In the design of ultracapacitor modules, it's often necessary to place multiple cells in series to achieve a certain module voltage. Ultracapacitors tend to be limited to roughly 3V maximum operating voltage. Thus, it wouldn't be unusual to see four or more ultracapacitors in series for medium to high voltage storage applications. Whenever capacitor cells are connected in series, it's important to understand cell balancing requirements and techniques.
To understand why cell balancing may be required, we first consider a simplified model of an ultracapacitor. Shown below is a basic, low frequency model of two ultracapacitors in series. Each Rs represents the cell's effective series resistance (ESR) and each Rp represents a parallel resistance to model internal leakage currents.
Low frequency model of two ultracapacitors in series
Variations in the cell manufacturing processes and environmental exposure will lead to variations in capacitance, ESR, and leakage current between cells in the module. Generally, capacitance and ESR may vary by +/- 10% while leakage current may vary +100/-50%. These parameter variations will inevitably cause the series connected cells to operate at slightly different voltages. Divergence will begin as a function of the initial variation between cells, however, cells that operate at a higher voltage will likely age faster than cells operating at a lower voltage potentially worsening performance variation as time continues.
Simulation considering +/- 10% variation in initial capacitance and +/- 50% variation in parallel resistance. Cells were left to dwell from 2.0V starting voltage. Divergence occurs due to variation in capacitance and leakage current.
Simulation considering a generic module of five series cells being discharged at 200mA and charged to a module voltage of 13.5V. Voltage variation between cells differs due to capacitance, ESR, and leakage current differences. Differences grow worse over time as leakage and ESR contribute to unequal losses per cell.
Whether or not a module requires balancing is only answered with the expected performance and environment of the module. Generally, for modules that undergo many high power charge/discharge cycles, passive balancing will not suffice and active balancing is recommended. For modules that may be used for voltage bus hold-up application or a backup energy supply, passive balancing may be suitable. In some rare instances, modules may take advantage of leakage rate characteristics to eliminate the need for additional balancing circuitry.