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Lecture 8 - EE743

Direct Current (DC) Machines - Part II. Lecture 8 - EE743. Professor: Ali Keyhani. DC Machines. Shunt-connected DC Machine. DC Machines. The dynamic equations (assuming r fext =0) are:. Where L ff = field self-inductance L la = armature leakage inductance

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Lecture 8 - EE743

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  1. Direct Current (DC) Machines - Part II Lecture 8 - EE743 Professor: Ali Keyhani

  2. DC Machines • Shunt-connected DC Machine

  3. DC Machines • The dynamic equations (assuming rfext=0) are: Where Lff = field self-inductance Lla= armature leakage inductance Laf = mutual inductance between the field and rotating armature coils ea = induced voltage in the armature coils (also called counter or back emf )

  4. DC Machines

  5. DC Machines - Shunt DC Machine • Time-domain block diagram • The machine equations are solved for:

  6. DC Machines - Shunt DC Machine • Time domain block diagram + - Va ia G2 if Vf G1 Laf X + - Vf G3 ia X if

  7. DC Machines - Shunt DC Machine • State-space equations Let ; Re-writing the dynamic equations,

  8. DC Machines - Permanent Magnet • The field flux in the Permanent Magnet machines is produced by a permanent magnet located on the stator. • Therefore, • Lsfif is a constant determined by the strength of the magnet, the reluctance of the iron, and the number of turns of the armature winding.

  9. DC Machines - Permanent Magnet • Dynamic equations of a Permanent Magnet Machine

  10. DC Machines - Permanent Magnet • Dynamic equations,

  11. DC Machines - Permanent Magnet • Time domain block diagram • The equations are solved by,

  12. DC Machines - Permanent Magnet • Time domain block diagram Va + - r Te ia + - ea Kv G2 G1 TL Kvr Kv

  13. DC Machines - Permanent Magnet • State-space equations • re-writing the equations as function of states,

  14. DC Machines - Permanent Magnet • In a matrix form,

  15. DC Machines - Permanent Magnet • Transfer Function, • Let

  16. DC Machines - Permanent Magnet • The, we will have • Re-arranging the equation,

  17. DC Machines - Permanent Magnet • In a matrix representation,

  18. DC Machines - Permanent Magnet • Solving for ia

  19. DC Machines - Permanent Magnet • Let m be, • The equation is then reduced to,

  20. DC Machines - Permanent Magnet

  21. DC Machines - Permanent Magnet

  22. DC Machines - Permanent Magnet • The characteristic equation (or force-free equation) of the system is as shown below,

  23. DC Machines - Permanent Magnet • If  < 1 , the roots are a conjugate complex pair, and the natural response consists of an exponentially decaying sinusoids. • If  > 1, the roots are real and the natural response consists of two exponential terms with negative real exponents.

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