harmonics and transient overvoltages due to capacitor switching

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1184 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 29, NO. 6, NOVEMBERIDECEMBER 1993

Harmonics and Transient Overvoltages

Due to Capacitor SwitchingAdly A. Girgis, Fellow, IEEE, Christopher M. Fallon, Jay C. P. Rubino, and Ray C. Catoe, Member, IEEE

Abstract-This paper presents a study of the steady stateand transient effects of power factor correction capacitors onthe utility and on the customer. In the presence of harmonicproducing loads, capacitors used for power factor correctioncan cause parallel or series resonance problems which tend toincrease the total harmonic distortion (THD) of the voltage andcurrent waveforms. The cases studied in this paper consider theaddition of a power factor correction capacitor, in the presenceof downstream harmonic loads and at the harmonic load site.In both cases the resonance created by the addition of thecapacitor caused the harmonic distortion of the voltage andcurrent waveforms to increase. Another problem is transientovervoltages created by switching the capacitor. The overvoltageat the customer bus created by switching the capacitor canbe harmful to sensitive electronics equipment. A case study isreported where the operation of semiconductor controlled motordrive is effected by transient overvoltages. The first section ofthis paper looks at the steady-state concerns associated with theapplication of power factor correction capacitors in the presenceof harmonic loads and unbalance. The latter section of this paperdiscusses the transient problems associated with the switching ofpower factor correction capacitors.

I. INTRODUCTION

HE increased use of power electronic devices promptsT wo areas of concern. The first area of concern is the

harmonic distortion of the 60 Hz voltage and current wave-

forms. The second area of concern is the quality of powerserving these sensitive electronic devices. Power electronics is

the most significant source of harmonic distortion. However,

power electronics are not the only source of harmonic dis-

tortion, there are other sources such as arcing devices andequipment with saturable ferromagnetic cores [11-[4]. The

harmonic distortion from sources can be magnified by theapplication of power factor correction capacitors. For years,

capacitors have been used for power factor correction and

voltage regulation. However the use of these capacitors may

create parallel or series resonance problems increasing theharmonic distortion of the voltage and current waveforms.

The second concern is the switching of the power factor cor-

rection capacitors. During a capacitor switching, the transient

overvoltages produced contain high frequency components.

Paper ICPSD 92-43, approved by the Rural Elect ric Power Commit tee ofthe IEEE Industry Applications Society for presentation at the 1992 RuralElectric Power Conference, New Orleans, LA, May 3-5. This work wassupported by the members of the Clemson University Electric Power ResearchAssociation, “CUEPRA.” Manuscript released for publica tion March 17, 1993.

A. A. Girgis is with Clemson University , Clemson, SC 29634.C. M. Fallon is with the Duke Power Company, Charlotte, NC 28201.J. C. P. Robino lives in Wyoming, PA 18644.R. C. Catoe is with Jake Rudisil l Associates, Inc., Charlotte, NC 28236.

IEEE Log Number 9212386.

These transient overvoltages, if large enough, can damage

sensitive power electronic devices [ 5 ] - [ 6 ] .Short duration over-voltages that do not damage electronics equipment may still

cause the drive’s protective devices to operate, disconnecting

the load from the circuit.

11. HARMONICMPLIFICATIONUETO

POWER ACTOR ORRECTIONAPACITORS

The harmonics generated by the load may be modeled

as current sources at the harmonic frequencies. In general,

the harmonics flowing into the system and the harmonics

flowing into the capacitor can be obtained from the harmonicsequence components and an equivalent network model. The

sequence components for the different harmonics can beobtained as described in reference [7]. System unbalance,which is common on distribution systems, is also a factor

in the amplification of harmonics and distortion. A simple

example is used to illustrate how the harmonic load interactswith the power system and the capacitor. Fig. 1 represents

a simplified equivalent model of the power system and theharmonic load. The harmonic load is modeled as a harmonic

current source; the system and the capacitor are modeled as

frequency dependent impedances.

