Simulation of Six Phase Split Winding Induction Machine Using the Matlab/Simulink Environment

Transcription

1 Simulation of Six Phae Split Winding nduction Machine Uing the Matlab/Simulink Environment Ogunjuyigbe A.S.O, Nnachi A.F, Jimoh A.A member EEE and Nicolae D. member EEE Electrical Engineering Department, Thwane Univerity of Technology P.O.Box X680, Pretoria 000. South Africa Abtract: Six-phae induction machine preent everal benefit over their conventional three-phae counterpart. Thi paper thu preent the model and decribed in detail the imulation of a Six-phae plit winding induction machine in a Matlab/Simulink environment. The Simulink model i built in uch a flexible manner uch that variou variable of the machine can be acceed eaily for further purpoe uch a control. Finally, imulation reult howing free acceleration a well a dynamic repone of the machine were preented for both direct ac upply and the PWM inverter voltage ource. Keyword: Six phae nduction machine, Matlab/Simulink, Split winding, PWM inverter.. ntroduction Electrical machine exit for the bulk of it time in the teady tate, thu it ha often been imulated in circuit imulator uing the teady tate model; however, it i during the brief period of tranient, non-tationary behaviour that mot of the tree occur which limit the life of the machine. Simulink i known to have the advantage of being capable of complex dynamic ytem imulation, graphical environment with viual real time programming and broad election of tool boxe. The imulation environment of Simulink ha a high flexibility and expandability which allow the poibility of development of a et of function for a detailed analyi of the electrical ive. t graphical interface allow election of functional block, their placement on a workheet, election of their functional parameter interactively, and decription of ignal flow by connecting their data line uing a moue device. Sytem block are contructed from lower level block grouped into a ingle makable block. t alo provide an open ytem environment which provide acce to algorithm and ource code. Simulink ha been ued to model and imulate induction machine, but mot often on three phae induction machine model [-4]. Motly, thee model do not preent the internal detail and ome commonly ue the S-function programming knowledge. n addition, the complete model of three phae induction machine exit within the imulink power ytem blocket. Thi alo make ue of the S-function which i not eay to work with a the ret of the imulink block. ikewie, it i intereting that ix phae induction machine ha continued to gain reearch interet for ac ive application, becaue of the benefit it offer compared to it conventional three phae counterpart [5, 6]. Thi paper ue Matlab/Simulink environment to imulate the dynamic behaviour of a ix phae dual tator plit winding nduction motor that i fed by two arrangement of voltage ource, firtly with the utility upply and econdly uing a PWM voltage ource inverter. A imilar machine wa dicued in [6, 7, 8], however they ued an entirely different imulation environment, and did not expre in detail the tep in the development of the imulation model a preented in thi work. 2. Electrical Model The non-linear differential equation that decribe the dynamic behavior of an induction machine with multi-phae and arbitrary diplacement between them i preented in [5] where the ix phae induction machine wa ued a an example,

2 and the equivalent circuit ha been preented. Alo, the dqo model for a ix phae machine wa developed in [6, 7]. The equation that decribe the behavior of the ix-phae induction machine when expreed in the arbitrary reference frame are lited in equation through 3 = r + pλ + ω λ q q q k d = r + pλ ω λ 2 d d d k q 0 = r 0 + pλ0 3 = r + pλ ω ω λ 4 r k r = r + pλ ω ω λ 5 r k r = r + pλ 6 0r r 0r 0r = r + pλ + ωλ 7 q2 2 q2 q2 d 2 = r + pλ ωλ 8 d 2 2 d 2 d 2 q2 02 = r pλ02 9 where ω k i the peed of the reference frame, ω r i the rotor peed. Alo, the expreion for tator and rotor flux linkage are: λ = q l lm q lm q q2 m q q 2 λ = d l lm d lm d d2 m d d2 λ 0 = l 0 + lm λ = q2 l2 lm q2 lm q q2 m q q2 λ = d2 l2 lm d2 lm d d2 m d d2 λ 02 = l lm λ = lr m q q2 λ = lr m d d 2 λ = 8 or lr 0r The electromagnetic torque equation i written in term of λ md and λ mq a: 3 P Te = 2 2 λmd q + q2 λmq d + d 2 9 Similarly, the mechanical model of thi machine comprie of the equation of the motor and the iven load, and thi i uually repreented a: dω 2 r J P = Tem T 20 dt where J i the inertia and T i the load torque. 3. Preparing the Equation for Simulation Thee equation that decribe the electrical and mechanical behaviour of the machine contain mixed variable flux linkage and current. Either of thee two quantitie could be eliminated from the differential equation by algebraic manipulation of equation -8. n thi paper, the flux linkage i reolved a the tate variable and current a dependent variable. Thu, the current when olved in term of flux linkage are obtained a: d = A l + lm λ d l λmd lm λd ldq λq λ 2 q q = A l + lm λq l λmq lm λq + ldq λd λ d d2 = 2 A l + lm λd l λmd lm λd + ldq λq λ mq q2 = 2 A l + lm λq l λmq lm λq ldq λd λ md mq lr λ λ = 25 λ λ = 26 md lr λ = λ + λ λ λ m d D d l 2 d 2 l ldq q 2 q λmq = Q λql 2 + λq 2 l + ldq λd 2 λ d where = + + A D l l 2 m A l l 2 lm l l = = + + A Q l l 2 m 3 Subtituting equation 2-28 into 8 and olving the equation in the rotor reference frame, that i ω k become ω r the integral form of the machine voltage and torque equation with flux linkage a tate variable i given a: { } R λd = d ωλ q A l2 lm λd l2λmd lm λd 2 ldq λq 2 λ + + mq { } 32 R λq = q ωλ r d A l2 + lm λq l 2λmq lm λq 2 ldq λd 2 λmd 33 R λd 2 = d2+ ωλ r q2 A l + lm λ d2 l λmd lm λd + ldq λq λ 34 mq 2 { } { } 35 R2 λq 2 = q2 ωλ r d2 A l lm λq 2 lλ mq lm λq ldq λd λ + md r = md lr λ λ λ r = mq lr λ λ λ ω = [ ] P r 2 em J T T dt 38 θ = ω dt r r 39 Thu equation 9, 2-39 eentially will be ued to imulate the ix phae dual plit winding induction machine. Thee equation are arranged in integral form rather than in the differential form 2

