05Armonicos.pdf

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 2, MARCH/APRIL 2011 973

Designing Passive Harmonic Filtersfor an Aluminum Smelting Plant

Babak Badrzadeh, Member, IEEE, Kenneth S. Smith, Senior Member, IEEE, andRoddy C. Wilson, Member, IEEE

Abstract—This paper presents the results of harmonic analysisand harmonic filter design for a grid-connected aluminum smelt-ing plant. Harmonic-penetration-analysis studies are carried outto determine the system resonance frequencies and the individualand total harmonic voltage distortions for a wide range of possiblesystem operating conditions including scenarios with N-1 and N-2generation, an outage of a harmonic filter, and an outage of a rec-tifier transformer. A conceptual harmonic-filter-design procedurefor the filters required for the smelting plant is presented. Thesuitability and robustness of the proposed harmonic filter con-figuration in terms of the filter’s component current and voltageratings and corresponding rms values are investigated.

Index Terms—Harmonic impedance, harmonic penetration,multipulse rectifier transformers, passive harmonic filters,reactive-power compensation.

I. INTRODUCTION

A LUMINUM smelting is the process of extracting alu-minum from its oxide alumina. This is realized by an

electrolysis process which requires a dc current source. Theelectrolysis process takes place in a large number of series-connected steel pots collectively referred to as a potline. Eachpotline is fed from an ac supply by a number of diode rec-tifiers and step-up transformers collectively termed rectifiertransformers. To mitigate the harmonic currents produced bythe uncontrolled diode rectifiers, multipulse conversion usingphase-shifting transformers is adopted. The smelting processis generally a nonstop process with a practically constant loadyear-round.

A large grid-connected aluminum smelting plant in theMiddle East is being expanded with new smelting loads. Atpresent, there is no surcharge for reactive-power import fromthe utility grid, but the grid connection requirements are beingchanged such that no reactive power can be imported from thegrid and the circulation of the reactive power through the twoincoming grid transformers has to be practically eliminated.

Manuscript received June 11, 2010; revised October 17, 2010; acceptedOctober 19, 2010. Date of publication January 6, 2011; date of currentversion March 18, 2011. Paper 2010-PSEC-164.R1, presented at the 2010Industry Applications Society Annual Meeting, Houston, TX, October 3–7,and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY

APPLICATIONS by the Power System Engineering Committee of the IEEEIndustry Applications Society.

B. Badrzadeh is with Vestas Technology R&D, 8200 Århus N, Denmark(e-mail: [email protected]).

K. S. Smith and R. C. Wilson are with the Transmission and DistributionDivision, Mott MacDonald, Glasgow, G2 8JB, U.K. (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIA.2010.2103544

Fig. 1. Electrical power system of the aluminum smelting plant.

The latter is generally found to be more demanding in termsof the required reactive-power compensation.

Preliminary studies indicate that, without any harmonic fil-ters in service, the individual and total harmonic voltage dis-tortion levels exceed the limits specified in the InternationalElectrotechnical Commission (IEC) 61000 standards [1], [2].At present, no means of harmonic control is installed at thesmelting plant, but the harmonic distortion limits are beingenforced by the utility grid. The expansion of the smelting loadsand unbalanced operation of some of the smelting loads wouldraise further concerns about the level of harmonic distortionwithin the plant and at the point of common coupling (PCC)with the utility. A well-designed harmonic filter is a cost-effective solution to maintain the acceptable harmonic levelsand to double as a reactive-power compensator.

This paper presents the results of extensive power systemstudies conducted to investigate and maintain the harmoniclevels within the IEC-specified limits. The detailed design of therequired harmonic filters will be elaborated. For the harmonic-penetration analysis and harmonic filter design, the InteractivePower System Analysis (IPSA+) software tool is used.

II. SYSTEM UNDER CONSIDERATION

The electrical system of the smelting plant after completionof the proposed network expansion is shown in Fig. 1. Thesmelting load is approximately 90% of the total system load.This figure shows that the bulk of smelting load is connectedto a 132-kV voltage level. The total potline loads connected toeach of the three 132-kV substations are different.

0093-9994/$26.00 © 2011 IEEE

974 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 47, NO. 2, MARCH/APRIL 2011

The severe operating temperatures during summer conditionsdo not allow full utilization of the reactive power that couldbe supplied by the on-site generators. The results of load-flowstudies indicate that as much as 40 Mvar of reactive power needto be imported from the main grid during summer conditions.To eliminate the circulation of reactive power through the twoincoming grid transformers, three units of 26-Mvar capacitorbanks are required at each of the 132-kV substations shown inFig. 1. The additional 38-Mvar reactive-power supply wouldcause a leading power factor at the PCC. To achieve a unitypower factor at the PCC while eliminating the reactive-powercirculation through the two incoming transformers, the reactivepower generated by some of the on-site generators must bereduced. This is achieved by modification of the set point ofthe respective automatic voltage regulators.

The smelting plant under consideration includes six potlines,designated as 5, 6, 7, 9, 21, and 43, as shown in Fig. 1. Eachrectifier is a 12-pulse current-source diode rectifier. To limit thelevel of harmonics, multipulse conversion is adopted. For allpotlines, the multipulse rectifiers are of the parallel-type designwhere all the 12-pulse rectifiers are connected in parallel ontheir dc side.

