Voltage Control of a 12/8 Pole Switched Reluctance Generator Using Fuzzy Logic

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Intenational Jounal of Moden Nonlinea Theoy and Application, 22,, 7-2 http://dx.doi.og/.4236/ijmnta.22.36 Published Online Septembe 22 (http://www.scirp.

1 Intenational Jounal of Moden Nonlinea Theoy and Application, 22,, Published Online Septembe 22 ( Voltage ontol of a 2/8 Pole Switched Reluctance Geneato Using Fuzzy Logic Najmeh Faidnia, Masume Seyedyazdi 2, Faidoon Shabaninia 3 Fas Regional Electic ompany, Shiaz, Ian 2 Pasagad Highe Education Institute, Shiaz, Ian 3 Shiaz Univesity, Shiaz, Ian faidnia@fec.co.i, ma.seyedyazdi@gmail.com, shabani@ecs.csus.edu Received June 8, 22; evised July 5, 22; accepted August 8, 22 ABSTRAT This pape pesents a voltage contolle fo a 2/8 switched eluctance geneato (SRG). SR machines have a obust with simple stuctue because they have no windings o pemanent magnets on the oto, so they ae capable of woking at high speed application and at ough condition. Howeve, due to nonlinea natue, doubly salient poles, time vaiant paametes, and non-ideal cuent wavefom, The SRG output voltage inheently contains ipples. The poposed voltage contolle is based on fuzzy logic that is vey efficient ove uncetainty and paamete vaiations. The effectiveness of the poposed contol method is veified by compaing the obtained esult with that of a PI-contolle. Keywods: Wind Enegy; Switched Reluctance Geneato; Voltage ontol; Fuzzy Logic ontol. Intoduction Nowadays electicity demands is inceasing highly, so the use of small powe plants whose design and constuction ae less time consuming is vey essential. One of the small powe plants is a wind powe plant that in addition to being less time consuming in constuction, it has many othe advantages. Due to thei small size, small wind tubines have the advantages of easy tanspotation fom manufactoy to powe plant, easy installation in evey whee e.g. nea any load cente, and easy opeation in high speed wind. Small wind tubines using high eliable geneatos ae the best candidates fo woking in stand-alone application eithe in emote aeas o in uban aeas []. Among seveal kinds of geneatos used as wind geneatos, switched eluctance geneato (SRG) is one of the best candidates fo this application. The SRG has obust with simple stuctue due to the fact that it has no windings o pemanent magnets on the oto. Theefoe it is capable of woking at high speed application and at ough condition. The main advantages of the SRG ae high efficiency, simple topology, the equiement of no stating toque and obustness. SRG is inheently a vaiable speed machine. The vaiable speed opeation in wind geneation leads to the extaction of exta enegy fom the wind steam and the decease of the mechanical stesses within the system [2]. Recently, many studies have been done on SRG in vaious applications such as wind geneation. Many papes have been pesented and examined diffeent types of dive cicuits fo SRG in vaious applications [3,4]. In [3] the application of the switched eluctance geneato in diect dive wind tubine was discussed. In [4] a new stuctue is pesented fo vaiable speed wind SRG. In [5] switched eluctance machine was consideed as subsidiay wind powe geneation in the gid connection. The pocued esults have demonstated that the SRG in tems of constant speed is stable and at vaiable speed condition woks well. On the othe hand, some studies have been made on contolling of SRG s output signals fo wind geneation application in ode to educe its dawbacks [6]. Howeve, offeed contol methods ae not complete and compehensive, and numeous challenges ae ahead of these methods Because of nonlinea natue, doubly salient poles, Time vaiant paametes, and non-ideal cuent wavefom, the SRG output voltage inheently contains ipples. In [7], a closed loop contol of output powe of a SRG diven by a vaiable speed wind tubine is pesented. The pulse wih modulation contol method is adopted fo contol the phase cuent of the SRG in medium and low speed ange. The pape uses the single pulse mode contol method fo contol the SRG s output powe in high speeds. In [8], to educe the output voltage ipples of SRG, a PI-configued D-link filte is pesented. In ode to lessen the effects of paametes uncetainty in switched eluctance geneation systems, some studies ae done on the use of fuzzy contol method to detemine the opyight 22 SciRes.

