59594535-harmonic-analysis-report-1.pdf

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Harmonic Study Done By - VT Page 1 of 22

HARMONICSTUDY REPORT


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CONTENT

1.INTRODUCTION............................................................................................................2

2.BASIC CONCEPT ...........................................................................................................4

3.EFFECT OF HARMONICS ON POWER SYSTEM......................................................73.1 MOTORS ...............................................................................................................................................7

3.2 TRANSFORMERS ................................................................................................................................7

3.3 CAPACITOR BANKS .................................................................................................................. ...... ....8

3.4 CABLES ................................................................................................................................................9

3.5 NEUTRAL .............................................................................................................................................9

4.HARMONIC LIMITING STANDARD IEEE 519 1992 AT A GLANCE.................115.HARMONIC DISTORTION..........................................................................................13

5.1 HARMONIC DISTORTION AT 415 V BUS ..........................................................................................13

5.2 HARMONIC DISTORTION AT 33 KV LEVEL ......................................................................................13

5.3 CONCLUSIONS ...........................................................................................................................14

6.EFFECT OF HARMONICS ON TRANSFORMERS...................................................156.1. AN OVERVIEW OF DIFFERENT STANDARDS FOR TRANSFORMERS HANDLING NON-

SINUSOIDAL LOAD ...................................................................................................................................15

6.2. DERATING CALCULATIONS FOR CENTRAL UTILITY TRANSFORMERS.....................................16

6.2.1 OPERATION PHILOSOPHY .......................................................................... 16

6.2.2 TRANSFORMER DETAILS ........................................................................... 176.2.3 FACTOR K CALCULATIONS (BS 7821, PART 4) ......................................17

6.3 CONCLUSIONS ............................................................................................................................... ....19

7.CAPACITOR BANKS...................................................................................................207.1 SYSTEM DETAILS ..............................................................................................................................20

7.2 CALCULATION OF RESONANCE FREQUENCY ...............................................................................20

7.3 CONCLUSIONS ............................................................................................................................... ....22

1. INTRODUCTION

With increasing use of non-linear loads such as variable frequencydrives, UPS, SMPS, electronic ballast etc the power systems are gettinghighly polluted by harmonics which is leading to premature failures of



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electrical and electronic equipments as well as nuisance trippingleading to production loss. So it is imperative that a study of powerquality of the electrical distribution system of a plant should be madeto asses the level of pollution due to harmonics and adequatemeasures should be taken to control it.

The standard which is used to deal with the harmonic limits in thesystem is IEEE 519-1992. This standard is basically designed forUtilities to frame limits of harmonic distortion by the users of utilitypower supplies on grid to which they are connected; so a word to wordapplication of this standard to a distribution system in a plant mayresult in over-design, so a fair amount of approximation is requiredwhile applying this standard at industrial plant level and same as beendone here.



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2. BASIC CONCEPT

A pure sinusoidal voltage is a conceptual quantity produced by an idealAC generator built with finely distributed stator and field windings thatoperate in a uniform magnetic field. Since neither the windingdistribution nor the magnetic field are uniform in a working ACmachine, voltage waveform distortions are created, and the voltage-time relationship deviates from the pure sine function. The distortion atthe point of generation is very small (about 1% to 2%), but nonethelessit exists. Because this is a deviation from a pure sine wave, thedeviation is in the form of a periodic function, and by definition, thevoltage distortion contains harmonics.

When a sinusoidal voltage is applied to a certain type of load, thecurrent drawn by the load is proportional to the voltage and impedanceand follows the envelope of the voltage waveform. These loads arereferred to as linear-loads (loads where the voltage and current followone another without any distortion to their pure sine waves). Examplesof linear loads are resistive heaters, incandescent lamps, and constantspeed induction and synchronous motors.

In contrast, some loads cause the current to vary disproportionatelywith the voltage during each half cycle. These loads are classified as

nonlinear loads, and the current and voltage have waveforms that arenon-sinusoidal, containing distortions, whereby the 50-Hz waveformhas numerous additional waveforms superimposed upon it, creatingmultiple frequencies within the normal 50-Hz sine wave. The multiplefrequencies are harmonics of the fundamental frequency. Normally,current distortions produce voltage distortions. However, when there isa stiff sinusoidal voltage source (when there is a low impedance pathfrom the power source, which has sufficient capacity so that loadsplaced upon it will not

effect the voltage), one need not be concerned about currentdistortions producing voltage distortions.

