Open-loop Control for Permanent Magnet Synchronous Motor Driven by Square-wave Voltage and Stabilization Control

Transcription

1 Ope-loop Cotrol for Peraet Maget Sychroous Motor Drive by Square-wave Voltage ad Stabilizatio Cotrol Daisuke Sato Departet of Electrical Egieerig Nagaoka Uiversity of Techology Nagaoka, Niigata, Japa Ju-ichi Itoh Departet of Electrical Egieerig Nagaoka Uiversity of Techology Nagaoka, Niigata, Japa Abstract I this paper, the ope-loop cotrol for peraet aget sychroous otor (PMSM) drive by a square-wave voltage is proposed. The proposed cotrol is able to trasit fro the PWM regio to the square-wave voltage regio via the over odulatio regio sealessly. Whe the PMSM is drive by the square-wave voltage usig the proposed cotrol, the lowfrequecy torque vibratio except 6th or th order haroics occurs due to the trasitio to the square-wave voltage regio. Therefore, a variable bad pass filter (BPF) is itroduced as the reductio ethod of the low-frequecy torque vibratio. The lowfrequecy copoet i the active curret for the stabilizatio cotrol is extracted by the filter. As a experietal result, the proposed ethod reduces the low-frequecy vibratio which ca be represeted for the torque by over 4%. Keywords Peraet aget sychroous otor; Squarewave voltage; Ope-loop cotrol; ow-frequecy torque vibratio I. INTRODUCTION Recetly, adjustable speed drive systes with a peraet aget sychroous otor have bee actively studied [-5]. A voltage source iverter is applied to the drive systes widely, whereas the PMSM is drive by the PWM voltage, the over odulatio voltage or the square-wave voltage. I additio, the PMSM is typically cotrolled by a field orieted cotrol. However, it is difficult to cotrol the PMSM by the typical field orieted cotrol i the over odulatio regio ad the squarewave voltage regio because the cotroller becoes istable due to the haroic currets [6]. Therefore, the cotrol strategies i the over odulatio regio ad the square-wave voltage regio have bee proposed, respectively [7-8]. The haroic copoet is reoved fro the detected curret by a low pass filter i order to ipleet a curret feedback cotrol i the over odulatio regio [7]. O the other had, the torque is cotrolled by adjustig the voltage phase i the square-wave voltage regio [8]. However, the switchover of the cotroller is ecessary accordig to each voltage regio. Therefore, the ipleetatio of the cotroller becoes coplex ad the stability of the syste is difficult to desig. I additio, it is proposed that the haroic curret is estiated fro the otor ad the iverter paraeters used for a positio sesorless cotrol i order to ipleet the curret feedback cotrol i the over odulatio regio [9]. This cotrol is able to be applied ito both the PWM regio ad the over odulatio regio. However, the operatio is ot cosidered i the square-wave voltage regio. Furtherore, the istataeous curret cotrol i the square-wave voltage regio has bee proposed []. This cotrol ethod is also applied to both the PWM regio ad the over odulatio regio. Therefore, the switchover of the cotroller is ot ecessary, although a fieldprograable gate array (FPGA) is required i order to apply a space vector odulatio to the iverter. The iverter is required to switch every 8 degrees i order to geerate the square-wave voltage. Therefore, the FPGA which operates i several MHz is required. I other words, it is ipossible to switch every 8 degrees accuracy oly by the sigle-chip icrocoputer which geerates PWM based o triagular-wave copariso ethod. Therefore, the error i the iverter output voltage occurs. As a result, low-frequecy torque vibratio except 6th or th order haroics occurs i the square-wave voltage regio. This paper proposes a cotrol strategy for the PMSM based o the ope-loop cotrol ipleeted ito the sigle-chip icrocoputer, the cotrol period of which is costat. The proposed ethod is able to trasit fro the PWM regio to the square-wave voltage regio via the over odulatio regio sealessly. I particular, V/f cotrol ipleeted with the stabilizatio cotrol is applied i both the PWM regio ad the over odulatio