Control of permanent magnet synchronous generator wind turbine for stand-alone system using fuzzy logic

Transcription

1 EUSFLAT-LFA 0 July 0 Ax-les-Bans, France Control of permanent magnet synchronous generator turbne for stand-alone system usng fuzzy logc Huynh Quang Mnh, Nollet Frédérc, Essounboul Najb, Hamzaou Abdelazz URCA CReSTIC, IUT de Troyes, 9, rue de Québec, B.P TROYES Cedex, FRANCE mnh.huynh-quang@etudant.unv-rems.fr, {frederc.nollet, najb.essounboul, abdelazz.hamzaou}@unv-rems.fr Abstract In ths paper, the control scheme of a energy converson system for remote stes usng fuzzy logc s presented. Two fuzzy controllers are proposed: the frst one s dedcated to the maxmum power pont trackng (MPPT) of a varable speed permanent magnet synchronous generator turbne. The second fuzzy controller has the the objectve to manage both the producton and the storage of electrcty for optmum performances of the system n respectng load demand. Several smulaton results are gven to show the effectveness and the good performances of the proposed control structure. Keywords: energy, permanent magnet synchronous generator, maxmum power pont tracker, stand-alone system, battery, fuzzy control.. Introducton In recent years, the producton of electrcty from renewable energy sources lke energy ncreases due to envronmental problems and the shortage of tradtonal energy sources n the near future []. Wnd power depends manly on geographcal condtons and weather condtons. Therefore, t s necessary to construct a system capable of generatng maxmum power under these constrants []. Nowadays, permanent magnet synchronous generators (PMSGs) are used n turbne because of ts advantages: better relablty, less mantenance and more effectve ([3],[4]). In addton, explotng the case of of varable speed allows to obtan an optmal effcency of the system [5]. For remote stes located far from the utlty, a practcal approach for power generaton s to use a varable speed turbne to create an autonomous system. It often ncludes batteres, used when the cannot provde suffcent power. If condtons are favorable, these autonomous energy systems can provde electrcty at low cost. If power exceeds the load demand, the surplus can be stored n batteres and f power cannot meet load demand, the batteres can compensate t ([],[6]). Recently, M. Dal worked on the duty cycle of a boost converter, managed n the same tme the MPPT control and the load voltage by usng a PI controller for current and voltage [4]. Although conventonal PI controller have been well developed and appled for ndustral automaton and process control due to ther smplcty of operaton, ease of desgn and effectveness for most lnear systems, t generally does not work well for nonlnear systems, hgher order and tme-delayed lnear systems, and partcularly complex and vague systems that have no precse mathematcal models [7]. To overcome these dffcultes, varous types of controllers usng artfcal ntellgent such as fuzzy logc, genetc algorthm... were developed lately [8]. In energy, T. F. El-Shatter has desgned two fuzzy controllers to deal wth two boost converters, one for the MPPT and the other for voltage regulaton [9]. In ths paper, we propose a energy converson system for remote ste usng a varable speed PMSG, a battery bank and two fuzzy controllers to optmze the operaton of both the turbne and the battery accordng to speed and load demand. The frst boost converter (DC/DC ) s used to change the voltage output of the generator. Thus, by controllng the converter, the rotor speed of PMSG s controlled to acheve the optmum value to maxmze the power recovered. To manage the energy producton, we use another fuzzy controller to set the duty rato of the second boost converter (DC/DC ) n order to () adjust the DC output voltage, () to choose the moment to charge/dscharge the battery and () the moment to dsspate excess energy n a dumb resstance. Fuzzy logc provdes a formal methodology for the representaton, manpulaton and mplementaton of knowledge of a human beng. We no longer need an accurate model of the complex system (synchronous generator wth converters, nverters...) when desgnng of our controllers. Wth proposed controllers, energy s prmarly provded drectly to load wthout gong through a passve element (battery). As a result, the number of charge/dscharge rate s greatly reduced thereby extend battery lfe.. System descrpton Our system conssts of a PMSG (67Nm, 700rpm) to power a kw pump, a 3kW nducton machne, a 4kW water heater, and a lead acd battery for backup storage. A dode brdge rectfer and two boost converters are used for MPPT purpose and for electrcal producton management. A pulse wdth modulaton nverter s used to provde a 380V, 50Hz voltage to load. 0. The authors - Publshed by Atlants Press 70

