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Lecture1Sept16

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Lecture1Sept16

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    3. Course Text Book: Electric Machinery Fundamentals by Stephen J. Chapman, 4th Edition, McGraw-Hill, 2005 Electric Motor Drives – Modeling, Analysis and Control by R. Krishnan Pren. Hall Inc., NJ, 2001 Power Electronics – Converters, Applications and Design by N. Mohan, J. Wiley & Son Inc., NJ, 2003 Power System Stability and Control by P. Kundur, McGraw Hill Inc., 1993 Research papers Grading Policy: Attendance (5%) Project (20%) Midterm Exam (30%) Final Exam (45%)

    4. Course Content Working principles, construction, mathematical modeling, operating characteristics and control techniques for synchronous machines Working principles, construction, mathematical modeling, operating characteristics and control techniques for induction motors Introduction to power switching devices Rectifiers and inverters Variable frequency PWM-VSI drives for induction motors Control of High Voltage Direct Current (HVDC) systems

    5. Exam Dates Midterm Exam: Final Exam:

    6. Term Projects Group 1: Student 1 (---@uwindsor.ca) Student 2 (---@uwindsor.ca) Student 3 (---@uwindsor.ca) Project Title: Group 2: Student 1 (---@uwindsor.ca) Student 2 (---@uwindsor.ca) Student 3 (---@uwindsor.ca) Project Title: Group 3: Student 1 (---@uwindsor.ca) Student 2 (---@uwindsor.ca) Student 3 (---@uwindsor.ca)

    7. Synchronous Machines Construction Working principles Mathematical modeling Operating characteristics

    8. CONSTRUCTION

    10. Salient-Pole Synchronous Generator

    11. Cylindrical-Rotor Synchronous Generator

    12. Damper Windings

    13. Operation Principle The rotor of the generator is driven by a prime-mover A dc current is flowing in the rotor winding which produces a rotating magnetic field within the machine The rotating magnetic field induces a three-phase voltage in the stator winding of the generator

    14. Electrical Frequency

    15. Direct & Quadrature Axes

    16. PU System

    17. Classical Model of Synchronous Generator The leakage reactance of the armature coils, Xl Armature reaction or synchronous reactance, Xs The resistance of the armature coils, Ra If saliency is neglected, Xd = Xq = Xs

    18. Phasor Diagram

    21. Direct and Quadrature Axes The direct (d) axis is centered magnetically in the center of the north pole The quadrature axis (q) axis is 90o ahead of the d-axis q: angle between the d-axis and the axis of phase a Machine parameters in abc can then be converted into d/q frame using q Mathematical equations for synchronous machines can be obtained from the d- and q-axis equivalent circuits Advantage: machine parameters vary with rotor position w.r.t. stator, q, thus making analysis harder in the abc axis frame. Whereas, in the d/q reference frame, parameters are constant with time or q. Disadvantage: only balanced systems can be analyzed using d/q-axis system

    23. Small disturbances in a power system Gradual changes in loads Manual or automatic changes of excitation Irregularities in prime-mover input, etc.

    24. Related Terms Generator Modeling using the d- and q-axis equivalent circuits Transmission System Modeling with a RL circuit A Small Disturbance is a disturbance for which the set of equations describing the power system may be linearized for the purpose of analysis Steady-State Stability is the ability to maintain synchronism when the system is subjected to small disturbances Loss of synchronism is the usual symptom of loss of stability Infinite Bus is a system with constant voltage and constant frequency, which is the rest of the power system Eigen values and eigen vectors are used to identify system steady-state stability condition

    25. The Flux Equations

    26. Rearranged Flux Linkage equations

    27. The Voltage Equations

    28. The Mechanical Equations

    29. Linearized Form of the Machine Model

    30. Terminal Voltage

    31. Substituting ?Vtd and ?Vtq in the flux equations:

    32. Rearranging the flux equations in a matrix form:

    33. and…

    35. and thus,

    36. where,

    37. System to be Studied

    38. System State Matrix and Eigen Values

    39. Eigen Values Eigen values are the roots of the characteristic equation Number of eigen values is equal to the order of the characteristic equation or number of state variables Eigen values describe the system response ( ) to any disturbance

    40. Analyzing the Eigen Values of the System State Matrix Compute the eigen values of the system state matrix, A The eigen values will give necessary information about the steady-state stability of the system Stable System: If the real parts of ALL the eigen values are negative Example: A system with the above eigen values is on the verge of instability

    41. Machine Parameters

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