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EPRI Proprietary Licensed Material the capacitor, the positive electrode voltage increases and concurrently the negative electrode voltage decreases, both at approximately the same rate. Provided the rest potential (zero charge) of the electrode material in the electrolyte is midway between its stability limits, both reach their potential limits at the same state of charge. This allows the full operating voltage window to be realized. In practical implementations, the type I capacitors usually do not have a rest potential in the middle of the voltage window and do not have exactly the same capacitance in each electrodes. This reduces the maximum operating voltage in some cases from 1.2 V to below 1 V. For type II capacitors, with organic electrolytes, voltages are higher and the window is increased. Instead of 0.8V operation as shown in the figure, this voltage could be perhaps 2.3 to 2.7 V. Also, in practical products the non-aqueous symmetric designs make up for Symmetric Aqueous C + C - C + = C - = C o C total = 1 / 2 C o + - operates at ~ 0.8 V = V o E = 1 / 2 ( 1 / 2 C o )V 2 o E = 1 / 4 C o V 2 o up to 16 times more Upper Limit + - Asymmetric Aqueous C + C - =2 C o C + >> C - E = 4C o V 2 o V + C total = C - = 2C o operates at ~ 1.6 V = 2V o E = 1 / 2 (2C o )(2V o ) 2 V + - Lower Limit - Q Q Upper Limit Lower Limit some of the difference in capacitance by choice of electrode material. Figure 33 Comparison of type I and type III electrochemical capacitor energy calculation 4 Type IV electrochemical capacitors operate in the same fashion as type III devices except the operating voltage can be higher due to the use of an organic electrolyte. Some type IV capacitors have been reported to operate at 4.0 V or higher in contrast to the 2.7 V value for the highest type II products. Consequently, the V 2 dependence of energy on the operating voltage represents at least a two-fold increase in energy density. The net 4 The figure is intended to illustrate a fundamental difference between the symmetric and asymmetric capacitor designs. Specific energy in practical products also depends on specifics of the electrode and electrolyte materials, operating voltage per cell, device design life, and type of packaging. Electrochemical Capacitors 62
EPRI Proprietary Licensed Material benefit of type IV technology over type II technology, both having non-aqueous electrolytes, is a factor of eight because of these voltage and capacitance effects. The graph, bottom right of Figure 4, shows voltage as a function of charge for type III and type IV devices. As shown, the positive electrode voltage is relatively flat, independent of state of charge, and the negative electrode voltage decreases towards some lower limit. Of note is the gap at zero state of charge. It indicates that the uncharged capacitor will have a voltage on it. Figure 4 also depicts the reason why high cycle life can be obtained from type III and IV capacitors even with the use of a battery–like electrode. As shown, the relative change in charge state of the positive electrode is very small due to the asymmetry in electrode capacity. The reported capacity ratio of the electrodes for this type capacitor is at least 3:1 and preferably 10:1. This means that during a discharge cycle the positive electrode only discharges 10% of its capacity while the negative electrode is fully discharged. Consequently, high cycle life is available from such devices due to the low depth of discharge by their battery-like electrode. Comparison with Ideal RC Behavior It is useful to examine the power/energy relationship when discharging a series-RC circuit. The energy delivered to a load, E del , at a specified average power P ave , can be derived for a series-RC circuit under various discharge conditions. For a constant current discharge from V 0 to V 0 /2, the delivered energy to total energy ratio available in that voltage window can be calculated. The equation is: Edel Etot = 3 8 + 3 8 8 Pave 1− 9 P max − 1 2 Pave P max This relationship is plotted as a dotted line in Figure 34. It applies to any capacitor of any type, provided it can be represented by a series-RC circuit. At low power levels, the value of the delivered energy approaches 0.75 E tot , the total energy stored in the voltage window. As the power level increases to its maximum value, Pave/P max =1, E del approaches 0, as expected for a matched load. An important trend to note is that the delivered energy decreases monotonically as the power level rises. For example, Figure 34 shows that operating at 0.5 of the maximum power point will yield an energy delivery ratio of 0.4, about one-half the total energy available in the operating voltage window. Electrochemical Capacitors 63
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