2 P m s the mechancal power of the (Nm/s). The maxmum power coeffcent C pm s Ths coeffcent s also known as Betz lmt. It can be expressed n terms of reduced velocty Ƌ and angle of lght ƈ: C p = C p (Ƌ, ƈ). If W s the rotor speed, the reduced speed Ƌ s defned: Fg. : Proposed system. A fuzzy logc controller (FLC ) s desgned to vary the operatng tme (or duty cycle) D of the frst converter to track the optmum rotor speed, thus maxmzng the power recovered by the turbne. Input s the error between the actual speed of the rotor and the optmal speed reference. Output s the duty rato D of the frst converter to acheve optmal rotor speed. Another fuzzy logc controller (FLC ) s desgned to adjust the DC voltage to a value sutable for battery chargng and also sutable for the proper operaton of the PWM nverter. If condtons are favorable, the turbne wll be the man suppler for load. If the does not gve enough power to load, and the battery capacty s suffcent, the battery wll start to provde the necessary power. If the power of the turbne exceeds the load demand, the surplus s stored n the battery and f the battery s full, the surplus wll be dsspated n a resstor. Thus, the battery s not the man suppler, so that the number of charge/dscharge rate s reduced, and consequently the lfe of the battery s extended. For ths, we need two nformatons: the battery state-ofcharge (SOC) and the error between avalable power and load demand (DeltaP). The controller wll decde the value of the duty cycle (D ), the moment to swtch the battery (S ) and the moment to dsspate the excess n the resstor (S ). 3. Model of turbne The statc characterstc of the turbne (output as a functon of speed) can be descrbed by the relatonshp between the total power and mechancal energy of the ([],[]): l WR v turbne = (3) Assumng a constant speed v, the reduced speed Ƌ vares proportonally to the rotor speed [0]. The maxmum value of C p s generally obtaned for values of Ƌ around 8 to 9 (when the tp of the movements of blade s 8 to 9 tmes faster than the ). On modern turbnes, t s possble to adjust the angle of the blades through a control mechansm []. If C p -Ƌ curve s known for a specfc wth a radus of turbne rotor R turbne, t s easy to construct the curve of C p as a functon of rotatonal speed əә for a speed v. The output torque of the turbne s calculated : T P W m m = = C rp R v 3 p turbne W (4) If the speed rato Ƌ s mantaned at ts optmal value Ƌ opt, the power coeffcent s at ts maxmum value C pm =C p (Ƌ opt ), the maxmum power of the turbne wll be: opt 3 Pm = C pm rp Rturbnev (5) On the other hand, the speed rato assumed to be mantaned at the optmum value, we obtan the optmum speed rotor: l WR v opt opt turbne opt = f W = (6) l R v turbne Thus, for each speed v, there s a maxmum rotor speed əә opt whch made a maxmum power recovered from the turbne (Fg. ). 3 P = rp Rturbnev () where Ɠ s the ar densty (,5 kg/m3), R turbne s the rotor radus (m), v s the speed (m/s). It s mpossble to extract all the knetc energy of, so t extracts a fracton of the power of as shown n () as the power coeffcent C p. 3 Pm = C prp Rturbnev () Fg.. Maxmum power n functon of rotor speed 7

