Math Model and Calculation Analysis of Inter-harmonic of Double PWM Speed Control System in Distribution Network

Transcription

1 Sensors & Transders Vol. 8 sse Noveber 4 pp Sensors & Transders 4 by FSA Pblshng S. L. Math Model and Callaton Analyss of nter-haron of Doble PWM Speed Control Syste n Dstrbton Network Yang Wen-Han * L L-Yang L Zheng L Rong-Gao Shool of Optl-Eletrl and Copter Engneerng Unversty of Shangha for Sene and Tehnology Shangha 9 Chna Tongsheng Eletrty Power Copany Ltd. Pdong Dstrt Shangha Chna * Tel.: * E-al: llyangnj@6.o Reeved: 4 Agst 4 /Aepted: Otober 4 /Pblshed: Noveber 4 Abstrat: Ang at the proble that the dstrbton network voltage wll fltate bese of the nterharon rrents njeted nto the network by doble PWM speed ontrol syste when reglatng the speed of the asynhronos otor we establshed the nter-haron rrent ath odel of doble PWM speed ontrol syste aordng to swthng fnton based on a real brdge rane. The dstrbton law of the nter-haron s got by llatng the grd-sde rrents and ther spetr whle lettng the otor rn at dfferent qadrants and freqenes. The reslt whh s verfed by slaton and experent shows that the ontent of the nter haron rrents s ore than that of haron rrents n doble PWM speed ontrol syste the freqeny of the nter harons of the grd-sde rrent anly fos on the sope lower than the fndaental freqeny and when the otor rns at low freqenes the THD of the grd-sde rrent s hgh. The reslt has verfed the reason why the voltage of a brdge rane dstrbton syste of a deepwater port n Shangha flkers. Copyrght 4 FSA Pblshng S. L. Keywords: Doble PWM Swthng fnton Grd-sde rrent Harons nter-harons.. ntrodton Wth the developent of power eletron tehnology doble PWM onverters are wdely sed n hgh power appltons whh have low grd-sde harons [ ]. Bt as a reslt of the load fltaton and the speed governng of asynhronos otor the grd-sde rrent ontans nter-harons. When the nber of doble PWM onverter reahes a ertan aont the voltage of the dstrbton network wll flker wth nter-haron rrent freqeny whh have has seros pat on the power qalty n dstrbton networks and eqpent onneted nto the network [-5]. t s reported that the dstrbton network of a deepwater port n Shangha has experened low-freqeny voltage flker when too any brdge rane were pt to se. n reent years sholars of dfferent ontres have rred ot extensve researh on the haratersts [6-8] and llaton ethods [9-] of nter-harons bese of ts great har and the reslts are appled to the analyss of HVDC transsson syste and hgh power varable freqeny speed reglaton syste [4-9]. Lteratre [8] establshes the atheat odel of AC speed ontrol syste based on swth fnton bt t doesn t analyze the nter-haron rrent of the syste njeted nto the dstrbton network. 8

2 Sensors & Transders Vol. 8 sse Noveber 4 pp Lteratre [9] analyzed grd sde nter-haron rrent of freqeny onvertng speed reglatng syste wth dode retfer rt. Bt dode retfer n t pass energy to power grd so the onlson n t be sed to analyss doble PWM doble PWM speed ontrol syste. So far no report on researh fndngs abot grd sde nter-haron rrent of doble PWM speed ontrol syste n fond. n ths paper we establsh nter-haron atheatl odel of doble PWM speed ontrol syste based on swth fnton. Then we llate and analyze the harons and nter-harons njeted nto the power grd when asynhronos ahne work at dfferent freqenes by takng brdge rane sed n the Port of Shangha as a physl odel. At last soe experents are ondted. The