For potlines 5, 6, 7, and 9, each potline consists of four mainand one standby rectifier transformers. The original intendedoperation of the rectifier transformers for these potlines wasto use four rectifier transformers in normal operating con-ditions such that a balanced 48-pulse harmonic performanceis obtained at the 132-kV points of connection. To realize a48-pulse system, the rectifier transformers are wound such thatthe phase displacement between the two successive secondaries(potline side) of the phase-shifting transformers is 360/48 =7.5◦. When referred to the primary (network side) of the trans-former, harmonic cancellation results in a 48-pulse system. Thismeans that the six dominant harmonic currents of the 12-pulsesystem including the 11th, 13th, 21st, 23rd, 35th, and 37th arepractically eliminated.

To maximize the process efficiency, the present operatingphilosophy of the plant is to use all five rectifier transformersunder normal operating conditions. The fifth (standby) rectifiertransformer of these potlines has the provision to be phaseshifted by one of the following phase angles: +15◦, −15◦,+7.5◦, −7.5◦, or zero. Choosing any of these five possiblephase displacements will create an unbalanced 48-pulse system.This implies that the magnitude of the harmonic currents isincreased compared with a balanced 48-pulse system wherethere are four rectifier transformers, phase shifted by 7.5◦ withrespect to each other.

Potlines 21 and 43 were originally designed as 60-pulserectifiers with five rectifier transformers being used in normaloperating conditions. For these potlines, the phase shift betweenthe two successive secondaries of phase-shifting transformersis 360/60 = 6◦. The dominant harmonics will be the 59th and61st orders.

A total number of 30 individual rectifier transformers forthe 132-kV potlines and four for the 33-kV potline 6B will beinstalled after the completion of network expansion. There is asmall auxiliary potline connected at the 11-kV voltage level notshown in Fig. 1.

Fig. 2. Schematic representation of potlines for IPSA harmonic analysis.

III. RECTIFIER-TRANSFORMER REPRESENTATION

For the potline transformers, the zero sequence impedancesare assumed equal to the positive sequence impedances. Thewinding connection of all rectifier transformers is convertedto YNyn0 in the model. This permits full flow of the zero-sequence triplen harmonics from the harmonic source side(potlines) to the network side with no phase shift. From thetriplen-harmonics point of view, the worst possible case istherefore investigated. The schematic representation of thepotlines for harmonic analysis is shown in Fig. 2.

As discussed in Section II, all the six 132-kV potlines areoperated with five rectifier transformers in service. In the IPSAtool, the rectifier transformers of potlines 23 and 41 are phaseshifted by 6◦ such that a balanced 60-pulse system is achieved.In the model, additional phase-shifting transformers with zeroimpedance are used. For potlines 5, 6, 7, and 9, a phase shiftof 7.5◦ is applied between the two successive main rectifiertransformers. Preliminary harmonic studies showed that thechoice of any of the five possible phase angles for the fifthrectifier transformer will have a very marginal impact on thelevel of harmonic currents reflected at the 132-kV substations.For the fifth rectifier transformer, a phase angle of zero ischosen, which results in a marginally lower level of harmonic-current distortion compared with other possible choices. Fig. 2shows how the correct phase shifts are taken into account inthe IPSA model using the phase-shifting transformers. Thisarrangement gives the correct harmonic-current injections inthe 132-kV network.

IV. HARMONIC-CURRENT INJECTION

The converters used for the potline ac/dc rectifiers areharmonic-current sources when viewed from the input powersystem. The dc at the output of the rectifier is reasonablyconstant, and the converter acts like a source of harmonicvoltage on the dc side and of harmonic current on the ac side.The impact of harmonics on the power system can thereforebe analyzed by current sources injected into the points wherethe potlines are connected. The actual measurements suppliedby the plant owner provide information on the harmonic-current magnitudes of up to the 40th order. These values arerelatively smaller than those obtained from a theoretical Fourieranalysis and were used as a starting point for the calculationsof harmonic-current injections. The harmonic-current measure-ments were not suitable for direct entry in the harmonic analysistool, and some preprocessing was needed. This is because, foreach potline, the harmonic measurements were only carried

BADRZADEH et al.: DESIGNING PASSIVE HARMONIC FILTERS FOR AN ALUMINUM SMELTING PLANT 975

TABLE IHARMONIC-PENETRATION-STUDY CONFIGURATIONS

TABLE IISUMMARY OF THE TOTAL HARMONIC VOLTAGE DISTORTIONS AT THE 400-, 132-, AND 33-kV SUBSTATIONS

out for one individual rectifier transformer and no informationon the harmonic-current magnitude of the other four recti-fier transformers was available. Additionally, no informationon the phase angle of the harmonic currents was provided.Calculations have therefore been developed to estimate theharmonic phase angle for the characteristic harmonics [3]. (Thecharacteristic harmonics of the 12-pulse rectifier transformersare 11th, 13th, 23rd, 25th, 35th, 37th, 47th, and 49th.) Includingthe phase angles for the characteristic harmonics provides someharmonic cancellation due to a difference in the phase shifts ofdifferent rectifier transformers in a given potline. Conventionalharmonic-penetration studies are normally performed for upto the 50th order. As no information on the magnitude of the47th and 49th harmonics is provided, mathematical calculationswere utilized to provide an estimation of these harmonics [3].