The sequence system current and the sequence capacitorcurrent at each harmonic is expressed as

where

z S u S i ( w h )

Z c i ( w h )

ISYSih

ICih

h is the harmonic order

i =0 , l or 2 zero, positive and negative sequence

is the system impedance at the harmonic

frequency, R(h)+hwLis the impedance of the capacitor at the

harmonic frequency,&is the system harmonic current

is the capacitor harmonic current

components

Examining (1) and ( 2 ) , it can be seen that the harmonic

currents will have their greatest magnitude when the denomi-

nator, (z SYSi (wh)+ z c i (Wh)) , is a minimum. This term will bea minimum when jhw L is equal to &. The value of (h) which

satisfies this requirement is the resonant harmonic frequency.Sometimes there is more than one resonant harmonic due to

combinations of series and parallel components.

0093-9994/93$03.00 0 1993 IEEE



GIRGIS et al.: HARMONICS AN D TRANSIENT OVERVOLTAGES DUE TO CAPACITOR SWITCHING 1185

TABLE I

Z 4532.8 24.5% 5766.1 81.9% 3406.9 129 %

Fig. I. Equivalent network model.

TABLE II

HARMONICNALYSIS OF TRANSFORMERND CAPACITOR CURRENTS

Transformer Current Capacitor CurrentHarmonic RMS RMS AngleOrder Current gkes) Current (Degrees)Fund. X 4437.1 42.9 2076.5 120.0

Y 4215.6 163.2 2074.2 -120.3Z 4461.2 -15.0 2085.5 -0.2

5th. x 77.7% -98.4 125.6% 79.8Y 91.1% 139.4 132.0% -41.5Z 81.5% 20.9 125.9% -163.4

9th. X 2.7% -162.4 11.9% 18.913.1% -102.21.7% 116.5

z 1.4% -86.0 12.3% 133.6

11th. X 2.7% -162.4 11.9% 18.9Y 1.7% 116.5 13.1% -102.2Z 1.4% -86.0 12.3% 133.6

13th. X 0.5% 160.8 7.5% -106.97.0% 14.91.5% -150.8

z 1.0% -100.2 7.1% 130.8

17th. X 0.8% -7 1.4 3.2% 114.1Y 0.6% -94.1 3.9% -3.9Z 0.5% -53.6 3.7% -135.0

2MoKV Az= 6.78 %

Fig. 2. One-line diagram of the industrial load.

19th. X 0.3% -67.2 2.9% -14.2Y 0.6% -57.1 2.8% 108.3

-31.2 2.1% -136.30.4%- 7OOO I , , . - , , , . , , ,- , . , . 4

0 2 1 I3 8 10 1 2 I 1 16 I 8 21)

IWK (*SEC)

Industrial load three-phase currents.ig . 3.

increase in the harmonic distortion of the voltage and current

waveforms. The increase in the harmonic distortion is due to an

amplification of the harmonic components. The amplificationof harmonic components is caused by resonance conditionswhich has been discussed previously. Another problem en-

countered on this circuit is a high degree of unbalance. The

unbalanced conditions contributed to the increase of harmonic

distortion of the voltage and current waveforms. An interestingoccurrence in this example is the unsymmetrical amplification

of the harmonic components. The spectral contents of the

current and voltage waveforms before and after the capacitor

was added to the circuit are given in Table I11 and Table IV,

respectively. The THD of the voltage and current waveformsis given in Table V. Examining these results, it can be seen

that the effect on the X-phase is more pronounced than on

the other phases. Another observation in this case is the factthat dominant harmonic frequencies for voltage and current

are not necessarily the same.

Two examples are used here to illustrate the effect powerfactor correction capacitors can have on the harmonic dis-

tortion of the 60 Hz voltage and current waveforms [8]. Inthe first example, it was reported [7] that a delta connected

1800 kVAR capacitor contributed to cause severe harmonicdistortion at the load site. A diagram of the system is shown

in Fig. 2. The industr ial load consists of four production linesof induction heating with two single-phase furnaces per line.

The induction furnaces operate at 8500 Hz and are used to

heat 40 ft steel rods which are cut into railroad spikes [7].

Problems were created by excess harmonics flowing in thecapacitor bank overheating of the capacitor circuit breaker.