3 In ths paper, a turbne s smulated by usng a look-up table, where nputs are speed and rotor speed and output s the mechancal torque. V DC 3 6 TL = w k - ( ) - D p k e e s T (7) 4. Model of PMSG Permanent magnet machnes have been wdely used. Indeed, ths technque can replace the feld ng of synchronous machnes and has more well known advantages of compact sze, the hgher power densty, the loss reducton, hgh relablty and good robustness. In addton, the smple desgn of the rotor wthout feld ngs, no rngs and no exctaton system also ncreases the effcency of the machne []. The dynamc model of PMSG can be represented n the Park's system usng the followng equatons [3]: dd Vd =-RSd - Ld + w Lqq dt (7) dq Vq =-RSq -Lq - wldd+ wlm dt (8) The expresson of electromagnetc torque n the rotor s gven by: 3 Te = p [( Ld - Lq ) qd - lmq ] (9) W= pw (0) where p s the number of pole par, l m s the magnetc flux, L d s the drect axs nductance, L q s the nductance n quadrature, R s s the stator resstance and ƛ s the electrcal angular frequency. If the rotor s cylndrcal, L d & L q & L s so: 3 Te = plm () q PMSG n the relatonshp between the torque and nduced voltage [3] s: Te = ktia () E = k w (3) E So the torque s determned by the rotor speed and speed: a specfc value of the voltage s estmated for a specfc rotor speed and speed. Now, for a gven value of rotor speed, voltage can be obtaned and appled to the system. By applyng ths control strategy, speed and voltage vary contnuously untl they reach ther equlbrum. In ths case, the maxmum power of energy s acheved. Hence, the voltage optmal value s reached by varyng the duty rato D of the frst converter as follows: V -V W -W D = = V W DC DC _ opt opt DC (8) 5. Fuzzy controller for the MPPT of the PMSG In ths secton, we present the fuzzy controller used for trackng the rotor speed to acheve the MPPT. Fuzzy controllers belong to the class of knowledge based systems. Ther man goal s to mplement human knowledge n the form of a computer program. The fuzzy controller has four man components: () the!rule-base" holds the knowledge, n the form of a set of rules, of how best to control the system; () the nference mechansm evaluates whch control rules are relevant at the current tme and then decdes what the nput to the plant should be; () the fuzzfcaton nterface smply modfes the nputs so that they can be nterpreted and compared to the rules n the rule-base and () the defuzzfcaton nterface converts the conclusons reached by the nference mechansm nto the nputs to the plant [6]. In our MPPT controller (FLC ), we use the error between reference speed and the real rotor speed and the change of ths error as nputs. Output s the duty cycle D of the frst boost converter. where I a s the stator current. On the other hand: E = V + ( I L w ) (4) a s V s the voltage phase and L s s the nductance of the generator. The output voltage of the rectfer s gven by [4]: Vrec 3 6 = V (5) p and the output voltage of the frst converter [5]: V DC = V (6) rec - D Fg. 3. Controller MPPT The lngustc term sets used are: Error [Very Negatve, Negatve, Small Negatve, Zero, Small Postve, Postve, Very Postve]. Dervatve of error [Negatve, Zero, Postve]. 7

4 FnalOutput = N Â w. DD N Â w (3) where N s the number of rules. Fg. 4. Seven terms of varable "Error" Fg. 5. Three terms of varable "Dervatve of error" The method of nference rules for descrbng the dynamc method used s the mn-max one. Ths type of method nvolves a smple treatment of data and generates lnear features (for two or more szes of entres) wth marked dscontnutes. µ A«B( x) = mn( µ A( x), µ B( x)) (9) µ A» B( x) = max( µ A( x), µ B( x)) (0) Here, we used Takag-Sugeno system [7]. Example: "If the error between reference speed and rotor speed s Postve and the dervatve of that error s Zero, then ' D = +5%". Then: D (k) = D (k-) + ' D(k) () The varous fuzzy rules used n our system are summarzed n table. ' D (%) Dervatve of error Negatve Zero Postve VN N SN Error Z SP P VP Table. Rules of! D The output level ' D of each rule s weghted by the frng strength w of the rule. For example, wth (Speed error s P) and (Dervatve of speed error s Zero), the frng strength s: Fg. 6. Defuzzfcaton n case error=-0 and derror= 6. Fuzzy controller for the producton process Inputs for ths controller are the battery state of charge (SOC) and the error power DeltaP (dfference between power and load power). The outputs are the duty rato D appled to the second boost converter for chargng the battery (ensurng a safe and effectve) and ensure that the nput voltage s suffcent for the PWM nverter, the tme to charge/dscharge the battery and the tme to dspel the surplus to a dscharge resstor. The lngustc term sets used for: Power error DeltaP [Negatve, Small Postve, Postve, Very Postve]. Battery's state-of-charge SOC [Empty, Average, Full]. Duty cycle D [Very Small, Small, Medum, Bg, Very Bg]. Swtch S and S [Opened, Closed]. Fg. 7. Four terms of varable "DeltaP" w = mn( µ ( P), µ ( Zero)) () Error DervatveOfError The fnal output of the system s the weghted average of all rules output, computed as: Fg. 8. Three terms of varable "SOC" 73