With several sources of harmonics in the system, harmoniccurrents of the same order generally have different phase anglesand some harmonic cancellation will occur. This is referred toas the diversity effect [4]. This reduces the net total harmonicvoltage distortion at the PCC. In the studies reported in thispaper, this phase cancellation has been taken into account dueto the following reasons.

1) Different size and length of the cables connecting potlinesto the three 132-kV substations.

2) Different impedances for the phase-shifting transformersconnecting potlines to the three 132-kV substations.

3) A very minor difference between the short-circuit im-pedance of the five phase-shifting transformers withineach potline due to manufacturing tolerances.

4) As the total potline loads connected to each of the three132-kV substations are different, the amplitude of theharmonic currents of the same order at the three 132-kVsubstations will be different. The theoretical calculationof phase angles is based on a methodology describedin [3], where the harmonic phase angle depends on thecommutation overlap angle and, hence, the reactance of

the line. As discussed previously, the line reactance is dif-ferent for different rectifier transformers. This indicatesthat the phase angle of harmonic currents of the sameorders will be different at the three 132-kV substations.

Note that the size of the required harmonic filters are deter-mined based on the reactive-power requirements of the smeltingplant and that inclusion or neglect of the diversity effect doesnot result in savings in terms of the total filter size.

V. HARMONIC-PENETRATION STUDIES

This section presents the results of the harmonic-penetrationstudies performed on the smelter-plant electrical network underconsideration. The analysis has been performed for a numberof the most onerous maintenance configurations with the aimof identifying potentially problematic operating conditions.The system configurations for the individual cases are givenin Table I.

The case studies discussed in this section are based on anassumed harmonic filter configuration, details of which willbe discussed in Section VII. Several case studies presented inthis section allow evaluation of the filtering scheme perfor-mance under the most onerous operating conditions. The casestudies presented include the harmonic signature of the systemwith and without the proposed harmonic filter configuration.For (N-1) generator outages, only the scenarios which giverise to highest total harmonic voltage distortion have beeninvestigated. Note that, in cases where a harmonic filter is outof service, the filter outage that causes the highest distortion hasbeen reported.

The levels of total harmonic voltage distortion at the400-kV interconnector, as well as the 132- and 33-kV sub-stations at the points where the potlines are connected, aresummarized in Table II. The system configuration for each casestudy is given in Table I. Instances where the IEC 61000-3-6(for the 400- and 132-kV voltage levels) or IEC 61000-2-4


TABLE IIISUMMARY OF MAXIMUM INDIVIDUAL DISTORTING COMPONENTS AT THE 400-, 132-, AND 33-kV SUBSTATIONS

(for the 33-kV voltage level) planning level is not maintainedare highlighted in bold. All other cells in the table indicatean acceptable total harmonic voltage distortion. Note that sub-stations 33 kV-A1 and 33 kV-A2 represent the front and rearbusbars for the substation 33 kV-A, since, with this substation,the bus section is operated as normally open.

The maximum individual distorting components are summa-rized in Table III; those exceeding the recommended limits arehighlighted in bold. The tables can be used as follows: Forcase 02, the THDV at the 132-kV switchboard 132 kV-A is2.1%, and the 5th and 7th harmonic voltages have the greatestmagnitude at 1.4% (of nominal 132-kV substations), which iswithin the recommended individual limit of IEC 61000-3-6.The individual harmonic voltage distortions for the 400-kV gridare practically zero and therefore not shown in Table III.

Case studies indicate that, without the harmonic filters inservice, the total harmonic voltage distortion as well as the indi-vidual harmonic components for the majority of the substationsis higher than the permissible IEC 61000-3-6 (for the 400- and132-kV voltage levels) and IEC 61000-2-4 (for 33-kV voltagelevel). This indicates the need to install harmonic filters at thethree 132-kV substations where the potlines are connected. Asdiscussed previously, these harmonic filters are also required toeliminate the reactive-power exchange with the main grid.

The harmonic distortion observed during (N-1) generationwhen all the potlines are operated with five rectifier transform-ers and with all filters in service is well within the limits definedin IEC 61000-3-6 or IEC 61000-2-4. Under these operatingconditions, the highest predicted THDV value is 2.4% on the132-kV network. In all cases, the individual harmonic voltagesare maintained within the acceptable limits of IEC 61000-3-6.

When a rectifier transformer is out of service in potline 43or 21, i.e., case study 03, the operating current of the otherfour rectifier transformers is increased by 125% to maintain thereal power required for the potline. In this case, the original60-pulse system becomes an unbalanced 48-pulse system andthe harmonic current and voltage magnitudes increase on the132-kV switchboard 132 kV-C. In the case studies consideredhere, the THDV on a number of the 132-kV substations increaseto a maximum of 3.4%, which is below the 3.5% compatibilitylevel of IEC 61000-3-6.

Inspection of case 04 reveals that there is a slight increase inthe predicted values of total harmonic voltage distortion whenthe system is operated with (N-2) generation outage duringsummer conditions. The total harmonic voltage distortion andthe largest individual harmonic voltage component for all sub-stations are maintained within the acceptable IEC limits.