regio [-]. I the square-wave voltage regio, oly the frequecy is cotrolled. I priciple, the torque icludes the ripple, the frequecy of which is six ties the fudaetal frequecy. However, a additioal lower order haroic copoet also occurs i the square-wave voltage regio, which fluctuates the torque. Hece, a reductio ethod of this low-frequecy torque vibratio is ecessary. Therefore, a variable BPF is itroduced. It extracts the low-frequecy copoet fro the active curret for the stabilizatio cotrol. This ethod reduces the low-frequecy torque vibratio without a additioal sesor. First, this paper presets the characteristic of the ope-loop cotrol for the PMSM. The, the operatio verificatio of the PMSM is siulated i the square-wave voltage regio. Next, the cause of the torque fluctuatio is clarified ad the low-frequecy torque-vibratio reductio

2 δ q e v i i δ ϕ γ s i γ d Fig. Relatioship betwee d-q coordiate ad γδ coordiate. iδ is active curret ad iγ is reactive curret. ethod is proposed. Fially, the proposed ethod is verified by the siulatio ad the experiet. Fig. Cotrol block diagra of ope-loop cotrol with stabilizatio cotrol for PMSM. The stabilizatio cotrol is esessary for the PMSM drive. II. OPEN-OOP CONTRO OF PMSM A. Square-wave Voltage Drive by Ope-loop Cotrol Geerally, the directio of the flux i the peraet aget is defied as d-axis ad the directio of the back electrootive force is defied as q-axis i the field orieted cotrol of the PMSM. However, d-q coordiate is ot able to be defied i the ope-loop cotrol because the positio of the agetic pole is ukow. Therefore, the directio of the iverter output voltage is defied as δ-axis, whereas the axis which lags by π/ rad fro δ-axis ca be defied as γ-axis i the ope-loop cotrol syste. Fig. shows the relatioship betwee the d-q coordiate ad the γδ coordiate. The δ-axis copoet of the curret vector iδ expresses the active curret because the δ-axis aligs i the sae directio of the output voltage vector. Siilarly, the γ-axis copoet of the curret vector iγ expresses the reactive curret. Fig. shows the cotrol block diagra of the ope-loop cotrol with the stabilizatio cotrol for the PMSM [-]. The PMSM is drive by the V/f cotrol i the PWM regio ad the over odulatio regio. I particular, the relatioship betwee the fudaetal aplitude of the output voltage ad the odulatio idex is oliear i the over odulatio regio. Hece, the trasitio cotrol, the odulatio idex i which is corrected, is ecessary [9, ]. I additio, the voltage aplitude is costat ad the frequecy is cotrolled oly i the squarewave voltage regio. Furtherore, i case that the PMSM is drive by a siple ope-loop cotrol, the cotrol syste becoes istable due to the fluctuatio of the load agle. Therefore, the active curret iδ is fed back i order to adjust the output frequecy coad ω *. By this ethod, the cotrol syste becoes stable because the equivalet feedback of the load agle is realized []. Fig. 3 shows the triagular-wave copariso ethod i each voltage regio. The aplitude of the odulatig wave is saller tha that of the triagular-wave i the PWM regio. O the other had, the aplitude of the odulatig wave becoes larger tha that of the triagular-wave by the trasitio cotrol i the over odulatio regio ad the square-wave voltage regio. Therefore, each voltage wavefor is able to be geerated by the triagular-wave copariso ethod. (c) (b) (a) PWM regio. Over odulatio regio. Square-wave voltage regio. Fig. 3 Triagular-wave copariso ethod i each voltage regio. The each voltage wavefor is able to be geerated by the triagular-wave copariso ethod. The, the PMSM is drive by the ope-loop cotrol ad trasited fro the PWM regio to the square-wave voltage regio i siulatio. The paraeters of the PMSM i the siulatio as well as the experiet are show i Table. The two-level iverter, the carrier frequecy of which is khz is applied i the siulatio. Fig. 4 shows the siulatio results of the PMSM drive by the ope-loop cotrol. The speed is cotrolled soothly fro

