By Jillian Kunze
Quickly charging the batteries in cell phones, laptops, or electric cars is a tantalizing prospect for people in a hurry. But to design faster charging systems, one must contend with several dangers associated with the lithium-ion batteries in many of these devices.
Luis Couto of the Université Libre de Bruxelles, Belgium is interested in reducing these dangers through mathematical controls. During a minisymposium presentation at the SIAM Conference on Control and Its Applications, which is taking place virtually this week concurrently with the SIAM Annual Meeting, Couto presented a control strategy for the safe and fast charging of lithium-ion batteries and provided experimental results for this new approach. “The objective was to develop and experimentally validate a battery fast-charging control strategy that is optimization-free—i.e., in real time—and does not compromise battery lifetime,” Couto said.
Figure 1. Complex electrochemical reactions take place inside lithium-ion batteries.
Complex electrochemical reactions take place inside batteries as they charge and discharge (see Figure 1). When things go awry, undesired consequences can degrade the battery. Overcharging, for example, may cause the battery to overheat and explode, posing a significant safety risk. Another damaging effect is lithium plating, in which metallic lithium forms around the anode of the battery during charging. Over time, this can cause the battery to malfunction and lose charging capacity. “The work here is to try to prevent lithium plating in lithium-ion batteries,” Couto said.
Rapid battery charging has been a popular research topic in recent years, but few studies have accounted for mitigating battery degradation while charging. The default protocol for battery charging at present is constant-current/constant-voltage (CCCV), which is widely used in commercial products. However, neither this protocol nor any extensions of it are designed to satisfy constraints that might prevent degradation.
Another approach to battery charging is the offline optimal charging profile, which uses electrochemical models to minimize charging time and capacity loss, maximize stored charge, or place other constraints. However, this is an open-loop strategy, meaning that no output information is incorporated in the control of the system. The system thus does not take advantage of real-time information about the battery’s state like its voltage, temperature, or state of charge, which makes it susceptible to uncertainties in the model and variations in the initial state of charge.
A paradigm shift from open-loop to closed-loop charging strategies could improve the battery charging process. In a closed-loop scheme, the controller uses information from the system to define and update the control strategy and determine what voltage should be applied to charge the battery at a given time (see Figure 2). While this strategy can sometimes be very computationally demanding, a promising closed-loop approach called the reference governors method provides a computationally efficient, predictive control law.
Figure 2. The current paradigm in lithium-ion charging strategies is to use open-loop systems, in which output information is not incorporated in the control. Couto proposed to instead use a closed-loop system, in which the controller uses information from the system to set the control strategy.
In designing the new closed-loop control strategy, Couto used a straightforward model based on hydraulics to represent the complicated electrochemical reactions in a battery. The several simplifying assumptions in this model make it possible to write out the dynamics of the entire battery in terms of only the negative electrode, so that it is not necessary to mathematically describe the positive electrode.
Couto wanted to improve upon the current standard battery management system, which cannot access all of the possible states of safe operation and at times may allow dangerous lithium plating to occur. The controls in an advanced battery management system should actively prevent the battery from reaching a state that could cause lithium plating. Couto set out to make an improved control design that incorporates certain constraints on what level of voltage can be applied to the battery.
To prevent the constraints from being violated—which might lead to disaster!—Couto introduced an intermediary between the user and the primary controller in the form of a reference governor. “The idea of a reference governor is to use an applied reference to satisfy constraints,” Couto said. After mathematically defining the safe operating parameters for the battery, he embedded these constraints into the reference governor. Based on the user’s input and the current state of the battery, the reference governor enforces electrochemical constraints in the control strategy to maintain proper and safe battery operation.
Figure 3. The reference governors (RG) strategy performed faster than constant-current/constant-voltage (CCCV) charging, while not causing lithium plating.
Since these constraints on battery operation were nonconvex—a less conventional form—it was necessary to develop a new, computationally efficient formulation of the reference governor. Couto’s new approach consists of checking what the current parameters in the system are, finding out what constraints the system is closest to surpassing, and using this information accordingly to decide how to charge the battery. This strategy allows the system to operate less conservatively than previous techniques, thereby enabling faster charging.
Couto tested out these new control strategies in real-world experiments done in collaboration with the University of California, Berkeley. The researchers performed 99 discharge and recharge cycles of a battery using the reference governor strategy as well as two common varieties of CCCV charging, testing the battery’s performance every 11 cycles.
The experimental results were encouraging — the reference governor approach charged the battery 22 percent faster than a high current CCCV, while degrading the battery at a similarly low rate as a mild current CCCV (see Figure 3). “The reference governor strategy is able to fast-charge batteries while satisfying degradation constraints,” Couto said. These promising results could improve the safety and speed of lithium-ion battery charging.
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Jillian Kunze is the associate editor of SIAM News. |