Power converter circuit for a switched reluctance motor using a flyback t:ransformer

K.Y. Cho and J.Y. Lim

Abstract: A power-converter circuit for a switched reluctance motor is proposed. It consists of one switching device per phase and a dump mpacitor. auxiliary switch and flyback transformer. In this Converter circuit, thc demagnetising current of an off-going phase is stored in the dump capacitor and is returned to the DC link capacitor through the transformer. The dump capacitor voltage ciln be controlled by the duty ratio control of the auxiliary switch. The auxiliary switch is PWM- controlled in high frequency, so that the size of the transformer can be reduced. The voltage rating of the auxiliary switch and dump capacitor is lower than that of the main switches and DC link capacitor. The modes of operation are described and the effectiveness of the proposed converter circuit is verified through simulatioii and expeiiment.

List of symbols

A. B, and C phase voltages A, B, and C phase currents phase resistance A, B, and C phase inductance primary and secondary inductance of transformer primary and secondary currents of trans- former number of tums of primary and second- ary transformcr windings number of phases and rotor poles angular velocity of rotor rotor position electrical and mechanical frequency of motor speed duty ratios of main and auxiliary switches

1 Introduction

A switched reluctance motor (SRM) has been a promising candidate for industry and home appliances, due to its simple and rugged structurr, as well as an inverter with a reduced number of power switches compared with induc- tion motor and PM synchronous motor drives [ I , 21. The stator and rotor of an SRM have a doubly salient pole and the rotor has no windings and magnets. The drive circuit of an SRM has an inherent protection against a shoot through fault and the current of each phase may be controlled to be unidirectional. The cost and perfomrance of SRM drives are highly depcndent on the converter topologies and motor structure. so that developments in the converter topologies have been made in parallel with the machine design There have been many converter topologies presented, but, unlike

50 IEE. 2003 IEE Proceeding$ online no. 20030058 d~,~l0.1019/ipepa:ZW30058 Paper fin1 receiied 161h October 2WI and in revised fonn ?3rd April 2002 Tho authors arc with lhc Disiiii Applii in~~ Rmarch Lahoralory. LG Elclronics. 327-23 Cawin-Dong. Keumchun-Cu. Seoul 153-802, South Korea

88

the conventional inverter circuits, SRM drives have not been standardised. In addition, in contrast with induction motor drives. the optimum converter concept for SRM drives appears to be much more application dependent. The basic requirements for the SRM drive circuit can be summarised as follows: (i) capability to track a commanded current pulse very quickly and accurately for good drive performance: (ii) as low a converter power VA rating as possible for a given drive rating for low cost, (iii) low switch per phase, and (iv) low noise and torque pulsation.

The converter topologies for an SRM developed to date can be characterised by the means in which the energy stored in the magnetic field associated with the phase winding is recovered at the end of each motoring stroke. The presented converter topologies can be divided into six basic categories [3]: half-bridge converters, capacitive energy recovery converters, magnetic energy recovery converters, CxtCrndl DC-DC energy recovery circuits, dissipative converters and self-commutating converters. These cou- verter topologies have lhcir own characteristics including the driving performance and drive cost. so that the choice of the converter topologies is higlily dependent on their application areas [2-131.

The asymmetric half-bridge converter [2], as shown in Fig. la, has good drive perfomiance by the independent control of the motor phase currents and voltages. The drive cost. on the other hand, is high duc to two switches per phase and the associated drive circuitry such a s the isolated gate drive circuits.

Power converters with external DC-DC energy recovery circuits [5-lo], such as C-dump converters: series capacitor dump converters, and modified C-dump converters, have received considerable attention because it used only ( N + I ) switches to achieve independent phase magnetisation and full suppressing voltage. It transfers the energy stored in the magnetic field of an off-going phase to a dump capacitor. A DC-DC converter, including an inductor and auxiliary switch. is used to transfer energy from the dump capacitor to the system and to ensure that no capacitor becomes under or overcharged.

The C-dump converter [5, 61, as shown in Fig. Ib, consists of one switch and diode per phase, a dump

IEE Proc-€1~~0: Power Appl., Vol. I5Y No. I, Juiii~iy 2W3

a

b

Fig. 1 Conwrrio,rd cuncu~er rircuie ci Asymmetric bridge convener h C-dump converter i' Modilied C-dump con~eiter

capacitor and DC-DC converter including a switch, inductor and diode. The phase windings are energised from C,,? by closing TA, TB or Tc. Opening the phase winding switch causes current to freewheel into DC link capacitor CCr. The dump capacitor volt~igc is generally maintained a t 2V,c. in order to supply - V,/, to the off-going phase. The converter also has full capability to program the current pulse. duiing both 'turns on' and 'turns off, and high efficiency operation results. The drawbacks of this converter arc the high switching device voltagc ratings, the expense of the additional switch_ the dump capacitor and inductor, and the losses associated with reactive elements.

A modified C-dump converter [I, as shown in Fig. IC, reduces the VA rating of the switches and voltage rating of the dump capacitor. An additional diode has been added. A zero voltage loop is possible, for example, through phase one, freewheeling diode DR and T/ . The energy of the dump capacitor can bc discharged through c; L,, and D,. The dump capacitor voltage can be controlled within V,,+d Vcc, by hysteresis voltage control and PWM chopping, but the demagnetising time of the ofr-going phasc current may be increased because the demagnetising voltage across the off- going phase is zero when the auxiliary switch T/ is turned on. This problem is severe when the turn-on time of rf is large during the demagnetising period, for example. in the case of high speeds, small dump capacitor and small DC link capacitor. The small inductor can reduce the demabme- tising time by returning the overcharged energy in the dump capacitor through the inductor and auxiliary switch in a short time, but the peak of inductor current becomes high and the power rating of thc auxiliary switch has to be increased. Hence, it is desirable that the dump capacitor and D C link capacitor is sufficiently large.

