Coupling a Supercapacitor with a Small Energy Harvesting Source

Small wireless sensors are becoming ubiquitous. Applications for sensors include building control, industrial control, security, location tracking, RFID and many others. It is much more convenient and cost effective if a small energy-harvesting source can power these sensors autonomously without expensive wires, or batteries that will need replacing over and over.

The environment provides infinite ambient energy (piezoelectric, thermal, vibration, photovoltaic) but at very low power which falls short of the peak power needed to transmit data across wireless networks such as IEEE 802.15.4 (Zigbee), 802.11 (WLAN) or GSM/GPRS. A battery or supercapacitor is required as a power buffer to store enough energy to provide the power bursts needed to acquire and transmit data. These energy-storage devices are charged at low power and deliver the burst power when needed.

This article will review the characteristics of supercapacitors and canvass the key issues designers should consider when pairing them with small energy-harvesting sources.

Sizing the supercapacitor

Supercapacitor cells are low voltage, typically rated between 2.3V and 2.8V. The most efficient and cost-effective strategy is to limit the supercapacitor charge voltage to less than the cell-rated voltage and store enough energy for your application. We will further explore this strategy in the section on charging circuits.

A simple approach to sizing the supercapacitor is to calculate the energy required to support the peak power of the application = P.t and set this = 1/2.C.(V²initial - V²final). However, this does not allow for any losses in the supercapacitor equivalent series resistance (ESR). The voltage seen by the load = Vinitial - ESR.I_LOAD, where Vinitial is the supercapacitor voltage just before the peak power burst. Since the load voltage drops, the load current increases to achieve the load power. Referring to Fig 1, designers can model supercapacitor discharge as:

V_LOAD = V_SCAP - I_LOAD.ESR

P_LOAD = V_LOAD.I_LOAD

             = (V_SCAP - I_LOAD.ESR).I_LOAD

             = V_SCAP.I_LOAD - I_LOAD².ESR

which gives an equation for ILOAD:

I_LOAD².ESR - V_SCAP.I_LOAD + P = 0

Solve for I_LOAD.

 

Supercapacitor discharge can then be simply modelled in Excel as:

 I_LOAD(t) = [V_SCAP(t) - SQRT(V_SCAP(t)²-4.ESR.P)]/(2.ESR)

V_LOAD(t) = V_SCAP(t) - I_LOAD(t).ESR

V_SCAP(t+dt) = V_SCAP(t) - dt.ILOAD/C

This is important if I_LOAD.ESR is significant compared to the final supercap voltage. In this case, a simple energy balance approach will undersize the supercapacitor. This is likely to be the case at low temperatures, when ESR will typically be 2 - 3 times higher than at room temperature.

The supercapacitor C and ESR should also allow for aging. Supercapacitors will slowly lose C and increase ESR over time. The aging rate will depend on cell voltage and temperature. The designer should select initial C and ESR so the end-of-life C and ESR can support the applications.

Supercapacitor Charging

A discharged supercapacitor looks like a short circuit to an energy source. Fortunately, many energy-harvesting sources, such as solar cells or micro-generators, can drive into a short circuit and directly charge a supercapacitor from 0V. ICs used to interface energy sources such as Piezo-electric or thermo-electric must be able to drive into a short circuit to charge a supercapacitor.

The industry has invested much effort in maximum peak power tracking (MPPT) to most efficiently draw power from energy-harvesting sources. This is applicable when charging a battery which needs to be charged at constant voltage. The battery charger is typically a DC:DC converter that is a constant power load to the energy source, so it makes sense to draw that power at the most efficient point using MPPT.

In contrast to a battery, a supercapacitor does not need to be charged at a constant voltage but will charge most efficiently by drawing the maximum current the source can supply. If the open circuit voltage of a solar cell array is less than the supercapacitor-rated voltage, then the simplest and most effective charging circuit is shown in Fig 2. The diode prevents the supercapacitor from discharging back through the solar cell if it goes dark. If the energy source open circuit voltage is greater than the supercapacitor voltage, then the supercapacitor will need over-voltage protection. Fig 3 shows this concept using a shunt regulator. A shunt regulator is used because it is cheap and simple, and once the supercapacitor is fully charged, it does not matter that the excess energy dissipates. The energy harvester is like a hose with an endless supply of water filling a barrel which is analogous to the supercapacitor.

Once the barrel is full and the hose is still running, the water may as well run over the side. This is different from a battery, where the supply of energy is limited, so a series regulator would be used.

 
The design principles for a supercapacitor charging circuit with an energy-harvesting source are:

In the Fig 2 circuit, the supercapacitor will draw short circuit current from the solar cell when it is at 0V. As it charges, the current reduces according to the solar cell V-I characteristic, but at all times, the supercapacitor is drawing the maximum current it can, so it is charging at the fastest possible rate. We chose the TLV3011 solar cell since it has an integrated voltage reference, draws only ~3µA quiescent current, and is open drain so the output is open circuit when the regulator is off. We chose the BAT54 diode since it has a low V_F at low currents, V_F < 0.1V at I_F < 10µA.

A micro-generator is ideal for industrial-control applications, such as monitoring rotating machinery, since by definition they will be vibrating if running.

