**7. Conclusions**

Two test benches were designed and built to test two different energy storage systems: a hydraulic accumulator and an ultracapacitor with identical energy capacities. The energy efficiency under the test conditions for the hydraulic accumulator was 87.7%, and the energy efficiency of the ultracapacitor was 78.7%.

The efficiency map from this study can be used to determine a control strategy for a regenerative system with hydraulic accumulators. This efficiency map can be replicated for different hydraulic pumps by using numerical models for a pump. In addition, the analysis of the efficiency map for a piston pump shows that a hydraulic accumulator would be more efficient if a piston pump is used instead of a gear pump.

This study also shows that energy segments of the radar plot were dominated by the ultracapacitor, while the power segments were dominated by the hydraulic accumulator. It is interesting to note that there were segments in the radar plot that were not covered by either of the three energy storage systems. In other words, none of the systems showed a good score in cost/power and energy/volume. This means that energy storage systems with high energy density can provide high power but at a high cost. Moreover, there was no system with a high score in power/volume and cost/energy, which means that the energy storage systems with good power density can be used to store energy but at a high cost.

The higher energy efficiency in the hydraulic accumulator and the better power density compared with ultracapacitors could be determining factors in choosing a hydraulic system over an electric system for a specific application, where there is a need to rapidly charge or discharge energy storage devices, such as in the case of regenerative breaking.

**Author Contributions:** Conceptualization, J.L.-Q., J.G.-B. and M.K.; methodology, J.L.-Q., J.G.-B. and M.K.; software, J.L.-Q.; validation, J.L.-Q., B.N., M.K., A.G.-M., and J.G.-B.; formal analysis, J.L.-Q., and J.G.-B.; investigation, J.L.-Q., M.K., A.G.-M., and J.G.-B.; resources, B.N., and J.G.-B.; data curation, J.L.-Q.; writing—original draft preparation, J.L.-Q.; writing—review and editing, J.L.-Q., B.N., M.K., A.G.-M., and J.G.-B.; visualization, J.L.-Q., B.N., M.K., A.G.-M., and J.G.-B.; supervision, B.N., M.K., A.G.-M., and J.G.-B.; project administration, B.N., and J.G.-B.; funding acquisition, B.N., and J.G.-B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Purdue Polytechnic, office of the vice dean of research, and the school of Engineering Technology at Purdue University.

**Acknowledgments:** Special thanks for Sun Hydraulics for providing testing components.

**Conflicts of Interest:** The authors declare no conflict of interest.
