**6. Comparative Evaluation**

The results for energy density and power density are presented in Table 13. Three energy systems were compared: a battery, which is the principal source of energy, the ultracapacitor, and the hydraulic accumulator.


**Table 13.** Energy density and power density.

The radar plot presented in Figure 29 better illustrates these results. The radar plot shows the results in a scale from 0 to 10 for the three energy storage systems used in this study. The "*Score*" value for each component of the radar plot was determined using this equation:

$$Score = \frac{System\ Value}{Best\ Value} \cdot 10\tag{14}$$

In Equation (14), the "*System Value*" is the value of each system: battery, ultracapacitor, or accumulator, and "*Best Value*" is the best value among the three energy storage systems. This "*Best Value*" depends on the specific characteristic to be studied. For instance, in energy/volume, the "*Best Value*" would be the highest value among the three systems, but in cost/power, the "*Best Value*" will be lowest.

**Figure 29.** Radar plot comparing three energy storage systems.

From the radar plot, it is possible to see that the energy side of the plot is mostly covered by the battery. Neither of the other two systems could compete against the battery in terms of energy storage. On the other hand, the hydraulic accumulator dominates the power part of the plot. This means that the hydraulic accumulator is suited for high power applications. A comparison between the hydraulic accumulator and the ultracapacitor is shown in Figure 30.

**Figure 30.** Radar plot comparing ultracapacitors and hydraulic accumulators.

From Figure 29, it is possible to see that the hydraulic accumulator is more suitable than the ultracapacitors in the power segment of the plot, while the ultracapacitor is better in the energy segment of the plot. However, the battery was better than these two systems for storing energy. It is important to note that the energy efficiency for the ultracapacitor was around 78.7%, and the energy efficiency of the hydraulic accumulator was 87.7%. This improvement in energy efficiency and the better power density compared with ultracapacitors could be a determining factor in choosing a hydraulic system over an electric system for a specific application when needing to rapidly charge or discharge energy storage devices, such as in the case for regenerative breaking.

The net cost of each system is presented in Table 14, but the information of this table is not enough to make an effective cost analysis of the energy storage systems considered in this study. It is necessary to consider the results presented in Table 14 and in the radar plots of Figures 29 and 30.



From the comparative results presented in the radar plots of Figures 29 and 30, it is possible to see that regarding cost/energy ratio, the battery was far better than ultracapacitors and hydraulic accumulators. The cost per unit of energy in the battery was 0.45 USD/Wh, the cost per unit of energy in the ultracapacitors was 138.7 USD/Wh, and the cost per unit of energy in the hydraulic accumulator was 404.7 USD/Wh. Regarding the cost per unit of power, the best system was the hydraulic accumulator with 75 USD/kW, the ultracapacitor had a cost/power ratio of 217 USD/kW, and the battery had a cost/power ratio of 270.8 USD. These results demonstrate the potential of hydraulic accumulators for applications that require a high power density. Nevertheless, it is necessary to consider how expensive an accumulator could be if it is required to store energy for a large period, because its cost per unit of energy is not the best.