The increased harmonic currents also caused problems with

the 100-A individual capacitor fuses and the 3000-A main linefuse. The capacitor was connected across the load for voltage

regulation and power factor correction; however, the resulting

resonance in the system increased the harmonic distortion anddecreased the power factor. Actual recorded waveforms for

the three-phase load current are shown in Fig. 3. Tables I and

I1 describe the RMS currents of the system and the harmonic

spectrum of the currents, respectively.The second examples illustrates the harmonic problems that

can occur after a capacitor is added to a circuit. In this casean 1800 kVAR wye-ungrounded capacitor bank is switched

on in the presence of downstream harmonic loads. A one line

diagram of the distribution system is shown in Fig. 4. Theaddition of this capacitor to the distribution circuit caused an

111. EFFECTOF HARMONIC FILTERING

One possible solution to the steady-state harmonic problem

created by the use of power factor correction capacitors is aharmonic filter. A harmonic filter tuned to the system’s domi-

nant harmonic frequency can reduce harmonic distortion while

providing voltage regulation and power factor correction. Asingle-tuned harmonic filter is a shunt RL C element, shown in

Fig. 5 . The L and C elements may be tuned to the resonant



I

1186

Fig. 4.

tEricSimplified one-line diagram of the distribution

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 29, NO. 6, NOVEMBEIUDECEMBER 1993

Harmonic

1800KVAR

system.

TABLE III

HARMONIC ANALYSIS OF CURRENT WAVEFORMS

Before. After

Harmonic RMS Angle RMS AngleOrder Current (Degrees Current (Degrees

) )Fund. X 148.3 -141.7 140.4 -136.7

Y 156.3 95.3 148.1 101.6z

2nd. XYZ

5th. xYZ

8th. XYZ

10th. xYZ

11th. xYZ

12th. xYZ

~..151.9

4.21.50.8

10.710.99.6

5.10.10.3

6.60.20.5

8.02.52.2

5.20.30.2

-22.7 148.0

112.6 11.6-136.12 3.2-70.9 1.5

149.9 13.6-83.2 10.840.8 11.1

131.5 6.3-102.8 8.7131.9 4.5

-106.8 16.0

-112.7 0.3

81.1 18.743.4 3.0155.5 2.7

-158.7 5.1

-63.5 15.1-124.9 1.94-55.2 0.3

-24.2

109.8-8.7-73.0

152.1

41.7

-100.2-102.2-85.5

-107.2

-27.90.8-64.3

-119.913.3170.2

131.9

-7.6-134.9

harmonic frequency. Determination of the L and C values used

in the filter can be found from the following relationships:

jhwL =-jhwC-1

h2wL =-c

h21x1,= IXc

where h is harmonic order to which the filter is tuned.

IV. ASD TRANSIENT OVERVOLTAGES

CREATED BY CAPAClTOR SWITCHING

The transient overvoltage of a capacitor switching eventfrequently causes protection equipment to operate and discon-

nect the customer load. Adjustable speed drives (ASD) tend tobe particularly susceptible to this problem because overvoltage

protection thresholds are lower than other customer equipment

to protect the semiconductor components [9]. Fig. 6 shows

TABLE IV

HARMONIC NALYSISF VOLTAGE WAVEFORMS

Before After

Harmonic RMS RMS AngleOrder VolrageFund. X 7344.5 -110.1 7357.6 -110.1

Y 7333.7 130.3 7359.2 130.1Z 7268.8 9.8 7262.9 9.9

5th . X 104.3 8.0 109.9 8.14Y 108.7 102.7 116.0 81.6Z 107.8 -138.2 118.2 -129.5

1Oth.X 52.8 152.2 122.1 -121.4Y 51.2 177.9 113.1 -175.4Z 53.1 171.5 58.3 -108.6

11th. X 84.8 -162.4 166.8 136.5Y 74.1 116.5 94.5 76.6Z 51.3 -86.0 71.9 119.3

12th. X 47.2 -162.4 163.2 36.6Y 45.3 116.5 40.4 -11.5z 53.9 -86.0 69.9 66.2

13th.X 49.8 -71.4 127.2 -47.9Y 54.4 -94.1 55.9 140.4z 44.3 -53.6 30.0 -32.7

TABLE VHARhfONlC DISTORTIONF VOLTAGE AN D CURRENT WAVEFORMS

Before After

Phase THD THDIX 7.1% 24.1%

IY 7.8% 13.7%

IZ 7.2% 8.8%VX 2.4% 5.7%

VY 2.6% 3.5%

VZ 2.1% 2.9%

i:i;‘f

Fig. 5. Single-tuned FUC shunt filter.

