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### Lecture12

Course: EEL 3216, Spring 2011
School: FSU
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Word Count: 500

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No-Load SM Characteristic Rotor flux magnitude Induced stator voltage magnitude EA k Characteristic of the iron (stator and rotor) Rotor field current Rotor field current Effect of saturation: for large field currents the no-load armature voltage magnitude scales sub-proportionally with IF and the voltage waveform becomes non sinusoidal (distorted). Fundamentals of Power Systems Lecture 12 1 SM Armature...

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No-Load SM Characteristic Rotor flux magnitude Induced stator voltage magnitude EA k Characteristic of the iron (stator and rotor) Rotor field current Rotor field current Effect of saturation: for large field currents the no-load armature voltage magnitude scales sub-proportionally with IF and the voltage waveform becomes non sinusoidal (distorted). Fundamentals of Power Systems Lecture 12 1 SM Armature Reaction I Unloaded generator at arbitrary rotor position Phase-A induced voltage can be represented by a space vector EA which aligns with rotor field vector BR y EA x Rotor field axis The time evolution of phase-A voltage and current is the projection of the respective space vector onto the y-axis Phase A Fundamentals of Power Systems Lecture 12 Page 1 2 SM Armature Reaction II Generator with lagging load current (balanced) Phase-A current space vector IA is rotated (in space) out of the rotor BR axis by the load phase angle y EA x IA It will require the time / for the IA space vector to reach the rotor axis The phase-A current produces a magnetic excitation in the x-axis only Fundamentals of Power Systems Lecture 12 3 SM Armature Reaction II The balanced 3-phase stator current system generates a rotating magnetic field BS which is another 90 behind the phase-A current space vector Reasoning: BS points in xdirection when when iA(t) is at its peak, i.e. when IA reaches the y-direction BS itself induces voltages Estat in the stator Fundamentals of Power Systems Lecture 12 Page 2 y EA x IA 90 Estat 4 SM Armature Reaction II y The resulting terminal voltage the of machine is V EA EA x Estat Which aligns with the resulting (net) magnetic field B BB net IA R -jX S Since Estat is proportional to IA the relationship in phasor quantities becomes V EA Estat X is a factor jXI A -j accounts for the -90 rotation Lecture 12 Fundamentals of Power Systems 5 SM Single-Phase Equivalent Circuit Model Armature reaction Armature (self) reactance V EA jX jX A V EA jX S Synchronous reactance EA RA I A RA I A Armature resistance kI F (below saturation) Fundamentals of Power Systems Lecture 12 Page 3 6 SM 3-Phase Equivalent Circuit Model Y-connection -connection Neutral possible VT terminal (line-line) voltage IL line current Fundamentals of Power Systems Lecture 12 7 SM Phasor Diagrams (incl. RA), Generator EA V Same active current component => same active power P jX S RA I A Unity PF Lagging Leading Same terminal voltage Fundamentals of Power Systems Lecture 12 Page 4 8 Measuring Machine Parameters Parameters required for machine model EA = f(IF) XS RA Losses (other than I2RA) Lecture 12 Fundamentals of Power Systems 9 Open Circuit Test Air gap line (linear) EA, rated Saturation IA = 0 ! Rotor field current Fundamentals of Power Systems Lecture 12 Page 5 Results: EA = kF,OCIF (only in linear region) No-load losses (windage, core & bearing) 10 Short Circuit Test IA VA = 0 ! Results: IA = kF,SCIF Load losses (windage, copper & bearing) IA, rated EA ( I F ) I A (IF ) XS Rotor field current Fundamentals of Power Systems IF Lecture 12 Page 6 RA RA XS jX S EA IA 11
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