Many system applications require that capacitors be connected together, in series and/or parallel combinations, to form a "bank" with a specific voltage and capacitance rating. The most critical parameter for all capacitors, including ultracapacitors, is voltage rating. Subjecting almost any capacitor to a substantially higher voltage than it was designed to withstand usually results in an irreparably damaged, nonworking capacitor. This is especially true for ultracapacitors, so they must be protected from overvoltage conditions.
Capacitors typically have two voltage ratings. Whatever voltage the capacitor can sustain indefinitely, without damage or performance degradation, is called the continuous-working voltage. On the other hand, the voltage that a capacitor can handle for just a short period of time, like a few hundred milliseconds, is the momentary peak or surge rating.
When an ultracapacitor is subjected to more than a tolerable voltage, the organic electrolyte within the cell begins to decompose, producing a gaseous byproduct. If the overvoltage condition persists long enough, the pressure may build up until the safety vent on the ultracapacitor's package opens. Consequently, more of the electrolyte will decompose and vaporize until the ultracapacitor's effective internal resistance increases and becomes an open circuit.
In short, impressing more voltage on an ultracapacitor than it's rated to withstand usually necessitates replacement. Therefore, prevention is the most sensible practice, as it may effectively eliminate ultracapacitor repair and maintenance costs. It also eradicates other potential causes of equipment downtime.
After voltage rating, the two most significant parameters for all types of capacitors are their capacitance and equivalent series resistance (ESR). When many ultracapacitor cells are connected together in a series string, these three parameters are affected as follows:
Overall Voltage Rating Of A Series-Capacitor String: The total voltage that can be im-pressed across a string of capacitor cells connected in series equals the sum of each cell's individual voltage rating. Ultracapacitors are usually connected together in series so that they can be subjected to a higher voltage than the available individual cells are rated to withstand.
Overall Capacitance Value Of A Series-Capacitor String: The net capacitance of a string of capacitor cells is the reciprocal of the sum of the reciprocals of every cell's capacitance. This is most easily understood if all members of the string have equivalent capacitance value. Then, the capacitance of the whole string will equal the individual cell capacitance divided by the number of cells in the string. For example, connecting 100 cells, each with 1000 Farads (F) of capacitance in a series string, will produce an overall effective capacitance of 10 F.
Overall ESR Of A Series-Capacitor String: The total ESR of the string has the same cumulative characteristic as the cell voltage. In other words, it equals the sum of all individual ESR values. A 100-cell string with 5 mΩ of dc ESR each will have an overall dc ESR of 500 mΩ.
Capacitors connected in series are subject to the "weakest-link" principle. The poorest performer in the string sets the performance "pace" for the rest of the string. Therefore, five individual 500-F cells in series have 100 F of capacitance. Yet four 500-F cells in series with one 400-F cell each have only 95 F of capacitance.
Moreover, the failure of any component within the string effectively causes the unit to "fail" due to the serial connection be-tween the individual string members. In particular, an open circuit in any series-connected component effectively renders the entire string as open circuited. Plus, ultracapacitors eventually fail open circuit, so it's a significant concern when many cells are connected together in a long string. That's because the mean time between failure (MTBF) of any system is inversely proportional to the number of components in that system.
Need For Voltage Equalization: Because sustained overvoltage can cause an ultracapacitor to fail, the voltage across each cell in a series string must not exceed the maximum continuous-working-voltage rating of the individual cells in the string. Thus, preventing the voltage impressed upon each cell in the string from exceeding its continuous-working-voltage rating is the most important preventive measure for ensuring trouble-free operation during the string's life. The designer must either reduce the "rate of charge" being delivered to a cell, or completely stop charging a cell whose voltage approaches its surge-voltage rating.
The easiest way to reduce the current that's charging an ultracapacitor cell is to divert some of it around the cell. One such method employs a passive bypass component. The other, more complicated procedure uses an active bypass circuit. Both techniques have advantages and disadvantages.
Passive Cell Voltage Equalization: The simplest implementation of the passive method involves a resistor "ladder" that has a "rung" or node connected to each node where all ultracapacitor cells join. This places a resistive element in parallel with every ultracapacitor cell (Fig. 1). The value of each resistor in the ladder should be selected so that the current flowing through it is within the range of two to 10 times the typical initial leakage current of the ultracapacitor cells in the string. That can be as high as 1 to 3 mA. So with a VC(MAX) of 2.7 V, the resistance range is:
VC(MAX)/IC(BYPASS) = R 2.7 V/(2 × 1 mA) = 1.35 kΩ to 2.7V/(10 × 3 mA) = 90Ω
But the exact value may need to be determined by the maximum-possible charging rate that the string will likely see. This ensures that enough current will be by-passed to prevent the cell from overcharging.
The primary benefits of this parallel-resistor ladder circuit are its low cost and ease of implementation. This circuit's main downside is that it is always discharging the string, so it's not very energy efficient.
Active Cell Voltage Equalization: The simplest implementation of the active-circuit method uses a resistor ladder that's identical to the one just described for the passive method. But the active circuit has an active switching device, like a bipolar transistor or a MOSFET, connected in series with each bypass element of the ladder.
The switches are controlled by voltage-detection circuits that only turn a switch "on" when the voltage across that particular cell approaches a value just slightly below the continuous-working-voltage rating of the cell (2.68 V in the example to follow). This is called the bypass threshold voltage. Figure 2 depicts a typical block diagram of an active charging-current diversion circuit.
The value and wattage of each resistive element should be sized so that approximately 1 A of diversion current is siphoned off from each cell whose voltage exceeds the bypass threshold voltage. The turning "on" of one or more charging-current diversion switches could (and should) also be used as a signal to the charging circuit to terminate the current cell-charging cycle. Figure 3 depicts the current in the bypass circuit versus cell voltage, showing the circuit becoming active at the bypass threshold voltage.
This circuit is more energy efficient because the switches are "on" only when a cell needs to have some of its charging current diverted. If the voltage across each cell is under the threshold set for the detection circuit, the switch is "off" and the resistor isn't diverting charging current from the cell. The main disadvantage here is that separate voltage-detection and switch-control circuits are necessary for every cell in the string, making it potentially more costly and difficult to deploy. Yet, it provides the most protection for the individual capacitor cells in the string.
Implementing Active Equalization: Figure 4 provides a practical example of a series string comprising capacitor cells that have active capacitor cell voltage-equalization circuits. Here, 18 1700-F, 2.7-V NESSCAP ultracapacitor cells are linked in series to form a string with an overall capacitance of 94 F, a voltage rating of 48 V dc, and an ESR of 12.6 mΩ.
Every ultracapacitor cell in the string contains a pc board mounted across its terminals. Each pc board has its own voltage-detection circuitry, switch, and bypass element. Figure 5 shows a circuit diagram of the pc board. The bypass element, R9, is an axial-lead 2.7-Ω 5-W metal-oxide resistor. The switch, T2, is a BC868 or equivalent, npn SMT bipolar transistor in an SOT89 package. IC1 is a precision reference, such as a TL431, used to set the threshold voltage (2.68 V) at which T2 turns on.
Series ultracapacitor strings can usually be ordered from ultracapacitor manufacturers. They come as preassembled banks, complete with active capacitor cell voltage-equalization circuits installed, tested, and guaranteed to function properly.