SystemResponse Resonance

7/24/2019 SystemResponse Resonance

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System Response Characteristics

AC Resonance


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There are three primary variables affecting thesystem response characteristics,

the system impedance,

the presence of a capacitor bank,

the amount of resistive loads in the system.


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System Impedance

Where:

Zsc = short-circuit impedance

Rsc = short-circuit resistanceXsc = short-circuit reactance

kV = Line-Line voltage, kVMVAsc

= 3-Phase short-circuit MVA, MVA

Isc

= short-circuit current, A

scsc

scscscI

kV

MVA

kVjXRZ

3

10002


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System Impedance

ZSC

is a complex quantity, consisting of both resistance andreactance. For industrial power systems and most utility

systems, the impedance is assumed purely reactive.

The inductive reactance portion of the impedance changeswith frequency. The reactance at the hth

harmonic is

determined from the fundamental impedance reactanceX1by:Xh=hX1

.

Generally, in most power systems, the resistance does not

change significantly when studying the effects of harmonics

less than the ninth.


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System Impedance

At utilization voltages, such as industrial power systems, theequivalent system reactance is often dominated by the servicetransformer impedance. A good approximation forXSC

may bebased on the impedance of the service entrance transformer only:

Xsc= XTX

Transformer impedance in ohms can be determined from thepercent impedanceZtx

found on the nameplate by:

where MVA3ph

is the kVA

rating of the transformer. This assumes

that the impedance is predominantly reactive. For example for a1500-kVA, 6 % transformer, the equivalent impedance on the480-V side is

100/; (%))()(

3

2

)( TXpuTXpuTX

ph

TX XXXMVA

kVX

0092.006.0

5.1

48.02

)(

3

2

)( puTX

ph

TX X

MVA

kVX


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Capacitor Impedance

Shunt capacitors, either at the customer location for power factorcorrection or on the distribution system for voltage control,

dramatically alter the system impedance variation with

frequency.

Capacitors do not create harmonics, but severe harmonic

distortion can sometimes be attributed to their presence.

While the reactance of inductive components increases

proportionately to frequency, capacitive reactance XC

decreases

proportionately:

Power capacitors are rated in terms of kvar

or Mvar

at a given

voltage. The equivalent line-to-neutral capacitive reactance at

fundamental frequency for a capacitor bank can be determined

by:

fCCXC

2

11

MVAR

kVXC

2


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Harmonic ResonanceNatural Resonant Frequencyfo = 1/2 LC

fh = fo Resonance

Voltage and Current will be dominated by the resonantfrequency and can be highly distorted.

The true impact of the nonlinear load on harmonic voltage

distortion can be determined from the response of the powersystem at each harmonic.

Power System Harmonic Resonance

Series ResonanceParallel Resonance


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Parallel Resonance

Parallel Resonance

Parallel combination of power system inductance andpower factor correction capacitor at the nonlinear load

The highest voltage distortion is at the nonlinear load


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Parallel Resonance

At the resonant frequency, the apparent impedance of the

parallel combination of the equivalent inductance XL and

and

capacitance XC and as seen from the harmonic current source

becomes very large, i.e.,

LCL

p

LpCpLC

CL

LCCLCp

XR

R

X

R

XQ

XQXQR

XX

hXhXjR

XXhXjRjhXRhXjZ

;

)()//(


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Parallel Resonance

Qp: is the quality factor of a resonantcircuit that determines the sharpness of

the frequency response.

During parallel resonance, a small

harmonic currentIh can cause a large

voltage drop across the apparent

impedance, Vp=QpIhXL=QpIhXC and

IC=QpIh=IL

The voltage near the capacitor bank will

be magnified and heavily distorted.

Currents flowing in the capacitor bank

and through the transformer will also be

magnified Q times. This phenomenon

will likely cause capacitor failure, fuse

blowing, or transformer overheating.,


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Parallel Resonance

Power systems analysts typically do not haveL and C readilyavailable and prefer to use other forms of this relationship.

