【正文】 di and qi respectively. Therefore, system control can be pleted by current feedback loops as follows: ))((211 qqiiskkx ?+=? (14) ))((212 ddiiskkx ?+=? (15) Fig. 10 shows the control block diagram of the gridside inverter. It should be noted that the given active and reactive power should be set at two times of the desired values, because the imaginary circuit will not deliver any active and reactive power to the grid. θωω Fig. 10. The vector control block diagram of the gridside inverter IV. SIMULATION RESULTS A simulation model in Matlab/Simulink is developed based on above theoretical analysis, and the system simulation block diagram is shown in Fig. 11. Fig. 11. The system simulation block diagram A. The simulation results of the machineside converter In the simulation model, the Reference speed represents the wind speed. At the beginning of the simulation (. 0s), the generator speed is 4rpm and its input torque is 50Nm. At the time of , the generator speed is 17 rpm and the input torque maintains at the value of 50Nm. At 1s, the generator speed maintains at 17 rpm and the input torque is 80Nm. The simulated waveforms are shown in Fig. 12, Fig. 13, Fig. 14, Fig. 15, respectively. It can be seen from Fig. 12 and Fig. 13, the error between the estimated rotor position angle and the actual measurement of the rotor position angle is very small in the steady state, there are some fluctuations in the dynamic response, but the rotor position angle is stabilized quickly. It can be seen from Fig. 14 and Fig. 15, there is a small error between the estimated and measured generator rotor speed at low speed. At high speed, however, the error is very small and can be ignored, and the transient response is very short. At the time 1s, the input torque increase affects the generator rotor speed slightly, and soon the transient disappears. 0 1 201234567θ∧θ?,(deg)θθ()ts Fig. 12. The estimated and measured rotor position angle 60 1 20(rad/s)θθ∧?(s)t Fig. 13. The error of estimated and measured rotor position angle t(s)()nrpm Fig. 14. The measured generator rotor speed t(s)t()esirpmn Fig. 15. The estimated generator rotor speed The simulation waveforms of the machineside converter demonstrate that the sensorless vector control algorithm can estimate the rotor angular position accurately, and the vector control strategy of the machineside converter can realize generator speed control for the wind turbine to follow the optimized power curve, . MPPT when the wind speed is below rated wind speed. B. The simulation results of the gridside inverter The simulation results of the gridside inverter is shown in Fig. 16, Fig. 17 and Fig. 18 respectively. It can be seen from Fig. 16, when the generator output torque increases, the DC bus voltage is maintained constant. Fig. 17 shows that θu follows av very well, and Fig. 18 shows that ai follows av very well. Fig. 16. The simulated DC voltage avuθuθ Fig. 17. The generator output A phase voltage and the grid voltage vector angle Fig. 18. The output voltage and current of the gridside inverter From the simulation results of the gridside inverter, it can be seen that the singlephase PLL algorithm can accurately track the gridside voltage, and the vector control strategy of the gridside inverter can stabilize the DC bus voltage, and control the grid power factor. V. CONCLUSION This research developed a power electronic converter for a small directdriven PMSG wind turbine using the backtoback pulsewidth modulation (PWM) topology. The simulation results demonstrate that 1) The machineside converter can control the generator speed and torque for the wind turbine to follow the optimized power curve, . maximum power point tracking (MPPT) when the wind speed is below rated wind speed. 2) The sensorless phaselocked loop (PLL) control 7algorithm can realize the vector control of the generator. 3) The gridside inverter control algorithm based on singlephase PLL can stabilize the DC bus voltage of the converter and control the grid power factor. VI. REFERENCES Periodicals: [1] De Tian, “The wind power technology status and development trend in the world,” New Energy Industry, in press. [2] Ruzhen Dou, Lingyun Gu, Baotao Ning, “Sensorless control of the PMSM based on the PLL,” Electric Machines amp。 ω is the generator electrical angular velocity of the generator。 dLqL and sR are the inductance and resistance of the stator。 Control Application, vol. 32, pp. 5357, 2020. Books: [3] Qingding Guo, Yibiao Sun, Limei Wang, Modern permanent mag AC servo motor system. China Electric Power Press, Beijing. In press. Papers from Conference Proceedings (Published): [4] S. Song, S. Kang, and N. Hahm, “Implementation and control of grid connected ACDCAC power