armonici_monitorizare

8/13/2019 Armonici_monitorizare

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MONITORIZAREA PERTURBATIILOR SUB FORMA DE ARMONICI

I NESIMETRIE

HARMONIC AND UNBALANCE DISTURBANCES MONITORING

Hermina ALBERT Luminia ELEFTERESCUISPE Bucureti, Romania,

B-dul Lacul Tei nr. 1, Sector 2 BucuretiTel. 021/2061307; E-mail [email protected]

Valentin RCANU, Claudiu PUN, Dan PUNSC FELIX SA, Bucureti Romania

Str. Ing. G. Constantinescu Nr.2, 78009 BucuretiTel. 021/2422120; Fax 021/2420750; E-mail [email protected]

Nicolae GOLOVANOV

Universitatea POLITEHNICA din BucuretiSplaiul Independenei 313, Sector 6

Tel/Fax 021/4029446; E-mail: [email protected]

Rezumat: Sunt prezentate aspecte teoretice i experimentalecare au stat la baza dezvoltrii i realizrii practice a unuiechipament care asigurmonitorizareai prelucrarea informaiilor

rivind perturbaiile armonice i nesimetria, n concordancunormele europene n domeniu. n urma prelucrrii informaiilorachiziionate, pe termen lung, sunt oferite date privind carac-teristicile statistice ale perturbaiilor, variaia puterilor activ,reactiv i aparent pe fiecare faz (conform definiiei

Budeanu) i pe fiecare armonic, variaia factorului de putere

e faz. Informaiile privind factorii de nesimetrie se refer ladefiniia actual a acestora, dar echipamentul permite iobinerea de date, n scopul comparrii, pe baza definiieianterioare.

Keywords: monitorizare, armonici, nesimetrie.

Abstract: The paper presents the theory and experiments whichare the basis of the performance and manufacture of an equipmentwhich provide the monitoring and information processing oharmonic disturbances and unbalance in compliance with the

European standards in the field. Further to acquiredinformation processing, on long-term, there are provided datarelated to disturbance statistical features; active, reactive andapparent power variation by each phase (according to Budeanudefinition) as well by each harmonic, phase power factor

variation. The information concerning unbalance factors arerelated to their current definition but the equipment allows alsoto obtain data for comparison based on the previous definition.

Keywords: monitoring, harmonics, unbalance.

1. Introducere

Dezvoltarea tehnologiilor industriale moderne, cretereaponderii consumurilor din sectorul de servicii i sectorulcasnic, avnd n dotare echipamente bazate pe schemeactuale de reglare i control, determinapariia n reeauaelectrica unor importante perturbaii sub formde armonicii nesimetrie. Propagarea acestor perturbaii n reeaua

electricdetermindistorsiuni ale formei curbelor de ten-siune i nesimetrii pe barele de alimentare a consumatorilori deci reducerea nivelului de calitate a energiei electricefurnizate.

De cele mai multe ori, consumatorii sursde perturbaiisunt chiar ei nii sensibili la abaterile dela indicatorii decalitate. De asemenea, furnizorul de energie electricsuport

pierderi datorate propagrii perturbaiilor n reeaua sa.Evaluarea nivelului de calitate a energiei electrice la

barele de alimentare a consumatorului i n noduri ale reeleielectrice, precum i stabilirea msurilor pentru ncadrare anivelului de perturbaii n limitele acceptate de standardeledin domeniu, impun cunoaterea principalilor indicatori

1. Introduction

The development of the modern industrial technologies,increase of the share of consumtions in the services sectorand domestic sector, fitted with equipment relying on up-to-date adjustment and control diagrams triggers theoccurrence in the electric network of significant disturbancesunder the form of harmonics and unbalance. The disturban-

ces propagation in the power network determines distortionsof the voltage curves shape and unbalances on theconsumers supply bars and consequently reduction of thedelivered electric power quality level.

Most of the times, the consumers source of disturbancesthemselves are sensitive to nonconformity with the qualityindicators. Also, the electric power supplier bears lossesdue to disturbances propagation within his network.

