Hassan II University, Casablanca, Morocco

Transcription

1 Internatonal Journal of Enhanced Research n Scence Technology & Engneerng, ISSN: Vol. 3 Issue 4, Aprl-214, pp: ( ), Impact Factor: 1.22, Avalable onlne at: Comparson of PI and Fuzzy logc DC-Lnk Voltage Controller for DPC PWM-Rectfer J. Lamterkat 1, M. Khafallah 2, L. Ouboubker Department of Electrcal Engneerng at the Natonal Hgher School of Electrcty and Mechancs (ENSEM), Hassan II nversty, Casablanca, Morocco Abstract: Ths paper treats drect power control (DPC) for three-phase PWM rectfers usng a new swtchng table, wthout lne voltage sensors and the fuzzy logc theory. The nstantaneous actve and reactve powers, drectly controlled by selectng the optmum state of the converter, are used as the PWM control varables nstead of the phase lne currents beng used. These strateges are used to elmnate harmoncs currents and consequently to reduce total harmonc dstorton (THD) of the lne current and mprove the power factor wth mantan the dc-bus voltage at the requred level. Conventonal PI and a desgned fuzzy logc-based controller, n the dc-bus voltage control loop, have been used to provde actve power command. A dgtal smulaton, n Matlab/smulnk, was carred. The steady-state and dynamc results llustratng the operaton and performance of the proposed control scheme are presented. As a result, t was confrmed that the novel DPC s much better than the classcal one. Smulaton results show clearly the effectveness of the adopted control strateges. Keywords: Drect power control (DPC), fuzzy control, nstantaneous actve and reactve powers, PWM rectfer, PI controller, THD, voltage estmaton. Introducton The ncreasng use of electronc devces n power electrcal systems has led to more and more problems assocated wth dstorton harmoncs n electrcal networks. Harmonc currents are manly ssued by non-lnear loads based electronc power devces. These harmoncs wll generate harmonc voltages at dfferent connecton ponts to the network. Many of harmonc reducton method exst. These technques based on passve components, mxng sngle and three-phase dode rectfers, and power electroncs technques as: mult-pulse rectfers, actve flters and PWM rectfers [1]. They compensate for dsturbances due to a non-lnear load n feedng back opposte phase on the network harmoncs and reactve current drawn by the load so that the network s not only to provde a snusodal current n phase wth the voltage. Performance of these methods, ncludng the reducton of total dstorton of source current and mproved power factor, are not only related to the performance of the generaton of harmonc current references, but also depend on the control strategy. Pulse Wdth modulaton (PWM) rectfer are extensvely used n AC varable speed drve, reactve compensaton and actve power flter for ther hgh power factor, small total harmonc dstorton (THD) systems, bdrectonal power flow and fast dynamc response. Varous control strateges were proposed n recent works for the PWM rectfer [2]. Whle they can reach the same total objectve, such as a hgh power factor and snusodal current, but ther prncples vary. Partcularly, the voltage orentaton control (VOC) and vrtual flux orentaton control (VFOC), can guarantee a hgh dynamcs and statc performances by nternal loops of current control [4]. These control strateges became very popular and consequently they are developed and mproved. Fnal confguraton and performances of the VOC technque depend largely on the qualty of the current control strategy [3]. Other approach reles on nstantaneous drect actve and reactve power control, and s named drect power control (DPC) [2]. Approprate swtchng states are selected for next swtchng table, based on hysteress controller s outputs and the poston of the lne voltage space vector. However, hgh samplng frequency requrement s a man drawback of the swtchng table based drect power control scheme [4]. In more DPC shames for PWM rectfer, the actve power exchange must be stable by nsurng a DC voltage equal to ts reference so that the PWM rectfer operates wth a good effcency. Ths can be carred out by usng a control system able to regulate DC voltage. Ths paper presents a drect power control (DPC) of three phases PWM rectfer based on fuzzy logc control approach s; makng t possble to acheve unty power factor operaton by drectly controllng ts nstantaneous actve and reactve power, wthout any power source voltage sensors. The dc bus voltage s regulated by controllng actve power usng fuzzy logc controller, whch provdes actve power command. Although the reactve power command s close to zero to ensure unty power factor operaton. Fnally, the developed fuzzy controller s compared to classcal PI controller. The smulaton results shown that the proposed controller based on fuzzy logc control s ntroduced to mprove the performances of the system behavor. Lke a good rejecton of mpact load dsturbance, a good dynamc behavor for dc output voltage regulaton, for more reducton of THD and power rpple [][6]. Page 321