Examples of nonlinear loads are battery chargers, electronic ballasts,variable frequency drives, and switching mode power supplies. As



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nonlinear currents flow through a facility's electrical system and thedistribution-transmission lines, additional voltage distortions areproduced due to the impedance associated with the electrical network.Thus, as electrical power is generated, distributed, and utilized, voltageand current waveform distortions are produced.

Power systems designed to function at the fundamental frequency,which is 50-Hz in India, are prone to unsatisfactory operation and, attimes, failure when subjected to voltages and currents that containsubstantial harmonic frequency elements. Very often, the operation ofelectrical equipment may seem normal, but under a certaincombination of conditions, the impact of harmonics is enhanced, withdamaging results.

Thus the harmonics are AC voltages and currents with frequencies thatare integer multiples of the fundamental frequency. On a 50-Hz

system, this could include 2nd order harmonics (100 Hz), 3rd orderharmonics (150 Hz), 4th order harmonics (200 Hz), and so on.Normally, only odd-order harmonics (3rd, 5th, 7th, and 9th) occur on a3-phase power system. If we observe even-order harmonics on a 3-phase system, we more than likely have a defective rectifier in oursystem. Let us understand this by superimposing the third harmonicand fifth harmonic voltage on perfectly sinusoidal harmonic voltageand resulting harmonically distorted waveform.

The figure 1 is the fundamental sinusoidal waveform, figure 2 is thethird harmonic and figure 3 is the fifth harmonic waveform. Figure 4 is

the resultant distorted wave form.

FIGURE - 1Perfectly Sinusoidal Waveform.U (t) = U1 Sin (wt)

+



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=

FIGURE- 2 FIGURE - 4Third Harmonic Waveform. Resultant Distorted Waveform.U 3(t) = U3 Sin (3wt) U(t) = U1 Sin (wt) + U3 Sin (3wt) + U5 Sin (5wt)

+

FIGURE- 3

Fifth Harmonic Waveform.U 5(t) = U5Sin (5wt)



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3. EFFECT OF HARMONICS ON POWER SYSTEM

We have seen that a harmonic affected voltage and current consist of

voltage and current of multiple frequencies; this gets circulated alongthe fundamental component in the power system. This presence ofcurrent and voltages of multiple frequencies results in increased lossesand overloading in the power system, the effects of harmonic ondifferent component of power system are discussed in brief below.

3.1 MOTORS

There is an increasing use of variable frequency drives (VFDs) that

power electric motors. Voltage supplied to a motor sets up magneticfields in the core, which create iron losses in the magnetic frame of themotor. Hysteresis and eddy current losses are part of iron losses thatare produced in the core due to the alternating magnetic field.Hysteresis losses are proportional to frequency, and eddy currentlosses vary as the square of the frequency. Therefore, higherfrequency voltage components produce additional losses in the core ofAC motors, which in turn, increase the operating temperature of thecore and the windings surrounding in the core. Application of non-sinusoidal voltages to motors results in harmonic current circulation inthe windings of motors. The net rms current is [I.sub.rms] = [square

root of [([I.sub.1]).sup.2] + [([I.sub.2]).sup.2] + [([I.sub.3]).sup.2] +] ...,where the subscripts 1, 2, 3, etc. represent the different harmoniccurrents. The [I.sub.2]R losses in the motor windings vary as thesquare of the rms current. Due to skin effect, actual losses would beslightly higher than calculated values. Stray motor losses, whichinclude winding eddy current losses, high frequency rotor and statorsurface losses, and tooth pulsation losses, also increase due toharmonic voltages and currents.

3.2 TRANSFORMERS

The harmful effects of harmonic voltages and currents on transformerperformance often go unnoticed until an actual failure occurs. In someinstances, transformers that have operated satisfactorily for longperiods have failed in a relatively short time when plant loads were



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changed or a facility's electrical system was reconfigured. Changescould include installation of variable frequency drives, electronicballasts, power factor improvement capacitors, arc furnaces, and theaddition or removal of large motors.

