# Power: Battery Boost

March 1, 2009

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Electrochemical capacitors are a relatively new contender in the energy storage ball game. While electrochemical capacitors are related to batteries, they use a different energy storage mechanism. Batteries move charged chemical species (ions) from one electrode to another through an electrolyte. The ions interact chemically, i.e. undergo chemical reactions with the electrodes, to store energy. These reactions take time and limit the peak power batteries are able to provide.

By contrast, electrochemical capacitors store electrical charge physically, without using chemical reactions. Because the charge is stored physically, the process is highly reversible, and millions of charge/discharge cycles are possible. Of more interest for the applications discussed here, however, is the fact that no time consuming chemical reactions are occurring, so electrochemical capacitors can move energy in and out quickly. Their power densities (W/kg) are 100 to 1,000 times higher than even advanced battery technologies. This is shown in the Ragone Plot in Fig. 1.

In addition to electrochemical capacitors having high power density and lifetimes of more than 1 million charge/discharge cycles, they also require no maintenance and they work well over broad temperature ranges. Before exploring how to design them into a circuit, one should first understand how electrochemical capacitors operate.

An electrochemical capacitor does not store energy between two plates like a traditional capacitor. Instead, it stores energy within an electrical double-layer that forms at the electrode/electrolyte interface. The capacitance is directly proportional to the area of the electrode and inversely proportional to the distance between the layers of charge as shown by Equation 1.

This shows that the combination of extremely high surface area with extremely small charge separation allows electrochemical capacitors to store orders of magnitude more energy than traditional capacitors.

Most electrochemical capacitors (also known as supercapacitors or ultracapacitors) are manufactured using high surface area carbon as the electrode material. Some designs utilize less expensive carbon cloths or papers, which can be made from recycled sources as an electrode backing material. These materials can have relatively good electrical conductivity but their surface area is not extremely large. The new designs create high surface areas by depositing coatings of very small nanoparticles onto these electrode backing materials.

A schematic of this new design is shown in Fig. 2. The carbon backing material is shown in gray. It provides structure and electrical conductivity. The nanoparticle coating is shown in blue, and the red circles represent charged ions in the electrolyte. When the capacitor is charged, a layer of positive charge accumulates on the high surface area nanoparticle coating on the positive electrode. Negative ions in the electrolyte are attracted to this positive layer and are absorbed into the pores of the coating, thus creating a double-charged layer. The process is reversed on the negative electrode.

Portable battery-powered devices that operate in pulsed modes can benefit greatly from the incorporation of electrochemical capacitors into their design. In general, parallel power sources combining batteries with electrochemical capacitors can meet high-power pulsed loads more effectively than batteries alone. Often significant reductions in system size, weight, and cost are possible using a combined system.

A basic hybrid battery/capacitor circuit is shown in Fig. 3. The battery is modeled as an ideal voltage source Vb in series with the internal resistance Rb. The electrochemical capacitor is modeled as a capacitance Cc in series with an equivalent resistance Rc. By using this simplified circuit model it is possible to derive useful design equations that can be used to estimate the peak power available for a given battery, capacitor and load duty cycle.

For a pulsed load current, io, as a function of time, t, with a period of T and pulse duty ratio D, the current for k pulses is given by Equation 2, where Io is the amplitude of the current and Φ(t) is the Heaviside function. Solving the circuit for the external voltage, vo, yields Equations 3 and 4.

Once one has solved for the external voltage, it is relatively straightforward to obtain the battery and capacitor currents with Equations 5 and 6.

A detailed description of these equations can be found in the article: Power and Life Extension of Battery – Ultracapacitor Hybrids by R.A. Dougal, Shengyi Liu, and Ralph E. White, IEEE Transactions on Components and Packaging Technologies, Vol. 25, No. 1, March 2002, pp 120-131. The article serves as the basis for much of SolRayo’s battery/capacitor modeling work at frequencies lower than 1 kHz.

By plotting Equations 1, 5 and 6, one can see in Fig. 4 the load current and the current supplied by the battery and the electrochemical capacitor. The figure shows the results for: D = 0.1, T = 10 s, Cc = 40 F, Rb = 0.15 Ω, and Rc = 0.0125 Ω.

For this combination of parameters, most of the pulsed load is being met by the electrochemical capacitor. If we increase the pulse-duty ratio, D, to 0.25, the electrochemical capacitor still meets a significant part of the pulsed load, as seen in Fig. 5.

The battery voltage for the initial conditions with the pulse-duty ratio, D, of 0.1 is shown in Fig. 6. The battery voltage drops during the load pulse and then recovers as the battery charges the electrochemical capacitor.

The figures show that, by incorporating an electrochemical capacitor into the circuit, the battery current is reduced to a fraction of the load peak current. This substantially reduces the internal voltage drop in the battery.

Simplifying the design so that the output voltage is constant, which is reasonable in light of Fig. 6, one can assume that the peak power drawn from the battery occurs at the same time the battery current is at its maximum value. As the figures show, the maximum battery current occurs at t = (k+D)T. The previous equations can be used to estimate the peak battery current, as seen in Equations 7, 8, and 9.

Assuming that the battery maximum operating current is equal to its rated current (Ib, peak = Irated) then Equation 10 is also true. Thus, γ is a multiplier that reveals how much more current the hybrid system can deliver than the battery alone can deliver. In a similar fashion, the power which can be delivered by the hybrid system is shown in Equation 11, where Prated is the rated power of the battery. Fig. 7 shows the calculation of γ for a variety of periods as a function of pulse duty ratio (D).

As the figure shows, the peak power delivered by the hybrid system can be more than 10 times the rated battery power. The plot also shows that the hybrid system will perform better for systems with a smaller duty cycle.

Many battery applications having high-current pulse loads can greatly benefit from the addition of electrochemical capacitors. As this modeling demonstrates, the incorporation of an electrochemical capacitor into a battery application can result in a 10-fold increase in maximum power, thereby allowing for significant reductions in size, weight, and cost for battery/electrochemical capacitor hybrid systems.

For more information, email: contactsolrayo@solrayo.com

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