high frequency waveform distortiongrouper.ieee.org/groups/harmonic/simulate/panel...
TRANSCRIPT
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1
A. Testa, Fellow Member IEEE
R. Langella, Senior Member IEEE
Second University of Naples, Italy
High Frequency Waveform Distortion:
theoretical and modeling considerations
Panel Session Harmonics from 2 kHz to 150 kHz: Immunity, Emission, Assessment and
Compatibility Denver GM2015
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QUESTIONS
• Q1 - does it make sense to distinguish among harmonics and interharmonics at HF?
– Q1.1 - How do fluctuate vs time waveform RMS values at HF?
– Q1.2 - How do vary (H and IH) waveforms PEAK values with phase angles and how do fluctuate waveform PEAK values (only IH) vs time at HF?
2
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QUESTIONS
• Q2 - Is it still possible to utilize simplified line models (RL, Pigrec…) at HF?
– Q2.1 - Is it needed to account for parameter (r, l, c,…) variability versus frequency at HF?
– Q2.2 - How to model lines at HF?
• Q3 - Do classical transformer models still work accurately or acceptably at HF?
3
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Q1 - DOES IT MAKE SENSE TO DISTINGUISH AMONG HARMONICS AND INTERHARMONICS AT HF?
4
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Q1.1 - How do fluctuate vs time waveform RMS values at HF?
5
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RMS20ms: max fluctuations vs fn
6
Hz,...,,f,tfcos.tcos nnn 15000021 with 2010250212 1
1001
1
A
AAmax
n
Q1.1 - How do fluctuate vs time waveform RMS values at HF?
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Q1.2 - How do vary (H and IH) waveforms PEAK values with phase angles and how do fluctuate waveform PEAK values (only IH) vs time at HF?
7
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Peak values vs fn (An=1%)
8
20msT and 921 with 2010250212 w1 kHz,...,,f,tfcos.tcos nnn
Q1.2 - How do vary waveforms PEAK values…
1001
1
A
AAmax
n
1001
1
A
AAmin
n
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Peak effects on Useful Life of Components
pn
pnnp kLkL
,
][
1][np
pn kEL
LE
kp time varing -> random variable
Normalized
Expected Life
Nominal
Operating
Temperature
1A
Ak p
9
Q1.2 - How do vary waveforms PEAK values…
pndepends on
component
insulation
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L Values for Component Parameter np
Component np value L/Ln
0.99-np
L/Ln
1.01-np
L/Ln U~(0.99-np-
1.01-np)
film capacitors 6 1.06 0.94 1.0002
asynchronous motors
9
1.09 0.91 1.0007
transformers 11 1.12 0.90 1.0012
cables 15 1.16 0.86 1.0025
HF LF
Q1.2 - How do vary waveforms PEAK values…
Go to Case Study Q1.2
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Q2 - IS IT STILL POSSIBLE TO UTILIZE SIMPLIFIED LINE MODELS (RL, PIGREC…) AT HF?
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Cable and Over-Head Lines Distributed and Concentrated Parameters
Distributed Parameters model
of a finite x length line Concentrated Parameters
model of a finite x length line
short line
The resonance frequencies, fr, are located at frequencies:
Q2 – Is it still possible…
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from
50Hz to 2.5kHz
from
2.5kHz to 9kHz
from
9kHz to 100kHz
10-2
10-1
100
101
102
10-1
100
101
102
103
104
Frequency [kHz]
/4
[km
]
2.5 kHz50 Hz9 kHz 100 kHz
1000km
30km
10km
0.75km
Cable and Over-Head Lines What does mean “short line”?
Q2 – Is it still possible…
Go to Case Study Q2
0.50km at 150kHz
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Q2.1 - IS IT NEEDED TO ACCOUNT FOR PARAMETER (R, L, C,…) VARIABILITY VERSUS FREQUENCY AT HF?
