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Short Paper Proc. of Int. Joint Colloquium on Emerging Technologies in Computer Electrical and Mechanical 2011

A Study of Space –Vector Pulse –Width Modulation for two –Phase Induction Motor Mrs A.Y.Fadnis1, Dr. D.R.Tutakne2, Dr. R.M.Moharil3,Mr. Gaurav Gondhalekar4, Mr Atul Lilhare5 1

Y.C.College of Engg. Dept of Elec.Engg. Nagpur ,Maharashtra, ayfadnis@gmail.com RKNCE, Dept of Elect Engg, Nagpur, Maharashtra, dhananjaydrt2@rediffmail.com 3 Y.C.College of Engg. Dept of Elec.Engg. Nagpur ,Maharashtra , mm_ycce_ep@yahoo.com 4 Y.C.College of Engg. Dept of Elec.Engg. Nagpur, Maharashtra, gauravgondhalekar@hotmail.com 5 Y.C.College of Engg. Dept of Elec.Engg. Nagpur, Maharashtra, atul.lilhare@gmail.com 2

The zeroes of Vâ are displaced from corresponding zeroes of Vá by 5 millisecond (1/4th of the periodic time) What we have done is to mimic the two –phase supply which is ideally sinusoidal .In fact there is afundamental 50Hz sinusoidal two phase supply incorparated in this arrangement. .But there are also other harmonic components as well which are not desirable. However ,let us have a diferent look at the situation

Abstract— In this paper detailed analysis of Space-Vector Pulse –width modulation (SVPWM) for a balanced two – phase induction motor using two H-bridges (incorporating 8 semiconductor switches ) is presented .Improvement in SVPWM is shown in successive steps .Finally the performance of the 2H –bridge configuration is compared with other alternative schemes discussed by other paper.

Index Terms— two phase induction motors, Pulse Width modulation, SPWM (sinusoidal pulse–width modulation) SVPWM (space vector pulse –width modulation)

I. INTRODUCTION Over the last twenty years ,use of inverter using , semiconductor switches for the excitation of two phase induction motors , both balanced and unbalanced types has received substantial attention [1] -[7] In this paper we deal with balanced two–phase induction motors only .The simple 2H bridge inverter is considered .Using this inverter ,the concept of space vector modulation is introduced and developed in stages . In the end the performance of the simple 2H bridge inverter is compared with the performances of other configurations discussed in [7].

The voltage Vα corresponds to a space –vector which we call as Vα along the axis of phase α .Similarly the voltage Vβ can be considered to be a space vector Vβ along the axis of phase β. The two space vectors will give a resultant U= Vα+jVβ and hence from the waveform of fig. 2 (a) and (b) we get

II. EXCITATION OF A TWO PHASE BALANCED INDUCTION –MOTOR USING TWO H- BRIDGE INVERTERS The scheme which suggests itself for the excitation of a balanced two –phase induction is the use of a separate Hbridge for each phase .This is shown in Fig.1. The d.c. voltage shown in fig.1 is a battery but in real applications it could be the output of a rectifier plugged into single –phase a.c. mains .The first H-bridge gives a square –wave output if Q1Q2' and Q2Q1’are switched periodically. Thus if the switching sequence is as follows , 0< t < 10msec Q1 Q2’ are on 10msec< t < 20msec Q2Q1' are on 1 the output Vα of the bridge is as shown in Fig. 2(a) .Similarly if Q4Q3' and Q4'Q3 are turned on as per the following sequence.

Q4'Q3 on 0< t < 5msce Q4Q3' on 5 < t< 15msec Q4’Q3 on 15< t< 20msec and so on ,we get the output Vβ of the second bridge as shown in fig.2(b). The output Vα and Vβ are square waves of amplitude Vd and a frequency of 50 Hz. © 2011 ACEEE DOI: 02.CEM.2011.01. 522

Fig. 2 The square wavw-outout V(alpha) and (beta)

