5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 79 83 85 89 91 95 97101

1030.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

Individual Current Harmonics in Percent of IL

Simulation

IEEE limit

5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 79 83 85 89 91 95 97101

1030.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

Individual Current Harmonics in Percent of IL

Simulation

IEEE limit

harm_volt

Page 3

5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 79 83 85 89 91 95 97 101 103

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

Individual Voltage Harmonics in Percent of the PCC voltage

Simulation

IEEE limit

POWER : 15 MVAZ : 8 %

DEMAND: 13000 kVA Ie (Estimated Waveform) Harmonic Calculator WEG

V1.00 Isc: 16.4 kA Copyright(C) 2009 WEG. All rights reserved. IL: 1137.2 Amp

Voltage at PCC (rms)

Volts

Case Study: Company Name

% LOAD 10.66 %Ie(1) 139.9 AmpIe RMS 146.4 Amp

Motor Voltage (rms)IL 1137.2 Amp

IEEE-519 THDi 32.49 %

Volts TDD 4.00 %

Motor Rated Current (rms)THDv 1.70 %

Isc / IL 14.4310.0 Amp

Motor Power

1523.8 kW

6 pulse

12 pulse

18 pulse

VFD Rectifier

Estimated Results

Motor

Graphs (PCC)

FP: 0.86MotorPower: 1523823.66

Ni 0.953PCCPower: 1598975.51

Fund_IL: 139.87

I_source: 1312.1597027037freq: 60

L_pcc: 0.000616247939651819

limite_TDD: 5limite_TDD: 0.05ISC/IL: 14.4230769230769

pcc_power_kV 1598.97550837665

ctrl thdv 0ctrl tdd 0soma ctrl 0

0

amarelo 0

vermelho 0

Lfonte 0.000616247939651819 Henryrelação tr 0.5Lfonte_ref 0.000154061984912955 HenryQueda%_Ref 0.0094500692060958QuedasS 0.059450069Queda%LIM 0.0594500692060958

Harmônicas de Corrente

N (N-1) (N+1) (N-1)^2 (N+1)^2 THDi 3.25E-011 0.2 0.1428571 0.04 0.02040816326530612 0.0909091 0.0769231 0.00826446280991736 0.005917159763313613 0.0588235 0.0526316 0.00346020761245675 0.002770083102493074 0.0434783 0.04 0.00189035916824197 0.00165 0.0344828 0.0322581 0.00118906064209275 0.001040582726326746 0.0285714 0.027027 0.000816326530612245 0.000730460189919657 0.0243902 0.0232558 0.000594883997620464 0.0005408328826392648 0.0212766 0.0204082 0.000452693526482571 0.000416493127863399 0.0188679 0.0181818 0.000355998576005696 0.000330578512396694

10 0.0169492 0.0163934 0.000287273771904625 0.00026874496103198111 0.0153846 0.0149254 0.000236686390532544 0.00022276676319893112 0.0140845 0.0136986 0.000198373338623289 0.000187652467629949

13 0.012987 0.0126582 0.000168662506324844 0.00016023073225444614 0.0120482 0.0117647 0.000145158949049209 0.0001384083044982715 0.011236 0.010989 0.000126246686024492 0.00012075836251660416 0.0105263 0.0103093 0.000110803324099723 0.00010628122010840717 0.009901 0.0097087 9.80296049406921E-05 9.42595909133754E-0518 0.0093458 0.0091743 8.73438728273212E-05 8.4167999326656E-0519 0.0088496 0.0086957 7.83146683373796E-05 7.56143667296787E-0520 0.0084034 0.0082645 7.06164818868724E-05 6.83013455365071E-0521 0.008 0.007874 0.000064 6.2000124000248E-0522 0.0076336 0.0075188 5.82716624905309E-05 5.65323082141444E-05

23 0.0072993 0.0071942 5.32793435984869E-05 5.17571554267378E-05

24 0.006993 0.0068966 4.89021468042447E-05 4.75624256837099E-0525 0.0067114 0.0066225 4.50430160803567E-05 4.38577255383536E-0526 0.0064516 0.0063694 4.16233090530697E-05 4.05695971439004E-0527 0.0062112 0.006135 3.85787585355503E-05 3.76378486205729E-0528 0.005988 0.0059172 3.58564308508731E-05 3.50127796645776E-0529 0.0057803 0.0057143 3.34124093688396E-05 3.26530612244898E-0530 0.0055866 0.0055249 3.12100121719048E-05 3.05240987759836E-0531 0.0054054 0.0053476 2.9218407596786E-05 2.85967571277417E-0532 0.0052356 0.0051813 2.74115292892191E-05 2.68463582914978E-0533 0.0050761 0.0050251 2.57672189440594E-05 2.52518875785965E-0534 0.0049261 0.004878 2.42665437161785E-05 2.37953599048186E-0535 0.0047847 0.0047393 2.28932487809345E-05 2.24613103928483E-0536 0.0046512 0.0046083 2.16333153055706E-05 2.12363821699335E-0537 0.0045249 0.0044843 2.04746012571405E-05 2.01089907297553E-05

38 0.0044053 0.0043668 1.94065477692173E-05 1.9069049026525E-0539 0.0042918 0.0042553 1.84199377406104E-05 1.81077410593029E-0540 0.0041841 0.0041494 1.75066963113391E-05 1.72173344122863E-0541 0.0040816 0.0040486 1.66597251145356E-05 1.6391024275107E-0542 0.0039841 0.0039526 1.58727639243822E-05 1.5622803043322E-0543 0.0038911 0.003861 1.51402746445821E-05 1.49073508146867E-0544 0.0038023 0.0037736 1.44573436076855E-05 1.42399430402278E-0545 0.0037175 0.00369 1.38195989552383E-05 1.36163723260849E-0546 0.0036364 0.0036101 1.32231404958678E-05 1.30328819611881E-0547 0.0035587 0.0035336 1.26644799331315E-05 1.24861092035111E-0548 0.0034843 0.0034602 1.21404897473564E-05 1.19730367213036E-0549 0.003413 0.0033898 1.16483593285886E-05 1.1490950876185E-0550 0.0033445 0.0033223 1.11855572085323E-05 1.10374057681483E-0551 0.0032787 0.0032573 1.07497984412792E-05 1.06101921505798E-0552 0.0032154 0.0031949 1.03390163459848E-05 1.02073104757627E-0553 0.0031546 0.0031348 9.95133795738837E-06 9.82694745531196E-0654 0.003096 0.0030769 9.58506263838434E-06 9.46745562130177E-0655 0.0030395 0.0030211 9.2386433976035E-06 9.12733545696005E-0656 0.0029851 0.0029674 8.91067052795723E-06 8.80521973425847E-0657 0.0029326 0.0029155 8.59985724236978E-06 8.49985975231409E-0658 0.0028818 0.0028653 8.30502703286299E-06 8.21011321746127E-0659 0.0028329 0.0028169 8.0251025206847E-06 7.93493354493156E-0660 0.0027855 0.0027701 7.75909559981689E-06 7.67336039471766E-0661 0.0027397 0.0027248 7.50609870519797E-06 7.42451128154489E-0662 0.0026954 0.002681 7.26527706134074E-06 7.18757412185813E-0663 0.0026525 0.0026385 7.03586178753105E-06 6.96180060010721E-0664 0.002611 0.0025974 6.81714375311032E-06 6.74650025299376E-0665 0.0025707 0.0025575 6.60846809101182E-06 6.54103518422826E-0666 0.0025316 0.0025189 6.40922929017786E-06 6.3448153341497E-0667 0.0024938 0.0024814 6.21886679809205E-06 6.15729423861978E-0668 0.002457 0.002445 6.03686107371611E-06 5.97796522019835E-0669 0.0024213 0.0024096 5.8627300388699E-06 5.80635796196836E-0670 0.0023866 0.0023753 5.69602588274161E-06 5.64203542069837E-0671 0.0023529 0.0023419 5.5363321799308E-06 5.48459104146899E-0672 0.0023202 0.0023095 5.3832612873531E-06 5.33364624057945E-0673 0.0022883 0.0022779 5.23645198958993E-06 5.18884812760415E-0674 0.0022573 0.0022472 5.09556736594836E-06 5.04986744097968E-0675 0.0022272 0.0022173 4.9602928556902E-06 4.91639667454929E-0676 0.0021978 0.0021882 4.83033450066417E-06 4.78814837514185E-0677 0.0021692 0.0021598 4.70541734699159E-06 4.66485359356997E-06

