Remote Assessment & Monitoring of Flicker Indices in a Large Power System

Transcription

1 emote Assessment & Montorng of Flcker Indces n a Large Power System M.MAZADI, S.H.HOSSEINIAN Department of Electrcal Engneerng Amr-Kabr Unversty of Technology (Tehran Polytechnc) Hafez Ave., P.O.Box 594 TEHAN, IAN Abstract: - In a deregulated electrcty ndustry, new concerns have emerged regardng the qualty of power supply as each company nvolved wll focus on ts own objectves and nterest. One of the man concerns regardng the qualty of power supply s the voltage fluctuaton. Ths paper addresses a method for montorng the voltage flcker usng state estmaton (FSE). The method s based on WLSM (weghted least squares method) of voltage. IEEE 4 bus grd s consdered as the test network for the valdaton of the new FSE algorthm. The new FSE algorthm can be used by operators as well as dstrbuton companes to montor the flcker severty throughout the network. Key-Words: - Power Qualty, Voltage Flcker, Flcker-meter, State Estmaton Introducton Power qualty montorng s necessary to characterze electromagnetc phenomena at a partcular locaton on a power system. In some cases, the objectve of the montorng s to dagnose the ncompatbltes between electrc power source and load. In stll others, montorng may be used to predct the future performance of load equpment or power qualty mtgatng devces, however there are several mportant reasons to power qualty montorng. The prmary reason underpnnng all others s economc, partcularly f crtcal process loads are beng adversely affected by electromagnetc phenomena. Effects on equpment and process operaton can nclude dsoperaton, damage, process dsrupton and other such anomales. Such dsruptons are costly snce a proft-based operaton s nterrupted unexpectedly and must be restored to contnue producton. In addton equpment damage and subsequent repar cost both money and tme. Product damage can also result from electromagnetc phenomena requrng that damaged product ether recycled or dscarded, both of whch are economc ssues. In addton to resolvng equpment dsrupton, a database of equpment tolerances and senstvty can be developed from montored data. Such a database can provde a bass for developng equpment compatblty specfcatons and gudelnes for future equpment enhancement. As per most power contracts, power qualty ndces such as flcker and harmonc shall be mantaned n an acceptable range. In partcular flcker and harmoncs are of real concern to utltes when other consumers are nearby and can be adversely affected. Sources of voltage flcker are numerous. Arc furnaces and arc welders head the lst. Motor startng, fans, pumps, elevators and swtchng of power factor capactor are among the most common cause of voltage flcker. Cyclc voltage flcker exst when there s a slow change n the voltage magntude wth frequences between 0.5 to 30 Hz whch appears as a supermposed sgnal on the fundamental sgnal. The supermposed sgnal, whch s generated due to the voltage flcker, appears as a change n fundamental sgnal envelope and s commonly known as Instantaneous Flcker Level (IFL). Many technques were proposed n lterature for the evaluaton of flcker level such as FFT technque [], least absolute value LAV sate estmaton [2, 3], wavelet [4, 5]. Leakage effect error s one of the major problems assocated wth FFT applcaton. As the system frequency devates from the nomnal value, the leakage effect error may be very serous To overcome such dsadvantage wavelet transform were proposed. LAV method proposed the applcaton of a least absolute value state estmaton to measure voltage flcker magntude and ts frequency. The models presented n the references are a lnear model of voltage flcker magntude, ts phase angle and frequency devaton. Lnearzng the system equaton may lead to naccurate result n envronments wth hgh nose and bad data. Envelope trackng were proposed n [6], [7], [8] usng ADALINE, Genetc algorthm and Teager

