FFT Based Spectrum Analysis of Three Phase Signals in Park (d-q) Plane

Transcription

1 Proceedngs of the 00 Internatonal Conference on Industral Engneerng and Operatons Management Dhaka, Bangladesh, January 9 0, 00 FFT Based Spectrum Analyss of Three Phase Sgnals n Park (d-q) Plane Anuradha Guha, and Surajt Chattopadhay Electrcal Engneerng Department Hooghly Engneerng & Technology College West Bengal, Inda Samarjt Sengupta Department of Appled Physcs Unersty of Calcutta, Kolkata-9, Inda Abstract In ths paper, spectrum produced by a balanced three phase sgnals and ther consequent form n Park (d-q) plane has been analyzed. The spectrums show that the peaks of the dfferent orders of spectrums hae changed after Park Transformaton. Thus well renowned Park transform technque s ntroducng the new spectrum. The spectrum characterstcs of sgnals from a balanced system n Park doman hae been analyzed. Obseraton reeals the wdenng nterrelaton among the spectrums. Key words FFT based spectrum, FFT, Park Doman, Park Transformaton. Introducton Modern machne and power system desgnng technologes hae ntroduced aretes of new rotatng machnes and dfferent desgnng methods. Dfferent mathematcal models hae been ntroduced to study ther performance. A lot of research works are gong on to study the system performance wth respect to dfferent reference frame. Some of them are statonary some others are rotatng. Such a reference frame s Park Frame consstng of d, q and 0 axes []. Dfferent models hae been deeloped wth respect to ths reference frame. Normal poly phase sgnals are transformed nto ths frame wth the help of Park transformaton matrx. Ths matrx and the frame hae been wdely used n the study of system performance and power qualty assessment. Harmonc assessment n qualty study s done wth the help of spectrum analyses of a sgnal. In ths regard dfferent mathematcal tools hae been ntroduced []-[6]. One of the commonly used technques s FFT []-[8]. In some recent research work, Park transformaton has been used along wth the FFT n power qualty assessment. The use of Park transformaton n power qualty assessment has rased a queston whether the transformaton method s tself ntroducng some qualty related problems [], []. Here an attempt has been taken to study the changes of spectrums obtaned from Fast Fourer Transform, n Park doman and to compare the result wth the spectrums obtaned n phase plane.. Theoretcal Background Park plane s used to assess three phase sgnal wth respect to a non statonary reference sgnals rotatng at synchronous speed. Sgnals n Park planes are obtaned from three phase sgnals multpled by Park transformaton matrx as pctorally shown n Fgure. Fgure : Park Transformaton

2 The method s well used n performance analyss of both three phase power system and three phase rotatng machne. Voltages and currents n Park Doman can be dered from phase oltage multplyng by Park transformaton matrx as follows = B Y R q d sn sn sn 0 () Smlarly, currents n d-q plane can be wrtten as = B Y R q d sn sn sn 0 () In general, [ ] [ ] [ ] ThreePhaseSgnals ParkTransformaton Matrx nparkplane Sgnals =. Computer Smulaton In computer smulaton, as shown n Fgure, a dscrete - phase programmable source has been consdered. Three phase sgnals hae been take and ther spectrums hae been obtaned wth the help of Fast Fourer Transform. Then the sgnals are transformed nto Park doman usng Park transformaton matrx, wherefrom d and q axes sgnals are obtaned. Then FFT based spectrums are obtaned usng these sgnals. A comparate study has been made among the spectrums of d-axs, q-axs and other three phase sgnals. Fgure : Smulated network. Smulated Results Ampltude of the phase sgnals hae been ncreased and transformed n Park Doman. Then spectrums of d-axs and q axs sgnals are obtaned. Some such spectrums are presented n tabular form n Table. Three parameters FPP, SPP and NP hae been ntroduced to express the peaks of each spectrum, FPP sgnfes frst poste peak, SPP sgnfes second poste peak and NP sgnfes negate peak. Values of FPP, SPP and NPP of the phase a, phase b, phase c, d-axs and q-axs sgnals are presented n Table,,, 5 and 6 respectely.

3 Table : FFT based Spectrum n Park plane Ampltude d axs Spectrum q axs Spectrum Table : Data of FFT base spectrum of oltage of phase a Table : Data of FFT base spectrum of oltage of phase b

4 Table : Data of FFT base spectrum of oltage of phase c Table 5: Data for spectrum n d axs Table 6: Data for spectrum n q axs 5. Obseraton Tables -6 show that the spectrums are changng wth respect to the change of ampltude of the sgnals. Change of FPP, SPP and NP of the frst spectrums wth respect to the araton of ampltude are plotted n Fgures and. The obseraton are summarzed as Change of peaks are lnear The dstance between the peaks are ncreasng wth the ncrease of ampltude. Peaks of d axs sgnals are always ncreasng n nature. Fg. shows that peaks of q axs sgnals are decreasng up to certan ampltude of the phase sgnals. The Fg. shows that peaks of q-axs sgnals are ncreasng agan wth the ncrease of ampltude of phasesgnals. The most mportant obseraton s obtaned from the spectrum comparson among phase sgnals from Table, and wth the spectrum of d-q sgnals. It s seen that the hgher order spectrums n phase sgnals are zero where as Park doman sgnals (d and q axes sgnals) contan consderable amount of hgher order spectrums.

5 Fgure : Frst spectrums ersus ampltude of range n Park Doman Fgure : Frst spectrums ersus ampltude of range 0.0-0,000 n Park Doman 6. Concluson The obseraton shows that the nature of spectrums of d axs sgnals and q axs sgnals are dfferent. Secondly some consderable amount of hgher-order-spectrums s obsered to be ntroduced after Park transformaton, whch should be taken nto consderaton n performance analyss and power qualty assessment n Park doman. The man cause of hgh order spectrum ntroducton after Park transformaton may or may not be due the transform method but more research should be done to fnd out the answer.

6 Reference. Surajt Chattopadhyay, Madhuchhanda Mtra, and Samarjt Sengupta, Harmonc Analyss n a Three-Phase System usng Park Transformaton Technque, AMSE perodcal-a, on modelng and smulaton, France, Surajt Chattopadhyay, Madhuchhanda Mtra, and Samarjt Sengupta, Power qualty analyss n park plane, Best of 006-olume on modelng and smulaton, AMSE(France), 006. C. Lguor, Uncertanty on sgnal parameter estmaton n frequency doman, Proc. th IMEKO TC-, pp , 00.. G. Betta, M. D Apuzzo, C. Lguor, and A. Petrosanto, An ntellgent FFT-analyzer, IEEE Trans. Instrum. Meas., ol. 7, pp. 7 79, Oct R. I. Becker and N. Morrson, The errors n FFT estmaton of the Fourer transform, IEEE Trans. Sgnal Processng, ol., pp , Aug N. B. Lawrence, "Extenson of the fast Fourer number theoretc transform to multde radx wth radar applcatons", Ph.D. dssertaton, The Unersty of Alabama n Huntslle, R. Adham and R.J. Polge, "Fast Fourer transformatonbased on number theoretc transforms", Journal of Frankln Insttute. Vol. 5, No. 5, pp. 5757, R. Adham, "Spe'ctral analyss usng ncrrber theoretc transforms wth fast Fourer transforc: mplementaton", Ph.D. dssertaton, The Unersty of Alabama n Huntslle, C. Wensten and A. Oppenhem, Effects of Fnte Regster Length n Dgtal Flterng and the Fast Fourer Transform, Proceedngs of IEEE, ~0.60p, p , 97.