78 0.0021413 0.0021322 4.58528398956389E-06 4.54626047344757E-0679 0.0021142 0.0021053 4.4696932449526E-06 4.43213296398892E-0680 0.0020877 0.002079 4.35841893994534E-06 4.32224964449497E-0681 0.0020619 0.0020534 4.25124880433627E-06 4.21640264958743E-0682 0.0020367 0.0020284 4.14798345784197E-06 4.11439668544203E-0683 0.0020121 0.002004 4.04843548210794E-06 4.01604812832077E-0684 0.0019881 0.0019802 3.95242856973467E-06 3.92118419762768E-0685 0.0019646 0.0019569 3.85979674310351E-06 3.82964219652958E-0686 0.0019417 0.0019342 3.77038363653502E-06 3.74126881390555E-0687 0.0019194 0.001912 3.68404183597909E-06 3.65591948202933E-0688 0.0018975 0.0018904 3.60063227102679E-06 3.57345778495646E-0689 0.0018762 0.0018692 3.52002365455896E-06 3.49375491309285E-0690 0.0018553 0.0018484 3.44209196581314E-06 3.4166891598703E-0691 0.0018349 0.0018282 3.36671997306624E-06 3.34214545685457E-0692 0.0018149 0.0018083 3.29379679250068E-06 3.27001494396829E-0693 0.0017953 0.0017889 3.22321748015304E-06 3.20019457182997E-0694 0.0017762 0.0017699 3.15488265413968E-06 3.13258673349518E-0695 0.0017575 0.0017513 3.08869814461902E-06 3.06709892314157E-0696 0.0017391 0.0017331 3.02457466918715E-06 3.00364341946781E-0697 0.0017212 0.0017153 2.96242753161651E-06 2.94213699178261E-0698 0.0017036 0.0016978 2.9021763420389E-06 2.88250062694389E-0699 0.0016863 0.0016807 2.8437447568456E-06 2.8246592754749E-06

100 0.0016694 0.0016639 2.7870602367329E-06 2.76854161533329E-06

Ie - spectrum Vpcc - spectrum(N-1) (N+1) (N-1)^2 (N+1)^2 IL_rms 146.4388733735 (N-1) (N+1)

27.97481637 19.98201169 782.5903508994 399.2807912752 TDD: 0.309951484389 32.49554669465 32.4955466946512.71582562 10.75954476 161.6922212602 115.7678033875 32.49554669465 32.495546694658.227887167 7.361793781 67.69812724043 54.19600768001 32.49554669465 32.495546694656.081481819 5.594963274 36.98442112001 31.30361403598 32.49554669465 32.495546694654.823244202 4.512067156 23.2636846284 20.3587500234 32.49554669465 32.495546694653.996402338 3.78038059 15.97123165101 14.29127740868 32.49554669465 32.495546694653.411562972 3.252885624 11.63876191106 10.58126488506 32.49554669465 32.495546694652.976044295 2.854573099 8.856839643497 8.148587577045 32.49554669465 32.49554669465

2.63913362 2.543165124 6.9650262629 6.467688850408 32.49554669465 32.495546694652.37074715 2.293017735 5.620442048976 5.257930333912 32.49554669465 32.49554669465

2.151908951 2.087672863 4.630712135499 4.358377984514 32.49554669465 32.495546694651.970057491 1.916083313 3.881126517057 3.671375262242 32.49554669465 32.49554669465

1.816546517 1.770557998 3.299841250208 3.134875624497 32.49554669465 32.495546694651.685229902 1.645577433 2.839999821815 2.707925089617 32.49554669465 32.495546694651.571618897 1.537077822 2.469985957895 2.362608232398 32.49554669465 32.495546694651.472358756 1.442000844 2.167840307201 2.079366433466 32.49554669465 32.495546694651.384891899 1.358000795 1.917925573227 1.844166158213 32.49554669465 32.49554669465

1.30723441 1.283248457 1.708861802121 1.646726603189 32.49554669465 32.495546694651.237823733 1.216296364 1.532207594368 1.4793768448 32.49554669465 32.495546694651.175412452 1.155984147 1.381594433478 1.336299349258 32.49554669465 32.495546694651.118992655 1.101370723 1.252144561439 1.213017469929 32.49554669465 32.495546694651.067741083 1.051684826 1.140071019899 1.106040973062 32.49554669465 32.49554669465

1.0209787 1.006288359 1.042397505061 1.012616260674 32.49554669465 32.49554669465

0.978140432 0.96464884 0.956758705682 0.930547385136 32.49554669465 32.495546694650.938752227 0.926318423 0.881255743997 0.858065820468 32.49554669465 32.495546694650.902413431 0.890917719 0.814350000936 0.793734381617 32.49554669465 32.495546694650.868783117 0.858123202 0.75478410449 0.736375428977 32.49554669465 32.495546694650.837569352 0.827657289 0.70152242004 0.685016588092 32.49554669465 32.495546694650.808520704 0.799280468 0.653705729309 0.63884926604 32.49554669465 32.495546694650.781419452 0.772784983 0.61061635943 0.5971966293 32.49554669465 32.495546694650.756076118 0.747989742 0.571651096347 0.55948865488 32.49554669465 32.495546694650.732325036 0.724736175 0.536299958128 0.525242523893 32.49554669465 32.49554669465

0.71002072 0.702884833 0.504129422878 0.494047089025 32.49554669465 32.495546694650.689034886 0.682312594 0.474769074049 0.465550476442 32.49554669465 32.49554669465

0.66925398 0.662910341 0.447900889917 0.43945011955 32.49554669465 32.495546694650.650577125 0.644581022 0.423250595403 0.415484694355 32.49554669465 32.495546694650.632914397 0.627238035 0.400580634559 0.393427552786 32.49554669465 32.49554669465

0.616185383 0.610803851 0.379684425711 0.373081344225 32.49554669465 32.495546694650.600317948 0.595208859 0.360381638499 0.35427358574 32.49554669465 32.495546694650.585247204 0.580390381 0.342514290235 0.336852994482 32.49554669465 32.49554669465

0.57091462 0.566291829 0.325943503082 0.320686435976 32.49554669465 32.495546694650.557267258 0.552861984 0.310546797233 0.305656372893 32.49554669465 32.495546694650.544257128 0.54005437 0.29621582117 0.291658722626 32.49554669465 32.495546694650.531840615 0.527826724 0.282854440175 0.278601050516 32.49554669465 32.495546694650.519977999 0.516140523 0.270377119892 0.266401039916 32.49554669465 32.495546694650.508633025 0.504960584 0.258707554016 0.254985191681 32.49554669465 32.495546694650.497772533 0.494254706 0.247777494871 0.244287714574 32.49554669465 32.495546694650.487366139 0.483993363 0.237525753287 0.234249575226 32.49554669465 32.495546694650.477385945 0.47414943 0.227897340359 0.224817681959 32.49554669465 32.495546694650.467806294 0.464697946 0.218842728521 0.215944181328 32.49554669465 32.495546694650.458603547 0.455615902 0.210317213356 0.207585849956 32.49554669465 32.49554669465

0.44975589 0.446882051 0.202280360754 0.199703567174 32.49554669465 32.495546694650.44124316 0.438476746 0.1946955266 0.192261856433 32.49554669465 32.49554669465

0.433046693 0.43038179 0.187529438339 0.18522848542 32.49554669465 32.495546694650.425149185 0.422580308 0.180751829459 0.178574116451 32.49554669465 32.495546694650.417534573 0.415056623 0.174335119381 0.172272000039 32.49554669465 32.495546694650.410187923 0.407796157 0.168254132425 0.166297705654 32.49554669465 32.495546694650.403095337 0.400785335 0.162485850497 0.160628884594 32.49554669465 32.495546694650.396243858 0.394011498 0.157009194942 0.155245060682 32.49554669465 32.495546694650.389621398 0.387462831 0.151804833703 0.150127445097 32.49554669465 32.495546694650.383216663 0.381128288 0.14685501049 0.145258772227 32.49554669465 32.495546694650.377019089 0.374997538 0.14214339312 0.140623153854 32.49554669465 32.495546694650.371018785 0.369060902 0.13765493863 0.136205949363 32.49554669465 32.49554669465

0.36520648 0.363309303 0.133375773047 0.131993650008 32.49554669465 32.495546694650.359573475 0.357734225 0.129293084056 0.127973775502 32.49554669465 32.49554669465