2 Energy Operator (TEO). These methods suffer the senstvty to hgh frequency components (TEO) or hgh computatonal burden (GA and ADELINE). After all none of the above mentoned references provde Pst (Short term flcker level) and Plt (Long term flcker level) ndces that are more useful n flcker assessment and montorng rather than flcker magntude and ts frequency. In order to have an accurate montorng of power qualty ndces, some measurements from grd are strongly requred, however full measurement of the system states and extractng flcker ndces and sendng them to central control room, s prohbtve for a large system. Ths s why state estmaton can be wdely used to alter raw measurements to precous database. State estmaton has been played a bg role n power flow studes snce the late 960s. It s now an essental part n energy management system. ecent contrbutons [9-2] have extended the concept to harmonc state estmaton (HSE) and dentfcaton of harmonc sources. Many of power qualty ndces such as Pst and Plt are combnaton (often weghted) of ndvdual states and are not suted to drect state estmaton. Instead only harmonc (or nter-harmonc) or nstantaneous voltage and current are normally state estmated and those ndces are then calculated from these estmates. Ths paper presents the FSE technque for the on-lne assessment of voltage flcker. The framework of flcker state estmaton s llustrated n Fg.. On the bass of the network topology, an nstantaneous state estmator s formulated from the system admttance matrx n tme doman and the placement of measurement ponts. Measurement of nstantaneous voltage and current at selected bus bars and lnes are sent to a central workstaton for the estmaton of bus voltages. These estmated voltages then appled n a flcker-meter software to extract Pst and Plt [3]. Measurement placement shall make all the buses observable. The mplementaton of ths technque wll, n practce, be lmted by poor synchronzaton and accuracy of conventonal nstrumentaton scheme, lack of contnuty of measurement or lack of processng speed. The FSE can be mplemented contnuously n real tme f the measurement s contnues and the processng speed fast enough. Potentally, the measurements nstruments and estmator can then be ntegrated nto one exstng supervsory control and data acquston (SCADA) system. The performance of the proposed technque s tested by IEEE 4 bus sample grd. esults are obtaned and dscussed. Ths paper s dvded nto fve sectons. State estmaton s ntroduced n secton 2. Buldng up the measurement matrx s demonstrated n secton 3. The example s gven n secton 4. Fnally, secton 5 concludes the paper. Network Topology Admttance Matrx Power System State Estmator Flcker-meter Pst&Plt Synchronzed measurements of nstantaneous voltage & current Fg. Framework for flcker state estmaton 2 Measurements and State Varable Model The task of state estmaton s to generate the best estmate of voltage from lmted measured lne currents or bus voltages, corrupted wth measurement nose. The three ssues nvolved are the choce of state varables, some performance crtera and the selecton of measurement ponts and quanttes to be measured. State varables are those, f known, completely specfy the system. The nstantaneous voltages at all buses are chosen, snce they allow all branch currents, shunt currents to be determned. Varous performance crtera are possble; the most wdely used beng the Weghted Least Squares (WLS). Ths method mnmzes the weghted sum of the squares of the resduals between the estmated nstantaneous voltage and actual voltage measured. Ths can be shown to be the maxmum lkelhood estmate assumng that the nose dstrbuton s Gaussan. For a gven

3 measurement set and system topology, the basc crcut laws lead to the followng measurement equaton: Z = h(x) + ε () T Mnmze J ( x) = [ Z h( x)] [ Z h( x)] (2) 2 Where Z and x are the vectors of measurements and state varables, respectvely, and ε s the measurement error vector whch s assumed to be made of ndependent random varables wth Gaussan dstrbuton. Although n general, the measurement equaton can be nonlnear, by choosng the bus voltages as state varables and real and reactve power as measurements, lne currents and bus voltages measurements make Equaton() lnear. In ths case, the task of estmatng x gven Z measurements n the presence of nose ε s expressed as: Z = [ h] x + ε (3) In whch [h] s the measurement matrx. State estmaton can be classfed as over-determned, completely determned or under-determned on whether the number of ndependent measurement equaton are greater, equal or less than the number of unknown state varables. A unque soluton (Equaton 4) s only possble for over determned and completely determned systems. est T T meas x = [[ h] [ ][ h]] [ h] [ ] Z (4) Matrx s a dagonal and contans the covarances of the measurements (f they are known). Ths permts applyng hgher weghtngs to measurements that are known to be more accurate. The measurement matrx [h] has more rows than columns but [ h] T [ ][ h] (known as the gan matrx) s a square matrx and can be easly solved usng standard technques. If not solved, there s a non-observablty for gven measurements. 3 Buldng up the Measurement Matrx Each lne current measurement adds a row to the measurement matrx. The measurement for a lne connected between buses and j, as shown n Fg.2 has two possble non-zero entres. Quanttes beng measured (n ths case lne current) are themselves functons of other varables that we wsh to estmate (n ths case bus voltage). If the sendng-end lne current s measured then: ( t) = ( t) ( t) (5) s c + L c s t = 2 + α + α ( ) ( + ) v ( t) ( ) vj( t hc + hl ( + α) ) + ( + α) + ( + α) (6) In whch hc, hl are hstory terms of capactve and nductve components of the lne respectvely and α s the compensatng factor that shows how much the ntegratng method s close to Euler( α = )or Trapezodal ( α = 0 )rule wth Sample tme t. hc, hl can be calculated as follows: 2c α hc = v ( t ) c( t ) (7) ( + α) + α ( α) α ( ( ) ( )) t hl = v t v j t + L( t ) + ( + α) + ( + α) (8) Fg2. Tme doman equvalent of a branch Equaton (6) can be wrtten for all branches and shown n matrx form as below: I s( t) = hv ( t) + I hst (9) If there are Nm measurements and N s states (bus voltage) then I s (t) s a Nm vector of measurements, h s a N m Ns measurement matrx, V (t) s a N s vector of bus voltages and I hst s a Nm vector of hstory term combnaton. Now equaton (9) s the same as equaton (3) and bus voltages can be calculated by equaton (4).

