EV Calculations

SOME BASIC EV CALCULATIONS (taken from http://www.ev-propulsion.com/EV-calculations.html) Electric Vehicle Conversions: What’s - What? As with ICE (Internal Combustion Engine) vehicles, speed, distance, MPG, etc.. will vary between vehicles due to driving habits, road conditions, etc.. The same will be for an EV (Electric Vehicle). However, here are some basic guidelines to help get you started. SPEED: Voltage! The higher the voltage of your Battery System, the faster a given EV can go. Trade Off: As with ICE's, the faster you go the more fuel is used - the faster an EV goes the more power is used. This will impact how far you can travel on a single charge. Distance: Speed,  Pack KWh rating, driving conditions, aerodynamics, vehicle weight, hills, temperature, driving styles and several other factors play into the distance question. The basic formula for determining distance is: ( KWh of pack / wh/m ) = Distance *note: there are adjustments that have to be made to this formula, see usable pack size below* Watt-Hour per Mile (Wh/m): The basic rule of thumb for vehicle is: Small Vehicle                       250-300wh/m Small Pickup                        350-400wh/m The calculation is: Volts x (Amp Draw / MPH ) = Wh/m Battery Pack Size (KWH): Pack Voltage x Amp-Hour rating of battery = KWH Usable Battery Pack Size: Unfortunately, we can not use all of our battery Pack or we will kill our batteries extremely fast. To extend the life of the battery pack, we do not want to discharge the batteries more than 80%. In addition, because an EV will discharge the batteries faster than the manufacturer tested and rated, we get an effect called “Peukerts”. Therefore, we will need to correct our calculations for this effect. LiFePO4 Batteries are only marginally effected and we can ignore Peukerts effect. However if we use Lead-Acid batteries the Peukerts effect if considerable, where we only get to use about 55% of the power in the Battery. Usable Pack size: KWh x 0.80 x Peukerts = Usable KWh Peukerts: Lead-Acid = 0.55 LiFePO4 = 1.0 Yes, you get a BIG hit on your available power when using Lead-Acid. However, they are generally cheaper than LiFePO4 batteries. Putting all this together - Example: Vehicle:                  Miata Batteries:               12 - 12V Lead-Acid, rated at 100 ah Pack Voltage:        144V  (12 batteries x 12V each = 144V) Pack Size:              14.4 Kwh (144V x 100 ah = 14.4 Kwh - Remember, we can not use all this) Usable Pack:         6.336Kwh  (14.4 x 0.8 x 0.55 = 6.336 Kwh usable) From experience, we know that a Miata using a 144V system will draw around 90amps at 50MPH. Therefore, the Wh/m usage = 144V x ( 90Amps / 50MPH ) = 259Wh/m The distance our Miata will travel on this setup is:  6.336kwh / 259wh/mi = 24 Miles (at 50MPH) If we had a lithium pack of equal voltage and ah, the range would be  44 miles (because Peukerts effect does not play a role) 14.4 x 0.8 = 11.52 kwh usable / 259 = 44 On a side note, 144 volt pack of lithium ( LifePO4) cells would consist of 45 of the lithium cells (they are nominal 3.2 volts each) To CALCULATE this in reverse, (using LifePO4 cells) say you need to go 44 miles per charge at 50 mph and want to know what size batteries you need...... we will use the 259 wh/mi avg. wh per mile / pack voltage = ah per mile So in our "car"   259/144= 1.8ah per mile   so you would need   ah per mile x miles per charge needed x 1.2 (so you still had 20% charge left after the drive) in our "car"   1.8 x 44 = 79.2 x 1.2 = 95 ah batteries at 144 volts needed to go the 44 miles. A lot of people wish to go close to 100 miles in our experience. To make it simple, for this car to go say 88 miles (double the 44 it is capable of now) the total Kwh of the pack has to be doubled. This can be done in a few different ways, most common would be to double the ah rating of the batteries used or double  the voltage by using double the amount of the same 100 ah batteries. In our above case, that would be 45 of the 200 ah cells, or 90 of the 100 ah cells. Keep in mind the components used must be rated for the voltage and amperage Be careful here, just because you raise the voltage so high or don't need a long range, you should not use batteries much lower than 100ah rating, because of the "C" rating, see explanation below. With todays Lithium batteries, it is not recommended to draw more than 3 times the C rating for more than @ 10 seconds. 1C for a 100ah battery would be 100amp draw, and 3C is 300 amps. So if you limited your controller to draw the max of 300 amps from the batteries at 144 volts, the acceleration would be Ok. With a 300 amp limit at 288 volts the acceleration would be impressive. The usual recommendation is to use larger ah batteries, from 160-200 ah and adjust your voltage to get your needed KWh pack, so that 3C is between  480 - 600 amps. Some things to remember: A 5%  grade requires twice the power that is needed on level roads. Poor aerodynamics will use more energy Poor wheel alignment, low tire pressure, other mechanical drags will use more power Weight is very important-the lighter the less energy needed to move the vehicle   TEMPERATURE- battery temperature below 50 degrees will diminish the range of the vehicle. Generally, lead acid batteries will lose 30% of their useful ah at 30* F,  and LifePO4 about 15-20% Driving on hills Higher voltage comes in handy when going up hills- a long drawn out hill (remember a 5% grade doubles power needed)  can easily demand more than 3C for longer than the recommended time  from our 100 ah batteries-putting them in an area that may reduce their lifespan and create heat in the cell. If the vehicle is to be used in mountainous areas or for high performance use, larger ah batteries are needed because of this C factor. A side benefit of course would be longer range- but a costlier pack. Performance Now we get to the fun part, calculating HP V x A = watts,    and  watts/746 = HP      so  V x A / 746 = HP If we had a 144 volt pack of 200ah batteries, and a 1000 amp controller, using the above formula we could have  193 HP, (at a 5C draw)   and if we had 288 volt pack of 100ah batteries we could have potentially  386 HP ! (these are calculated without efficiency included, figure about 85% efficient)   Only one problem, that much electrical power put into the motor could easily destroy it rather quickly !  The common "in the field" estimate of KW power a 9" motor can handle (for short periods) is 100 KW.  So using the above formulas, 144 volt system should be limited to about 700 amps, and the 288 volt system to 350 amps. Still, 135 hp is pretty good for a small car.  NOTE: use high power levels at your own risk for motor damage. Using a generator And for those looking to add a generator as a range extender..... As you can see from the calculations above, the instantaneous watts needed to drive about 50 mph is about 13,000 watts. So to drive your car strictly on a generator (at a steady speed), your would need a large one in the neighborhood of 15KW. For any type of acceleration or resistance (hills) the load could easily be 50 KW, and up to 100KW !   If you used a smaller one, say a 2000 watt generator, you can see it would add about 10 % to your range. It may be better to use the cost of a generator this size to just add more cells and skip the generator and its complexity to the system (and exhaust emissions). Heaters Lastly, the subject of heaters. Generally you need about 2500-3000 watts to raise the temp in a car to a comfortable level in a reasonable amount of time, and about 1500 watts to maintain that temp.  So those in a cold climate will lower their range about 15%, or you will need to add about 15% to the battery KW capacity. Now the disclaimer: These are all calculation based on theoretical values, averages and assumptions. There are several factors (such as but not limited to weather, tire pressure, driving habits, battery condition, etc..) which effect all the calculations listed above which are not used. All calculations should be considered estimates only and can not be relied on as fact.