As part of a battery pack configuration, a major problem experienced with the EVs is the premature decline of battery capacity, which ulti- mately leads to battery failure. The primary cause of the battery pack failure is owing to repeated nonuniform discharging and charging of the cells. Both the battery charging and discharging are highly dependent upon temperature. Owing to the large temperature difference between the coolest battery or batteries on the outer edge of the battery pack, and the hottest battery or batteries on the inner side of the battery pack, there is a corresponding variation in the available battery discharge capacity.
DEFINITION OF VRLA BATTERY CAPACITY 117
11.5 12 12.5 13 13.5
0 1000 2000 3000
Discharge Time (secs)
Battery Voltage (V)
Figure 6–1 Dynamic driving battery discharge test profile.
The battery pack cut-off point is normally determined by a pre- defined total pack voltage. This pack voltage is with respect to a partic- ular current. As the battery pack undergoes discharge, the coolest cells with less available capacity are discharged further to a lower state of charge (SOC) than their hotter counterparts. During the discharge, the capacity of the coolest batteries may be reduced enough to force them into reversal of polarity (i.e., the batteries are reverse charged while the other batteries in the pack are discharged normally). Gradually these repeated over-discharges reduce the battery life. Equalization charges applied to the battery pack balance the batteries. However, the varia- tions in temperature bring back the same discharge and charge limita- tions as before the equalization.
The temperature gradient affects larger battery packs more signifi- cantly, resulting in capacity imbalance and charge acceptance problems that lead to early battery failures. The capacity (CT) of the battery pack is determined on a per cell basis using a linear two-hour discharge curve based on the equation below. This equation may overestimate the capac- ity at extreme temperatures.
CT=C30¥[1 +0.008 ¥(T -30)] where T is the temperature in °F.
118 ELECTRIC VEHICLE BATTERY DISCHARGING
Discharge Current (A)
Capacity (AHr)
400 350 300 250 200 150 100 50 40 30 20 10
T = 100F T = 50F T = 0F T = 110F
T = 60F T = 10F T = 120F
T = 70F T = 20F T = 130F
T = 80F T = 30F T = 140F
T = 90F T = 40F 180
160 140 120 100 80 60 40 20 0
Figure 6–2 Variation of battery capacity with respect to discharge temperature.
In addition, a variation of temperature and its effect on battery capac- ity for an 85 AHr battery results in a capacity spread to less than 40 AHr at 0°C. Assume that for a 50 A discharge the highest battery temperature in the pack is 38°C and the lowest battery temperature in the pack is 20°C, the corresponding discharge capacity drops from 52 AHr to 40 AHr.
This large difference in the available capacity can cause the lower- capacity batteries to overdischarge and possibly reverse in case most of the batteries are at elevated temperatures and the total pack voltage is used to determine the battery pack cut-off voltage.
Figure 6–3 illustrates the variation of useful battery capacity and battery voltage with changing current discharges at 80°F.
DEFINITION OF NIMH BATTERY CAPACITY
NiMH batteries are also rated with an abbreviation C, the capacity in Ah. The C rating is obtained by the NiMH battery by thorough condi- tioning of the individual NiMH cells. This is done by the user subject- ing the cell to a constant-current discharge under room temperature.
DEFINITION OF NIMH BATTERY CAPACITY 119
10 10.5 11 11.5 12 12.5 13
0 20 40 60 80 100
Depth Of Discharge (%)
Load Voltage (V)
0 10 20 30 40 50 60 70 80 90 100
C/3 Load Voltage C/2 Load Voltage C/1 Load Voltage C/3 Capacity C/2 Capacity C/1 Capacity
Figure 6–3 Variation of load voltage at varying battery capacities.
Since the cell capacity varies inversely with the discharge rate, capacity ratings depend on the discharge rate used during the discharge process.
For NiMH batteries, the rated capacity is normally determined at a discharge rate that fully depletes the cell voltage in five hours. For the purpose of electrical analysis of the battery cell, the Thevenin equiva- lent circuit is used. This circuit models the circuit as a series combina- tion of the voltage source (E0), a series resistance (Rh = the effective instantaneous resistance), and the parallel combination of a capacitor (Cp=the effective parallel capacitance) and the resistor (Rd=the effec- tive delayed resistance).
Under steady state conditions, the cell voltage at a known current draw is E0-iRe, where Re is the effective internal resistance of the NiMH cell. Re is the sum of the Rhand Rd. Under transient discharge condi- tions, as shown in Figure 6–4 the initial voltage drops immediately to E0-iReh and then transfers exponentially, with time constant Cp ¥Rd
to a steady state voltage. This discharge condition reverses once the load being applied is removed from the battery as seen in Figure 6–4. Note that the slow recovery of cell voltage after removal of the load after 11 minutes is attributed to the delayed resistance Rd. This behavior is iden- tical to the effect noticed during discharge between 4 to 11 minutes.
120 ELECTRIC VEHICLE BATTERY DISCHARGING
0 1 2 3 4 5 6 7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Time (min)
Cell Voltage (V)
Cell Voltage
Figure 6–4 Variation of battery discharge voltage.
For most applications, unlike EV applications, the steady state voltage is adequate for describing the battery performance. This is owing to the fact that the time constant for most cells is small—typically less than 3% of the discharge time. Although the instantaneous resistance of the NiMH cell is comparable with NiCd cell, the delayed resistance is 10%
higher. For this reason, the steady-state voltage for the NiMH cell is lower than that of NiCd.