Power and energy are often key design aims of an electrochemical system for energy storage and conversion. The instantaneous power produced by a cell is simply the current multiplied by the potential of the cell. Even if the current is constant, the potential is not generally flat and changes during discharge. Therefore, integration is required to determine the average power.

(7.19)

The power is measured in W or kW. Similarly, the electrical energy available during discharge can be obtained by integration. The most common ways of reporting the power and energy available are to normalize these quantities to the mass or volume of the cell. The four commonly used terms are specific power [kW·kg⁻¹], specific energy [kW·h·kg⁻¹], power density [kW·L⁻¹], and energy density [kW·h·L⁻¹].

The trade-off between power and energy can be represented with a Ragone plot. Here the specific energy is plotted against the specific power of a battery. Figure 7.10 shows the range of values for batteries, as well as for fuel cells, double-layer capacitors, and the internal combustion engine. The large rectangle for batteries reflects the important impact of battery chemistry, and the large number of possible types of batteries. Also, since cell design can be tailored for either capacity or power, each battery chemistry would itself be represented by a range of values on the plot, as shown in Illustration 7.4. A similar plot can be constructed using energy and power density.

Also of note on the log–log Ragone plot are the 45° lines, where each line corresponds to a constant ratio of specific energy to specific power. As shown, the lines are identified as the battery run time and represent the time that would be required to fully discharge the battery. Battery run time is the inverse of the C-rate, and is one of the most important characteristics used in selecting or designing a battery.

As discussed previously, battery chemistry is perhaps the foremost design factor. But for a particular chemistry, there can be a large difference in performance due to differences in cell and battery design to address the needs of specific applications. For example, the lead–acid battery used to start your car engine needs to produce high currents for a short period of time, but does not need to have a high energy density. Therefore, these batteries are designed to optimize power. In fact, because of the importance of power, the required cold-cranking amps (CCA) is typically specified rather than the capacity in A·h. CCA is the maximum current that the battery can sustain for 30 seconds at −18 °C. A typical automotive starting battery may have a capacity of 35 A·h and a CCA of 540 A. The corresponding discharge rate is 540/35, or 15 C, which corresponds to a 4-minute discharge time. In contrast, lead–acid batteries can also be used as backup power for a telecommunication system where they may need to provide power for hours. Lead–acid batteries are also commonly used as the energy storage component for off-grid solar power systems. In both of these stationary applications, the capacity is more important than the rate capability. The cell design for these last two applications, specifically the design of the separator and electrodes, is very different from that used for the starting battery discussed previously. The relationship between battery design and performance is discussed in more detail in Chapter 8.

ILLUSTRATION 7.4

The relationship between specific power and energy is shown on a Ragone plot. In Figure 7.10, the different technologies are represented loosely by rectangles. That single-frame labeled “battery” encompasses everything from an implantable primary lithium battery to the lead–acid battery for starting your car. Here we explore the behavior of a specific battery as depicted on a Ragone plot. To do this, we need a voltage model; that is, we need an understanding of how voltage changes with current and DOD. For illustration purposes, we’ll use the battery model presented in Illustration 7.3.

Assuming the discharge is performed at constant current, the Shepherd equation provides cell voltage as a function of time. The energy and power can be obtained from

where t_d is the discharge time, determined by when the cell reaches a cutoff potential. These calculations are repeated for a series of discharge currents and normalized by the mass of the cell components. At very low current, the cells discharge nearly completely and polarization losses are small; thus, the specific energy reaches a maximum value at low values of the specific power, as shown in the diagram. As the current is increased, the power increases. However, polarization losses also increase and the cutoff voltage is reached before the cell is completely discharged. Thus, the specific energy is lower at higher discharge currents. There is also a limit to the maximum power since, at some value of current, the ohmic losses are so great that the cell reaches the cutoff potential instantaneously without any appreciable capacity.

Clearly, high power requires a low internal resistance.