## 4 Simulation and Experimental Results
### Simulation Results
#### 4.1.1 Operation of the PQ-MRAS in Open-Loop Mode  
The main goal of the first test was to check the general performance of the PQ-MRAS. The results are presented in Figures 5 and 6. It can be observed that both estimated parameters tracked real values with high accuracy.  
Figure 4: Operation of the PQ-MRAS estimator: (**a**) open-loop mode, (**b**) closed-loop mode.  
Figure 5: Operation of the PQ-MRAS estimator: (**a**) estimated rotor resistance, (**b**) reference and estimated reactive power, (**c**) estimated stator resistance, (**d**) reference and estimated active power; (simulation results), (\(\omega_{m}\)\({}^{mrf}\)\(=\)\(\pm\)0.5 \(\omega mN\), \(t_{L}\)\(=\)\(\pm\)0.75 \(tN\), \(R_{r}\)\(=\)\(R_{rN}\), \(R_{s}\)\(=\)\(R_{sN}\)).  
Even during speed reversal variations the estimated parameters were negligible (maximum estimation error for stator resistance increased to 2%). During the second test, the robustness of the estimator to load torque variations was considered. The obtained results (Figures 7 and 8) show that both parameters were calculated with high accuracy even for load variations.  
Figure 8: State variables of the drive: (**a**) reference and simulated rotational speed, (**b**) electromagnetic torque and stator current component \(i_{\text{sy}}\), (**c**) estimated rotor flux vector module and stator current component \(i_{\text{ss}}\), (**d**) stator current components \(i_{\text{sa},\beta}\); (simulation results), (\(\omega_{m}{}^{\prime\prime}=0.5\ \omega mN\), \(t_{L}=\text{var}\), \(R_{r}=R_{NN}\), \(R_{s}=R_{NN}\)).  
Figure 6: State variables of the drive: (**a**) reference and simulated rotational speed, (**b**) electromagnetic torque and stator current component \(i_{\text{sy}}\), (**c**) estimated rotor flux vector module and stator current component \(i_{\text{ss}}\), (**d**) stator current components \(i_{\text{sa},\beta}\); (simulation results), (\(\omega_{m}{}^{\prime\prime}=\pm 0.5\ \omega mN\), \(t_{L}=\pm 0.75\)\(tN\), \(R_{r}=R_{NN}\), \(R_{s}=R_{NN}\)).  
Figure 7: Operation of the PQ-MRAS estimator: (**a**) estimated rotor resistance, (**b**) reference and estimated reactive power, (**c**) estimated stator resistance, (**d**) reference and estimated active power; (simulation results), (\(\omega_{m}{}^{\prime\prime}=0.5\ \omega mN\), \(t_{L}=\text{var}\), \(R_{r}=R_{NN}\), \(R_{s}=R_{NN}\)).  
The aim of the next analysis was to check how the values of adaptation mechanism coefficients impact the estimator performance. Figure 9 shows a comparison of estimator signals for different sets of coefficients: nominal values (Appendix B), nominal values multiplied by 5 and nominal values divided by 5. The coefficient values have a major impact on the dynamics of the estimator, nevertheless it operated in a stable manner.  
During the next test, it was assumed that both resistances increased up to 150% of their nominal values, which was related to the changes of machine windings temperatures. It can be seen that both resistances were estimated correctly (Figure 10). Due to rotor resistance variations, the estimation error of the rotor flux can be observed (Figure 11), because the current model is directly influenced by this parameter (17). The inaccurate calculation of the rotor flux vector results in the coupling of flux and torque control paths, which consequently results in the deterioration of drive performance.  
Figure 9: Operation of the PQ-MRAS estimator for different values of parameters in adaptation mechanisms: (**a**) estimated rotor resistance, (**b**) reference and estimated reactive power, (**c**) estimated stator resistance, (**d**) reference and estimated active power; (simulation results), (\(\omega_{m}\)_ref_ = 0.5 \(\omega mN\), \(t_{L}\) = 0.75 \(tN\), \(R_{r}\) = \(R_{rN}\), \(R_{s}\) = \(R_{sN}\)).