Three-phase Magnitude-phase Detection Based on T/4 Time-lapse Elimination Method

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1 JOURNAL OF SOFWARE, VOL. 9, NO., FEBRUARY hree-phase Magitude-phase Detectio Based o / ime-lapse Elimiatio Method Xiaoyig Zhag School of Electrical ad Iformatio Egieerig, Lazhou Uiversity of echology, Lazhou, Chia zhy55@gmail.com Zheg Jiag School of Electrical ad Iformatio Egieerig, Lazhou Uiversity of echology, Lazhou, Chia oweroger@163.com Nig Dig School of Electrical ad Iformatio Egieerig, Lazhou Uiversity of echology, Lazhou, Chia d @163.com Abstract Affected by the egative sequece compoet ad harmoic compoet of three-phase grid, the covetioal three-phase software phase-locked loop (SPLL circuits were uable to etract the magitude-phase iformatio of three-phase fudametal positive sequece compoet accurately, ad the dyamic respose speed was slow. I order to solve this problem, this paper itroduces / time-lapse elimiatio detectio, a ovel method of detectig three-phase magitude-phase based o double d-q sychroous referece frame, fuctioig i decouplig positive ad egative sequeces of fudametal wave. Whe the voltage (or curret fudametal positive ad egative sequece compoets are separated, the positive sequece compoet as well as the magitude ad phase positio of egative sequece compoet from three-phase fudametal ca be detected, so it is effective to restrai the impact o detectio precisio from egative sequece compoet. o verify the performace of this ovel method, simulatio eperimets like trasiet respose uder ormal grid coditio, dyamic respose uder three-phase ubalace with harmoic pollutio coditio ad dyamic respose uder phase jump coditio are carried out. he simulatio results verify that the proposed method overcomes the shortcomig of covetioal three-phase phase-locked loop ad tracks accurately the magitudes ad phases of the foudatioal positive-sequece voltage uder harmoic pollutio coditio. Ad the results also verify that the proposed method ca suppress odd harmoic propagatio ad has a higher detectig precisio comparig with /16 time-lapse elimiatio method. he improved / time-lapse elimiatio detectio ca be wildly applied i three-phase power electroic devices. Ide erms magitude-phase detectio; / time-lapse elimiatio; three-phase ubalace; d-q trasformatio; software phase-locked loop. I. INRODUCION Voltage coverter based FACS (Fleible Alterative Curret rasmissio System devices eed sychroizatio with power grid, ad they detect the positive sequece compoet ad egative sequece compoet at all times. he egative sequece compoet i real time is required i trasformer protectio ad motor protectio. o improve the ruig capacity of large grid-coected wid geeratio system, the frequecy, phase positio ad magitude of the power grid must be detected accurately ad quickly [1, ]. Due to most devices coect to the three-phase grid, three-phase phase lockig ad magitude detectio are especially sigificat. I aterior refereces, sigle phase phase-locked loop adopts hardware phase-locked method [3], trackig the phase positio of power grid through zero-cross detectio, but it is hard to use where harmoic pollutio is heavy. At the momet, three-phase software phase-locked loop (SPLL is widely spread ad applied, ad SPLL improves the importace of detectig magitude to the same positio as trackig phase positio [-10]. But affected by egative sequece ad harmoic compoets, the phase-locked system eeds select steady-state accuracy. So reducig the cut-off frequecy of the loop filter is the mai process, but it badly impacts the system dyamic respose [7, 11]. o solve this problem, refereces [10, 1-1] offer modified three-phase SPLL system structures; also, refereces [15-19] improve the PI cotroller of ordiary three-phase SPLL structure, presetig various plas of cotroller desig ad parameter tuig. Besides, referece [0] itroduces least squares to detect the three-phase voltages positive sequece phase positio; referece [1] adopts chirp-z trasform method ad referece [] gives out a three-phase magitude-phase-lock loop system based o eteded variable step size least mea square algorithm. Some refereces idicate that the previous three-phase phase-locked loop has bee improved, but the dyamic respose speed of grid ubalace disturbace is still greater tha 1.5 frequecy period [1-18]; although the dyamic respose of least squares is fast, harmoic has a big impact o the steady accuracy; although Chirp-Z trasform method is better tha the frequecy-domai aalysis result of DF(Discrete Fourier rasform, the steady-state performace of trackig lie frequecy is 01 ACADEMY PUBLISHER doi:10.30/jsw

2 5 JOURNAL OF SOFWARE, VOL. 9, NO., FEBRUARY 01 worse tha modified SPLL [11], ad the eteded variable step size least mea square algorithm method requires much iterative process, so the calculatio amout is large. his paper, based o dual d-q trasformatio, itroduces a ovel process to detect the three-phase magitude ad phase of the voltage. Detectig system based o this process ca decouple positive ad egative sequece compoets of fudametal wave. Also, the system ca detect the positive sequece compoet as well as the magitude ad phase of egative sequece compoet, havig a fie dyamic respose property. Sice the egative sequece of fudametal wave will ot lead to two times harmoic compoet i the dual d-q frame ad oly have harmoic compoet, the low-pass filter desig badwidth is epaded ad the filter delay is reduced. Cosequetly, without affectig the detectig precisio, the dyamic respose speed is improved. II. D-Q RANSFORMAION ANALYSIS IN HARMONIC AND HREE-PHASE UNBALANCE CONDIION Let d-q trasformatio epressio to be ua ud cosωt cos( ωt π/ 3 cos( ωt π/ 3 u b u = q 3 siωt si( ωt π/ 3 si( ωt π/ 3 (1 u c Suppose the 5th ad the 7th harmoics are i grid, ad total harmoic distortio (HD rate is 18.03%, the voltage of phase A drops durig 0.1s~0.6s, leadig to three-phase ubalace. he remaiig value of phase A is 156V. he d-q trasformatio result of three-phase voltages is show i Fig.1. order Butterworth filter [3] is used as low-pass filter (LPF. Beig filtered by 0Hz low-pass filter, the d-q trasformatio result is show i Fig.. Voltage(V d 轴电压 d-ais voltage q-ais q 轴电压 voltage ime(s Figure. D-q trasformatio result by 0Hz low-pass filter I the same way, suppose the harmoic coditio is the same as above, but all the three-phase-balace voltages drop durig 0.1s~0.6s, ad the remaiig value of each phase is 156V. Fig.3 is the d-q trasformatio result. Obviously, the harmoic spectrum aalysis of Fig.3 does ot iclude the secod order harmoic compoet caused by three-phase ubalace, while the other harmoics aalysis is similar to able I. It is show i able II. Figure 3. D-q trasformatio result of three-phase voltages uder harmoic ad balace coditio Figure 1. D-q trasformatio result of three-phase voltages uder harmoic ad ubalace coditio able I is the spectrum aalysis betwee 0.1s~0.6s from Fig.1. Accordig to the spectrum aalysis data, the secod order harmoic caused by three-phase ubalace is oe of the mai harmoic compoets. ABLE I SPECRUM ANALYSIS FOR D-Q RANSFORMAION RESULS OF HREE-PHASE VOLAGES UNDER HARMONIC AND UNBALANCE CONDIION harmoic order/k d-ais voltage /V q-ais voltage /V I Fig.1, the d-q trasformatio results caot be used directly i voltage sag characteristic aalysis, because low-pass filterig is required. I this paper, the secod ABLE II SPECRUM ANALYSIS FOR D-Q RANSFORMAION RESUL OF HREE-PHASE VOLAGES UNDER HARMONIC AND BALANCE CONDIION harmoic order/k d-ais voltage /V q-ais voltage /V Similarly, the d-q trasformatio result caot be used directly i voltage sag characteristic aalysis ad eed low-pass filterig. Fig. is the d-q trasformatio result by 70Hz low-pass Butterworth filter. Figure. D-q trasformatio result by 70Hz low-pass filter 01 ACADEMY PUBLISHER

