Analyzing Performance of Lithium Batteries in Electric Bikes (Part 2)

Continuation from Part 1

In order to understand the behavior of the batteries, let us run some actual tests. We are using a standard bike purchased from Dick's sporting goods such as this one.

500W Falco System (e5.3) Level 5 Assistance Test

Introduction:

A diamondback mountain bicycle was used with the 500W Falco e5.3 system. It has also been equipped with a Cycle Analyst V3 and a Cycle Analogger, which logs volts, watts, amps and amp-hours. In addition, a Falco console has been installed to control the level of assist. In order to observe the technical specifications of the motor and battery on the 500W Falco e5.3 systems, several tests are performed. The objectives of the tests are to investigate the capabilities and limitations of the system as a whole.

Figure 1 - Diamond Back 26" with Falco e5.3 System

Figure 2 - Falco Lithium Battery Li 3

Figure 3 - Falco 500W Rear Wheel Installation

Figure 4 - Hxd Console and Cycle Analyst on the Handlebars

Figure 5 - Cycle Analogger attached to the frame

Test Method:

The test was performed on level five (+5) assistance, which is controlled by using the Falco console mounted on the handlebars shown in Figure 4. There are a total of five levels of assistance available. Level one being the least assistance and level five providing the highest assistance possible from the motor. The bike with the full system installed weighed in at 38 lbs and the rider weighed in at 172lbs for a total weight of 210 lbs. The test was performed on the Washington Old Dominion Trail starting at the route 28 entrance and headed west through Leesburg and back again for a total of 30 miles roundtrip. Figure 6 shows the route. The Cycle Analyst V3 and the Cycle Analogger (shown in figure 4 and 5 respectively) were used to log the ride data for the 500W Falco e5.3 system.

Figure 6 - Route used for testing

Figure 7 - Strava iPhone App was used to record the ride data as well

Figure 7 depicts the data from Strava iPhone app which was used to track the distance, elevation, speed and power. The ride averaged a total distance of 30.2 miles, a moving time of a little over 2 hours with an average speed of 14.3 mph. 

The trail ascends in elevation towards Leesburg and descends back towards the starting point with periods of slight elevation changes in between. Figure 8 shows a total elevation change of 300 ft. recorded by Strava.

Figure 8 - Change in levation during the ride

Figure 9 - Plot of Battery Voltage and Current during the ride. Battery voltage decreases slowly as the ride progresses. 

Figure 10 - Plot of input Power draw from the Battery. Regenerative can be seen below the orange line

Figure 11 - Battery Consumed during the ride. Speed is kept between 15 and 20 mph for this test. A total of 10Ah consumed during the ride.

Figure 9 shows a plot of the battery voltage and current. Figure 10 shows a plot of the input power draw from the battery measured in watts. It shows that on level 5 assistance it nearly reached a peak of 1000 Watts at times. Furthermore, it shows an interesting trend in where there are periods when the power measured is negative indicating regeneration capturing energy normally lost in braking and coasting. The Cycle Analyst measured this regeneration value to be 0.43Ah added  back into the battery. That is about 4.3% of the total battery consumed.

Ride Analysis

Given the data above, what can you conclude regarding the battery performance. Let us look at the facts:

1. 10 Ah of battery capacity was consumed (Figure 11);
2. 30 miles distance was covered (Figure 7);
3. Average speed is 15 mph (Figure 7).

From the above two, what can we conclude?

We need one more piece of data. Let us look at Watt-Hours consumed.

Figure 12 - Watt hours consumed during the ride

From fig. 12, we can deduce that approximately 340 watt-hours were consumed during the ride. Battery is rated at 417 Wh. Approximately 81% of the battery is used.

What is important for understanding an impact on the battery?

For optimum battery performance we want to know the following:

1. Average current draw from the battery (Lower the current, longer the battery life);
2. Average temperature of the cells (Lower the temperature, longer the life).

Average current can be calculated as follows:

Average Current = Watt-Hours/Ride hours/Nominal Battery Voltage ...(1)

In this case, including the regeneration, the average current comes out to be:

340/2/36 = 4.8 Amps (approximately)  ...(2)

You could also use

Amp-Hours/Number of Hours  ... (3)

calculation to calculate average current:

10/2 = 5 Amps ...(4)

Both equations 1 & 3 result in approximately the same number.

Although, we do not have the average temperature of the cells, we can safely assume about 10 deg C temp rise of the cells during the ride. We can analyze the stress level on the battery cells with this data. Since we have 4 of the series arrangement in parallel (10S4P), the average current draw from each cell is about 1.2A approximately. Peak stress level is reached during acceleration or a hill climb. In this case assuming 1000W of peak power and 36V of nominal voltage, peak current can reach 28A or 7A per cell.

Important question to ask is as follows:

1. What do peak stress levels do to a battery pack?
2. How does average current and temperature determine battery capacity and life?

We will address these questions in Part 3. 

to be continued....