Measurement of Reactive Power in Three-Phase Electric Power Systems by Use of Walsh Functions

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1 87 JOURNAL OF COMPUERS VOL. 5 NO. 2 DECEMBER 2 Mesurement of Retive Power in hree-phse Eletri Power Systems y Use of Wlsh Funtions Adlet Aiyev Memer IEEE Girne Amerin University/Dertment of Eletril nd Eletronis Engineering RNC urkey Emil: iyev@gu.edu.tr Astrt his er resents new method for mesuring of three-hse retive ower (RP in three-hse systems. Extrtion of three-hse retive ower RP from entire instntneous ower signl is hieved y multilition the hse instntneous owers with the Wlsh funtion(wf. his method simlifies the multilition roedure required for the evlution the tree-hse retive ower omonents due to the use of the eulir roerties of the WF. In ontrst to the existing methods involving hse shift oertion etween the inut voltge nd urrent signls roosed mesurement roh does not require the hse shift of the hse urrent signls to the / 2 with reset to the voltge signls. Limittions nd roosls for future erformne enhnements of the suggested method re lso disussed. Vlidity nd effetiveness of the suggested method hve een tested y use of simultion tools develoed on the se of Mtl 6.5. he results otined demonstrte tht the omuttionl demnds n e sustntilly redued y using the roosed method. Index erms retive ower mesurement unlned three-hse systems nlog signl roessing DSP instntneous ower signl Wlsh funtion hse shift. I. INRODUCION Strong demnds to the eletril energy svings in the three-hse trnsmission nd distriutions systems require the effiient methods nd instrumenttions for urte evlution of RP drwn y the industril lods. he RP influenes diretly to the ower ftor nd s result overlods the trnsmission lines etween the eletril energy soures nd energy users nd lys vitl role in the stle oertion of ower systems [. he fundmentl ositive-sequene retive ower is of utmost imortne in ower systems euse it governs the fundmentl voltge mgnitude nd its distriution long the feeders nd ffets eletromehnil stility s well s the energy loss [2. Eletri ower distriution systems re hrterized y unlned oertion nd these hrteristis imose serious hllenges for the develoment of effiient omuttionl ower flow tehniques [3. When system is unlne the three urrent hsors do not hve equl mgnitudes nor re they shifted extly with reset to eh other [2. Lod unlne leds to symmetril urrents tht in turn n use voltge symmetry. here re situtions when the three voltge hsors re not symmetril. his leds to symmetril urrents even when the lod is erfetly lned [2. Moreover in unlned ower systems the RP my e used y the unlnes [4 nd the RP n e indutive or itive nd so n e dded or n omenste the trditionl retive ower due to the retnes. When there re unlnes t soures nd t lods in the sme time the RP n hve vlues different from zero even in resistive systems nd generlly when there is not ny symmetry in the system [4. Anlysis of the known sientifi reserh works onfirmed tht the vrious methods hve een develoed for three-hse RP mesurement in oth the sinusoidl nd noise(in resene of hrmoni distortion onditions. Most of the known reserh works re sed on the method of verging the vlue of the rodut of the urrent smles nd the voltge smles with shifting to