The evaluation of the electric power quality level onthe consumers supply busbars and in electric network nodesas well as establishing the measures to put the disturbanceslevel within the limits allowed by the standards in thefield, impose knowledge of the main quality indicators in


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The 5thInternational Power Systems Conference20

de calitate n punctul analizat i, mai ales, variaia acestorape intervale mari de timp.

n acest sens, a fost dezvoltat un mare numr de echipa-mente de monitorizare, care urmresc sofere informaii ctmai ample privind nivelul i variaia perturbaiilor analizate.O atenie special este acordat n prezent monitorizrii

parametrilor curbelor deformate de tensiune i de curentelectrice, precum i a nesimetriei acestor curbe.

Necesitatea monitorizrii unui mare numr de puncte,n primul rnd barele, sursde perturbaii n alimentareaconsumatorilor, impune existena unor echipamente spe-cializate, cu o fiabilitate corespunztoare i un pre decost rezonabil. O atenie deosebit la realizarea i utili-zarea acestor echipamente este stabilirea exact a scopuluiacestora i a algoritmilor utilizai pentru determinareaindicatorilor i prelucrarea datelor nregistrate.

Echipamentele utilizate pentru achiziia i prelucrareadatelor privind calitatea energiei electrice prezintcarac-teristici diferite n funcie de tipul operaiei pentru caresunt destinate. Din acest punct de vedere, echipamentele

pentru achiziia i prelucrarea datelor se mpart n trei

categorii [1]: categoria 1-a: pentru monitorizare permanent (deexemplu pentru verificarea clauzelor contractuale);

categoria 2-a: pentru urmrire temporar(de exemplu,pentru verificarea caracteristicilor reelei electrice de ali-mentare sau n cazul unor reclamaii ale consumatorilor);

categoria 3-a: pentru investigaii generale.Exactitatea echipamentelor pentru achiziia i prelucrarea

datelor, corespunztoare celor trei categorii de operaii,trebuie scorespundvalorilor indicate n Tabelul 1.

the analyzed point and mostly, their variation over largetime periods.

To this effect, a large number of monitoring equipmentwas developed, that are focused on supplying as muchinformation as possible regarding the analyzed disturbanceslevel and their variation. Special attention is currently paidto monitoring the parameters of the deformed voltage andcurrent curves as well as unbalance of these curves.

The need to monitor a large number of points, first ofall the bus bars, source of disturbances on consumers supply,calls for specialized equipment with adequate reliabilityand reasonable cost. Upon manufacturing and using suchequipment, special attention is paid to the accurate settingof the scope and algorithms used to determine the indicatorsand process the recorded data (acquired data processing).

The equipment used for the acquisition and processingof the data regarding the electric power quality have variousfeatures according to the type of operation they are destinedto perform. From this viewpoint, the data acquisition and

processing equipment fall in three categories:category 1: for uninterrupted monitoring (i.e. for contract

clauses check);category 2: for temporary monitoring (i.e. to check thepower supply network features or in case of consumerscomplaints);

category 3: for general investigations.The accuracy of the data acquisition and processing

equipment corresponding to the three operation categories,must meet the values in Table1.

Tabelul 1 Erori admise la echipamentele pentru achiziia i prelucrarea datelor privind calitatea energiei electriceTable 1 Errors allowed at the electric power quality data acquisition and processing equipment

Allowed errorAnalyzed size Meas scope.Categ.1 Categ.2 Categ.3

Frequency 42,557,5 2r

Voltage amplitude Nominal value 15% 2r

Flicker level (Pst) 04 4r

Voltage dipsDip voltage duration up to 1.5 s;Dip voltage amplitude up to 99%

Interruptions Up to 4 hours

Unbalance 05%

Harmonics (THD) 015%

Interharmonics (atany freq.) 3%

Transientovervoltages

2 kV

r 2r

4r

La realizarea i utilizarea echipamentelor de monitorizareeste necesar a lua n consideraie aspecte specifice reelelorelectrice n care mrimile variaz n mod continuu, iar

perturbaia ntr-un nod oarecare rezultprin suprapunereaperturbaiilor diferitelor surse din reea, avnd astfel unpronunat caracter aleatoriu. n acest sens, o atenie deosebittrebuie acordatcunoaterii n amnunt a algoritmuluiutilizat pentru definirea mrimilor i prelucrarea acestora.