0.3541116 0.352327662 0.12539502498 0.124134781469 32.49554669465 32.495546694650.348813172 0.347082089 0.121670628743 0.12046597647 32.49554669465 32.495546694650.343670963 0.34199042 0.11810973065 0.116957447483 32.49554669465 32.495546694650.338678164 0.33704598 0.114702898959 0.113599992873 32.49554669465 32.495546694650.333828358 0.332242475 0.111441372358 0.110385061992 32.49554669465 32.495546694650.329115487 0.327573962 0.108317003585 0.107304700692 32.49554669465 32.495546694650.324533833 0.323034831 0.105322208496 0.104351502075 32.49554669465 32.49554669465

0.32007799 0.318619776 0.10244992 0.101518561924 32.49554669465 32.495546694650.315742848 0.314323779 0.099693546324 0.098799438316 32.49554669465 32.495546694650.311523568 0.310142088 0.097046933162 0.096188114967 32.49554669465 32.495546694650.307415564 0.306070201 0.094504329296 0.093678967927 32.49554669465 32.495546694650.303414494 0.302103848 0.092060355318 0.091266735267 32.49554669465 32.49554669465

0.299516235 0.29823898 0.089709975159 0.08894648948 32.49554669465 32.495546694650.295716875 0.294471751 0.087448470125 0.086713612288 32.49554669465 32.495546694650.292012697 0.290798507 0.085271415189 0.084563771649 32.49554669465 32.495546694650.288400169 0.287215774 0.083174657339 0.082492900727 32.49554669465 32.49554669465

0.28487593 0.283720247 0.081154295745 0.080497178645 32.49554669465 32.495546694650.281436784 0.280308781 0.079206663613 0.078573012849 32.49554669465 32.495546694650.278079686 0.27697838 0.077328311532 0.076717022929 32.49554669465 32.495546694650.274801733 0.273726188 0.07551599219 0.07492602576 32.49554669465 32.495546694650.271600159 0.270549481 0.073766646329 0.073197021847 32.49554669465 32.495546694650.268472326 0.267445663 0.072077389829 0.071527182758 32.49554669465 32.495546694650.265415715 0.264412253 0.070445501811 0.069913839546 32.49554669465 32.495546694650.262427921 0.261446882 0.068868413675 0.068354472085 32.49554669465 32.495546694650.259506645 0.258547286 0.067343698984 0.066846699213 32.49554669465 32.495546694650.256649691 0.255711301 0.065869064128 0.065388269646 32.49554669465 32.495546694650.253854958 0.252936857 0.064442339691 0.063977053561 32.49554669465 32.495546694650.251120434 0.250221971 0.06306147247 0.062611034823 32.49554669465 32.495546694650.248444195 0.247564747 0.061724518084 0.061288303775 32.49554669465 32.495546694650.245824397 0.244963366 0.06042963412 0.060007050563 32.49554669465 32.495546694650.243259273 0.242416086 0.059175073792 0.05876555894 32.49554669465 32.495546694650.240747129 0.239921238 0.057959180037 0.05756220052 32.49554669465 32.49554669465

0.23828634 0.237477219 0.056780380047 0.056395429428 32.49554669465 32.495546694650.235875349 0.23508249 0.055637180178 0.055263777339 32.49554669465 32.495546694650.233512658 0.232735577 0.054528161216 0.054165848856 32.49554669465 32.49554669465

Vpcc - spectrumQuedas Computadas até 100º Harmônica(N-1)^2 (N+1)^2 Quedas 459.556428523001

1055.96055498408 1055.96055498408 THDv: 0.1206022853252621055.96055498408 1055.960554984081055.96055498408 1055.96055498408 6P Simu1055.96055498408 1055.96055498408 5 30.3601%1055.96055498408 1055.96055498408 7 8.7074%1055.96055498408 1055.96055498408 11 5.9768%1055.96055498408 1055.96055498408 13 3.3221%1055.96055498408 1055.96055498408 17 2.1238%1055.96055498408 1055.96055498408 19 1.7261%1055.96055498408 1055.96055498408 23 1.0817%1055.96055498408 1055.96055498408 25 0.9834%1055.96055498408 1055.96055498408 29 0.6410%

1055.96055498408 1055.96055498408 31 0.6056%1055.96055498408 1055.96055498408 35 0.4795%1055.96055498408 1055.96055498408 37 0.3896%1055.96055498408 1055.96055498408 41 0.3676%1055.96055498408 1055.96055498408 43 0.3186%1055.96055498408 1055.96055498408 47 0.2590%1055.96055498408 1055.96055498408 49 0.2510%1055.96055498408 1055.96055498408 53 0.1991%1055.96055498408 1055.96055498408 55 0.1894%1055.96055498408 1055.96055498408 59 0.1669%

1055.96055498408 1055.96055498408 61 0.1508%

1055.96055498408 1055.96055498408 65 0.1397%1055.96055498408 1055.96055498408 67 0.1268%1055.96055498408 1055.96055498408 71 0.1172%1055.96055498408 1055.96055498408 73 0.1108%1055.96055498408 1055.96055498408 77 0.0950%1055.96055498408 1055.96055498408 79 0.0944%1055.96055498408 1055.96055498408 83 0.0829%1055.96055498408 1055.96055498408 85 0.0774%1055.96055498408 1055.96055498408 89 0.0749%1055.96055498408 1055.96055498408 91 0.0693%1055.96055498408 1055.96055498408 95 0.0649%1055.96055498408 1055.96055498408 97 0.0615%1055.96055498408 1055.96055498408 101 0.0615%1055.96055498408 1055.96055498408 103 0.0615%

1055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.96055498408 5%1055.96055498408 1055.96055498408 HARMONIC NORMALIZED1055.96055498408 1055.96055498408 NO COMPONENT1055.96055498408 1055.960554984081055.96055498408 1055.96055498408 5 3.23E-011055.96055498408 1055.96055498408 7 9.31E-021055.96055498408 1055.96055498408 11 6.50E-021055.96055498408 1055.96055498408 13 3.29E-021055.96055498408 1055.96055498408 17 2.48E-021055.96055498408 1055.96055498408 19 1.91E-021055.96055498408 1055.96055498408 23 1.12E-021055.96055498408 1055.96055498408 25 1.10E-021055.96055498408 1055.96055498408 29 6.81E-031055.96055498408 1055.96055498408 31 6.29E-031055.96055498408 1055.96055498408 35 5.26E-031055.96055498408 1055.96055498408 37 4.21E-031055.96055498408 1055.96055498408 41 3.98E-031055.96055498408 1055.96055498408 43 3.40E-031055.96055498408 1055.96055498408 47 2.83E-031055.96055498408 1055.96055498408 49 2.73E-031055.96055498408 1055.96055498408 53 2.11E-031055.96055498408 1055.96055498408 55 2.06E-03

1055.96055498408 1055.96055498408 59 1.78E-031055.96055498408 1055.96055498408 61 1.59E-031055.96055498408 1055.96055498408 65 1.54E-031055.96055498408 1055.96055498408 67 1.37E-031055.96055498408 1055.96055498408 71 1.26E-031055.96055498408 1055.96055498408 73 1.21E-031055.96055498408 1055.96055498408 77 1.03E-031055.96055498408 1055.96055498408 79 1.01E-031055.96055498408 1055.96055498408 83 8.95E-041055.96055498408 1055.96055498408 85 8.32E-041055.96055498408 1055.96055498408 89 8.09E-041055.96055498408 1055.96055498408 91 7.32E-041055.96055498408 1055.96055498408 95 7.11E-041055.96055498408 1055.96055498408 97 6.67E-041055.96055498408 1055.96055498408 1011055.96055498408 1055.96055498408 1031055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.960554984081055.96055498408 1055.96055498408

Quedas Computadas até 100º Harmônica

Harm_IL Queda Queda^2 12P Simu4.25E+01 8.54E+01 7299.88549146397 0 0.0248%1.22E+01 3.43E+01 1176.91723334639 0 0.0036%8.36E+00 3.70E+01 1369.28245635238 11 6.7073%4.65E+00 2.43E+01 590.864242069958 13 4.3728%2.97E+00 2.03E+01 412.96530751678 0 0.0049%2.41E+00 1.85E+01 340.712340136809 0 0.0062%1.51E+00 1.40E+01 196.073506082741 23 1.0662%1.38E+00 1.38E+01 191.463382541203 25 0.8701%8.97E-01 1.05E+01 109.474923170073 0 0.0012%