2 Internatonal Journal of Enhanced Research n Scence Technology & Engneerng, ISSN: Vol. 3 Issue 4, Aprl-214, pp: ( ), Impact Factor: 1.22, Avalable onlne at: The PWM Rectfer Structure The boost rectfer confguraton s shown schematcally n Fg. 1. The brdge crcut s constructed of sx controllable power swtches and ant-parallel dodes. The power network voltage s connected to the grd assocated wth a RL flter. Network Converter DC bus L O A D Fgure 1. Structure of PWM rectfer Fgure 2. Sngle-phase equvalent crcut of the PWM rectfer The voltage equaton for ths sngle phase crcut can be wrtten as: a a a sa d R L b b b sb dt c c c sc (1) For the balanced three-phase voltage we can wrte PWM rectfer equaton n statonary coordnates. L L ab 3 2 L 2 bc 3 (2) L L a 3 3 L 3 b 2 (3) Also we can wrte PWM rectfer equaton n synchronous rotatng coordnates(r s neglected): Ld d Ld Lq sd L dt Lq Lq Ld sq The equaton (4) can be transformed to vector form n synchronous d-q coordnates defnng dervatve of current as: (4) Page 322

3 Internatonal Journal of Enhanced Research n Scence Technology & Engneerng, ISSN: Vol. 3 Issue 4, Aprl-214, pp: ( ), Impact Factor: 1.22, Avalable onlne at: d Ldq L Ldq jlldq sdq Voltages vector generated by the rectfer can be gven by Table 1: dt () Table 1. Dfferent swtches confguratons and the correspondng voltages vector S a S b S c sa sb sc sα sβ V V 1 -dc/3 -dc/3 2dc/3 -dc/ 6 -dc/ 2 V 1 -dc/3 2dc/3 -dc/3 -dc/ 6 dc/ 2 V dc/3 dc/3 dc/3-2/3.dc V 4 1 2dc/3 dc/3 dc/3 2/3.dc V dc/3-2dc/3 dc/3 dc/ 6 -dc/ 2 V dc/3 dc/3-2dc/3 dc/ 6 dc/ 2 V V 7 The vector representaton of voltage vectors generated by the rectfer s llustrated n fg.3: Fgure 3. Voltage vectors generated by the rectfer The Control Strategy Of The DPC DPC of PWM rectfers can be generally classfed used two types of estmaton:[2][7] - Voltage estmaton, - Vrtual flux estmaton, PWM Rectfer Control Voltage Estmaton Vrtual Flux Estmaton VOC DPC VFOC VF-DPC Fgure 4. Dfferent control strateges of a PWM rectfer The DPC prncple s based on a control vector selecton accordng to a swtchng table found on the dgtzed errors Sp, Sq of nstantaneous actve and reactve powers, provded by two level hysteress regulators, as well as on angular poston of the estmated voltage vector. Accordng to ths poston value, the plan (α -β ) s dvded nto twelve sectors where one Page 323