2 8 N. FARIDNIA ET AL. conducting angles. In [9], a vaiable speed SRG is intoduced and the tun-on angle contol stategy is pesented. In this pape a fuzzy logic algoithm fo maintaining output powe is explained, and the vaiation of the D output voltage and cuent ae the two inputs and the tun-on angle is the output contol paametes. This pape consides a switched eluctance geneato diven by a wind tubine in Figue, and pesents a fuzzy logic based contolle fo smoothing the SRG output voltage fluctuations. The obtained esults fom fuzzy contolle ae compaed with the esults obtained fom a PI contolle. The oganization of this pape is as follow. Section 2 pesents a summay about SRG theoy and its mathematical model. Section 3 descibes the poposed fuzzy logic contol method and the elated ules and membeship functions ae consideed in Section 4. The simulation esults ae shown and discussed in Section 5. Section 6 pesents the conclusions. 2. A Bief Review on SRG Theoy and Voltage ontol SR machines have vey simple stuctue that lead to the advantages of these machines. In these machines, the 3-phase windings ae placed on stato poles and thee is no winding o magnet on oto poles. The stato windings seve both the oles of amatue windings and excitation windings in diffeent times. Both stato and oto has salient-pole stuctue. This doubly salient stuctue offes highe speed opeation and highe efficiency. Lack of windings on the oto is the cause of no electic losses in oto, small moment of inetia, fast esponse, low manufactuing cost and high eliability. Figue 2 shows the basic configuation of the 2/8 pole-thee phase SR machine that used in this pape. Anyway the SR geneato has few disadvantages such as complicated powe electonic dive cicuit, acoustic noise and output voltage ipple. Fotunately by the use of advanced dive method and advanced contol method these dawbacks can be emoved. In SR machine, enegy convesion is based on inductance vaiation due to pole saliency of stato and oto. In SR geneato, the tendency of oto to esist changing the position whee the inductance of excited phase is maximized poduces enegy. In geneating mode of SR ma- Powe onvete V Out chine, when a oto pole is aligned with a stato pole, the phase elated to that stato pole will tun on to esist moving oto. This action causes that the enegy is saved in magnetic field and electical powe is poduced. Theefoe it is essential fo this machine to have a diving system that can identify the oto position and can switch on o off the pope phase in accodance with oto position. Figue 3 shows the elation between one-phase inductance pofile of SR machine and oto position angle θ. As undestand fom Figue 3, to use SR machine as a geneato the phases should be tuned on at the negative slope of the phase inductance pofile i.e. dl when d. This point can be confimed efeing to SR machine s toque fomula in (). θ B A A A B A Figue 2. onfiguation of a thee phases 2/8 pole SR machine. Inductance Moto aligned position Geneato dl d B unaligned position B θ on θ off Roto angle Figue. SRG wind tubine system [4]. Figue 3. Idealized phase inductance vesus oto position cuve. opyight 22 SciRes.

3 N. FARIDNIA ET AL. 9 dl i 2 d 2 () The equation indicates that in the egion of d L d the toque is negative, so using the machine in this egion is compatible with geneato opeation. As peviously mentioned, SR machine needs a dive that ecognizes oto position and then switches pope phase on o off coesponding to the oto position. In this pape a thee-phase asymmetic bidge convete shown in Figue 4 is used as the dive system fo SR geneato. The inductances L a, L b and L c illustate the inductance of phase A, B and, espectively and esisto shows winding esistance of each phase. In Figue 4, the two tansistos pe phase tun on and off simultaneously. In a SR geneato at each moment, thee is only one phase that is on. Theefoe at each moment thee is only one phase that is connected to D powe supply. As explained in ou pevious wok [4], Figue 5(a) shows an equivalent cicuit of one phase of SR geneato when the switches of this phase ae tuned on and then the D powe supply excites the windings of the phase. Equations (2)-(5) descibe the dynamics of one phase of SR geneato fo Figue 5(a). VD eph iph (2) V D e a e b L a L b L c Figue 4. Basic schematic of thee phase convete fo switched eluctance geneato. V D i ph (a) L ph e ph i ph L ph Figue 5. Opeation modes of the phases of SRG. (a) Exciting mode; (b) Geneating mode. e ph (b) e c R L i L R L whee e ph is the voltage acoss the phase and i ph is the cuent that flows though the phase. d ph eph Nph (3) whee φ ph is the phase flux and N ph is the numbe of windings of the phase. Because φ ph = Lph i ph, d Lph iph diph dlph eph Nph Nph Lph iph m d (4) Substituting (4) in (2) dl ph diph VD Nph iph m Nph Lph iph (5) d whee d m and ω m is the otational speed of oto. Equation (5) is the basic voltage of one phase if the phase is tuning on. The fist tem on the ight hand of (5) is the back EMF that the geneated electical powe is popotional to this tem. Figue 5(b) shows an equivalent cicuit of the same phase of SRG when the switches ae tuned off. In this case the inductance cuent that can not be zeo immediately flows though feewheeling diodes and supplies esistance load. Equations (6)-(8) descibe the dynamics of the phase of SRG fo Figue 5(b). eph iph RL i ph (6) Substituting e ph fom (3) into (6), d ph Nph iph RL iph (7) Substituting φ ph fom (4) into (7), dlph diph Nph iph m Nph Lph iph RL iph (8) d 3. Fuzzy Logic ontol Duing the past decade, fuzzy logic contol has emeged as one of the most active and fuitful eseach aeas in the application of fuzzy set theoy, fuzzy logic and fuzzy easoning. In contast to conventional contol techniques, fuzzy logic contol is efficiently utilized in complex ill-defined pocesses that can be contolled by a skilled human opeato without much knowledge of thei undelying dynamics. The basic idea behind fuzzy logic contol is to incopoate the expet expeience of a human opeato in the design of a contolle in contolling a pocess whose input-output elationship is descibed by a collection of fuzzy contol ules (e.g. IF-THEN ules) involving linguistic vaiables. Also fuzzy logic contolle povides the best answes in system outputs with uncetainties. In this pape fuzzy appoach is used to get a opyight 22 SciRes.