3 the PWM regio to the square-wave voltage regio via the over odulatio regio. However, the torque fluctuatio icreases i particular speed of the square-wave voltage regio. Fig. 5 shows the torque haroics aalysis result at several poits of speed i the square-wave voltage regio. I priciple, whe the PMSM is drive by the square-wave voltage, the haroic copoets, the orders of which are the ultiples of six copared to the fudaetal frequecy occur i the torque. However, the lower order haroic which is ot the ultiple of six also occurs. This sigificatly icreases the torque fluctuatio at ω =.74 p.u. ad ω =.96 p.u. Because the excessive torque fluctuatio worses the speed respose, the reductio of the low-frequecy torque vibratio is ecessary. B. Aalysis of Cotrol Syste The cause of the icrease i the low-frequecy torque vibratio is ivestigated. Therefore, the gai characteristics of the cotrol syste are obtaied. I additio, the PMSM subjected to the aalysis is a surface PMSM which the d-axis iductace equals to the q-axis iductace i order to siplify the aalysis. First, the state equatio ad the output equatio of the cotrol syste are obtaied. The voltage of the PMSM o the γδ coordiate syste is expressed i (), TABE I. PARAMETERS OF THE PMSM Rated power 3 kw Rated torque 8 N Maxiu speed i - Rated curret 7.3 Ars Pole uber 4 d-axis iductace.4 H q-axis iductace.4 H Widig resistace 33 Ω iked flux.66 Vs/rad Moet of iertia.3 kg v v γ δ d R = dt ω ω i d R i dt γ δ siϕ ω cosϕ (), where vγ is the γ-axis voltage, vδ is the δ-axis voltage, R is the arature widig resistace, is the arature iductace, is the axiu value of arature liked flux, ω is the agular frequecy of the PMSM, ω is the agular frequecy of iverter output ad ϕ is the phase differece betwee the d-q coordiate ad the γ-δ coordiate. Next, the torque is expressed i (), ( i siϕ i cosϕ ) T = Pf iq = Pf γ δ (), where P f is the uber of the pole pairs ad i q is the q-axis curret. I additio, the relatioship betwee the agular frequecy of the PMSM ad the torque is expressed i (3). d Pf ω = T (3) dt J Furtherore, the rotatioal speed of the γ-δ coordiate is sae as that of the d-q coordiate i the steady state. However, the rotatioal speed of two coordiates is varied by chagig the rotatioal speed ad the stability cotrol i the trasiet state. Therefore, the differetial of the phase differece is derived as i (4), Fig. 4 Siulatio results of PMSM drive by ope-loop cotrol. The torque fluctuatio icreases i the square-wave voltage regio. Torque [p.u.].5..5 ower order haroics 6th order haroics.74 p.u..85 p.u..96 p.u. th order haroics Frequecy [Hz] Fig. 5 Torque haroics i square-wave voltage regio. The lower order haroic which is ot the ultiple of six also occurs.

4 d ϕ = ω ω Kiδ (4), dt where K is the gai of the stability cotrol. I additio, the phase differece ϕ is sae as the load agle by the defiitio of the γ- δ coordiate. The ope-loop cotrol syste is expressed as the fourthorder state equatio by (), (3) ad (4). These equatios are oliear. Therefore, these equatios are liearized i the steady-state operatig poits. The state equatio ad the output equatio after the liearizatio ca be expressed i (5) ad (6), respectively. Suffix iplies the values at the steady-state operatig poits. The, the gai characteristics of the cotrol syste are obtaied by (5) ad (6). I additio, i order to evaluate the relatioship betwee the gai characteristics ad the speed of the PMSM, the gai characteristics are obtaied at several differet poits of speed. Fig. 6 shows the gai characteristics of the ope-loop cotrol for the PMSM. I the cotrol syste, these are three gai characteristics because the state equatio has three iput variables. However, Δω is zero at the steady-state operatig poits. Therefore, oly the gai characteristics of Δvγ ad Δvδ are verified. Fro Fig. 6, it is uderstood that the cotrol syste has resoace frequecy. The resoace frequecy equals to the iverter output frequecy. Hece, i case that Δvγ ad Δvδ cotai the resoace frequecy copoet whose frequecy is siilar to the iverter output frequecy, the lowfrequecy torque vibratio icreases. The γ-axis voltage ad the δ-axis voltage are fluctuated due to the trasitio to the square-wave