BU-206a: Finding the Optimal Runtime and Power Ratio of Li-ion

Optimizing the selection of a Li-ion system that includes specific energy, specific power and runtime.

Batteries can be made to perform as an Energy Cell that stores a large amount of energy, or a Power Cell that is capable to deliver high load currents. An analogy is a water flask that is designed to hold a large volume of liquid while offering a wide opening to permit quick pouring.

The physical dimensions of a battery are specified by volume in liter (l) and kilogram (kg). Adding dimension and weight provides specific energy in Wh/kg, power density in Wh/l and specific power in W/kg. Most batteries are rated in Wh/kg, revealing how much energy a given weight can generate. Wh/l denotes watt/hours per liter. See Battery Definition and what they mean.)

The relationship between energy and power of a battery can best be represented in a Ragone plot. This plot places energy in Wh on the horizontal x-axis and power in W on the vertical y-axis. The diagonal lines across the field disclose the time the battery cells can deliver energy at various loading conditions. The derived power curve provides a clear demarcation line of what level of power a battery can deliver. The Ragone plot is logarithmic to display performance profiles of very high and low values.

Figure 1 illustrates the Ragone plot reflecting the discharge energy and power of four classic lithium-ion systems packaged in 18650 cells. The battery chemistries featured are the most common power-based lithium-ion systems, which include lithium-iron phosphate (LFP), lithium-manganese oxide (LMO), and nickel manganese cobalt (NMC).

18650 Ragone Plot
Figure 1: Ragone plot reflects Li-ion 18650 cells. 
Four Li-ion systems are compared for discharge power and energy as a function of time.
Courtesy of Exponent

Legend: The A123 APR18650M1 is a lithium iron phosphate (LiFePO4) with 1,100mAh and a continuous discharge current of 30A. The Sony US18650VT and Sanyo UR18650W are manganese–based Li-ion cells of 1500mAh each with a continuous discharge current of 20A. The Sanyo UR18650F is a 2,600mAh cell for a moderate 5A.discharge. This cell provides the highest discharge energy but has the lowest discharge power.

The Sanyo UR18650F [4] has the highest specific energy and can power a laptop or e-bike for many hours at a moderate load. The Sanyo UR18650W [3], in comparison, has a lower specific energy but can supply a current of 20A. The A123 [1] has the lowest specific energy but offers the highest power capability by delivering 30A of continuous current.

The Ragone plot helps choosing the best Li-ion system to satisfy optimal discharge power and energy as a function of discharge time. If an application calls for very high discharge current, the 3.3 minute diagonal line on the chart points to the A123 (Battery 1) as a good pick; it can deliver up to 40 Watts of power for 3.3 minutes. The Sanyo F (Battery 4) is slightly lower and delivers about 36 Watts. Focusing on discharge time and following the 33 minute discharge line further down, Battery 1 (A123) only delivers 5.8 Watts for 33 minutes before the energy is depleted whereas the higher capacity Battery 4 (Sanyo F) can provide roughly 17 Watts for the same time; its limitation is lower power.

For best results, battery manufacturers take the Ragone snapshot on new cells, a condition that is only valid for a short time. When calculating power and energy thresholds, design engineers must include battery fade that will develop as part of cycling and aging. A battery operated systems should still provide full function with a battery that has faded to 70 or 80 percent. A further consideration is temperature as a battery loses power when cold. The Ragone plot does not include these discrepancies.  

It should be noted that loading a battery to its full power capability increases stress and shortens life. When a high current draw is needed continuously, the battery pack should be made larger. Tesla does this with their Model S cars by doubling and tripling the battery. An analogy is a heavy truck fitted with a large diesel engine that provides long and durable service as opposed to installing a souped-up engine of sports car with similar horsepower.

The Ragone plot also calculates power requirements of other energy sources and storage devices, such as capacitors, flywheels, flow batteries and fuel cells. As fuel cells and internal combustion engines draw fuel from a tank, a conflict develops because energy-delivery can be made continuous. The Ragone plot may also be deployed to establish the optimal energy/power ratio and loading condition of a renewable power source, such as solar cells and wind turbines.

Last Updated 2016-04-01

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On October 27, 2015 at 11:31pm
Dhananjay wrote:

some one let me know which voltage represents the 100% in the mobile phone batteries.