Upon manufacturing and using the monitoring equip-ment it is necessary to consider the aspects specific to theelectric power networks where the values keep changing,while the disturbance in any node results by overlappingthe disturbances of the various network sources, having inthis way a marked random character. To this effect, specialattention must be paid to the knowledge in detail of thealgorithm used for the values definition and processing.


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06-07.11.2003, Timioara, Romania 21

Astfel, un consumator cu o putere absorbitfoarte redus(de exemplu, n orele de gol de sarcin) poate absorbi uncurent puternic deformat dar care nu prezintimportan

pentru reeaua electric, determinnd influene nesemni-ficative asupra tensiunilor din nodurile reelei. Luarea nconsiderare a acestuia n calculul THD poate conduce lavalori mari, care, ns, sunt nesemnificative.

Existena, n prezent, n literatura de specialitate a unor

definiiidiferitepentrumrimilemonitorizateimpuneverifica-rea procedurilor de calcul i concordana acestora cu stan-dardele n vigoare n Europa (conform recomandrilor CEI).

Realizarea, de ctre autorii lucrrii, a unui echipamentde monitorizarea a regimurilor distorsionate i nesime-rice (MOD) a urmrit obinerea unui instrument specializat

pentru categoria 2 de echipamente, bazat pe recomandrileCEI, agreate i n ara noastrca normative naionale.

Thus, a consumer with very low power taken up (forexample during the light hours) can take a highly distortedcurrent, determining insignificant influences over thevoltages in the network nodes. The consideration of it onTHD calculation can lead to large values, which nonethelessare of no practical interest.

The current existence, in the speciality literature, ofvarious definitions for the monitored values requires

checking the calculation procedures and their observanceof the European standards in force (as per CEI recomman-dations).

On manufacturing the equipment for disturbed andunbalanced regimes monitoring (MOD), the paper authorsaimed at obtaining a tool specialized equipment, relyingon CEI recommendations, also approved by our countryas national norms

2. Analiza distorsiunii curbelor de tensiunei de curentelectric

n analiza polurii armonice este larg utilizatn prezenttransformarea Fourier care permite descompunerea unei

curbe deformate, n regim permanent, n armonici de frec-vene multiplu ntreg al armonicii fundamentale. n cazulgeneral, n reeaua electric, datorit suprapunerii aleatorii a

perturbaiilor datorate diferitelor surse, regimul nu estepermanent, ceea ce face ca utilizarea transformrii Fouriersnecesite stabilirea unui regim periodic echivalent, care smodeleze ct mai bine regimul nesinusoidal real.

Conform reglementrilor internaionale [2, 3, 4, 5],adoptate i n Romnia, analiza curbelor nesinusoidale seface n domeniul frecven, pe curbe mediate pe (520)

perioade ale tensiunii din reea. Datoritvariaiei n timp amrimilor din reelele electrice, caracterizarea unui nod alreelei din punctul de vedere al regimului nesinusoidal, se

poate face numai pe baza prelucrrii statistice a datelornregistrate pe intervale mari de urmrire n timp (n moduzual, o sptmn). Valorile determinate vor avea o anumit

probabilitate de realizare 99%, 95% sa.Analiza n domeniul timp, mai adecvat regimurilor

reale din reelele electrice, necesitstudii pentru elaborareade noi indicatori.

Principalii indicatori de calitate ai regimului periodicnesinusoidal, normalizai n prezent, sunt:Valoarea efectivYa mrimii nesinusoidale:

=

+==1

220

2/

0

22

k

k

T

YYdtyT

Y (1)

n care Teste perioada curbei deformate, iar Yk- valoareaefectiva componentei de rang kobinutn urma analizeiFourier.

