# 6- Fundamentals of Harmonics

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### Fundamentals of Harmonics

Electric Power System Engineering

Electric Power System Engineering

Palestine Polytechnic University

Palestine Polytechnic University

Joint MSc in Electrical Engineering (JMEE) Program

Joint MSc in Electrical Engineering (JMEE) Program

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## Harmonic Distortion

• Harmonics take place inHarmonics take place in steady statesteady state and are integer multiples of theand are integer multiples of the fundamental frequency.

fundamental frequency.

• The waveform distortion that produces the harmonics is continuously present orThe waveform distortion that produces the harmonics is continuously present or at least for several seconds.

at least for several seconds.

• Usually, harmonics are associated withUsually, harmonics are associated with the continuous operation of a loadthe continuous operation of a load.. •

• Harmonic distortion is caused byHarmonic distortion is caused by nonlinearnonlinear devicesdevices in the distribution system.in the distribution system. •

• AA nonlinear devicenonlinear device is defined as the one in which the current is not proportionalis defined as the one in which the current is not proportional to the applied voltage.

to the applied voltage.

• In a distribution system, mostIn a distribution system, most nonlinearitiesnonlinearities can be found in itscan be found in its shunt shunt elements,elements, that is, loads.

• harmonics study, it is customary to treat these harmonic-generating loads simplyharmonics study, it is customary to treat these harmonic-generating loads simply as harmonic current sources, that is,

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## Harmonics Cause

### Extra power losses in

–

– distribution transformers,distribution transformers,  –

– feeders,feeders,  –

– motors.motors.

(4)

## Distribution Factors

### (THD)

where

where

• V V hhis the harmonic is the harmonic voltagvoltage at harmonic frequencye at harmonic frequency““hh””ininrmsrms

• V V 11is the rated fundamental voltage inis the rated fundamental voltage in rmsrms

• hh is the harmonic order (is the harmonic order (hh= 1 corresponds to the = 1 corresponds to the fundamentalfundamental))

where

where

• IIhhis the harmonic current at harmonic frequency “is the harmonic current at harmonic frequency “hh” in” inrmsrms

• II11is the rated fundamental current in rmsis the rated fundamental current in rms 

 For balanced three-phase voltagesFor balanced three-phase voltages, the , the line-to-neutralline-to-neutral

voltage is used to

voltage is used to find THDv.find THDv.

 in the unbalanced casein the unbalanced case, it is necessary to calculate a, it is necessary to calculate a

different THD for each phase.

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(6)

## Total Demand Distortion (TDD)

• The current THD definition causes some confusion because there is a nonlinearThe current THD definition causes some confusion because there is a nonlinear relation

relationshipship between the magnitubetween the magnitude of the harmonic componede of the harmonic components and percennts and percent THD.t THD.

• a waveform with 120% does not contain twice the harmonic components of aa waveform with 120% does not contain twice the harmonic components of a waveform with 60% distortion.

waveform with 60% distortion.

• a small current may have a high THD but not be a significant threat to the system.a small current may have a high THD but not be a significant threat to the system. •

• This difficulty may be avoided by referring THD toThis difficulty may be avoided by referring THD to the fundamental of the peakthe fundamental of the peak

demand current rather than the fundamental of the present sample demand current rather than the fundamental of the present sample..

• This is calledThis is called total demand distortion (TDD)total demand distortion (TDD) and serves as the basis for the guidelinesand serves as the basis for the guidelines in IEEE Std. 519-1992. Therefore,

in IEEE Std. 519-1992. Therefore,

where

where

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The average

The average

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## Apparent Power

where

where SS11is the apparent poweris the apparent power at the fundamental frequency.

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## Power Factor

### true average active power)

cos

cos θ θ is the poweris the power

factor (PF) factor (PF)

For the sake of simplicity For the sake of simplicity

This PF is now called the

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### case

Note that here, the

Note that here, the VVhhandand IIhhquantities are the peak quantities:quantities are the peak quantities:

Therefore, because of harmonic distortion,

Therefore, because of harmonic distortion,

(11)

(12)

## True Power Factor (TPF)

• DD represents all cross products of voltage and current at different frequencies,represents all cross products of voltage and current at different frequencies, which yield no average power.

which yield no average power.