8.47E-01 1.06E+01 111.664608141921 0 0.0010%6.71E-01 9.45E+00 89.2340146199858 35 0.5160%5.45E-01 8.11E+00 65.8288920228449 37 0.4809%5.14E-01 8.48E+00 71.9724323981408 0 0.0005%4.46E-01 7.71E+00 59.4386231351568 0 0.0019%3.62E-01 6.85E+00 46.932472031486 47 0.2748%3.51E-01 6.92E+00 47.9158772823371 49 0.2352%2.78E-01 5.94E+00 35.2669813492199 0 0.0005%2.65E-01 5.86E+00 34.3909972791673 0 0.0010%2.33E-01 5.54E+00 30.7158470409436 59 0.1707%

2.11E-01 5.18E+00 26.8106547582713 61 0.1725%

1.95E-01 5.11E+00 26.1341871862769 0 0.0004%1.77E-01 4.78E+00 22.8659379853539 0 0.0011%1.64E-01 4.68E+00 21.9165965481901 71 0.1264%1.55E-01 4.55E+00 20.7426809520221 73 0.1131%1.33E-01 4.12E+00 16.9613517486617 0 0.0003%1.32E-01 4.20E+00 17.6040702005146 0 0.0008%1.16E-01 3.87E+00 14.9802311043736 83 0.0850%1.08E-01 3.70E+00 13.6963034684595 85 0.0829%1.05E-01 3.75E+00 14.0892947985154 0 0.0001%9.69E-02 3.55E+00 12.5803397664127 0 0.0008%9.08E-02 3.47E+00 12.0434548140502 95 0.0681%8.61E-02 3.36E+00 11.281501505052 97 0.0659%8.61E-02 3.50E+00 12.2311188067845 0 0.0659%8.61E-02 3.57E+00 12.7203155985861 0 0.0659%

Soma 12537.657667223Raiz 111.971682434547THD06p 1.70%

Queda% 6%

10% 15% 20%NORMALIZED NORMALIZED NORMALIZEDCOMPONENT COMPONENT COMPONENT

pol 6P ^22.44E-01 2.02E-01 1.72E-01 5a H 30.3601% 9.2174%7.42E-02 7.47E-02 7.24E-02 7a H 8.7074% 0.7582%4.14E-02 2.75E-02 2.25E-02 11a H 5.9768% 0.3572%3.05E-02 2.28E-02 1.69E-02 13a H 3.3221% 0.1104%1.36E-02 1.32E-02 1.15E-02 17a H 2.1238% 0.0451%1.19E-02 9.61E-03 9.28E-03 19a H 1.7261% 0.0298%8.98E-03 6.58E-03 5.74E-03 23a H 1.0817% 0.0117%6.94E-03 5.98E-03 4.68E-03 25a H 0.9834% 0.0097%5.19E-03 4.40E-03 3.66E-03 29a H 0.6410% 0.0041%4.90E-03 3.62E-03 3.33E-03 31a H 0.6056% 0.0037%3.49E-03 2.89E-03 2.60E-03 35a H 0.4795% 0.0023%3.07E-03 2.70E-03 2.25E-03 37a H 0.3896% 0.0015%2.75E-03 2.17E-03 1.78E-03 41a H 0.3676% 0.0014%2.46E-03 1.90E-03 1.65E-03 43a H 0.3186% 0.0010%1.92E-03 1.61E-03 1.44E-03 47a H 0.2590% 0.0007%1.87E-03 1.54E-03 1.32E-03 49a H 0.2510% 0.0006%1.59E-03 1.29E-03 1.08E-03 53a H 0.1991% 0.0004%1.42E-03 1.17E-03 9.99E-04 55a H 0.1894% 0.0004%

1.29E-03 1.03E-03 8.93E-04 59a H 0.1669% 0.0003%1.22E-03 9.89E-04 8.54E-04 61a H 0.1508% 0.0002%1.02E-03 8.59E-04 7.35E-04 65a H 0.1397% 0.0002%9.66E-04 7.87E-04 6.84E-04 67a H 0.1268% 0.0002%8.94E-04 7.14E-04 6.04E-04 71a H 0.1172% 0.0001%8.32E-04 6.86E-04 5.80E-04 73a H 0.1108% 0.0001%7.29E-04 6.09E-04 5.34E-04 77a H 0.0950% 0.0001%7.26E-04 5.65E-04 4.99E-04 79a H 0.0944% 0.0001%6.33E-04 5.20E-04 4.43E-04 83a H 0.0829% 0.0001%6.03E-04 5.04E-04 4.20E-04 85a H 0.0774% 0.0001%5.66E-04 4.54E-04 3.94E-04 89a H 0.0749% 0.0001%5.46E-04 4.25E-04 3.80E-04 91a H 0.0693% 0.0000%4.78E-04 3.97E-04 3.42E-04 95a H 0.0649% 0.0000%4.66E-04 3.86E-04 3.27E-04 97a H 0.0615% 0.0000%

101a H 0.0615% 0.0000%103a H 0.0615% 0.0000%

thdi 6P32.49%

Harm_IL Queda Queda^2 18P Simu Harm_IL0 0 0 0 0.0055% 00 0 0 0 0.0031% 0

9.38E+00 41.5266322413 1724.4611853039 0 0.0053% 06.12E+00 31.99506439555 1023.68414567536 0 0.0031% 0

0 0 0 17 1.4485% 2.03E+000 0 0 19 1.4667% 2.05E+00

1.49E+00 13.80240870704 190.506486116256 0 0.0014% 01.22E+00 12.24306404542 149.892617220232 0 0.0011% 0

0 0 0 0 0.0014% 0

0 0 0 0 0.0011% 07.22E-01 10.16484770338 103.324128832862 35 0.3847% 5.38E-016.73E-01 10.01507217198 100.301670610002 37 0.3820% 5.34E-01

0 0 0 0 0.0008% 00 0 0 0 0.0007% 0

3.84E-01 7.270407704314 52.8588281869507 0 0.0007% 03.29E-01 6.485530237914 42.062102466894 0 0.0006% 0

0 0 0 53 0.1765% 2.47E-010 0 0 55 0.1696% 2.37E-01

2.39E-01 5.669131898378 32.1390564812062 0 0.0005% 0

2.41E-01 5.923648562941 35.0896122972321 0 0.0006% 0

0 0 0 0 0.0005% 00 0 0 0 0.0005% 0

1.77E-01 5.049934708055 25.5018405556225 71 0.0976% 1.37E-011.58E-01 4.645577586007 21.5813911076071 73 0.0961% 1.34E-01

0 0 0 0 0.0005% 00 0 0 0 0.0005% 0

1.19E-01 3.972431642538 15.7802131546375 0 0.0004% 01.16E-01 3.965547812259 15.7255694513134 0 0.0004% 0

0 0 0 89 0.0619% 8.66E-020 0 0 91 0.0632% 8.84E-02

9.52E-02 3.639318948474 13.2446424087216 0 0.0004% 09.22E-02 3.598241446144 12.9473415047496 0 0.0004% 0

0 0 0 0 0.0004% 00 0 0 0 0.0004% 0

Soma 3559.10083137354Raiz 59.6582000346435THD12p 0.90%

6P 5% Fatorpol 12P ^2 pol 18P ^2

0.0248% 0.0000% 0.0055% 0.0000% 32.2400% 0.00081580.0036% 0.0000% 0.0031% 0.0000% 9.3030% 0.00040906.7073% 0.4499% 0.0053% 0.0000% 6.4880% 1.12222564.3728% 0.1912% 0.0031% 0.0000% 3.2980% 1.31625230.0049% 0.0000% 1.4485% 0.0210% 2.4750% 0.00228770.0062% 0.0000% 1.4667% 0.0215% 1.9100% 0.00358171.0662% 0.0114% 0.0014% 0.0000% 1.1190% 0.98570150.8701% 0.0076% 0.0011% 0.0000% 1.0990% 0.88480440.0012% 0.0000% 0.0014% 0.0000% 0.6788% 0.00191070.0010% 0.0000% 0.0011% 0.0000% 0.6289% 0.00164890.5160% 0.0027% 0.3847% 0.0015% 0.5246% 1.07605790.4809% 0.0023% 0.3820% 0.0015% 0.4207% 1.23437130.0005% 0.0000% 0.0008% 0.0000% 0.3982% 0.00144480.0019% 0.0000% 0.0007% 0.0000% 0.3397% 0.00601410.2748% 0.0008% 0.0007% 0.0000% 0.2824% 1.06126060.2352% 0.0006% 0.0006% 0.0000% 0.2727% 0.93692700.0005% 0.0000% 0.1765% 0.0003% 0.2105% 0.00271450.0010% 0.0000% 0.1696% 0.0003% 0.2058% 0.0054859