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0 10 20 30 40 50 60 70 80 90 1000.5
1
1.5
2
2.5
3
3.5
4
Frequency [kHz]
resis
tance [
]
0 10 20 30 40 50 60 70 80 90 1001.1
1.105
1.11
1.115
1.12
1.125
1.13
1.135
1.14
1.145
1.15x 10
-3
Frequency [kHz]
Inducta
nce [
H]
Cable and Over-Head Lines
Q2.1 – Is it needed to account for parameter (r, l, c, …)…
Go to Case Study Q2.1
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Q2.2 - HOW TO MODEL LINES AT HF?
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DP and P Models vs frequency
1. Coincidence of the
behaviour in the
frequency range from 0 to
2.5 kHz;
2. Difference of series
resonance frequency
values in the frequency
range from 2.5 to 9 kHz;
3. Entity of the damping
effects and the little shift
in the resonance
frequencies due to the
skin effect.
0 10 20 30 40 50 60 70 80 90 100
100
101
102
103
104
105
Frequency [kHz]
Impedence M
agnitude [
]
DP
P
DPno skin
Pno skin
Impedance Magnitude[0-100kHz]
Q2.2 – How to model lines at HF?
Positive sequence - 1 Equivalent
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Q3 - DO CLASSICAL TRANSFORMER MODELS STILL WORK ACCURATELY OR ACCEPTABLY AT HF?
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HF Power Transformers Model [1]
• ZH and ZL are the longitudinal impedances of high-voltage side and low-voltage side;
• Rm and Lm are the core losses;
• The capacitances CH, CL, and CHL take into account the capacitive coupling among high
frequency windings which values increase with transformer size .
[1] …….
Q3 – Do classical transformer…
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Capacitive and Inductive Reactances vs frequency for a power Transformers (1MVA | 20/0.4kV)
1.00E+00
1.00E+01
1.00E+02
1.00E+03
1.00E+04
1.00E+05
1.00E+06
1.00E+07
1.00E+08
0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 110000 120000 130000 140000 150000 160000
XHL XCH Xcc
Q3 – Do classical transformer…
Go to Case Study Q3
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CONCLUSION: ANSWERS (1)
• Q1 - Does it make sense to distinguish among harmonics and interharmonics at HF?
– NO! DIFFERENCES QUICKLY REDUCE INCREASING FREQUENCIES
• Q1.1 - How do fluctuate vs time waveform RMS values at HF?
– FLUCTUATIONS REACH NEGLIGIBLE VALUE BEFORE FEW kHz
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CONCLUSION: ANSWERS (2) • Q1.2 - How do vary (H and IH) waveforms PEAK values with
phase angles and how do fluctuate waveform PEAK values (only IH) vs time at HF?
– NEGLIGIBLE VARIATIONS STARTING FROM FEW kHz (VALUES DEPEND ON H OR IH AMPLITUDE). ALWAYS MAX PEAK VALUES TO BE EXPECTED!
– LIMITS FOR HF COMPONENTS SHOULD TAKE CARE OF PEAK RELATED EFFECTS
22
– THEY STILL FLUCTUATE. AT FREQUENSIES THAT CAN BE VERY LOW (99990 Hz GIVES THE SAME FLUCTUATION FREQUENCY (10 HZ) OF 90 Hz). FLUCTUATION AMPLITUDES ARE NEGLIGIBLE STARTING FROM FEW kHz.
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CONCLUSION: ANSWERS
• Q2 - Is it still possible to utilize simplified line models (RL, Pigrec…) at HF?
– NO!
• Q2.1 - Is it needed to account for parameter (r, l, c,…) variability versus frequency at HF?
– YES, IT IS!
• Q2.2 - How to model lines at HF?
– BY MEANS OF DISTRIBUTED PARAMETER OR MULTIPLE-P MODELS
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CONCLUSION: ANSWERS
• Q3 - Do classical transformer models still work accurately or acceptably at HF?
– NO! MODELS ACCOUNTING FOR CAPACITIVE COUPLING ARE STRICTLY NEEDED: HF PROPAGATION TROUGH TRANSFORMERS CANNOT BE EXCLUDED!
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Thank you for your attention!
Alfredo Testa: [email protected]
Roberto Langella: [email protected]
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Q1 - DOES IT MAKE SENSE TO DISTINGUISH AMONG HARMONICS AND INTERHARMONICS AT HF?