3 JOURNAL OF SOFWARE, VOL. 9, NO., FEBRUARY Comparig Fig. with Fig., their voltage-sag overshoots are ±13.6V ad ±10.6V. he d-q trasformatio low-pass filterig results are similar, but the secod oe has a better step respose ad amplitude-frequecy characteristic by usig 70 Hz filter. Hece, without reducig detectio precisio, the three-phase ubalace elimiatio epads the desig badwidth of low-pass filter ad reduces the low-pass filter delay. III. DECOUPLING POSIIVE AND NEGAIVE SEQUENCES IN DOUBLE D-Q SYNCHRONOUS REFERENCE FRAME Let the epressio of three-phase system voltages (or currets to be k k a = a a 0 ( a a k = k k b = b b 0 ( b b ( k = k k c = c c 0 ( c c k = I (, a, b ad c are three-phase voltages or currets; a, b ad c are fudametal positive sequece - - compoets; ā, b ad c are fudametal egative k sequece compoets; k k a, b ad c are positive sequece compoets of k th k harmoic wave; a, k b ad k c are egative sequece compoets of k th harmoic wave; 0 is zero sequece compoet. Furthermore, let A epresses vector effective value, φ epresses phase agle, the ca get: a = A si( ωt φ b = A si( ωt π /3 φ (3 c = A si( ωt π /3 φ a = A si( ωt φ b = A si( ω t π / 3 φ ( c = A si( ω t π / 3 φ k k k a = A si( ωkt φ k k k b = A si( ωkt π /3 φ (5 k k k c = A si( ωkt π /3 φ k k k a = A si( ωkt φ k k k b = A si( ω kt π /3 φ (6 k k k c = A si( ω kt π /3 φ ( = ( a b c Covert ( ito - coordiate, so that: 1 1 a b = 0 c (8 a = C 3 b c Substitute ( ~ (6 ito (8, the get, : ( t = 3A si( ωt φ 3A si( ωt φ k k k k [ ] 3A si( ωkt φ 3A si( ωkt φ ( t = 3A cos( ωt φ 3A cos( ωt φ (9 k k k k [ ] 3A cos( ωkt φ 3A cos( ωkt φ Fig.5 gives the vector relatioship betwee double d-q sychroous referece frame ad - coordiate, he we ca trasform ad i - coordiate ito d, q ad d-, q- i double d-q sychroous referece frame. X ( dq X ( dq X ( Figure 5. Vectors ad aes of double sychroous referece frame Accordig to Fig. 5, the trasformatioal matri is: d cosθ siθ (10 = q siθ cosθ d cos( θ si ( θ (11 = q si ( cos( θ θ Accordig to (9~(11, the mathematical descriptio of three-phase system i double d-q sychroous referece frame is obtaied. Referece [] adopts the trasformatioal matri show i (10 ad (11, ad trasforms ad ito double d-q sychroous referece frame. But fudametal compoets of d ( q ad d- ( q- caot be decoupled i this way, o the cotrary, superposed frequecy-doubled compoet of opposite phase sequece appears i the epressios. I fact, from (10 ad (11, we ca get: 01 ACADEMY PUBLISHER

4 56 JOURNAL OF SOFWARE, VOL. 9, NO., FEBRUARY 01 ( ( d cosθ siθ t = q siθ cosθ t ( d cosθ siθ t (13 = q siθ cosθ ( t I (1 ad (13,,, ad d q are fudametal positive sequece compoets;,, ad are d q fudametal egative sequece compoets. Apparetly, d ( q ad d ( q are decouplig. I order to get,, ad, we ca aalyze ad i fudametal positive ad egative sequeces. From (9, we fid k k ( t ( t ( t ( t ( t = k k ( t ( t ( t ( t ( t si ( ωt φ si ( ωtφ = 3A 3A cos( ωt φ cos( ωtφ (1 k k k k A si ( ωkt φ A si ( ωkt φ 3 3 k k k k A cos( ωkt φ A cos( ωktφ Let ad from (1 delay for 0.005s (/, we ca get: k k ( t ( t ( t ( t ( t = k k ( t ( t ( t ( t ( t cos ( ωt φ cos ( ωtφ = 3A 3A si ( ωt φ si ( ωt φ (15 k kπ k k kπ k A si ( ωk t φ A si ( ωk t φ 3 3 k kπ k k kπ k A cos ( ωkt φ A cos ( ωkt φ From (1 ad (15, we fid: ( t ( t = ( t ( t (16 k k k k ( t ( t ( t ( t k k k k 1 ( t ( t ( t ( t k k k k ( t ( t ( t k = ( t k k k k ( t ( t ( t ( t After / time-lapse elimiatio ad low-pass filterig, from (16 we ca get,, ad, that are from fudametal positive ad egative sequece compoets. hus, we ca get the decoupled d,, q d, ad qi double d-q sychroous referece frame. hat is why this paper calls the decouplig method / time-lapse elimiatio method. IV. SRUCURE MODELS OF HREE-PHASE MAGNIUDE-PHASE DEECION SYSEM (1 he decouplig progress of three-phase fudametal positive ad egative sequece compoets i double d-q sychroous referece frame is show i previous sectio. With (8, (1, (13, (15 ad (16, block diagram of the three-phase magitude-phase detectio ca be draw as Fig.6. C 3 ( t ( t,, a b c ( t ( t d q d q ( d ( q ( d ( q Figure 