reslts of the llaton and experents show that the grd sde rrent of doble PWM speed ontrol syste has a ertan aont of harons and nter-harons; nter-harons freqenes are anly onentrated n the range below the net sde rrent fndaental freqeny; the aont of grd sde nter-haron rrent wll nrease when the otor operates at a low freqeny so the THD of the grd sde rrent s hgh. These reslts ay explan why the voltage of power dstrbton syste of brdge rane loted n the deep-water port n Shangha flker. T e Load torqe S Swth of grd sde onverter (k=a b ) k S k Swth of otor sde onverter (k=a b ) s k Swth fnton of grd sde onverter (k=a b ) s KO Swth fnton of grd sde onverter (k=a b ) DC lnk voltage ω Anglar freqeny of Modlaton wave Anglar freqeny of rrer ω Ω φ Z Anglar freqeny of the otor Eqvalent pedane angle of the otor. nter-haron Matheat Model of Doble PWM Speed Control Syste The rt of doble PWM speed ontrol syste s shown n Fg.. As the fgre shows the syste s onssts of the eqvalent odels of power grd two onverters and a otor. Relevant varables and the referene dreton are shown n ths fgre too. Noenlatre x s the DC oponents of x ~ x s the AC oponents of x x N xn s the rated vale of x e a Voltage of power grd (also: eb e ) a Grd sde rrent of doble PWM speed ontrol syste (also: b ) Stator rrent of the otor (also: A B C ) Crrent of pator DC sde rrent of otor sde onverter DC sde rrent of grd sde onverter Stator rrent of the otor Rotor rrent of the otor Extaton rrent of the otor L Grd sde eqvalent ndtane Haron order of rrer M Modlaton rato n Haron order of Modlaton wave R S of swthng loss eqvalent resstane and the eqvalent resstane of transforer R R s Stator resstor Rotor resstor onverted to stator sde Slp Fg.. Sheat of doble PWM speed ontrol syste... Matheat Model of Grd Sde PWM Converter When wrtng the eqaton aordng to Krhhoff's voltage law the grd sde rrent has the for (take a as exaple) []: a = ea ( sa sb s) L () When sng the syetrl swth saplng the expresson n be expanded nto the followng for by sng Forer seres: sa =.5 +.5M sn( ωt θ) + n ( ) sn n[.5os( nωst) + n = n.5m sn( ωt θ)os( nω t)] s () 8

3 Sensors & Transders Vol. 8 sse Noveber 4 pp n be expanded nto the s of ts DC oponent and AC oponent so the swthng fnton expresson of grd sde rrent s: a = ea [ sa ( sb s) ] L L + () [ s ( )] a sb + s L Eq. () shows that grd sde haron rrent and AC oponent of have great relatonshp. Slarly b n be desrbed. The relatonshp between and a b s: = s + s + s (4) a a b b.. Matheat Model of DC Bs Voltage Fltaton By sng Krhhoff's rrent law at the postve node of the pator has the for [ ]: d C = (5) Eq.(5) shows that the fltaton oponent of n be sed by the fltaton of ea eb e the hange of and the otor speed reglatng: = + = + = + (6) t s not hard to get expresson of DC lnk by sbstttng Eq.(6) n Eq.(5): d d d C = C( + ) = ( + ) ( + ) The AC expresson s: The DC expresson s: So: d = C + (7) (8) d = C + = = (9) t s not hard to fnd that the DC oponent n be transtted between grd sde and otor sde. The AC oponent n be expressed as: = n os ν = t ( νω ) = os t ( λω ) d d λ = () n ths expresson ωd andω are the freqeny of and respetvely. ν ( ν > ) s the haron order of ω ; λ ( λ > ) s the haron order of ω.the patve rrent s: d d C = dλ os λω νnos νωt ν = ( ) ( ) () λ= ν= = dλos( λω) ν os( νωt) C λ= ν= dλ = sn( λω + β ) λ= λωdc ν sn ( ωt + γ) νω C () Eq. () shows that the lower the freqeny s the greater the voltage wll fltates. Eq.