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H and IH: Nomenclature (1)
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Q1 - does it make sense to distinguish among harmonics and interharmonics at HF?
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H and IH: Nomenclature: RMS (2)
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Q1 - does it make sense to distinguish among harmonics and interharmonics at HF?
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H and IH: Nomenclature: Peak (3)
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Q1 - does it make sense to distinguish among harmonics and interharmonics at HF?
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H and IH: Nomenclature: Peak (4)
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nAAAmaxn
1
ˆˆ with HFfor ˆˆ
ˆˆ with MFfor ˆcosˆ
ˆˆ with LFfor ˆˆ
ˆmin
11
11
1
11
nn
nn
n
nn
AAAA
AAAA
AAAA
An
Q1 - does it make sense to distinguish among harmonics and interharmonics at HF?
Go to Case Study Q1
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Definitions
• Frequency ranges
– From 0 to 2 kHz (IEC)
– From 2 to 9 kHz (IEC Annex)
– From 9 to 150 kHz (?????)
• DC
• Subharmonics
• Harmonics
• Interharmonics
32
Q1 - does it make sense to distinguish among harmonics and interharmonics at HF?
1/10 Go to Q1.1
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Effects
• Thermal stress (RMS)
• Electric stress (PEAK)
• Components and Equipment Sensitivity
– Thermal stress depends on time constant
• Lamps t ~ 10 ms
• …….
• Cables t ~ hours
33
Q1 - does it make sense to distinguish among harmonics and interharmonics at HF?
2/10 Go to Q1.1
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Time window Tw
• Tw=TF = Fourier fundamental period
• Tw=10 ms
• Tw=20 ms
• Tw=200 ms
34
Q1 - does it make sense to distinguish among harmonics and interharmonics at HF?
3/10 Go to Q1.1
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RMS variability with frequency • ATF
(f)= const.
• ATW (f,phi,t,TW)=> oscillates between MIN and
MAX
– For harmonics RMS_TW = const.
– For interharmonics
• RMS_TW (f,phi,t,TW) for lower frequencies with a reducing sensitivity for higher TW (eg 200ms)
• RMS_TW = const. for higher frequencies
35
Q1 - does it make sense to distinguish among harmonics and interharmonics at HF?
4/10 Go to Q1.1
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PEAK variability with frequency • ÂTF
(f,phi)
– PEAK_TW (f,phi) for lower frequencies
– PEAK_TW =const. for higher frequencies
• PEAK_TW (f,phi,t)=> oscillates between MIN and MAX
– For harmonics and interharmonics PEAK_TW =const. for lower frequencies (in a range function of An)
– For harmonics and interharmonics PEAK_TW = const. for higher frequencies
36
Q1 - does it make sense to distinguish among harmonics and interharmonics at HF?
5/10 Go to Q1.1
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Time fluctuations 0402102050212 tcos.tcos
Q1 - does it make sense to distinguish among harmonics and interharmonics at HF?
6/10 Go to Q1.1
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Time fluctuations: Rms
0402102050212 tcos.tcos
20ms
Q1 - does it make sense to distinguish among harmonics and interharmonics at HF?
8/10 Go to Q1.1
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Time fluctuations: Peak
0402102050212 tcos.tcos
maxÂ
minÂ
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Time fluctuations: Rms
0402102050212 tcos.tcos
20ms
0402102050212 tcos.tcos
Q1 - does it make sense to distinguish among harmonics and interharmonics at HF?
9/10 Go to Q1.1
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0402102050212 tcos.tcos
A20ms(k20ms)
maxA20ms
minA20ms
A20ms(t)
A
Q1 - does it make sense to distinguish among harmonics and interharmonics at HF?
Time fluctuations: Rms
10/10 Go to Q1.1
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Q1.1 - How do fluctuate vs time waveform RMS values at HF?
42
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RMSTF: max fluctuations vs fn
43
Hz,...,,f,tfcos.tcos nnn 15000021 with 2010250212 1
1001
1
A
AAmax
n
Q1.1 - How do fluctuate vs time waveform RMS values at HF?
