Dynamics of supercapacitor bank with uncontrolled active balancer for engine starting

• Analytic performance of an open-loop operated supercapacitor balancer is revealed.
• Natural balancing is shown to be always attained.
• Excessive currents arise when the initial voltage misbalance is significant.

In this paper, analytical investigation of an actively balanced open-loop operated supercapacitor bank is presented. Supercapacitor unit is utilized for 28 V auxiliary power unit diesel engine starting, allowing relieving the battery from multiple starting stresses. Dynamical equations of the system based on a synchronous bidirectional buck-boost converter are developed by splitting the solution into zero-input and zero-state responses. It is revealed that the system, which is typically nonlinear because of buck-boost converter presence, becomes linear when operated in open loop. Moreover, natural balancing is achieved when the converter is operated with 50% duty cycle. It is shown that balancing time is independent on initial conditions while system damping strongly depends on parasitic resistances especially in practical case of large capacitors and small inductance. Inductor current peak value and balancing time are obtained analytically and validated by simulations. It is revealed that while natural balancing is always achieved, excessive currents may arise when the initial voltage misbalance is significant. In addition, it is shown that one-switching-cycle averaged model is in close agreement with detailed switched model. The presented findings are fully supported by extended simulations.