# Rotor Position Alignment of FSTPI Based PMSM Drive Using Low Frequency Signal Injection
## 5 Implementation and Experimental Results
With the proposed scheme, LF signal allows fluctuation on the DC-link offset voltage, as shown in Figure 9 enabling current flowing through the center tap connected to phase \(a\) which results in proper zero rotor angle alignment. The amplitude of the fluctuated DC-link voltages matches with the \(k\) value that is theoretically calculated in Equation (10). The frequency of oscillated DC-link voltages equals to the injected LF signal frequency. Steady-state phase \(a\) current waveform is given in Figure 6.0 It is seen that no low frequency fluctuations are reported on the phase current. This will not cause mechanical oscillation in the motor when the rotor is locked with the zero angle. When the rotor is aligned to the proper zero position, the speed of the rotor is dropped to zero as well at the same time with the position, as shown in Figure 6.1  
The sensitivity analysis based on the input applied voltage amplitude \(V_{LF}\) and the injected signal frequency \(f_{LF}\) versus the time duration of the alignment are depicted in the Figure 6.2 It is observed in the sensitivity analysis that when the \(V/f\) ratios is around 0.005, the faster alignment is achieved. The motor current increases when the input voltage amplitude is selected higher than 0.25 pu which is selected to be the optimum voltage amplitude. If the inertia and/or load of the system are higher than expected, a proper offset can be added as a bias to the injected signal to achieve zero angle alignment. Since the application of this method is only used for the initial alignment procedure, it will only run for a few seconds. As can be seen in Table 3 that higher \(V_{LF}\) values with proper injected frequency (close to the motor nominal operating frequency) considering the \(V/f\) ratio generate more \(V_{C}(t)\) at the DC-link and the alignment time is reduced. The optimum \(V_{LF}\) amplitude is selected to be 25% of the nominal voltage at 50 Hz (nominal operating frequency of the motor). The proposed zero angle rotor position alignment method at start-up could be used in applications such as centrifugal pump, fan and blower where initially light load or no-load occur including permanent magnet synchronous generators that are mounted on small scale wind turbines. Since the basis of the proposed method is an open-loop, alignment time depends on the system inertia, applied voltage, and the frequency of the injected signal. After the alignment procedure is completed, switching to the closed-loop control algorithm is enabled which drives the four-switch PMSM system. If the desired zero rotor position has not been achieved while the speed is not close to zero for a certain amount of time, the applied frequency is lowered properly to speed up the alignment procedure. \begin{table}
\begin{tabular}{c c c} \hline \(V_{LF}\) **(pu)** & \(f_{LF}\) **(Hz)** & **Alignment Time (s)** \\ \hline
0.1 pu & 50 Hz & 11 s \\
0.1 pu & 40 Hz & 9 s \\
0.1 pu & 30 Hz & 2.8 s \\
0.1 pu & 20 Hz & 2.2 s \\
0.2 pu & 50 Hz & 2.2 s \\
0.2 pu & 40 Hz & 1.5 s \\
0.2 pu & 30 Hz & 1.9 s \\
0.2 pu & 20 Hz & 2 s \\
0.25 pu & 50 Hz & 1.2 s \\
0.25 pu & 40 Hz & 1.3 s \\
0.25 pu & 30 Hz & 1.4 s \\
0.25 pu & 20 Hz & 1.5 s \\ \hline \end{tabular}
\end{table} 
Table 3: The sensitivity analysis results based on the input applied voltage amplitude \(V_{LF}\), the injected signal frequency \(f_{LF}\) versus the time duration of the alignment.