the qurter one of the smles (urrent or voltge reltively to nother. Referene [5 demonstrtes n extension of the wvelet trnsform to the mesurement of RP omonent through the use of rod-nd qudrture hse-shift networks. his wvelet-sed ower metering system requires the hse shift of the inut voltge signl. In [6 the lition of new frequeny insensitive qudrture hse shifting method for retive ower mesurements hs een verified y using time-division multilier tye wttmeter. he hse shift oertion requires the orresonding hrdwire whih my result in the dditionl mesurement error [6. An eletroni shifter sed on stohsti signl roessing for simle nd ost-effetive digitl imlementtion of retive ower nd energy meter ws develoed in [7. A new lition of the lest error squres estimtion lgorithm for identifying the retive ower from ville smles of voltge nd urrent wveforms in the time domin for sinusoidl nd non sinusoidl signls is roosed in [8. In [9 different RP mesurement methods re desried. he ommon drwk of the desried methods is relted to the neessity of mesuring of the RMS vlues of the voltge nd urrent. he 2-Dimensionl digitl FIR filtering sed lgorithms for mesuring of the RP re roosed in [. he develoment of method using rtifiil neurl networks to evlute the instntneous retive ower is desried in [. In this method the k-rogtion neurl network is used to roximte the retive 2 ACADEMY PUBLISHER doi:.434/j

2 JOURNAL OF COMPUERS VOL. 5 NO. 2 DECEMBER 2 87 ower evlution funtion. In [2 the digitl infinite imulse resonse filters re used to mesure the retive ower. Although roosed lgorithm llows to evlute the hrmoni omonents of the RP the suggested method is still omlex euse the erforming of the filtering roedures. he Fourier trnsform (F sed digitl or nlogue filtering lgorithms llow the evlution of RP without shifting oertion ut lrge numer of multilition nd ddition oertions re required when lying F lgorithms for RP evlution. For exmle for 6 oint DF omlex multilitions nd omlex ddition oertions re required [3. he vrious lgorithms (for exmle FF known s the Cooley uky lgorithm hve een develoed to redue the numer of multilition nd ddition oertions y use of the omuttionl redundny inherent in the DF. Unfortuntely F sed lgorithms re still omuttionlly omlex. For unlned systems the symmetril omonents n e used nd the nlysis n e done sertely for the zero-sequene ositive-sequene nd negtivesequene networks[4 [5. Referenes [2 [6 suggest the ositive negtive nd zero sequene omonents evlution sed lgorithm for mesuring RP in threehse iruits. Min drwk of this lgorithm is relted to the omlex oertions required for evlution of voltge nd urrent symmetril omonents. In[7 the uthors hve nlyzed W lgorithms emloyed to energy mesurement roess nd they hve shown tht the Wlsh method reresents its intrinsi high-level ury due to oeffiient hrteristis in energy stirse reresenttion. Referene [8 sttes tht deimtion lgorithm sed on fst W(FW hs etter erformne due to the elimintion of multilition oertion nd low or omrle hrdwre omlexity euse of the FW trnsform kernel. In [ the WF sed existing RP mesurement lgorithm is ited. he si ide of this WF sed lgorithm onsists in the resolving of the voltge nd urrent signls sertely long the WFs t first nd then otining the RP s the differene of the roduts