0.1707% 0.0003% 0.0005% 0.0000% 0.1790% 1.02290500.1725% 0.0003% 0.0006% 0.0000% 0.1590% 1.14402520.0004% 0.0000% 0.0005% 0.0000% 0.1545% 0.00265440.0011% 0.0000% 0.0005% 0.0000% 0.1362% 0.00867840.1264% 0.0002% 0.0976% 0.0001% 0.1258% 1.07869630.1131% 0.0001% 0.0961% 0.0001% 0.1199% 1.02001670.0003% 0.0000% 0.0005% 0.0000% 0.1019% 0.00293230.0008% 0.0000% 0.0005% 0.0000% 0.1008% 0.00898710.0850% 0.0001% 0.0004% 0.0000% 0.0896% 1.02635400.0829% 0.0001% 0.0004% 0.0000% 0.0832% 1.07152300.0001% 0.0000% 0.0619% 0.0000% 0.0811% 0.00169280.0008% 0.0000% 0.0632% 0.0000% 0.0731% 0.01151130.0681% 0.0000% 0.0004% 0.0000% 0.0707% 1.04868380.0659% 0.0000% 0.0004% 0.0000% 0.0668% 1.07128950.0659% 0.0000% 0.0004% 0.0000% 0.0668% 1.07128950.0659% 0.0000% 0.0004% 0.0000% 0.0668% 1.0712895

thdi 12P thdi 18P8.17% 2.15%

Queda Queda^2 24P Simu Harm_IL Queda0 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0

13.85970617836 192.091455350449 0 0 015.68480357502 246.013063186928 0 0 0

0 0 23 0.00E+00 00 0 25 0.00E+00 00 0 0 0 0

0 0 0 0 07.57906890762 57.4422855064565 0 0 0

7.955357733377 63.2877166659945 0 0 00 0 0 0 00 0 0 0 00 0 47 0.00E+00 00 0 49 0.00E+00 0

5.264337002059 27.7132440712486 0 0 05.248879955245 27.5507407845731 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 00 0 0 0 0

3.900023267533 15.2101814872975 71 0.00E+00 03.94665176767 15.5760601752558 73 0.00E+00 0

0 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0

3.10198323364 9.62229998178413 0 0 03.235160104461 10.4662609014991 0 0 0

0 0 95 0.00E+00 00 0 97 0.00E+00 00 0 0 0 00 0 0 0 0

Soma 664.973308111486 SomaRaiz 25.7870763777417 RaizTHD18p 0.39% THD24p

12P 5% Fator 18P 5%

0.0263% 0.0001827 0.0059%0.0038% 0.0003581 0.0033%7.2810% 0.0008875 0.0058%4.3410% 0.0009482 0.0031%0.0057% 0.6820202 1.6880%0.0068% 0.8497382 1.6230%1.1030% 0.0013047 0.0015%0.9724% 0.0010728 0.0012%0.0013% 0.0021523 0.0015%0.0010% 0.0017920 0.0011%0.5645% 0.8023256 0.4209%0.5193% 0.9805087 0.4125%0.0006% 0.0021067 0.0008%0.0020% 0.0022788 0.0008%0.2997% 0.0028527 0.0008%0.2555% 0.0025567 0.0007%0.0006% 0.8864608 0.1866%0.0011% 0.8950437 0.1842%

0.1831% 0.0032369 0.0006%0.1819% 0.0038434 0.0006%0.0004% 0.0038718 0.0006%0.0012% 0.0041278 0.0006%0.1357% 0.8330684 0.1048%0.1223% 0.8665555 0.1039%0.0003% 0.0050677 0.0005%0.0009% 0.0051746 0.0005%0.0919% 0.0050832 0.0005%0.0891% 0.0048684 0.0004%0.0001% 0.8264086 0.0670%0.0008% 0.9121150 0.0666%0.0741% 0.0056340 0.0004%0.0715% 0.0065808 0.0004%0.0715% 0.0065808 0.0004%0.0715% 0.0065808 0.0004%

Gráficos

Corrente Isc_IL 14.42308 TensãoPulsos 6 Pulsos 6harm Amp % of IL Limite IEEE harm AMP_V

Queda^2 pulsos 1 139.8741 12.30% 10 6 5 42.46595 3.73% 4.00% 0 5 85.439370 fator lim cor 7 12.17945 1.07% 4.00% 0 7 34.306230 1 11 8.360006 0.74% 2.00% 0 11 37.003820 13 4.646792 0.41% 2.00% 0 13 24.30770 17 2.970713 0.26% 1.50% 0 17 20.321550 19 2.41431 0.21% 1.50% 0 19 18.458390 23 1.512984 0.13% 0.60% 0 23 14.002620 25 1.375484 0.12% 0.60% 0 25 13.837030 29 0.896628 0.08% 0.60% 0 29 10.46303

0 31 0.847128 0.07% 0.60% 0 31 10.567150 35 0.670733 0.06% 0.30% 0 35 9.4463760 37 0.544953 0.05% 0.30% 0 37 8.1135010 41 0.514224 0.05% 0.30% 0 41 8.4836570 43 0.445573 0.04% 0.30% 0 43 7.7096450 47 0.362236 0.03% 0.30% 0 47 6.8507280 49 0.351072 0.03% 0.30% 0 49 6.922130 53 0.278459 0.02% 0.30% 0 53 5.9386010 55 0.26498 0.02% 0.30% 0 55 5.8643840 59 0.233444 0.02% 0.30% 0 59 5.542188

0 61 0.210949 0.02% 0.30% 0 61 5.177901

0 65 0.195454 0.02% 0.30% 0 65 5.1121610 67 0.177367 0.02% 0.30% 0 67 4.7818340 71 0.163863 0.01% 0.30% 0 71 4.6815160 73 0.155047 0.01% 0.30% 0 73 4.5544130 77 0.132921 0.01% 0.30% 0 77 4.1184160 79 0.131987 0.01% 0.30% 0 79 4.195720 83 0.115887 0.01% 0.30% 0 83 3.870430 85 0.108202 0.01% 0.30% 0 85 3.7008520 89 0.104811 0.01% 0.30% 0 89 3.7535710 91 0.096863 0.01% 0.30% 0 91 3.5468770 95 0.090783 0.01% 0.30% 0 95 3.4703680 97 0.086053 0.01% 0.30% 0 97 3.3587950 101 0.086053 0.01% 0.30% 0 101 3.4973020 103 0.086053 0.01% 0.30% 0 103 3.566555

00 Limite I 0

0.00%

AMP% Limite IEEE THDi calculadaHarm_i_simu ao quadr

1.29% 3% 0 0.303601 0.0921740.52% 3% 0 0.087074 0.0075820.56% 3% 0 0.059768 0.0035720.37% 3% 0 0.033221 0.0011040.31% 3% 0 0.021238 0.0004510.28% 3% 0 0.017261 0.0002980.21% 3% 0 0.010817 0.0001170.21% 3% 0 0.009834 9.67E-050.16% 3% 0 0.00641 4.109E-05

0.16% 3% 0 0.006056 3.668E-050.14% 3% 0 0.004795 2.299E-050.12% 3% 0 0.003896 1.518E-050.13% 3% 0 0.003676 1.352E-050.12% 3% 0 0.003186 1.015E-050.10% 3% 0 0.00259 6.707E-060.10% 3% 0 0.00251 6.3E-060.09% 3% 0 0.001991 3.963E-060.09% 3% 0 0.001894 3.589E-060.08% 3% 0 0.001669 2.785E-06

0.08% 3% 0 0.001508 2.274E-06

0.08% 3% 0 0.001397 1.953E-060.07% 3% 0 0.001268 1.608E-060.07% 3% 0 0.001172 1.372E-060.07% 3% 0 0.001108 1.229E-060.06% 3% 0 0.00095 9.03E-070.06% 3% 0 0.000944 8.904E-070.06% 3% 0 0.000829 6.864E-070.06% 3% 0 0.000774 5.984E-070.06% 3% 0 0.000749 5.615E-070.05% 3% 0 0.000693 4.796E-070.05% 3% 0 0.000649 4.212E-070.05% 3% 0 0.000615 3.785E-070.05% 3% 0 0.000615 3.785E-070.05% 3% 0 0.000615 3.785E-07

soma 0.105571Limite V 0 raiz q 0.324917

20 of 35

Joable Andrade Alves & Paulo José TorriWEG Automação S.A.