5 Where x s a pont n the unverse U of the concluson ( =, # ), and ƌ c (x ) ts membershp of the resultng concluson set. Fg. 9. Fve terms of varable "D " Fg.. Defuzzfcaton n case DeltaP=0 and SOC=50% Fg. 0. Two terms of varable "S " and "S " The method of nference rules s also the mn-max nference and the mplementaton of the rules was based on fuzzy rules of Mamdan type [7]. Example: "If the error between power and load demand s Postve and battery state-of-charge s Full, then, swtch should be Opened and swtch should be Closed". 7. Smulaton and results The system descrbed n Secton s mplemented n Matlab Smulnk (Fg. ). For the MPPT purpose, we use both fuzzy and PI controllers to compare the results between these two controllers. For power management purpose, a PI controller s not sutable so we keep ths controller unchanged. The fuzzy rules used n our FLC are summarzed n table, 3 and 4. DeltaP DeltaP DeltaP D S S SOC Full Average Empty N Bg Bg Small SP Very Bg Bg Small P Very Bg Very Bg Medum VP Very Bg Very Bg Medum Table. Rules of D SOC Full Average Empty N Close Close Open SP Open Open Open P Open Open Open VP Open Open Open Table 3. Rules of S SOC Full Average Empty N Open Open Open SP Open Open Open P Open Open Open VP Close Open Open Fg.. Smulaton n Smulnk Suppose that the battery state-of-charge s 95% (Full), n ths case we can verfy the dsspaton of surplus power to prevent the battery from gassng (operaton of swtch ). Frst the water heater and pump functon (request for a total load of 6 kw). After 4 seconds the machne s started (total load 9kW) and 8 seconds later, the heater s dsconnected (total load 5kW). The speed decreases from 9m/s to 8m/s at the 8 th second, then ncreases to 0m/s at the 6 th second (Fg. 3, 4). Table 4. Rules of S The overall fuzzy subset representng output control varable s defuzzfed usng centre of gravty method: Â Â µ C ( x ). x µ C = () µ ( x ) C Fg. 3. Load demand (kw) 74

6 In the next four seconds, the nducton machne operates, load demand now s 9kW, DeltaP s -.kw (Negatve) then the battery s actvated by the closure of S (S = ) to gve necessary power to load. The duty rato D s ncreased from % to 9% to keep the rotor speed n ts optmal value of 450rpm. Fg. 4. Wnd speed (m/s) In the frst four seconds, the load s 6kW. The speed s 9m/s, whle D s %, whch rotates the rotor at a speed of 450rpm to reach the maxmum power of 7.kW (Fg. 5, 6). The error power DeltaP = 0.7kW (Small Postve), so S s opened (S = 0). D s 74% (Fg. ) whch causes a voltage of 75V DC at the output of the nd boost converter, then the battery s charged. Fg. 7. Wnd turbne power (kw) After 8 seconds, speed decreases to 8m/s, n whch optmal rotor speed s 37rpm (D = %). Wnd turbne power decreases to 5.kW whle the power requred by the load s stll 9kW, then the battery gves more power to load (P bat = -4.kW). Fg. 5. Duty cycle of the st converter D (%) Fg. 8. Battery power (kw) From th to 6 th second, the water heater stop, the load s reduced to 5kW, D decreased to % to keep the rotor speed n optmal value 37rpm. DeltaP remans Negatve (-0.kW), so S s stll closed. Fg. 6. Rotor speed (kw) Both controllers gve almost the same settlng tme and steady-state operaton by respondng step changes n reference nput. However, we can see that fuzzy controller s more stable whle PI controller has more rpple (nose). Moreover, wth the PI controller, we have to choose a sutable value of k p, k when system parameters change, whle fuzzy controller works well wth all system parameters. The responses from both fuzzy and PI MPPT controllers are plotted on the same graph for better comparson. Fg. 9. Power error DeltaP (kw) 75

