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Electrochemical Capacitors

Overview

Electrochemical capacitors (ECs) have been an important development in recent years in the field of energy storage. These devices operate between rechargeable batteries and electrolytic capacitors with respect to energy and power performance. Electrochemical capacitors differ from batteries in that they do not store energy in redox reactions that occur in the electrode structure. Electrochemical capacitors store energy through electrostatic interactions that occur in the electrode and solution interface region, also known as the double layer.   Ionix manufactures a variety of cell designs and configurations for high reliability applications.  Please contact us for more information concerning our products. 

Performance Comparison of Energy Storage Technologies

A key advantage of this technology is the reversible nature of this process.  As a result, an electrochemical capacitor can be charged and discharged hundred of thousands of times in comparison to batteries, which can only withstand thousands of discharge cycles. At Ionix we are developing advanced materials that improve the performance of these emerging devices.  In addition to their unique combination of power and energy and their high cycle life there are a host of additional characteristics that make electrochemical capacitor attractive in a variety of applications.  These characteristics are outlined in the table below.

There are many applications that can benefit from the unique combination of high reliability, power, and energy provided by electrochemical capacitor technology. Several applications have drawn considerable attention. These applications include: regenerative braking in hybrid vehicles, cold engine starting, load leveling PEM fuel cells, ride-through backup power systems, and digital electronic devices. Each one of these applications represents a multi-billion dollar opportunity, if the technology can be successfully commercialized. 

Electrochemical Capacitor Development

Ionix is developing advanced technologies to improve and commercialize electrochemical capacitor technology.  Currently, electrochemical capacitors are relatively expensive, making it difficult for the technology to achieve widespread market penetration.  Ionix has active programs to improve operating voltage, power performance, and materials/manufacturing costs.  These programs have the potential of dramatically reducing the application cost of the technology.

Modeling of Electrochemical Capacitors

Mathematic models of electrochemical capacitors can serve as a powerful tool for application and development programs.  The following section will review models that have been developed to describe the electrical performance, physical processes, and thermal processes occurring in electrochemical capacitors.  Only a brief overview is given here, please contact Ionix if you require additional information.  

Models that describe electrical performance

A single capacitance and resistance model of an electrochemical capacitor can be used in many applications.  Electrochemical capacitors deviate from this simple model only in the initial phases of charge and discharge processes.  For applications where the application time is long in comparison to the internal RC time constant  a single capacitance and resistance model work well. Most commercial devices have a lumped RC time constant that ranges between 0.5 to 3 seconds at room temperature (growing to 2 to 12 seconds at –40 C).  If the application discharge time is long in comparison to this RC time constant, a single capacitance and resistance model provides adequate results. 

If the discharge time is short, transient effects will dominate the discharge profile and performance will be under predicted.  Some system designers use a ladder network of capacitors and resistors to more adequately describe the performance in these short time regimes.  Such a model is shown in below.  The values of capacitance and resistance can be fitted from impedance data taken at frequencies over the time range of interest, typically, 0.001 to 1000 Hz.  The figure below compares the experimental data and model fit for a 2500 farad electrochemical capacitor.  The model accurately predicts the performance of the device and can be used as a useful tool by application engineers to accurately describe the device over a wide frequency domain. 

Model that describes physical processes -- Distributed Capacitance and Resistance Model

Single capacitance and ladder network models are not useful in designing capacitors because they do not describe the physical processes occurring in the cell.  Several models have been developed that depict performance of the double layer charging mechanism.  Posey and Morozumi developed a porous electrode model of double layer capacitance.  The model considered double layer interactions in a porous electrode and the effect of ionic conductivity in solution ([i]).  Johnson and Newman extended this model to include the effects of distributed resistance throughout a porous electrode to describe a desalination process in dilute electrolytic solutions ([ii]). Farahmandi adapted this model to describe the performance of electrochemical capacitors, specifically describing the transient effects that occur due to charge distributed throughout the porous electrode ([iii]). The model was used to predict how voltage profiles, current distributions, and equivalent series resistance develops during the initial phases of the charge and discharge mechanism.  Dunn and Newman extended this model to optimize energy and power performance in electrochemical capacitor designs ([iv]).  The distributed capacitance and resistance model has advantage over lumped capacitance models and ladder network models in that it can be used as a design tool in optimizing electrochemical capacitors for specific applications.  