• Since the PF is a measure of the power utilization efficiency of the load,Since the PF is a measure of the power utilization efficiency of the load,

where

where

 DF = P/SDF = P/S11is the displacement is the displacement power factorpower factor

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## Factor (TPF)

• The unity PF The unity PF is attainable only with pure sinusoids. What is actually is attainable only with pure sinusoids. What is actually provideprovided is d is thethe displace

displacement PFment PF..

• Power quality monitoring instruments now commonly report both the displacementPower quality monitoring instruments now commonly report both the displacement factors as well as the TPFs.

factors as well as the TPFs.

• The displacement factoThe displacement factor is r is typically used in determining PF adjustments on a utilitytypically used in determining PF adjustments on a utility bill since it is related to the displacement of the fundamental voltage and current.

bill since it is related to the displacement of the fundamental voltage and current.

• sizing capacitors for PF correction is no longer simple. It is not possible to get unitysizing capacitors for PF correction is no longer simple. It is not possible to get unity PF due to the distortion power presence.

PF due to the distortion power presence.

• Capacitors basically compensate only for the fundamental frequency reactive powerCapacitors basically compensate only for the fundamental frequency reactive power and cannot completely correct the TPF to unity when there are harmonics present.

and cannot completely correct the TPF to unity when there are harmonics present.

• In fact, capacitors can make the PF worse by creating resonance conditions thatIn fact, capacitors can make the PF worse by creating resonance conditions that magnify the

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## Example

Based on the output of a harmonic analyzer, it has been determined that a

Based on the output of a harmonic analyzer, it has been determined that a

nonlinear load has a total rms

nonlinear load has a total rms currencurrent of 75 A. It also has 38, 21, 4.6, and 3.5 A fort of 75 A. It also has 38, 21, 4.6, and 3.5 A for

the third, fifth, seventh, and ninth harmonic currents, respectively. The instrument

the third, fifth, seventh, and ninth harmonic currents, respectively. The instrument

used in has been programmed to present the resulting data in amps rather than in

used in has been programmed to present the resulting data in amps rather than in

percentages. Based on the given information,

percentages. Based on the given information,

determine the following: determine the following:

a.

a. ThThe fe funundadamementntal al cucurrrrenent it in an ampmpss

b.

b. The amoThe amounts ounts of the thif the third, fird, fifth, sefth, sevenventh, and nith, and ninth hanth harmonrmonic curric currents ients in percen percentantagesges

c

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’’

b. b. Or Or

(16)

(17)

## Example

A 4.16 kV three-phase feeder is supplying a purely resistive load of 5400 kVA. It has

A 4.16 kV three-phase feeder is supplying a purely resistive load of 5400 kVA. It has

been determined that there are 175 V of zero-sequence third harmonic and 75 V of

been determined that there are 175 V of zero-sequence third harmonic and 75 V of

negative-sequence fifth harmonic.

negative-sequence fifth harmonic.

Determine the following: Determine the following:

a.

a. ThThe te tototal al vovoltltagage de disistotortrtioion.n.

b.

b. Is the Is the THD beTHD below tlow the IEEhe IEEE StE Std. 519d. 519-1992 -1992 for for the 4.the 4.16 kV 16 kV distdistriburibution stion systystem?em?

### Solution

(a) (a) (b) (b) the THD

the THDVV limit for 4.16 kV is 5%. limit for 4.16 kV is 5%. Since the THD calculated is 4.58%, it is less than Since the THD calculated is 4.58%, it is less than thethe

limit of

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## Power in Passive Elements

### effect, then

where

where RRhhis the resistance at theis the resistance at the hhththharharmonmonic.ic.