Introduction

Figure 1 - six-pulse rectifier

Figure 2 - Voltage distortion caused by currents drained by a non-linear load.

Where:h : harmonic order

IEEE-519 Recommended Practices for Applications with Variable

Frequency Drives

The indirect frequency converters or variable frequency drives (VFDs) are usually composed of an input diode rectifier stage. The three-phase full-wave bridge rectifier, also known as Graetz Bridge or six-pulse rectifier (Figure 1) is one of the most used configurations for the input stage of VFDs. The currents drained by this converter are of pulsed-type, containing low-order harmonics that may cause voltage harmonic distortion at the electric power supply system where VFDs are connected. The voltage distortion is related to the magnitude of the current harmonics of the electrical equipment and also to the network impedance, i.e., to the network capacity and to the ratio between the installed drives capacity and the network capacity.

In several applications, the six-pulse variable frequency drive with an input line reactor or a DC reactor may perfectly meet the IEEE-519 recommendations. When it is not possible, the following options are available for reducing the harmonic currents: 1) Increase the number of pulses of the input rectifier using 12, 18 or even 24-pulse;2) Use an active front-end rectifier (regen-drive).

The greater the number of pulses of the rectifier, the lower the current harmonic content at low frequencies. The characteristic harmonics can be represented as follows:

n = 1, 2, 3, 4, ....¥

P : number of rectifier pulses

At the same time that the harmonic currents at low frequencies are reduced, there are other disadvantages in increasing the number of rectifier pulses such as: the need of using phase-shifting transformers and increase on the cost of the configuration. Particular attention needs to be given to the increase on the equipment complexity and to the reduction on the efficiency and reliability of the whole system (due to the use of a larger number of components).

D1 D2 D3

D4 D5 D6

+

-

Other Loads

Distorted Voltage Non-linear Load

PCC

h=P .n±1

21 of 35

Multipulse Configuration

The characteristic harmonics of the six-pulse rectifier are given by:

The magnitudes of these harmonics, in respect of the fundamental, are given by:

Figure 3 - Theoretic harmonic spectrum of the input current for a six-pulse rectifier.

In the industry, the term “multipulse”, when related to frequency converters, means the association, in series or in parallel, of six-pulse three-phase rectifiers and the mandatory use of phase-shifting transformers to feed the rectifiers. The fundamental idea of the multipulse configurations can be understood as the interconnection of six-pulse rectifiers so that the characteristic harmonics generated by these rectifiers are cancelled by the harmonics generated by other sets of rectifiers. This mitigation is performed by appropriate design of the phase-shifting transformer with multiple secondaries. The harmonics of the six-pulse rectifier that are present on the secondary of the transformer will be cancelled and will not appear at the primary of the transformer that is connected to the utility.

The following figure shows the spectrum of these harmonics and their magnitude (as a percentage of the fundamental).

The increase in the number of the rectifier pulses and the use of an appropriate phase-shifting transformer allow the mitigation of the harmonic components at the primary of the transformer. Figure 4 shows the expected typical waveforms of the input currents and their respective harmonic spectrum to the 6, 12 and 18-pulse configurations.

It is important to emphasize that the harmonics multiple of the 3rd are cancelled in a balanced three-phase system (zero sequence).

In practice, however, the non-characteristic harmonics usually present a magnitude different from zero. This is due to the pre-existing imperfections of the electrical system, such as, voltage unbalance, pre-existing harmonic distortion, etc. Another factor that contribute to the appearance of non-characteristic harmonics is the transformer imperfections, which blocks the mitigation of non-characteristic harmonics at the primary of the transformer.The data presented in the following figures were obtained considering an ideal system. In the numerical simulation the system was modeled as: power electric system, input impedance, rectifier, capacitive filter and load (current source).

h=6 .n±1

Ah=1

6 .n±1

20.0% 14.3%

9.1% 7.7% 5.9% 5.3% 4.3% 4.0% 3.4% 3.2% 2.9% 2.7% 2.4% 2.3% 2.1% 2.0%

100.0%

1 5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49

22 of 35

6-pulse

12-pulse

18-pulse

Figure 4 - Typical input currents for the 6-pulse recifier or at the primary of the phase-shifting transformer input (12 and 18-pulse) and their respective harmonic spectrum (harmonic components expressed as a percentage of the fundamental).

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 79 83 85 89 91 95 97 101 103

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 79 83 85 89 91 95 97 101 103

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

1.6%

1.8%

5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 79 83 85 89 91 95 97 101 103

23 of 35

Notch Depth 10% 20% 50%THD (Voltage) 3% 5% 10%

Notch Area [V*us] 16400 22800 36500

* Special applications include hospitals and airports.

IEEE-519 - Table 10.2 - “Low-Voltage System Classification and Distortion Limits”.

Isc / IL < 11 TDD(%)< 20 4 2 1,5 0,6 0,3 5

20 < 50 7 3,5 2,5 1 0,5 850 < 100 10 4,5 4 1,5 0,7 12

100 < 1000 12 5,5 5 2 1 15> 1000 15 7 6 2,5 1,4 20

Maximum Harmonic Current Distortion in Percent of ILIsc - maximum short-circuit current at PCC

IL - maximum demand load current (fundamental frequency component) at PCC

IEEE-519 - Table 10.3 - “Current Distortion Limits for General Distribution Systems”.

IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power System: IEEE-519

This recommendation (it is not a standard) prepared by IEEE describes the main factors that may cause harmonic distortion, indicates the measurement methods and states the distortion limits.The scope of this recommended practice is to analyze the harmonic distortion caused by all the loads (linear and non-linear) at the Point of Common Coupling (PCC) and not the distortion caused by one individual device. The main concern of IEEE is what the installation reflects to the other consumers connected to the same power supply and not what occurs within the installation.The distortion limits are different according to the voltage and short-circuit levels at the PCC. The higher the short-circuit current (Isc) in respect of the load current, the higher the admissible current distortion, since they will cause a lower voltage distortion at the PCC. As the voltage level increases, the acceptable limits decrease.The TDD – Total Demand Distortion – is defined as the current harmonic distortion, in percentage of the maximum demand load current (15 or 30 minutes demand). This means that the TDD shall be measured at the peak consumption.

Tables 10.2 and 10.3, obtained from IEEE-519, show the recommended limits for the THDv (Total Voltage Harmonic Distortion) and for the TDD (Total Demand Distortion).

Special Applications*

General System

Dedicated System**

** A dedicated system is exclusively dedicated to the converter load.

In section 10.2 (Development of Current Distortion Limits), of IEEE-519, it is established 3% as the individual limit of the voltage components at PCC in respect of its fundamental component.

11£n<17 17£n<23 23£n<35 35£n

The table 10.3 is applicable to six-pulse rectifiers and general distortion situations. However, when phase shift transformers or converters with pulse numbers higher than six are used, the limits for the characteristic harmonic orders are increased by a factor equal to: 1.414 for 12-pulse and 1.732 for 18-pulse.

Although the IEEE-519 is not a standard, this recommendation is being used as a reference to specify the harmonic distortion limits allowed by the utility companies and in the design of industrial power systems.

24 of 35

Case Study: Company Name date: 7-Apr-23

The voltages and currents are expressed in RMS values.

Power Capacity: 15.00 MVASource reactance (%): 8.00 %

Voltage: 6600 VoltsDemand Current (IL): 1137 A

Short-circuit Current (Isc): 16.40 kA Ratio Isc/IL: 14.42

Rectifier: 6 pulse

Voltage: 3300 VoltsCurrent: 310 A

0.86

The THDi current at the PCC is calculated by the following expression:

Where:

This case study aims to show how to obtain, in a simple way and with a good precision, the Voltage Harmonic Distortion (THDv) and the Total Demand Distortion (TDD) values for a system composed of a main bus bar with known power and impedance, feeding a non-linear load with an input rectifier with the specified number of pulses. This is a simple study, since practical aspects are being disregarded such as: the network is not ideal, phase unbalance, influence of other loads connected to the PCC, transmission line impedance, system efficiency, etc. The values presented herein are useful for a preliminary analysis of the harmonic distortion level of the system. For a complete analysis, taking in account all the variables listed above, it is necessary to perform a numerical simulation.

For this type of rectifier, it is recommended to use an input line reactor (or DC choke) with a minimum voltage drop of 4%.

cos(f):

Considering that the fundamental is the only component that provides active power to the motor, it is possible to calculate its value at the PCC by taking in account the typical motor displacement power factor - cos(f). With the calculated fundamental component, the theoretical harmonic components of the current at the PCC can be known as a function of the number of pulses of the rectifier.

