# Study of System Integral Energy Efficiency of a Hybrid Pneumatic Power System
## 4 Discussion
### HPPS Efficiency  
From Equation (13), the integral efficiency can be calculated as:  
\[\eta_{t-HPPS}W=\mathrm{Q}_{3}\eta\ \Leftrightarrow\ \eta_{t-HPPS}W=(\eta_{t}\eta_{C}W+\eta_{exhaus }W)\eta,\]  
where, the best working area of HPPS (Figure 12), \(\eta\) (air motor efficiency) is 0.719; \(\eta_{t}\) (ICE efficiency) is 0.28; \(\eta_{C}\) (compressor efficiency) is 0.7. According to Ref. [28], the exhaust heat loss can be determined to be approximately 45% of the total net power. Substitute the values of \(\eta\), \(\eta_{t}\), \(\eta_{C}\), and \(\eta_{exhaus}\) in Equation (13):  
\[\eta_{t-HPPS}=(\eta_{t}\eta_{C}+\eta_{exhaus})\eta=(0.28*0.7+0.45)*0.72\approx 0.465\]  
Based on the experimental results of the ICE efficiency in Figure 5, ICE fuel consumption in Figure 4, compressor efficiency in Figure 6, air motor efficiency in Figure 9, and Ref. [24], we determined the integral efficiency of the HPPS. The system was run at five different ICE speeds (3000, 3250, 3600, 3800, and 4250 rpm). When the ICE is running, compressed air is created and charged into the storage air tank. In case of the cross-section area set at the best position [24], the control electric valve was used to control the pressure and flow rate of the air tank outlet. Then, this air mixes with the exhaust from the ICE. For different ICE speeds, the HPPS will have different stable operations for the air motor. Based on this, the input and output powers of the HPPS were measured, which are summarized in Table 1.  
By applying Equation (14), we obtained the efficiency of the HPPS. The experimental result of the HPPS integral efficiency is shown in Figure 13.  
Figure 12: Relationship between the ICE speed, fuel consumption, ICE efficiency, and compressor efficiency. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ICE Speed (rpm)** & **Number of Tests** & \begin{tabular}{c} **Air Motor Speed** \\ **(rpm)** \\ \end{tabular} & \
\begin{tabular}{c} **Air Motor Torque** \\ **(Nm)** \\ \end{tabular} &
\begin{tabular}{c} **Fuel Consumption** \\ **of ICE (mL/min)** \\ \end{tabular} \\ \hline \multirow{4}{*}{3000} & \(1\) & 1375 & 9.25 & 12.46 \\ \cline{2-5}  & 2 & 1300 & 9.20 & 12.41 \\ \cline{2-5}  & 3 & 1305 & 9.00 & 12.72 \\ \cline{2-5}  & 4 & 1351 & 9.30 & 12.15 \\ \cline{2-5}  & 5 & 1328 & 9.22 & 12.35 \\ \hline \multirow{4}{*}{3250} & \(1\) & 1545 & 11.00 & 13.01 \\ \cline{2-5}  & 2 & 1573 & 10.85 & 12.86 \\ \cline{2-5}  & 3 & 1515 & 10.90 & 12.96 \\ \cline{2-5}  & 4 & 1525 & 11.01 & 13.25 \\ \cline{2-5}  & 5 & 1539 & 11.10 & 13.15 \\ \hline \multirow{4}{*}{3600} & \(1\) & 1765 & 16.25 & 14.63 \\ \cline{2-5}  & 2 & 1800 & 16.10 & 14.61 \\ \cline{2-5}  & 3 & 1805 & 16.15 & 14.51 \\ \cline{2-5}  & 4 & 1750 & 16.30 & 14.86 \\ \cline{2-5}  & 5 & 1755 & 16.31 & 14.76 \\ \hline \multirow{4}{*}{3800} & \(1\) & 1885 & 16.75 & 14.79 \\ \cline{2-5}  & 2 & 1851 & 16.35 & 15.00 \\ \cline{2-5}  & 3 & 1825 & 16.80 & 14.50 \\ \cline{2-5}  & 4 & 1856 & 16.55 & 15.00 \\ \cline{2-5}  & 5 & 1871 & 16.50 & 14.90 \\ \hline \multirow{4}{*}{4250} & \(1\) & 1975 & 17.00 & 18.10 \\ \cline{2-5}  & 2 & 2000 & 16.85 & 18.36 \\ \cline{2-5}  & 3 & 2001 & 17.01 & 17.95 \\ \cline{2-5}  & 4 & 1951 & 17.20 & 17.87 \\ \cline{2-5}  & 5 & 1985 & 16.80 & 18.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Input and output specifications of HPPS. Figure 13: HPPS integral efficiency. Figure 13 depicts that the HPPS integral efficiency was different for different ICE speeds. As can be seen in Figure 13, low speeds for the ICE were 3000 and 3250 rpm. The system's integral efficiency was about 0.215 at 3000 rpm, and about 0.282 at 3250 rpm. At this position, based on Figures 5 and 6, the ICE efficiency was about 0.254 at 3000 rpm, and 0.26 at 3250 rpm. Additionally, the compressor efficiency was about 0.602 at 3000 rpm, and about 0.62 at 3250 rpm. Therefore, the compressed air in the tank has a much lower efficiency in comparison with the ICE efficiency.