3 Fig. : Flow diagram of the electrical part for the imulation of the ix-phae machine o a to avoid having pike a a reult of differentiation of ignal with ripple 4. mplementation in Simulink n order to implement thi in imulink, the equation are arranged into four major block a lited below: nput three-phae voltage and load torque Output three phae current, electrical torque and other component a may deired for identification Electrical part of the machine Mechanical part of the machine Similarly, to maintain a proper flow of variable and for convenience of imulation, the equation have been eparated into the q-axi and the d-axi block a indicated in figure. With the flow of ignal hown in Fig. the external input d, d2, q, q2 will be obtained from the tranformation of the three phae variable to the two phae rotating reference frame. Thu, the imulation block that implement the tranformation of the abc phae variable to the dq rotating reference frame and vice vera i here firtly dicued. 4. nverter modelling equation The converter output line-to-ground voltage are related to the witching tate and the dc link voltage by the equation [9, 0, ]: ag Sa dc bg S = b n S cg c 40 Where ag, bg, cg are the phae node a, b, c to the negative rail of the dc bu, dc i the dc bu voltage, n i the number of level and in thi cae equal 3 and S a, S b, S c are the witching tate. The witching tate i however determined by Pule width Modulator, hence depict the inverter output. The line-to-neutral voltage are determined directly from the line-to-ground voltage uing the equation an 2 ag bn 2 = bg 3 4 cn 2 cg 4.2 Tranformation Block The three phae voltage variable in abc obtained from either the power utility or the PWM inverter ource i converted to the rotating reference frame uing: 0 0 q a d 0 = 3 3 b o c 42 = coθ inθ 43 q q r d r = inθ coθ 44 d q r d r Thee et of equation are implemented in the imulink environment by the ue of baic imulink function block a hown in Fig. 2 The entire block in figure 2 i eaily cat into a ingle ubytem block identified a abc_dq in figure 7. n a imilar way, the invere tranformation of the dq component can be done to obtain the phae variable e.g current uing the following equation. Fig. 2: abc to dq tranformation block 3