In are the harmonic components of the PCC current

I(1) is the fundamental component of the PCC current

PCC Data

VFD System

Three-phase Induction Motor

THD i=√∑n=2

∞

I n2

I (1 )

25 of 35

The TDD is calculated as the current harmonic distortion at the PCC in respect of its demand current (IL):

Where:

L is the physical inductance at the PCC

Final Results

% of load 10.66 % Ratio between the load power and the PCC capacity

139.87 A RMS value of the fundamental component of the current Ie

146.44 A RMS value of the Ie current

IL 1137.21 A RMS value of the demand current at PCC

32.49 % Harmonic current distortion of the current Ie

TDD 4.00 %Total Demand Distortion (considering IL as the demand current)

Meets IEEE-519 Isc/IL = 14 the limit is: 5%

1.70 %Voltage Harmonic Distortion at the PCC

Meets IEEE-519 including for 'Special Applications'

Figure 5 - Individual Current Harmonics expressed as a percentage of IL.

Observing figure 5 it can be concluded that: Meets IEEE 519 - table 10.3

With the given power and impedance (%) it is possible to calculate the physical inductance (L) at the PCC and, therefore, calculate the voltage drops caused by the components of the current harmonics.

Fn are the characteristic harmonic frequencies

Vn are the harmonic components of the voltage at the PCC

V(1) is the fundamental component of the voltage at the PCC

The results of the harmonic analysis are presented in the following table. These calculations were performed up to the 100th harmonic.

Ie(1)

Ie RMS

THDi

THDv

5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 79 83 85 89 91 95 97 101 103

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

Simulation

IEEE limits

TDD=√∑n=2

∞

I n2

IL

THDV=√∑n=2

∞

V n2

V ( 1 )

V n=I n . (2. π . Fn ). L

26 of 35

Figure 6 - Individual Voltage Harmonics expressed as a percentage of the fundamental voltage at the PCC.

Observing figure 6 it can be concluded that: Meets the individual limit of 3%

Summary

1.70 %Voltage Harmonic Distortion at the PCCMeets IEEE-519 including for 'Special Applications'

Individual Limit for the Voltage Harmonics at the PCC: Meets the individual limit of 3%

TDD 4.00 %Total Demand DistortionMeets IEEE-519 Isc/IL = 14 the limit is: 5%

Current Harmonics (table 10.3): Meets IEEE 519 - table 10.3

References

[1]

[2]

[3]

[4]

(in portuguese)

[5]

THDv

PAICE, DEREK A., "POWER ELETRONIC CONVERTER HARMONICS - MULTIPULSE METHODS FOR CLEAN POWER", IEEE PRESS, USA, 1996

IEEE, "IEEE RECOMMENDED PRACTICES AND REQUIREMENTES FOR HARMONIC CONTROL IN ELECTRICAL POWER SYSTEMS - IEEE-519", IEEE PRESS, USA, 1993

POMILIO, J. A., "PRÉ-REGULADORES DE FATOR DE POTÊNCIA", PUBLICAÇÃO FEE 03/95, BRASIL, 2004 (in portuguese)

ALVES, JOABLE A., & HORNBURG, EDSON, "HIGH AND LOW ORDER HARMONICS FOR FREQUENCY INVERTERS", ANAIS DO VI INDUSCON, JOINVILLE-BRASIL, 2004

ROSSA, A. J. & TORRI, P. J., “EFEITOS DA DISTORÇÃO HARMÔNICA DA REDE ELÉTRICA SOBRE MOTORES ELÉTRICOS”, REVISTA ELETRICIDADE MODERNA, ANO XXIX, Nº 324, BRASIL, 2001 (in portuguese)

5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 79 83 85 89 91 95 97 101 103

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

Simulation

IEEE limit

27 de 35

Joable Andrade Alves & Paulo José TorriWEG Automação S.A.

Introdução

Fig. 1 - Retificador de 6 pulsos

Fig. 2 - Distorção da tensão provocada por correntes drenadas por uma carga não-linear

Onde:h : ordem da harmônica

Atendimento a Recomendação IEEE-519 em Aplicações

com Inversores de Freqüência

Os conversores indiretos de freqüência, ou inversores de freqüência, são normalmente constituídos por um estágio retificador a diodos na entrada. O retificador trifásico de onda completa, também conhecido como Ponte de Graetz ou retificador de 6 pulsos (Fig. 1), é uma das estruturas mais empregadas como estágio de entrada dos conversores. As correntes drenadas por este retificador são pulsadas, contendo harmônicas de baixa ordem e que podem causar distorções harmônicas na tensão de rede da planta a qual estão conectados os inversores. A distorção de tensão depende das amplitudes das harmônicas de corrente dos equipamentos e também das impedâncias da rede, isto é, da capacidade da planta e da relação entre a capacidade instalada de inversores em relação a capacidade da planta.

Em muitas aplicações, o inversor de freqüência com retificador de 6 pulsos adicionado a uma reatância na entrada ou um indutor no barramento CC atende perfeitamente as recomendações da IEEE-519. Quando isto não é possível, algumas das soluções disponíveis para redução das correntes harmônicas são o aumento do número de pulsos do retificador utilizando 12, 18 ou até 24 pulsos ou a utilização de retificadores de entrada ativos (regenerativos).

Quanto maior o número de pulsos do retificador menor o conteúdo harmônico da corrente nas baixas freqüências. As harmônicas características podem ser expressas por:

n = 1, 2, 3, 4, ....¥

P : número de pulsos do retificador

Em contrapartida ao benefício da redução das correntes harmônicas de baixa freqüência existem as desvantagens em aumentar o número de pulsos do retificador, tais como a necessidade de utilização de transformadores defasadores e o aumento do custo da estrutura. Deve-se atentar para o aumento da complexidade dos equipamentos, da redução da eficiência e da confiabilidade do sistema pois são necessários um número maior de componentes.

Outras Cargas

Tensão Distorcida Carga Não-Linear

PCC

h=P .n±1

D1 D2 D3

D4 D5 D6

+

-

28 de 35

Estruturas Multi-pulsos

As harmônicas características do retificador de 6 pulsos são dadas por:

As amplitudes destas harmônicas, relativas a componente fundamental, são dadas por:

Fig. 3 - Espectro harmônico teórico da corrente de linha para um retificador de 6 pulsos

Na indústria, o termo multi-pulsos relacionado a inversores de freqüência tem conotação com a associação, em série ou paralelo, de retificadores trifásicos de 6 pulsos e a obrigatória utilização de transformadores defasadores para alimentá-los. A idéia básica das estruturas multi-pulsos pode ser entendida como a conexão de retificadores de 6 pulsos de tal forma que as harmônicas características geradas por estes retificadores sejam canceladas pelas harmônicas geradas por outros conjuntos de retificadores. Este cancelamento é possível pelo adequado projeto do transformador defasador com múltiplos secundários. As harmônicas dos retificadores de 6 pulsos estão presentes nos secundários, são canceladas no transformador e não aparecem no primário que está conectado a rede.

O gráfico seguinte ilustra o espectro destas harmônicas e a sua amplitude expressa em percentual da componente fundamental.

O aumento do número de pulsos do retificador e a utilização do transformador defasador adequado, possibilita que sejam eliminadas as componentes harmônicas no primário do transformador. A figura 4 mostra as formas de onda típicas das correntes de linha esperadas e o seu respectivo espectro harmônico para estruturas de 6, 12 e 18 pulsos.

Cabe ressaltar que as harmônicas de ordem múltiplas de 3 são canceladas em um sistema trifásico equilibrado (seqüência zero).