4 Internatonal Journal of Enhanced Research n Scence Technology & Engneerng, ISSN: Vol. 3 Issue 4, Aprl-214, pp: ( ), Impact Factor: 1.22, Avalable onlne at: must assocate at each sector a logcal state of the rectfer. The reference of the actve power s obtaned by a PI controller of the DC voltage. In order to ensure a unt power-factor, the reactve power reference s chosen equal to zero. Hence the key pont for mplementng DPC strateges s a correct and a fast estmaton of actve and reactve lne powers. Fg. shows the block dagram of the DPC system and load [8][9]. Fgure. Drect power control method Block scheme Reactve power s estmated by the equatons 6, 7. In ths equaton a, b, c are the ac-lne measured current and the S a, S b, S c are the swtchng state of the converter. These two equatons requre knowledge of the lne nductance L [9]. q da db dc p L a b c dc Saa Sbb Scc dt dt dt da dc 1 3L c a dc Sa b c Sb c a Sc a b dt dt 3 (6) (7) The ac-lne current are measured and the values of the actve and reactve power are estmated by equatons.6,7 and then the lne voltage can easly be calculated from the equaton 8. l 1 l l 2 2 l l l l l (8) Fg.6 shows the nstantaneous actve power, reactve power and ac voltage estmator block Fgure 6. Instantaneous actve and reactve power estmaton The knowledge of the estmated voltage sector s necessary to determne optmal swtchng states. Determnaton of the number sector s gven by: ( n2) n ( n1) 6 6 Where: n=1,,12 n ndcate the sector number. It s nstantaneously gven by the voltage vector poston ant s computed as follows: (9) Page 324

5 Internatonal Journal of Enhanced Research n Scence Technology & Engneerng, ISSN: Vol. 3 Issue 4, Aprl-214, pp: ( ), Impact Factor: 1.22, Avalable onlne at: Fg. 6 shows the 12sector voltage plane for swtchng table. 1 l tan l (1) Fgure 7. α-β plant dvded nto 12 sectors In ths system the actve and reactve power s estmated at each tme. The dgtzed output sgnals of the reactve and actve power controller are defends as: p ˆ ref p hp S p 1 p ˆ ref p hp S p q ˆ ref q hq Sq 1 q ˆ ref q hq Sq Where hp, hq are the varatons of the hysteress regulators. The dgtzed error sgnals SP and Sq and the poston γn of fundamental nput voltage vector αβ are nputs to the swtchng table n whch every swtchng state (Sa, Sb, Sc) of the converter s stored, as shown n Table II. By usng our own swtchng table, proposed n [1][11], the approprate swtchng state of the converter can be selected n every specfc moment accordng to the combnaton of the dgtzed nput sgnals. The selected swtchng state allows the best restrcton of both power trackng errors to acheve smultaneous control of ph and qh wth good accuracy. Table 2: Swtchng table S p S q γ 1 γ 2 γ 3 γ 4 γ γ 6 γ 7 γ 8 γ 9 γ 1 γ 11 γ 12 1 V V 6 V 6 V 1 V 1 V 2 V 2 V 3 V 3 V 4 V 4 V 1 V 3 V 4 V 4 V V V 6 V 6 V 1 V 1 V 2 V 2 V 3 1 V 6 V 1 V 1 V 2 V 2 V 3 V 3 V 4 V 4 V V V 6 V 1 V 2 V 2 V 3 V 3 V 4 V 4 V V V 6 V 6 V 1 DC Voltage Regulaton In the proposed DPC scheme, magntude of fundamental nput currents s delvered from the outer proportonal-ntegral (PI) dc-bus voltage controller and wll be multpled by the dc voltage to obtan the reference of the nstantaneous actve power. To have unty power factor condton, reference reactve power must be equal to zero. The regulaton functon s ensured by a PI corrector shown n the fgure below: (11) dcref + - PI I ref P ref dc Fgure 7. DC voltage regulaton Where Kp and K are the proportonal and ntegral controller gans respectvely. To determne the parameters of the PI controller, we make the followng mathematcs development. Page 32