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Short Paper Proc. of Int. Joint Colloquium on Emerging Technologies in Computer Electrical and Mechanical 2011 This shows that the sequence of switching which gave the square wave outputs of fig.2 give a space-vector of constant magnitude but jumping by π/.2 radians every quarter cycle. There space vectors are shown in Fig.3The reason for calling them USE , UNE etc is to tie these directions to geographical conventions. In the discussion above we decided upon the waveforms of Vα and Vβ which we desired ,but have arrived at a space–vector modulation as an incidental consequences .We cannot therefore claim that we have deliberately attempted any space-vector modulation .However we had decided to have the space-vector tracking in time as per (1) and then arrived at the switching sequence required ,we could have said that we have implemented space –vector modulation. Hence space vector modulation implies as a goal ,a certain time behavior of the space –vector magnitude and angle and a sequence of switching tailored to achieve this goal. If we had done this with (1) as goal and the sequence of switching mentioned earlier was adjusted for this purpose we could have said that a deliberate space – vector modulation has been achieved . In this particular case our sampling time TPWM is 5 milliseconds, In addition to the space vectors of (1), space vectors U= Vd+j0=UE =0+j Vd=UN =- Vd +j0= UW ( 2) =0- jVd =US are also obtainable from the configuration by using only one of the bridges .Thus there are 8 non-zero space–vectors available to us by using different combinations of the switches .In addition we get four zero vectors also .The space–vectors available and the switch combinations which produce those space-vectors are tabulated in table 1.If therefore we so desire we can shift from UE to UNE to UN etc after every 1/8th of a period by changing the switching combinations in the following sequence 0< t<TP/8 1000 Tp/8<t <TP/4 1 0 10 TP/4<t<3TP/8 0010 3TP/8<t<Tp/2 0110 Tp/2<t<5TP/8 0100 (3) 5Tp/8<t<3TP/4 0101 3TP/4 <t<7TP/4 0001 7Tp/4<T<Tp 1,0,0 1 and So on

TABLE I. (SPACE _VECTORS AND CORRESPONDING COMBINATION OF SWITCHES)

Here our sampling time TPWM is now TP/8 (TP =periodic time) and we can see the space vector jumping by π/4radians every 1/8th of a cycle, The magnitude of the space vector also keeps on jumping from Vd to 2Vd back and forth. One feature that can be observed in the above sequence is that at each step we operate only one switch .This feature is desirable to reduce the switching losses that would occur. In the space –vector modulation executed in the above example ,we need successive constant space –vectors which are available by switchable switching combinations .But the switching combination was effective over the entire time interval TPWM. However ,l et us modify the schedule of (3) ,slightly. For each TPWM during which the space vector of magnitude 2Vd were obtained in the subsidiary directions (NE,NW, etc).Let us keep the combination effective only for 0.707 times TPWM, at the centre of that particular PWM .This reduction of time will reduce the magnitude of the space vector to Vd only.

Thus our switching schedule will be 0<t<TPWM 1000 TPWM< t< 1.15TPWM 0000 (4) 1.15TPWM< t<1.85T 1010 1.85Tpwm<t<2Tpw 0000 And so on .We have reduced the pulse-width of the outputs of both the bridges to 0.707 to get an average space vector magnitude of Vd even during those intervals where it was earlier. Thus the concept of pulse –width modulation gets associated with space-vector modulation, and we can designate the procedure as space –vector pulse width modulation. With this modification we shall get space-vector with a constant magnitude of Vd and jumping by 1/8th of a revolution during 1/8 of the periodic time However the jumps need to be through very small angle. It can be appreciated that with switching technique used, jumps are unavoidable ,but we can manage finer jumps .Since the switching combinations only give us space –vector in the eight directions, our attempt to get an average space –vector lying in between these direction consisting of using two space

Figure 3. Space vector available with the 2-h bridge

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Short Paper Proc. of Int. Joint Colloquium on Emerging Technologies in Computer Electrical and Mechanical 2011 vectors which are closer to the intended direction. Use these two space vectors over parts of the TPWM and let the space vector be zero for the remaining portion of TPWM. Let us take an intended space vector KVd( K  1) at an angle (0  θ  π/ 4). If this intended space vector average is to obtained by using the space vectors UE and UNE of figure 3 for times T1and T2 respectively, we must have KVd (cosθ+jsinθ)TPWM=VdT1+(Vd +jVd)T2 (5) This gives us (T1+T2) =K CosθTPWM, . .

(6) T2=KSinθTPWM (7) And hence T1= K (cosθ-sinθ) TPWM (8) The equation (6)-(8) tell us that K< < 1 to see that (T1+T2) does not spill over TPWM .This mean that a maximum amplitude of Vd is obtained for the space vector in this arrangement.