4 = coθ + inθ 45 q q r d r = inθ + coθ 46 d q r d r and 0 a 3 q b = 2 2 d 3 c Thi i likewie created in the imulink environment by uing the function, ignal routing, multiplexer block all lited under the imulink commonly ued block. Equation 44, 45, 46 are then arranged in imulink workheet a in Fig.3. Figure 3 i alo made a ingle block ubytem dq_abc, and it i baically ued to extract phae quantitie from the dq component. t i clearly een from figure 4 that mot of the block are preented a a ubytem, each of which i ued to olve the equation a labelled in figure. A an example, the ubytem AMQ in figure 4 i ued to olve equation 33 and it internal detail i preented in figure 5. Similarly, the internal detail of the ubytem that olve equation 9 and 38, that i, the mechanical part of the machine i hown in fig. 6 Fig. 5: nternal detail of ubytem AMQ Fig. 3: dq to abc tranformation block 4.3. dq model of the ix phae nduction Machine Thi model i developed by following the ignal flow diagram of Fig.. Thi ha been grouped into the d and q ubytem. Each block within the d and the q ubytem are imply taken and built one after the other uing the function block, Mux, and the integral block. A an example, the block that implement the q-ubytem of the ix phae induction machine i a hown in figure 4. Fig. 4: Q-axi ubytem Fig. 6 nternal detail of the ubytem that implement the mechanical part of the machine Furthermore, the PWM three level inverter voltage ource i achieved uing the imulink model block of figure 7. Thi format of implementation i carried out for each block that form a ubytem a indicated in figure. When all thee ubytem are built, they are combined together to form the complete imulation model for the ix phae plit winding induction machine hown in figure 8. Fig. 7: PWM inverter voltage ource 4.4 Data nput to the model Reference Following a ucceful preparation of the imulink model, neceary machine data obtained from experimental data ha to be allocated to every element already ued in the model. Thi i achieved by the liting of thee data in a Matlab M- file that i configured a an input into the imulink model. Thi M-file form the initialiation characteritic in the workpace from which the imulink model will extract all it neceary information for the effective imulation of the model. 4

5 5.0 Simulation Reult Fig. 8: Complete Simulink model for ix phae induction Machine The ix phae machine dicued in thi paper wa imulated with two different ource, firt with a direct ac tart up and econdly a an inverter fed machine. The free acceleration characteritic are a diplayed repectively in figure 8 and 9. The figure include the rotor peed, torque and the three phae current of the machine a well a the inverter ource voltage. t i oberved that the machine come to teady tate in about 0.6ec. The dynamic behaviour of the machine wa likewie examined with the application of a tep load torque of.0 p.u at a time of 2 econd. The dynamic repone of the machine i clearly diplayed in figure 0a-d. Thi i diplayed only for the PWM inverter voltage ource. The teady tate characteritic of thi machine can eaily be extracted from thee characteritic. n addition, the model imulated in thi paper can alo be arranged for different control arrangement a may be deired a a b b c c d Fig. 8: Free acceleration characteritic of ix phae induction machine uing direct ac ource d Fig. 9: Free acceleration characteritic of ix phae induction machine with PWM three inverter ource. 5

6 a b c d Fig. 0: Dynamic repone with the application of T=.0 p.u at time 2ec.a Rotor peed, oad Torque, b Electromagnetic Torque, oad torque, c winding current, rotor peed d nverter ource voltage, winding current 5. Concluion Thi paper demontrate the tepwie development of Matlab/Simulink model to imulate the tarting and dynamic behaviour of ix-phae plit winding induction machine. The free acceleration characteritic a well a the dynamic repone to load variation were teted on the imulation and the reult were likewie diplayed. The teady tate voltage and current were extracted and diplayed. The poor factor of thi machine under no load condition i eaily oberved from Fig.0 d. The imulink implementation in thi work provide acce to variou internal variable o a to be able get an inight into the machine operation. The performance of the machine wa imulated with both direct ac and a three level inverter voltage ource input. 6 Reference []. e-huy, H, Modelling and Simulation of electrical ive uing Matlab/Simulink Power Sytem Blocket, The 27 th Annual Conf. of the EEE ndutrial Electronic Society ECON 0, Denver/Colorado, pp [2]. Ozpinechi, B, Tolbert,.M, Simulink implementation of induction machine model- A modular approach EEE Electrical machine and ive conf. EMDC 03, Capo, ol. 2, pp , [3]. Okoro, O., Matlab imulation of induction machine with aturable leakage and magnetiing inductance The pacific journal of Science and Technology, ol. 5, No., pp. 5-4, [4]. Ong, C.M, Dynamic Simulation of Electric machinery uing Matlab/Simulink, Prentice- Hall PTR, New Jerey, 998. [5]. Nelon, R.H, Kraue, P.C, nduction Machine Analyi for Arbitrary Diplacement Between multiple winding et, Proc. EEE Tran. on PAS-93, pp , 974. [6]. ipo, T.A, A dq model of a ix-phae induction machine, nt. conf. of Electrical Machine, CEM, Athene, pp , 980. [7]. Singh, G.K, Pant,, Singh, Y.P oltage ource inverter iven multi-phae induction machine Computer and Electrical Engineering 29, pp [8]. A.R Munoz, T.A ipo, Dual tator winding induction machine ive, EEE Tran. nd. Appl. 36 5, pp , [9]. Smith, J.R, Repone analyi of A.C Electrical machine Computer model and Simulation. John Wiley and on, New-York, 990. [0]. Novotny, D.W and ipo, T.A, ector control and Dynamic of Electric Drive, Oxford Univerity Pre, New York, []. Corzine, K.A, Operation and deign of Multi-evel nverter. Univerity of Miouri Rolla. Keith@corzine.net, pp. -79,