IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 39, NO. 4, JULY/AUGUST 2003 1181

Even Harmonic Resonance—An Unusual ProblemPaul C. Buddingh, Member, IEEE

Abstract—This paper is a case study examining the cause, ef-fect, and solution of an actual “noncharacteristic” even harmonicproblem in an electrochemical plant. While issues concerning“characteristic” harmonics are well documented in the literature,limited information is available describing how noncharacteristicharmonic currents create operational problems. The authorhas not found any papers describing a case of even harmonicresonance and would like to share the experience of resolving a 4thharmonic resonance problem in the hopes it will benefit others.

Index Terms—Characteristic, harmonic instability, harmonics,noncharacteristic odd even, resonance.

I. INTRODUCTION

T HIS case study describes an investigation by the authorof harmonic filter failures at a chemical plant in North

America. The plant utilizes large static converters to takeincoming high-voltage low-current 60-Hz ac power and rectifyit into low-voltage very-high-current dc power for operationof the electrochemical cells. Harmonic current generation isexpected in this type of power system and harmonic filters arecommonly used to limit harmonic levels and protect powersystem components.

A call from the plant indicated that they were experiencingwhat appeared to be overheating of a set of reactors used ina harmonic filter associated with one of the plant’s convertersystems. The reactors in the 5th harmonic branch of the filterhad discolored, and dark bands were evident on the glass-fibersurface of the reactors (Fig. 1).

The filter was originally installed in 1988 and had a historyof problems. The 5th harmonic reactors had failed before, and aclear cause was never identified. As historical information wasreviewed and measurement data collected, it became apparentthat something unusual was occurring.

This paper outlines the power and harmonic filter systems atthe plant, discusses how uncharacteristic harmonics are gener-ated, analyzes the difficulty, identifies the cause, and providesan action plan used to correct the problem.

II. POWER SYSTEM CONFIGURATION

The plant has two production lines, Lines A and B, each con-sisting of a series of electrochemical cells (Fig. 2).

Paper PID 03–02, presented at the 2002 IEEE Petroleum and ChemicalIndustry Technical Conference, New Orleans, LA, September 23–25, and ap-proved for publication in the IEEE TRANSACTIONS ONINDUSTRYAPPLICATIONS

by the Petroleum and Chemical Industry Committee of the IEEE IndustryApplications Society. Manuscript submitted for review September 15, 2002and released for publication May 1, 2003.

The author is with Universal Dynamics Ltd., Richmond, BC V6V 2X8,Canada (e-mail: pbuddingh@ieee.org).

Digital Object Identifier 10.1109/TIA.2003.814556

Fig. 1. Line A harmonic filter.

Line A consists of a 1978 vintage six-pulse rectifier in asingle-way ANSI 45 configuration with inter-phase transformer(Fig. 3). The primary voltage is 13.8 kV. Each of the six phasesor “legs” has eight parallel thyristors. A phase-locked-loop(PLL)-type control system using discrete analog electronics isimplemented.

A three-branch harmonic filter is installed, consisting ofbranches tuned precisely to the 5th, 7th, and 11th harmonicwith 6.9 effective Mvar of capacitors.

The Line B rectifier system is supplied directly at 66 kV, inan ANSI 45/46 12-pulse configuration shifted an extra 15apartto make a 24-pulse system. The rectifiers are equipped with asingle branch harmonic filter, also at 66 kV, tuned at the 4.7thharmonic and rated at 15 Mvar effective.

III. B ACKGROUND

It has been well known, since at least the 1930s, that rectifiersproduce harmonic currents as they convert electric power fromac to dc. A classic paper from the days of the mercury arc recti-fiers, still relevant today, was written in 1945 by Read [1]. Theproliferation of large thyristor rectifiers in the late 1960s andearly 1970s created a resurgence and exacerbation of harmonicsissues, largely a result of the increased size of the converters(in the 20–30 MW range). These new larger rectifiers typicallyrequired large capacitor banks for power-factor correction, cre-ating an ideal environment for parallel resonance disturbances.In response, a number of excellent papers were produced ad-dressing this new twist on an old problem [2], [3].

This paper is not intended to be a primer or theoretical treatiseon harmonics. There are many excellent works referenced thatexplain power system harmonics in detail. In particular, [4] isrecommended. A few highlights pertinent to this case, however,will be summarized.