4 N. FARIDNIA ET AL. good pefomance of SRG output voltage. Fo fixing the geneato teminal voltage, it is necessay to find a suitable contolle keeping voltage in dc mode. Fuzzy logic based on linguistic ules has been chosen in this pape. Two input and one output vaiables ae selected fo fuzzy logic contolle. Fist Input vaiable is voltage eo (ε) and the second input vaiable is voltage eo diffeence in two consecutive intevals (Δε). The definition of ε and Δε can be expessed mathematically as (9) and (). The output vaiable is the amount of vaiation in conducting angle (θ d ) that is needed to ean an output voltage with minimum of deviation. The anges of the fist input, the second input, and the output vay fom 43 to 43, 3.5 to 3.5 and 3 to 3 espectively. The vaiation of Δε is pactically low. V V (9) c k ef () k 4. Fuzzy Set Membeship and ontol Rules The fuzzy sets consideed fo the inputs and the output ae similaly in seven anks: {NB (Negative Big), NM (Negative Medium), NS (Negative Small), ZE (Zeo), PS (Positive Small), PM (Positive Medium) and PB (Posi- tive Big)}. Mentioned membeship functions ae shown in Figue 6. As it is known fom SRG theoy, in ode to maintain V c at the desie level (equal to V ef ), if V c V ef is negative then θ d has to be inceased, and also if V c V ef is positive then θ d has to be deceased adequately. The ules shown in Table ae consideed to damp the oveshoot of the output voltage. It is obvious that these few ules ae utilized to omit the SRG teminal voltage oveshoot. Figue 7 shows thee dimensional elationships between two inputs and the output of the fuzzy sets used in this pape. Table. Fuzzy logic ules consideing two inputs and one output. Δε ε PB PM PS ZE NS NM NB PB NB NB NM PM NB NM PS - NM NS ZE - - NS ZE PS - - NS PS PM - NM NB NB NM NS ZE PS PM PB Degee of membeship eo (a) NB NM NS ZE PS PM PB Degee of membeship d-eo (b) opyight 22 SciRes.

5 N. FARIDNIA ET AL. NB NM NS ZE PS PM PB Degee of membeship teta d (c) Figue 6. (a) Membeship function of ε; (b) Membeship function of Δε; (c) Membeship functions of θ d. Table 2. SRG contol system paametes. Numbe of Stato pole 2 Ac of stato pole (degee) 4 tetad Numbe of oto pole 8 Ac of oto pole (degee) 6 Maximum inductance (mh) Vef (Volt) 23 Minimum inductance (mh) R L (ohm) Resistance pe phase (ohm) 5 (μf) d-eo 4 eo Figue 7. 3-D elationships between two inputs and the output of the fuzzy contol ules Output Voltage V c 5. Simulation Results Accoding to mentioned mateial on last section, this pape poposed a fuzzy logic based voltage contolle fo a 2/8 SRG diven by a wind tubine. The paametes of the simulated SRG wee shown in Table 2. Output voltage wavefom of applied SRG without any contolle was shown in Figue 8. In this case, the capacito paalleled with the extenal load is the only used means to smooth the output voltage. Howeve the wavefom has an undesiable oveshoot about 9% of V ef. Two kinds of contolles ae used to educe the voltage oveshoot and then smooth output voltage. Fist, a PI contolle is applied to the SRG system. Figue 9 shows the effects of the PI contolle on the output voltage. As shown in this figue, this contolle could omit the oveshoot completely. Howeve, the equied gain fo PI contolle is too high (k = ), and consequently so expensive. Futhemoe, the highe gain in PI contolle, the moe instability in system. In addition, this contolle esults in time(s) Figue 8. SRG output voltage wavefom without any contolle. an incease in settle time of the SRG output voltage wheeas deduction in settle time is desiable. Second, the fuzzy logic based contolle is applied to the SRG syst em that its output voltage simulation is shown in Figue. The esult shows this contolle is so helpful to dam pen the voltage oveshoot quickly and it is moe stable than PI contolle. In this case, the voltage is fluctuating be- tween 223 and 237 volt and the maximum of ou tput opyight 22 SciRes.