of the qudrture omonents. At lest four multilitionintegrtion two multilition nd one summtion oertions required for RP evlution mkes this lgorithm omrtively omlex nd less onvenient for imlementtion. In revious reserh works [9-[23 the WF sed RP mesurement method nd some sets of its reliztion [9 modified WF sed method for the mesurement of retive ower in sinusoidl s well s in noise onditions with the immunity to the distortion ower [2 new lgorithm for evlution the retive omonents from instntneous ower signl nd its reliztion on the eletroni elements [2 the effet of the hrmonis on the WF sed RP mesurement lgorithm nd rolems relted to the estimtion nd orretion of the error introdued y hrmonis [22 the signl roessing sed frequeny insensitive RP mesurement lgorithms involving eulir roerties of the WF[23 hve een investigted nd roosed. All of these methods nd lgorithms n e lied to oth the single-hse nd the lned three-hse systems. Mesurement of RP in unlned tree-hse systems hs own seifi eulirities. In unlned ower systems the RP my e used y the unlnes only nd the RP n e indutive or itive nd so n e dded or n omenste the trditionl retive ower due to the retnes. Moreover the RP n hve vlues different from zero even in resistive systems when there re unlnes t soures nd t lods in the sme time nd generlly when there is not ny symmetry in the system [4. ht is why the investigtions nd develoment of the RP mesurement methods nd lgorithms lile to the unlned three-hse systems re of the imortnt sientifi rolems. he min ontriution of this rtile is the develoment of the lgorithms for evluting the RP from instntneous ower signl in lned nd unlned three-hse systems using WF s therey voiding the hse shift oertion of / 2 etween the voltge nd the urrent wveforms in resetive hses of three-hse system. he ttrtion of WF sed roh to RP evlution in three-hse systems omes from the key dvntges suh s following[23: multilition oertion etween tow digitl is reled with the multilition oertion etween digitl nd ositive or negtive unit(+ or -. In other words the multilition oertion is erformed y simle ltering the sign of the given digitl from ositive to the negtive sign so tht to e multilied y -. hus the W nlyzes signls into retngulr wveforms rther thn sinusoidl ones nd is omuted more ridly thn for exmle FF [3. W sed lgorithm ontins dditions nd sutrtions only nd s result onsiderly simlifies the hrdwre imlementtion of RP evlution; requirement of IEEE/IEC definition of hse shift of / 2 etween the voltge nd the urrent signls tyil for retive ower evlution[6 is eliminted from signl roessing oertion. he er is orgnized s follows. In setion two derivtion of the WF sed nlogue signl roessing lgorithms for mesurement of RP in three-hse systems is desried. he simultion results nd disussions re given in the setion three. Setion four inludes the onlusion of the er. II. SIGNAL PROCESSING ALGORIHMS FOR HREE-PHASE RP EVALUAION In this setion we nlyze the RP lgorithms for the mesuring the RP in three-hse ower system. 2 ACADEMY PUBLISHER