9U

- IeeeuFig. 6. Plot of actual recorded data of voltage on the dc bus of an ASD

during a capacitor switching event.

the transient overvoltage on the dc bridge of the drive exceeded

the trip setting. The drive in this case was a PWM drive serving

an industrial load. The drive tripped off-line due to capacitoractual data recorded from a capacitor switching event where switching events on the ac system.



-GIRGIS et al.: HARMONICS AN D TRANSIENT OVERVOLTAGES DUE TO CAPACITOR SWITCHING

-1187

Link InductorlvvIC

Fig. 7. Adjustable speed drive model used in EMTP.

1.8WAR

Fig. 8. System used in EMTF' simulation.

C 0.00 0.01 0.02 0.03n

Time (Seconds)

Fig. 9. Simulated capacitor switching (ASD) dc voltage.

EMTP simulations were performed to illustrate the effect of

capacitor switching on an ASD and how certain parameters

effect the transient overvoltage on the ASD dc bridge. The

ASD was model in EMTP as a three-phase full wave rectifier.

The three-phase full wave rectifier converts three phase ac

to DC. The converter in its simplest form consist of six

diodes (see Fig. 7). A diode is connect anode (cathode) to

cathode (anode) from each ac phase to the positive (negative)

dc terminal. (Current flows from anode to cathode.) For a

controlled rectifier, the diodes are replaced with thyristors. The

dc voltage in a controlled rectifier can be varied by controlling

the thyristor gating pulses.

The system model used for the EMTP simulations is shown

in Fig. 8. The ASD is modeled as a three-phase full wave

controlled rectifier with a capacitor across the dc terminals.

The inverter or dc to ac converter was not modeled since the

major concerns are effects due to changes in the ac system.

A plot of the simulated dc bridge voltage during a capacitor

switching event is presented in Fig. 9.

EMTP is used to simulate capacitor switching operations

to determine the peak voltage magnitudes on the dc bridge.

Switching occurs when the phase C voltage is at its peak.For the purpose of the simulation the motor was modeled as

constant current load.

For PWM drives and for these simulations, the rectifier is

simply a three-phase converter. The capacitance value used in

the simulations s selected to minimize voltage ripple on the dc

bridge. This was done to duplicate actual conditions. During

gL- 11400

6 0 0 - I

0 20 40 60 80 1Link Inductance (mH)

0

Fig. 10. DC bridge voltage vs. link inductance.

TABLE VIDC BRIDGEOLTAGE DURING CAPACITOR SWITCHING

Per Unit 5% ReactorCaseNumber Overvoltage DCVoltage

1 1.70 7272 1.63 7323 1.65 1274 1.72 732

steady-state operation, the current supplied to the rectifier is

discontinuous since the capacitor maintains a voltage near thepeak of the ac system voltage.

A. Effect ofLink Inductance One method that is com-

monly used to limit the transient overvoltage on the dc bridge

during capacitor switching is to place inductance in the link

connection between the rectifier and converter.The link inductance was varied with values ranging from

.01 to 100 mH to determine its effect on the peak voltage at

the dc bridge. A plot of peak transient dc voltage is shown vs.

link inductance is shown for several values of link capacitance

in Fig. 10. Generally, the addition of inductance will decreasethe peak overvoltage.

B. Addition of Reactance on the AC Side Sometimes it may

not be practical to vary the link inductance. Often times

a reactor is placed in series with the converter ac input

terminals. This solution was tested at the PWM drive serving

the industrial load. A 5% line reactor was installed at the driveterminals and five capacitor switching tests were performed.

The results of these tests are presented in Table VI: thedc bridge voltage as a function of per unit overvoltage as

measured at the capacitor bank. In each of these tests, the

dc overvoltage was less than the overvoltage threshold of the

drive. Before the installation of the line reactor, overvoltages

of these magnitudes would have caused the drive to trip.

Simulations were performed where inductance was added infront of the drive and varied from .01 to 100 mH with a link

capacitor of 1000 uF. The result is plotted in Fig. 11 along

with the result obtained by varying the link inductance. For

this case, the addition of inductance on the ac side has a greater

effect on reducing the peak overvoltage on the dc bridge thanaddition of link inductance.