6 2 N. FARIDNIA ET AL. Output Voltage Vc time(s) Figue 9. SRG output voltage wavefom with PI contolle Output Voltage V c time(s) Figue. SRG output voltage wavefom with fuzzy logic contolle. voltage is 243 volt. 6. onclusion Due to the absence of windings o pemanent magnets on the oto, switched eluctance machines have a obust with simple stuctue. Theefoe they affod to wok at high speed applications and at ough conditions. Howeve, due to numeous nonlineaities, The SRG output voltage innately contains significantly ipples. In this pape a 2/8 SRG is fistly consideed and the mathematical model of its output voltage is extacted. Then, a Fuzzy logic based contolle is pesented to smooth the output voltage. The fuzzy contolle eceives the efe- ence voltage and the output voltage of the SRG as its inputs, and etuns the conducting angle as its output. The effect of mentioned contolle on the output voltage is compaed with that of a PI-contolle. The esult shows that in the pesence of significant nonlineaity and uncetainty, fuzzy logic contolle is moe apid and moe stable than the PI contolle. Theefoe the esults veify the effectiveness of the fuzzy logic based contolle ove the output voltage of a switched eluctance geneato. REFERENES [] R. Pena, R. adenas, G. M. Ashe and J.. lae, Vecto ontolled Induction Machines fo Stand-Alone Wind Enegy Applications, onfeence of Recod of the IEEE Industy Applications onfeence, Rome, 8-2 Octobe 2, Vol. 3, pp [2] D. A. Toey, Switched Reluctance Geneatos and Thei ontol, IEEE Tansactions on Industial Electonics, Vol. 49, No., 22, pp doi:.9/ [ 3] M. A. Muelle, Design and Pefomance of a 2 kw, pm, Switched Reluctance Geneato fo a Diect Dive Wind Enegy onvete, IEEE Intenational onfeence on Electic Machines and Dives, San Antonio, 5 May 25, pp [4] H. Kazemi Kaga, M. Yazdi and A. Siadatan, New Stuctue fo High Speed and Vaiable Speed Wind Tubine Based Switched Reluctance Geneato, IEEE Intenational onfeence on Powe and Enegy, Kuala Lumpu, 29 Novembe- Decembe 2, pp doi:.9/peon [5] A. Fleuy, D. A. de Andade, F. dos Santos e Silva and J. L. Domingos, Switched Reluctance Geneato fo omplementay Wind Powe Geneation in Gid onnection, IEEE Intenational Electic Machines & Dives onfeence, Antalya, 3-5 May 27, Vol., pp [6] A. Takahashi, H. Goto, K. Nakamua, T. Watanabe and O. Ichinokua, haacteistics of 8/6 Switched Reluctance Geneato Excited by Suppession Resisto onvete, IEEE Tansactions on Magnetics, Vol. 42, No., 26, pp [7] R. adenas, R. Pena, M. Peez, J. lae, G. Ashe and P. Wheele, ontol of a Switched Reluctance Geneato fo Vaiable-Speed Wind Enegy Application, IEEE Tansactions on Enegy onvesion, Vol. 2, No. 4, 25, pp doi:.9/te [8] D. B. Wicklund and D. S. Zinge, Voltage Feedback Signal onditioning in Switched Reluctance Geneation Systems, IEEE Applied Powe Electonics onfeence and Exposition, New Oleans, 6- Febuay 2, pp [9] H. hen and Z. Shao, Tun-On Angle ontol fo Switched Reluctance Wind Powe Geneato System, 3th Annual onfeence of IEEE Industial Electonics Society, Busan, 2-6 Novembe 24, pp opyight 22 SciRes.

where and are polynomials with real coefficients and of degrees m and n, respectively. Assume that and have no zero on axis.

where and are polynomials with real coefficients and of degrees m and n, respectively. Assume that and have no zero on axis. function whee is an unknown constant epesents fo the un-modeled dynamics The pape investigates the position contol of electical moto dives that can be configued as stuctue of Fig 1 This poblem is fomulated