Application of nonsinusoidal excitation voltages to transformersincreases the iron losses in the magnetic core of the transformer inmuch the same way as in a motor. A more serious effect of harmonicloads served by transformers is due to an increase in winding eddycurrent losses. Eddy currents are circulating currents in the conductorsinduced by the sweeping action of the leakage magnetic field on theconductors. Eddy current concentrations are higher at the ends of thetransformer windings due to the crowding effect of the leakagemagnetic fields at the coil extremities. The eddy current lossesincrease as the square of the current in the conductor and the squareof its frequency. The increase in transformer eddy current loss due to

harmonics has a significant effect on the operating temperature of thetransformer. Transformers that are required to supply power tononlinear loads must be de-rated based on the percentages ofharmonic components in the load current and the rated winding eddycurrent loss.

3.3 CAPACITOR BANKS

Many industrial and commercial electrical systems have capacitorsinstalled to offset the effect of low power factor. Most capacitors aredesigned to operate at a

maximum of 110% of rated voltage and at 135% of their KVAR ratings.In a power system characterized by large voltage or current harmonics,these limitations are frequently exceeded, resulting in capacitor bankfailures. Since capacitive reactance is inversely proportional tofrequency, unfiltered harmonic currents in the power system find theirway into capacitor banks, these banks act like a sink, attractingharmonic currents, thereby becoming overloaded.

A more serious condition, with potential for substantial damage, occursas a result of harmonic resonance. Resonant conditions are createdwhen the inductive and capacitive reactance become equal in anelectrical system. Resonance in a power system may be classified asseries or parallel resonance, depending on the configuration of theresonance circuit. Series resonance produces voltage amplification andparallel resonance causes current multiplication within an electrical



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system. In a harmonic rich environment, both types of resonance arepresent. During resonant conditions, if the amplitude of the offendingfrequency is large, considerable damage to capacitor banks wouldresult. And, there is a high probability that other electrical equipmenton the system would also be damaged.

3.4 CABLES

The flow of normal 50-Hz current in a cable produces [I.sup.2]R lossesand current distortion introduces additional losses in the conductor.Also, the effective resistance of the cable increases with frequency dueto skin effect, where unequal flux linkages across the cross section ofthe cable causes the AC current to flow on the outer periphery of the

conductor, higher the frequency of the AC current, the greater thistendency. Because of both the fundamental and the

harmonic currents that can flow in a conductor, it is important to makesure a cable is rated for the proper current flow.

3.5 NEUTRAL

In a three phase system the voltage waveform from each phase to theneutral star point is displaced by 120 so that, when each phase is equallyloaded, the combined current in neutral is zero. When the loads are notbalanced only net out of balance current flows in the neutral. In the past,installers (with the approval of standard authorities) have taken advantage ofthe fact by installing half sized neutral conductors. However, although thefundamental component cancels out but harmonic components do not -in factthose that are an odd multiple of three times the fundamental, the triple-N(triplen) harmonics, add in the neutral. Case studies in high harmonicaffected commercial buildings generally show neutral currents between 150% and 210 % of the phase current often in half sized neutral conductors. This

results in overloading and overheating of neutral and often failure of neutral.



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4. HARMONIC LIMITING STANDARD IEEE 519 1992 AT AGLANCE.

IEEE 519 was introduced in 1983 and was more recently revised in 1992. Itwas intended to provide direction on dealing with harmonic introduced bystatic converters and non-linear loads. The standard is basically prepared toset standard for limitation of harmonic distortion by the users of utility powersupplies on grid to which they are connected, it is also widely used to defineharmonic limiting standards inside the plant due to absence of any otherrelevant harmonic limiting standard for the systems, however use of thisstandard inside the plant makes it very stringent for the user.

Terms Pertaining to IEEE 519-1992

1. PCC: Point o f common coupl ing i s def ined as the point

where non-linear loads are connected to main bus.2. ISC: Short circuit current of the bus under consideration.3. IL: 15 or 30 minute (average) maximum demand current.4. TDD: Total demand d is tort ion. TDD i s ident ical to THDexcept IL (as def ined previous ly) is used instead of thefundamental current component.

5. Ih: Individual harmonic current component.

I t may be noted tha t there a re no l imi ts recommended forindividual loads l ike V.F.Ds etc but only for the overall system.