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RMS200ms: max fluctuations vs fn
44
Hz,...,,f,tfcos.tcos nnn 15000021 with 2010250212 1
1001
1
A
AAmax
n
Q1.1 - How do fluctuate vs time waveform RMS values at HF?
Go to Case Study Q1.1
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RMS10ms: max fluctuations vs fn
45
Hz,...,,f,tfcos.tcos nnn 15000021 with 2010250212 1
1001
1
A
AAmax
n
Q1.1 - How do fluctuate vs time waveform RMS values at HF?
1/3 Go to Q1.2
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46
Hz,...,,f,tfcos.tcos nnn 15000021 with 2010250212 1
RMS20ms: max fluctuations vs fn
1001
1
A
AAmax
n
Q1.1 - How do fluctuate vs time waveform RMS values at HF?
2/3 Go to Q1.2
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47
Hz,...,,f,tfcos.tcos nnn 15000021 with 2010250212 1
RMS200ms: max fluctuations vs fn
1001
1
A
AAmax
n
Q1.1 - How do fluctuate vs time waveform RMS values at HF?
3/3 Go to Q1.2
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Q1.2 - How do vary (H and IH) waveforms PEAK values with phase angles and how do fluctuate waveform PEAK values (only IH) vs time at HF?
48
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49
20msT and 921 with 20010250212 w1 kHz,...,,f,tfcos.tcos nnn
Peak fluctuations vs fn (An=1o/oo)
1001
1
A
AAmax
n
1001
1
A
AAmin
n
Q1.2 - How do vary waveforms PEAK values…
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Peak fluctuations vs fn (An=1%)
50
20msT and 921 with 2010250212 w1 kHz,...,,f,tfcos.tcos nnn
1001
1
A
AAmax
n
1001
1
A
AAmin
n
Q1.2 - How do vary waveforms PEAK values…
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51
20msT and 921 with 210250212 w1 kHz,...,,f,tfcos.tcos nnn
Peak fluctuations vs fn (An=10%)
1001
1
A
AAmax
n
1001
1
A
AAmin
n
Q1.2 - How do vary waveforms PEAK values…
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Peak fluctuations
52
0402102050212 tcos.tcos
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 -1.5
-1
-0.5
0
0.5
1
1.5
time [s]
sig
na
l
Amaxn
Aminn
Q1.2 - How do vary waveforms PEAK values…
1/7 Go to Q2
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Peak fluctuations
53
089402102050212 tcos.tcos
AmaxAmin
Q1.2 - How do vary waveforms PEAK values…
2/7 Go to Q2
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Peak fluctuations vs n (LF)
54
tcos.tcos 30020102050212 030020102050212 tcos.tcos
Q1.2 - How do vary waveforms PEAK values…
3/7 Go to Q2
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55
Approximated Min Peak
(pu)009510105000
50001 ..cos.
tcos.tcos 500020102050212
ih
ih
Af
fcosA 22 1
1
Peak fluctuations vs n (HF) Q1.2 - How do vary waveforms PEAK values…
4/7 Go to Q2
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56
Approximated Min Peak
ih
ih
Af
fcosA 22 1
1
tcos.tcos 900020102050212
(pu)0110109000
50001 ..cos.
Corresponds to Algebric
Max Peak
Peak fluctuations (HF) Q1.2 - How do vary waveforms PEAK values…
5/7 Go to Q2
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57
20msT and 921 with 025022010250212 w1 kHz,...,,f,tcostfcos.tcos nnn
Peak fluctuations vs fn (An=1% mod)
Q1.2 - How do vary waveforms PEAK values…
6/7 Go to Q2
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Peak fluctuations
58
tcos.tcos 900020102050212
,tcostcos.
tcos
2502900020102
050212
Q1.2 - How do vary waveforms PEAK values…
7/7 Go to Q2
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Q2 - IS IT STILL POSSIBLE TO UTILIZE SIMPLIFIED LINE MODELS (RL, PIGREC…) AT HF?
59
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60
1. Coincidence of the
behaviour of the two
different models in the
frequency range from 0 to
2.5 kHz;
2. Difference of series
resonance frequency
values for the two models
in the frequency range
from 2.5 to 9 kHz;
3. Entity of the damping
effects and the little shift
in the resonance
frequencies due to the
skin effect.
