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The windmill model we used in Computer Lab 4 has a rotor with blades R = 3.8m in length, and a maximum efficiency coefficient C,(1) = 0.4 with A = 6.4 . It has a gear ratio GR= 12. Also let the generator be a Doubly Fed Induction Generator (DFIG) with the following parameters: P = 4 number of poles r, = 0.228 N rotor resistance r, = 0.082 N stator resistance L, = L, = 8.0e – 04 H rotor and stator inductance losses Ly = 0.0347 H magnetizing inductance Let the stator be connected to the grid with V. = 360V rms line voltage, at 60HZ . Let the wind have a speed of 12m/sec and assume the windmill is operating at its optimum point (maximum power from the wind) and no reactive power from the stator (only real power). Let the controller be as described in class, so that, in steady state, the rotor current is I„ = Imef , I = Iaref , where rref> V, 3V, T eref %3D 3 PV. Using the steady state equivalent circuit model (don't write a simulation) without neglecting stator losses: Q1: compute the mechanical power P, from the wind turbine;

The windmill model we used in Computer Lab 4 has a rotor with blades R = 3.8m in length, and a maximum efficiency coefficient C,(1) = 0.4 with A = 6.4 . It has a gear ratio GR= 12. Also let the generator be a Doubly Fed Induction Generator (DFIG) with the following parameters: P = 4 number of poles r, = 0.228 N rotor resistance r, = 0.082 N stator resistance L, = L, = 8.0e – 04 H rotor and stator inductance losses Ly = 0.0347 H magnetizing inductance Let the stator be connected to the grid with V. = 360V rms line voltage, at 60HZ . Let the wind have a speed of 12m/sec and assume the windmill is operating at its optimum point (maximum power from the wind) and no reactive power from the stator (only real power). Let the controller be as described in class, so that, in steady state, the rotor current is I„ = Imef , I = Iaref , where rref> V, 3V, T eref %3D 3 PV. Using the steady state equivalent circuit model (don't write a simulation) without neglecting stator losses: Q1: compute the mechanical power P, from the wind turbine;

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Problem 3 (Wind Power and DFIG) The windmill model we used in Computer Lab 4 has a rotor with blades R= 3.8m in length, and a maximum efficiency coefficient C (2) = 0.4 with 1 = 6.4 . It has a gear ratio GR= 12. Also let the generator be a Doubly Fed Induction Generator (DFIG) with the following parameters: P = 4 number of poles r, = 0.228 Q rotor resistance 1, = 0.082 Q stator resistance L, = L, = 8.0e – 04 H rotor and stator inductance losses Ly = 0.0347 H magnetizing inductance Let the stator be connected to the grid with V. = 360V rms line voltage, at 60HZ . Let the wind have a speed of 12m/sec and assume the windmill is operating at its optimum point (maximum power from the wind) and no reactive power from the stator (only real power). Let the controller be as described in class, so that, in steady state, the rotor current is qr grref > dr drref ' V, Ime = V2 grref drref 3 PV. 12(2) @. Using the steady state equivalent circuit model (don't write a simulation) without neglecting stator losses: Q1: compute the mechanical power P, from the wind turbine; Q2: compute the electric power generated by the stator, by the rotor and the power losses in the resistors;
Transcribed Image Text:Problem 3 (Wind Power and DFIG) The windmill model we used in Computer Lab 4 has a rotor with blades R= 3.8m in length, and a maximum efficiency coefficient C (2) = 0.4 with 1 = 6.4 . It has a gear ratio GR= 12. Also let the generator be a Doubly Fed Induction Generator (DFIG) with the following parameters: P = 4 number of poles r, = 0.228 Q rotor resistance 1, = 0.082 Q stator resistance L, = L, = 8.0e – 04 H rotor and stator inductance losses Ly = 0.0347 H magnetizing inductance Let the stator be connected to the grid with V. = 360V rms line voltage, at 60HZ . Let the wind have a speed of 12m/sec and assume the windmill is operating at its optimum point (maximum power from the wind) and no reactive power from the stator (only real power). Let the controller be as described in class, so that, in steady state, the rotor current is qr grref > dr drref ' V, Ime = V2 grref drref 3 PV. 12(2) @. Using the steady state equivalent circuit model (don't write a simulation) without neglecting stator losses: Q1: compute the mechanical power P, from the wind turbine; Q2: compute the electric power generated by the stator, by the rotor and the power losses in the resistors;
Q3: compute the actual mechanical power P from the equivalent circuit and verify that it is тech consistent with the electric powers computed in Q2. Also notice that it is not exactly the same as in Q1, why? In what case they will be the same? Q4: determine an expression for the rotor voltage in the time domain. Assume the three phase stator voltage vaber (1) is given by vas (t) = /2 V, cos(120at – 15°) and the rotor's intial position is at zero degrees. NOTE: since the model of the DFIG is made using motor conventions, then recall that, in steady state: Electric Power generated by the DFIG is negative (e.g. power generated by the stator P <0 ); The reference torque for the control is Tref = -P / om with P the aerodynamic power from the turbine.
Transcribed Image Text:Q3: compute the actual mechanical power P from the equivalent circuit and verify that it is тech consistent with the electric powers computed in Q2. Also notice that it is not exactly the same as in Q1, why? In what case they will be the same? Q4: determine an expression for the rotor voltage in the time domain. Assume the three phase stator voltage vaber (1) is given by vas (t) = /2 V, cos(120at – 15°) and the rotor's intial position is at zero degrees. NOTE: since the model of the DFIG is made using motor conventions, then recall that, in steady state: Electric Power generated by the DFIG is negative (e.g. power generated by the stator P <0 ); The reference torque for the control is Tref = -P / om with P the aerodynamic power from the turbine.
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