Case study 05 considers the system operation with one of theharmonic filters out of service. As a result of a filter outage atthe 132-kV switchboard 132 kV-B, the THDV at that switch-board increases to 3.9% [from 2.4% when all three harmonicfilters are in service (case 02)], with a maximum individualharmonic distortion of 1.5% at the 7th harmonic. This meansthat, with one of the harmonic filters out of service, the impactof the other two filters on the harmonic control of switchboard132 kV-B would be reduced. This is because the three 132-kVsubstations in the electrical network of the smelting plant aresomewhat isolated by the two current-limiting reactors R11and R12.

VI. HARMONIC SENSITIVITY SCAN

Impedance/frequency scans are determined at the pointswhere the harmonic sources, i.e., the rectifier transformersare connected. For this calculation, all potline loads are dis-connected in the model. This will accentuate the presence ofparallel resonances in the network, as the studies are performedwith practically no load on the system, i.e., minimal damping.

Using the impedance scanning tool, provided in IPSA, theharmonic impedance sensitivity at the 132-, 33-, and 11-kVvoltage levels was derived for the individual cases listed inTable I. Space limitations do not allow inclusion of the im-pedance scans for the 33- and 11-kV busbars. Harmonic im-pedance plots indicate that, for the 33- and 11-kV voltagelevels, the impact of the variation of the generation lineup andthe introduction of the harmonic filters are practically negligi-ble. This is due to the impedance “buffer” of the step-downtransformers.

As an example, the simulated harmonic impedance plots atthe 132-kV voltage level for cases 01-A and 01-B are shown inFigs. 3 and 4, respectively. The harmonic impedance plots showthat, without the harmonic filters in service, large resonancepeaks occur. The impedance plots reveal two dominant parallelresonances between the 27th and 28th harmonics and betweenthe 17th and 18th harmonics for the 132-kV voltage level witha peak impedance of 620 and 550 Ω. With the introduction ofthe three 26-Mvar shunt harmonic filters, significant dampingwill be provided for the three 132-kV substations, where theimpedance at the peak resonance point is reduced to 130 Ω.

VII. HARMONIC FILTER DESIGN

This section presents the conceptual design procedure forthe single-tuned and damped high-pass filters employed inthe proposed harmonic filter configuration for the aluminum


Fig. 3. Case 01: Simulated harmonic impedance up to the 100th harmonic for 132-kV substations.

Fig. 4. Case 02: Simulated harmonic impedance up to the 100th harmonic for 132-kV substations.

smelting plant. The filter components, i.e., capacitor, inductor,and resistor, are calculated from the following parameters,which will be discussed in this section:

1) branch tuning harmonic order hn;2) branch type: tuned or damped;3) branch size (in megavars);4) branch quality factor Q;5) number of branches.

The general design procedure of passive harmonic filters andsome of the main practical issues associated with them arediscussed in the technical literature [5]–[10].

A. Harmonic Filter Types

A discussion on the main features of the two most widelyused types of passive shunt filters, namely, single-tuned anddamped high-pass filters, is provided next.

Single-Tuned Filter: A single-tuned filter is a capacitor de-signed to trap a certain harmonic by adding a reactor suchthat XL = XC at the tuned frequency fn. This configurationis shown in Fig. 5.

For a single-tuned filter tuned to the hn harmonic with thecapacitor size QC (in megavars), the capacitor reactance at

Fig. 5. Typical configuration of a single-tuned filter.

fundamental frequency is

XC =kV 2

QC. (1)

To trap the hn harmonic, the reactor should have a size of

XL =XC

h2n

. (2)

The reactor resistance is found as

R =Xn

Q(3)


Fig. 6. Typical configuration of a damped high-pass filter.

where Q is the quality factor of the filter and a typical value isbetween 30 and 100 [11], [12]. A high Q filter is usually tunedto one of the lower harmonic frequencies, e.g., 5th harmonic.Filter size is defined in terms of the reactive power produced atfundamental frequency

Qfilter =kV 2

XC − XL=

kV 2

XC − XC

h2n

(4)

=h2

n

h2n − 1

· kV 2

XC=

h2n

h2n − 1

· QC . (5)

In this configuration, the capacitor, inductor, and resistor areseries connected, and each element must be capable of carryingthe capacitor (filter) current, i.e.,

IRh= ILh

= ICh. (6)

For a single-tuned filter, the use of an inductor in series with acapacitor results in a voltage rise at the capacitor terminal givenby [11]

VC =(

h2n

h2n − 1

)Vbus1 (7)

where Vbus1 is the fundamental component of the voltage at thebusbar to which the harmonic filter is connected.

