22 Battery Parameters

2.2.1 Cell and battery voltages

All electric cells have nominal voltages which gives the approximate voltage when the cell is delivering electrical power. The cells can be connected in series to give the overall voltage required. Traction batteries for electric vehicles are usually specified as 6 V or 12 V, and these units are in turn connected in series to produce the voltage required. This voltage will, in practice, change. When a current is given out, the voltage will fall; when the battery is being charged, the voltage will rise.

This is best expressed in terms of 'internal resistance', and the equivalent circuit of a battery is shown in Figure 2.1. The battery is represented as having a fixed voltage E, but the voltage at the terminals is a different voltage V, because of the voltage across the internal resistance R. Assuming that a current I is flowing out of the battery, as in Figure 2.1, then by basic circuit theory we can say that:

Note that if the current I is zero, the terminal voltage is equal to E, and so E is often referred to as the open circuit voltage. If the battery is being charged, then clearly the voltage will increase by IR. In electric vehicle batteries the internal resistance should clearly be as low as possible.1

1 A good quality 12 V, 25 Amphour lead acid battery will typically have an internal resistance of about 0.005 ohms.

External load

Figure 2.1 Simple equivalent circuit model of a battery. This battery is composed of six cells

External load

Figure 2.1 Simple equivalent circuit model of a battery. This battery is composed of six cells

Generally this equation (2.1) gives a fairly good prediction of the 'in use' battery voltage. However, the open circuit voltage E is not in fact constant. The voltage is also affected by the 'state of charge', and other factors such as temperature. This is dealt with in more detail in Section 2.11, where we address the problem of modelling the performance of batteries.

2.2.2 Charge (or Amphour) capacity

The electric charge that a battery can supply is clearly a most crucial parameter. The SI unit for this is the Coulomb, the charge when one Amp flows for one second. However, this unit is inconveniently small. Instead the Amphour is used: one Amp flowing for one hour. The capacity of a battery might be, say, 10 Amphours. This means it can provide 1 Amp for 10 hours, or 2 Amps for 5 hours, or in theory 10 Amps for 1hour. However, in practice, it does not work out like this for most batteries.

It is usually the case that while a battery may be able to provide 1 Amp for 10 hours, if 10 Amps are drawn from it, it will last less than one hour. It is most important to understand this. The capacity of the large batteries used in electric vehicles (traction batteries) is usually quoted for a 5 hour discharge. Figure 2.2 shows how the capacity is affected if the charged is removed more quickly, or more slowly. The diagram is for a nominally 100 Amphour battery. Notice that if the charge is removed in one hour, the capacity falls very considerably to about 70 Amphours. On the other hand, if the current is drawn off more slowly, in say 20 hours, the capacity rises to about 110 Amphours.

This change in capacity occurs because of unwanted side reactions inside the cell. The effect is most noticeable in the lead acid battery, but occurs in all types. It is very important to be able to accurately predict the effects of this phenomenon, and that is addressed in Section 2.11, when we consider battery modelling.

The charge capacity leads to an important notation point that should be explained at this point. The capacity of a battery in Amphours is represented by the letter C. However, somewhat confusingly, until you get used to it, this is also used to represent a current.

Suppose a battery has a capacity of 42 Amphours, then it is said that C = 42 Amphours. Battery users talk about 'a discharge current of 2C', or 'charging the battery at 0.4C'. In these cases this would mean a discharge current of 84 Amps, or a charging current of 16.8 Amps.

Graph showing change in battery capacity with discharge time

Graph showing change in battery capacity with discharge time

320 2 4 6 8 10 12 14 16 18 20 Discharge time / hours

Figure 2.2 Graph showing the change in amphour charge capacity of a nominally 42Amphour battery. This graph is based on measurements from a lead acid traction battery produced by Hawker Energy Products Inc

320 2 4 6 8 10 12 14 16 18 20 Discharge time / hours

Figure 2.2 Graph showing the change in amphour charge capacity of a nominally 42Amphour battery. This graph is based on measurements from a lead acid traction battery produced by Hawker Energy Products Inc

A further refinement is to give a subscript on the C symbol. As we noted above, the Amphour capacity of a battery varies with the time taken for the discharge. In our example, the 42 Amphour battery is rated thus for a 10 hour discharge. In this more complete notation, a discharge current of 84 Amps should be written as 2C10.

