The Ragone Plot

From experimental measurements it was found that there was a fairly good linear relation between the SC capacitance and current, the slope being dependent on the electrode material and electrolyte. If the dependence is known, it can be used to make the Ragone plot calculations more accurate. Therefore, the following method was employed in our evaluations. 

At matched impedance, half of the energy is lost inside the capacitor in its internal resistance. This occurrence is represented by the position of the last point on the right in the Ragone plot. From... 

The overall performance of our V2O5-based supercapacitors is summarized in the Ragone plot describing the relation between energy density and power density (Fig. 5.15a) [51]. The highest obtained energy density of nontemplated vanadia supercapacitors is 1 Wh kg at a power density of 50 W kg , which drops to one-half at a power density of 0.4 kW kg . Such low values arise from the limited ion diffusion... 

The main difference between batteries and supercapacitors becomes clear in the Ragone plot in Figure 36.8. They mainly differ in their energy density and power density. Whereas batteries could have high energy density, and also high power density in the case of hthium ion batteries, supercapacitors only have high power density. 

To obtain the relationship shown in the Ragone plot, assuming the external load of a supercapacitor cell is R, the entire system is shown schematically in Figure 2.21. It is assumed that the leakage current does not exist r °°) in mathematical treatment. 

The Ragone plot also shows that although ES devices have lower energy densities than batteries and fuel cells, their power densities are 10 times greater than those of batteries and fuel cells. Several other advantages of the ES are worthy of mention ... 

Generally, engineers use the Ragone plot [RAG 68] to present the performances of electricity storage devices. This plot traces the specific energy of the element as a function of its specific power, both on a log/log scale. Of the six relevant criteria mentioned above, this method considers only the first two, which are essentially linked to the initial performances of the elements and the technological aspects. 

To trace the Ragone plot in a generic case, let us take the example given in Figure 6.4. In this scheme, the energy storage device feeds a charge with a constant (active) power P>0. 

Figure 6.4. Generic circuit associated with the tracing of the Ragone plot...

We are interested here in tracing the Ragone plot for an ideal battery (meaning no inductive effect is taken into account, no frequency-dependency of the values, no intrinsic nonlinearity of the component). The battery is assumed to preserrt a charge Q0 at the initial time and an internal resistance of value R. It is connected to a charge/discharge system with constant power P (see the diagram below). 

Trace the Ragone plot for this ideal battery, assuming there to be no leakage resistance Rf = > on the diagram above). 

In order to identify the appropriate valne of/, we focns on the case where P 0. In this case, two possibilities can be envisaged /+ - Uq /R (which in practice corresponds to a short-circnited operation) and / 0 (which in practice corresponds to an open-circnit operation). Clearly, in the context of tracing the Ragone plot, only the second scenario here is of interest to ns, so / = /. ... 

Draw the Ragone plot for an ideal capacitor, whose capacity C is supposed to be constant and whose only imperfection is an internal series resistance R. The initial voltage at the edges of the capacity is notated as Uqq. The ensemble is... 

In view of the technical specifications, this power needs to be continuously furnished for at least 1 hour therefore, it has to be supplied by a permanent energy source (here the fuel-cell system). If we refer to the Ragone plot shown in Figure 6.5, we note that a fuel-cell system presents a specific power of around 00 Wlkg], which gives us ... 

Thus, in terms of power, the maximum power demand of the supercapacitors will therefore be 22120 [IT]. Given the Ragone plot shown in Figure 6.5, if we... 

The Ragone plot shown in Fig. 7.13 obtained from the high-rate discharge curves is totally different from the ordinary one (Fig. 7.1), because it contains the nanosize effects in nanociystalline LiCo02. The Ragone plot clearly suggests that the energy density... 

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