7 Fg. 0. Battery state-of-charge SOC (%) The last four seconds, the speed s ncreased to 0m/s, so the rotor rotates at the optmum speed of 63rpm and the gves a maxmum power of 9.7kW. So DeltaP s 4.kW (Very Postve) whle the battery s fully charged (SOC = 94.7%), keep on chargng may cause gassng phenomenon, thus S s closed to dsspate the surplus to a dscharge resstor. Fg. 4. Power delvered to load (kw) We can see that avalable power s delvered to the load before usng the battery as supplement (Fg. 8). Load demand s assured despte condtons of speed (Fg. 4). Fg. 5. DC voltage nput of PWM nverter (V) Fg.. Duty cycle of the nd converter D (%) In the load sde, the voltage nput to the PWM nverter s mantaned at a sutable value (Fg. 5), thus the qualty of the chargng voltage s mantaned correctly n 380V, 50Hz n any condtons (Fg. 6). Fg.. State of swtch S Fg. 6. Load lne voltage (V) These smulatons show that our proposed controller has good results. It assured the load demand, despte the condtons wth good strength and qualty of the battery wth the chargng process of the battery to prevent a release of hydrogen and oxygen and/or sulfatng. 8. Concluson Fg. 3. State of swtch S Power management results are almost the same when we use the PI controller or the fuzzy controller for MPPT purpose because the power management controller (FLC ) s unchanged. Ths paper presents the control system usng fuzzy logc for the dstrbuton of electrcty for stand-alone system. Wth nformaton about rotor speed, load demand, battery state-of-charge and smple rules of fuzzy logc, control sgnals were generated for a maxmum power recovered from the n respect of load demand, and can extend battery lfe. The smulaton results show 76

8 good behavor of our controllers to acheve these objectves. As perspectve, we wll develop ths system by addng an addtonal source (solar, hydro...) and optmze the dstrbuton of energy for remote stes. Then we wll verfy t by expermental work. [4] M. H. Rashd, Power electroncs handbook, 00. [5] R. W. Erckson, Fundamentals of Power Electroncs Second Edton, 004. [6] K. M. Passno, Fuzzy Control, 998. [7] H. Yng, Fuzzy Control and Modelng : Analytcal Foundatons and Applcatons, 000. References [] H. Erch, Wnd turbnes: Fundamentals, Technologes, Applcaton, Economcs, nd Edton, 005. [] M. Stebler, Wnd Energy Systems for Electrc Power Generaton, 008. [3] T. Zouag, Varable Speed Drve modelng of Wnd Turbne Permanent Magnet Synchronous Generator, Internatonal Conference on Engagng Pedagoges, 004. [4] M. Dal, J. Belhadj and X. Roboam, Desgn of a stand-alone hybrd Photovoltac-Wnd generatng system, Journal of Electrcal Systems, 008. [5] R. Wernher and G. Henderson, Synchronous and Synchronzed Wnd Power Generaton, New Zealand Wnd Energy Assocaton, 004. [6] F. Dragomr, Fuzzy Control Technques Used n Load Process of Pb Batteres Connected to a Photovoltac System, 8th Medterranean Conference on Control and Automaton, 00. [7] Pundaleek B. H., Mansh G. R. and Vjay K. M. G., Speed Control of Inducton Motor: Fuzzy Logc Controller v/s PI Controller, Internatonal Journal of Computer Scence and Network Securty, Vol.0 N 0, October 00. [8] M. Kalantar and S.M. Mousav G., Dynamc behavor of a stand-alone hybrd power generaton system of turbne, mcro turbne, solar array and battery storage, Appled Energy 87, pp. 305$ 3064, 00. [9] T. F. El-Shatter, M. N. Eskander and M. T. El- Hagry, Energy flow and management of a hybrd /PV/fuel cell generaton system, Energy Converson and Management 47, pages 64$ 80, 006. [0] J. Tande, Applyng Power Qualty Characterstcs of Wnd Turbnes for Assessng Impact on Voltage Qualty, Wnd Energy, pages 37-5, 00. [] A. Jorgensen, Power Qualty and Grd Connecton of Wnd Turbnes, IEEE Conference Publcaton, pages 438, 997. [] S. Belakehal, Power maxmzaton control of small system usng permanent magnet synchronous generator, Revue des Energes Renouvelables, Vol. N, pages , 009. [3] M. B. Sharfan, Maxmum power control of varable speed turbne connected to permanent magnet synchronous generator usng chopper equpped wth superconductve nductor, Journal of Appled Scences 9, pages ,