, where

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### A. Power in a Pure Resistance

ContCont’’dd

• Alternatively, expressed in terms of current,Alternatively, expressed in terms of current,

• Note that the aforNote that the aforementionementioned equations can be re-eed equations can be re-expressed in puxpressed in pu asas

• For aFor a purely resi purely resistive elemestive element nt , it can be observed from, it can be observed from

  = =   1 +     1 +    = =   1 +     1 +    That That where where P

P is the total power loss in the resistanceis the total power loss in the resistance

P

P11is the power loss is the power loss in the resistance at the in the resistance at the fundamentfundamental frequencyal frequency

, where

(20)

### B. Power in a Pure Inductance

• Power in a pure inductance can be expressed asPower in a pure inductance can be expressed as

• • WhereWhere • • ThusThus • • So thatSo that  

 is the is the fundamental frequencyfundamental frequency

(21)

### C. Power in a Pure Capacitance

• Power in a pure capacitance can be expressed asPower in a pure capacitance can be expressed as

• TheThe negative signnegative sign indicates that the reactive power is delivered to the loadindicates that the reactive power is delivered to the load

• ThusThus

(22)

## Harmonic Distortion Limits

### .

–

– gives the recommended practice for electric power system designers to control thegives the recommended practice for electric power system designers to control the harmonic distortion that might otherwise determine electric power quality.

harmonic distortion that might otherwise determine electric power quality.

–

– a guideline in the design of power system with nonlinear loads.a guideline in the design of power system with nonlinear loads.  –

– The limits set are for steady-state operation and are recommended forThe limits set are for steady-state operation and are recommended for ““worse- worse-case

case”” conditions.conditions.

–

– The underlying philosophy is thatThe underlying philosophy is that the customer should limit harmonic currents andthe customer should limit harmonic currents and

the electric utility should limit harmonic voltages. the electric utility should limit harmonic voltages.

–

– It does not specify the highest-order harmonics to be limited.It does not specify the highest-order harmonics to be limited.  –

– it does not differentiate between single-phase and three-phase systems. Thus, theit does not differentiate between single-phase and three-phase systems. Thus, the recommended harmonic limits equally apply to both.

recommended harmonic limits equally apply to both.

It does also address direct current that is not a harmonic.

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## Voltage Distortion Limits

• The PCC is The PCC is the location wherethe location where

another customer can be served from

another customer can be served from

the system.

the system.

• It can be located at either the primaryIt can be located at either the primary

or the secondary of a supply

or the secondary of a supply

transformer depending on whether

transformer depending on whether

or not multiple customers are

or not multiple customers are

supplied from the transformer.

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(25)

(26)

## Current Distortion Limits

• The harmonic currents from an individual customer are evaluated at the PCCThe harmonic currents from an individual customer are evaluated at the PCC where the utility can supply other customers.

where the utility can supply other customers.

• The limits are dependent on the customer load in relation to the system short-The limits are dependent on the customer load in relation to the system short-circuit capacity at the

circuit capacity at the PCC.PCC.

• Note that all current limits are expressed as a percentage of the customerNote that all current limits are expressed as a percentage of the customer ’’ss average maximum demand load current.

average maximum demand load current.

• The current distortion limits vary by the size of the user relative to the utilityThe current distortion limits vary by the size of the user relative to the utility system capacit

(27)

scsc

LL

### Determine the three-phase short-circuit duty

IISC SC at the PCC.at the PCC.

DD

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## Harmonics Evaluation at PCC

• The harmonic characteristics of the utility circuit seen from the PCC are oftenThe harmonic characteristics of the utility circuit seen from the PCC are often not known accurately.

not known accurately.

• Therefore, good engineering judgment often dictated to review a case-by-caseTherefore, good engineering judgment often dictated to review a case-by-case basis.

basis.

• However, through a judicious application of the recommended practice, theHowever, through a judicious application of the recommended practice, the interferences between different loads and the system can be minimized.

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### nonlinear loads includes the following:

1.

1. DeDefifininitition on of of ththe Pe PCCCC

2.

2. DeDetterermiminanatition oon of thf thee IIscsc,, IILL, and, and IIscsc//IILL at the PCCat the PCC

3.

3. FindFinding the hing the harmoarmonic cunic currerrent and cnt and currurrent dient distostortion ortion of the nonf the nonlinelinear loadar load

4.

4. DetDetermierminatination of wheon of whether or nother or not the harmt the harmonic cuonic currerrent and cunt and currerrent disnt distorttortionsions

in step 3 satisfy IEEE 519-1992 recommendation limits

in step 3 satisfy IEEE 519-1992 recommendation limits

5.