6 Internatonal Journal of Enhanced Research n Scence Technology & Engneerng, ISSN: Vol. 3 Issue 4, Aprl-214, pp: ( ), Impact Factor: 1.22, Avalable onlne at: The relatonshp between the power absorbed by the capactor and the termnal voltage can be wrtten: d 1 2 p f ( Cdc ) (12) dt 2 Based the Laplace transform: p CS. The transfer functon of the PI controller can be expressed by: k 1 S k p S T S The transfer functon of the closed loop system s gven by: 2 (1 ) FS ( ) 2 2 S 2 S 2 Wth: and: CT We found: k p and: T 2 2 dc f 1 k T For a good performance of DC voltage control, n partcular n the case of change of DC reference voltage level, the PI controller s replaced by a fuzzy controller. 2CT Proposed Fuzzy Control Scheme The prncpal scheme of the proposed fuzzy logc control s gven by fg 8. [12]. The dc bus voltage dc s sensed and compared wth a reference value dcref.the obtaned error e(n)= dcref (n)- dc (n) and ts ncremental varaton de(n)=e(n)- e(n-1) at the n th samplng nstant are used as nputs for fuzzy controller. The output s the nstantaneous actve P ref. the dc bus voltage s controlled by adjustng the actve power usng fuzzy controller. (13) (14) () Fuzzy controller dcref e K 1 + de 1/P - d/dt K 2 K3 P ref dc Fgure 8. DC voltage fuzzy control The fuzzy controllers allow the regulaton of the DC bus voltage and generate the ampltude of the reference currents. The error of the DC bus voltage and ts varaton are used as nputs of the fuzzy process. These two nput varables are dscredted wth a samplng perod T s and normalzed usng the normalzaton gans (Ge) for error and (GΔe) for the varaton of the error they are defned by the followng expressons. The settng error n the DC bus voltage devaton s defned by: e The ncremental change n the settng error s defned by: de( n) e( n) e( n 1) The fuzzy controller output s consdered the varaton of the ampltude of the reference currents ΔIM(n). The ampltude of the reference currents for the nth sample IM (n) s obtaned by addng the ampltude IM (n-1). Wth the varaton ΔIM (n) as the followng equaton: dcref dc I ( n) I ( n) I ( n) M M M The output s the nstantaneous actve power reference Pref, the dc bus voltage s controlled by adjustng the actve power usng fuzzy controller. The man characterstcs of fuzzy controller are: - Seven fuzzy sets for e(n), de(n), ΔIM(n); - Fuzzyfcaton usng contnuous unverse of dscourse; - Implcaton usng Mandan s operator; Page 326

7 Degree of membershp Degree of membershp Degree of membershp Internatonal Journal of Enhanced Research n Scence Technology & Engneerng, ISSN: Vol. 3 Issue 4, Aprl-214, pp: ( ), Impact Factor: 1.22, Avalable onlne at: - Defuzzyfcaton usng heght method; The nternal structure of fuzzy controller used s shown n Fg.9. e(n) G e de(n) G Δe Fuzzyfcaton Decson rules Defuzzyfcaton ΔI M Fgure 9. Internal structure of the fuzzy controller For fuzzyfcaton, we used trangular membershp functons for the error e (n), the varaton of de(n) and output ΔIM (n), and we chose the seven fuzzy sets: NB negatve bg, NM negatve medum, NS negatve small, EZ zero, PS postve small, PM postve medum and PB postve bg. [13] NL NM NS ZR PS PM PL 1 NL NM NS ZR PS PM PL e de Fgure.1: Membershp functons of nput NL NM NS ZR PS PM PL OT Fgure.11: Membershp functons of output For the nference rules we have establshed are summarzed n followng Table: Table 3. The rules of the fuzzy controller Smulaton Results In order to confrm the effectveness of the proposed DPC scheme and evaluate ts performance under dfferent nput voltage condtons, a model of three-phase PWM rectfer, ncludng the control system, has been smulated n Matlab/Smulnk envronment. Smulatons have been carred out usng the man electrcal parameters of power crcut Page 327

8 a(a) and Va(v) a(a) and Va(v)/1 a(a) a(a) dc(v) dc(v) Internatonal Journal of Enhanced Research n Scence Technology & Engneerng, ISSN: Vol. 3 Issue 4, Aprl-214, pp: ( ), Impact Factor: 1.22, Avalable onlne at: and control data showed n Table 4. Several tests were conducted to verfy feasblty and performance of the fuzzy DPC scheme compared to the voltage estmate DPC wth PI regulator. Table 4. Electrcal parameters of power crcut Sample tme T s 1 - s Reactance of reactors R.3Ω Inductance of reactors L 8mH dc-bus capastor C 2mF Resstance load R load 8Ω Peak ampltude of lne voltage 31V Source voltage frequency Hz DC voltage dc 6V 8 (a) (a ) (b) (b ) (c) a(a) Va(v)/ (c ) Va(v)/1 a(a) (d) (d ) Page 328

