**4. Results for the Hydraulic Accumulator**

Instantaneous power in the accumulator could be calculated as the product of pressure and flow rate. These variables were measured during charging and discharging. The results for energy calculation and energy efficiency for the hydraulic accumulator are shown in Table 10. The energy cycle efficiency is the ratio between the total energy released while discharging and the total energy stored while charging.

**Table 10.** Results for energy calculation in the hydraulic accumulator.


The efficiency of the hydraulic system in transferring power from the shaft of the hydraulic pump to the hydraulic accumulator is shown in Table 10. For vehicular application, the kinetic energy of the wheels would move the shaft of a hydraulic pump, which would move the fluid to the hydraulic accumulator in order to absorb the kinetic energy of the vehicle. In the test bench, the wheel was replaced by an electric system. In previous studies, it has been demonstrated that using hydraulic accumulators in vehicle drivetrains can have a positive impact in the efficiency of a vehicle. Wang et al. [19] demonstrated the advantages of a simulated drivetrain for a light passenger

vehicle, where, although the energy used for the simulated drive cycle was better using the pure electric drivetrain, the acceleration performance was better for the hydraulic drivetrain thanks to its higher power density. Moreover, Hui et al. [18] studied the effect of using a hydraulic accumulator for extending the state of charge of a battery when hybridizing an electric drivetrain with a hydraulic regeneration with positive results due to the high efficiency of hydraulic accumulators. The power in the hydraulic pump shaft was calculated as the product of the shaft torque and the rotational speed. The torque was estimated based on the pressure at outlet of the pump. The pressure and the torque were correlated according to the next expression.

$$T = \frac{D\Delta p}{\eta\_{\text{nr}}}\tag{13}$$

In Equation (13), η*<sup>m</sup>* is the mechanical efficiency of the pump. The efficiency is a function of the pressure and the flow rate in the system, so the efficiency changes throughout the experiment. The pressure and the flow rate were measured, and with the datasheets provided by the manufacturer of the pump, it was possible to estimate the efficiency and the torque at any operating conditions. Thus, at any time in the experiment, the input power in the hydraulic pump could be estimated, as could the power going to the accumulator. Then, the instantaneous efficiency of the system could be obtained. At any instant of the experiment, the flow rate and the pressure could be measured. At the same instant, the power input could be measured. With this information, it was possible to create an efficiency map for the hydraulic accumulator, which is shown in Figure 14. The same map without the data points is shown in Figure 15. The map between datapoints was estimated with linear interpolation using the Matlab function griddata [21].

**Figure 14.** Instantaneous efficiency of the hydraulic accumulator with data points.

**Figure 15.** Instantaneous efficiency of the hydraulic accumulator using a gear pump.

The map presented in Figures 14 and 15 is important in identifying operating conditions that would be optimal for a system like the one proposed in this study. According to these plots, the highest efficiency was around 80% and was obtained for flow rates of approximately 1 gpm and pressures of approximately 1800 psi.

The current and voltage of the electric system were also measured during the experiment. A similar map of efficiency could be made for the conversion of electric power to hydraulic power. The map is shown in Figure 16.

**Figure 16.** Instantaneous efficiency for conversion of electric power to hydraulic power.

The maximum efficiency was around 50%, relatively low because this was the efficiency of converting the electric power taken from the battery to hydraulic power in the accumulator. The electric power from the battery had to be converted into AC power in the inverter. After that, the AC power was converted into mechanical power by the electric motor. This mechanical power was used to move the shaft of the hydraulic pump, and the hydraulic pump moved the fluid from the reservoir to the accumulator through the hydraulic system, which had some power losses due to friction.

Another important aspect to consider was that the current of the battery was very high during the charging process, which was not the most efficient way to use the battery. The results for the battery for one of the charging experiments are shown in Figure 17.

**Figure 17.** Experimental results for current, voltage, power, and load.

The maximum current during this experiment was 66 A, which was much higher than the continuous current recommended for the efficient operation of this battery, according to the technical data presented in Table 4. The efficiency results for a system with a model of a piston pump were estimated. The model of the piston pump was made by using commercially available datasheets of different piston pumps and then estimated with interpolation for a piston pump with a volumetric displacement of 0.73 *in*3/*rev*, which was 11.9 *cc*/*rev*. The results of the numerical estimation are shown in Figure 18.

**Figure 18.** Instantaneous efficiency of the hydraulic accumulator using a piston pump (estimated).

The estimated results of Figure 16 show that the instantaneous efficiency of the system using a model of a piston pump could be improved, mostly because axial piston pumps had higher efficiencies. The results for the efficiency including the electric motor are shown in Figures 19 and 20. These figures show the efficiency of conversion of electric power to mechanical power in the electric system using a gear pump (experimental) and a piston pump (estimated).

**Figure 19.** Efficiency of the electric system in the charging process using a gear pump.

**Figure 20.** Efficiency of the electric system in the charging process using a piston pump (estimated).

From Figures 19 and 20, it can be observed that the electric system worked better when using a gear pump. The difference in the results was due to the input torque needed to turn the shaft of the hydraulic pump, which in this case is lower for the gear pump than for the piston pump used. The overall efficiency of the system was highly dependent on pump efficiency.

### **5. Results for the Ultracapacitors**

The tests in the ultracapacitor test bench were made by changing the number of boards connected and the resistance used in the circuit. For each of the six possible board configurations, five different values of resistance were used. Starting with one board of six ultracapacitors, the charge and discharge tests were performed five times, and each time, the resistance selected was different. In total, thirty experiments were conducted for charging and thirty experiments for discharging. The results during charge and discharge cycles are presented below.

From Figure 21, it can be seen that the maximum voltage level of the system was reached faster when fewer boards were used—that is, when fewer ultracapacitors were energized. In Figures 21 and 22, each line represents one experiment for one value of resistance.

**Figure 21.** Voltage while charging according to the number of boards connected.

**Figure 22.** Power while charging according to the number of boards connected.

Now the same results are presented, but they are presented according to the number of the test (Figures 23 and 24). Test number 1 had the highest value of resistance, and test number 5 had the lowest value of resistance. The individual lines represent the number of boards connected in the electric system. The time to reach maximum voltage value was lower at a lower resistance. The value of the resistance used in each test is presented in Table 11.

**Table 11.** Resistance value for the tests.

**Figure 23.** Voltage while charging according to the value of resistance.

**Figure 24.** Power while charging according to the value of resistance.

A discharging experiment was conducted for each charging experiment. The results according to the number of boards are presented on Figures 25 and 26, and the results according the number of the test are presented in Figures 27 and 28.

**Figure 25.** Voltage while discharging according to the number of boards connected.

**Figure 26.** Power while discharging according to the number of boards connected.

**Figure 27.** Voltage while discharging according to the number of the test.

**Figure 28.** Power while discharging grouped according to the number of the test.

Using results presented in Figures 21–28, it was possible calculate the energy stored in the ultracapacitors and the efficiency. The results for energy calculations in the ultracapacitors are presented in Table 12.


**Table 12.** Results for energy calculation in the ultracapacitors.
