We begin our discussion of vehicles by first exploring the use of a battery to store energy for an all-electric vehicle. In a battery electric vehicle (BEV), the battery provides all of the power and energy needs. As mentioned earlier in the chapter, here are three key aspects to sizing the battery: energy capacity, power, and life. Each of these is influenced by the operating voltage of the cells. Figure 12.5 shows three types of voltages discussed for any electrochemical device: maximum, nominal, and minimum. The nominal voltage is a typical or average value seen during normal operation. Of course, the potential changes with current, state of charge (SOC), temperature, and age. Nonetheless, characterization by a nominal voltage is still a useful concept for almost any electrochemical device. The maximum and minimum voltages represent limits on the operating potential and define the operating range. There are many reasons for placing maximum and minimum limits on the potential of the electrochemical storage system, such as preventing damage to the cells or allowing for proper operation of the power electronics.
Figure 12.5 Range of operating voltage for electrochemical device.
Since the battery is the only source of energy for vehicle, its energy capacity, typically expressed in kWh, must be sufficient to achieve the desired range. This energy is used to overcome the rolling resistance of the wheels, the aerodynamic drag, and losses in the drive train and in power conversion, as well as to provide power to the accessories. As discussed previously, the energy needed is obtained from a representative driving schedule and the specific vehicle design. For a passenger vehicle, a good rule of thumb is that it is possible to travel 6 km·kWh−1 on the battery alone. You’ll note from the last row in Table 12.1 that, under the right conditions, a greater distance can be covered per kWh. It is important to remember, however, that the values in Table 12.1 are reference energy at the wheels and do not account for losses in the powertrain.
As the energy of the battery is stored chemically in the active material, battery capacity is proportional to the mass of active material as we saw in Chapter 7. Thus, to double the range of the vehicle, the mass of active material must be doubled. This would double the rating, expressed in either A·h or kWh, for the battery. In determining the required mass, an important consideration is the useable SOC window of the battery. Rather than operating the battery from fully charged to fully discharged, it is common to use less than the rated capacity or, in other words, to restrict the window for the variation in state of charge. The most important reason for shrinking the SOC window is to improve cycle life (discussed below). As the SOC window is reduced, a larger battery is needed to achieve the same range, but the useable lifetime of the battery is increased.
The battery must also supply all of the power needed to meet the driving requirements of the vehicle. This power depends on the performance targets for the vehicle (acceleration, speed) and, of course, is highly dependent on the size of the vehicle. The power requirement for the vehicle might be estimated as the power needed to complete a UDDS driving schedule or, alternatively, the power to maintain 90 km·h−1 speed on a 6% grade at 2/3 of maximum power. A typical value of the power required for a passenger vehicle is 50 kW, but again this value is highly dependent on the performance targets for the vehicle.
For our purposes in evaluating its power capability, we use a simple resistance model to describe the battery. Specifically, we assume that the potential of the cell is given by
(12.1)
We seek an expression for the maximum power available from the battery. Recalling that power is the product of current and voltage, we can use Equation 12.1 to express the voltage, V, as a function of current. We then multiply V, which is now expressed as a function of current, by I to get an expression for power as a function of current. That expression for the power can be differentiated with respect to current to find the maximum, followed by rearrangement to yield:
(12.2)
Since is inversely proportional to the area, it follows from Equation 12.2 that, for a fixed cell capacity, the maximum power produced from a battery is roughly proportional to the area of the separator.
Run-Time Is the Key Design Criterion for Battery Design
The energy of the battery scales with the mass of active material (kWh).
The power of the battery scales with the separator area (kW).
The energy to power ratio is the run-time of the battery.
According to Equation 12.2, the maximum power corresponds to a cell voltage equal to half of the open-circuit potential. That voltage, however, may be unacceptably low. In practice, as we discussed before, there will be a minimum limit on the potential, referred to as the cutoff voltage. If the cutoff voltage is greater than half of the open-circuit potential, then the maximum power is limited to
(12.3)
Both the energy and power requirements must be met simultaneously. The ratio of the two requirements has units of time and is called the run-time of the battery. This value is perhaps the key criterion for battery selection and design. As you might have guessed, the battery design used to provide power for a few seconds is quite different from one that needs to supply power for hours. The difference in battery design, discussed in Chapter 8, is largely reflected in changes in the thickness of the electrodes.
A third factor in sizing the battery is its useable lifetime. From our own experience with batteries in consumer devices, we know that the capacity of any battery decreases over its lifetime. Predicting life of a battery is complex, and here we adopt a primitive approach. Namely, we assume that the battery is degraded in proportion to the number of coulombs passed in the battery or what is called capacity turnover. The cell can only charge and discharge a certain number of coulombs before it no longer has an acceptable capacity. Clearly, however, a large battery is capable of passing more charge than a small battery. Consequently, the capacity turnover, which is dimensionless, is defined as the coulombs passed before the capacity is no longer acceptable divided by the nominal capacity of the battery. In a sense, the capacity turnover represents the number of times that the nominal capacity of the battery can be used before the per-cycle capacity is no longer adequate. Figure 12.6 shows a generic set of curves. Capacity turnover is highly dependent on battery chemistry, but generally decreases as the SOC window expands and as the temperature increases.
Figure 12.6 Capacity turnover for a hypothetical rechargeable battery.
Cycle life is the number of cycles possible from a battery over its lifetime, and is related to the capacity turnover as follows:
(12.4)
where the middle term provides a measure of the charge passed per cycle. These three factors are needed to size a battery for an electrical vehicle, and their use is shown in Illustration 12.2.
ILLUSTRATION 12.2
The building block for the energy storage device is an electrochemical cell with a nominal voltage of 3.2 V. Of these cells, 100 are connected in series to form the battery.
Using a value of 6 km·kWh−1, estimate the size of the battery required to achieve a range of 100 km. Express the size in kWh and A·h. The capacity of the battery in kWh is determined directly.
The capacity of the individual cells is also 52 A·h, but each has an energy capacity of 0.167 kWh.
How is the size changed if the SOC window for the battery is limited to (0.15–0.85)? Since the SOC is varied over 0.7 (i.e., only 70% of the capacity is used), the size must be increased to 52/0.7 = 74 A·h per cell and 24 kWh for the battery.
What value for battery resistance is required to achieve a maximum power of 75 kW from the battery? Assume the cutoff potential for the cell is 2.5 V. Since the cutoff potential is more than half of the nominal potential, use Equation 12.3:
If the capacity turnover is 1300 for the 70% SOC window, and assuming that on average the vehicle travels 50 km·day−1, what is the useable life for the battery?
The total charge available over the lifetime of the battery can be obtained from the capacity turnover and the nominal capacity. We also know the energy required to travel 6 km, and the · for the battery.
The round-trip efficiency of a battery is typically quite high. Why, then, isn’t the BEV the right solution for all applications? The principal reasons are range and cost. This challenge is illustrated with the Ragone plot, Section 7.5. The energy density (and specific energy) of the typical battery is too low to achieve a range of say 400 km in a practical vehicle. Of course, the battery can be made larger, but takes up more space, adds mass to the vehicle, and increases the cost for the battery. In addition, the efficiency of the vehicle operated over a fixed driving schedule decreases as the mass of the vehicle increases. More advanced batteries offer better specific energy, but their cost is high.
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