EV Battery Pack How to calculate battery capacity

Battery Pack Capacity Calculations

The importance of a battery pack in the electric vehicle power train system is equally important to motor. If the motor provide torque to drive EV than battery pack is the source of power. The travel range of any electric vehicle is completely depends on the battery pack capacity. It's a big confusion to decide the battery pack capacity to get the desired travel range. Normally people considering battery pack capacity on some assumptions which caused the overrated or underrated capacity. In cases they will suffer higher investment or low travel range respectively.

So how to calculate the battery pack capacity to get desired travel range in your EV.

Before starting the battery pack capacity calculation it's required to understand some variable factors of battery power consumption.

1. Motor 

Normally the motor used in EV is bldc specially in ebike. Although the efficiency of bldc motor is quite good ranging from 70-86%. How ever it's depending on the motor RPM. On higher speed and lower speed its economy is low thus it's consume more power and output is low. In short motor efficiency varies on different speeds.

1Kw BLDC Motor Current reading during initial acceleration

2. Acceleration and deceleration 

When we drive the EV in that case the starting torque is higher thus the power consumption is higher. Similarly during the acceleration. But when we drive bldc motor on constant or stabilize the rpm than power consumption  reduced. In other words acceleration and deceleration is reduced motor efficiency. Similarly the power losses increased due to brakes of vehicle inspite of regenerative braking. This losses is high in heavy traffic.

3. Efficiency of Battery pack:

The lithium ion battery has its own efficiency. Normally a A grade lithium cells have 90% efficiency and B grade cell has about 85% efficiency. Which further reduces with the charging life of Lithium ion battery.

The above variable factors need to be considered during calculate for precise capacity determination of battery pack.

To calculate battery capacity there is 2 methods practical  and theoretical method.

Although practical method is more precise but it's difficult.

Let's start the calculation with practical method.

For this we use at ebike to determine the current readings on different RPM. The purpose to get the power consumption of motor in variable speeds.

Gross Weight = 150 + 100 Kg  = 250Kg

I am taking reading of Okinawa Praise bldc hub motor of 1000watt rated power and 72volt.

The current readings of 1kw bldc hub on various speeds are

Speed 20kmph 4-5amp will consider 5amp

Speed 30kmph 6-7 amp will consider 7amp

Speed 40kmph 10-11 amp will consider 11amp

Speed 50kmph 14-15amp will consider 15amp

Let's start calculate the battery capacity for 200km travel on 20kmph speed:

The current withdraw by bldc motor on 20kmph is 5amp.

Consideration the acceleration losses is about 5% for low traffic

Effective current = 5 x 1.05 = 5.25amp

Power P = V x I

P = 72v x 5.25amp = 378watt

378 watt power withdraw by motor on 20kmph speed.

Now because we are designing battery pack for 200km so 

travel ratio = total travel / travel speed

= 200 / 2 = 10

Now the power required to travel 200km is 

P = 378 x 10 = 3780watt. 

To travel 200km with the speed of 20kmph.

Battery pack efficiency considered 85% 

Thus battery pack Power = 3780 / 0.85 = 4449watt

So we required A battery pack of 4.4 kw to travel 200km with the speed of 20kmph.

Designing Battery Pack for 200Km Travel

Speed of bike– 30kmph

Current Taken = 7 amp

Acceleration Current = 5%

Effective Current = 7 x 1.05 = 7.35 amp

Power P = V x I

P30 = 529watt

Travel factor = total travel / Travel in speed

Travel factor = 200 / 30 = 6.67

Power Required to travel 200km = 529 x 6.67 = 3528 watt

Say P30 =  3.5Kw

discharge efficiency of Li-Ion battery = 85%

Power P = 3.5Kw

Battery Pack Capacity = 3.5 / 0.85

Battery Pack Capacity = 4151 = 4.2Kw 

Speed of bike– 40kmph

Current Taken = 11 amp

Acceleration Current = 5%

Effective Current = 11 x 1.05 = 11.55 amp

Power P = V x I

Power required at 40kmph P = 72 x 11.55

P40 = 832watt

Travel factor = total travel / Travel in speed

Travel factor = 200 / 40 = 5

Power Required to travel 200km = 832 x 5 = 4160 watt

Say P40 =  4.2Kw

discharge efficiency of Li-Ion battery = 85% 

Power P = 4.2Kw

Battery Pack Capacity = 4.2 / 0.85

Battery Pack Capacity 4.89Kw = 5Kw 

Speed of bike– 50kmph

Current Taken = 15 amp

Acceleration Current = 5%

Effective Current = 15 x 1.05 = 15.75 amp

Power P = V x I

Power required at 50kmph P = 72 x 15.75

P50 = 1134 watt

Travel factor = total travel / Travel in speed

Travel factor = 200 / 50 = 4

Power Required to travel 200km = 1134 x 4 = 4536 watt

Power Required to travel 200km = 1134 x 4 = 4536 watt

discharge efficiency of Li-Ion battery = 85%

Power P = 4.5Kw

Battery Pack Capacity = 4.5 / 0.85

Battery Pack Capacity 5336 Kw = 5.3Kw

 From the power calculation you can see the power pack required for 30kmph speed is of less capacity in all different speed. Because in Okinawa Praise 30-35kmph speed is the economical speed range so the efficiency is high on this travel range.

On the basis above calculation you can calculate the battery pack capacity by selecting the your average travel speed. But if you run in high traffic than considering 40-50kmph speed is recommended.

You can make this kind of excel sheet table  for battery pack capacity calculation. On more thing you should note that this all calculate based for 1kw motor with 250kg load capacity.

If you use motor of 2kw than you can consider power consumption about 15- 20% higher than 1kw bldc motor. Although the high power motor has higher efficiency by losses like acceleration etc is high. Similarly for high weight or low weight you can reduced or increase the power consumption on the basis of percentage change.

Theoretical Calculation

The Theoretical Method of Battery Pack capacity calculation.

For this higher speed should consider above to average speed say 50kmph.

Motor 1000 watt BLDC

Efficiency Considered 80%

Speed Considered 50 kmph

For 200 Km = 200/50 = 4

Battery Pack Capacity = Power x travel factor/ (Motor + pack efficiency)

P = 1000 x 4 /0.80 x 0.85 = 5.882watt = 5.8Kw

If you want to calculate the theoretical efficiency more precise than you can also refer the 
Motor performance curve to determine the desired data for battery pack capacity Calculations.