DP and P Models vs frequency
Impedance Magnitude[0-9kHz]
0 1 2 3 4 5 6 7 8 910
0
101
102
103
104
105
Frequency [kHz]
Impedence M
agnitude [
]
DP
P
DPno skin
Pno skin
2.5:9kHz
Positive sequence - 1 Equivalent
Q2.2 – How to model lines at HF?
2/4 Go to Q2.1 Go to Q2.2 Go to Q3
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61
0 10 20 30 40 50 60 70 80 90 10010
1
102
103
104
105
Frequency [kHz]
Impedence M
agnitude [
]
DP
P
More resonances (18)
in respect to positive
sequence (13) from 0 to
100 kHz due to the LC
product which value
increases in zero
sequence.
More sensible damping
effects.
The zoom evidencies
once again the
criticality of one P over
2.5kHz
DP and P Models vs frequency Impedance Magnitude[0-100kHz]
Q2.2 – How to model lines at HF?
Zero sequence - 1 Equivalent
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62
More resonances (18)
in respect to positive
sequence (13) from 0 to
100 kHz due to the LC
product which value
increases in zero
sequence.
More sensible damping
effects.
0 1 2 3 4 5 6 7 8 910
1
102
103
104
105
Frequency [kHz]
Impedence M
agnitude [
]
DP
P
The zoom evidencies
once again the
criticality of one P over
2.5kHz
DP and P Models vs frequency Impedance Magnitude[0-9kHz]
Zero sequence - 1 Equivalent
Q2.2 – How to model lines at HF?
Go to Case Study Q2.2
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63
1. It is well known that under the hypotheses of
transposed lines disposed in a simmetrical
manner, a three-phase line can be represented
by a single-phase equivalent circuit.
2. For a finite length x line a succession of series
and parallel resonances of impedance equally
spaced in the frequency appears.
3. Tipically, for short lines, with length x less than
/4, reference is made to concentrated
parameter models.
Distributed Parameters Model of a
infinitesimal length dx line element
Model of a line based on a single P
equivalent
1/4 Go to Q2.1 Go to Q2.2 Go to Q3
Q2 – Is it still possible…
Q2.2 – How to model lines at HF?
Q2.1 – Is it needed…
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64
CASE-STUDY
Wind turbine of 100 kW rated power connected to the MV network (20 kV) by
means of a 10 km length over-head line.
Full-power static converter with a switching frequency of 22.6 kHz
Simulations have been performed using either P and Distributed
Parameter models, both built-in in the EMTP-RV library.
2/4 Go to Q2.1 Go to Q2.2 Go to Q3
Q2 – Is it still possible…
Q2.2 – How to model lines at HF?
Q2.1 – Is it needed…
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65
CASE-STUDY(2)
Using P equivalent,
the single harmonic
components around
the switching
frequency of 22.6 kHz,
appear lower than the
compatibility levels
(0.27 %) for harmonic
voltages.
Voltage measured at wind turbine terminals using P equivalent
(a1, b1), 50 P equivalents in cascade (a2, b2) and Distributed
Parameter (a3, b3) models not considering the skin effect: a) time
waveforms; b) spectra.
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02-20
0
20
time [s]V
oltage [
kV
]
a1
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02-20
0
20
time [s]
Voltage [
kV
]
a2
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02-20
0
20
time [s]
Voltage [
kV
]
a3
22 22.2 22.4 22.6 22.8 23 23.20
1
2
frequency [kHz]
Voltage [
%]
b1
22 22.2 22.4 22.6 22.8 23 23.20
1
2
frequency [kHz]
Voltage [
%]
b2
22 22.2 22.4 22.6 22.8 23 23.20
1
2
frequency [kHz]
Voltage [
%]
b3
P
DP
P50
P
DP
P50
3/4 Go to Q2.1 Go to Q2.2 Go to Q3
Q2 – Is it still possible…
Q2.2 – How to model lines at HF?
