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This lecture from ece 528 covers various aspects of power quality, including harmonic phase sequence, system response, parallel and series resonance, effects of harmonic distortion, and derating transformers serving non-linear loads. The document also discusses real-world examples and the importance of keeping heating due to harmonics below rated load without harmonics.
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Lecture 20
1
Paul Ortmann [email protected] 208-733-7972 (voice) 208-736-3248 (fax)
http://www.ece.uidaho.edu/ee/power/ECE528/
Lecture 20 2
Today…
Lecture 20 3
Harmonic phase sequence clarification
A
B
C
Sequence is ABC for fundamental, ACB for 2nd harmonic
Lecture 20 4
Third harmonic waveforms are in phase – they add in the neutral
C
A
B
Lecture 20 7
Series resonance
Lecture 20 8
A real-world example
Lecture 20 9
Effects of harmonic distortion
Lecture 20 10
Derating transformers serving non-linear loads
Lecture 20 13
Derating transformers serving non-linear loads FPQ pg 216-
I 2 R
I 2 R R− h
Ih
IR
⎛ ⎜ ⎝
⎞ ⎟ ⎠
2
The summation is a factor that increases the RMS value of the current in the I^2 R losses based on harmonic content. IR is rated current.
P I^2 R
( pu) h
Ih 2
Lecture 20 14
Derating transformers serving non-linear loads FPQ pg 216-
The summation is a factor that increases the eddy current losses by the square of the frequency causing the losses.
PEC PEC R− h
Ih IR
2 ⋅h 2
PEC ( pu) PEC R− ( pu) h
2 h 2
⋅
Lecture 20 15
Derating transformers serving non-linear loads FPQ pg 216-
( pu) +PEC ( pu)
PLL ( pu) h
∑ ⎡ ⎣I h^2 (pu^ )⎤ ⎦ PEC R− (^ pu) h
PLL( pu ) h
∑ ⎡ ⎣I h^2 (^ pu)⎤ ⎦^1 PEC R− (^ pu)^
h
⎡Ih (pu^ ) ⎣ ⎤⎦
⎡^2 ⋅h 2 ⎣
⎤ ∑ ⎦
h
∑⎡ ⎣I h^2 (^ pu)⎤ ⎦
⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎣
⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎦
⋅
Lecture 20 16
Derating transformers serving non-linear loads FPQ pg 216-
FHL h
∑⎡⎣⎡⎣ I h (^ pu)⎤⎦^2 ⋅h^2 ⎤⎦
h
∑⎡ ⎣I h^2 (pu^ )⎤ ⎦
See other forms of this equation in eq. 6.60, p. 218.
Lecture 20 19
Derating transformers serving non-linear loads
FHL
:= FHL =6.
Lecture 20 20
Derating transformers serving non-linear loads
Derating
1 +PEC_R 1 +FHL ⋅PEC_R
The “allowable current” calculation in P.U. translates directly to a derating factor
Lecture 20 21
Derating transformers serving non-linear loads
K_factor h
∑⎛ ⎝ Ih^2 h^2 ⎞ ⎠
IR 2
Lecture 20 22
Other impacts