They commonly compute the resonant harmonic hrbased on

fundamental frequency impedances and ratings using one of thefollowing:

wherehr: resonant harmonic order

XC: Capacitor reactance

Xsc: System short-circuit reactance

MVAsc: System short-circuit MVA

MVARcap(kVARcap) : MVAR (kVAR) rating of capacitor bank

kVATX: kVA

rating of step-down transformer

ZTX: step-down transformer impedance

(%)

100

TXcap

TX

cap

sc

L

Cr

ZkVAR

kVA

MVAR

MVA

X

Xh


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An industrial load bus where the transformer impedance is

dominant, the resonant harmonic for a 1500-kVA, 6 %transformer and a 500-kvar capacitor bank is approximately

Parallel Resonance

ExampleExample

harmonic

ZkVAR

kVAh

th

TXcap

TXr

707.7

6500

1001500100

(%)


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Parallel Resonance

Effect of Capacitor Size on the Impedance seen by the

Harmonic Source


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Series Resonance

There are certain instances when a shunt capacitor and theinductance of a transformer or distribution line may appear as

a seriesLC circuit to a source of harmonic currents.

If the resonant frequencyfr corresponds to a characteristicharmonic frequencyhf1 of the nonlinear load, theLC circuit

will attract a large portion of the harmonic current that is

generated in the distribution system.

A customer having no nonlinear load, but utilizing power

factor correction capacitors, may in this way experience high

harmonic voltage distortion due to neighboring harmonic

sources.


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Series Resonance

Series ResonanceThe system inductance and capacitors are in series with

respect to the nonlinear load

The highest voltage distortion is at a remote point or on an

adjacent feeder served by the same substation transformer.


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Series Resonance

During resonance, the power factor correction capacitor forms aseries circuit with the transformer and harmonic sources. The

harmonic source represents the harmonics produced by a nonlinear

load. The series combination of the transformer inductance and the

capacitor bank is very small (theoretically zero) and only limited by

its resistance.

Thus the harmonic current corresponding to the resonant frequency

will flow freely in this circuit. The voltage at the power factorcorrection capacitor is magnified and highly distorted. This is

apparent from the following equation

hXhXXRX

RhX

RhXQ

VQV

VR

hXVhXhXjR

hXjV

cLrrLc

s

hsc

hc

h

cL

cc

;

)(


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Series Resonance

where Vh and Vc are the harmonic voltage corresponding to theharmonic currentIh, and the voltage at the power factor

capacitor bank, respectively. The resistanceR of the series

resonant circuit is small compared to the reactance.

The negligible impedance of the series resonant circuit can be

exploited to absorb desired harmonic currents. This is indeedthe principle in designing a notch filter.


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Series Resonance

In many systems with potential series resonance problemsparallel resonance also arises due to the circuit topology.

One of these is shown, where the parallel resonance is formed

by the parallel combination betweenXsource

and a seriesbetweenXT andXC. The resulting parallel resonant frequency

is always smaller than its series resonant frequency due to the

source inductance contribution.

The parallel resonant frequency can be represented by the

following equation:

sourceTX

Cr

XX

Xh


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Series Resonance

Frequency response of a circuit with series resonance


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Frequency Impedance Scan

Peaks Parallel Resonance

Valleys Series Resonance


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Effect of Resistance & Resistive Load

The damping provided by resistance in the system is oftensufficient to prevent catastrophic voltages and currents.

Variation of the parallel resonant circuit impedancecharacteristic for various amounts of resistive load in parallel

with the capacitance is shown below. As little as 10 percentresistive loading can have a significant beneficial impact onpeak impedance.

Effect of resistive loads on parallel resonance


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Likewise, if there is a significant length of lines or cablesbetween the capacitor bus and the nearest upline

transformer, the

resonance will be suppressed.

Lines and cables can add a significant amount of the resistance to

the equivalent circuit.

Loads and line resistances are the reasons why catastrophic

harmonic problems from capacitors on utility distribution feeders

are seldom seen.

The most troublesome resonant conditions occur when capacitorsare installed on substation buses, either utility substations or

in

industrial facilities.


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In these cases, where the transformer dominates the system impedance

and has a highX/R ratio, the relative resistance is low and the

corresponding parallel resonant impedance peak is very sharp and

high.

This is a common cause of capacitor, transformer, or load equipment

failure.

While utility distribution engineers may be able to place feeder

banks

with little concern about resonance, studies should always be performed

for industrial capacitor applications and for utility substation

applications.

Utility engineers familiar with the problems indicate that about

20

percent of industrial installations for which no studies are performed

have major operating disruptions or equipment failure due to resonance.

In fact, selecting capacitor sizes from manufacturers

tables to correct the

power factor based on average monthly billing data tends to result in a

combination that tunes the system near the fifth harmonic. This is one of

the worst harmonics to which to be tuned because it is frequently thelargest component in the system.

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SystemResponse Resonance