Damped High-Pass Filter: A typical configuration of adamped high-pass filter is shown in Fig. 6. The capacitor andreactor reactances can be calculated from (1) and (2) but theresistance is reciprocal to that given in (2) which is

R = Xn.Q (8)

For a damped filter, typical values of Q vary between 0.5and 5 [11], [12]. With a high Q, e.g., Q = 5, the filtering actionis more pronounced at the tuning frequency, while at higherfrequencies, the filter impedances rise steadily; hence, the filterhas little impact on the higher order harmonics. With lowervalues of Q, e.g., Q = 0.5, the response at the tuning frequencyis as good, but as the frequency increases, the impedance isnearly constant; therefore, higher order harmonics are mitigatedas well. To mitigate two major harmonics such as 11th and 13thharmonics with the use of only one damped filter, it is necessaryto select a fairly high Q in the range of 10–50 [12]. With a veryhigh Q, the damped filter resistance increases and losses maybecome an important issue.

The filter size is defined in terms of the reactive powerproduced at fundamental frequency

Qfilter =kV 2

XC − XL=

kV 2

XC − XC

h2n

(9)

=h2

n

h2n − 1

· kV 2

XC=

h2n

h2n − 1

· QC . (10)

The current in the capacitor is

ICh= IFh

(11)

where IFhis the filter current at harmonic order h.

The current in the reactor is

ILh=

R√R2 + X2

Lh

IFh=

Q√Q2 + (h/h2

n)IFh

(12)

where h is the harmonic order and hn is the filter tuning order.The current in the resistor is calculated as [11]

IRh=

XLh√R2 + X2

Lh

IFh=

hhn√

Q2 + (h/h2n)

IFh(13)

=h

hn· ILh

Q=

hXL

R· ILh

. (14)

Power loss in the resistor is

PR =∑h=1

RI2Rh

=XL

R

∑h=1

(hILh)2 . (15)

B. Harmonic-Filter Conceptual Design

For the smelting plant under consideration, each rectifierconsists of a 12-pulse diode bridge. The lowest order charac-teristic harmonics are therefore expected to be the 11th and13th harmonics. Some 5th and 7th harmonics will be producedas the rectifier transformers are not ideal due to manufacturingtolerances. The current operating philosophy of potlines 5, 6, 7,and 9 is to use standby rectifier transformers in normal oper-ating conditions. Noncharacteristic harmonics such as the 5th,7th, 17th, and 19th are therefore present and have a magnitudecomparable to those of the 11th and 13th when summed at eachindividual switchboard.

Harmonic filter banks are typically tuned to approximately2%–10% below the desired harmonic frequency. If a filter istuned exactly at the frequency of concern, an upward shift in thetuned frequency will result in a sharp increase in impedance, asseen by harmonics. Tuning the harmonic filter at a frequencyslightly lower than the desired frequency allows for the oper-ation of the filter bank in the event of the removal of a fewcapacitor units.

In order to mitigate the low-order 5th and 7th harmonics,a damped high-pass filter tuned at the 4.8th harmonic wasinitially investigated. With this arrangement, it was realized thatthe harmonic filter makes no contribution to the suppressionof the 7th harmonic. The second alternative considered wasto replace the single arm with two damped arms tuned atthe 4.8th and 6.8th harmonics. In this case, the magnitude ofthe 5th harmonic voltage remained the same before and after


TABLE IVVARIATION OF THE TOTAL HARMONIC VOLTAGE DISTORTION VERSUS NUMBER OF FILTER ARMS

filtering. The best configuration is therefore found to be theuse of two arms tuned at the 4.8th and 6.8th harmonic, but thedamped filter for the 4.8th harmonic is replaced with a single-tuned filter. To achieve an acceptable THDV and acceptableindividual harmonic components, the quality factors of thetuned and damped filters are found as 100 and 10, respectively.

To mitigate the 11th and 13th harmonics, it was observed thatthe filter design can be simplified by combining the filter armsfor the 11th and 13th harmonics into a single arm tuned at the10.8th harmonic. With this arrangement, the 11th harmonic isnearly eliminated and the 13th is reduced to acceptable limits.The quality factor of this filter is set to 10. An alternative wouldhave been to tune the filter to about the 12th harmonic; the asso-ciated total harmonic voltage distortions are shown in Table IV.

Table IV summarizes the total harmonic voltage distortionusing various filter configurations and different tuning frequen-cies. The system configuration corresponds to an outage ofST18 under summer conditions at 45 ◦C and with connectionto the main grid. In all cases, a constant filter size of 26 Mvarat each 132-kV switchboard is considered. The filter size wasdetermined to eliminate the reactive-power import from themain grid and minimize the flow of reactive power through thetwo incoming grid transformers. In the table, instances wherethe THDV exceeds the acceptable limit of 3% are highlightedin bold. As indicated in this table, by tuning the filter to the12th harmonic, the total harmonic voltage distortion is slightlyhigher than that achieved by the proposed filter configuration,i.e., tuning the filter at the 10.8th harmonic.

The concept of using a single damped filter to mitigate the11th and 13th harmonic has been emulated for the mitigation ofthe 17th and 19th harmonics. In this case, with a single dampedarm tuned at the 16.7th harmonic, the total harmonic voltagedistortion can be maintained within the permissible limits.

Inspection of Table IV reveals that the optimal harmonic filterconfiguration comprises four branches (arms). The optimaldesign is highlighted with cells in gray pattern. Designing the

harmonic filter with five arms marginally increases the THDV

compared with the use of four arms (assuming the total filtermegavar remains the same). A harmonic filter with five arms isalso more expensive. Note that, for this study, all the filters aresized the same. The intention of sizing filters the same is to useonly filters that are “standardized.” With this approach wheninstalling the units in the field, it will be more practical to orderthem all sized at the same value. This will assist with carryingspares, e.g., capacitor units.