voltage. I the square-wave voltage regio, the cotrol respose becoes slow because the voltage chages oly twice a period. Furtherore, the error of the voltage occurs because it is ipossible to switch every 8 degrees by the sigle-chip icrocoputer which geerate the PWM based o triagular-wave copariso ethod. Therefore, the load agle easily fluctuates with the iverter output frequecy which results i the fluctuatio of the γδ-axis voltage. Cosequetly, the low-frequecy torque vibratio occurs ad the δ-axis curret which is fed back to the stabilizatio cotrol also fluctuates. The fluctuatio of the δ-axis curret leads to the Gai [db] Gai [db] fluctuatio of the γδ-axis voltage, which worses the torque fluctuatio. III. REDUCTION METHOD OF OW-FREQUENCY TORQUE VIBRATION Agular frequecy [rad/s] (a) (b).67 p.u..79 p.u..85 p.u..9 p.u.. p.u. Characteristic fro Δvγ to ΔΤ. Characteristic fro Δvδ to ΔΤ..67 p.u..79 p.u..85 p.u..9 p.u.. p.u. Agular frequecy [rad/s] Fig. 6 Gai characteristics of ope-loop cotrol for PMSM. The cotrol syste has resoace frequecy, which equals to the iverter output frequecy. The reductio ethod of the low-frequecy torque vibratio is cosidered. The low-frequecy torque vibratio icreases d dt R Δi γ Δiδ ω = Δω Pf Δϕ si δ J ω K i δ R Kiγ Pf cosδ J K si δ cosδ ω cosδ ω si δ P f J ( i cosδ i si δ ) γ δ Δiγ Δiδ Δω Δϕ iδ Δvγ i γ Δvδ Δω (5) ΔT = Δiγ Δiδ si f f γ δ si (6) Δω Δϕ [ P ϕ P cosϕ P ( i cosϕ i ϕ )] f

5 because the γ-axis voltage ad the δ-axis voltage are fluctuated by the trasitio to the square-wave voltage. Therefore, it is ecessary to suppress the effect of the fluctuatio of the δ-axis curret for the drive syste. Fig. 7 shows the cotrol block diagra of the ope-loop cotrol with the low-frequecy torque vibratio reductio cotrol i the square-wave voltage regio. The proposed cotrol cosists of the bad pass filter (BPF). The resoace frequecy copoet i the δ-axis curret is extracted by the BPF. The, it is fed back to adjust the iverter output frequecy coad. I additio, the id-bad frequecy of the BPF is chaged by the iverter output frequecy coad (variable BPF) because the resoace frequecy of the cotrol syste chages accordig to the speed, i.e. the iverter output frequecy. The variable BPF cosists of the biquad filter. Furtherore, the proposed cotrol is ot ecessary i the PWM regio ad the over odulatio regio. Therefore, the filter gai K is zero i these regios. Fig. 8 shows the block diagra of the variable biquad filter. The coefficiets are varied by the iverter output frequecy. I additio the biquad filter is expressed by (7), f/v cov. HPF K Variable BPF K ow-frequecy torque vibratio reductio cotrol Trasitio cotrol - v v s i i uvw uvw Fig. 7 Cotrol block diagra of ope-loop cotrol with low-frequecy torque vibratio reductio cotrol i square-wave voltage regio. The reductio cotrol is cosist of the valiable BPF. i u i v i w S u S v S w y = b u b z u b z u a z y a z y (7), where u is the iput sigal, y is the output sigal ad a, a, b, b ad b are the coefficiets. If the BPF cosists of the biquad filter, the coefficiets are expressed by (8) ~ (), cosωc a = (8), α Fig. 8 Block diagra of variable biquad filter. The coefficiets are varied by the iverter output frequecy. where α a = (9), α α b = (), α b = (), b α = = α b ω πf (), c c = (3), f s siωc α = (4). Q f c is the ceter frequecy, f s is the saplig frequecy ad Q is Q factor. I this case, oly a, a ad b is calculated due to b = ad b = -b. I additio, the coefficiets are chaged by the ceter frequecy. Fig. 9 shows the coefficiet characteristics of the BPF o the biquad filter. The saplig frequecy is khz ad Q factor is.7. The all coefficiets are proportioal to the ceter frequecy, i.e., the coefficiets are expressed by the liear equatio. Therefore, the eory usage of the cotroller is ot large. Fig. shows the siulatio result of the PMSM drive by the ope-loop cotrol with the low-frequecy torque vibratio reductio cotrol. The siulatio coditio is sae as Fig. 3. It is cofired that the fluctuatio of the torque is reduced by the proposed ethod i the square-wave voltage regio.