De precizat faptul c, n prezent, se impune determinareavalorii efective corespunztoare fiecrei semiperioade acurbei analizate. Aceast condiie prezint o importandeosebit n special la monitorizarea tensiunii pe barelede alimentare.Factorul de distorsiunenormal (THD)

=

=40

22

1

2

k

kU

Y

Y(2)

n care Y1este amplitudinea armonicii fundamentale.

2. Analysis of the electric current and voltage curves

distortions

Currently, in harmonic pollution analysis, the Fouriertransformation is widely used; it allows splitting of a

deformed curve, under steady load, in whole multiplefrequency harmonics of the fundamental harmonic. Gene-rally, in the electric network, due to random overlappingof disturbances due to various sources, the load is not steady,which makes the Fourier transformation utilization requiressetting an equivalent periodic load to model as well as

possible the actual nonsinusoidal load.According to international recommendation [2,3,4,5],

adopted in Romania too, the nonsinusoidal curves analysisis performed in the frequency field, on curves averaged

by (5...20) periods of the network voltage. Due to thevariation in time of the network values, the charac-terization of a network node, from the nonsinusoidal loadviewpoint, can only be performed based on the statistic

processing of the data recorded over large periods of time(usually one week). The values determined will have acertain performance probability 99%, 95%

The main quality indicators of the periodic nonsinusoidalload, currently normalized, are the following:Rms of the nonsinusoidal Y value:

The analysis in the field time, more adequate for theactual loads in the electric networks requires studies todraw up new indicators.

=

+==1

220

2/

0

22

k

k

T

YYdtyT

Y (1)

where T is the period of the nonsinusoidal curve whileY - rms value of the component of rank k obtained throughFourier transformation.

Mention should be made, that currently, it is requiredthe ascertainment of the actual value corresponding toeachsemiperiod of the analyzed curve. This condition isof special importance, mainly on monitoring the voltageon the supply bus bars.The total distortion factor (THD):

=

=40

22

1

2

k

kU

Y

Y(2)

where Y1is the fundamental harmonic amplitude.


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Pentru aplicaiile practice se considerca semnificativearmonicile pnla rangul 40.

Deoarece distorsiometrele actuale indic valoareafactorului de distorsiune cu raportare la valoarea efectiva curbei i nu la valoarea efectiva armonicii fundamentale,trebuie luat n consideraie i aceast definiie. n acestsens, unele dintre echipamentele de monitorizare indicvaloare THD Fund, determinat conform relaiei (2) i

valoarea THD Rmsn care raportarea se face la valoareaefectiv.

n cazurile practice prezint interes monitorizarea petermen lung, n mod obinuit o sptmn, a factorului dedistorsiune i prelucrarea statisticpentru obinerea valorilorcu probabilitate de 99% (corespunztor valorii maxime), de95% (valoare de dimensionare), valoarea medie i abatereamedie ptratic.nivelul armoniciide rang k

1Y

Ykk= (3)

Ca i n cazul factorului de distorsiune, nivelul armoniciipoate fi definit numai statistic prin valorile cu probabilitate99%, 95%, 50% i prin abaterea medie ptratic.

n analiza curbelor deformate de curent electric seconsiderc intervalele n care curentul absorbit este redus(se propune limita de 20% din curentul contractat) snufie luate n considerare n analiza statisstic a factoruluide distorsiune i a nivelului armonicii.

Stabilirea aportului diferitelor surse de perturbaii subformde armonici, n fiecare dintre nodurile reelei electricede alimentare, necesitcunoaterea sensului de circulaiea puterilor armonice. n acest sens, echipamentele de moni-torizare trebuie sofere posibilitatea determinrii corectea defazajul fiecrei armonici i calculul puterilor armonicecu semnul corespunztor.

Echipamentul realizat MOD permite o monitorizareon-line, memorarea pe termen lung a informaiilor achizi-ionate i prelucrarea statistic ulterioar a acestora. nacest sens, echipamentul compatibil cu standardul EN50160/1999, are caracteristici corespunztoare clasei deexactitate 1% i prezintschema bloc indicatn fig. 1.