9 udc(v) dc(v) a, b, c(a) a, b, c(a) Actve power (kw) Actve power(kw) Internatonal Journal of Enhanced Research n Scence Technology & Engneerng, ISSN: Vol. 3 Issue 4, Aprl-214, pp: ( ), Impact Factor: 1.22, Avalable onlne at: 3 (e) (e ) Fgure 12: smulated results were obtaned for purely snusodal supply lne voltage and dcref =6V sng PI regulator, (a) output voltage, (b) lne current, (c) lne current wth lne voltage/1, (d) harmonc spectrum of lne current and (e) nstantaneous actve power (kw). Fgure 13: smulated results were obtaned for purely snusodal supply lne voltage and dcref =6V sng Fuzzy logc controller, (a ) output voltage, (b ) lne current, (c ) lne current wth lne voltage/1, (d ) harmonc spectrum of lne current and (e ) nstantaneous actve power (kw). The effcency of the DC voltage fuzzy control s llustrated by fg.12 (a ). We can see that the system became more stable and robust compared to the PI regulator (fg 13. a). The system response s acceptable and does not present any overshoot. It s seen that the lne current (fg 13.b) presented a rpples more than the lne current (fg 12.b ). From the fgure (13.c ), t can be seen that the lne current are very close to sne wave and n phase wth power source voltage because the reactve power q ref s set to zero. The actve power s constant on average (Kw) (fg 13.e ). The THD of lne current s reduced to 3.2% because of the unty power factor operaton. Fgure show a result of a step response aganst the dsturbance load power under the unty power factor operaton. The load power was changed step wse from kw to 1kw n ths test. It can be observed that the unty power factor operaton s successfully acheved, even n ths transent state. Notce that, after a short transent (Tr=.s), the output voltage s mantaned close to ts reference value (fgure.g ) compared to the PI regulator (Tr=.7s) (fgure 14.g). 3 (f) 3 (f ) (g) 66 (g ) Page 329

10 dc(v) dc(v) a, b, c(a) Reactve power (kvar) Reactve power (kvar) Actve power (kw) Actve power (kw) Internatonal Journal of Enhanced Research n Scence Technology & Engneerng, ISSN: Vol. 3 Issue 4, Aprl-214, pp: ( ), Impact Factor: 1.22, Avalable onlne at: (h) (h ) () 2 ( ) Fgure 14: transent of the step change of the load, load ncreasng (%) usng PI regulator. From the top: (f) lne current, (g) output voltage, (h) nstantaneous actve power, and () nstantaneous reactve power. Fgure : transent of the step change of the load, load ncreasng (%) usng fuzzy controller. From the top: (f ) lne current, (g ) output voltage, (h ) nstantaneous actve power, and ( ) nstantaneous reactve power. The dynamc behavor under a step change of dc s presented n fgure 17. After a short transent, the output voltage s mantaned close to ts new reference and the actve power s mantaned constant after a short transent. Reactve power s mantaned zero. (j) (j ) (k) 8 (k ) Page 33