Example: Express the current 21 Amps from our example 42 Amphour battery, in C notation.

As a ratio of 42 Amps, 21 is 1/2 or 0.5. Thus the current 21 Amps = 0.5C10.

This way of expressing a battery current is very useful, as it relates the current to the size of the battery. It is almost universally used in battery literature and specifications, though the subscript relating to the rated discharge time is often omitted.

2.2.3 Energy stored

The purpose of the battery is to store energy. The energy stored in a battery depends on its voltage, and the charge stored. The SI unit is the Joule, but this is an inconveniently small unit, and so we use the Watthour instead. This is the energy equivalent of working at a power of 1 Watt for 1 hour. The Watthour is equivalent to 3600 Joules. The Watthour is compatible with our use of the Amphour for charge, as it yields the simple formula:

Energy in Watthours = Voltage x Amphours or Energy = V x C (2.2)

However, this equation must be used with great caution. We have noted that both the battery voltage V, and even more so the Amphour capacity C, vary considerably depending on how the battery is used. Both are reduced if the current is increased and the battery is drained quickly. The stored energy is thus a rather variable quantity, and reduces if the energy is released quickly. It is usually quoted in line with the Amphour rating, i.e. if the charge capacity is given for a five hour discharge, then the energy should logically be given for this discharge rate.

2.2.4 Specific energy

Specific energy is the amount of electrical energy stored for every kilogram of battery mass. It has units of Wh.kg-1. Once the energy capacity of the battery needed in a vehicle is known (Wh) it can be divided by the specific energy (Wh.kg-1) to give a first approximation of the battery mass. Specific energies quoted can be no more than a guide, because as we have seen, the energy stored in a battery varies considerably with factors such as temperature and discharge rate.

We will see in Section 2.2.6 below, and in the Ragone plot of Figure 2.3 how much the specific energy of a battery can change.

2.2.5 Energy density

Energy density is the amount of electrical energy stored per cubic metre of battery volume. It normally has units of Wh.m-3. It is also an important parameter as the energy capacity

Ragone plot for Lead Acid and Nickel Cadmium traction batteries

Ragone plot for Lead Acid and Nickel Cadmium traction batteries

Ragone Plot Vehicle

20 30

Specific Energy/Wh.kg-1

Figure 2.3 A Ragone plot - specific power versus specific energy graph - for typical lead acid and nickel cadmium traction batteries

20 30

Specific Energy/Wh.kg-1

Figure 2.3 A Ragone plot - specific power versus specific energy graph - for typical lead acid and nickel cadmium traction batteries of the battery (Wh) can be divided by the battery's energy density (Wh.m-3) to show the volume of battery required. Alternatively if a known volume is available for batteries, the volume (m3) can be multiplied by the batteries energy density (Wh.m-3) to give a first approximation of how much electrical energy can be made available. The battery volume may well have a considerable impact on vehicle design. As with specific energy, the energy density is a nominal figure.

2.2.6 Specific power

Specific power is the amount of power obtained per kilogram of battery. It is a highly variable and rather anomalous quantity, since the power given out by the battery depends far more upon the load connected to it than the battery itself. Although batteries do have a maximum power, it is not sensible to operate them at anywhere near this maximum power for more than a few seconds, as they will not last long and would operate very inefficiently.

The normal units are W.kg-1. Some batteries have a very good specific energy, but have low specific power, which means they store a lot of energy, but can only give it out slowly. In electric vehicle terms, they can drive the vehicle very slowly over a long distance. High specific power normally results in lower specific energy for any particular type of battery. This is because, as we saw in Section 2.2.2, taking the energy out of a battery quickly, i.e. at high power, reduces the energy available.