3 872 JOURNAL OF COMPUERS VOL. 5 NO. 2 DECEMBER 2 A. Mesurement lgorithm for hse retive ower o otin the lgorithm for mesuring the retive ower in hse we multily oth sides of Eq. A9 (See Aendix y the third order WF [23 Wl ( 3. nd integrte over the eriod of ower system frequeny: Wl (3 Wl (3 his Eq. n e rewritten s Wl (3 Sine [23 [ P ( P os 2ωt + Q sin 2ωt Wl (3 P os 2ωt Wl (3 P Wl (3 Q sin 2ωt ( (2 Wl(3 P (3 os 2 Wl t P ω t (3 nd the (2 is rewritten s (See [23 for detils Wl (3 or [23 Wl (3 Q sin 2ω t (4 2 Wl(3 Q (5 Solution of this eqution for the hse fundmentl retive ower Q results in Q 2 Wl (3 B. Mesurement lgorithm for hse retive ower In se of hse we multily oth sides of Eq.(A4 (See Aendix y the third order WF nd integrte over the eriod of : Wl(3 Wl(3 Wl(3 [ P os 24 Q sin 24 [ Q os 24 + P sin 24 P Wl (3 os(2ω sin(2ωt Similr to the (3 we write (See [23 for detils (6 (7 nd Wl(3 Wl (3 t P [ P os 24 Q sin 24 os(2ωt Considering these in (7 we hve Wl (3 Wl (3 [ Q os 24 + P sin 24 sin( 2ωt Considering the solution of the right side integrl (See [23 for detilsof this Eq. we hve 2 Wl (3 24 [ Q os 24 + P sin Solution of this eqution for the hse RP in Q Wl (3 3P (8 Q results C. Mesurement lgorithm for hse retive ower For the hse we multily oth sides of Eq.(A9 (See Aendix y the third order WF nd integrte over the eriod : Wl(3 Wl(3 Wl(3 [ P os24 + Q sin 24 [ Q os24 P sin 24 Wl(3 P Similr to the Eq.(3 we write nd Wl(3 Wl (3 t P os(2ω sin(2ω (9 ( [ P os 24 + Q sin 24 os(2 Considering these the ( is rewritten s follows ω. 2 ACADEMY PUBLISHER

4 JOURNAL OF COMPUERS VOL. 5 NO. 2 DECEMBER Wl(3 Wl(3 t [ Q os 24 P sin 24 sin( 2ω (. Considering the solution of the right side integrl of this Eq. we hve 2 Wl(3 24 Solution of (2 for the hse RP [ Q os 24 P sin Q results in Q Wl(3 + 3P (2 (3 As seen from the right hnd sides of the (9 nd (3 evlution of the nd hse retive owers Q Q requires the nd hse tive owers P nd P resetively. o find the reltionshis etween the tive owers of P nd P nd the resetive instntneous owers of nd we multily oth sides of eh of the (A4 nd (A9 (See Aendix y the zero-order WF Wl ( nd integrte over the eriod of : Wl ( Wl ( Wl ( Wl ( Wl ( Wl ( [ P os 24 Q sin 24 [ Q os 24 + P sin 24 P Wl( [ P os 24 + Q sin 24 [ Q os 24 P sin 24 Wl ( P os(2ωt sin(2ω os(2ω sin( 2ωt (4 (5 Sine Wl ( equls to the + over the full eriod of the integrl terms on the right hnd sides of (4 nd (5 tht involve os 2ωt nd sin 2ωt onverge to zero(see [23 for detils. hus Wl ( PWl ( (6 Wl( P Wl( (7 king into ount the roerties of zero-order WF mentioned ove we get from (6 nd (7 the reltionshis etween the tive owers of P nd P nd the resetive instntneous owers of nd resetively: P Wl t ( (8 P Wl t ( (9 Sustituting the (8 nd (9 into the (9 nd (3 resetively we get the finl exressions for evluting nd hse retive owers Q nd Q s nd Q Wl t Wl t (3 3 ( (2 Q Wl t Wl t (3 + 3 ( (2 III. SIMULAION RESULS AND DISCUSSIONS A simultion iruit of the three hse retive ower mesurement instrument whih is sed on the roosed lgorithms given y (6 (2 nd (2 hs een uilt (Fig.. Simultion tests were imed t verifying (i the rtiility nd vlidity of the roosed lgorithms (ii n effet of the lod unlne on the ury of the RP mesurement results nd (iii the good erformne hrteristis of the mesurement instrument in wide rnge vrition of the unlned lod. Simultion exeriments hve een erformed y use of the tools of the Mtl 6.5. During simultion the line-to-neutrl voltges were tken s follows V 22 V V 22 2 V nd V 22 2 V. he unlned lod imednes hve een hnged to over the rnge of Z 3 + j2ω ; Z 5 + j5ω ; 5 + j6ω Z 2 + j5ω ; Z 2 + j6ω ; 8+ j3ω Z 25 + j4ω ; Z 2 + j5ω ; 4 + j3ω he simultion results re reresented on the les I II nd III. he true vlues of three-hse RP for the different lods hve een lulted y use of the lssil lgorithms [2 [3. Comrison the mesurement results otined y use of the roosed method with the true vlues shows tht the reltive error introdued y the roosed method is less thn.9%. Z Z Z 2 ACADEMY PUBLISHER

