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How to Calculate Battery Runtime(2)
Apr 17, 2017

# How to Calculate Battery Runtime(2)

Know about hidden battery losses when estimating the energy reserve.

If the battery was a perfect power source and behaved linearly, charge and discharge times could be calculated according to in-and-out flowing currents, also known as
coulombic efficiency. What is put in should be available as output in the same amount; a 1-hour charge at 5A should deliver a 1-hour discharge at 5A, or a 5-hour discharge at 1A. This is not possible because of intrinsic losses and the coulombic efficiency is always less than 100 percent. The losses escalate with increasing load, as high discharge currents make the battery less efficient.

Ragone Plot

Lithium- and nickel-based batteries are commonly evaluated by the Ragone plot. Named after David V. Ragone, the Ragone plot looks at the battery’s capacity in watt-hours (Wh) and discharge power in watts (W). The big advantage of the Ragone plot over the Peukert Law is the ability to read the runtime in minutes and hours presented on the diagonal lines on the Ragone graph.

Figure 2 illustrates the Ragone plot of four lithium-ion systems using 18650 cells. The horizontal axis displays energy in watt-hours (Wh) and the vertical axis is power in watts (W). The diagonal lines across the field reveal the length of time the battery cells can deliver energy at given loading conditions. The scale is logarithmic to allow a wide selection of battery sizes. The battery chemistries featured in the chart include lithium-iron phosphate (LFP), lithium-manganese oxide (LMO), and nickel manganese cobalt (NMC).

 Figure 2: Ragone plot reflects Li-ion 18650 cells. Four Li-ion systems are compared for discharge power and energy as a function   of time. Not all curves are fully drawn out.

The Sanyo UR18650F [4] Energy Cell has the highest specific energy and can run a laptop or e-bike for many hours at a moderate load. The Sanyo UR18650W [3] Power Cell, in comparison, has a lower specific energy but can supply a current of 20A. The A123 [1] in LFP has the lowest specific energy but offers the highest power capability by delivering 30A of continuous current. Specific energy defines the battery capacity in weight (Wh/kg); energy density is given in volume (Wh/l).

The Ragone plot helps in the selection of the optimal Li-ion system to satisfy discharge power while retaining the required runtime. If an application calls for a very high discharge current, the 3.3 minute diagonal line on the chart points to the A123 (Battery 1); 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. By 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. The higher capacity Battery 4 (Sanyo F) can provide roughly 17 watts for the same time; its limitation is lower power.

A design engineer should note that the Ragone snapshot taken by the battery manufacturers represents a new cell, a condition that is temporary. When calculating power and energy needs, engineers must take into account battery fade caused by cycling and aging. Battery-operated systems must still function with a battery that will eventually drop to 70 or 80 percent capacity. A further consideration is low temperature as a battery momentarily loses power when cold. The Ragone plot does not take these decreased performance conditions into account.

The design engineer should further develop a battery pack that is durable and does not get stressed during regular use. Stretching load and capacity boundaries to the limit shortens battery life. If repetitive high discharge currents are needed, the pack should be made larger and with the correct choice of cells. An analogy is a truck that is equipped with a large diesel engine instead of a souped-up engine intended for a sports car.

The Ragone plot can also calculate the power requirements of capacitors, flywheels, flow batteries and fuel cells. A conflict develops with the internal combustion engine or the fuel cell that draws fuel from a tank, as on-board re-fueling cheats the system. Similar plots are also used to find the optimal loading ratio of renewable power sources, such as solar cells and wind turbines.

The instruments for testing the battery

We have a series of instruments which can be used to tets the battery, such as SAT-AG Series Stationary Battery Comprehensive Tester, AT-ALU UPS Battery Discharger Tester, AT-AM Stationary Battery Data Logging Device,