摘要
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 &null 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 <formula><tex>$L_{max}$</tex></formula> loads under the constraint that the total voltages of these loads do not exceed a design constant <formula><tex>$V_{max}$</tex></formula>. 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 <formula><tex>$F_{max}$</tex></formula> 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.