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## Harmonic controls

### The objectives are the following:

1)

1) CustCustomeromers should lims should limit harmit harmonic curonic currenrents, sincts, since they hae they have conve controtrol over thel over their loadsir loads;;

2)

2) ElecElectric utitric utilitilities shoules should limit had limit harmonirmonic voltc voltageages, sincs, since they hae they have conve control otrol over thever the

system impedances;

system impedances;

3)

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## tation of a

• In power systems, the nonlinear load can be modeled as a load for theIn power systems, the nonlinear load can be modeled as a load for the fundamental current and as a current source for the harmonic currents.

fundamental current and as a current source for the harmonic currents.

• The harmonic currents flow from the nonlinear load toward the power source,The harmonic currents flow from the nonlinear load toward the power source, following the paths of least impedance

(32)

### General flow of harmonic currents in a radial power system

without power capacitors

(33)

## ransformers

• Transformers serving nonlinear loads exhibit increased eddy current losses dueTransformers serving nonlinear loads exhibit increased eddy current losses due to harmonic currents generated by those loads.

to harmonic currents generated by those loads.

(34)

## K-Factor

• K-factorK-factor is an indication to transformer’s suitabilityis an indication to transformer’s suitability fofor nonsinur nonsinusoidsoidalal loadload currents.

currents.

• K-factor relates transformer capability to serve varying degrees of nonlinear loadK-factor relates transformer capability to serve varying degrees of nonlinear load without exceeding the rated temperature rise limits.

without exceeding the rated temperature rise limits.

• It is based on the predicted losses of a transformer.It is based on the predicted losses of a transformer. •

• InIn per unit  per unit , the, the K K -factor is-factor is

where

(35)

## K-Factor

• Manufacturers build specialManufacturers build special K K -factor transformers. Standard-factor transformers. Standard K K -factor ratings are-factor ratings are 4, 9, 13, 20, 30, 40, and 50.

4, 9, 13, 20, 30, 40, and 50.

• For linear loads, theFor linear loads, the K K -factor is always one.-factor is always one. •

• For nonlinear loads, if harmonic currents are known, theFor nonlinear loads, if harmonic currents are known, the K K -factor is calculated-factor is calculated

and compared against the transformer’s

and compared against the transformer’s nameplatenameplate K K -factor.-factor.

• As long as the loadAs long as the load K K -factor is equal to, or less than, the transformer-factor is equal to, or less than, the transformer K K -factor-factor, , thethe transformer does not need to be derated.

(36)

## Derating

• For transfFor transformers, ANSI/Iormers, ANSI/IEEE Std. C75.110 prEEE Std. C75.110 provides a method to derateovides a method to deratethethe transformer capacity when supplying nonlinear loads.

transformer capacity when supplying nonlinear loads.

• The transformer derating is based on additional eddy current losses due to theThe transformer derating is based on additional eddy current losses due to the harmonic current and that these losses are proportional to the square of the

harmonic current and that these losses are proportional to the square of the

frequency. Thus,

frequency. Thus,

where

where

• PPec-rec-ris the maximum transformer per unitis the maximum transformer per unit eddy current loss factor (typically, between

eddy current loss factor (typically, between

0.05 and 0.10 per units for dry-type

0.05 and 0.10 per units for dry-type

transformers).

transformers).

• IIhhis the is the harmonic current, normalized byharmonic current, normalized by dividing it by the fundamental current.

dividing it by the fundamental current.

(37)

(38)

## Example

Assume that the per unit harmonic currents are 1.000, 0.016, 0.261, 0.050, 0.003,

Assume that the per unit harmonic currents are 1.000, 0.016, 0.261, 0.050, 0.003,

0.089, 0.0

0.089, 0.031, 0.00231, 0.002, 0.048, 0.026, 0.048, 0.026, 0.001, 0.033, 0.001, 0.033, and 0.021 pu, and 0.021 pu A for the harmonicA for the harmonic

order of 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, and 25, respectively. Also assume

order of 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, and 25, respectively. Also assume

that the eddy current loss factor is 8%. Based on ANSI/IEEE Std. C75.110,

that the eddy current loss factor is 8%. Based on ANSI/IEEE Std. C75.110,

determine the following: determine the following:

a

a.. TThheeK K -factor of the transformer-factor of the transformer

b.

(39)

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