This difference in change of specific power with specific energy for different battery types is very important, and it is helpful to be able to compare them. This is often done using a graph of specific power against specific energy, which is known as a Ragone plot. Logarithmic scales are used, as the power drawn from a battery can vary greatly in different applications. A Ragone plot for a good quality lead acid traction battery, and a similar NiCad battery, is shown in Figure 2.3.

It can be seen that, for both batteries, as the specific power increases the specific energy is reduced. In the power range 1 to 100 W.kg-1 the NiCad battery shows slightly less change. However, above about 100 W.kg-1 the NiCad battery falls much faster than the lead acid.

Ragone plots like Figure 2.3 are used to compare energy sources of all types. In this case we should conclude that, ignoring other factors such as cost, the NiCad battery performs better if power densities of less than 100W.kg-1 are required. However, at higher values, up to 250 W.kg-1 or more, then the lead acid begins to become more attractive. The Ragone plot also emphasises the point that a simple single number answer cannot be given to the question 'What is the specific power of this battery?'.

2.2.7 Amphour (or charge) efficiency

In an ideal world a battery would return the entire charge put into it, in which case the amp hour efficiency is 100%. However, no battery does; its charging efficiency is less than 100%. The precise value will vary with different types of battery, temperature and rate of charge. It will also vary with the state of charge. For example, when going from about 20% to 80% charged the efficiency will usually be very close to 100%, but as the last 20% of the charge is put in the efficiency falls off greatly. The reasons for this will be made clear when we look at each of the battery types later in the chapter.

2.2.8 Energy efficiency

This is another very important parameter and it is defined as the ratio of electrical energy supplied by a battery to the amount of electrical energy required to return it to the state before discharge. A strong argument for using electric vehicles is based on its efficient use of energy, with resulting reduction of overall emissions; hence high energy efficiency is desirable. It should be clear from what has been said in the preceding sections that the energy efficiency will vary greatly with how a battery is used. If the battery is charged and discharged rapidly, for example, energy efficiency decreases considerably. However it does act as a guide for comparing batteries, in much the same way as fuel consumption does for cars.

2.2.9 Self-discharge rates

Most batteries discharge when left unused, and this is known as self-discharge. This is important as it means some batteries cannot be left for long periods without recharging. The reasons for this self-discharge will be explained in the sections that follow. The rate varies with battery type, and with other factors such as temperature; higher temperatures greatly increase self-discharge.

2.2.10 Battery geometry

Cells come in many shapes: round, rectangular, prismatic or hexagonal. They are normally packaged into rectangular blocks. Some batteries can be supplied with a fixed geometry only. Some can be supplied in a wide variation of heights, widths and lengths. This can give the designer considerable scope, especially when starting with a blank sheet of paper, or more likely today a blank CAD screen. He/she could, for example, spread the batteries over the whole floor area, ensuring a low centre of gravity and very good handling characteristics.

2.2.11 Battery temperature, heating and cooling needs

Although most batteries run at ambient temperature, some run at higher temperatures and need heating to start with and then cooling when in use. In others, battery performance drops off at low temperatures, which is undesirable, but this problem could be overcome by heating the battery. When choosing a battery the designer needs to be aware of battery temperature, heating and cooling needs, and has to take these into consideration during the vehicle design process.

2.2.12 Battery life and number of deep cycles

Most rechargeable batteries will only undergo a few hundred deep cycles to 20% of the battery charge. However, the exact number depends on the battery type, and also on the details of the battery design, and on how the battery is used. This is a very important figure in a battery specification, as it reflects in the lifetime of the battery, which in turn reflects in electric vehicle running costs. More specific information about this, and all the other battery parameters mentioned, are given in the sections that follow on particular battery types.

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