5 874 JOURNAL OF COMPUERS VOL. 5 NO. 2 DECEMBER 2 Figure. he simultion struture for the reliztion of the tive nd retive ower mesurement lgorithms. ABLE I HE SIMULAION RESULS OF RP EVALUAION ALGORIHMS : UNBALANCED LOAD PARAMEERS: Z 3 + j2ω ; Z 5 + j5ω ; Z 5 + j6ω Clssil formul Proosed method Phse A Phse B Phse C otl Phse A Phse B Phse C otl Error% Ative Power Retive Power ABLE II HE SIMULAION RESULS OF RP EVALUAION ALGORIHMS UNBALANCED LOAD PARAMEERS: Z 2 + j5ω ; Z 2 + j6ω ; Z 8 + j3ω By lssil formul By suggested method Phse A Phse B Phse C otl Phse A Phse B Phse C otl Error% Ative Power Retive Power ABLE III HE SIMULAION RESULS OF RP EVALUAION ALGORIHMS UNBALANCED LOAD PARAMEERS: Z 25 + j4ω ; Z 2 + j5ω ; Z 4 + j3ω By lssil formul By suggested method Phse A Phse B Phse C otl Phse A Phse B Phse C otl Error% Ative Power Retive Power ACADEMY PUBLISHER

6 JOURNAL OF COMPUERS VOL. 5 NO. 2 DECEMBER IV. CONCLUSIONS A vriety of methods to mesure the RP in the threehse systems were develoed. In resented method the requirement of IEEE/IEC definition of hse shift of / 2 etween the voltge nd the urrent signls tyil for retive ower evlution is eliminted from signl roessing oertion. hree hse RP is evluted without the hse-shift oertion to hieve inresed effiieny of omuttionl oertions nd hrdwre imlementtion; he multilition of the smle vlues of the instntneous ower signl y orresonding order WF is erformed simly y ltertion of sign of the signl smles from + to - only during even qurters of the inut signl eriods; Proosed lgorithms llow the mesurement of three hse ower in lned s well s in unlned three hse systems. he uthor is urrently working towrds the estimtion nd orretion of the highest order hrmoni distortions influene on the roosed three hse RP evlution lgorithms. APPENDIX. INSANANEOUS POWER IN HREE-PHASE UNBALANCED SYSEMS In three-hse unlned systems the three urrents I I nd I in resetive hses do not hve equl mgnitudes nor re they shifted extly with reset to eh other [2. he instntneous line-to-neutrl voltges v v nd v in the resetive hses re s follows: v v v 2V 2V 2V sin( ω (A where V V nd V re the rms vlues of the line to neutrl voltges for the hses nd resetively ω 2f is the ngulr frequeny in rd / s f is the frequeny in Hz. he line urrents i i nd i in the hses nd resetively re s follows: i i i θ θ 2 θ + 2. (A2 where θ θ nd θ re the imedne ngles in the hse nd resetively. he three-hse instntneous ower t is given y [2: v i + v i + v i (A3 t or + + (A4 t where re the resetive hse instntneous owers. A. Instntneous ower in hse Considering (A nd (A2 the hse instntneous ower is exressed s vi 2V sin( ω 2V I sin( ωsin( ωt θ θ A5 where I I nd I re the re the rms vlues of the line urrents in the hses nd resetively. Alying the trigonometri identity of 2sin α sin β os( α β