11 REactve power (kvar) Reactve power (kvar) Actve power (kw) Actve power (kw) Internatonal Journal of Enhanced Research n Scence Technology & Engneerng, ISSN: Vol. 3 Issue 4, Aprl-214, pp: ( ), Impact Factor: 1.22, Avalable onlne at: (l) (l ) Fgure 16: transent of the step change of the dc from 6V to 8V, usng PI regulator. From the top: (j) lne current, (k) output voltage, (l) nstantaneous actve power, and (m) nstantaneous reactve power. Fgure 17: transent of the step change of the dc from 6V to 8V, usng PI regulator. From the top: (j ) lne current, (k ) output voltage, (l ) nstantaneous actve power, and (m ) nstantaneous reactve power. Fg.17 shows that when the DC voltage reaches the new reference value and the overshoot completely dsappears (fg 17.k ) compared to the fgure (16.k), the actve power and consequently the lne current ncrease (fg 17.j ). In ths case the power ncrease s lmted (fg 17.m ), what avods dangerous over currents for the system operaton and we can see that the reactve power flow s small, what s very benefcal for the system performances. The wave shape of the lne current close to the snusod, and hence the THD (Total Harmonc Dstorton) was reduced. Concluson / Results Ths paper has presented the development and the mplementaton of a new drect power control (DPC) scheme for three-phase PWM rectfer usng a fuzzy control system on the DC sde. The man goal of the proposed control strategy s to acheve near-snusodal nput current waveforms of the converter under dfferent nput voltage condtons and mantanng the dc-bus voltage at the requred level. The actve and reactve power can be regulated drectly by relay control of the power and a swtchng table. Smulaton results have proven excellent performance of the proposed DPC scheme whch s much better than conventonal DPC based on PI regulator. Even n both transent and steady states. Nearly snusodal waveforms of nput currents are successfully acheved and guarantee a good regulaton of the output voltage wth a near unt power factor. References [1]. S. Hansen, P. Nelsen, P. Thogersen,.Harmonc dstorton and reducton technques of PWM adjustable speed drves - a cost beneft analyss., n proc. Norpe Conf., pp , 2. [2]. Malnowsk M, Kazmerkowsk MP, Trzynadlowsk A. Revew and comparatve study of control technques for three-phase PWM rectfers. Mathematcs and Computers n Smulaton, Volume 63, Issues 3-, 17 November 23, Pages [3]. Kazmerkowsk MP, Malesan L. Current control technques for three-phase voltage-source PWM converter: a survey. IEEE Trans Ind Electron 1998;4: [4]. Malnowsk M, Kazmerkowsk MP, Hansen S, Blaabjerg F,Maeques GD. Vrtual flux based drect power control of three phase PWM rectfers. IEEE Trans Ind Appl 21; 37: []. Carlo Cecat, Antono Dell Aqula, Marco Lserre,, and Antono Ometto, A Fuzzy-Logc-Based Controller for actve rectfer, eee transactons on ndustry applcatons, vol. 39, no. 1, january/february 23. Page 331

12 Internatonal Journal of Enhanced Research n Scence Technology & Engneerng, ISSN: Vol. 3 Issue 4, Aprl-214, pp: ( ), Impact Factor: 1.22, Avalable onlne at: [6]. Roland, P. Burgos, Eduardo P. Wechmann, Jose R. Rodrguez, A Smple Adaptve Fuzzy Logc Controller for Three-phase PWM Boost Rectfers, n proc. IEEE- Ind. Elec. Conf., pp , [7]. D.C. Lee, and D.S. Lm, AC Voltage and Current Sensorless Control of Three-Phase PWM Rectfers, IEEE Transactons on Power Electroncs, VOL. 17, NO. 6, November 22, pp [8]. M. M. Maran, P.Kazmerkowsk, A. Tryznadlowsk," Drect power control wth vrtual flux estmaton for three-phase PWM rectfers" Industral Electroncs, 2. ISIE 2. Proceedngs of the 2 IEEE Internatonal Symposum on Publshed: 2 Volume: 2, Page(s): vol.2. [9]. M.m. Maran, P.Kazmerkowsk, F. Blaabjerg "Vrtual-flux based drect power control of three phase PWM rectfer", IEEE, vol.37, no.4, july/august 21. [1]. A. Bouafa, J. P. Gaubert, and F. Krm, Analyss and desgn of new swtchng table for drect power control of three-phase PWM rectfer, 13th Internatonal Power Electroncs and Moton Control Conference (EPE-PEMC 28), pp , 28. [11]. A. Bouafa, F. Krm, and J. P. Gaubert, Desgn and mplementaton of hgh performance drect power control of three-phase PWM rectfer, va fuzzy and PI controller for output voltage regulaton, ELSEVIER, Energy Converson and Management, vol., No.1, pp. 6-13, Jan.29. [12]. Lokman H. Hassan & all. Takag-Sugeno Fuzzy Gans Scheduled PI Controller for Enhancement of Power System Stablty, Amercan Journal of Appled Scences 7 (1): 14-2, 21. [13]. S.M. Gadoue, D. Gaours, J.W. Fnch Artfcal ntellgence-based speed control of DTC nducton motor drves. A comparatve study, Electrc Power Systems Research. vol. 79, pp , 29. Page 332