The limits specified may however, be discretionally to variousP.C.Cs to understand the impact the existing level of harmonicsmay have on o ther l oads on the common bus . The point of analysis (POA) can be chosen as per the guidelines with specif icaim in view.

IEEE 519 -1992 recommends di ff eren t limi ts on IndividualHarmonics (Ih) and Total Demand Distortion (THD), depending onthe ISC/IL ratio. ISC isthe short circuit current at the PCC, and ILis the maximum demand

load current (fundamental) at the PCC. More current distortion isallowed at higher ISC/IL ratios, since voltage distortion decreasesas the ratio increases. IEEE 519-1992 classif ies systems in threecategories viz. Special Application, General System & DedicatedSystem to set l imit for voltage THD. Table 1 below specif ies theharmonic current limits at PCC.



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Table 1 - Harmonic Distortion Limits as per IEEE 519-1992.


The THD of Voltage specified for General Systems in IEEE 519-1992 is 5%.If THD for current complies with this standard then no need to calculate TDD.


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5. HARMONIC DISTORTION

5.1 HARMONIC DISTORTION AT 415 V BUS

Sr.No

Feeder/Drive

ISC (kA) ISC / IL TDD (%)Permitted

TDD (%)Actual

Distortion

1 Trafo 1(MLTP A)

100 115 15 12.85SAFE

2 Trafo 2(MLTP A

100 64 12 4.70SAFE

3 Trafo 3(MLTP A

100 99 12 2.12SAFE

4 MDB 3 100 598 15 13.13 SAFE5 MDB 1 100 170.6 15 12.4 SAFE6 UPS 1 10 1221 20 19.34 SAFE7 UPS 2 10 2778 20 19.6 SAFETABLE 2(Refer Annexure A for detail data.)

Sr.No

Feeder/Drive


TDD(%)Actual

Distortion

1 Printing 1 100 164 15 8.5 SAFE2 Printing 2 100 266 15 6.8 SAFE

3 Biscuit 1 100 233 15 20.35 UNSAFE4 Biscuit 2 100 605 15 21.4 UNSAFE5 Soap 1 100 143 15 18 UNSAFE6 Soap 2 100 132 15 12.45 SAFE7 Snacks 100 140 15 16.85 UNSAFE8 Cream &

Shampoo100 540 15 13.9 SAFE

TABLE 3(Refer Annexure A for detail data.)

5.2 HARMONIC DISTORTION AT 33 KV LEVEL

Sr.No

Feeder/Drive


TDD (%)Actual

Distortion

1 33 KVIncomer

26.2 757.74 15 8 SAFE

TABLE 4(Refer Annexure A for detail data.)



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5.3 CONCLUSIONS

1. The more serious voltage harmonic distortion level (THD) at allbuses is well below the safe limit of 5 %.(Refer Annexure A)

2. The current distortion level at 33 KV bus is under safe limits.3. The current harmonic distortion on 415 bus (Main LT Panel) is

under safe limits.4. The current harmonic injection from PCC of Division indicates

that the harmonic distortion at the PCC of Printing, Soap PCC 2and Cream & Shampoo PCC are at safe level.

5. The current harmonic injection from PCC of Division indicatesthat the harmonic distortion at both the PCC of Biscuit, PCC ofSnacks, Soap PCC 1 are unhealthy level with apredominance of 5th and 7th harmonic; so a detailed harmonicanalysis is required and suitable harmonic mitigation measuresshould be taken thereafter.

6. The TDD of both Lighting UPS of Utility are alarmingly closed to

limits, this high TDD should be discussed with OEM to identify thereason.



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6. EFFECT OF HARMONICS ON TRANSFORMERS

6.1.AN OVERVIEW OF DIFFERENT STANDARDS FOR TRANSFORMERS

HANDLING NON-SINUSOIDAL LOAD

REF.STANDARD

FORMULA REMARK

K-Factor;UL-1561, UL-

1562(UnderwriterLaboratories)

WhereIh = Individual Harmonic

componentIR= Rated RMS load current of

transformer.

h = The harmonic order

1. Firstthe K-factor of the non-sinusoidal load which theproposed transformer has tofeed is calculated.

2. Thena transformer of K-Factorrating above the K-Factorrating of the load is chosen,

typical K-Factor rating oftransformers is1,4,9,13,20,30,40,50.

