high frequency waveform distortiongrouper.ieee.org/groups/harmonic/simulate/panel...

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

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

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

Q1 - DOES IT MAKE SENSE TO DISTINGUISH AMONG HARMONICS AND INTERHARMONICS AT HF?

4

Q1.1 - How do fluctuate vs time waveform RMS values at HF?

5

RMS20ms: max fluctuations vs fn

6

Hz,...,,f,tfcos.tcos nnn 15000021 with 2010250212 1

1001

1

A

AAmax

n


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

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

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


pndepends on

component

insulation

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


Go to Case Study Q1.2

Q2 - IS IT STILL POSSIBLE TO UTILIZE SIMPLIFIED LINE MODELS (RL, PIGREC…) AT HF?

11

12

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…

13

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”?


Go to Case Study Q2

0.50km at 150kHz

Q2.1 - IS IT NEEDED TO ACCOUNT FOR PARAMETER (R, L, C,…) VARIABILITY VERSUS FREQUENCY AT HF?

14

15

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, …)…


Q2.2 - HOW TO MODEL LINES AT HF?

16

17

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

Q3 - DO CLASSICAL TRANSFORMER MODELS STILL WORK ACCURATELY OR ACCEPTABLY AT HF?

18

19

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…

20

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


Go to Case Study Q3

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

21

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.

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

23

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!

24

25

Thank you for your attention!

Alfredo Testa: [email protected]

Roberto Langella: [email protected]

Q1 - DOES IT MAKE SENSE TO DISTINGUISH AMONG HARMONICS AND INTERHARMONICS AT HF?

27

H and IH: Nomenclature (1)

28

Q1 - does it make sense to distinguish among harmonics and interharmonics at HF?

H and IH: Nomenclature: RMS (2)

29


H and IH: Nomenclature: Peak (3)

30


H and IH: Nomenclature: Peak (4)

31

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


Go to Case Study Q1

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


1/10 Go to Q1.1

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


2/10 Go to Q1.1

Time window Tw

• Tw=TF = Fourier fundamental period

• Tw=10 ms

• Tw=20 ms

• Tw=200 ms

34


3/10 Go to Q1.1

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


4/10 Go to Q1.1

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


5/10 Go to Q1.1

37

Time fluctuations 0402102050212 tcos.tcos


6/10 Go to Q1.1

38

Time fluctuations: Rms

0402102050212 tcos.tcos

20ms


8/10 Go to Q1.1

39

Time fluctuations: Peak

0402102050212 tcos.tcos

maxÂ

minÂ

40


0402102050212 tcos.tcos

20ms

0402102050212 tcos.tcos


9/10 Go to Q1.1

41

0402102050212 tcos.tcos

A20ms(k20ms)

maxA20ms

minA20ms

A20ms(t)

A



10/10 Go to Q1.1


42

RMSTF: max fluctuations vs fn

43


1001

1

A

AAmax

n



44


1001

1

A

AAmax

n




45


1001

1

A

AAmax

n


1/3 Go to Q1.2

46



1001

1

A

AAmax

n


2/3 Go to Q1.2

47



1001

1

A

AAmax

n


3/3 Go to Q1.2

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?

48

49


Peak fluctuations vs fn (An=1o/oo)

1001

1

A

AAmax

n

1001

1

A

AAmin

n


Peak fluctuations vs fn (An=1%)

50


1001

1

A

AAmax

n

1001

1

A

AAmin

n


51


Peak fluctuations vs fn (An=10%)

1001

1

A

AAmax

n

1001

1

A

AAmin

n


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


1/7 Go to Q2

Peak fluctuations

53

089402102050212 tcos.tcos

AmaxAmin


2/7 Go to Q2

Peak fluctuations vs n (LF)

54

tcos.tcos 30020102050212 030020102050212 tcos.tcos


3/7 Go to Q2

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

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

57

20msT and 921 with 025022010250212 w1 kHz,...,,f,tcostfcos.tcos nnn

Peak fluctuations vs fn (An=1% mod)


6/7 Go to Q2

Peak fluctuations

58

tcos.tcos 900020102050212

,tcostcos.

tcos

2502900020102

050212


7/7 Go to Q2

Q2 - IS IT STILL POSSIBLE TO UTILIZE SIMPLIFIED LINE MODELS (RL, PIGREC…) AT HF?

59

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


2/4 Go to Q2.1 Go to Q2.2 Go to Q3

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]


Zero sequence - 1 Equivalent

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



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




Q2.1 – Is it needed…

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.





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





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)





Q3 - DO CLASSICAL TRANSFORMER MODELS STILL WORK ACCURATELY OR ACCEPTABLY AT HF?

67

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


1/5 Go to Conclusion

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).



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



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.



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



RMS and Peak Fluctuation frequency

fn=149990 Hz gives fF=10 Hz as fn=90 Hz

73

90 Hz

149990 Hz

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