Q2.1 – Is it needed…
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66
22 22.2 22.4 22.6 22.8 23 23.20
0.1
0.2
frequency [kHz]
Curr
ent
[%]
b1
22 22.2 22.4 22.6 22.8 23 23.20
0.1
0.2
frequency [kHz]
Curr
ent
[%]
b2
22 22.2 22.4 22.6 22.8 23 23.20
0.1
0.2
frequency [kHz]
Curr
ent
[%]
b3
22 22.2 22.4 22.6 22.8 23 23.20
1
2
frequency [kHz]
Voltage [
%]
b1
22 22.2 22.4 22.6 22.8 23 23.20
1
2
frequency [kHz]
Voltage [
%]
b2
22 22.2 22.4 22.6 22.8 23 23.20
1
2
frequency [kHz]
Voltage [
%]
b3
P
DP
P50
P
DP
P50
Voltage Distortion Current Distortion
CASE-STUDY(3)
4/4 Go to Q2.1 Go to Q2.2 Go to Q3
Q2 – Is it still possible…
Q2.2 – How to model lines at HF?
Q2.1 – Is it needed…
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Q3 - DO CLASSICAL TRANSFORMER MODELS STILL WORK ACCURATELY OR ACCEPTABLY AT HF?
67
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68
Power Transformers Calculation Parameters
This informations is usually available for any
transformer:
• Power rating (S); Voltage ratings (Vp, Vs); Excitation
current (Iexc); Excitation voltage (Vexc);Excitation losses
(Pexc); Short-circuit current (Ish); Short-circuit voltage
(Vsh); Short-circuit losses (Psh).
a is the percentage of the
resistance to be placed at the high-
voltage (HV) side and is the turn
ratio.
Resistances Total leakage reactance
Q3 – Do classical transformer…
1/5 Go to Conclusion
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69
Power Transformers Calculation Parameters: Inductance
- For concentric winding designs, the inner winding has smaller reactance
than the outer winding, and most often, the inner winding is the lower-
voltage winding.
- When the core saturates, the division between primary and secondary inductance,
can provide wrong results. The following default assumptions can be made for
leakage split: 1. Assumes concentric winding with HV side as outer;
2. Put most leakage impedance on the HV side, 75%–90% of total
inductance as LH:
3. Adjust the slope of the saturation curve, so that (LM + LH)
became a reasonable estimate of (0.3 to 0.8 pu. on self-cooled
base for large, high BIL transformers; 0.05 to 0.15 pu. for
distribution transformers).
Q3 – Do classical transformer…
2/5 Go to Conclusion
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70
Power Transformers Calculation Parameters: magnetizing components
Saturation can be incorporated into the magnetizing inductance of a power
transformer model using test data/manufacturer’s curves. In this case several
factors are to be taken into account:
1. The exciting current includes core loss and magnetizing
components;
2. Manufacturers usually provide root-mean-square (rms)
currents, not crest. Winding capacitance can significantly affect
low current data;
3. Hysteresis biases saturation curve . CORE LOSSES
Q3 – Do classical transformer…
3/5 Go to Conclusion
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71
Power Transformers Calculation Parameters: Capacitances
Disk windings Helical windings
e0 dielectric permittivity of vacuum;
et relative dielectric permittivity of the insulating material that
covers the conductor;
ed relative dielectric permittivity of the insulating
material between disks;
D average diameter of the winding;
h height of the conductor strip;
dt thickness of the insulation covering the conductor;
dd thickness of the insulation between the discs;
N winding sections;
n number of turns per section;
r thickness of the disk.
d distance between turns;
d0'=d0+d with d0 the outer diameter;
di'= di+d with di the inner diameter;
nt numbers of turns.
Q3 – Do classical transformer…
4/5 Go to Conclusion
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72
Power Transformers Calculation Parameters: Capacitances
e relative dielectric permittivity of the intervening
medium;
re internal radius of the external coil;
ri internal radius of the inner coil;
b axial distance between coils;
d diameter of the coil.
Concentric windings Different windings
Q3 – Do classical transformer…
5/5 Go to Conclusion
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RMS and Peak Fluctuation frequency
fn=149990 Hz gives fF=10 Hz as fn=90 Hz
73
90 Hz
149990 Hz