Cooper - Capacitors - Harmonics and Capacitors - Dynamic Ov.pdf

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Issue 3 of the Kilovar Briefs discussed steady statesources of harmonics. These included arc furnaces,

solid state energy conversion equipment, rotatingmachinery and transformers. During steady state opera-tion of an AC power system, harmonics in the trans-former magnetizing current are a small percentage ofthe load current. Energizing a transformer results insubstantial amounts of harmonic current in the trans-former inrush current. This is a transient event lastingup to a few seconds. If the transformer is switched withcapacitors, it is possible that a resonant condition mayexist that results in dynamic overvoltage caused by aninteraction of the inrush current and capacitors.

Dynamic overvoltages are defined as long-term reso-nant overvoltages lasting many cycles and evenseconds that can result in damage to capacitors, trans-

formers, surge arresters and/or solid state powerconversion equipment. In this issue of the Kilovar Briefs,we will examine the mechanism of creating dynamicovervoltages and the means to prevent them fromoccurring when switching capacitors.

Consider the basic circuit shown in Figure 1, whichincludes a supply transformer feeding an industrial load,a switch used to energize the load and a load trans-former. Often, these types of systems are energizedwith no load applied to the transformer. Figure 2 showsa typical inrush current wave form following transformerenergization. This is a non-sinusoidal wave that expo-nentially decays to a steady state magnetizing current

level.Typically, inrush current is rich in second, third, fourth,and fifth harmonics. A Fourier analysis of the harmoniccomponents of this wave form is tabulated in Table 1.The exact shape and magnitude of the inrush currentdepends on the transformer characteristics and theinitial condition of the residual transformer flux.Substantial low order harmonic currents momentarilyexist in the transformer inrush current. Figure 3 showsthe bus voltage on the load side of the switch. Despitethe harmonic content of the current, the voltage is notnoticeably distorted.

Printed in USA

September 2000 — Greenwood S

Capacitors

Harmonics and Capacitors —Dynamic Overvoltages KILOVAR BRIEFS 6

September 2000 • Supersedes 11/85

Harmonic % of Fundamental Amps

0 64.70 275.0

1 100.00 425.0

2 25.40 108.0

3 8.49 36.1

4 5.46 23.2

5 3.32 14.1

Figure 1.Typical Industrial Load Transformer.

0.00

A

MPS

TIME 400 MSEC

Figure 2.Typical Inrush Current Wave Form FollowingTransformer Energization.

TABLE 1Harmonic Components of Inrush Current in TransformerEnergization

0

-2.00

PU

2.00

TIME 400 MSEC

Figure 3.Bus Voltage Following Switching in Figure 1.



In Issue 4 of the Kilovar Briefs, we discussed this samecircuit. A shunt capacitor was applied on the converterbus to correct the system power factor from 75% to98%. The equivalent circuit is shown in Figure 4 alongwith its impedance spectrum. This circuit is resonant at310.2 hertz. This means that any fifth harmonic currentpresent in the circuit will be substantially amplified,resulting in a resonant overvoltage. The inrush current

shown in Figure 2, whose harmonic components areshown in Table 1, is the current injected into the circuitfrom the transient current source. The fifth harmoniccontent of the inrush current results in a resonantdynamic overvoltage. An example of the dynamic over-voltage is shown in Figure 5. This overvoltage conditionis a direct result of injecting a harmonic current into atuned tank circuit, which amplifies harmonic currents atthe timed frequency, resulting in the high overvoltage. Ifthe capacitor had tuned the circuit to the 4th harmonic,the overvoltage would have been more severe.

In Issue 5 of the Kilovar Briefs, a filter design wasdiscussed as a measure for preventing steady state

harmonic resonance caused by the fifth harmoniccontent of the steady state load current. The equivalentcircuit and the impedance diagram is shown in Figure 6.The presence of the filter reduces the system parallelresonant frequency from 310 hertz to 211 hertz (3.5 xthe fundamental frequency). A filter always forces theparallel resonant frequency to a level below that of thefilter tuning frequency. Since the transformer inrushcurrent is richer in the lower order harmonics, applyinga filter circuit can actually make the switching problemmore severe. Figure 7 shows the dynamic overvoltagein this case is more onerous than without the filter.

We, therefore, have the situation where capacitors canbe applied successfully in a steady state harmonic envi-

ronment, possibly requiring the use of a filter reactor todetune the circuit. However, the design may not beadequate for the transient harmonic environment;caused by switching the capacitor and transformerstogether.

Harmonics and Capacitors — Applying Capacitors in the Harmonic Environment

2

Figure 4a.Equivalent Circuit for Power Factor ConnectorCapacitor.

Figure 4b.Impedance Spectrum.

Figure 5.Dynamic Overvoltage across Capacitors FollowingTransformer Energization.

12

8

4

0

-4

-8

-12

1 2 3 4 5 6 7 8

-ZS(n)

ZS(n)

Parallel ResonantFrequency

I m p

e d a n c e ( O h m s )

ZF(n)

Harmonic Number

ZS

(n)

IS

(n)

ZF(n)

IF(n) I

H(n)

0 TIME 400 MSEC

-1.50

PU

1.50



There is a simple solution to this problem — switchthe capacitor and/or the filter circuit separately fromswitching the transformer. The network configuration fothis solution is shown in Figure 8. For energizing thecircuit, switch A should be closed to energize the loadtransformer, followed by closing switch B some secondor minutes afterward to energize the capacitors and/orthe filter network. By following this simple switchingscheme, the capacitors are never in the circuit duringthe time that the inrush current is present. As a result,the circuit is not tuned to a frequency present in thetransformer inrush current and, therefore, there is nochance of a dynamic overvoltage occurring!

The distribution engineer reading this discussion maywonder if reclosing a distribution feeder with its capaci-tors and transformers could also result in dynamic overvoltages. The resonant frequency of the circuit isanalyzed in a manner similar to that already described.With the capacitors in service, it is likely that the systemresonant frequency is 300–500 hertz. Fortunately, there

is normally adequate load on the distribution feeder anthis load acts as damping, preventing dynamic overvoltages from occurring. The combination of switching anunloaded transformer and a capacitor bank is mostsusceptible to dynamic overvoltages. The lower thesystem natural frequency is, the more likely is thechance of dynamic overvoltages occurring followingswitching.

KILOVAR BRIEFS

Figure 6a.Equivalent Circuit for Tuned Filter.

Figure 6b.Impedance Spectrum.

Figure 7.Dynamic Overvoltage across the Capacitor Bankfollowing Switching of the Filter and LoadTransformer Together.

A

B

8

4

0

-4

-8

-12

1 2 3 4 5 6

-ZS(n)

ZS(n)

ParallelResonantFrequency

I m p

e d a n c e ( n ’ s )

ZF(n)

Harmonic Number

ZS

(n)

IS

(n)

ZL(n)

IF(n) I

H(n)

0-2.00

PU

2.00

TIME 400 MSEC

Figure 8.Typical Industrial Load with Capacitor Filter.



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P.O. Box 1640Waukesha, WI 53187http://www.cooperpower.com

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Cooper - Capacitors - Harmonics and Capacitors - Dynamic Ov.pdf