The effectiveness of using three damped filters tuned to the6.8th, 10.8th, and 16.7th harmonics instead of three single-tuned filters of the same size and the same tuning orders isshown in Fig. 7 (in both cases, a single-tuned filter tunedto the 4.8th is used as the fourth branch). This figure showsthat, with three damped filters, the peak resonance point issignificantly decreased, which confirms the choice of filterbranches proposed for the smelting plant. For comparison, theimpedance plot for the case of having no filter in service isalso shown. With four single-tuned filters, the peak resonanceis increased, which indicates a parallel resonance caused by thesingle-tuned filters.

Using the equations stated previously, the parameters of theproposed harmonic filter can be determined as stated in Table V.A schematic diagram of the proposed harmonic filter is shownin Fig. 8. This filter configuration is proposed for all the three132-kV substations.

C. Harmonic Impedance Plot for the ProposedHarmonic Filter

If shunt harmonic filters are not selected carefully, they canresonate with existing electrical components and cause addi-tional harmonic currents. In order to ensure that the proposedharmonic filter does not cause any new resonance point on thesystem, a harmonic impedance sensitivity plot for the filter wasproduced, as shown in Fig. 9.


Fig. 7. Harmonic impedance plot for the 132-kV switchboard 132 kV-C.

TABLE VPARAMETERS OF THE PROPOSED HARMONIC FILTER CONFIGURATION

Fig. 8. Schematic diagram of the proposed harmonic filter configuration.

Fig. 9. Harmonic impedance characteristics of the proposed harmonic filter.


TABLE VIHARMONIC CURRENTS FLOWING THROUGH THE CAPACITOR

Common traits observed in the impedance plot of the pro-posed harmonic filter configuration are as follows.

1) Low impedance at the 11th and 13th harmonics—thecharacteristic harmonics of the 12-pulse rectifier.

2) Low impedance at the 5th and 7th harmonics.3) A shifted resonance peak at the 8th harmonic, due to

filtering of the 7th harmonic.4) A shifted resonance peak at the 14th harmonic, due to

filtering of the 17th harmonic.5) The shifted resonance peaks produced by the harmonic

filter are located at the noncharacteristic harmonics, andthe resulting impedance is fairly small, i.e., 160 Ω for the8th and 60 Ω for the 13th harmonic.

6) Low impedance above the 17th harmonic.

Based on these characteristics, it can be concluded that theproposed filter does not, by itself, cause any new resonancepoint on the system and that no voltage amplification is causedby the filter.

D. Harmonic Filter Rating

So far, in this section, it has been shown that the proposedharmonic filter configuration is effective in avoiding the reso-nance problems and bringing the system into compliance withIEC standards. With the optimal filter configuration discussedearlier, filter currents and voltages should be analyzed to checkthe rating of filter elements (capacitor, resistor, and reactor) inthe presence of harmonics.

Capacitors: ANSI/IEEE Standard 18 “Shunt power capaci-tors” [13] states that a capacitor can be continuously operatedin the presence of harmonics provided that the following aresatisfied.

1) The peak current does not exceed 130% of the ratedcurrent: Irms < 1.3I1, where I1 is the fundamentalcapacitor current which implies that

Irms

I1=

√1 + THD2

i ≤ 1.3. (16)

2) The rms voltage does not exceed 110% of the rated:Vrms < 1.1V1, where V1 is the fundamental capacitorvoltage which implies that

Vrms

V1=

√1 + THD2

v ≤ 1.1. (17)

3) The peak voltage does not exceed 120% of the rated:Vpeak < 1.2V1, where V1 is the fundamental capacitorvoltage which implies that

∑h

VCh< 1.2V1. (18)

The reactive power does not exceed 135% of the rating:QC < 1.35QC1 , where QC1 is the fundamental reactivepower generated by the capacitor. This implies that

QC

QC1

=∑

h

h

(Vh

V1

)2

=∑h=1

1h

(Ih

I1

)2

=∑h=1

I2hpu

h≤1.35. (19)

These requirements reflect the fact that the capacitor of afilter tuned to a certain harmonic frequency will absorb partsof other harmonic frequencies and that safety factors are there-fore required. Note that IEEE Standard 18 has a more com-prehensive requirement than the corresponding IEC standardfor the capacitors (IEC 60871-1 [14]) and is therefore usedfor determining the rating of the filter components. Anothersafety measure which can be applied in conjunction with theaforementioned requirements is to have the capacitor bankrated at a voltage higher than the busbar voltage to whichit is connected. This allows the filter to perform successfullyin the event of system overvoltages and capacitor/filter bankunbalance conditions.

The harmonic currents flowing through the harmonic filtersconnected to the three 132-kV substations 132 kV-A, 132 kV-B,and 132 kV-C are shown in Table VI. This table shows thatthe rms current through the capacitor and the reactive powergenerated by the capacitors are practically 1 p.u. and, hence,within the 1.3- and 1.35-p.u. limits required by IEEE Standard18. The current harmonics are taken from the harmonic studiescarried out in the IPSA simulation tool. As an example, thesystem configuration is for an outage of ST18 at 45 ◦C ambienttemperature with connection to the main grid. Note that the perunit values are on the proposed capacitor megavar rating.