6. Block diagram of the three-phase magitude-phase detectio I Fig.6, X is the fudametal positive sequece compoet magitude, X is the fudametal egative sequece compoet magitude; θ is offered by ramp sigal geerator, ad LPF restrais harmoic disturbace i positive ad egative sequece compoets. As a result of (16, we get 1 ( ca restrai the egative sequece compoet of the k th harmoic wave; ( ca restrai the positive sequece compoet of the k th harmoic wave. Ulike the priciple i Fig. 6, referece [] metios /16 time-lapse elimiatio detectio method based o double sychroous referece frame, which also decouple the positive ad egative sequeces of fudametal compoet. But compared the two methods, / time-lapse elimiatio method has superiority o harmoic suppressio ad phase detectio. he details will be discussed i et sectio. V. SIMULAION o prove the feasibility of preseted magitude-phase detectio method, simulatio was fiished. / time-lapse elimiatio method compares with previous three-phase SPLL ad /16 time-lapse elimiatio method, trasiet respose uder ormal grid coditio, dyamic resposes uder three-phase ubalace with harmoic pollutio coditio ad phase jump coditio were obtaied respectively. A. rasiet Respose uder Normal Grid Coditio Aalyze the trasiet respose of three methods uder ormal grid coditio. Parameters: phase voltage effective value 0V, rated frequecy 50Hz, with the 3rd ad the 5th harmoic, HD rate.3% 5.0%. After detectig the voltage magitude ad phase of three-phase fudametal wave, the simulatio result as show as the followig Fig.7. X X φ φ 01 ACADEMY PUBLISHER

5 JOURNAL OF SOFWARE, VOL. 9, NO., FEBRUARY (a Positive sequece voltage amplitude of three-phase fudametal wave (b Positive sequece phase positio of three-phase fudametal wave Figure 8. Dyamic respose uder harmoic ad ubalaced coditio (b Positive sequece phase positio of three-phase fudametal wave Figure 7. Respose curves uder ormal grid coditio As show i Fig.7(a, all the three trasiet overshoots uder ormal grid coditio are approimate. But three-phase SPLL, which takes the least settig time, has the best trasiet respose. he other two methods with time-lapse have more settig time, but the settig time do t eceed 5/ frequecy period. Fig.7(b shows that i the first frequecy period, /16 time-lapse elimiatio method has a obvious wave distortio, while the wave shapes of the other two methods coicide maily. B. Dyamic Respose uder Harmoic ad Ubalaced Coditio Fig.8 is the simulatio result uder three-phase ubalace with harmoic pollutio coditio. Parameters: phase voltage effective value 0V, rated frequecy 50Hz, with the 3rd ad the 5th harmoic, HD rate 5.01%, oe phase voltage sag durig 0.0s~0.1s ad the three-phase ubalace. As show i Fig.8, sice voltage has ubalace disturbace with serious grid distortio, traditioal three-phase SPLL caot track the magitude ad phase of the fudametal positive sequece voltage; he /16 time-lapse elimiatio method caot suppress harmoic ad its positive sequece voltage detectio result has a bad steady state relative error is equal or greater tha 5.0%; / time-lapse elimiatio method, of which the relative steady state error of positive sequece voltage detectio is equal or smaller tha 0.5% ad dyamic respose time is 0.018s obtais a good dyamic respose property. his simulatio eample verifies the aalysis result of (16 i previous sectio, ad eplais that / time-lapse elimiatio method ca suppress odd harmoic ad ca track magitude ad phase of the fudametal positive sequece voltage uder harmoic distortio coditio. C. Detectio Result uder Phase Jump of hree-phase Voltages Parameters: phase voltage effective value 0V, rated frequecy 50Hz, with the 3rd ad the 5th harmoic, HD rate.3% 5.0%, three-phase voltage phase jumpig at 0.05s, phase jump agle is -30, system restoratio at 0.16s. After detectig the fudametal positive sequece voltage magitude ad phase, the result is show i Fig.9. (a Positive sequece voltage amplitude of three-phase fudametal wave (a Positive sequece voltage amplitude of three-phase fudametal wave 01 ACADEMY PUBLISHER

