The laboratory tests to determine the capacity and rate capability of a cell that were described in Chapter 7 can also be applied to a battery and are not repeated here. Rather, the focus in this section is on the use of resistance to provide information on the power capability and health of the battery. Health in this context is a measure of the condition of the battery relative to its initial “full performance” state.
There are a number of resistances defined and used by specialists, and some care is needed in identifying the specific quantity of interest. We begin with the ohmic resistance, which was used extensively in Chapters 6 and 7, and throughout the book. Ohmic resistance is determined from the high-frequency intercept of an electrochemical impedance spectrum or, equivalently, from current interruption. Its measurement and meaning are unambiguous. Although this ohmic resistance is used extensively in research, it is not the cell or battery resistance commonly used in practice. The resistance used commercially is a more loosely defined term that depends on the specific application. While there are many variations, the general idea is the same. The concept and its relationship to the ohmic resistance are illustrated in Figure 8.12. After a period of rest, two short current pulses are applied, one for charging and one for discharging. During discharge, the potential of the cell drops instantaneously and then decreases with time. The immediate drop represents the ohmic resistance of the cell as described in Chapter 6. The further decrease that occurs in the time interval from 
(just after the instantaneous drop) to t1 is due to activation and concentration polarizations in the cell. The discharge resistance for the cell or battery includes all of these polarizations (ohmic, activation, and concentration) and is defined as the change in potential divided by the change in current:
where the superscript d refers to discharge. Whereas the ohmic resistance depends on temperature and slightly on the SOC, the battery resistance defined by Equation 8.21 can have a strong dependence on SOC. It is also evident from Figure 8.12 that the resistance may vary with changes in the width or magnitude of the discharge pulse. Analogous to Equation 8.21, a resistance for charging can be defined, 
. These two values are different because the activation and concentration polarizations will change depending on whether a cell is being charged or discharged. To account for differences in battery size, the resistance is often normalized by the separator area of the cell. This quantity is the area-specific resistance (ASR) with units of Ω·m2. Again, as measured, this quantity includes ohmic, activation, and concentration polarizations.
For preliminary analysis of batteries, we assume that the measured cell resistance is constant so that voltage losses vary linearly with the current. In fact, this practice is used extensively in this chapter. With use of the newly defined cell resistance, we can estimate the cell voltage as
Clearly, the magnitude of the resistance will directly affect the power capability of the battery. To quantify that impact, remember that the power is equal to IVcell, the current multiplied by the potential of the battery. Therefore, we can use Equation 8.22 and the definition of power to approximate the current at maximum power.
and
Equation 8.23 shows the relationship between the power and the cell resistance. It must be remembered that this relationship is approximate due to the simplifications we have made. In order for the maximum power and current to be meaningful, the pulse width (time) used in measuring the resistance must be similar to the time over which the power is required by the battery. So, a 10 or 30 seconds pulse may be appropriate for a charge-sustaining power assist hybrid-electric vehicle, but the time of the pulse would be too long to correspond to the current spike associated with starting an electrical motor. The same pulse would be too short for an application where the battery is supplying power for 5 or 10 minutes or more while a generator is started.
In this section, we defined a cell or battery resistance that includes ohmic, activation, and concentration losses. We estimated the effect of the cell resistance on the cell voltage and, therefore, the capacity of the cell, since the lower voltage limit will be reached more quickly by a battery with a higher resistance. We have also examined the impact of the resistance on the power or rate capability of the cell. Given its impact, resistance is a convenient way of characterizing battery performance, and the change in resistance with time as the battery is cycled provides a measure of the state of health (SOH) of the battery, defined generically as
(8.24)
SOH relates to the ability of the cell to meet its specified performance ratings. From the manufacturer, we assume that the battery meets its design goals, and therefore the “as received” SOH is 100%. There are numerous physical processes that cause the performance of the cell to degrade over time. Many of these processes also cause an increase in the cell resistance. Therefore, the cell resistance is one of the best ways to assess the SOH of the cell. While it is not the only method, it represents a common and effective way to make the desired assessment. Finally, we note that cell resistance changes with temperature, an effect that must be accounted for in order to make an accurate assessment.
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