4 4 Numercal Example IEEE 4-bus grd s used as an example. Data can be found n ef. [4]. Fg.3 shows the grd wth measurement n all sendng-end of the lnes. Voltage of bus s measured as well as 7 current measurements. One of the transformers between buses 4 and 9 s gnored for smplcty and as a result 4 buses are reduced to 2. Actual values are gathered from smulaton of the grd n tme doman wth tme step 0. m-sec for 0 mnutes. As per standard, ths tme nterval s requred for Pst calculaton. Arc furnace s modeled as a varable current source as n Equaton 0 and connected to bus 0. f ( t) = ( cos( ω f t)) cos( ωt) (0) In whch ω f = 2 π 9 andω = 2 π 50. These values are optonal and can be changed by user. esult from the smulaton were used at the measurement locaton and suppled to FSE algorthm. All measured quanttes are then polluted wth Gaussan nose wth zero mean and 3 σ = 0.% and appled n state estmaton. Measurement matrx [h] s constructed by means of grd data andα = Ths factor shows that the ntegratng method s closer to Trapezodal method rather than Euler for more accurate results. Equaton (9) s wrtten for all the branches. The FSE estmated the unmeasured quanttes to be compared wth the exact soluton. As t s clear only 2 measurements would be enough to determne the bus voltages however the more measurements would result n the more accurate values. The estmated nstantaneous voltages are then fed to flcker-meter smulaton n order to obtan IFL. Flckermeter has two man tasks, frst to classfed flcker sensaton levels accordng to ther value, thus obtanng ther frequency dstrbuton, second to establsh cumulatve probablty functon (CPF) when the observaton perod expres. Ths method has been called Tme at level classfcaton. The foundaton of the CPF concept s that tme at a gven level (class) gves the more useful ndcaton. Class wdth can be selected by user n both smulaton and real flckermeter. Here t s consdered to be 0.. For the mentoned locaton of measurements, the results of the smulaton are shown n Fgures 4 to 7. Fg3. IEEE 4-Bus as the test system Whle maxmum voltage error n Fg.4 s under 3.5%, IFL s oscllatng n the class between 0.4 and 0.5. eal and estmated IFL n bus 6, are compared n Fg.5. Estmaton has been done n two dfferent stuatons, wth and wthout measurement nose. The dfferences between real and estmated values are due to the appled nose and the ntegratng method; however values are stll n the same class. Beng n the same class, causes the CPF (Cumulatve Probablty Functon) of the real and estmated IFL to be smlar as t s shown n Fg.6. Ths fgure shows that each class s exceeded wth correspondng probablty. The dfference s n class 6; however ts probablty s less enough and does not affect the Pst values largely. Fg.7 shows the P st n all the network buses. Bus 0 experences hgher Pst snce arc furnace s there. Buses 7 and 9 are n adjacent and suffer next. Buses, 2, 3, 4, 5 are n safe area. Plt, whch s a Pst average n 2 hours, also can be calculated f measurements are contnuously avalable.

5 Maxmum Error IEEE4 nose free wth nose Nose free eal Wth nose Pst IEEE Error Pst Bus Bus Fg4. Maxmum Error n voltage Fg7. Pst comparson n all grd buses Ampltude Nose Free eal Wth nose IFL Bus6 IEEE4 Wth Nose Nose Free eal In comparson to other methods, t s clearly observed that computaton burden s very lght. Because recevng end of each branch has not been consdered and only sendng end was consdered. Ths reduces the number of nvolved equatons; though they may lead to more accurate soluton. Not any flcker model or any arc furnace model s requred, besdes no Lnearzng s mposed nto equatons. Probablty tme(msec) x Fg5. IFL comparson n Bus 6 eal Nose Free CPF Bus6 IEEE4 Wth nose Class Fg6. CPF comparson n Bus 6 5 Concluson In ths paper a new technque for wdely flcker montorng n a large power system has been proposed. Flcker ndex Pst was calculated usng nstantaneous voltage n a large power system. By means of lne current measurements and state estmaton method (WLSM), nstantaneous voltage was estmated. These estmated values are then appled to flcker-meter to extract Pst n all the network buses. No flcker model s requred n ths technque and t s sutable for every knd of flcker dsturbance. esults show that the Pst can be estmated accurately whle computatonal burden s less than smulaton. Besde, not any knd of Lnearzng has been consdered. eferences: [] K.Srnvasan, Dgtal Measurement of Voltage Flcker IEEE Transacton on Power Delvery, Vol.6, No.4, 99, PP [2] A.Grgs, J.W. Stephan, E.Makram Measurement and Predcton of Voltage Flcker Magntude and Frequency IEEE Transacton on Power Delvery, Vol.0, No.3, July995, pp

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