ece 330: power circuits and electromechanics...example on the board •a 3-phase 550 v line-line...
TRANSCRIPT
ECE 330: Power Circuits and Electromechanics
Lecture 23
2019-11-20
Last Time
• Rotating magnetic field
• Inductance matrix
• Started looking at synchronous machines
•!"#!$#!"%
='# 0 )cos(.)0 '# )sin(.)
)cos(.) )sin(.) '%
2"#2$#2"%
• Frequency condition: 34 = 3# − 3%
Today
• Why move at the synchronous speed?
• Equivalent circuit for synchronous machines
• Power consumed
• Poles
Synchronous machine
•!"#!$#!"%
='# 0 )cos(.)0 '# )sin(.)
)cos(.) )sin(.) '%
2"#2$#2"%
• Assume: 2"# = 6# cos 3#7 , 2$# = 6#sin(3#7)
2"% = 6%, . = 347 + .:
• Frequency condition: 34 = 3#
Synchronous speed
Synchronous demonstration starts at 3:30 on video.
https://www.youtube.com/watch?v=lV8iPKY-3ms
a Phase Stator Voltage
• ;"# = <#2"# +=>?@=A
• ;"# = <#6# cos 3#7 − '#6#3# sin 3#7 − )6% 3#sin 3#7 + .:• Writing as phasors
• B?@C∠.E = <#
F@C∠0° + H3#'#
F@C∠0° + I@JFK
C∠.: + 90°
Per phase circuit
• M"% =I@JFK
C: excitation voltage. Dependent on 6%
• N: torque angle
Power consumed
• OPQ = 3OSQ → OPQ = 3<U{M"% W6"∗}
• Simplifying gives: OPQ = −PZ?KB?[ \]^ _`@
• For a motor, OPQ > 0 → N < 0• For a generator, OPQ < 0 → N > 0• NOTE: to analyze a generator, flip current direction in circuit
Complex Power
• cPQ = 3d"e W6"∗ → cPQ = OPQ + HfPQ
• fPQ < 0: over-excited (supplies VARs)
• fPQ > 0: under-excited (consumes VARs)
Example
• A 3-phase 550 V line-line generator produces 250 kW of power. The excitation voltage of the generator is 460 V/phase and the synchronous reactance is 1.2 Ω. What is the torque angle?
• a) N = 43.2°• b) N = −43.2°• c) N = 0.754°• d) N = −0.754°
Example
• A 3-phase 550 V line-line generator produces 250 kW of power. The excitation voltage of the generator is 460 V/phase and the synchronous reactance is 1.2 Ω. What is the torque angle?
• a) N = 43.2°• b) N = −43.2°• c) N = 0.754°• d) N = −0.754°
Example
• A 3-phase 550 V line-line generator produces 250 kW of power. The excitation voltage of the generator is 460 V/phase and the synchronous reactance is 1.2 Ω. What is the power factor of the generator?
• a) Ol = 0.998 lead
• b) Ol = 0.998 lag
• c) Ol = 0.8 lag
• d) Ol = 0.8 lead
Example
• A 3-phase 550 V line-line generator produces 250 kW of power. The excitation voltage of the generator is 460 V/phase and the synchronous reactance is 1.2 Ω. What is the power factor of the generator?
• a) Ol = 0.998 lead
• b) Ol = 0.998 lag
• c) Ol = 0.8 lag
• d) Ol = 0.8 lead
Example on the board
• A 3-phase 550 V line-line generator produces 250 kW of power. The excitation voltage of the generator is 460 V/phase and the synchronous reactance is 1.2 Ω. If the power generated and the terminal voltage are the same, how much should the rotor current change to get a new
power factor of 0.8 lag?
Poles
• Everything up till now was a 2-pole system
Poles (Continued)
Equations with Multiple Poles
• Frequency condition: 34 = Cn3# where p is the number of poles
• Need because we don’t have to travel as far in θ to change current direction
• O = op34 → op = qrsI@
Example
• A 3-phase, 60 Hz, 6 pole, 550 V line-line generator produces 250 kW of power. The excitation voltage of the generator is 460 V/phase and the synchronous reactance is 1.2 Ω. What is the mechanical rotation rate?
• a) 34 = 377 tuv/x• b) 34 = 126 tuv/x• c) 34 = 189 tuv/x• d) 34= 1131 tuv/x
Example
• A 3-phase, 60 Hz, 6 pole, 550 V line-line generator produces 250 kW of power. The excitation voltage of the generator is 460 V/phase and the synchronous reactance is 1.2 Ω. What is the mechanical rotation rate?
• a) 34 = 377 tuv/x• b) 34 = 126 tuv/x• c) 34 = 189 tuv/x• d) 34= 1131 tuv/x
Example
• A 3-phase, 60 Hz, 6 pole, 550 V line-line generator produces 250 kW of power. The excitation voltage of the generator is 460 V/phase and the synchronous reactance is 1.2 Ω. What is the torque?
• a) op = 1.984 {|• b) op= 198.4 {|• c) op= 19.84 {|• d) op= 1984 {|
Example
• A 3-phase, 60 Hz, 6 pole, 550 V line-line generator produces 250 kW of power. The excitation voltage of the generator is 460 V/phase and the synchronous reactance is 1.2 Ω. What is the torque?
• a) op = 1.984 {|• b) op= 198.4 {|• c) op= 19.84 {|• d) op= 1984 {|