Tham khảo tài liệu 'electric machines and drives part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Electric Motor Performance Improvement Using Auxiliary Windings and Capacitance Injection 29 The capacitor C2 much smaller than Cl is connected to mitigate the voltage spikes during switching off the main capacitor. Thus the equivalent capacitor can be written as Ceq S C1 C2 1 Variable capacitor H-topology Figure 7 shows a single-phase H topology to achieve a variable capacitor. This configuration using H-bridge bidirectional topology obtains a higher equivalent capacitance for the same fixed one as reference. In this configuration the reactor Lr has the same purpose of limiting the surge capacitive current while C2 also of small value mitigates the voltage spikes. The equivalent capacitance could be express as Ceq C2 C1 2S-1 2 2 It can be notice that the equivalent capacitance could increase significant when the duty cycle approaches 50 . In practice the switches are not ideal and there is no infinite increase of the equivalent capacitance. Fig. 7. Variable capacitor using H-bridge bidirectional topology Fig. 8. Variable capacitor using three-phase H-bridge topology 30 Electric Machines and Drives Another solution to achieve a variable capacitance or rather to generate a capacitive current was proposed using a three-phase H topology as PWM inverter E. Muljadi et al 1989 Tamrakan and Malik 1999 as presented in Figure 8. The converter injects capacitive reactive power into auxiliary windings and thus improving the power factor of the motor. 3. Mathematical model The machine is treated as having two three-phase windings and the voltages equations system can be written as Ị. R b 4 v 3 dt R2 Ixyz d- Ầxyz Vc- 2 IR a. - . 5 dt where Vbc Va Vb Vc T 6 IabcS Pa Ib Ic T Vb. A Àb Ấc T 7 ra rx R1 rb R2 ry 8 . rc . I rz J Note that indices 1 refer to the main winding and 2 to the auxiliary winding. V Labc L. a csxyz Labcsr I . yz Lxvzabcs x y zaucs Lxyz Lxyzabcr Ixyz 9 bcr _ Labcrs Lb a crxyz Labcr .Iabcr _ The inductances in eq. 9 are time dependent and this make the .
