POWER SYSTEM ANALYSIS TADP 641 - Gonzaga University

POWER SYSTEM ANALYSISTADP 641

HARMONICSIN DISTRIBUTION

SYSTEMS

Juan Manuel Gers, PhD

Introduction

One of the main purposes of this chapter is to determine possibilitiesof harmful conditions that may arise when a feeder reconfigurationtakes place, due to the coincidence of harmonic sources andcapacitors installed in the system.

General Considerations About Harmonics

Consider the case of a feeder with capacitors that is operatingnormally and to reduce losses in the system, receives load fromanother feeder that has harmonic sources.

This situation could bring about :

Resonance conditionsDeteriorate the power qualityProduce dangerous overvoltages.


Likewise, if a feeder with harmonic sources receives load fromanother feeder that has capacitors, resonance conditions could beproduced and so the undesirable effects referred to before.

In the two cases mentioned, it is clear that both feeders, havenormal operating conditions before any reconfiguration takes place.


Before any switching should be verified

Harmonic sourcesCapacitorsOr both

That no nasty effects will be produced in thefeeder that receives such a load.

Being that the case, the reconfiguration should be discarded although it could produce important losses savings, unless the reason that caused the difficulty is cleared, by changing for example the size of the capacitors.


Harmonics are voltage or current sinusoidal signals withfrequencies that are multiples of the power frequency whichcan produce harmful conditions in power systems

The harmonic signals in power and distribution systems areproduced by different equipment :

Arc furnacesDC and AC drivesAC/DC rectifiers.


In low voltage there are other harmonic sources as follows:

Electric welders,Devices with saturated cores,Fluorescent lamps,UPS for computers and so on, which although havelower values, their huge usage has increased theeffect on distribution systems.


The harmonics produce in general negative effects such us:

Overheating of cables, transformers and rotative machines.Mal-operation of protection, control and measurement devices especially if they are electronic made.Overvoltages especially when resonance conditions appear due to capacitors.



Mathematical BackgroundFourier series allows to represent any continuous periodic function by asum of a sinusoidal component plus a series of sinusoidal harmonics ofhigher order with frequencies multiples of the fundamental one. Anyperiodical signal can be expanded by Fourier Series if it satisfies theDirichlet’s conditions:

To have a definite number of discontinuities in a period.To have a finite number of maximums and minimum in a period.The integral of the function in a period should have a finite value

Mathematical Background

Therefore the Fourier Series gets the following form:

( ) ( )( )∑∞

=

++=1

0

2)(

nnn tnSinBtnCosA

Atf ωω

∫−

=2

2

)(20

T

T

dttfT

A ( )∫−

=2

2

)(2T

T

dttnCostfT

An ω

( )∫−

=2

2

)(2T

T

dttnSintfT

Bn ω ...,3,2,1=n

Where :


This equation can be written as follows:

( )22nnn BAC +=

Cn represents the magnitude and an the n-th harmonic phase of the function f(t).

Where:


Once the harmonic decomposition of a signal is done, the magnitudeand phase angle of each harmonic are obtained. This information isthe base to calculate the Total Harmonic Distortion (THD), definedas:

( ) %100.....

%1

223

22 ×

+++=

CCCC

THD n

C1: Magnitude of the component of the fundamental frequency

Cn: Magnitude of the n-th harmonic component

Where:

Resonance

The presence of capacitors to compensate the power factor canbring about resonances since the equivalent of most electricalsystems is reactance type. The resonances can produce highlevels of current and/or voltages that affect the installed equipment.

• Series Resonance• Parallel Resonance

Parallel ResonanceA parallel resonance occurs when a capacitor and an inductor areconnected in parallel and the impedance magnitudes of bothelements are equal. In this case the equivalent impedance tends toinfinite and therefore harmonic currents of the resonant frequencycan produce very high voltage values. This condition therefore hasto be avoided as equipment can be seriously affected.

Series ResonanceA series resonance occurs when a capacitor and an inductor areconnected in series and the impedance magnitudes of bothelements are equal. In this case the equivalent impedance tends toinfinite and therefore harmonic currents of the resonant frequencycan produce very high voltage values. This condition therefore hasto be avoided as equipment can be seriously affected.

Resonance

The harmonic load flow requires a proper model for the harmonicsources, for the system equivalent, for the loads and for thebranches that considers the frequency of the respective harmonic

Models

Harmonic Sources

The harmonic sources considered in the harmonic load flow arerepresented as independent current sources, each with adetermined number of harmonic frequency. For each harmonicfrequency the source has a definite magnitude in Amps.