3. Thisis used when choosing newtransformers; the K-Factortransformers have tolerance intheir design to accommodatethe losses due to harmonics.

FHL, HarmonicLoss Factor;IEEE C57.110-1998

Ih= Individual HarmonicComponent.I1=Fundamental Component; IRMScan

also be used as FHL depends on

harmonic distribution and noton

relative magnitude.Ih / I1= This quantity can bedirectly

computed from the harmonicmeasuring meters.

1. FHL isused to take into account theincrease in eddy currentlosses in the windings andother stray losses in tank,core of transformers due toharmonics.

2. Based on these new straylosses, the full load currentcarrying capacity of dry typetransformer is de-rated and

the full load current as well astop oil temperature rise forliquid filled transformer is de-rated.

3. The std. is applicable fordesigning

REF.STANDARD

FORMULA REMARK



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new transformer as well as tode-rate transformers underuse; to de-rate the transformerunder use, differentparameters are required from

certified test reportsparticularly those which arementioned in appendix of IEEEStd. C57.12.90.1993 or IEEEStd C57.12.91-1995.

Factor KBS 7821, Part 4. K=

[1+(e/1+e)( I1/I)2 (Nn=1 nq

( In/I)2)]0 .5

e = Eddy current loss atfundamental

frequency divided by loss

due toDC current equivalent to RMSvalue of sinusoidal current.

I1 = Fundamental component ofcurrent.

I = RMS value of currentincluding all

harmonicsn = nth order harmonic.q = Exponential constantdependent

on type of winding andfrequency.

q = 1.7, for rectangular andround

cross sectional conductor.q = 1.5, for low voltage

winding.

1. Above two std. were Americanpractice and this one isEuropean practice.

2. This also takes in account theeddy current loss in windingdue to harmonics.

3. It directly gives a de-rating

factor for transformers whichare in use.4. Transformer is de-rated by

factor 1 / KHere also as thetransformers are in use,we have used Factor K todetermine the de-rating ofthe transformers.

Estimation ofExtra Lossesdue toHarmonics;IEC 61378-1

This std. deal with convertertransformers and takes intoaccount the effect of harmonicson the losses of transformers.

Table - 5; Transformer De-Rating Standards

6.2. DERATING CALCULATIONS FOR CENTRAL UTILITY TRANSFORMERS.

6.2.1OPERATION PHILOSOPHY

I. The Central Utility has 3 Nos. of transformers, each supplyingindividually to each sections of MLTP. Depending on the load,



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only one transformer can feed to two or three sections of MLTPor only two transformers can feed entire MLTP.

II. Due to fault level considerations, none of the transformers areparalleled.

III. To achieve energy saving any two of transformers are loaded

and one transformer remains OFF.IV. So the harmonic distribution of any or all three sections can beapplied to all of the transformers.

6.2.2TRANSFORMER DETAILS

Name KVARating

VectorGroup

VoltageRatio

LeakageImpedance

Full LoadLT Current

TR-1 3500 Dyn11 33/0.433 KV 10.15% 4666.9 A

TR-2 3500 Dyn11 33/0.433 KV 10.17% 4666.9 ATR-3 3500 Dyn11 33/0.433 KV 10.06% 4666.9 A

TABLE 6

For the purpose of Factor K calculation, we can safely assume for allthree transformers that eddy current losses are 10% of resistive losses.Therefore for Factor K Calculation, from Table 3, value of e for all threetransformer can be assumed as 0.1 and q = 1.7 as rectangularconductors are used.

6.2.3 FACTOR K CALCULATIONS (BS 7821, PART 4)

Harmonic distribution for all three buses of MLTP was taken (seeAnnexure A).