Fig 4 shows the V-I characteristic of a micro-generator. This is similar to a solar cell characteristic and delivers maximum current into a short circuit. A micro-generator has the added advantage that the diode bridge around the generator prevents the supercapacitor from discharging back into it. This leads to the simple charging circuit shown in Fig 5.

Fig 4: Typical V-I curve for a microgenerator. (Click here for a larger PDF.)

Fig 4 shows that the open circuit voltage is 8.5V. In this case, we selected a dual-cell supercapacitor, the CAP-XX HZ202, rated to 5.5V. We again used a shunt regulator for over-voltage protection, and a low-current active balance circuit to ensure that the two cells have their voltage evenly distributed.

 Fig 5: Supercapacitor charging circuit for a microgenerator. (Click here for a larger PDF.)

Leakage current

Because some energy harvesters only deliver a few micro amps, leakage current becomes very important. It is futile to waste a significant portion of the energy harvester's power in leakage current. Supercapacitors can have leakage currents < 1µA, making them suitable for energy-harvesting applications. Fig 6 shows the leakage current for a selection of supercapacitors.

Fig 6: Leakage current for various supercapacitors. (Click here for a larger PDF.)

When a supercapacitor is charged, the leakage current decays over time as the ions in the carbon electrodes diffuse into the pores. The leakage current settles to an equilibrium value which depends on capacitance, voltage and time. Leakage current is proportional to cell capacitance. For a CAP-XX supercapacitor, a good rule of thumb for equilibrium leakage current at room temperature is 1µA/F. In Fig 6, the two CAP-XX GZ115s, 150mF, have leakage currents of 0.2µA and 0.3µA after 160hrs. Leakage current increases exponentially with temperature. The time it takes to settle to the equilibrium value decreases with increased temperature as the ions diffuse more rapidly. This leakage means that a minimum current is required to charge the supercapacitor from 0V. Depending on the supercapacitor, this will range from 5µA - 50µA. I recommend testing the minimum charging current when selecting a supercapacitor for your energy-harvesting circuit.

Cell Balancing

If the circuit requires that the supercapacitor terminal voltage is greater than the cell-rated voltage, e.g. 5V or 12V, then several supercapacitor cells will be in series to reach the rated voltage. In this case, a cell-balancing circuit is necessary; otherwise there is a risk that one of the cells will go over-voltage. This is because the cells all have slightly different leakage currents, with different V-I_L characteristics, but since they are in series, they are all forced to

We chose the op amp for very low supply current (750nA for the MAX4470) and it should be rail-rail on input and output. R14 limits the output current in case one cell goes short circuit. As shown in Fig 8, the total solution (green trace) draws 2 - 3 µA after 160hrs balancing a

CAP-XX HW207 supercapacitor which is 0.5F. To suit a log scale, the absolute value of cell balancing current (yellow trace) is shown, since this can be positive or negative.

Temperature Performance

A major advantage of supercapacitors for energy-harvesting applications is the wide temperature performance. Examples include powering location-tracking units using vibration transducers, which may be operating in sub-zero northern winter temperatures, or solar panels in winter sunlight. Supercapacitor ESR at -30°C is typically two to three times ESR at room temperature, so peak power can still be delivered even at these low temperatures. In contrast, the internal impedance of thin-film batteries may reach several KΩ at such low temperatures.

Supercapacitors Can Complement Batteries

In some applications, supercapacitors are an alternative to batteries while in others they are best used to support them. In situations where a supercapacitor may not be able to store sufficient energy, a battery is required. For example, when the ambient energy source is intermittent, such as solar at night, then energy must be stored not just for peak power delivery, but also to support the application for an extended time. If the peak power needed exceeds the amount the battery can supply, e.g. for GSM calls, or for low-power transmission in cold temperatures, then the battery can charge the supercapacitor at low power and the supercapacitor can deliver the high power bursts. This arrangement also means the battery is never cycled deeply, extending battery life. Supercapacitors store energy by physical-charge storage, not chemically as in batteries, so supercapacitors have an effectively infinite cycle life.

The leakage current characteristic of supercapacitors means that when a supercapacitor is charged from a battery to supply peak power bursts, then there is a critical interval between bursts where if the bursts arrive more often, it is more energy efficient to leave the supercapacitor always on charge. But if the bursts arrive less often, then it is more energy efficient to charge the supercapacitor only prior to the peak-power event. This interval will depend on several factors, including the charge absorbed by the supercapacitor before reaching equilibrium leakage current (area under the curves in Fig 6), the self discharge characteristic of the supercapacitor, and the charge drawn from the supercapacitor to supply the peak-power event. This is only possible if you know beforehand when the peak-power event will occur, and is not possible if it is in response to an unpredictable event, such as battery fail or an external stimulus.

Conclusion

This article has reviewed the characteristics of supercapacitors and canvassed the key issues designers should consider when using a supercapacitor with a small energy-harvesting source. It is our goal to help facilitate self-powering energy-harvester designs for the rapidly-growing wireless sensor market.

About the Author

Pierre Mars is the VP of Quality and Applications Engineering for CAP-XX Ltd. He jointly holds three patents on supercapacitor applications. Mr. Mars has a BE electrical (1^st class hons) and an MEng Sc from the University of NSW, Australia, in addition to an MBA from INSEAD, France. He is also a member of the IEEE. Based in Sydney, Australia; the company can be reached at sales@cap-xx.com. Design tools, application notes and other details are available at http://www.cap-xx.com.