## 5 Results and Analysis
### Performance of the Sensorless BLDCM Drive Control  
Figures 13-15 show the steady-state performance of the BLDCM drive across three different speed ranges: low (100 rpm), medium (500 rpm), and high (above 1000 rpm). It is evident from these figures that the sensorless operation of the drive works effectively across a wide speed range without any delay. The rotor position (\(\theta\)), terminal voltage of the motor (\(V_{ab}\)), stator phase current (\(i_{a}\)), and speed (\(N\)) are illustrated in these figures. Smooth motor currents are obtained, free of oscillations and ripple. The estimated rotor position shows a satisfactory correlation with the actual rotor position. Using the obtained position information, the estimated Hall pulses (\(H^{*}\)\({}_{a}\), \(H^{*}\)\({}_{b}\), \(H^{*}\)\({}_{c}\)) can be derived. These virtual Hall signals play a crucial role in determining the switching sequences of the VSI. The spikes in line voltages in Figures 13-15 are caused by inductive voltage build-up due to the sudden change in current in the motor windings, which are inductive in nature. The implemented QPLL, with its inherent filtering capability, filters out all high-order harmonics caused by distorted voltage and current waveforms. The estimated angular positions remain unperturbed throughout all speed ranges. Figure 16 depicts both the starting performance and the steady-state behavior of the drive. Figure 17 illustrates the estimated Hall pulses (\(H_{a}\)\") and the reference current signal (\(i_{a}\)\") for phase \"a\" at 400 rpm. The reference current is fed to the current controller to  
Figure 12: Experimental MPPT performance [(a) 1000 W/m\({}^{2}\) irradiance; (b) 500 W/m\({}^{2}\) irradiance]. generate the gate pulses. The filtered back-EMF from the observer in the \(\alpha\beta\) domain (\(E_{n}\)) is also shown in Figure 17.  
Figure 14: Steady-state performance of the BLDCM drive at 500 rpm. Time per division: 4 ms.  
Figure 13: Steady-state performance of the BLDCM drive at 100 rpm. Time per division: 10 ms.  
Figure 15: Steady-state performance of the BLDCM drive at 1000 rpm. Time per division: 4 ms. The dynamic performance of the sensorless algorithm-based BLDCM drive, incorporating speed control, is shown in Figure 18. This figure illustrates the actual and reference speeds (\(N^{*}\) and \(N\)), motor current for phase \"a\" (\(i_{a}\)) and rotor angular position (\(\theta\)). The motor is tracking a reference speed of 800 rpm, and the speed then dips to 200 rpm. The system operates with a 10 Nm load torque. The actual stator current is shown with minimal ripple, controlled by the current controller. The rotor position remains constant throughout the operation, ensuring that the drive is stable during speed dynamics across a wide speed range. Figure 19 demonstrates the regenerative braking performance. As seen in this figure, the drive is in regenerative braking mode. Due to the incorporated regenerative braking control, the battery is charged during braking. Negative battery current (\(i_{bat}<0\)) and torque (\(T^{*}<0\)) confirm that the drive is in regenerative mode. Drive performance is recorded at 500 rpm and a 5 Nm load torque. With a torque of 5 Nm, the battery charges with an average current of 7 A, while the peak current is recorded as 10 A. As the load torque increases, the charging current rises, leading to a higher amount of regenerative energy being recovered. Figure 16: Dynamic performance of the BLDCM drive: motor starting. Time per division: 2 s.  
Figure 17: Dynamic performance of the BLDCM drive: observer performance during sensorless control. Time per division: 10 ms. The evaluation of the regenerative braking motor efficiency, based on the system's ability to recover part of the motor's kinetic energy spent during braking and store that energy in the battery [42], led to a peak efficiency of 30.60%.