Informaiile privind tensiunile pe cele trei faze i neutrulde lucru sunt preluate prin intermediul unor divizoare detensiune DT cu raport de divizare adecvat. Informaiile

privind curenii prin cele trei faze i nulul de lucru suntpreluate prin intermediul unor transformatoare de msurare(cleti de msurare) care transmit semnalul de msurat latraductoarele TCmde tip LEM. Semnalul de la bornele

rezistoarelor de msurare RC este transmis convertoruluianalog-numeric care asigursimultan conversia pe cele 8canale. Sincronizarea conversiei se face n raport cutensiunea de pe faza A.

Pe baza datelor de la ieirea convertorului pot fi deter-minai factorii de asimetrie i disimetrie.

Procesarea semnalului asigur obinerea mrimilorspecifice regimului nesinusoidal, iar informaiile privindarmonica fundamental sunt utilizate i pentru calcululfactorilor de nesimetrie negativi zero.

Datele obinute on-line sunt memorate, prelucratestatistic i afiate, la sfritul intervalului de urmrire.

For the practical applications, the harmonics up to rank40 are considered significant.

Since the actual equipment indicate the distortion factoras referred to the curve effective value not the effectivevalue of the fundamental harmonic, this definition shouldalso be taken into consideration. To this effect, somemonitoring equipment indicate value THD Fund, determinedaccording to relation 2 and value THD Rms which is

referred to the effective value.In practice, it is of importance the monitoring over

large periods of time, usually one week, of the distortionfactor and the statistic processing to obtain values with99% probability (corresponding to maximum value), 95%(sizing value), average value and mean square valuedeviation.level of rank k harmonic

1Y

Ykk= (3)

Just like in the case of distortion factor, the harmoniclevel can only be defined statistically through values with

probability 99%, 95%, 50% and mean square valuedeviation.

In the analysis of the distorted electric current curves,it is considered that the periods when the current taken islow (it is proposed 20% of the contracted current) shouldnot be taken into consideration in the statistical analysisof the distortion factor and harmonic level.

Setting the share of various harmonic disturbancesources, within each power supply network node, requiresknowledge of the harmonic powers circulation way. To thiseffect, the monitoring equipment must provide the possibilityof accurate determination of each harmonic phase shiftingand calculation of the harmonic powers with suitable sign.

The MOD equipment manufactured provides on-line

monitoring, long term storing and further statistic processingof the acquired information. To this effect, the equipmentcompatible with standard EN 50160/1999 has characteristicscorresponding to accuracy class 1% and has the blockdiagram indicated in Fig.1.

The information regarding the voltages on the threephases and operation neutral is taken over throughvoltage divider VD with adequate dividing ratio. Theinformation regarding the currents through the three

phases and the operation null is taken over via measuringtransformers (clamp meters) that transmit the signal to bemeasured to transducers TC, LEM type. The signalfrom the RC measuring resistors terminals is transmitted

to the analog-digital converter that simultaneously providesconversion on the 8 channels. The conversion synchro-nization is performed as referred to the voltage on phase A.

Based on the converter output data, the unbalance(negative and zero) factors can be determined.

Through the signal processing can be obtained the valuesspecific to the nonsinusoidal load, while the informationregarding the fundamental harmonic is used for the calcula-tion of the negative and zero unbalance factors, too.

The data obtained on-line is stored, statistically pro-cessed and displayed, at the end of the monitoring term.

Mention is made, that by the end of each measuringterm, the equipment allows corresponding values display.


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A B CNL

NP T

CA

TC

B

TC

C

TC

N

TC

m RC

m

Digitalanalogconvertor

with8channels

D

T

U

ref

Clock

Signalprocessing

unit

(FFT)

Voltageandcurrent

curvespassing

throughzero

determinatio

n

ka

;kd

Calcu

lation

ks

;ks0

Calcu

lation

cUk;cIk;

Uk;Ik;

U

;I;Uk;Ik

U

;I;

Uk;Ik

ks;

ks0

Data

storing

Data

storing

Statistic

processing

Statistic

processing

U

med;U99;U95;

I

med;I99;I95;

Uk

med;Uk99;Uk95;

Ik

med;Ik99;Ik95;

ksmed;ks99;

ks95;

0

0

Fig.

