However, initial rough performance estimation could be done with simple equations in excel spreadsheet.

Major choice of power drive system was made early on - as of this writing the only available EV AC inverter I could get is 200kW peak power EV-200, designed and manufactured by Dutch company EVISOL. This inverter is replacing Siemens inverters (which no longer can satisfy market of individuals and small OEMs working on single prototypes) and will run Siemens motors. The inverters are capable of up to 900VDC battery input, which makes them ideal for high speed operation and reducing current drawn from the battery. (Dec. 2009 update: inverters do not work and will have to be either modified or replaced - EVISOL was incapable delivering promised inverters because chose dead solution). Main three advantages of higher input voltage:

- the higher voltage, the higher RPM at which you still generate linear torque. Because of significant BEMF (Back Electro-Magnetic Force) motor generates at high speed, you must have battery voltage higher than this BEMF to still feed amps the motor in and make appreciable torque up there.

- low battery current while maintaining output power. This reduces stress on the battery prolonging its life.

- simplifying wiring. The cable interconnecting individual batteries or cells can be much thinner than in typical lower voltage systems - about 25m m2 (roughly equivalent of AWG 3).

Of course, as always, there are disadvantages as well:

- You need more batteries in series now. The battery is not necessarily bigger and heavier overall, since each cell/battery now can be smaller (for the same total energy storage) as for lower voltage systems, but there are more connections to make and more work to do.

- Higher voltage requires greater respect. The battery I will be ultimately using consists of 192 lithium polymer cells in series, 3.7VDC nominal voltage and 40Ah nominal capacity each, which yields 710VDC battery storing 28.4kWh. (More about battery - on special battery related page). This might sound a lot of volts, and it sure is, but given right circumstances, 36VDC can kill you as well. You'd need to pay attention, observe basic rules, insulate everything well, use OEM hardware (quality fuses, feed through glands, connectors, etc.) and don't compromise on safety. I'm comfortable with high voltage. My traction battery will be split in 6 sub-batteries in individual boxes 118VDC each, fitted with the battery management system. As everything power in the vehicle, the battery will be water cooled with own thermal management system. That system will not actually cool the battery, it will maintain its temperature within programmed limits, cooling or warming it as necessary.

The cells I will be using are Lithium Polymer power cells manufactured by Kokam - Korean company well known in RC market. Unlike lithium phosphate chemistry everyone seem to prefer, lithium polymer has higher energy density (higher than for instance A123 cells) and each cell has 0.5V higher nominal terminal voltage. As I mentioned, the current consumed from high voltage pack is relative tiny, but there is plenty of power available. I'm not big fan of the concept of paralleling cells to gain capacity, as there is never assurance they share the load equally no matter how optimistic your assumptions are. Better to pick right capacity cells to start with, and connect them in series. Fortunately, now Kokam manufactures EV size cells - 40, 70, 100, 200 and 240Ah capacity.

Anticipating usual question how far my pack will move me, we can do some basic calculation on the back of virtual napkin. I know based on the shape and size of my vehicle that it is going to consume about 250 Wh worth of electricity per mile. May be a bit more on freeway, less in stop and go traffic (while taking advantage of regen) but 250Wh/mile in average is close enough estimation. That is 1kWh per 4 miles. So 28,4 kWh pack (710VDC*40Ah) will move me 28.4*4=113.6 drop dead miles. Given that I should not discharge the battery completely, about 80% of that energy is actually available, which makes practical range equal to about 91 miles. Not spectacular range, but 40Ah is quite tiny capacity pack taking very little space. And already expensive enough. Battery technology is improving, new players expected to appear, and by the time the vehicle will be ready and drivable, I'm sure broader choices for upgrade will present themselves. Granted, I'm going to design the battery system with real possibility of future upgrade to a higher capacity battery in mind.

