# Investigation of Regenerative Braking Performance of Brushless Direct Current Machine Drive System
## 4 Experimental Study and Results
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Phase-to-phase resistance (\(\Omega\)) & 2.24 \\ Diode voltage drop (V) & 1.2 \\ MOSFET on–resistance (\(\Omega\)) & 0.024 \\ Diode on–resistance (\(\Omega\)) & 0.05 \\ Maximum duty ratio & 0.78 \\ Maximum battery voltage (V) & 56.4 \\ Terminal back-electromotive force (EMF) at starting (V) & 48.4749 \\ Initial internal resistance of a battery (\(\Omega\)) & 0.909 (at 25 \({}^{\circ}\)C) \\ \hline \end{tabular}
\end{table} 
Table 2: Braking operation parameters. Figure 5: Experimental measurement results of temperature vs. internal resistance variation. Figure 8: Experimental results for battery voltage and charging current of Case-3 at \(T_{3}\). Figure 6: Experimental results for battery voltage and charging current of Case-1 at \(T_{1}\). Figure 7: Experimental results for battery voltage and charging current of Case-2 at \(T_{2}\). The most critical indication of the experiments is that the regenerative braking performance decreases dramatically if the calculated duty ratio remains unchanged despite varying temperatures. Thus, in order to recover the same amount of energy, 0.78 should be recalculated as 0.792 for 30 \({}^{\circ}\)C and 0.81 for 35 \({}^{\circ}\)C.  
The electrical measurements are made at the battery terminals, so only the regenerated power and energy values are calculated, the charging efficiency which can be easily calculated by means of the non-ideal battery model is excluded. When all non-ideal variables and the battery temperatures in the energy recovery calculations are taken into consideration, 2.9 kWs of energy is regained as a result of the selected specific duty ratio. The recovered power calculation is performed by capturing the current and voltage variations in the dc-link during the active regenerative braking period. By integrating the product of the current and voltage values on the dc-link, the regenerated energy value is calculated. In the no-load deceleration tests, the maximum recovered energy is 3.2 kWs. In Case-1, it can be seen that energy recovery is achieved with a high performance with a ratio of 2.9 kWs/3.2 kWs. Contrary to this, the energy recovery measurements have shown that in Case-2 and Case-3, 2.65 kWs and 2.47 kWs of energy obtained for 30 \({}^{\circ}\)C and 35 \({}^{\circ}\)C, respectively. Filtered voltage waveforms obtained during regenerative braking for Case-1, Case-2, and Case-3 are presented in Figure 9. Instantaneous battery voltage risings are presented for the same duty ratio (0.78). When the same duty ratio (0.78) is applied, peak value variations of voltages are presented for \(T_{1}\), \(T_{2}\), and \(T_{3}\) temperatures for different scenarios. In Figure 10, the conversion ratio (\(V_{d}/E_{L}\)) variation is shown for \(T_{1}\), \(T_{2}\), and \(T_{3}\). The machine deceleration times, which are shown in Figure 11, have been recorded as 128 s at temperature \(T_{2}\), and as 137 s at temperature \(T_{3}\). The performance expected from braking can be measured by the duration of the deceleration time. It is also possible to see how much braking power the vehicle requires to accomplish the expected deceleration time. When all non-ideal variables and battery temperature variation are taken into account, the regained energy amount is about 8.73% and the value of the calculated duty ratio in the control cycle is revealed.