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The Need for Probabilistic Limits of Harmonics:Proposal for IEEE Std 519 Revision

Paulo Ribeiro

Calvin College / BWX Technologies, Inc

Guide Carpinelli

University of Cassino, Italy

Porto Alegre, Brasil

Agosto 2001

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THDV

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0.8%

1.2%

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THDV

The causes of variations are the continuous changes in system configurations, linear The causes of variations are the continuous changes in system configurations, linear load demands and operating modes of non linear loadsload demands and operating modes of non linear loads

Time-Varying Nature of Harmonics

An Inevitable Reality

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““The variations generally have a The variations generally have a random character and the only way one random character and the only way one can describe the behavior of such can describe the behavior of such characteristics is in statistical terms”characteristics is in statistical terms”

Time-Varying Nature of Harmonics

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Harmonic IndicesHarmonic Indices

Probability FunctionsProbability Functions

Statistical measuresStatistical measures

Summation LawsSummation Laws

Harmonic ImpedancesHarmonic Impedances

Time-dependent LimitsTime-dependent Limits

Aspects to be Considered

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Usual indices are referred only to the Usual indices are referred only to the harmonic amplitudeharmonic amplitude

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2h

2h

V V

V

THD

1

hh V

Vv

neglecting the harmonic phase anglesneglecting the harmonic phase angles

Indices

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Harmonic phases angles are Harmonic phases angles are randomly varying:randomly varying:

Im(V5)

Re(V5)

Im(V23)

Re(V23)

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Marginal probability density functionMarginal probability density function

-4 -3 -2 -1 0 1 2 3 40

0.1

0.2

0.3

0.4

fX

X

Time-Varying Nature of Harmonics

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Time ranges involved (hours, day, etc.)Time ranges involved (hours, day, etc.)

Multimodal patternsMultimodal patterns

Time interval between readings and the Time interval between readings and the window widthwindow width

Application to estimate the thermal effectsApplication to estimate the thermal effects

Time-Varying Nature of Harmonics

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Application to estimate the thermal effects Application to estimate the thermal effects of harmonicsof harmonics

The time factor is completely lost and the same The time factor is completely lost and the same pdf can correspond to different time varying pdf can correspond to different time varying harmonics, with consequent different thermal harmonics, with consequent different thermal responses of electrical componentsresponses of electrical components

Time-Varying Nature of Harmonics

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If new statistical data is used properly, a more accurate If new statistical data is used properly, a more accurate and reliable prediction of thermal effects should be and reliable prediction of thermal effects should be possiblepossible

0

5

10

15

.0001 .001 .01 .1 1τ/Tp

Per

cent

err

or 2D

3D

Time-Varying Nature of Harmonics

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Example: pdf of the 5Example: pdf of the 5thth Harmonic Voltage given that its Harmonic Voltage given that its amplitude is greater than or equal to 6%amplitude is greater than or equal to 6%

0

0.5

1

1.5

2

V5

fV5

5V 6%V

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

V5

f*V5

6%V 5V

Time-Varying Nature of Harmonics

Conditional probability density functionsConditional probability density functions

to reduce the volume of data to be analyzedto reduce the volume of data to be analyzed

to represent extreme eventsto represent extreme events

to introduce intriguing new statistical measuresto introduce intriguing new statistical measures

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standardstandard deviation deviation 95% 95% probabilityprobability value PC95% value PC95% 99% 99% probabilityprobability value PC99% value PC99% maximummaximum value MAX value MAX

The IEC 1000-3-6 and EN 50160 refer to PC95% and MAXThe IEC 1000-3-6 and EN 50160 refer to PC95% and MAX

average value average value

Statistical Measures

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Harmonic pdfs with the same PC95% and Harmonic pdfs with the same PC95% and MAX can cause different effectsMAX can cause different effects

= 0.70 = 0.27 = 0.27 = 0.16

x0.95 x0.95

Statistical Measures

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Expected value, probabilities calculated from Expected value, probabilities calculated from the conditional pdf can be useful numerical the conditional pdf can be useful numerical measuresmeasures

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

V5

f*V5

6%V 5V

Statistical Numerical Measures

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hh

α

j

αhjh UU

j

hjhjh IkI

kkhjhj = diversity factor = diversity factor

ααhh = summation exponent = summation exponent dependent on harmonic orderdependent on harmonic order

Two semi-empirical approaches have been proposed in Two semi-empirical approaches have been proposed in literature in order to allow easy and fast evaluation in literature in order to allow easy and fast evaluation in practical applications such as standardspractical applications such as standards

Summation Laws

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The laws should be continuously The laws should be continuously verified to take into account:verified to take into account:

new electronic componentsnew electronic components

the presence of unbalanced conditionsthe presence of unbalanced conditions

the influence of the network supplying the influence of the network supplying the harmonic sourcesthe harmonic sources

