The open-circuit voltage in Li–ion batteries shows fairly linear dependence on the state of charge. However, it is not recommended to assume that open-circuit voltage is an accurate indication of the state of charge. The relationship between the two battery parameters is more complex and open-circuit voltage only gives a rough indication of the battery state of charge.
State of Charge, %
0 20 40 60 80 100
45
40
35
30
25
20
Temperature,°C
1 C 2 C
0.7 C
0.5C
Fig. 6.11 Cell temperature as a function of state-of-charge at different C rates. Particular curves are adapted from a variety of sources and are not representative of any particular battery or experiment
104 6 Lithium Batteries
The shape of the voltage curve for 1 C current shows typical behavior, with initial drop and then gradual decrease until the end of discharge is nearly reached and the voltage sharply drops (Fig.6.12).
The shape of voltage curves for 2 C and 3 C currents is more unexpected. There is a depression in voltage in the first third of discharge, then voltage increases, stabilizes, and decreases again near the end of discharge. It is important to under- stand that this particular performance behavior or shape of voltage curves is not universal for all lithium–ion batteries. This is just one example for a battery used in automotive applications. Other batteries of different size and construction may have different heat generation and dissipation properties and their voltage profiles would be different.
The limitation or“cutoff”voltage at the end of discharge is also a very sensitive issue for lithium–ion batteries. In order to prevent overdischarge, most cells are disconnected, that means that discharge is completed when voltage reaches 2.7–3.0 V (typically 3.0 V). The safety protection circuit is ordinarily part of a battery and it disconnects the current if the battery is inadvertently discharged below 2.50 V per cell. If this voltage is reached, the cell is considered unserviceable, it is put to sleep and regular recharge is not possible. Instead, a cell might be recoverable, but only through a special“wake-up”protocol.
A complex situation may develop during prolonged storage of lithium–ion batteries. Most manufacturers ship batteries with about 40% state of charge to compensate for some self-discharge during storage. The safety circuitry is not activated during storage and cannot protect against deep discharge below 2.5 V until thefirst, even brief, charge cycle. Before this activation step, in the case of very
Depth of Discharge, %
0 20 40 60 80 100
4.2 4.0 3.8 3.6 3.4 3.2 3.0
Voltage, V
Open Circuit Voltage
1 C 2 C
3 C
Fig. 6.12 Conceptual trends for voltage versus depth of discharge for Li–ion battery and different C rates. The trends in this graph reflect only one type of Li–ion battery
6.7 Discharge 105
long storage, it is theoretically possible that self-discharge drains the battery below 2.5 V and causes damage. In the case of any doubt or certainly if voltage drops to close to 1.5 V—a recharge should be avoided. At that point, an electrical short might have formed as a result of copper shunts and charging the battery further would cause immediately excessive heat and hazardous conditions.
There are process inefficiencies any time chemical energy is converted to electri- cal. For electrochemical reactions, these inefficiencies are related to electrochemical processes such as currentflow against resistance or charge transfer resistance from ionic to electrical. These are called overvoltages in electrochemistry. The result of these overvoltages or inefficiencies is the evolution of heat. Consequently, heat is also evolved during the discharge of a lithium–ion battery. The less efficient the process for converting chemical energy of active masses to electricity, the larger heat generation becomes.
It is intuitive that heat generation depends on current drawn from a cell. High current causes more heat generation as itflows through resistors and also faces more resistance to convert electrical to ionic charge, which then travels through the electrolyte in the form of Li+ions. It also comes instinctively that heat generation should be proportional to the difference between the equilibrium or open-circuit voltage of a battery and the operational voltage in the moment of observation. The higher this voltage difference is, the greater the resistance the current faces as itflows through the system, both in the form of electrons through the external circuit and in the form of Li+ions through the electrolyte. Heat generation in a lithium battery is given by the equation below, whereEis the voltage at the time of observation,Iis the current, andTis the temperature.
Q¼I EocET∂Eoc
∂T
ð6:7Þ
Especially resistive is the last step in the intercalation mechanism where Li+-ions drift toward their intercalation sites inside the crystalline structure of the host cathode compound, for example, CoO2. At that point, near the end of discharge, most of the available sites for lithium intercalation have already been occupied and the incoming Li+-ions have to meander in somewhat torturous path to find available sites for reduction by the electrons from the outside circuit. This causes resistance and heat generation.
It is also evident from the equation that heat generation is also dependent on the rate of voltage change with time. From examination of familiar voltage trends and comparison with the temperature curve (Fig.6.13), it becomes apparent that in the beginning of discharge the voltage drops steeply and in the same period temperature sharply increases. Then, for the majority of discharge, voltage is stable, or it slowly declines, while the temperature gradually rises. Finally, in the last stage of discharge, voltage sharply drops, while temperature abruptly rises. It can be said that the temperature curve is roughly an inverted image of the voltage curve and our reasoning supports that.
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It is also clear that temperature depends on discharge current and hazardous conditions can ensue along with high currents if battery internal resistance causes excessive heat generation and temperature increases beyond safe limits. For 3 C currents, for example, the temperature can rise over 50 C. It should be noted, however, that different battery types and different chemistries exhibit different behavior and individual temperature profile must be understood for each specific battery. Most cells have protection circuits that will disconnect and disable the battery if unsafe temperature is reached.