1.B

lockdia

gramo

fdistortedandunbalancevaluesmo

nitoringequipment.


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De precizat faptul c la sfritul fiecrui interval demsurare echipamentul permite afiarea valorilor cores-

punztoare.Echipamentul MOD-108 prezint urmtoarele carac-

teristici principale:posibilitatea de achiziie de date, simultan pe 8 canale

(4 de tensiune i 4 de curent electric); realizeaz o msurare continu, pe intervale mari de

timp (o sptmni mai mult);posibilitatea vizualizrii grafice a rezultatelor;permite determinarea tuturor parametrilor de interes n

analiza armonic: amplitudinea i faza armonicii, dis-torsiunea armonic, puteri armonice etc., la sfritulfiecrui interval de msurare corespunztoare proba-

bilitilor de realizare de 50%, 95% i 99%, lasfritul intervalului de urmrire,

posibilitatea de fixare a curentului minim de sarcin(consum) de la care se face determinarea indicatorilorcaracteristici;

rangul armonicii pnla care se face analiza este 50; este accesibil din punctul de vedere al costului, are

dimensiuni reduse, este uor de utilizat.De remarcat faptul caparatul MOD permite determi-

narea puterii reactive Q conform definiiei Budeanu, casuma puterilor reactive pe armonicile kluate n considerare

=

=40

1

sink

kkk IUQ (4)

Valoarea Qastfel obinutpoate sdifere mult, n cazulregimurilor nesinusoidale, fa de valoarea puteriireactive Q definitca putere nonactivi indicatde uneleechipa-mente de monitorizare

22' PSQ = (5)

n care S este puterea aparent pe faz, determinatdin produsul valorilor efective ale tensiunii i curentuluielectric, iar puterea activPeste determinatca valoareamedie, pe fereastra de eantionare, a puterii instantanee.

Aparatul se poate conecta la un nivel ierarhic superiorn scopul descrcrii datelor prin intermediul unei interfeeEthernet 10MHz TP sau a unei interfee seriale RS-485/422.

Achiziia se face cu 256 eantioane/perioad pentrufiecare din cele 8 mrimi analizate.

Fereastra de eantionare, cuprinznd numrul deperioade consecutive achiziionate poate fi reglat la 8 sau16 perioade ale tensiunii de reea.

Intervalul de msurare, definit ca intervalul de timp ntredouachiziii necesare, este de 3s (dacintervalul de urm-rire este o orsau o zi) sau 10 minute pentru un intervalde urmrire de o sptmn.

Datele pot fi obinute:la cerere, pentru un interval de urmrire dat;opional, pe un interval de urmrire limitat, n care se

determini puterile active i reactive pe armonici.

The equipment MOD 108 has the following mainfeatures:simultaneous data acquisition on 8 channels (4 voltage

and 4 current);continuous measuring over large periods of time (one

week and more); graphic visualization of the data statistic processing

results;

determines all the parameters of interest in the harmonicanalysis: harmonic amplitude and phase, harmonicdistortion, harmonic powers etc., by the end of eachmeasuring term and their values corresponding to

performance probabilities 50%, 95%, and 99 %, bythe end of the monitoring term.

fixes the minimum load current (consumption) fromwhich the characteristic distorsion indicators aredetermined;

the harmonic rank up to which is performed the analysisis 50;

it is affordable in terms of cost, has small size, easy touse.

Mention is made that MOD equipment allows deter-mination of reactive power Q, according to Budeanudefinition, as sum of reactive powers on harmonics kconsidered

=

=40

1

sink

kkk IUQ (4)

The value Q obtained in this way may differ a lot, incase of nonsinusoidal loads, as referred to the reactive powervalue Q defined as nonactive power and indicated bysome monitoring equipment.

22' PSQ = (5)

where S is the apparent power on the phase, determinedfrom the product of the effective voltage and electric currentvalues, while the active power P is determined as averagevalue, on the sampling window of the momentary output.

The equipment can be connected with a higher hierarchiclevel in order to unload the data through Ethernet 10 MHzinterface or serial interface RS-485/422.