6 58 JOURNAL OF SOFWARE, VOL. 9, NO., FEBRUARY 01 (b Positive sequece phase positio of three-phase fudametal wave Figure 9. Dyamic respose uder phase jump of three-phase voltages I Fig.9, the traditioal three-phase SPLL method has the best real-time property o detectig three-phase voltage phase jump; / time-lapse elimiatio detectio method ca detect phase jump although its real-time property is ot 100% well; the /16 time-lapse elimiatio detectio method has obvious peak o the positive sequece voltage magitude, ad the phase positio has obvious deviatio. VI. CONCLUSION his paper itroduces / time-lapse elimiatio method, a ovel magitude-phase detectio method based o double sychroous referece frame. his method achieves decouplig positive ad egative sequeces of fudametal wave with double d-q trasformatio ad detects the magitude ad phase positio of three-phase voltages (or currets fudametal positive sequece compoet ad egative sequece compoet respectively. Simulatio results idicate that the ovel method solves the problems i traditioal three-phase SPLL circuits ad eve ejoys a high precisio of measure. Compared with /16 time-lapse elimiatio method, this method has superiority o harmoic suppressio ad phase trackig. Detectig system model based o this method is simple, ad they ca be used i occasio where harmoic distortio is heavy ad three-phase ubalace, especially lots of applicatio values eist i detectig voltage sychroous sigal of wid eergy geeratio system. ACKNOWLEDGEMEN he authors also wat to give their thaks to the Natural Sciece Foudatio of Chia (No ad Ecellet Youth eacher Foudatio of Lazhou Uiversity of echology (No. Q0081. REFERENCES [1] D. H. Huag, J. J. Che ad L. Zhag, Impact of Large-scale Wid Power Itegratio o Power System, Guagdog Electric Power, Vol. 3, No. 7, pp. 7 30, July 010. 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7 JOURNAL OF SOFWARE, VOL. 9, NO., FEBRUARY o Magetics, Vol. 6, No. 3, pp , 010. [0] S.J. Lee, M. Kim ad S. K. Sul, A ovel cotrol algorithm for static series compesators by use of PQR istataeous power theory, EEE rasactios o Power Electroics, Vol. 19, No. 3, pp , 010. [1] AIELLO M, CAALIOI A, NUCCIO S, A chirp-z trasform-based sychroizer for power system measuremets, IEEE rasactios o Istrumetatio ad Measuremet, Vol. 5, No. 3, pp , 005. [] GUO Weyog, ZHAO Caihog, ZHANG Zhifeg, et al, A ovel three-phase magitude-phase-lock loop system based o eteded variable step size least mea square algorithm, Automatio of Electric Power Systems, Vol. 3, No. 11, pp , 008. [3] W. Wu, J. Y. Liu ad Y. B. Liu, Research summary of itelliget sales ad marketig of smart grid, Electric Power Automatio Equipmet, Vol. 30, No. 5, pp , May 010. [] ZHOU Peg, HE Yikag, SUN Da, et al, Cotrol ad protectio of a DFIG-based wid turbie uder ubalaced grid voltage dips, Proceedig of IEEE Idustry Applicatios Society Aual Meetig, pp. 1-8, 008. Xiaoyig Zhag was bor i Sichua Provice, Chia, i She is curretly a associate professor at Lazhou Uiversity of echology, Gasu, Chia. She obtaied a first class BEg degree i 1998 ad a Master s degree i 001 from Xi a Uiversity of echology, P R Chia. Her research iterests iclude the stability of power system, wid power geeratio cotrol. Zheg Jiag was bor i Ahui Provice, Chia, i1987. He is curretly a graduate studet at Lazhou Uiversity of echology, Gasu, Chia. He received his BEg degree i electrical egieerig ad automatio from Wuha Uiversity i 008. His research iterests iclude the voltage stability of power system, sesitivity aalysis i power system. Nig Dig was bor i Shadog Provice, Chia, i1988. He is curretly a graduate studet at Lazhou Uiversity of echology, Gasu, Chia. He received his BEg degree i electrical egieerig ad automatio from Wuha Polytechic Uiversity i 010. His research iterests iclude the stability of power system, flow calculatio of power system. 01 ACADEMY PUBLISHER