0093-9994/03$17.00 © 2003 IEEE

1182 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 39, NO. 4, JULY/AUGUST 2003

Fig. 2. Electrical single-line drawing showing main power distribution.

Fig. 3. Schematic of a six-pulse double-wye connection with inter-phasetransformers.

IV. SOME THEORY

Half-controlled converters consisting of a mix of diodes andthyristors will not be contemplated in this paper. Half-controlledconverters inherently produce even harmonics and are not usedin high power applications.

As discussed in detail in the reference papers, a well-balanced“ideal” static converter—that is, a converter with equal currentsin each phase of the rectifier will produce harmonics on the acside of the converter according to

(1)

whereharmonic order;any integer ( );pulse number of the circuit;

with a magnitude

(2)

whereharmonic current;

fundamental current magnitude;

harmonic order.

In practice, the commutating reactance and phase retard angleof the thyristors will somewhat reduce the amplitude of the cur-rent at each of the characteristic harmonics shown at the bottomof the next page.

These normal or “characteristic” harmonic frequenciesstarting at the 5th and 7th harmonics are expected from asix-pulse rectifier. Similarly, a 12-pulse system will havecharacteristic harmonics starting at the 11th and 13th and a24-pulse will have characteristic harmonics starting at the23rd and 25th harmonics, etc. The rectifier acts as a harmoniccurrent source, injecting these harmonic currents back intothe ac system. If the ac system is reasonably symmetrical andtiming of the rectifier firing is exact, the resulting harmoniccurrents will be equal in all three phases.

Fourier’s theory is used to mathematically explain the re-sulting harmonic spectrum. A six-pulse rectifier is made up oftwo single-way three-pulse rectifiers, either connected in se-ries in the form of a bridge configuration, or in parallel, asin this case. Fourier’s theory shows that for three-pulse sys-tems the 3rd, 9th, 15th, etc., harmonics are zero. A single-waythree-pulse system is not half-wave symmetrical about the zeroaxis and produces even harmonics 2, 4, 6, etc. The 180config-uration of the two parallel rectifiers creates a six-pulse symmet-rical system, which ordinarily eliminates the even frequencies.

BUDDINGH: EVEN HARMONIC RESONANCE—AN UNUSUAL PROBLEM 1183

In the real world, there are always some residual abnormalodd and even harmonics on the ac power supply side. These areclassified as “uncharacteristic” harmonic frequencies.

Commonly, “uncharacteristic” harmonics are caused by im-perfections in the ac power supply system including tolerancesin transformer winding phase angles, commutation reactanceand the presence of incoming ac power supply harmonicvoltages. These imperfections in the ac power side affect thethyristor firing timing, as its synchronization signal is takenfrom the ac fundamental frequency. Normally, the asymmetry isminor, the resulting distortion is small and the effects minimal.

It is assumed that phase-control timing or firing is identicalfor all semiconductors on a phase, phase-to-phase timing is co-ordinated, and that each phase group is precisely fired with re-spect to each other. For cancellation, we need precise and repeat-able firing. This is another area where tolerances play a largepart. Deviations in firing will also generate uncharacteristic har-monic currents. In a properly designed and operating rectifier,the “uncharacteristic” harmonics are normally minimal, and arenot a concern.

Harmonic filters are designed, therefore, based on accepted“theory,” only to treat the normal characteristic harmonics. Forcost reasons, they are not normally designed to handle excessive“uncharacteristic” harmonic currents.

V. ANALYSIS

There were a number of obstacles in the investigation andanalysis of the plant converter system. One was analyzing theoverheating problem without the ability to directly measure the5th harmonic filter branch in the current. This made it difficultto get a complete picture of the existing harmonic conditions.The harmonic filter consists of three branches tuned preciselyto the 5th, 7th, and 11th harmonic. Each branch consists of anair-core reactor with a set of capacitors for phases A, B, and C.The filter is supplied by one metal clad “Teck” cable via a circuitbreaker equipped with current transformers. The only practicalpoint of connection for taking measurements was at the currenttransformer that supplies all three branches of the filter.

The harmonic currents produced by the rectifier were reason-able with the uncharacteristic components higher than ideal, butnot that unusual for a 1978-vintage rectifier (Table I). It was no-table, however, that measurements at the input of the rectifierhad a lower amount of 4th harmonic current than at the input ofthe filter. This provided the first hint that uncharacteristic har-monic currents were the source of the reactor distress.