The acquisition is provided with 256 samples/periodfor each of the 8 values analyzed.

The sampling window, comprising the number of con-secutive periods acquired can be adjusted to 8 or 16 periodsof the supply voltage.

The measuring period, defined as the time periodbetween two necessary acquisitions, is 3s (if the monitoringperiod is one hour or one day) or 10 minutes for one weekmonitoring period.

The data can be obtained, as follows:by request, for fixed monitoring period;optional, for a limited monitoring period, during which

the active and reactive powers by harmonics are deter-mined too.

3. Analiza nesimetriei curbelor de tensiune i decurent electric

Existena unor definiii diferite pentru factorii de nesi-metrie necesitcunoaterea exacta relaiei utilizat nalgoritmul de calcul. n echipamentele de monitorizare

3. Analysis of Voltage & Electric Current Curves

Unbalance

The existence of various definitions for the unbalancefactors requires accurate knowledge of the relation usedin the calculation algorithm. In the monitoring equipment


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existente n Romnia pot fi ntlnite urmtoarele relaiiimplementate n algoritmul de calcul:factorul de nesimetrie negativpe armonica fundamen-

tal(conform IEC):

+

=

U

Uks , (6)

n care U +este componenta de secvenpozitiva tensiunii

(curentului), iar U

- componenta de secvennegativatensiunii (curentului).factorul de nesimetrie zero pe armonica fundamental

(conform CEI)

+=

U

Uks

00 (7)

n care U 0este componenta de secvenzero a tensiunii(curentului). factorul de nesimetrie pentru tensiunile intre faze

BCAB

BCABs

UaU

UaUk

=

2(8)

n care

3

3

2

1ja += ; (9)

factorul de abatere fade simetrie

medievaloarea

medievaloareadefatamaximaabaterea=ask ; (10)

factorul de nesimetrie a tensiunilor de faz

13

++

=

CBA

Abs UUU

Uk ; (11)

factorul de nesimetrie a tensiunilor ntre faze

+

=

1

1csk (12)

n care

( )( )2222

44463

CABCAB

CABCAB

UUU

UUU

++

++= ; (13)

factorul de nesimetrie a tensiunilor ntre faze

+

=

631

631dsk (14)

n care

( )2222444

CABCAB

CABCAB

UUU

UUU

++

++= ; (15)

factorul de nesimetrie a abaterilor fade valoarea medie

( )2223

2CABCAB

esk ++= (16)

n care

U

UU

U

UU

U

UU

CACA

BCBC

ABAB

med

medmed ;;

=

=

=

(17)

3medCABCAB UUUU

++=

operating in Romania, the following relations implementedin the calculation algorithm can be found: the negative unbalance factor on the fundamental

harmonic (as per IEC):

+

=

U

Uks , (6)

where U+ is the component of positive voltage (current)

sequence, while U

-

the component of negative voltage(current) sequence.the unbalance factor zero on the fundamental harmonic

(as per IEC):

+=

U

Uks

00 (7)

where U0 is the component of zero voltage (current)sequence.the unbalance factor for the voltage between phases:

BCAB

BCABs

UaU

UaUk

=

2(8)

where

3

3

2

1ja += ; (9)

the balance deviation factor:

medievaloarea

medievaloareadefatamaximaabaterea=ask ; (10)

phase voltages unbalance factor:

13

++

=

CBA

Abs

UUU

Uk ; (11)

factor of voltages unbalance between phases:

+

=

1

1csk (12)

where

( )( )2222

44463

CABCAB

CABCAB

UUU

UUU

++

++= ; (13)

factor of voltages unbalance between phases:

+

=

631

631dsk (14)

where

( )2222444

CABCAB

CABCAB

UUU

UUU

++

++= ; (15)

average value deviations unbalance factor

( )2223

2CABCAB

esk ++= (16)

where

U

UU

U

UU

U

UU

CACA

BCBC

ABAB

med

medmed ;;

=

=

=

(17)

3medCABCAB UUUU

++=


8/8


factorii de asimetrie i disimetrie, determinai pe bazaintervalelor de timp dintre trecerile prin zero (cu derivat

pozitiv) ale curbelor de tensiune sau curent electricanalizate.Aparatul MOD determinfactorii de nesimetrie negativ

i zero, conform CEI 61000-4-27/2000 pentru fundamental,dar oferi posibilitatea determinrii factorilor de asimetriei disimetrie, ncutilizai n practica curentdin Romnia.