() shows that the bgger the AC oponent of s the ore nter-haron grd sde rrent wll have espelly low freqeny nter-haron rrent. We set: λ dν = = λω C νω C ω C and ω ω then: d d ( ωd + ω) t + ( β + γ) = os ωc () ( ωd ω) t + ( β γ) sn Eq.() shows that the pator has sgnfnt effet to nhbt the AC oponent of and the bgger the patane s the less the AC oponent pass throgh the DC lnk s. For the grd sde onverter: the fndaental freqeny s always 5 Hz so the freqeny of the fltaton njeted nto DC lnk s relatvely hgh and fxed; the flterng effet of the pator s obvos. 8

4 Sensors & Transders Vol. 8 sse Noveber 4 pp Bese of the speed reglatng espelly low freqeny startng the otor sde onverter often works n several Hz. Therefore the flterng effet of the pator s lted and low freqeny fltaton has strong ablty to pass throgh the pator and njet nto the grd. So t s easy for the otor s low freqeny sgnal to njet nto the power grd... Matheat Model of Motor and Motor Sde PWM Converter The swthng fnton n be desrbed as follows when the onverter se synhronos SPWM odlaton and the startng pont of sne wave s the zero rossng of the fall edge of the tranglar rrer [-4]: J( M ) M = sn( ω ) + sn [ ( ω )] + =.5 ± J ( ) n M sn [ ( N + n )( ωt ) ] + =.5 n=± ± 4 ± J ( ) n M sn [ ( N + n )( ωt ) ] = 4 n=± ± ± 5 (4) s t N t AO where J and J n are zero order Bessel fnton of the frst knd and n are the order of the respetvely. Jn ( z) = os( nθ zsn θ) dθ (5) Aordng to the way the otor sde onverter works n be desrbe as: AO = s (9) AO AO A n be desrbed. Slarly BO CO The relatonshp between and AO' BO' CO' n be desrbed as: = s + s + s () AO ' AO ' BO ' BO ' CO ' CO ' The nter-haron atheat odel of doble PWM speed ontrol syste s onsttted by Eq.() () () (4) (5) (4)~().. Callaton and Analyss of nter-harons.. Callaton Proess of nter-harons Aordng to the atheat odel of the derved n last seton the grd sde rrents of the doble PWM speed ontrol syste nder dfferent workng onons n be llated. The llaton flow s shown n Fg.. Aordng to the flow shown n Fg. ths paper hooses a three phase sqrrel ge asynhronos otor sed n the brdge rane. ts paraeters are shown as follows: ean ebn e N are 4 V rated freqeny s 5 Hz T en s 576 N R s 7 Ω R s.98 Ω stator leakage reatane s.655 Ω rotor leakage reatane s.76 Ω sn s.67 pole pars are. Aordng to the prnple of eletro ehans there s onstrant relatonshp of three phase sqrrel ge asynhronos otor: T e R = (6) Ω s Aordng to T type eqvalent rt of otor the stator rrent n be desrbed as: ' = + (7) f s gnored A n be desrbed as: ( ω φ ) = os t (8) A Z Fg.. The llaton flow hart. 8

5 Sensors & Transders Vol. 8 sse Noveber 4 pp Callaton and Analyss n ths paper the otor s set to drag the potental energy load and work at the state of otor and generator respetvely. The freqenes of the otor s stator voltage range fro 5 Hz to 5 Hz and take Hz as the step vale. The reslts are as Fg. and Fg. 4. M ag (% of Fndaental) 4 5 Freqeny (Hz) 5 (a) the spetr of grd sde rrent when the otor works at 5 Hz. M ag (% of Fndaental) Freqeny (Hz) 5 As shown n Fg. and Fg. 4 the grd sde rrent nlde not only harons bt also nterharons. The nter-haron freqenes anly onentrate n the range below the fndaental freqeny of grd sde voltage. Besdes the llaton reslts show that when the otor works n the onon of generator the nter-haron njeted nto the network by grd sde PWM onverter s hgher than that when t works at the otor state. Frtherore along wth the nrease of