os( α + β (A6 to the (A5 we hve V I os θ V I os(2ωt θ (A7 Sine os( 2ωt θ os 2ωt os θ + sin 2ωt sin θ (A8 the (A7 is dedued to V I osθ [ V I osθ os 2ωt + V I sin θ sin 2ωt his Eq. n e rewritten s P [ P os 2ω t + Q sin 2ωt (A9 where P VI osθ is the verge or tive nd Q VI sinθ the fundmentl retive ower resetively in the hse. B. Instntneous ower in hse An instntneous ower in hse is exressed y using (A nd (A2 s follows vi 2V 2 2 θ 2V I 2 2 θ (A Considering the trigonometri identity of (A6 in (A we hve V I [ osθ os(2ωt 24 θ (A V I osθ V I os(2ωt 24 θ Sine os(2ωt 24 θ os(2ωt 24 osθ + sin(2ωt 24 sin θ the (A is dedued to 2 ACADEMY PUBLISHER

7 876 JOURNAL OF COMPUERS VOL. 5 NO. 2 DECEMBER 2 [ P os( 2 t 24 + Q sin(2ω 24 P ω t (A2 where P V I osθ is the verge or tive nd Q V I sinθ the fundmentl retive ower resetively in the hse. Sine os( 2ω t 24 os(2ω os 24 + sin 2ωt sin 24 sin( 2ωt 24 sin(2ω os 24 os 2ωt sin 24 he (A2 is rewritten s P [ P os(2 os 24 + P sin(2ωt sin 24 [ Q sin(2ω os 24 Q os(2ωt sin 24 ω (A3 Grouing the right hnd side terms of (3 y os( 2ωt nd sin( 2ω we otin required exression for the hse instntneous ower s P [ P os24 Q sin 24 [ Q os24 + P sin 24 sin(2ωt os(2ω (A4 C. Instntneous ower in hse An exression for hse instntneous ower is derived in similr fshion to the hse ower. Using (A nd (A2 n instntneous ower in hse is exressed s v i 2V 2V I θ θ (A5 Alition the trigonometri identity of (A6 to (A5 results in V I osθ V I os(2ωt + 24 θ. (A6 Sine os(2ωt + 24 θ os(2ωt + 24 osθ + sin(2ωt + 24 sinθ the (A6 is dedued to [ P os( 2 t Q sin(2ω + 24 P ω t (A7 where P VI osθ is the verge or tive nd Q V I sinθ the fundmentl retive ower resetively in the hse. Sine os( 2ω t + 24 os(2ω os 24 sin 2ωt sin 24 sin( 2ω t + 24 sin(2ωt os 24 + os 2ωt sin 24 the (A7 is rewritten s follows P [ P os(2ω os 24 P sin(2ωt sin 24 [ Q sin(2ω os 24 + Q os(2ω sin 24 (8 Grouing the right hnd side terms of (3 y os( 2ωt nd sin( 2ω we otin required exression for the hse instntneous ower s P [ P os 24 + Q sin 24 [ Q os 24 P sin 24 sin(2ωt os(2ωt (A9 he derived equtions (A9 (A4 nd (A9 exress the instntneous ower in the resetive hses of threehse unlned system. REFERENCES [ Firney W. Retive ower-rel or imginry? Power Engineering JournlVolume 8 Issue 2 Aril [2 IEEE Std IEEE ril Use Stndrd Definitions for the Mesurement of Eletri Power Quntities Under Sinusoidl Non-Sinusoidl Blned or Unlned Conditions Institute of Eletril nd Eletronis Engineers / -My-2 / 52 ges. [3 Jmes W. Nilsson Susn A. Riedel. Eletril Ciruits. 7th Edition. Prentie Hll. 25. [4 Viente León-Mrtínez Joquín Montñn-Romeu José Giner-Grí Antonio Czorl-Nvrro José Roger-Folh Mnuel A. Grñ-Lóez Power Qulity Effets on the Mesurement of Retive Power in hree-phse Power Systems in the Light of the IEEE Stndrd he 9 th Interntionl onferene. Eletri ower qulity nd Utilistion Brelon 9- Otoer 27. [5 W.-K. Yoon nd M.J. Devney. Retive Power Mesurement Usinq the Wvelet rnsform IEEE rns. Instrum. Mes.vol Aril 2. [6 Brnislv Djoki Eddy So nd Petr Bosnjkovi. A High Performne Frequeny Insensitive Qudrture Phse Shifter nd Its Alition in Retive Power Mesurements IEEE rns. Instrum. Mes.vol Ferury 2. [7 S.L.orl J.M.Quero nd L.G.Frnquelo. Retive ower nd energy mesurement in the frequeny domin using rndom ulse rithmeti IEE Pro.