Given the critical role that the battery plays in many applications, the specifications or requirements that a battery must meet can be numerous and detailed. For example, an engineering specification for an automotive battery may be 30 pages or more in length. In contrast, we will only consider design of the main features of a battery in this introductory treatment. For simplification, we assume that the cell chemistry has already been selected. Our task is to take a cell of known chemistry and determine the size, number, and arrangement of cells required to assemble a battery that meets a desired set of basic specifications. Some of the more important requirements are tabulated in Table 8.1. Note that three items, discharge time, nominal voltage, and energy, are highlighted in bold. These represent the three most critical design specifications for a battery once the desired chemistry has been determined. Other important characteristics of the battery can, for the most part, be derived from these. For example, battery size (mass and volume) is largely determined by the energy and the battery chemistry. The average power, which is important for many applications, can be determined from the energy and the discharge time. Peak power, on the other hand, requires an additional specification.

Table 8.1 Important Battery Requirements

Requirement	Units	Comments
Discharge time	hours	Nominal operation time for application, inversely proportional to rate capability
Nominal Voltage maximum, and minimum voltages	V	Output voltage of the battery string, not an individual cell
Energy	W·h	Capacity of the battery. Linked to average power and discharge time
Weight or mass	kg	Closely related to energy stored in battery
Volume	m3	Closely related to energy stored in battery
Peak power	W	Power for a short pulse of fixed time, 30 seconds, for instance
Cycle life	–	Number of charge/discharge cycles before capacity or power capability is reduced by 20%, for example
Temperature of operation, minimum, maximum	°C	Expected nominal, minimum, and maximum environmental temperatures
Calendar life	years	Beyond the scope of this text

To illustrate, let’s consider a lithium-ion battery for an electric vehicle application that requires a discharge time of 2 hours, 24 kW·h of energy, and a targeted battery voltage of 360 V. The nominal single-cell voltage depends on the cell chemistry and has a value of 3.75 V for the lithium-ion cell considered here. The number of cells in series is simply,

(8.1)

Thus, a minimum of 96 cells connected in series is needed. Later we will explore the advantage of using a high battery voltage. Cells connected in series are referred to as a string. Multiple strings of cells can be placed in parallel to increase the capacity of the battery or to reduce the single-cell capacity needed to meet the performance requirements. In this example, we will use two parallel strings, so that n = 2. The total number of cells is

(8.2)

which is the product of the number of cells in series (m) and the number of cell strings connected in parallel (n). Next, we can determine the capacity of each individual cell based on the energy storage requirement for the battery. The energy of an individual cell is just its capacity times its voltage (E_cell = Q_cellV_cell). The total energy of the battery (E_batt) is the sum of the energy from each individual cell (E_batt = N_cE_cell). It follows that

(8.3)

Thus, a configuration of a total of 192 cells, each with a capacity of 33 A·h, is required. The cells in the battery are arranged in two parallel strings to achieve a nominal voltage of 360 V. Note that the capacity per cell would have been twice as large if only one series string had been used.

ILLUSTRATION 8.1

The purpose of this illustration is to compare the energy, capacity, and voltage of a string of three cells in series with that of three cells in parallel.

1. For three cells in series, determine V_batt, E_batt, and Q_batt.
2. Repeat Part (a) for three cells in parallel.
3. Based on the results from Parts (a) and (b), compare the voltage and capacity for the two configurations.

SOLUTION:

1. The voltage in series is:   The total energy is For the capacity, we note that . Therefore, .
2. The voltage of the battery with cells in parallel is just the cell voltage. Therefore, .The total energy is For the capacity,  . Therefore, since  , .
3. The energy is the same for the two cases. For the series case we have higher voltage and lower capacity, and for the parallel configuration we have lower voltage and higher capacity.