Similar calculations can be done for space vectors lying in the ssssuccessive sector of π/4 radians.. For every sector ,the time associated with the main direction space vectors UE,UN,UW,US, is T1 and the time associated with the border line direction is T2. The time To =TPWM –T1 –T2 has to he ofcourse fitted in by a zero vector. The distribution of T1, T2 and To in the total time TPWM can be done in many different ways .However to minimize the switching operation needed, it is proposed to keep T2 at the centre of the time span TPWM flanked by T1 /2 and to/T0/2 at both ends of the intervals .When this is done, the switching operations required will be as shown in table 2 It can be seen that the switching operations per TPWM are four .These are the minimum needed and hence corresponds to minimum switching losses For any sector only two switches are operated in one TPWM, the other two remain off..The switches remaining off are different for different sectors and hence over a revolution of the spacevector, the heating losses are evenly distributed among the switches. It can be thus seen that the 2-H bridge configuration is very much amenable for SVPWM. Additionally; it can give maximum amplitude of Vd for the space-vector.

TABLE II. SWITCHING SCHEDULES FOR DIFFERENT SECTIONS

III. COMPARISON WITH OTHER SCHEMES The reason for recommending the schemes of (7)i.e. the H bridge and three leg converters is basically the less no. of switches in H bridge and the easy availability of three phase converter .The configuration of Fig1of this paper will change to three leg converter if Q2and Q4 are connected in parallel and made into a single switch, But with this configuration as has been discussed in [7], the space-vector UNE and USW are not feasible and hence instead of fig.3 of this paper, you get the hexagon of fig4 (below)

This reduces the maximum amplitude of space-vector possible with linear modulation as Vd/ 2 only. The 2 bridge configuration discussed in this paper gives a maximum amplitude of Vd with linear modulation .This is easily seen by the circles in fig.3 and fig. 4which touch the periphery of the space-vector polygon Thus the 2-H bridge configuration has a clear advantage over the three -leg configuration in making a higher a.c. voltage available .The voltage available is 200% of the one available with single H-bridge and 141% of the one available with the three leg configuration Additionally in the switching schedules needed for getting a certain average space-vector over one Tpwm ,the number of switching operations needed is 6 in the scheme of [7] ,whereas in the 2-H bridge configuration the number of switching needed per TPWM is only 4.This will reduce the switching losses to 2/3 compared with the scheme of [7] .Also all the eight switches of the 2-H bridge configuration will carry the same current, hence they need the same ratings Their heating is also equal IV. CONCLUSIONS The 2H bridge configuration is a very good choice for SVPWM of 2-phase balanced induction motor. Excepting for a large number of switches needed, the scheme is better than the other scheme studied earlier.

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Short Paper Proc. of Int. Joint Colloquium on Emerging Technologies in Computer Electrical and Mechanical 2011 REFERENCES

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Angle control of PWM inverters –fed 2 phase IEEE Trans. Power Electronics Vol. 3 pp. 377-283, July, 1994 [5] C. B. Jacobina, “Rotor –flux oriented control of a single –phase induction motor drive”, IEEE Tranc.InD. Electronics, Vol. 47, pp 832-831 Aug 2000 [6] S. S. Wekhande, B. M. Chaudhari and S. V. Dhopte ; “A low cost inverter drive for 2 phase induction motor ,” In Proc.

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[7] M. A. Jabbar, Ashwin M. Khambadkone, and Zang Yanfeng, “Space vector modulation in a two phase induction motor drive for constant power operation “, IEEEW transactions on Industrial Electronics Vol 51, No. 5, Oct 2004; pp 181-1088.

[1] L.M.C. Mhango and R, Perryman ,”Analysis and simulation of a high –speed two phase a.c. drive for aero space applications “ Proc. IEE – Electrical Power Applications Vol.144 no.2 pp 149157 March 1997 [2] I.R. Smith ,D. Creighton ,and L.M.C. Mhango, “Analysis and Performance of a novel two –phase drive for fan and water –pumping applications “IEEE Transactions Electronics Vol.36 pp 530-538 ,Nov. 1989 [3] D. Jang and G. Cho. “Phase –difference control of 2-phase inverter –fed induction motor “in Conf. Rec. PEEE –PAS Annual Meeting 1989 pp.377-383

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