A Mathematical Theory for Multistage Battery Switching Networks

In this paper, we propose a mathematical theory for multistage battery switching networks. The theory aims to address several design issues in managing a large-scale battery system, including flexibility, reliability, efficiency, complexity (scalability) and sustainability. Our multistage battery switching network is constructed by a concatenation of various rectangular "shapes" of battery packs. The shape of each battery pack is specified by its voltage and its capacity. We show that our multistage battery switching network can support a maximum number of L_{\max} loads under the constraint that the total voltages of these loads do not exceed a design constant V_{\max} . Moreover, the voltage of each battery pack can be determined optimally by solving a Simultaneous Integer Representation (SIR) problem. To determine the capacity of each battery pack, we propose a max-min fairness battery allocation scheme, and show by computer simulations that such a scheme outperforms the uniform battery allocation scheme. We also propose a fault tolerant battery switching network that can still be operated properly even after F_{\max} battery packs fail. Such a fault tolerant battery switching network enables a battery system to implement the Largest Remaining Capacity First (LRCF) policy that does not require the knowledge of the load profile.