the operatng freqeny of the otor sde onverter haron rrent and nter-haron rrent dereased. The hange relatonshp between grd sde rrent THD vale and the operatng freqeny of the otor sde onverter s shown n Fg. 5. Fg. 5 shows that when otor sde onverter operates n rated freqeny THD vale of grd sde rrent s the lowest. Bt the flterng effet of the pator s lted when the otor start at low freqeny. Therefore t s easer for low freqeny fltaton to transt to the power grd and the THD vale of grd sde rrent s the largest. (b) the spetr of grd sde rrent when the otor Fg.. The spetr of grd-sde rrent when lftng the weght. M ag (% of Fndaental) 4 5 Freqeny (Hz) 5 Fg. 5. THD of grd-sde rrent n dfferent onon. 4. Experent Analyss Mag (% of Fndaental) (a) the spetr of grd sde rrent when the otor works at 5 Hz. 4 5 Freqeny (Hz) 5 (b) the spetr of grd sde rrent when the otor Fg. 4. The spetr of grd-sde rrent when droppng the weght. n order to verfy the valy of the llaton ethod relevant experents have been done n a real brdge rane. As shown n Fg. 6 and Fg. 7 grd sde power fator s hgh and the wavefor of rrent s snsods bt the apltde hanges. t proves the exstenes of nter-haron of grd sde rrent. The spetr shows that the ontent of grd sde nter-haron when the otor works at 45 Hz s sgnfntly less than that when t works at 5 Hz. Bt the oon featres of both are: the freqenes of nter-haron anly onentrate n the range below the fndaental freqeny of grd sde voltage. t s onsstent wth the slaton reslts so the effetveness of the llaton odel and the orretness of the onlson are verfed. 84

6 Sensors & Transders Vol. 8 sse Noveber 4 pp (a) the grd sde rrent and ts spetr when the otor works at 5 Hz. sde voltage. The THD vale of grd sde rrent s larger when the otor operates at low freqeny. ) Grd sde nter-haron rrent s larger when the otor operates at the state of generator than that when t operator at the state of otor. THD has lttle dfferene. Ths paper has desgned the llaton flow of the grd sde nter-haron rrent of doble PWM speed ontrol syste based on ts atheat odel; revealed the dstrbton law of spetr of grd sde nter-haron rrent; and proved the effetveness of the llaton odel and the orretness of the onlsons. The odel and onlsons have pratl sgnfne for nhbtng the voltage flker sed by nter-haron n dstrbton network. (b) the grd sde rrent and ts spetr when the otor Fg. 6. The grd-sde rrent and ts spetr when lftng the weght. Aknowledgents Ths artle and relevant projet s spported by followng two fondatons: ) Shangha Sene and Tehnology Cottee (DZ8); ) The Hjang Fondaton of Chna (B4/D4). Referenes (a) the grd sde rrent and ts spetr when the otor works at 5 Hz. (b) the grd sde rrent and ts spetr when the otor Fg. 7. The grd-sde rrent and ts spetr when droppng the weght. 5. Conlson By llatng the grd sde nter-haron rrent when the otor operates at dfferent states and freqenes and oparng wth the experental reslts ths paper has got followng onlsons: ) The nter-haron ontent njeted nto the power grd by grd sde PWM onverter of doble PWM onverter s larger than the haron ontent. ) nter-haron freqeny anly onentrates n the range below the fndaental freqeny of grd []. Wan-We Wang Ha-Je Yn Gang Ln Dal- PWM freqeny-varable speed reglaton syste based on dret power ontrol Jornal of Soth Chna Unversty of Tehnology (Natral Sene Eon) Vol. 9 No. pp []. J. L-Png Q. Xao-Yan Z. R-We Developent present staton and applton of dal PWM onverter Chna Sene