The distributed model considers the capacitance, ionic conductivity, and solid phase conductivity as evenly distributed throughout the porous electrode.  The figure below is a discrete approximation of the distributed model.  The figure models an electrochemical capacitor consisting of two porous electrodes that are isolated by a porous electronic separator. Capacitance is distributed evenly through each electrode along with ionic and conductor conductivities.  The separator material only conducts in the solution phase.  Contact resistance is added to describe the current collector and electrode interface.   

Discrete Approximation of Distributed Capacitance and Resistance Model.  

The continuous version of this model uses the following equations to describe capacitor performance.  Current flowing in the solid phase, i₁, and solution phase, i₂, follows ohm’s law.

                                                                                               [1]

                                                                                               [2]

where;

            s is the effective conductivity of the solid phase (ohm^-1•cm^-1);

            k is the effective conductivity of the solution phase (ohm^-1•cm^-1);

            x is the distance from the front face of the porous electrode. (i.e. the side facing the separator; cm).

As the double layer capacitance is charged at each point in the electrode a balance of charge occurs that results in the following mathematic relationship between current densities and potential in the solid and solution phases, f₁ and f₂:

                 =    =                                                                         [3]

where,

            a is the interfacial area (cm²/cm³);

            C is the interfacial capacitance (F/cm²).

Farahmandi derived an analytical solution to these equations for the case of galvanostatic charging and discharging of a capacitor cell ([iii]).  Figure 1 plots the current distributions in the solution and solid phases during a constant current charge for a case where the electrode conductivity is much greater than the ionic conductivity in the solution phase.  The figure shows only a single electrode. The x-axis is the distance into the electrode with zero being the face in contact with the separator.  An actual capacitor device would consist of two electrodes in series.  The plot of the second electrode would mirror the image of the first with x =0 being the point of symmetry.  At the separator interface all current is in the solution phase.  All current transfers to the solid phase before it leaves or enters the capacitor through the capacitor terminals.  Initially current transfers to the solid phase close to the separator interface because of the high conductivity in the solid phase.  Charging in this region cannot continue indefinitely because a voltage profile develops between the solid and liquid phases as the double layer is charged.   The developing voltage profile forces the transfer to occur deeper and deeper into the electrode structure.  Eventually, a linear profile develops where current is uniformly transferred from the solution phase to the solid phase across the electrode structure. Once the linear profile is achieved the transient characteristics of the capacitor performance will cease and the capacitor can be described with a single capacitance and resistance.  A time constant was derived from the solution that can be used to predict the time it takes for the linear profile to develop.  This parameter is as follows:

              =    

where  

       = 

d = electrode thickness (cm)

This parameter shows that the transient performance of the capacitor is a function of the volumetric capacitance, electrode thickness, and conductivities in the solid and solution phases. 

Figure 1.  The current distribution as a function of time in a porous electrode. The plots show the current distribution at three different times for the case where s >> k.  At times greater than 0.4•t the current distribution reaches a linear profile.  At this point the effective resistance is constant. 

The model was then used to quantify the ohmic power losses that occur during transient and steady state periods.  Two key resistances were identified, the first is an initial resistance that occurs at the start of current flow.  This resistance, R_o, is defined as follows:

The first term on the right is related to the porous electrode properties as previously defined.  The second term is the effective resistance through the porous separator.  This term is related to the thickness of the separator material, d_s, and the effective solution conductivity in the separator region, k_s. The initial resistance, R_o, can be thought of as related to a resistance that develops when the solution and solid phase conductivities are in parallel.   Initially, current flows in both phases in response to the applied potential; however, charge balance requires current in the solution phase to transferred to the solid phase as it charges the double layer.  As the linear current profile develops, the resistance changes to its steady state value.  This series resistance, R_¥, is referred to as the steady state resistance and is defined as follows:

It is interesting to note that if one of the conductivities dominates, the first term on the right hand side of Ro will be determined by that conductivity; however, R_¥, will be dominated by the lower conductivity.  This is why some devices will have a high peak power density but efficiency and power performance will drop as discharge continues due to the developing resistance in the lower conductivity phase.  