Summation Laws

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Usually, the network harmonic impedances are assigned with Usually, the network harmonic impedances are assigned with reference to deterministic values and without taking into account reference to deterministic values and without taking into account the correlation with disturbing currentsthe correlation with disturbing currents

Harmonic Impedances

The network harmonic impedance has statistical behavior The network harmonic impedance has statistical behavior due to: due to:

• network component uncertaintiesnetwork component uncertainties

• load variability (including power factor correction load variability (including power factor correction capacitors)capacitors)

• supply system variabilitysupply system variability

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EquipmentEquipment

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Up to now the studies on harmonic effects mainly Up to now the studies on harmonic effects mainly (but not only) refer to static distortions (but not only) refer to static distortions

Studies are needed on harmonic effects when time-Studies are needed on harmonic effects when time-varying distortion is appliedvarying distortion is applied

Time-Dependent Limits

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Proposition For IEEE 519

IEEE 519-1992 introduced the concept of probability distribution plots to characterise variations in harmonic levels.

A reasonable method of using these types of plots to evaluate harmonic levels would be to compare the steady state harmonic limits with the measured harmonic level that is not exceeded 95% of the time (the 95% probability point). This is consistent with the evaluation of compatibility levels in IEC standards.

In order to further develop this topic the IEEE Probabilistic Aspect of Harmonics Task Force is preparing a proposal for the Std. 519 in which the time-varying nature of harmonics voltages are considered in the establishment of the limits.

Any limits on the short duration harmonic levels should be based on the possible impacts of these harmonic levels. Effects such as metering error and equipment ageing are the accumulated result of harmonic levels over time. Other effects include the sensitive electronics to short burst of high harmonic levels or certain types of waveform distortions.

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Proposition For IEEE 519

Recommendations are being prepared, with suggested procedures and values to be discussed by the members of the Std. 519 Revision Task Force. These recommendations will be consistent with the 519 Application Guide.

Probability distributions and short-term disturbance limits shall be established.

The “continuous limits” could be taken as, for example, the 95% probability limit.

The values will be established based on the impact of short-term harmonics on different equipment.

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THD B ins (% )

Fre

qu

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cy

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0 .7 0 .8 0 .9 1 1 .1 1 .2 1 .3 1 .4 1 .5 1 .6 1 .7 1 .8 1 .9

0 .00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

S ite 1092 THD His tog ramJ une 19 - J une 26 , 1992

C ount = 305M in im um = 0 .739M ax im um = 1 .949

R ange = 1 .211M ean = 1.406

M ed ian = 1 .489S tandard D evia t ion = 0 .318

S tandard E rro r = 0 .0182V arianc e = 0 .101

S k ew nes s = -0 .521K urtos is = -0 .777

Table 1 – Short-Term LimitsShort-Time

Limits Duration ofDisturbance

A x Continuous Limits a1 sec < T < b1 sec

B x Continuous Limits b1 sec < T< a2 min

C x Continuous Limits a2 min < T< b2 min

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Proposition For IEEE 519

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Observations

The harmonic limits have to be assigned on the basis of harmonic effects, which differ substantially depending on the characteristic of the affected equipment.

There are long-term effects such as the component aging which is the accumulated result of harmonic levels over time, and “instantaneous” effects such as the malfunction of electronic equipment caused by only one short burst of high harmonic level.

The probabilistic nature of harmonics thus requires the establishment of time-dependent limits.

Several standards recognize this need, but have not comprehensively dealt with the issue if at all. For instance, the IEC 1000-3-6 includes the time variation by setting limits in terms of percentile and accepting that the maximum weekly value of the voltage harmonic over very short 3 s periods should not exceed an A times the assigned planning/design continuous limits.

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Observations

At present, time-dependent limits can only be implemented by common sense engineering judgement. Previous studies have treated harmonic effects from a steady-state / static distortion point of view.

The IEEE Task Force on Probabilistic Aspects of Harmonics is working on the preparation of a proposal to be presented to the IEEE Std 519 Review Task Force with some suggestions for establishing time-varying harmonic limits.

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• Efforts should be made to simplify their practical Efforts should be made to simplify their practical application, by introducing global indices which are application, by introducing global indices which are able to capture more than one aspect of the Power able to capture more than one aspect of the Power QualityQuality

• Due to the high number of probabilistic aspects to be Due to the high number of probabilistic aspects to be taken into account, the IEEE 519 should be explicitly taken into account, the IEEE 519 should be explicitly consider this problem.n consider this problem.n

• The time-varying nature of harmonics requires the The time-varying nature of harmonics requires the adoption of probabilistic Standards adoption of probabilistic Standards

Conclusions