For all three transformer, k = 0.1 and q = 1.7. From Table - 2

Factor K = [1+ (e/1+e) (I1/I) 2 (Nn=1 nq(In/I) 2)] 0 .5

a. Factor K for Transformer 1 & 2The Harmonic Distribution of load (Annexure A, Item No -24) on TR 2(Load of MLTP Sec 1 & 2) and from Table 2



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I1 = 1839 A, I = 1949 A

Factor K = [1+ (e/1+e) (I1/I) 2 (Nn=1 nq(In/I) 2)] 0 .5,

Factor K = 1.03997,TR-2 to be de-rated by 1 / K = 0.9615 = 96.15 %.Transformer 1 should also be de-rated by same factor (96.15%)as during measurement load of MLTP Sec 1 & Sec 2 was on TR-2 whichis also load of TR - 1( MLTP Sec 1 & Sec 2).

b. Factor K for Transformer 3

The Harmonic Distribution of load (Annexure A, Item No -25) on TR 2(Load of MLTP Sec 1 & 2) and from Table 2Harmonic Order,

nIn/I1 (In/I1)

2 nq nq (In/I1)2

1 1 1 1 1

3 0.0020.00000

46.47300784 0.00003

5 0.02 0.0004 15.42584657 0.00617034

7 0.0040.00001

627.33170144 0.00043731

9 0 0 41.8998305 0

11 0.0020.00000

458.93422336 0.00023574

13 0.0030.00000

978.28953236 0.00070461

15 0 0 99.85162577 0

n=115 nq(In/I1)2 1.00757388

I1 = 1944 A, I = 1957 A


Harmonic Order,

nIn/I1 (In/I1)

2 nq nq (In/I1)2

1 1 1 1 1

3 0.0070.00004

96.47300784 0.000317177

5 0.016

0.00025

6 15.42584657 0.003949017

7 0.0170.00028

927.33170144 0.007898862

9 0.0030.00000

941.8998305 0.000377098

11 0.0130.00016

958.93422336 0.009959884

13 0.0050.00002

578.28953236 0.001957238

15 0.0010.00000

199.85162577 0.0000998516

n=1

15

nq

(In/I1)2

1.024559128


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Factor K = 1.04421,TR-3 to be de-rated by 1 / K = 0.9576 = 95.76 %.

c. Factor K When Load of All Three Sections of MLTP is on Single

Transformer.The Harmonic Distribution of load (Annexure A, Item No -26) when allthree section of MLTP are loaded on single transformer and from Table2Harmonic Order,

nIn/I1 (In/I1)

2 nq nq (In/I1)2

1 1 1 1 1

3 0.002 0.000004 6.47300784 0.000025892

5 0.002 0.000004 15.42584657 0.000061703

7 0.003 0.000009 27.33170144 0.000245985

9 0 0 41.8998305 0

11 0.003 0.000009 58.93422336 0.000530408

13 0.004 0.000016 78.28953236 0.001252633

15 0 0 99.85162577 0

n=115 nq(In/I1)2 1.002116621

I1 = 3856 A, I = 3888 A


Factor K = 1.04384,Transformer to be de-rated by 1 / K = 0.957699 = 95.8 %.

6.3 CONCLUSIONS

1. There is not much significant harmonic loading on all thetransformers consequently de-rating is not so significant.

2. For current load, the transformers should be de-rated astransformer 1 & 2 (TR-1 & TR-2) by 96%, transformer 3 (TR-3) by95%.

3. When all three sections of load are given on any of the singletransformer, the transformer should be de-rated by 95%.



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7. CAPACITOR BANKS

As discussed in sec 3.3, harmonics can result in resonance by making

the inductive reactance of the system equal to effective capacitance ofthe p.f. correction capacitor banks at a certain frequency. To avoid thissituation, the resonance frequency of the system is calculated andreactors are connected in series with the capacitor banks to from adetuned circuit which will shift the resonance frequency of the systemto a safe value.

7.1 SYSTEM DETAILS

1. There are 8 Nos. of Automatic Power Factor Correction Panels

connected to MLTP in Central Utility. Their distribution in 3sections of MLTP and rating are given in the table below.

MLTP BUS Number of APFC Panels

KVARRATING

MLTP BUS A(Section 1, TR 1) 3

503.91510.63510.63

MLTP BUS B(Section 2, TR

2)2

510.63510.63

MLTP BUS C(Section 3, TR

3)3

510.63507.63510.63

TABLE 72. The capacitors installed in the banks are rated for 525 V and

capacitors are effectively de-rated for use at 415V.3. The above mentioned banks are formed by combination of banks

of 25.2 KVAR, 50.39 KVAR and 53.75 KVAR. Each of these banksis connected with 7% detuned filter reactor.

4. Each of these banks are controlled by two APFC Relays, one isoperative when load of that particular section of MLTP is ontransformer and other relay is operational when load is on DGs.

