For most applications, a single ultracapacitor cell at low voltage is not very useful, so multiple ultracapacitor cells placed in series are required most of the time. Since ultracapacitor cells have a tolerance difference in capacitance and leakage current, there will always be an imbalance in the cell voltages of an ultracapacitor series stack. It is important to ensure that the individual voltage of any single ultracapacitor cell does not exceed its maximum recommended working voltage, as this could result in electrolyte decomposition, gas generation, ESR increase, and ultimately reduced life.
This voltage imbalance is immediately dominated by the capacitance difference between the ultracapacitor cells because a cell with a lower capacitance will charge to a higher voltage in a series string. For example, if two ultracapacitor cells of 10F each are connected in series, with one cell at +20% of nominal capacitance and the other at -10%, then the highest possible voltage for each ultracapacitor cell can be calculated as follows:
Vcap1=Vsupply x (Ccap1/(Ccap1 + Ccap2))
Vcap1=5.4 x (12/(12+9))
A voltage of 3.08V is too high for a single ultracapacitor cell; thus, series-connected ultracapacitor cells require a proper cell-balancing scheme to ensure that no cell sees a higher-than-rated voltage.
Ultracapacitor Balancing Scheme
When an ultracapacitor series stack is on charge for a period of time, leakage current may also affect the voltage distribution among the cells. In this case, a cell with a higher leakage current will go to a lower voltage, distributing the remaining voltage among the other cells and resulting in an over-voltage condition. Proper cell balancing can eliminate this imbalance.
There are two balancing schemes to tackle uneven voltage distribution and ensure a properly balanced ultracapacitor module: passive balancing and active balancing.
Passive Balancing: One technique to compensate for variations in individual cells is to place a same-valued bypass resistor in parallel with each cell, sized to dominate the total cell leakage current. This effectively reduces the variation in equivalent parallel resistance between the cells, which eliminates differences in the leakage current. For example, if the cells have an average leakage current of 10uA +/- 3uA, using a 1% resistor that will bypass 100uA in parallel to each cell will change the average leakage current to 110uA +/- 4uA and decrease the variation in leakage current from 30% to 3.6%. Having the same-value resistor in parallel with all cells also allows the cells with higher voltages to discharge through the parallel resistor at a higher rate than the cells with lower voltages. Together, these effects help to distribute the total voltage evenly across the entire series of ultracapacitor cells.
Passive Cell Balancing
Passive voltage balancing is only recommended for applications that do not regularly charge and discharge the ultracapacitor cells and that can tolerate the additional load current of the balancing resistors. If this method is appropriate, the balancing resistors should be selected to give an additional current flow of at least 10 times the worst-case cell leakage current. Higher ratios can be used to balance the cells faster, if the series can tolerate the increased current load. Once the system is balanced, the time it takes to keep the system in balance is less of an issue unless it is being severely cycled.
Active Balancing: An active balancing circuit works by forcing the voltage at the nodes of series-connected cells to stay below a fixed reference voltage. Active circuits typically draw much lower levels of current in a steady state and only require larger currents when the cell voltages go out of balance. These characteristics make active voltage-balancing circuits ideal for applications that charge and discharge the cells frequently, as well as those with a finite energy source.
Active Cell Balancing