Figure 6. Development of steady state resistance as a function of dimensionless time and conductivity. The steady state resistance will develop most quickly for the case where the ionic conductivity is equal to the electronic conductivity.  For all cases the steady state resistance is essentially achieved at a dimensionless time of t/t = 0.4.

A distributed model can be used as an important tool for optimizing capacitor design for a specific application.  Capacitor design characteristics of electrode geometry, porosity, solution condictivity , etc. can be optimized to maximize performance for a specific application.  More model detail can be provided upon request.

Thermal Modeling

Ionix has also developed detailed thermal models of many capacitor designs.  Many repetitive, high power applications of electrochemical capacitors will results in internal heating.  This condition can results in reduced cell life or even safety concerns.  Although it will not be detailed in this overview, Ionix has the capability to accurately predict internal heating in electrochemical capacitors. The following diagram is of the maximum temperature rise that occurs within a 2500 farad capacitor during a series of high current pulses that occur over a twelve minute period followed by a 90 minute rest.  The results showed a maximum 8 C temperature rise within the capacitor cell.  T

Battery and Capacitor Hybrid System Modeling

In many situations electrochemical capacitors are used in parallel with battery systems.  Such applications include cold engine starting and consumer electronics applications.   

In a cold engine starting application (detailed in the following section), a battery and capacitor bank are designed to act in unison to maximize starting power performance at –40 C while maximizing energy delivery by the battery system for low power applications.  The following section will outline a hybrid system model that can be used to maximize capacitor and battery performance.

R. A. Dougal and Ralph E. White developed a mathematical model that describes a battery---capacitor hybrid system that is used in high frequency pulse applications ([v]).  It has been noted that electrochemical capacitors can dramatically extend the life of alkaline batteries used in applications that require repetitive high current pulses.  Such applications include GSM cell phone transmissions, digital cameras, and two-way paging systems. In these applications a stand-alone system rapidly fails because the series resistance in alkaline batteries increases as the cell is discharged.  High current pulses cause a large resistance drop in the cells, which causes the voltage to drop below the application cutoff value in a relatively short period of time.  Electrochemical Capacitors are effective in reducing the battery peak current in these applications and thereby are able to extend battery life. 

Figure 4.  Idealized model of hybrid capacitor-battery starting system

The equations below represent the current response in the capacitor and battery that results from a constant current load.  Equations can also be developed for the load voltage and power.  These are not included for the sake of brevity.

              =            where,   =      and    =   

System Applications of Electrochemical Capacitors

Ionix is focusing on several key applications of electrochemical capacitors.  These applications include cold engine starting in large-vehicles and back-up energy storage systems.

Electrochemical Capacitors for Cold Engine Starting

The figure above shows how diesel engine starting requirements and battery performance changes as temperature is decreased.   A 250% increase in cranking power is needed at –20 C.  This increase in cranking power requirements is contrasted with a 55% drop in power delivery capability of a typical lead-acid battery.  The drop in battery performance combined with the increased power requirements demonstrates why it is difficult for battery systems to start diesel engines at low temperature.  

Electrochemical capacitors are attractive for this application because of their superior low temperature power and energy performance.  Capacitance performance is essentially constant over the temperature range from –40 C to +85.  This gives the capacitor a significant advantage over battery systems.  

Manually Driven Backup Energy System

Ionix is developing a Manually-Driven Electric Power Source that generates power to run emergency equipment in times of power outages.  The system generates power from a manual pedal system that is coupled to an electric generator. A diagram below shows the basic configuration of the device.  A user controllable DC converter is connected to the generator.  The operator is able to set pedal resistance to match personal taste and maximize generator efficiency.  A bi-directional DC converter is added to the system to control power into the energy storage so power can be immediately supplied to the critical loads.  The added DC converter is user selectable and micro-controlled.  The converter stage controls the output to a constant DC voltage.  An electrochemical capacitor bank is coupled to the output of the DC converter stage through a bi-directional converter.   

Manually Driven Backup Energy System

Electrochemical capacitors used in manually driven backup energy system. 

[v]   R. A. Dougal and Ralph E. White, IEEE Transactions on Componetns and Packaging Technologies, Vol 25, No. 1, March 2002. 

Copyright © 2006 Ionix Power Systems, LLC.
Last modified: January 02, 2006