7.2 CALCULATION OF RESONANCE FREQUENCY

The effective capacitance of these capacitor banks can form resonancecircuit with the inductance of the winding of the transformer to whichthey are connected. So given below is the sample calculation for



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finding inductance of transformer winding and capacitance of APFCCapacitor banks to find out the resonance frequency.

a. CALCULATION FOR INDUCTANCE OF TRANSFORMER

Given a transformer with line voltage on LT side VLL, phasevoltage on LT side VPH, leakage impedance Z, phase current onLT side IPH and vector group Dyn11; therefore

VPH= VLL/ 1.7312.Inductive Reactance of Transformer winding, XL = Z * (VPH / IPH).Therefore Inductance of the transformer winding, L (in Henry) =XL / 2F

Taking transformer data from Table 6, the inductances of threetransformer are here under in Table 8.

TRAFO VLL IPH Z (%) VPH Freq(Hz) XL (Ohms) L (mH)

TR-1 433 V 4666.9 A 10.15 250 V 50 0.005437228 0.017300271

TR-2 433 V 4666.9 A 10.17 250 V 50 0.005447942 0.017334361

TR-3 433 V 4666.9 A 10.06 250 V 50 0.005389016 0.01714687

TABLE 8

b. CALCULATION FOR EFFECTIVE CAPACITANCE OF CAPACITORBANKS.

Similarly to find out effective capacitance of capacitor banks;If per phase voltage applied to capacitor bank with KVAR rating Sconnected in delta is VPH, line voltage is VLL, line current to the bank isIL-CAP, phase current to the capacitor bank is IPH-CAP, capacitivereactance of the bank is XCand the effective capacitance of the bankis C, then

IL-CAP = S / (1.732 * VLL);

IPH-CAP = IL-CAP / 1.732;

XC = VPH / IPH-CAP;

C = 1 / (2F XC);

Resonance Frequency, FRES = 1 / [2(LC)0.5]

So from Table 6, 7, 8 and above formulae, the resonancefrequency when the different combinations of capacitor banks



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are operating in parallel to their respective transformers is givenbelow in Table 9 in page 23. It is considered that all the banksare operating at rated capacity and the combinations of bankslike operation of single bank, two banks and all three banks incorresponding bus are considered.

TABLE 9

7.3 CONCLUSIONS

1. The 5th harmonic is the predominant harmonic at the incomingof the APFC panels. (Annexure A; Item 3 to 10).

2. From Table 9, we can conclude that 10th, 7th and 6th harmoniccomponents can cause resonance. From harmonic spectrum inAnnexure A, it is clear that these harmonics are not present insignificant amount.

3. All the capacitor banks are connected in series with detuned

reactor of filter factor of 7%. This 7% detuned reactor will shiftthe resonance frequency to 189 Hz which is closer to 3rd

harmonic component. So choice of 7% detuned filter seems tobe adequate as the 5th harmonic is predominant here.


TRAFO KVAR IL-CAP(AMPS)

IPH-CAP(AMPS)

XC(OHMS

)

C(F)

L(mH)

FRES(Hz)

HarmonicOrder

Corresponding

to FRES

TR 1

510.63 710.41 410.17 0.58 0.005447 0.0173 518.27 10.41021.6 1421.30 820.61 0.29 0.010897 0.0173 366.41 7.3

1014.54 1411.47 814.94 0.29 0.010822 0.0173 367.68 7.4

503.91 701.06 404.77 0.59 0.005375 0.0173 521.71 10.4

1525.17 2121.89 1225.11 0.20 0.016269 0.0173 299.88 6.0

TR2510.63 710.41 410.17 0.58 0.005447 0.01731 518.12 10.4

1021.6 1421.30 820.61 0.29 0.010897 0.01731 366.30 7.3

TR3

510.63 710.41 410.17 0.58 0.005447 0.0171 521.29 10.4

507.63 706.24 407.76 0.59 0.005415 0.0171 522.83 10.5

1021.6 1421.30 820.61 0.29 0.010897 0.0171 368.55 7.4

1018.26 1416.65 817.93 0.29 0.010862 0.0171 369.15 7.4

1529.23 2127.54 1228.37 0.20 0.016312 0.0171 301.23 6.0

59594535-harmonic-analysis-report-1.pdf

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