In order to obtain a result that combines all the harmonic sources,the Superposition Theorem is applied. Depending on the sourcelocation a branch can have different currents and therefore it isessential to consider the phasor angles of voltages and currents.

Models

With the results obtained from the load flow at power frequency andthe harmonic load flow, the rms voltages of the nodes and currentsat the branches and capacitors are calculated as well as the THD(Total Harmonic Distortion) or TDD (Total Demand Distortion) asdefined in the Standard IEEE 519-1992. The following expressionsare applied:

Verification of Harmonic Values

222

21 ..... nrms VVVV +++=

222

21 ..... nrms IIII +++=

%100.....

1

223

22 ×

+++=

VVVV

THD nV

%100.....

1

223

22 ×

+++=

IIII

THD nI

%100..... 22

322 ×

+++=

D

n

IIII

TDD


Where:

Vrms rms voltage of a nodeIrms rms current through a branch or element of the systemTHDV Total harmonic voltage distortion in a nodeTHDI Total harmonic current distortion of the current

through a branch or element of the systemTDD Total harmonic current distortion of the current through a

branch or element of the system based on the maximumdemand current

V1 Fundamental component of the voltage in a node


Where:

I1 Fundamental component of the current trough a branch orelement of the system

Vn Harmonic component of order n of the voltage in a nodeIn Harmonic component of order n of the current through a

branch or element of the systemID Calculated maximum demand current through a branch or

element of the system


The distortion values allowed by IEEE Standards were consideredfor this work since they apply very clearly to distribution systems.Standard IEEE 519-1992 establishes that the THD of the voltageat any node should be maximum 5% for voltages lower than 66 kV.

The same Standard establishes a limit for the TDD in any currentwhich depends on the ratio existing between the three phase shortcircuit current and the load current at the location point of the load.


Table 1 shows the maximum distortion values for voltage signalscorresponding to several levels allowed by IEEE Standard 519-92.Table 2 shows the maximum current distortion values for systemsbelow 66 kV from the same Standard.


Table 1 –Maximum THD voltage values allowed by IEEE Standard 519-92

Bus Voltage at PCC

Individual Voltage

Distortion (%)

Total VoltageDistortion THD (%)

69 kV and below

3.0 5.0

69.001 kV through 161 kV

1.5 2.5

161.001 kV and above

1.0 1.5

Note: High-voltage systems can have up to 2.0%THD where the cause is an HVDC terminal that willattenuate by the time it is tapped for a user


Maximum Harmonic Current Distortionin Percent of IL

ISC/IL <11 11≤h<17 17≤h<23 23≤h<35 35≤h TDD

50 - 100 10.0 4.5 4.0 1.5 0.7 12.0

Even harmonics are limited to 25% of the odd harmonic limits above

Current distortions that result in a dc offset, e.g., half-wave converters, are not allowed

*All power generation equipment is limited to these values of current distortion, regardless of actual ISC/IL.

Individual Harmonic Order (Odd Harmonics)

<20* 4.0 2.0 1.5 0.6 0.3 5.0

20 - 50 7.0 3.5 2.5 1.0 0.5 8.0

100 -1000

12.0 5.5 5.0 2.0 1.0 15.0

>1000 15.0 7.0 6.0 2.5 1.4 20.0

WhereISC = maximum short-circuit current at PCCIL = maximum demand load current (fundamental frequency component) at PCC


For capacitor application, Standard IEEE 18-1992 should beapplied from which the following conditions are taken:

• The maximum permanent voltage including harmonics ofany capacitor bank should not be higher than 110% of itsnominal voltage.

• The maximum permanent current including harmonicsthrough any capacitor bank should not be higher than 180% ofits nominal current.

• The maximum permanent power including harmonics ofany capacitor bank should not be higher than 135% of itsnominal power.

If any of the above limits is overcome, the reconfigurationoption should be neglected and a message in this senseshould be given by the program implemented.


Whenever a resonance situation occurs in a distribution systemdue to a capacitor bank, the solutions to be considered first are therelocation and/or resizing of the banks in order to vary theresonance frequency to a value that does not correspond to anygenerated by the harmonic sources.

The relocation of a capacitor bank aims to move it away fromharmonic sources of frequencies near the resonance one. On theother hand, the short circuit level varies too, which also changesthe resonance frequency.

Resizing and Relocation of Capacitor Banks

Questions?

Documents

POWER SYSTEM ANALYSIS TADP 641 - Gonzaga University