Modelling and Analysis of Single-Phase Induction Motor with External Rotor

1. Modellingand Analysis of Single-Phase Induction Motorwith External Rotor Uma. R Edited By Sarath S Nair www.technologyfuturae.com www.technologyfuturae.com

2. Presentation Outline • Introduction • Why an external rotor? • Equivalent circuit of rotor • Lumped parameter equivalent circuit • Mathematical model • Role of conducting shell • Steady state and dynamic analysis • Summary • References www.technologyfuturae.com

3. Introduction • Many domestic appliances require low-power motors operating at constant speed that must start under load(compressors, pumps etc) • Because of the reliability in operation the single-phase induction motor is one of the most widely used types of AC machines • SPIM with external rotor is more advantageous for low power application • Constant speed at different load can be easily achieved by increasing the motor inertia, by using an external rotor www.technologyfuturae.com

4. Why an external rotor? • Allows a higher stability in operation at different loads due to higher inertia • The fan blades can be attached directly to the outside of the rotor, making the motor more compact • Heat generated within the rotor, is on the outside and can be dissipated easily • The start-up and operating characteristics of single-phase induction motors with external rotor can be improved by covering the rotor with a conducting shell joining the two end rings www.technologyfuturae.com

5. External rotor of an Induction motor Fig1. axial half cross-section Fig2. Fluxes in longitudinal section • L – laminations Φσbx - leakage fluxes of bar • B - rotor cage bars Φδx - airgap flux • R - end rings Φex - leakage flux of shell • S - conducting shell www.technologyfuturae.com

6. Magnetic fluxes and Induced voltages • Φσbx= Lσb Ibx Φσrx= Lσr Irk • Σ Irk= kr Ibx kr =1/(2sin2(Πp/Z)) • Φσrx= kr Lσr Ibx The induced voltage by these fluxes equals the resistive voltage drops on the path г b jω(Φδx + 2 Φσbx + 2Σ Φσrx )= 2Rb Ibx +2Rr Σ Irk On the path г e- (a closed path, consisting from two "external bars“) -jω(Φex + 2Σ Φσrx )= 2Re Iex +2Rr Σ Irk www.technologyfuturae.com

7. Equivalent circuit of the Rotor • U1, U2etc -the bar e.m.f.s • Each bar is represented by its complex impedance • Each ring by its ring-segment complex impedance www.technologyfuturae.com

8. Contd… • External shell • Due to the symmetry of the bar and ring segment currents, a star equivalent of impedance & for the ring segments can be established • equivalent impedance of a bar circuit is: without external conducting shell • with external conducting shell www.technologyfuturae.com

9. Lumped parameter Equivalent Circuit Assumptions • Only the fundamental space-harmonic component of the air-gap flux distribution is considered. • A nonlinear resistor that is associated with the total stator flux linkage models core loss in d and q axis. • Stray losses, temperature effects and rotational losses are neglected www.technologyfuturae.com

10. Mathematical Model • Mathematical model is described by the following state-variable matrix equations: www.technologyfuturae.com

11. Contd… • Where the inductance terms are calculated using the notations: • The induced voltages in the magnetising branch are readily determined with: www.technologyfuturae.com

12. Contd… • Where • Torque equation is: www.technologyfuturae.com

13. Role of conducting shell • The ring impedance is especially high in small external rotor motors, because of the increased ring mean diameter • The external conducting shell • ensures a parallel way for the ring currents • diminishes the equivalent ring impedance • decreases the rotor resistance and the leakage reactance • increases the cooling surface area www.technologyfuturae.com

14. Steady state and Dynamic analysis • A split phase induction motor with following parameters are considered for analysis • Rated output power: 60 W • Rated frequency: 50 Hz • Rated speed: 2850 rpm • Rated voltage: 220 V • Stator main winding resistance:37.57 ohm • Stator auxiliary winding resistance: 56.83 ohm • Rotor resistance: 76.23 ohm www.technologyfuturae.com

15. Contd… • 1) steady-state torque versus speed 2) steady-state torque versus for starting period speed for rated operating period www.technologyfuturae.com

16. Contd… Fig(1) Fig(2) • 1) instantaneous torque versus speed for motor with extemal rotor and without conducting shell • 2) instantaneous torque versus speed for motor with extemal rotor with conducting shell www.technologyfuturae.com

17. Contd… Fig(1) Fig(2) • 1)Start-up speed response for motor with external rotor and without conducting shell • 2)Start-up speed response for motor with external rotor with conducting shell www.technologyfuturae.com

18. Summary • This paper focused on a new construction of SPIM with external rotor and conducting shell • An equivalent circuit for analysis and modelling of the single-phase induction motor with external rotor is derived. • The torque and speed characteristics of the motor with and without the conducting shell is compared • A SPIM with external rotor and conducting shell finds its application in compressors, pumps, air conditioners etc www.technologyfuturae.com

19. References [l] M. Popescu, “Analysis and Modelling of Single-Phase Induction Motor with External Rotor for Domestic Applications”, IEEE Trans. Ind. Appl.,2000,pp463-470 [2]P.C. Krause, 0. Waszynchuk, S.D. Sudhoff: Analysis of Electrical Machinery, IEEE Press, New York, 1995 [3]S .D. Umans, “Steady-state, lumped-parameter model for capacitor-run, single-phase induction motors”, IEEE Trans. Ind. Appl., Vo1.32, no. 1, Jan/Feb 1996, pp.169-179 [4] E. Levi: “A unified approach to main flux saturation modelling in D-Q axis models of induction machines”, IEEE Trans. Energy Conv., Vol. 10, no.3, Sept. 1995,pp 455-461 www.technologyfuturae.com

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