V. CONCLUSION

Addition of capacitor for power factor correction may

amplify harmonics in the ac power system. Certainly, amplifi-



-1188 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 29, NO. 6, NOVEMBERIDECEMBER 1993

............ Reactoron DC side

Reactoron AC side

- ........_____.__.0) 7M)

Delively, vol. 4,no. 3,pp. 427-434, uly 1989.[8] M. Z. Lowenstein, “Power factor improvement for non-linear loads,”

presented at the 1991 Ann. Tech. Conf. Textile, Fiber, Film Ind.Committee, Greenville, S. C., May, 1991.

[9] M. F. McGranaghan, T. Grebe, G. Hensley, T. Singh, and M. Samo-tyj, “Impact of utility switched capacitors on customer systems: part11-adjustable speed drive concerns,” IEEE Trans. Powe r Delivery , vol.6,no. 3,pp. 1623-1628,Oct. 1991.

n o IO 20

Inductance (mH)

Fig. 11 . Peak dc voltage as a function of reactor position. Adly A. Girgis (S’80-SM’81-F’92),or a photograph and biography pleasesee page 1175 of this issue.

cation depends on the magnitude of the power factor correction

and the system impedance. In the case presented, the power

factor would not be improved as the total apparent powerincreases. The unbalance in harmonics may cause misoperationof ground relays. The amplification of harmonics may cause

overheating of transformers and other substation equipment.A possible solution to this problem is to design filters in to

the power factor correction.Transient overvoltage on an ASD ’may be reduced by adding

inductance on the ac system side of the drive or on the dc

link of the drive. For the case of the PWM drive serving anindustrial load, a 5% line reactor was installed and tested. The

results showed that this was an effective means of solving

nuisance tripping cased by transient overvoltages.

Christopher M. Fallon, for a photograph and biography please see page1175 f the

Jay C. P.Rubino was born in Wilkes-Barre, PA. Hereceived the B.S. degree in electrical engineering in1986 from Wilkes College, Wilkes-Barre, PA, andthe M.E. degree in electric power engineering fromRensselaer Polytechnic Institute, Troy, NY.

He began with the Power Systems EngineeringDepartment of General Electric, Schenectady, NY,in 1987.There he was involved in numerous power

system engineering studies encompassing concernswith adjustable-speed drives, power system stability,

REFERENCES

IEEE Working Group on Power System Harmonics, “Power systemharmonics: an overview,” IEEE Trans. Powe r Apparat. Sys t., vol. PAS-102,no. 8, pp. 2455-2459,Aug. 1983.J. F. Fuller, E. F. Fuchs, and D. J. Roesler, “Influence of harmonicson power distribution system protection,” IEEE Trans. Power Delive ry,vol. 3 , no. 2, pp. 549-557, Apr. 1988.J. Anillaga, D. A. Bradley, and P. S. Bodger, Power System Harmonics.New York Wiley, 1985.S . B. Davan and A. Straughen, Power Semiconductor Devices NewYork Wiley, 1987.A. Greenwood, Electrical Transients n Power SystemsNew York Wiley,

1991.T. Grebe, “Why power factor correction capacitors may upset adjustablespeed drives,’’ Power Quality Mag., p 14-18, May/June 1991.A. A. Gig is et al., “Measurement and characterization of harmonic and

parameter identification, and power system com-ponent modeling. From August 1991 through December 1992,he attendedClemson University, Clemson, SC, affiliated with the Clemson UniversityResearch Association.

Ray C. Catoe (M’82)eceived the B.S. degree withhonors in electrical engineering from North CarolinaState University, Raleigh, NC, in 1982.

From 1982 o 1992, e was a power quality engi-neer with Duke Power Company, Charlotte, NC. Hismajor areas of responsibility included specializedtesting, training, and resolving power quality prob-

lems for large industrial customers. He is presentlywith Jake Rudisill Associates, Charlotte, NC, as atechnical sales engineer.

Mr. Catoe is a member of the Power Engineeringhigh frequency distortion for a large industrial load,” IEEE Trans. Powe r Society, Eta Kappa Nu, and Tau Beta Pi.

harmonics and transient overvoltages due to capacitor switching

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