Measurements at the Line A circuit breaker indicated thatthe ac power supply system was acceptable and not a point ofconcern.

When measurements were taken on the Line A filter, every-thing looked reasonable. The currents measured did not exceed

TABLE IMEASUREDHARMONIC CURRENTS ATLINE A RECTIFIER INPUT

Fig. 4. Line A rectifier power section.

the rating of the reactors and ambient temperatures were withinthe 30 C test rating of the reactor.

So, what was causing the overheating? Additional clues wereuncovered as we reviewed the history of rectifier operation. Dis-cussions with plant maintenance personnel indicated that an ex-tensive retrofit of the rectifier power section had recently beencompleted, with oversize thyristors installed (Fig. 4). This hadeliminated the repeated thyristor failures that occurring prior tothe retrofit and was a strong indication that the problem was as-sociated with control irregularities.

1184 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 39, NO. 4, JULY/AUGUST 2003

Fig. 5. Series and parallel resonance of fifth filter and 13.8-kV bus.

If firing timing is not identical for a parallel set of thyristors,uneven loading can result producing individual semiconductorfailures and gravitate toward a subsequent cascade of failuresthrough the system as fewer devices carry more and more of theload. By installing larger oversize devices, the plant had elimi-nated the symptom.

Next, the power system was analyzed with particularemphasis on pinpointing any abnormal harmonic resonanceconditions.

Various power system configurations used during normalplant operations were checked. An interesting discovery wasmade when Line A was operating with the Line B rectifierand filter shut down. The 5th filter branch in Line A (seriestuned to exactly 300 Hz) was found to exhibit strong parallelresonance with the power system at the 4th harmonic when theLine B system is out of service. When the Line B system isoperating, the parallel resonance is still present, but not nearlyas significant (Fig. 5).

Subsequent analysis indicated that if Line B is shut down andthe rectifier produces as little as 5% 4th harmonic current, it isamplified and causes a 40% current overload in the fifth branchof the Line A filter.

This finding provided the theoretical basis for a growing sus-picion that an even harmonic resonance was the source of thereactor overheating. One question remained: the plant normallyoperates at full capacity, 24 hours per day, all year long—coulda short annual maintenance outage on Line B be sufficient tocause the overheating and resulting dark bands on the reactors?

Reactors have a normal maximum temperature rise of 60Cover a 30 C ambient temperature. The manufacturer reportsthat reactor insulation will not discolor until it reaches 130C.To reach this temperature, the total current in the reactor wouldneed to increase to 140% of the reactor rating. Since the reactorshave little thermal mass, this temperature would occur in theorder of minutes.

Armed with this data, the theory that high, uncharacteristicharmonics were causing the overheating could be tested. An-other set of measurements was taken on Line A to quantify in-termittent, uncharacteristic harmonic currents coming from therectifier and their amplification in the 5th harmonic branch ofthe filter.

A careful measurement protocol confirmed that amplificationwas in fact taking place. Measurements of 20%–40% of 4th har-monic current (as a percentage of the total filter current) wererecorded for a period of approximately 13 s at the Line A filter.It was found that the fifth branch filter was drawing almost halfthe total filter current, and 70% of the 4th harmonic current. Asa result, for short periods these reactors are loaded with morethan 200% of rated current. With Line B down, the effect wouldlikely be considerably worse.

This last piece of data completed the picture.

VI. M ORE THEORY

As discussed above, even harmonics can be created inrectifier systems by firing timing irregularities. Galloway [7]describes harmonic instability as the abnormal operation ofa converter system due to the harmonic voltage distortion ofthe power source caused by the harmonic currents. Ainsworthwrote a classic paper on this same topic 35 years ago [8].

Galloway [7] explains the various modes of timing irregular-ities. The irregularities are defined into three types.

Type 1—Pulse Deviation:One of the six pulses does notoccur in the correct time or manner. This results in an“across-the-board” increase in harmonic currents, withpoor cancellation of odd harmonics and production ofeven harmonic currents due to half-wave dissymmetryabout zero.Type 2—Phase Unbalance:Phase unbalance does not pro-duce evens; it acts like a single-phase rectifier and producesthe full spectrum of odd harmonics with modulation com-ponents of 2 of normal harmonic frequencies.Type 3—Group Unbalance:Pulses 1, 3, and 5 are displacedan equal amount from 2, 4, and 6. This results in the gen-eration of even harmonics, that is, multiples of 31.