The cells are capable of comfortably supplying current at 3C (120A) rate continuously and 5C (200A) peak. Let's estimate drive system current for steady driving at freeway speeds. From experience I know pretty accurately, the electric Audi will require around 15 kW of battery power to ride at 60mph. With 710VDC nominal pack voltage that amounts to 15,000/710=21A current draw from the battery That is about 0.5C rate, which is easy life for 40Ah cells.

Since I have a pack of ultracapacitors left from my previous project, to take advantage of it I might try another configuration: series connection of the 350VDC lithium pack and 350V capacitor stack. The stack voltage effectively adds to the pack voltage allowing total to swing within 350VDC...700VDC range. Based on previous experience driving Honda ACRX and burning rubber on the capacitors alone (no battery in the vehicle at all), I know that the energy stored in the stack will be plenty for acceleration, especially in addition to the battery energy. And the capacitors are good at storing and releasing small amounts of energy quickly, e.g. capable of providing high peak power. I still have to run some numbers and estimate the cost of the auxiliary DC-DC converter I would need to implement this concept.

Schematic  Block diagram of the ultracapacitor connection concept.

Pros and cons of this are:


- Saves on battery system complexity, weight and cost - I would need twice as few cells, BMS balancing boards, and also may need one less charger (if originally two were planned)

- Ultracapacitor pack gets cycled 100%, the voltage on it can swing from max 350VDC to near zero when they discharge supplying all the stored energy to the drive system. During regen capacitors absorb extra charge getting prepared for the next acceleration. Life of the stack is estimated in millions of cycles - at least far more than the battery life and certainly will exceed life of the vehicle, so unlike the only disposable item (the battery) will be permanent part of the installed hardware.


- If, instead, I'd install extra battery with the weight equal to the capacitor stack, I'd store far more energy on board which translates to better range. However, in my case I already have capacitors "for free". Might as well use them with an option to replace the stack with extra battery in future.

- It is preferred to have extra DC-DC converter maintaining the charge during steady cruising - extra weight and cost. Without DC-DC the system will work, but initial acceleration after long parking, when the stack is discharged will be only on the battery alone. During cruising at steady speed, the capacitor has no chance to work, and I'll be carrying "dead" weight around. Whether I can take advantage of the stack really depends on the driving pattern: if mostly freeway, no; if mostly stop-and-go, probably yes. I will simulate in software both scenarios and decide on this later.

Finally, one more critical estimation statistics: with single gear reduction and defined max. motor(s) RPM, what is the differentials reduction ratio needed? Before this question can be answered, I'm considering to fit front and rear differentials with deliberately different ratios, so transition from constant torque to the constant power will not happen at the same time for front and rear drive system, which makes vehicle dynamics smoother. However, I certainly will be restricted to very few available choices of stock diffs with unusually high ratios, so may end up using identical differentials and control transition points electronically. Will see.

So, what is the ratio? The motors I will be using (Siemens 1PV5135WS28) develop max power at around 6000...7000 RPM at high voltage available to the inverter input. But I must consider life of the motor shaft bearings, noise, windage losses too. So I can somewhat lower top RPM as long as I'm OK with power. Since motors are water cooled and there are no fans on shafts, running slower will not impact their temperature that much. On the other hand, I must be able to reach ~200km/h (120...130 MPH) without over-revving motors. For initial estimation, 5,000 RPM at typical these days 120km/h (75 MPH) freeway speeds would be fair choice. The tire diameter is 636 mm, resulting in almost exactly 2m tire circumference. At 120 km/h vehicle travels 120/60=2km/min or 2,000m/min. This means the wheel must make 2000/2=1000 RPM to cover that distance in 1 min which makes estimations simple: at 5,000 RPM of the motor shaft it then translates to exactly 1:5 final differentials R&P ratio needed; at 5,500 RPM it's 1:5.5 ratio, at 6,000 RPM - 1:6.0 etc. Now it's a matter of searching for closest R&P ratio differentials aftermarket industry has to offer...