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Modeling of Synchronous Generators

Modeling of Synchronous Generators. 99% of the electric power allover the world is generated by Synchronous Generators. System Components. The main components of power systems are: Generators (Synchronous Generators). Power Transformers. Transmission lines and cables. Loads:

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Modeling of Synchronous Generators

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  1. Modeling of Synchronous Generators 99% of the electric power allover the world is generated by Synchronous Generators

  2. System Components • The main components of power systems are: • Generators (Synchronous Generators). • Power Transformers. • Transmission lines and cables. • Loads: - Static (lighting, heating,…) - Dynamic (Motors).

  3. Generators • The Generator converts mechanical power into electrical power. • Synchronous generators are constant speed generators. • The conversion of mechanical power into electrical power is done through a coupling field (magnetic field). Magnetic Electrical Output Input Mechanical

  4. Construction Stator Armature Electrical Mechanical Field Rotor

  5. Synchronous Generators View of a two-pole round rotor generator and exciter. (Westinghouse)

  6. Synchronous Generators Armature Windings Field Windings Construction of a two-pole salient pole generator

  7. Salient Pole Generator Rotor of a four-pole salient pole generator

  8. Operation Concepts Operating concept of a synchronous generator

  9. Flux Linkage (a) Flux is perpendicular to phase A (b) Flux is parallel to phase A Flux linkage variation.

  10. Rotating Flux Rotating flux linkage to phase A.

  11. EMF Equation According to Faraday’s law, the induced emf in the armature coil of Nsta turns is given by:

  12. Speed and Frequency • nS is the synchronous speed (r/m) • f is the frequency in Hz. • 2P = total number of poles. Example: calculate the frequency of a 1800 rpm , 4 pole synchronous generator ns = 1800 r/m, 2P = 4 Then, f = 2*1800/60 = 60 Hz

  13. Armature Reaction The main field flux (Φf) and the load generated rotating fluxe (Φar)

  14. Armature Reaction Load current generates a rotating flux reducing the main flux and induced voltage

  15. Armature Reactance

  16. Equivalent Circuit Single-phase equivalent circuit of a synchronous generator.

  17. Phasor Diagram Ia

  18. Power Calculations The apparent Power S is given by Using the current expression derived from the equivalent circuit we get

  19. Power Angle Pmax = EV/X P d Power – Angle characteristics

  20. Example A 1,250-kVA, three-phase, Y-connected, 4,160-V , ten-pole, 60-Hz generator has an armature resistance of 0.126 ohms per phase and a synchronous reactance of 3 ohms per phase. Find the full load generated voltage per phase at a power factor of 0.8 lagging.

  21. Solution The magnitude of full load current is obtained as The terminal voltage per phase is taken as reference The synchronous impedance is obtained as

  22. The generated voltage per phase is calculated for a power factor of 0.8 lagging ( φ = -36.87°).

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