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Compared with the conventional homogeneous electrical energy storage (EES) systems, hybrid electrical energy storage (HEES) systems provide high output power and energy density as well as high power conversion efficiency and low self-discharge at a low capital cost. Cycle efficiency of a HEES system (which is defined as the ratio of energy which is delivered by the HEES system to the load device to energy which is supplied by the power source to the HEES system) is one of the most important factors in determining the overall operational cost of the system. Therefore, EES banks within the HEES system should be prudently designed in order to maximize the overall cycle efficiency. However, the cycle efficiency is not only dependent on the EES element type, but also the dynamic conditions such as charge and discharge rates and energy efficiency of peripheral power circuitries. Also, due to the practical limitations of the power conversion circuitry, the specified capacity of the EES bank cannot be fully utilized, which in turn results in over-provisioning and thus additional capital expenditure for a HEES system with a specified level of service. This is the first paper that presents an EES bank reconfiguration architecture aiming at cycle efficiency and capacity utilization enhancement. We first provide a formal definition of balanced configurations and provide a general reconfigurable architecture for a HEES system, analyze key properties of the balanced reconfiguration, and propose a dynamic reconfiguration algorithm for optimal, online adaptation of the HEES system configuration to the characteristics of the power sources and the load devices as well as internal states of the EES banks. Experimental results demonstrate an overall cycle efficiency improvement of by up to 108% for a DC power demand profile, and pulse duty cycle improvement of by up to 127% for high-current pulsed power profile. We also present analysis results for capacity utilization improvement for a reconfigurable EES bank.