A short guide to battery and electrical characteristics (A, V, W, Ah, Wh) and how to use them

[Eric0976]

This is what I figured after some readings (would gladly get corrected if I got something wrong). To summarize what the different battery characteristics look like when the battery is discharging (reverse arrows for charging), it helps to look at what happens to water in two leveled buckets linked by a pipe (Initially bucket A is full and B is empty).

Battery energy, measured in watt-hour (Wh), is the energy stored that is available to produce electricity. It is the volume of water in bucket A.

Battery capacity, measured in amp-hour (Ah), shows how fast energy can be released from a battery. Capacity is temperature dependent, colder temperatures reduce capacity. The viscosity of water rises as temperature falls and when it freezes solid it can’t be released from bucket A. Rated capacity is measured at a specific temperature, which may or may not be indicated on the battery (although it should because that influences how charging should be done as explained below). The graph shows the relation between actual capacity and temperature (25 Celsius/77 Fahrenheit provides the ideal balance of optimal battery life and optimal capacity and so probably is the implicit norm when rating the capacity of a battery).

Current, measured in amp (A), is the quantity of electrons in a wire. How much water flows through the pipe. Note that current depends on the width of the pipe (analogous to resistance in electrical circuits).

Voltage, measured in volt (V), determines the force that pushes electrons through the wire. The higher the voltage is, the faster the electricity flows through the wire. In terms of water, it is the difference between the level of water in each bucket. Note that as the water level in bucket A falls, the water level in bucket B rises so the difference falls, which means that voltage drops as a battery drains (the speed of the flow slows and reaches zero when levels are equalized).

Power, measured in watt (W), determines the amount of work done by a flow of electrons. Power depends on current and voltage: power = voltage x current. In terms of the water example, it is the strength of the stream of water coming out of the pipe (think pressure washer).


How to use these characteristics for ebikes?

Let’s take the following battery from my bike:

A voltage of 48V tells me that I can only use a 48V charger. The charging process restores the voltage of the battery to its nominal value (i.e. restores the water level differential by forcing water through the pipe back into bucket A). Chargers are designed to keep charging until they restore a certain voltage. If I use a 52V charger, I will damage the battery because the charger will try to cram too much energy in the battery (water will overflow in bucket A). If I use a 36V charger, I won’t recover the full voltage I could get from the battery (bucket A will only partially fill up) and the battery may actually not work because batteries are designed to shut off after a minimum voltage (called cut-off voltage) is reached.

Rated capacity of 10.5Ah also influences the type of charger to use because chargers deliver electricity at a specific amp:

• Time to fully charge to 100% from 0% = Charging capacity/Applied current. A 5A charger will charge my battery in 2.1 hours, a 2A charger will charge my battery in 5.25 hours. Good chargers slow down charging after 80% of energy is restored so it will take slightly longer to charge a battery than what the ratio states.
• Fast charging is applying an amperage that is higher than 30% of the battery capacity (some say 20%). So for my 10.5ah battery anything more than 3A is fast charging. For a 20ah battery anything above 6A is fast charging. Charging fast is nice but shortens battery life.
• What “fast charging” means also depends on the temperature of the battery because capacity is temperature dependent. At 25 Celsius, anything above 3A is fast charging for my 10.5ah battery. However, following the graph above, at 15 Celsius my battery capacity is now 80% of its rating (assuming rated capacity was measured at 25 Celsius) so actual capacity is 8.4ah. I should charge at 2A or I should bring my battery in area that allows it get to 20/25 Celsius before I charge it. Lithium-Ion battery should not be charged at freezing temperature (it is harder to put water back in bucket A through the pipe if water viscosity is high, all the more so if water is frozen). Battery should also not be charged at high temperature.

Rated energy of 504Wh is the product of voltage and battery capacity.

• When choosing a battery don’t look only at amp-hour or voltage, look at both. Compare batteries for a given V or a given Ah. The rated energy of 504Wh means that the fully-charged battery can theoretically provide 500W of power for one hour, or 250 W for 2 hours, or 125W for 4 hours, etc. The motor on my bike generates up to 500W of power at max assist and max torque so, theoretically, I could bike for one hour like mad. Practically, based on my experience with the bike, I guess I would drain the battery in 40 minutes at best. Rated energy is just a notional value most closely achieved under a controlled situation with optimal settings (a lab). Actual voltage and actual capacity vary depending on the external conditions and age of the battery. The battery will drain faster with higher cadence, higher torque, going up hills, the weight of the load carried on the bike, if there is wind resistance, temperature impacts capacity, etc.
• To improve battery life, it is best not to fully charge the battery every time. 80% or 90% is enough. A full discharge followed by a full recharge is recommended every 1 to 3 months.
• To improve battery life, it is best not to fully discharge the battery every time. Stick to a level of stored energy that cycles between 30% to 80% of energy storage ability (i.e. recharge at 30% and stop charging at 80%).
• Store a battery away for several months in a cool, fire proof area at 50% of its energy storage ability (252 Wh in my case, which would involve some guesswork unless I could find a charger that cuts off charging at 50%).

Here are several of my sources for the info above and for extra reading:
https://batteryuniversity.com/article/bu-410-charging-at-high-and-low-temperatures
https://www.electricbike.com/ebike-battery-longevity/
https://www.electricbike.com/ebike-charging-fast-or-slow/
https://www.prostarsolar.net/blog/temperature-effects-on-battery-capacity-and-service-life.html
https://batteryuniversity.com/article/bu-808-how-to-prolong-lithium-based-batteries
https://www.groovypost.com/howto/choose-right-power-adapter-charger-phone-laptop/
https://www.hioki.com/global/learning/electricity
https://batteryuniversity.com/article/bu-415-how-to-charge-and-when-to-charge
https://batteryuniversity.com/article/bu-706-summary-of-dos-and-donts
https://www.electrifybike.com/blogs/news/charging-and-caring-for-your-lithium-ion-ebike-battery

Hope this helps

 

[Stefan Mikes]

A good, comprehensive post.

The motor on my bike generates up to 500W of power at max assist and max torque so, theoretically, I could bike for one hour like mad. Practically, based on my experience with the bike, I guess I would drain the battery in 40 minutes at best.

One thing you have forgotten to mention is the motor efficiency. Whatever you described is about the electrical terms. However, the battery energy is not converted to the mechanical energy 100%. The efficiency of a good motor might be at 80%. Meaning, at least 20% of your battery charge is lost to the heat generated in the motor. There is some amount of energy lost to heat in the battery because of its internal resistance. That's why the motor and the battery both get warm when the e-bike is ridden at high assistance or on throttle only. (There are other energy losses, too).

The other thing is the rider's pedalling energy input. It could be zero (a throttle ride), or it could be 25 or 50% depending on the assistance level chosen (the rider's contribution grows as the assistance drops). Unassisted, the rider produces 100% contribution to the ride. This factor makes simple electrical/mechanical calculations a little bit fuzzy. What about the hills? Climbing converts the part of the battery energy into the potential energy, further contributing to shortening the ride time. What about the wind resistance? So many factors to take into account!

And... the motor power given by manufacturers is not always correct or clearly defined.