Measurements made in the plant seemed to indicate that aType 1 problem was occurring due to random timing variations,as periods of elevated harmonics across the spectrum, includingeven harmonics were noted. With the older control electronics,however, the failure mode was hard to isolate, and a Type 3problem, with inter-phase saturation, could be occurring.

The inter-phase transformers are typically designed to absorbonly a small amount of imbalance between the rectifier halvesand can quickly go into saturation. When the rectifier systemis not well balanced, the output currents of the two three-pulsegroups flowing in opposite directions in the inter-phase producesignificant dc magnetization of the core. As it goes into satura-tion and becomes ineffective, the rectifier operates as two sepa-rate three-pulse groups with the star points connected and semi-conductors only conducting over half of the normal 120. Theresulting 60 conduction angle results in about a 17% increasein semiconductor power (watts) loss. This results in a substantialincrease in heating of thyristors, fuses, as well as the secondaryof the transformers.

This unbalance also results in an effective dc current that thetransformer secondary must carry. The transformer can go intosaturation, increasing losses and creating large amounts of heatand a disproportionate amount of third harmonic current.

BUDDINGH: EVEN HARMONIC RESONANCE—AN UNUSUAL PROBLEM 1185

Fig. 6. Line A rectifier control system.

VII. FINDINGS

The pieces of the puzzle were starting to come together. Moreand more evidence pointed to an even harmonic resonance as thecause of the filter overheating.

The origin of the difficulties experienced is a thyristor firingcircuit problem. The age of the control system and resultingelectronic component “drift” appears to have created a Type 1timing irregularity.

Firing asymmetry was no longer directly affecting the opera-tion of the rectifier with the oversize thyristors that had been re-cently installed, but was still affecting the harmonic filter undercertain plant operating conditions.

The Line A rectifier is over 30 years old and, while well pastits original design life, continued operation of these robust ma-chines is common in the electrochemical industry. The Achillesheel of these units is typically the aging electronics of the controlsystem (Fig. 6). Electronic equipment has a bathtub-shaped reli-ability curve and this equipment is likely on the upward slope ofthat curve. In short, control system problems are to be expectedwith older rectifiers.

Measurements demonstrated that with Line B operating, largeamounts of 4th harmonic current overloaded the Line A filterfifth branch for short periods. The reactors have little thermalmass, and can reach extreme temperatures in the order of min-utes. The reactors were repeatedly exposed to a 200% load. IfLine B is shut down under these conditions, the currents arelikely to be significantly higher. A redeeming feature is that LineB is shut down infrequently for short intervals of maintenance.The cumulative effects of repeated overheating over time hasstressed the reactors.

In 1992, one of the 5th harmonic reactors was replaced. Thisexplains why only two of the three existing reactors are showingsigns of damage. The newer reactor has not been exposed tothe same degree of repeated overheating as the two older fifthharmonic reactors.

A secondary concern is the dc offset effects on the inter-phaseand secondary circuit of the transformer. While the transformeris in good condition, elevated dc currents can substantially in-crease heating and lead to long-term degradation. Tap changers,core clamps and other internal hardware can have localizedheating effects with increased levels on harmonic currents [10],particularly with the uncharacteristic harmonic currents forwhich the machine was never designed.

VIII. A CTION PLAN

A physical inspection of the fifth reactors on Line A was com-pleted, and although stressed, were not in immediate danger offailing, particularly if Line B is kept online.

The installation of a new rectifier control system is a substan-tial capital expenditure, and the plant is now considering thisstep. In the meantime, the following measures have been putinto place.

First, the peak sensing protection relay is being replaced witha modern programmable relay that is sensitive to the low orderharmonic frequencies experienced on this system. This will pro-vide alarming and tripping of the filter bank if the reactors arein danger of overload. This relay also measures and records har-monic levels.

Second, redesigned 5th harmonic filter reactors are being in-stalled to move the parallel resonance between the filter and thepower system to below the 4th. The new design will greatlydecrease the sensitivity to resonance. New reactors have beenordered and the replacement has been scheduled.

Finally, the interval between transformer dissolved gas sam-ples has been increased to improve monitoring of the trans-former condition. Dissolved gas analysis is a great tool to eval-uate the condition of transformers, particularly when faced withuncertain harmonic stress. Corrective action can then be takenas required.