6 -.65 a Ceter frequecy [Hz] (a) a a Ceter frequecy [Hz] b (b) a Ceter frequecy [Hz] (c) b Fig.9 Coefficiet characteristics of bad pass filter o biquad filter. The all coefficiets are proportioal to the ceter frequecy. Fig. shows the torque haroics whe the low-frequecy torque vibratio reductio cotrol is applied. The six-order copoet ad -order copoet do ot chage copared to Fig. 4. O the other had, the lower order copoet is reduced. Therefore, the stabilizatio of the torque is ca be achieved. Fig. shows the copariso of the low-frequecy torque vibratio. The low-frequecy torque vibratio decreases by approxiately 7% at the speed whe the torque fluctuatio becoes large (ω =.74 p.u. ad ω =.96 p.u.). However, the low-frequecy torque vibratio is ot reoved copletely because of the delay of the cotrol respose with the squarewave voltage as explaied above. Fig. Siulatio result of PMSM drive by ope-loop cotrol with low-frequecy torque vibratio reductio cotrol. The fluctuatio of the torque is reduced by the reductio ethod. Torque [p.u.] ower order haroics 6th order haroics.74 p.u..85 p.u..96 p.u. th order haroics Frequecy [Hz] Fig. Torque haroics with low-frequecy torque vibratio reductio cotrol. The lower order copoet is reduced copared to Fig. 4. IV. EXPERIMENTA RESUT I this sectio, the proposed cotrol is verificatio by the experiet. The cotrol period is 5 μs, whereas the variable B PF is cosist of two-order IIR filter. I additio, the paraeter of the PMSM i the experiet is show i Table. Fig. 3 shows the wavefor of the lie-to-lie voltage ad the phase curret. The otor speed is. p.u. Fro Fig. 3, it is Fig. Copariso of low-frequecy torque vibratio. The lowfrequecy torque vibratio decreases by approxiately 7% at the speed whe the torque fluctuatio becoes large (.74 p.u. ad.96 p.u.). cofired that the iverter is drive by the proposed cotrol ethod i the square-wave voltage regio.

7 Fig. 4 shows the wavefor of the speed ad the q-axis curret whe the PMSM is accelerated. I this experiet, it is difficult to easure the torque wavefor directly. Therefore, the q-axis curret is evaluated istead of the torque. I additio, the pole positio is detected by the positio sesor oly i order to calculate the q-axis curret. The cotroller does ot use the positio sesor. Furtherore, the acceleratio tie is 6.67 s fro ω =.6 p.u. to. p.u. because the torque fluctuatio is likely to have a egative effect o the drive syste whe the otor is accelerated slowly. Fro Fig. 9(a), it is uderstood that the fluctuatio of the q-axis curret icreases at several poits of speed i the square-wave voltage regio. O the other had, i Fig. 9(b), the fluctuatio of the q-axis curret is reduced by the proposed cotrol. Fig. 5 shows the wavefor of the speed ad the q-axis curret at ω =.943 p.u. The fluctuatio of the q-axis curret also occurs i the steady state as with the acceleratig. Moreover, the fluctuatio copoet of the q-axis curret is.35 p.u. without the low-frequecy torque vibratio reductio cotrol. If the proposed cotrol is applied, the fluctuatio copoet is iproved to.7 p.u. Fig. 6 shows the copariso of lower order haroic of the q-axis curret. The speed to copare are.848 p.u.,.98 p.u. ad.943 p.u. At ay copared speed, the fluctuatio of q-axis curret is large i Fig. 9. Fro Fig., the lower order haroic copoet of the q-axis curret decrease by over 4% at ay copared speed. Fig.3 Wavefor of lie-to-lie voltage ad phase curret i the squarewave voltage regio. The otor speed is. p.u. Square-wave voltage regio Speed. p.u./div =.6 p.u. =.99 p.u. =.847 p.u. =.943 