Na prática, no entanto, as harmônicas não características normalmente apresentam uma amplitude diferente de zero. Isto se dá devido às imperfeições já presentes na rede elétrica, tais como, desequilíbrio de tensões, distorções harmônicas pré-existentes, etc. Outros fatores que contribuem para o aparecimento de harmônicas não características são as imperfeições do transformador, as quais impedem o perfeito cancelamento destas no primário do mesmo.Os dados apresentados nas figuras seguintes foram obtidos considerando a perfeita idealidade do sistema. Na simulação numérica o sistema foi modelado como: rede de alimentação, impedância de entrada, retificador, filtro capacitivo e carga (fonte de corrente).

h=6 .n±1

Ah=1

6 .n±1

20.0% 14.3%

9.1% 7.7% 5.9% 5.3% 4.3% 4.0% 3.4% 3.2% 2.9% 2.7% 2.4% 2.3% 2.1% 2.0%

100.0%

1 5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49

29 de 35

6 pulsos

12 pulsos

18 pulsos

Fig. 4 - Correntes típicas na entrada do retificador (6 pulsos) ou no primário do transformador defasador (12 e 18 pulsos) e respectivos espectros harmônicos (componentes harmônicas expressas em percentual da fundamental)

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 79 83 85 89 91 95 97 101 103

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 79 83 85 89 91 95 97 101 103

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

1.6%

1.8%

5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 79 83 85 89 91 95 97 101 103

30 de 35

Notch Depth 10% 20% 50%THD (Voltage) 3% 5% 10%

Notch Area [V*us] 16400 22800 36500

* Special applications include hospitals and airports.

IEEE-519 - Table 10.2 - “Low-Voltage System Classification and Distortion Limits”.

Isc / IL < 11 TDD(%)< 20 4 2 1,5 0,6 0,3 5

20 < 50 7 3,5 2,5 1 0,5 850 < 100 10 4,5 4 1,5 0,7 12

100 < 1000 12 5,5 5 2 1 15> 1000 15 7 6 2,5 1,4 20

Maximum Harmonic Current Distortion in Percent of ILIsc - maximum short-circuit current at PCC

IL - maximum demand load current (fundamental frequency component) at PCC

IEEE-519 - Table 10.3 - “Current Distortion Limits for General Distribution Systems”.

Recomendação IEEE para práticas e requisitos para controle de harmônicas no sistema elétrico de potência: IEEE-519

Esta recomendação (não é uma norma) produzida pelo IEEE descreve os principais fenômenos causadores de distorção harmônica, indica métodos de medição e limites de distorção.Seu enfoque é a análise da distorção harmônica no Ponto de Conexão Comum (PCC) das cargas (lineares ou não-lineares) e não em cada equipamento individual. A filosofia é que não interessa ao sistema o que ocorre dentro de uma instalação, mas sim o que ela reflete para o exterior, ou seja, para os outros consumidores conectados à mesma alimentação.Os limites diferem de acordo com o nível de tensão e com o nível de curto-circuito do PCC. Quanto maior for a corrente de curto-circuito (Isc) em relação à corrente de carga, maiores são as distorções de corrente admissíveis, uma vez que elas distorcerão em menor intensidade a tensão no PCC. À medida que se eleva o nível de tensão, menores são os limites aceitáveis.A grandeza TDD - Total Demand Distortion - é definida como a distorção harmônica da corrente, em % da máxima demanda da corrente de carga (demanda de 15 ou 30 minutos). Isto significa que a medição da TDD deve ser feita no pico de consumo.

As tabelas 10.2 e 10.3, extraídas da IEEE-519, apresentam os limites recomendados de THDv (Total Harmonic Distortion) da tensão e TDD (Total Demand Distortion).

Special Applications*

General System

Dedicated System**

** A dedicated system is exclusively dedicated to the converter load.

Na seção 10.2 (Development of Current Distortion Limits), desta norma, é estabelecido 3% como o limite individual das harmônicas de tensão no PCC em relação a sua fundamental.

11£n<17 17£n<23 23£n<35 35£n

A tabela 10.3 é aplicável para retificadores com 6 pulsos. Para retificadores com 12 pulsos, deve-se multiplicar os limites individuais por 1.414. No caso de retificadores com 18 pulsos estes limites devem ser multiplicados por 1.732 .

Apesar de não ser uma norma, a IEEE-519, tem sido utilizada como base para a especificação dos limites de distorções harmônicas por concessionárias do setor elétrico e em projetos de plantas industriais.

31 de 35

Estudo de Caso: Company Name Data: 7-Apr-23

As tensões e correntes estão expressas em valores eficazes.

Potência Instalada: 15.00 MVAImpedância %: 8.00 %

Tensão: 6600 VoltsCorrente de Demanda (IL): 1137 ACorrente de Curto-Circuito: 16.40 kA

Relação Isc/IL: 14.42

Retificador: 6 pulsos

Tensão: 3300 VoltsCorrente: 310 A

0.86

onde:

Este estudo de caso tem como objetivo mostrar como obter, de maneira simples e com um bom grau de precisão, os valores das taxas de distorção harmônica da tensão (THDv) e da TDD, em um sistema formado por uma barra com potência instalada e impedância definidas, alimentando uma carga não-linear com um retificador de entrada com número de pulsos especificado. Este estudo é simplificado pois não estão sendo considerados aspectos práticos como não idealidades da rede, desbalanceamentos entre as fases de alimentação, a influência de outras cargas conectadas ao PCC, impedâncias da linha de transmissão, rendimento do acionamento, etc. Os valores calculados são úteis para se obter uma idéia inicial das distorções harmônicas no sistema apresentado. Para uma análise completa, considerando todos os aspectos apresentados é necessário conhecer todas as variáveis e realizar uma simulação numérica do sistema completo.

Para este retificador, recomenda-se uma reatância de entrada (ou bobina no link DC) com queda % mínima de 4%.

cos(f):

Considerando que a componente fundamental é a única a fornecer potência ativa para o motor, pode-se calcular o valor desta no PCC, considerando o cos(f) típico do motor. Com a componente fundamental calculada, as componentes harmônicas teóricas da corrente no PCC são conhecidas em função do número de pulsos do retificador.

A THDi da corrente no PCC é calculada pela expressão:

In são as componentes harmônicas da corrente no PCC

I(1) é a componente fundamental da corrente no PCC

Dados do PCC (Sistema)

Acionamento

Motor de Indução Trifásico

THD i=√∑n=2

∞

I n2

I (1 )

32 de 35

onde:

L é a indutância física até o ponto de conexão comum (PCC)

Resultados Obtidos

% carga 10.66 % Relação entre a potência da carga pela potência instalada do PCC

139.87 A Valor eficaz da componente fundamental da corrente Ie

146.44 A Valor eficaz da corrente Ie

IL 1137.21 A Valor eficaz da corrente de demanda no PCC

32.49 % Distorção harmônica da corrente Ie

TDD 4.00 %Total Demand Distortion

ATENDE IEEE-519 Isc/IL = 14 o limite é: 5%

1.70 %Distorção harmônica da tensão no PCC

Atende IEEE-519 inclusive para 'Special Applications'

Fig. 5 - Harmônicas Individuais de Corrente em percentual de IL

Observando a figura 5 constata-se que: Atende a tabela 10.3 da IEEE 519

A TDD será calculada como sendo a distorção harmônica da corrente no PCC em relação a corrente de demanda no mesmo (IL):

Com a potência, tensão e impedância % dadas, é possível calcular a indutância física (L) no PCC e assim, calcular as quedas de tensão provocadas pelas componentes harmônicas da corrente.

Fn são as freqüências harmônicas características

Vn são as componentes harmônicas da tensão no PCC

V(1) é a componente fundamental da tensão no PCC

Os resultados obtidos pelas expressões apresentadas estão compilados na tabela seguinte. Os cálculos foram efetuados com até a 100ª hamônica.

Ie(1)

Ie RMS

THDi

THDv

5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 79 83 85 89 91 95 97 101 103

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

Simulação

Limite IEEE

TDD=√∑n=2

∞

I n2

IL

THDV=√∑n=2

∞

V n2

V ( 1 )

V n=I n . (2. π . Fn ). L

33 de 35

Fig. 6 - Harmônicas Individuais de Tensão em percentual da tensão fundamental no PCC

Observando a figura 6 constata-se que: Atende ao limite individual de 3%

Resumo

1.70 %Distorção harmônica da tensão no PCCAtende IEEE-519 inclusive para 'Special Applications'

Limite individual das harmônicas de Tensão no PCC: Atende ao limite individual de 3%

TDD 4.00 %Total Demand DistortionATENDE IEEE-519 Isc/IL = 14 o limite é: 5%

Harmônicas de Corrente (tabela 10.3): Atende a tabela 10.3 da IEEE 519

Referências

[1]

[2]

[3]

[4]

[5]

THDv

PAICE, DEREK A., "POWER ELETRONIC CONVERTER HARMONICS - MULTIPULSE METHODS FOR CLEAN POWER", IEEE PRESS, USA, 1996

IEEE, "IEEE RECOMMENDED PRACTICES AND REQUIREMENTES FOR HARMONIC CONTROL IN ELECTRICAL POWER SYSTEMS - IEEE-519", IEEE PRESS, USA, 1993

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