How can Ultracapacitors Deliver high energy and power?

Ultracapacitor, or Electrochemical capacitors (EC) do not have separate distinguishable dielectric as in electrostatic or electrolytic capacitors. Electrode in ultracapacitor is highly porous, and is impregnated by and filled with electrolyte throughout its volume. The result is an extremely high electrode / electrolyte contact interface. Effective surface area available can be as high as 2000-3000 sq. m. /gm of electrode.

The figure above shows structure of carbon particles in electrode material of ultracapacitor. The nanometer size carbon particles have pores, which vary in sizes. They are called macropores, mesopores and micropores as per their sizes.  Electrolyte enters the pores, which increases effective area of contact with electrode significantly. Size of electrolyte molecules also matters as it must be able to occupy the pore spaces.

An extremely thin separation layer (Helmholtz layer) of sub-nanometer thickness is naturally formed at this interface, and acts as dielectric. Dielectric constant of this layer is high. These capacitors are called Electrochemical Double Layer Capacitors (EDLC). Consider the basic equation for capacitor.

C = ϵ₀ϵ_r A/d, with ϵ₀, the permittivity of free space being 8.854 x 10^-12

 With A in thousands of sq. m. /gm, and d of the order of 10¹⁰, it can be seen that the factor 10^-12 gets nullified, and capacitor values are in Farad range. Relative permittivity, or dielectric constant of electrolyte is also high, making high values possible in small volumes. Result is capacitance values millions of times those of electrolytic capacitors. Capacitance values of 60 Farads to 360 Farads, or even higher are achieved.

A second alternative for energy storage is through faradaic process, or pseudocapacitance, which transfers ions between electrode and electrolyte at contact surface (in addition to electrostatic action). Such capacitors are called pseudocapacitors, and store energy much higher energy than EDLC capacitors.

Voltage of EC capacitor is decided by the decomposing voltage of dielectric (depends on the type of electrolyte). Voltage ratings of these capacitors are low, from 1.5 V to 3.8 V for different types of capacitors. Values may vary from 0.1 F to 5000 F as standard, and few are rated as high as 30,000 F (even 100,000 Farads) in one single unit. Ultracapacitors are used in series / parallel combination to form modules of higher voltages and values.

Energy Density

Charge stored in EC is given by Q = CV for an applied voltage of V volts. Energy stored is E = ½CV² in Watt-seconds (or Joules). C being in Farads, both charge and energy levels are very large compared to either electrostatic or electrolytic capacitors, and are comparable to batteries (though much smaller) in energy levels. Energy densities are often mentioned in Watt-hours.

A capacitor of 1000 F charged at 2.7 V stores energy equal to (1000 x 2.7²/2=3645 watt-sec.= 1.01watt hour (Wh). This can be taken as general guideline for back-of-hand calculation. Charge on this capacitor will be 2700 Coulombs. Ultracapacitors fill the gap between capacitors and batteries in terms of energy storage and power delivery. Energy stored could vary from few Joules to over 100 KJ.

An electrolytic capacitor stores energy far below 1 Wh per Kg of its weight. As against this, an EDLC stores 5-20 Wh per Kg, while pseudocapacitors can store 45 Wh/Kg or more. Modern day hybrid capacitors can store as high as 100 Wh/Kg.

Power Density

Ultracapacitors store energy as electrical charges by electrostatic forces at surface (like any capacitor), in response to a voltage applied across its terminals. When a load is connected across it, these charges are transferred to load. Thus there is no conversion of energy when an ultracapacitor is charged (or energy is stored), or when it is discharged via a load, as current is drawn from it.

A battery stores energy by way of electrochemical reactions, which takes time to generate current, and also involves reaction losses. It again undergoes electrochemical reactions before it gets free electrons and delivers energy (current) to a load. Thus its response time is sluggish to that extent, and this puts a limit on how fast it can respond to a change in load, or adjust to surges and spikes. A comparative chart of capacitor, ultracapacitor and battery of energy density and specific power, called “Ragone’ Chart” as given below, is useful in understanding these differences in their power and energy capacity.