and Tehnology nforaton sse 8. []. V. B. Vrlkar M. V. Aware Modelng and slaton of flker de to nterharons n Proeedngs of the EEE nda nternatonal Conferene on Power Eletrons (CPE) pp. -5. [4]. J. Wang H. L A llaton ethod for nterharons-sed flker and flker sore dentfton Atoaton of Eletr Power Systes Vol. 5 sse pp [5]. Xong Jefeng L Qn Yan Xaodong Chen Bng Yang Zhhao Wang Boln Deteton ethods of harons and nterharons n power syste Atoaton of Eletr Power Systes sse pp. 5-. [6]. D. Zhang W. X Y. L On the phase seqene haratersts of nterharons EEE Transatons on Power Delvery Vol. sse 4 5 pp [7]. J. Yong T. Tayjasanant X. Wlsn et al Charaterzng voltage fltatons sed by a par of nterharons EEE Transatons on Power Delvery Vol. sse 8 pp [8]. T. Tayjasanant W. Wang C. L et al nterharonflker rves EEE Transatons on Power Delvery Vol. sse 5 pp [9]. D. Shartha Estaton of harons and nterharons sng phaseloked loop n 85

7 Sensors & Transders Vol. 8 sse Noveber 4 pp Proeedngs of the nternatonal Conferene on Power Energy and Control pp [7]. D. J. He A. R. Wood C. M. Osaskas Freqeny-doan odellng of nterharons n []. S. R. Hadan Are D. X Y. Lang A new HVDC systes EE Proeedngs-Generaton approah to harons and nterharons generaton n general VS/CS onverters n Proeedngs of the 7 th EEE Power Eletrons Spelsts Conferene (PESC'6) 6 pp. -7. Transsson and Dstrbton Vol. 5 sse pp [8]. R. Carbone F. De Rosa R. Langella et al A new approah for the optaton of harons and []. M. L X. Wang An atoregressve odel algorth nterharons proded by lne-otated for the nter-haron spetral estaton n the power syste Proeedngs of the CSEE Vol. sse pp []. Y. L J. H H. Yang Mltlayer DFT nterpolaton orreton approah for power syste haron analyss Proeedngs of the Chnese Soety of Eletrl Engneerng Vol. sse 5 pp []. J. Wang H. L H. Xao An approah to easre AC/DC/AC onverters EEE Transatons on Power Delvery Vol. sse 5 pp [9]. D. Bas npt rrent nterharons of varablespeed drves de to otor rrent balane EEE Transatons on Power Delvery Vol. 5 sse 4 pp []. Z. Chong-We Z. Xng PWM retfer and ts ontrol Chna Mahne Press Bejng pp (n Chnese). nterharons-flker based on synhronos []. R. Carbone D. Mennt R. E. Morrson et al deodlaton Proeedngs of the CSEE Vol. (Sppleent) 67-7 (n Chnese). [4]. B. Geethalaksh K. Bab S. S. Santhosha Analyss of nterharons n onventonal and atrx onverter fed adjstable speed drves n Proeedngs of the EEE 5 th nda nternatonal Conferene on Power Eletrons (CPE) Haron and nterharon dstorton odelng n ltonverter systes EEE Transatons on Power Delvery Vol. sse 995 pp []. L. Xnjn Z. Mn Haron analyss of three-phase SPWM nverter and ts nhbton shee Exploson- Proof Eletr Mahne sse 8 pp. 8-. []. Gary W. Chang Shn-Kan Chen An analytl pp. -6. approah for haraterzng haron and [5]. Q. L H. L Z. L et al Analyss on nterharons nterharon rrents generated by VS-fed generaton n the asynhronos nteronneton HVDC syste Sothern Power Syste Tehnology sse 8 pp [6]. L. H R. Yan Callaton of harons and adjstable speed drves EEE Transatons on Power Delvery Vol. sse 4 5 pp [4]. Gary W. Chang Shn-Kan Chen Ha-Jhe S et al Arate assessent of haron and nterharon nterharons n HVDC shees wth low DC sde rrents generated by VS-fed drves nder pedane EE Proeedngs Generaton nbalaned spply voltages EEE Transatons Transsson and Dstrbton Vol. 4 sse 6 99 pp on Power Delvery Vol. 6 sse pp Copyrght nternatonal Freqeny Sensor Assoton (FSA) Pblshng S. L. All rghts reserved. ( 86