Managing the power in wireless sensor networks powered by energy-harvesting circuitry

All these applications harvest energy from the environment and so effectively have a limitless, battery-free energy source. They also avoid the time-consuming and environmentally-sensitive task of replacing and disposing of batteries.

However, these environmental energy sources are typically very low power. Since power is the rate at which energy is delivered, the problem becomes how to power wireless transmission, which requires higher power levels, from a low-power source.

Supercapacitors are well suited as energy buffers
Figure 1 shows power design before supercapacitors. The entire system must be sized for the load’s peak power. In the example shown, the source must provide 2.6 A. Also, the internal impedance of the source means the voltage will drop from 3.7 V to 3.3 V during the peak load. The DC/DC converter enables this voltage drop to occur without interrupting operation of the load.

Figure 1: Power design before supercapacitors
(Click on image to enlarge)

The supercapacitor’s high energy storage and high power delivery make it a good choice to buffer a high-power load from a low-power, energy-harvesting source, Figure 2. The source sees the average load which, with appropriate interface electronics, will be a low-power constant load set at the maximum power point. The load sees a low-impedance source that can deliver the power needed for the duration of the high-power event.

Figure 2: Supercapacitor as a power buffer
(Click on image to enlarge)

In this example, the average load power is only 0.75 mW. A low-power energy-harvesting source only needs to supply a little more than this power level (to overcome losses) to charge the supercapacitor, which then provides the GPRS module with the power required for transmission.

The supercapacitor is placed after the interface electronics, so the interface electronics and DC/DC converter can be sized for the average power of 125 μW rather than the peak power of 7 W. A discharged supercapacitor will look like a short circuit to the source, so the interface electronics must manage the inrush current when the source is first connected to a supercapacitor at 0 V.

Low leakage current
If an energy-harvesting source only provides a few μA of current, you do not want to waste a significant proportion of this on capacitor leakage current. Small supercapacitors have low leakage current, typically between 1 μA ‎ 50 μA, depending on the capacitance. However, this is the equilibrium level leakage current after the supercapacitor has been held at voltage for several days. Figure 3 shows the leakage current over time for a 150 mF CAP-XX GZ065 supercapacitor.

Figure 3: CAP-XX GZ065 Supercapacitor leakage current over time
(Click on image to enlarge)

Supercapacitor cell balancing
Supercapacitors are low-voltage devices and several need to be strung in series to achieve a practical working voltage. However, different cells will have slightly different leakage currents, but since they are in series, they must have the same current flowing through them. In this case, the cells will redistribute charge between themselves, adjusting their voltage so their leakage currents will be equal.

This leaves one of the cells in danger of going over voltage. The balancing solution that draws minimal current is an active balance circuit using an ultra-low-current, rail-to-rail op amp. The circuit in Figure 4 is an example of this and draws only 2 ‎ 3 μA, including supercapacitor leakage current, once the supercapacitor has reached equilibrium leakage current.

Figure 4: Low-current active-balance circuit
(Click on image to enlarge)

The op amp chosen draws ~750 nA, supercapacitor leakage current is ~1 μA, and the current drawn through R12, R06 =250 nA if the supercapacitor voltage = 5 V, so total current ~2 μA.

In CAP-XX dual-cell supercapacitors, the two cells are matched by C. Because their voltages are balanced when first charged, designers can use a very low current-balance circuit to maintain balance.

Aging
All supercapacitors age over time, that is, their ESR slowly increases and their capacitance slowly decreases, Figure 5. The rate of aging depends on the supercapacitor operating voltage and temperature. The higher the voltage and/or temperature, the faster they age.

Figure 5: Aging, capacitance loss over time at room temperature, ambient relative humidity
(Click on image to enlarge)

Therefore, designers should size the supercapacitor so that the C is large enough and ESR low enough for successful operation at end of life, given the application’s expected operating profile. Figure 6a and 6b shows Capacitance over time for 1 year for a CAP-XX GW214 supercapacitor at 3.6 V, room temperature (23°C).