Table VII shows the harmonic components of the capacitorvoltages calculated as

VCh= ICh

· XC

h. (20)

The maximum peak voltage indicated in the table is 1.18 p.u.,which is within the 1.2-p.u. limit of IEEE Standard 18. Thistable also shows that the capacitor rms voltages are within the1.1-p.u. limit.


TABLE VIIHARMONIC VOLTAGES ACROSS THE CAPACITOR

TABLE VIIIHARMONIC CURRENTS FLOWING THROUGH THE RESISTOR

TABLE IXHARMONIC VOLTAGES ACROSS THE REACTOR

Tables VI and VII demonstrate that the capacitor rmscurrents and voltages are practically at 100% of their ratings.The peak harmonic voltages across the capacitors are closeto the 1.2-p.u. limit, and it would be advisable to allow somesafety margin for the capacitor operation during abnormalconditions. In general, of all the four ratings discussedpreviously, the peak capacitor voltage is the limiting factor inmost practical harmonic filter designs. A safety margin canbe provided by choosing the capacitors with higher voltages,i.e., 145-kV harmonic filters for the 132-kV busbar voltage.To allow for some margin in the case of system overvoltagesduring steady-state conditions, circuit breakers with a ratedvoltage of 170 kV are recommended for the proposed harmonicfilters. A local dedicated circuit breaker will also be required.By allowing this safety margin, the manufacturing tolerancesin the capacitors are accounted for.

Resistors: The resistor bank has to be rated to withstandthe current drawn in the presence of harmonics. The powerloss in the presence of harmonics can be significantly higherthan that at fundamental frequency. If a resistor bank is notrated appropriately, it will burn out. The current through theresistors can be calculated using (13). The resistor currents areindicated in Table VIII. The required kilowatt rating of the

resistor banks to withstand these currents are calculated using(15) and tabulated in the last column of the table.

Reactors: For the single-tuned filter, the current flowingthrough the reactor is identical to that of the capacitor. For thedamped filters proposed for this system, R � XL, as shown inTable V. For both single-tuned and damped filters, the currentthrough the reactors are therefore practically the same as thecurrent through the capacitors shown in Table VI. The reactorsmust therefore be rated to withstand the same currents as thecapacitors. Unlike resistors, the shunt reactors used in dampedfilters have generally significantly lower losses at harmonicfrequencies compared with those at fundamental frequency, andthe reactor losses at harmonic frequencies can be neglected.

To ensure that the stresses across the reactor do not exceedthe design capability, the rated voltage across the reactor shouldbe specified as

VL =∑h=1

ILh· XLh

=∑h=1

ILh· hXL. (21)

Considering ILh∼= ICh

and recalling Table VI for the capacitorcurrents, the reactor voltages can be calculated as shown inTable IX.


VIII. CONCLUSION

This paper has presented the results of the harmonic analysisand harmonic filter design conducted for an aluminum smelt-ing plant to address concerns raised due to the expansion ofthe smelting load. It was shown that, under (N-1) and (N-2)generation outages and without harmonic filters in service, theharmonic voltage distortion levels exceed those required byIEC 61000-3-6 (for the 400- and 132-kV voltage levels) andIEC 61000-2-4 (for the 33-kV voltage levels). With the introduc-tion of three identical 26-Mvar shunt passive filter banks, theharmonic voltage distortion levels are maintained well within theIEC limits during (N-1) and (N-2) generation outages and whenall five rectifier transformers are in service for each potline. Withan outage of one of the rectifier transformers, the harmonicdistortion levels marginally exceed the acceptable IEC limits.

The studies show that a four-branch harmonic filter compris-ing four equally sized branches is a practical and realizabledesign to maintain the harmonic levels within the IEC-specifiedlimits. Identical filters were proposed for each of the three132-kV substations. The proposed filter configuration makesit possible to build filters from identical components. Theproposed harmonic filter includes three damped filters tuned tothe 6.8th, 10.8th, and 16.7th harmonics and a single-tuned filtertuned to the 4.8th for the suppression of the 5th harmonic. Withthe use of three damped filters, the resonances caused by thefilter are very small and no voltage amplification is caused bythe filter.

The ratings of the proposed harmonic filter were checkedagainst IEEE Standard 18. It was confirmed that the rms andpeak voltage, the rms current, and the reactive power generatedby the capacitor in the presence of harmonics are maintainedwithin the limits specified by ANSI/IEEE Standard 18. To allowsome margin for overloading of the capacitor, the option ofincreasing the harmonic filter rated voltage to 145 kV wasrecommended. To allow for some margin in the case of systemovervoltages during steady-state conditions, circuit breakerswith a rated voltage of 170 kV were recommended for theproposed harmonic filters. A local dedicated circuit breakerwould also be required.

REFERENCES

[1] Electromagnetic Compatibility (EMC)—Part 3-6—Limits: Assessment ofthe Connection of the Distorting Installation to MV, HV and EHV PowerSystems, IEC Standard 61000-3-6, 2008.