p.u. q-axis curret. p.u./div s/div V. CONCUSION I this paper, the cotrol strategy for the PMSM based o the ope-loop cotrol i the sigle-chip icrocoputer is proposed. The proposed ethod is able to trasit fro the PWM regio to the square-wave voltage regio via the over odulatio regio sealessly. I additio, the low-frequecy torque vibratio except 6th or th order haroics occurs because the voltage is fluctuated by the trasitio to the square-wave voltage. Therefore, the low-frequecy torque vibratio reductio cotrol usig the variable BPF is proposed. As a experietal result, the low-frequecy vibratio decreases by over 4%. (a) Without low-frequecy torque vibratio reductio cotrol. The fluctuatio of the q-axis curret icreases at several poits of speed i the square-wave voltage regio. REFERENCES [] R. Taabe ad K. Akatsu, Advaced Torque ad Curret Cotrol Techiques for PMSMs with a Real-tie Siulator Istalled Behavior Motor Model, IEEJ Joural of Idustry Applicatios, Vol.5, No., pp (6) [] X. Ji ad T. Noguchi, Olie q-axis Iductace Idetificatio of IPM Sychroous Motor Based o Relatioship betwee Its Paraeter Misatch ad Curret, IEEJ Joural of Idustry Applicatios, Vol.4, No.6, pp (5) [3] T. Zaa, M. Kawasaki, K. iu, M. Hagio, ad A. Iura, Model Predictive Direct Torque Cotrol for PMSM with Discrete Voltage Vectors, IEEJ Joural of Idustry Applicatios, Vol.3, No., pp.-3 (4) [4] K. Ueda, S. Morioto, Y. Ioue, ad M. Saada, A Novel Cotrol Method i Flux-weakeig Regio for Efficiet Operatio of Iterior Peraet Maget Sychroous Motor, IEEJ Joural of Idustry Applicatios, Vol.4, No.5, pp (5) [5] T. Yaaguchi, Y. Tadao, ad N. Hoshi, Usig a Periodic Disturbace Observer for a Motor Drive to Dopesate Curret Measureet Errors, IEEJ Joural of Idustry Applicatios, Vol.4, No.4, pp (5) (b) With low-frequecy torque vibratio reductio cotrol. The fluctuatio of the q-axis curret is reduced by the proposed cotrol. Fig. 4 Wavefor of otor speed ad q-axis curret. The q-axis curret is evaluated istead of the torque. [6] A. M. Khabadkoe ad J. Holtz, Copesated Sychroous PI Curret Cotroller i Overodulatio Rage ad Six-Step Operatio of Space- Vector-Modulatio-Based Vector-Cotrolled Drives, IEEE Tras of Id. Electro., Vol.49, No.3, pp () [7] H. Nakai, H. Ohtai, ad Y. Iagua, Novel Torque Cotrol Techique for High Efficiecy/High Power Iterior Per aet Maget Sychroous Motors, R&D Review of Toyota CRD, Vol.4, No., pp (5)

8 Speed. p.u./div q-axis curret. p.u./div [8] H. Nakai, H. Ohtai, E. Satoh, ad Y. Iagua, Developet ad Testig of the Torque Cotrol for the Peraet-Maget Sychroous Motor, IEEE Tras. Id. Electro., Vol.5, No.3, pp.8-86 (5) [9] D. Asao, S. erdudosak S. Doki, ad S. Okua, Positio Sesorless Torque Cotrol Syste of PMSM i Overodulatio Rage, IPEC, pp.47-4 () [] Y. C. Kwo, S. Ki, ad S. K. Sul, Six-Step Operatio of PMSM With Istataeous Curret Cotrol, IEEE Tras. Id. Appl., Vol.5, No.4, pp (4) [] J. Itoh N. Noura, ad H. Ohsawa, A copariso betwee V/f cotrol ad positio-sesorless vector cotrol for the peraet aget sychroous otor, PCC, pp.3-35 () [] J. Itoh ad N. Ohtai, Square-Wave Operatio for a Sigle-Phase-PFC Three-Phase Motor Drive Syste Without a Reactor, IEEE Tras. Id. Appl., Vol.47, No., pp.85-8 () 5 s/div (a) Without low-frequecy torque vibratio reductio cotrol. Speed. p.u./div q-axis curret. p.u./div 5 s/div (b) With low-frequecy torque vibratio reductio cotrol. Fig. 5 Wavefor of otor speed ad q-axis curret at ω =.943 p.u. Fig. 6 Copariso of low-frequecy q-axis curret. The lower order haroic copoet of the q-axis curret decrease by over 4% at ay copared speed.