Multiple-source and multiple-destination charge migration in hybrid electrical energy storage systems

Hybrid electrical energy storage (HEES) systems consist of multiple banks of heterogeneous electrical energy storage (EES) elements that are connected to each other through the Charge Transfer Interconnect. A HEES system is capable of providing an electrical energy storage means with very high performance by taking advantage of the strengths (while hiding the weaknesses) of individual EES elements used in the system. Charge migration is an operation by which electrical energy is transferred from a group of source EES elements to a group of destination EES elements. It is a necessary process to improve the HEES system´s storage efficiency and its responsiveness to load demand changes. This paper is the first to formally describe a more general charge migration problem, involving multiple sources and multiple destinations. The multiple-source, multiple-destination charge migration optimization problem is formulated as a nonlinear programming (NLP) problem where the goal is to deliver a fixed amount of energy to the destination banks while maximizing the overall charge migration efficiency and not depleting the available energy resource of the source banks by more than a given percentage. The constraints for the optimization problem are the energy conservation relation and charging current constraints to ensure that charge migration will meet a given deadline. The formulation correctly accounts for the efficiency of chargers, the rate capacity effect of batteries, self-discharge currents and internal resistances of EES elements, as well as the terminal voltage variation of EES elements as a function of their state of charges (SoC´s). An efficient algorithm to find a near-optimal migration control policy by effectively solving the above NLP optimization problem as a series of quasi-convex programming problems is presented. Experimental results show significant gain in migration efficiency up to 35%.