IX. CONCLUSION

A sustained rectifier 4th harmonic level of 5% or more, at atime when Line B is off, has overloaded the reactors and causedthem to run hot and discolor. Over the years, there has beena cumulative effect intensifying the condition. If nothing wasdone, plant operating history has established that failure wouldfollow.

As a first step, the filter protection relay was modified to de-tect a 4th harmonic current overload and to alarm and trip asrequired.

The parallel resonant effects of tuning the Line A harmonicfilter exactly to each harmonic frequency to be treated was notconsidered in the original design. Tuning each of the 5th, 7th,and 11th branches to a frequency 2%–10% below the target fre-quency would have alleviated the parallel resonance.

A redesign of the damaged filter reactors is complete and thenew reactors are scheduled for installation.

The new larger thyristors, which were recently replaced, areable to withstand control system irregularities to a much greaterdegree, with a resulting improvement in reliability. Controlsystem irregularities that earlier caused rectifier problems,however, still affect the ac power system.

1186 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 39, NO. 4, JULY/AUGUST 2003

Even harmonics will also cause the rectifier transformer torun hotter by saturation of the magnetic circuit. Metal clamps,fixtures, and other components can overheat inside the trans-former, creating localized hot spots. This can significantly re-duce transformer life.

Steps have been taken to mitigate the immediate issues asnoted and a replacement control system is under considerationby the plant.

ACKNOWLEDGMENT

The author thanks J. Kirichenko and the Plant Staff for theopportunity to work on this very interesting challenge and, also,colleague B. Schmidtke for his outstanding work and insight onthis project.

REFERENCES

[1] J. C. Read, “The calculation of rectifier and inverter performance char-acteristics,”Proc. lEEE, pt. 2, vol. 29, pp. 495–509, Oct. 1945.

[2] A. P. Jacobs and G. W. Walsh, “Application considerations for SCR dcpower systems,”IEEE Trans. Ind. Gen. Appl., vol. 4, July/Aug 1968.

[3] D. E. Steeper and R. P. Stratford, “Reactive power compensation andharmonic suppression for industrial power systems using thyristor con-verters,” IEEE Trans. Ind. Applicat., vol. 12, pp. 235–255, Sept./Oct.1976.

[4] J. Arrillagaet al., Power System Harmonics. New York: Wiley, 1985.[5] Power Converter Handbook, Canadian General Electric Co. Ltd., Peter-

borough, ON, Canada, 1976.[6] IEEE Recommended Practices and Requirements for Harmonic Control

in Electrical Power Systems, IEEE 519–1992.[7] J. H. Galloway, “Harmonic instability in phase controlled rectifiers,” in

Conf. Rec. IEEE PCIC, 1999, pp. 171–175.

[8] J. D. Ainsworth, “Harmonic instability between controlled static con-verters and AC networks,”Proc. Inst. Elect. Eng., no. 7, pp. 949–957,July 1967.

[9] J. Arillagaet al., Power System Harmonic Analysis. New York: Wiley,1998.

[10] S. P. Kennedy, “Design and application of semiconductor rectifier trans-formers,” inConf. Rec. IEEE PCIC, 2001, pp. 153–159.

[11] J. Shaefer,Rectifier Circuits—Theory & Design. New York: Wiley,1965.

[12] B. M. Bird et al., An Introduction to Power Electronics. New York:Wiley, 1983.

[13] A. Kloss,A Basic Guide to Power Electronics. New York: Wiley, 1985.[14] P. C. Buddingh and J. St. Mars, “New life for old thyristor power rec-

tifiers using contemporary digital control,”IEEE Trans. Ind. Applicat.,vol. 36, pp. 1449–1454, Sept./Oct. 2000.

Paul C. Buddingh (S’89–M’90) received the degreein electrical engineering from Lakehead University,Thunder Bay, ON, Canada.

Upon graduation, he spent several years workingout of Toronto, ON, Canada, as an ElectricalConsulting Engineer working in heavy industry. In1991, he co-founded a company that developed anew magnetic approach to solving zero-sequenceharmonic problems in low-voltage systems. In 1997,he joined Universal Dynamics Ltd., Vancouver,BC, Canada. He has been designing and installing

harmonic filters for 15 years. His work is centered on designing high-reliabilitypower systems for difficult loads, power converter issues, and resolving powersystem problems for a number of industrial customers across the Americas. Hehas authored several IEEE papers.

Mr. Buddingh is a Registered Engineer in the Provinces of Ontario, Manitoba,and British Columbia, Canada.