An Algorithm for Optimal Charging of Li Ion Batteries Using a Single Particle Model*

Li-ion batteries are widely used in a variety of products ranging from consumer gadgets such as cell phones and laptops to electric vehicles. Their popularity can be attributed to high energy density and minimal maintenance. Charging these batteries can take anywhere from a few hours for low powered gadgets to many hours for high powered automobiles. Although theoretically possible, fast charging is not preferred because it can lead to unsafe operating temperatures and side reactions that degrade the life of a battery. An optimal algorithm to charge these batteries must therefore account for these constraints in addition to the complex battery dynamics. The battery dynamics are often defined by a large interconnected set of partial differential equations. However, this model is too complex and often takes many hours to solve for relevant battery variables. Single Particle Model is an approximation of this set of partial differential equations. In this article, we develop a constrained moving horizon algorithm to generate an optimal charging profile. The algorithm is based on minimizing the total charge time while meeting the operating safety constraints. The algorithm is illustrated through simulations. Simulations show that the Moving Horizon approach significantly reduces the total charging time by more than 20 percent, compared to a static optimization problem which produces a constant current over the entire charging period.