Harmonics: Theory, Sources, & Mitigation

Harmonics and Power Quality Conference

September 14-15, 2006

Outline

Waveform ReviewHarmonics and Fourier AnalysisHarmonic Analysis TechniquesHarmonic CharacteristicsHarmonic SourcesHarmonic TripleinsEffects of Harmonic DistortionMitigation TechniquesConclusionsReferences

Waveform Review

Current and voltage are represented by a sinusoidal wave form

Frequency=1/period, hertz

I(t)=Ipsin(θ)=Ipsin(2πft)=Ipsin(ωt)

V(t)=Vpsin(θ)=Vpsin(2πft)=Vpsin(ωt)

http://www.circuit-magic.com/sinusoidal_circuits_analysis.htm

Waveform Review

Balanced 3Ø system, phases 120° apart, zero current on the neutral

Unbalanced loads cause current to flow in neutral, In=Ia+Ib+Ic

http://www.tpub.com/doeelecscience/electricalscience2131.htm

Waveform Review

Linear loads produce a linear, straight-line, response

Purely resistive, capacitative, inductive loads

Non-linear loads produce a curved response

Response of each device is different

Harmonics and Fourier Analysis

Harmonic frequencies are integer multiples of the fundamental frequency

60 Hz: 120,180,240,300,360,420,480,54050 Hz: 100,150,200,250,300,350,400,450

Fourier transform: periodic complex waveforms can be expressed as the sum of an infinite series of sinusoidal signals

http://ecmweb.com/ar/606ecmINSIDEPQfig3.jpg

Harmonics and Fourier Analysis

f(t)=function of waveform

cn=Fourier component for the nth harmonic

ω0=2πf0, where f0=fundamental frequency

T0=period

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Harmonics and Fourier Analysis

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an, bn are the real and imaginary components of the nth harmonic phasor

θn= phase angle of the nth harmonic

a0=average value of the signal

Harmonic Characteristics

In symmetrical waveforms even harmonics are absentHigher harmonic frequencies tend to differ in phase angle and cancel more than the 1st-11th harmonics, phase angle affects harmonic power flowHarmonics are steady-stateCurrent distortion causes voltage distortion at same harmonic frequencySource impedance is inversely related to current distortion and directly related to voltage distortion

Harmonic Analysis TechniquesSpectrum analysis at different points of the system using software applying FFT (fast Fourier transform) analysis

Calculate amount of voltage or current at harmonic frequencies as percentage of that at the fundamental frequency, calculate phase angle of each harmonic, calculate THD, total harmonic distortion

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Harmonic Analysis Techniques: Results

THD is relative to the amount of voltage or current presentTHDV is more meaningful measurement than TDHIHarmonic amperes more useful than THDI, the greater the current the more significant THDI becomesIEEE-519 recommends THD levels for PCC with utility power

Current distortion: TDD 5% for Isc/IL <20, TDD 20% for ratios >1000Voltage distortion: 5% general systems, 10% dedicated systems, 3% for special applications

Levels within facility should be low enough to ensure correct operation and life expectancy of all equipment

Harmonic Sources

Saturable devices- transformers and non-linear reactors

Arcing loads- welding loads, arc furnaces, fluorescent lighting distort voltage as a result of non-linearity of electric arc

Power electronic equipment- VFD, DC motor drives, electronic power supplies, PWM drives without choke

Harmonic Sources: Pulsed

Harmonic TripleinsEven in a balanced system, third harmonics and third harmonic integer multiples (9,15,21…) will cause current to flow in the neutralPhase shift is also multiplied by the same integer as the fundamental frequencyTriplein harmonics do not cancel, but rather add in the neutral conductor of a 4 wire, wye connected loadThird harmonic neutral current is 300% of third harmonic phase current If current is balanced, little fundamental current in neutral, very high THDI% Amp rating of neutral transformer, very important, 1.73x IL Consider delta-delta connected source and loads

Effects of Harmonic DistortionCurrent distortion effects on linear loads in facility is minimal, path dependent, greater effect on distribution systemOnly fundamental current can power loadsCurrents at higher frequencies increase I2Z losses due to increased transformer impedanceCurrent distortion causes voltage distortionVoltage distortion caused at one location will be fed to all equipment on buses common to that point Voltage distortion worse the further it occurs from the transformer5th harmonic voltage distortion especially bad for 3Ø motorsHarmonics can be magnified due resonance caused by capacitor banksLarge electrical machine can excite higher frequency resonances, >20th harmonic

Mitigation Techniques

Central or localizedIsolation transformers

Line reactors

Tuned harmonic filters

Low pass harmonic filters

Active harmonic filters

Dynamic filters

Active (IGBT) rectifier front end

12 and 18 pulse bridge rectifiers

Conclusions

Solve harmonic problems at the sourceLook for harmonic current related problemsControl voltage distortion by keeping current distortion lowIncrease neutral conductor size, separate neutrals per phase, third harmonic filtersCombine methods to have the most effective and economical solution

ReferencesD. Mueller, Harmonics in Industrial and Commercial Facilities, EC&M Harmonics and Power Quality Conference, St. Louis, MO (2006).J. Houdek, Harmonic Mitigation Alternatives, EC&M Harmonics and Power Quality Conference, St. Louis, MO (2006).M. Lowenstein, Harmonic Current and Voltage Distortion, EC&M, http://ecmweb.com/mag/electric_harmonic_current_voltage/index.html (2002).J. Dedad, The How's and Why's of Harmonic Distortion, EC&M, http://ecmweb.com/mag/electric_hows_whys_harmonic/index.html (2006).Harmonic Distortion, Galco Industrial Electronics, http://www.galco.com/circuit/PFCC_har.htm (1996).E. Beroset, J. Starck, Lessons in Electronic Circuits, Vol. II, iBiblio, http://www.ibiblio.org/obp/electricCircuits/AC/AC_10.html (2002). J. Irwin, Basic Engineering Circuit Analysis, John Wiley and Sons, Inc., New York, NY(2002).E. Weisstein, Fourier Series, Wolfram MathWorld, http://mathworld.wolfram.com/FourierSeries.html (2004).