[2] Electromagnetic Compatibility (EMC)—Part 2-4—Environment:Compatibility Levels in Industrial Plants for Low Frequency ConductedDisturbances, IEC Standard 61000-2-4, 2002.

[3] E. W. Kimbark, Direct Current Transmission. New York: Wiley, 1971.[4] A. Mansoor, W. M. Grady, A. H. Chowdhury, and M. J. Samotyi, “An

investigation of harmonics attenuation and diversity among distributedsingle-phase power electronic loads,” IEEE Trans. Power Del., vol. 10,no. 1, pp. 467–473, Jan. 1995.

[5] D. A. Gonzalez and J. C. McCall, “Design of filters to reduceharmonic distortion in industrial power systems,” IEEE Trans. Ind. Appl.,vol. IA-23, no. 3, pp. 504–511, May 1987.

[6] A. B. Nassif, W. Xu, and W. Freitas, “An investigation on the selection offilter topologies for passive filter applications,” IEEE Trans. Power Del.,vol. 24, no. 3, pp. 1710–1718, Jul. 2009.

[7] J. C. Das, “Passive harmonic filters—Potentialities and limitations,” IEEETrans. Ind. Appl., vol. 40, no. 1, pp. 232–241, Jan./Feb. 2004.

[8] E. Makram, E. V. Subramaniam, A. A. Girgis, and R. Catoe, “Harmonicfilter design using actual recorded data,” IEEE Trans. Ind. Appl., vol. 29,no. 6, pp. 1176–1183, Nov./Dec. 1993.

[9] M. F. McGranghan and D. R. Mueller, “Designing harmonic filters foradjustable speed drives to comply with IEEE-519 harmonic limits,” IEEETrans. Ind. Appl., vol. 35, no. 2, pp. 312–318, Mar./Apr. 1999.

[10] S. M. Merhej and W. H. Nichols, “Harmonic filtering for theoffshore industry,” IEEE Trans. Ind. Appl., vol. 30, no. 3, pp. 533–542,May/Jun. 1994.

[11] G. J. Wakileh, Power Systems Harmonics: Fundamentals, Analysis andFilter Design. New York: Springer-Verlag, 2001.

[12] J. Arrilaga, D. A. Bradley, and P. S. Bodge, Power System Harmonics.New York: Wiley, 1985.

[13] IEEE Standard for Shunt Power Capacitors, Standard 18, 2002.[14] Shunt Power Capacitors for AC Power System Having Rated Voltage

Above 1000 V. General Performance, Testing and Rating—SpecialRequirements—Guide for Installation and Operation, IEC Standard60871-1, 2005.

Babak Badrzadeh (S’03–M’07) received the B.Sc.and M.Sc. degrees in electrical engineering fromIran University of Science and Technology, Tehran,Iran, in 1999 and 2002, respectively, and the Ph.D.degree in electrical engineering from Robert GordonUniversity, Aberdeen, U.K., in 2007.

After spending a short period as an AssistantProfessor at the Technical University of Denmark,he joined the Transmission and Distribution Divi-sion, Mott MacDonald, Glasgow, U.K., as a Sys-tem Analysis and Network Planning Engineer. Since

March 2010, he has been with Power Plant Solutions, Vestas TechnologyR&D, Århus N, Denmark, where he is acting in different capacities for variouswind-power plant projects. He has published several articles and presentedtutorials on different areas of power systems and power electronics. He hasprepared two two-part educational courses for the IEEE eLearning libraryon high-power variable-speed drives and HVdc transmission systems. Hisareas of interest include power system electromechanical and electromagnetictransients, applications of power electronics in power systems, wind powerplants, and modeling and simulation.

Dr. Badrzadeh was a Guest Editor for the special issue of the IEEE IndustryApplications Magazine on high-power variable-speed drives. He is an activemember of several IEEE Power and Energy Society and IEEE Industry Appli-cations Society working groups and task forces.

Kenneth S. Smith (SM’07) received the B.S. degreein engineering science (with first class honors) andthe Ph.D. degree for his work on the analysisof marine electrical systems from the Universityof Aberdeen, Aberdeen, U.K., in 1988 and 1992,respectively.

After completing his doctorate, he held academicteaching posts at the University of Aberdeen and atHeriot-Watt University, Edinburgh, U.K., where hewas appointed as an Honorary Professor in 2009.Since April 2002, he has been with the Power

Systems Analysis Section, Transmission and Distribution Division, MottMacDonald, Glasgow, U.K., where he is currently the Technical Manager forthe power systems studies group.

Dr. Smith is a Chartered Electrical Engineer (U.K.) and a Fellow of TheInstitution of Engineering and Technology.

Roddy C. Wilson (M’06) received the B.S. degree inelectrical engineering from Heriot-Watt University,Edinburgh, U.K.

He joined YARD Limited in 1984. Between 1993and 1997, he was with Foster Wheeler Energy Lim-ited. Since 1997, he has been with Mott MacDonald,Glasgow, U.K., where he is currently the BusinessDevelopment Manager of the Transmission andDistribution Division’s Power Systems AnalysisSection.

Mr. Wilson is a corporate member of The Institu-tion of Engineering and Technology and a Charted Electrical Engineer (U.K.).

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