-Si. ehnol. vol. 48 No Mrh 2. [8 Solimn S.A. Almmri R.A. El-Hwry M.E. Mostf M.A. Effets of hrmoni distortion on the tive nd retive ower mesurements in the time domin: single hse system Power eh Proeedings 2 IEEE Porto Volume -3 Set [9 Mundy M. Hrt D.G. Methods for eletri ower mesurements IEEE Power Engineering Soiety Summer Meeting Vol July 22. [ M. Kezunovi E. Soljnin B. Perunii S. Levi New roh to the design of digitl lgorithms for eletri ower mesurements IEEE rns. on Power Delivery vol. 6 No Ar. 99. [.W.S.Chow nd Y.F.Ym. Mesurement nd evlution of instntneous retive ower using neurl networks IEEE rnstions on Power Delivery Vol. 9 No. 3 July [2 Ozdemir nd A. Ferikoglu. Low ost mixed-signl miroontroller sed ower mesurement tehnique IEE Pro.-Si. Mes. ehnol. Vol. 5 No. 4 July [3 Emmnuel C. Ifehor Brrie W. Jervis. Digitl Signl Proessing. A rtil Aroh. Seond Edition. Prentie Hll22. 2 ACADEMY PUBLISHER

8 JOURNAL OF COMPUERS VOL. 5 NO. 2 DECEMBER [4 H. Wyne Bety. Hndook Of Eletri Power Clultions. hird Edition MCGRAW-HILL 2. [5 Mohmed E. El-Hwry. Eletril Energy Systems. 2 y CRC Press LLC. [6 J.-C.MontRo nd PSImeron Identifition of instntneous urrent omonents in three-hse systems IEE Pro.-Si. Mes. ehnol. Vol. 46 No. 5 Setemer [7 Brndolini A. Gndelli A. Veroni F. Energy meter testing sed on Wlsh trnsform lgorithms Instrumenttion nd Mesurement ehnology Conferene 994. Conferene roeedings -2 My vol.3. [8 Bi liyun Wen iyng Shen wei nd Wn xinrong. Smle rte onversion using Wlsh-trnsform for rdr reeiver Mirowve Conferene Proeedings 25. APMC 25. Asi-Pifi Conferene Proeedings.Volume 4-7 De [9 Aiyev R H. Aiyev A. N. Kmil D. he Wlsh Funtions Bsed Method for Retive Power Mesurement Proeedings of the 33rd Annul Conferene of the IEEE Industril Eletronis Soiety (IECON'7 iei iwn Nov [2 Adlet N. Aiyev A new signl roessing tehnique for evlution of the retive ower in the ower trnsmission nd distriution systems in Proeeding of Southeston 28 IEEE Hntsville AL USA. Aril [2 Adlet N Aiyev A new eletroni retive ower meter sed on Wlsh rnsform lgorithms in Proeeding of IEEE rnsmission nd Distriution Conferene nd Exosition 28 (&D. IEEE/PES Chigo IL USA Aril [22 Adlet N. Aiyev Kmil Dimililer Retive Power Mesurement in Sinusoidl nd Nonsinusoidl Conditions y Use of the Wlsh Funtions in Proeedings of I 2 MC 28 - IEEE Interntionl Instrumenttion nd Mesurement ehnology Conferene Vitori Vnouver Islnd Cnd My [23 Adlet Aiyev A New Signl Proessing sed Method for Retive Power Mesurements Journl Of Comuters vol. 4 no Adlet Aiyev ws orn in Azerijn in 952. Reeived Eletril Engineer degree nd Ph.D degree in Eletril nd Eletroni Engineering in 975 nd 986 resetively oth from the Azerijn Stte Oil Ademy(ASOA. From 986 to 99 he ws ssistnt rofessor nd then from 99 to 25- ssoite rofessor t the dertment of Automtis Remote Control nd Eletroni of ASOA. From 26-resent he is working s ssoite rofessor t the dertment of Eletril nd Eletroni Engineering of the Girne Amerin University. His reserh interests re eletroni ower mesurements nlogue nd digitl signl roessing testing nd dignosing of indution motors during mss rodution. Dr. Aiyev is the memer of IEEE hs ulished two ooks nd more thn 8 sientifi ers in the eletril nd eletronis engineering fields. 2 ACADEMY PUBLISHER