Valorile determinate ale factorilor de nesimetrie negativi zero sunt afiate la sfritul fiecrui interval de msurare,sunt memorate i la sfritul intervalului de urmrire sunt

prelucrate statistic i afiate valorile cu probabilitate de50%, 95% i 99%.

the negative & zero unbalance factors, determined basedon time periods between passings through zero (with

positive derivate) of the voltage or electric current curvesanalyzed, taking as reference still phase A.MOD equipment determines negative and zero unba-

lance factors, as per CEI 61000-4-27/2000 for the fundamen-tal, but it also provides the possibility finding out thenegative & zero unbalance factors, still used in the current

practice in Romania.The determined values of the negative and zero unbalan-

ce factors are displayed by the end of each measuring period,stored and by the end of the monitoring period are sta-tistically processed and the values with probability 50%,95% and 99% are displayed.

4. Concluzii

Echipamentul MOD este realizat ca un echipament careasigurtoate informaiile necesare caracterizrii completea unui nod din reeaua electric, din punctul de vedere alregimului nesinusoidal i al regimului nesimetric.

Echipamentul este realizat conform recomandrilor CEI,

adoptate n Romnia ca standarde. Asiguri posibilitateadeterminrii unor mrimi suplimentare: unghiuri de defazaja armonicilor, puteri armonice (conform definiiei Budeanua puterii reactive), factori de asimetrie i nesimetrie, valoriutile n cadrul unor studii privind nodul analizat pentrucompararea cu valori anterior determinate i cu cele pre-vzute prin contracte.

Valorile stabilite la sfritul fiecrui interval de msuraresunt afiate pe ecranul echipamentului, iar la sfritul inter-valului de urmrire sunt afiate mrimi obinute n urma

prelucrrii statistice a datelor.Echipamentul a fost verificat cu ajutorul echipamentului

Fluke 6100 A.

4. Conclusions

MOD equipment is designed as a device that providesall information required by the complete characterizationof a node in the electric network, under nonsinusoidalcondition and unbalance condition.

The equipment is manufactured as per CEI recommenda-

tion, adopted in Romania as standards. It also provides thepossibility to ascertain additional values: phase differenceangles of harmonics, harmonic powers (according toBudeanu definition of the reactive power), negative andzero unbalance factors, values useful for studies regardingthe node analyzed for the comparison with values previouslydetermined and those provided through contracts.

The values ascertained by the end of each measuringperiod are displayed on the equipment screen (monitor),while by the end of the monitoring period are displayedthe values resulting from data statistic processing.

The equipment was checked by means of equipmentFLUKE 6100 A electrical power standard.

Bibliografie (References)

1. *** Compatibilitate electromagnetic. Tehnici de ncercare i msurare. Ghid general relativ la msurarea armonicilor iinterarmonicilor ca i la aparatele de msurare, aplicabil n reeaua de alimentare i pentru echipamentul conectat la aceasta(Electromagnetic compatibility. Testing and measurement techniques. General guide for the harmonics and interharmonics measurement,measuring apparatus as well, applicable in the supply network and the equipment connected with it), SR CEI 61000-4-30/2001.

2. *** Testing and measurement techniques.Power Quality Measurement Methods, CEI 61000-4-30/2000.3. *** Voltage characteristics of electricity supplied by public distribution systems, EN 50160/1999.4. *** Power Quality in European Electricity Supply Networks, Eurelectric 2002.5. *** IEEE Trial-use Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal,

Balanced, or Unbalanced Conditions, IEEE 1459/2000.6. *** Guide to Quality of electrical supply for industrial installations. Part 4. Voltage Unbalance. Working group WG 2 Power

Quality 1998

armonici_monitorizare

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