FIGURE 3-3 Typical voltage discharge profiles. Nonideal battery properties: (a) voltage change; (b) loss of capacity; and (c) recovery.

SOURCE: Adapted from Linden, 1995.

capacity. Figure 3-3 shows that for a real battery, the rate of discharge affects the battery’s apparent capacity. Figure 3-3a shows that voltage drops more rapidly for the higher discharge rate represented by curve 2 than for the lower discharge rate represented by curve 1. Figure 3-3b compares the percent of initial capacity and how it is affected by discharge rate. If C represents the capacity available at a standard discharge rate, then discharge rates from 0.1C to 10C are portrayed on the abscissa. As can be noted, initial capacity drops from 100 percent at 0.50C to approximately 70 percent at 10C. Figure 3-3c shows that if the discharge is intermittent, some recovery in cell output voltage occurs between periods of discharge.

Figure 3-4 presents another analysis of a battery system used on various duty cycles. For continuous discharge, the battery specific energy drops from approximately 138 Wh/kg at a specific power of 75 W/kg (point B) to about 90 Wh/kg at a specific power of 300 W/kg (point A). When intermittent operation is added, it is the peak power rather than the average power that determines capacity. In Figure 3-4, point B and point C are loads with the same average power, 75 W/kg, but the battery delivers a much higher capacity for point B than for point C. The reason for this is that the load of point B is a constant 75 W/kg, but the load of point C is an intermittent discharge with a peak power of 300 W/kg and a 25 percent duty cycle. The capacity delivered for the intermittent discharge of point C is much closer to the capacity delivered for a continuous discharge at the peak power value of 300 W/kg (point A) than it is to the capacity for a continuous discharge at the average power value (point B). Using the average power, the capacity would be estimated at 140 Wh/kg, nearly 30 percent greater than the actual capacity.

There is a slight dependence on the duty cycle, as shown by the family of curves representing intermittent loads with peaks of 100, 200, and 300 W and duty cycles of 25, 50, and 75 percent. However, despite this dependence, for intermit-



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