Figure 6a and 6b: Model for solving the constant power case. Note that V_SUPERCAP is not physically measureable, since C and ESR are idealized parameters within the supercapacitor.
(Click on image to enlarge)

Sizing the supercapacitor
Many people calculate the capacitance required by performing an energy balance:

Supercapacitor Energy, ½C (V_init² – V_final²)
= Load Energy, E_LOAD
=Average Load Power × Load duration

Therefore, C = 2 × E_LOAD/(V_init² – V_final²), where:
V_init is the initial supercapacitor voltage and V_final is the minimum voltage the supercapacitor can discharge to at the end of the peak load.

However, this approach ignores ESR and is only a good approximation if the voltage drop from I_LOAD × ESR << V_final. There are two cases to consider:

1) Constant current
In this case, the load current is constant and does not vary with voltage, so as the supercapacitor discharges, and the load voltage drops, the load current remains constant. An LED is a good example of this type of load. The final load voltage is given by:

V_final = V_init ‎ (I_LOAD × ESR) ‎ I_LOAD ‎ T_LOAD/C

Now a supercapacitor can be selected with both C and ESR adequate to support the load for duration T_LOAD.

2) Constant power
In this case, the load power remains constant, so as the supercapacitor discharges and the load voltage drops, the load current increases to maintain the V_LOAD × I_LOAD product constant. The input to a DC/DC converter is a constant power load, so this will be the most common case in energy harvesting applications. You need to solve:

Example: Supercapacitor interface circuit
The energy-harvesting source will typically have a maximum power transfer operating point, which is defined by a preferred output voltage. An example is the V_max power point for solar cells.

The example shown in Figure 7 illustrates all the key features that might be needed in a circuit to interface an energy-harvesting source to a supercapacitor:

• Maximum power tracking, maintaining the output voltage or current of the energy-harvesting source so it delivers the maximum possible power.
• Over-voltage protection, to ensure the supercapacitor-rated voltage is not exceeded
• Active balancing to maintain the supercapacitor cells at the same voltage with a low-current circuit.

Figure 1: Example of a supercapacitor interface circuit
(Click on image to enlarge)

Keep these notes in mind for the schematic of Figure 7:

1. U1 provides Max Power Point tracking. When V_solar < V_th1 - Hyst1, Q1 is turned OFF, When V_solar > V_th1 + Hyst1, Q1 is turned ON. If the open circuit voltage of the solar cell > max desired V_scap, then overvoltage protection is needed.
2. U3 provides supercapacitor overvoltage protection if required. When V_SCAP > V_th2 + Hyst2, Q2 is turned ON, which turns Q1 OFF. When V_scap < V_th2 ‎ Hyst2, Q2 turns OFF.
3. R7 ensures Q2 remains off if V_scap is insufficient to turn U3 ON.
4. MAX9017 dual comparator or 2 × MAX9015 chosen for U1, U3 since they only draw ~1 mA each and have a push-pull output, and include an internal reference.
5. MAX4470 single op amp selected for U2, since it draws <1 μA supply current.
6. D1 ensures the supercapacitor cannot discharge back into the solar cell if V_solar < V_scap
7. D1 prevents the supercapacitor from discharging into the output of U1 when Q2 is turned ON due to over-voltage protection but U1 is low, trying to turn Q1 ON.
8. R4 limits the current from the solar cell into the output of U1 when Q2 is turned ON due to overvoltage protection.
9. When Q2 is OFF and Q1 ON, U1 will not charge the supercapacitor, since the U1 output will be at the same voltage as V_solar (U1 is a rail-rail op amp) hence there will be no forward voltage across the body diode of Q2 to enable current flow.

Conclusion
Supercapacitors offer an important benefit for energy-harvesting applications, including the ability to buffer a high-power load from a low-power source in a small form factor, but they do not behave like classical capacitors. This article has explored some key properties of supercapacitors that engineers should understand when designing energy-harvesting circuits, and culminated with an example circuit that can be used as a reference design and modified for other applications.

About the Author
Pierre Mars is the Vice President of Applications Engineering for CAP-XX Ltd. , Sydney, Australia. He jointly holds three patents on supercapacitor applications. Mr. Mars has a BE electrical (1st class honors) 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.