IEE Pruc.-EI~~fr . P m w Ajipl., Vol. I5U. A+,. I , Jri,iuirr) ZfM3

In this paper, a power converter consisting of an auxiliary switch, dump capacitor, diodes and flyback transfonner is presented. The phase voltages and curreins ciln bc controlled independently by PWM chopping. To reduce the voltage rating of the auxiliaty switch, thc maximum dump capacitor voltage is controlled below half of the DC link voltage. The dump capacitor stores the demagnetising and freewheeling currents of the phase windings and returns this energy to the DC link capacitor through the Hyback transformer.

2 Proposed converter circuit

Fig. 2 shows the proposed converter circuit for a three- phase switched reluctance motor. It consists of one switch and diode per phase and DC-DC converter including a dump capacitor. auxiliaty switch and transfonner. Main switches TA, TB and Tc control the voltages and currents or three phase windings. Both the demagnetising current of an off-going phase and the freewheeling currcnt of the conducting phase are stored in the dump capacitor. The flyback convcrter first stores the energy in the transfoimer during 'on time' of the auxiliary switch T,; and subsequently transfers this energy to the DC link capacitor during 'off time' of the switch T1: When the switch T, is tunied on, the dotted ends of the transfonner windings are positive with respect to the undotted ends. During this time interval, the energy stored in the dump capacitor is transferred to the primary winding of the transfomier, while there is no current flow in the secondary winding because the diode Of is reverse biased. With TI turned off, the energy of the primary winding is transferred to the secondary winding of thc transfonner. This energy is returned to the DC link capacitor C,, and is also used to energise the next conducting phase. I f thc current in the secondary winding has decreased to zero before the switch T, turns on again, the converter is operating in the discontinuous current mode. The converter can be operating in the continuous current mode. if the switch ?is tumed on while the energy is k i n g returned to the DC link capacitor.

Fig. 2 Propoe'l coiiiwlm circoii

The dump capacitor voltage depends on the incoming current from the phase windings and the outgoing current to DC-DC converter. The incoming current consists of the demagnetising currcnt of an off-going phase and free- wheeling current of the conducting phase. The outgoing current depends on the chopping frequency of the auxiliary switch, dump capacitor voltage and DC link capacitor voltage.

In thc proposed converter; hysteresis or PWM control of the auxiliary switch can control the dump capacitor voltage, so that the voltage, level across the phase windings for magnetising and demagnetising modes can be controlled independently. The lower dump capacitor voltage is beneficial to device ratings. but it increases the detnagnetis- ing time so that the drive performance is deteriorated.

89

Hence, the trade off between the dump capacitor voltage and drive perfomiance has to he considered according to thc application areas. In the case of constant dump capacitor voltage for low-cost drive, the maximum dump capacitor voltage may he chosen below half of the DC link voltage. This allows lower voltage rating of the auxiliary switch and dump capacitor than that of main switches and DC link capacitor. The size of the transformer becomes sinaller as the chopping frequency of the auxiliary :switch becomes higher, but this increases the switching losses. It is desirable to select the chopping frequency of the auwiliary switch by considering the switching losses and current ratings of the auxiliary switch and size of the transformer.

3 Modes of operation

Fig. 3 illustrates the gating sequence of main switches corresponding to three phases and the switching pattems of

TA

TB

TC

a

freewheeling magnetising demagnetising

TA

TS

TI

phase A phase A, B B conduction conduction overlapping A demagnetising

b

Fig . 3 a Gating signals h Enlarged \vavefoms of A of N

Sii~itdiiny puIferfLs uf proposed cunt'erter

Table 1: Switching status of operating modes

the auxiliary switch for energy transfer to the DC link capacitor. The switched reluctance motor operates in the motoring mode throughout the increasing inductance region and in the regenerating mode throughout the decreasing inductance region. For three-phase switched reluctance motors, the inductancc profiles for three phases have similar waveforms with phase delay of 120 electrical degrees for each phase. According to the switching status of main switches and auxiliary switch, the converter circuit has ten operating modes. Table 1 shows these operating modes and they can be classified into three main modes: (i) when only one phase is conducting, (ii) when two phases are conducting (overlapping), and (iii) one phase is demagnetising and another phase is conducting. With only one phase conducting. that is magnetising and freewheeling, it has four operating modes according to on/off status of main switch and auxiliary switch. With two phases conducting, where two phases are overlapped_ it has four operating modes. With one phase demagnetising and another phase conducting. it has four operating modes. But two modes: for example, if the auxiliary switch is turned on and off when the phase A is demagnetising and phase B is freewheeling, have the same operating character- istics of the mode (ii), where both phase A and B are freewheeling.

Fig. 4 shows basically ten operating modes corresponding to the status shown in Fig. 3. The modes l(lJ-4(llb) are the cases that only phase A is conducted and PWM- controlled. The modes 5(lllJ-8(lVb) arc the cases that phases A and B are overlapped. In these modes, the B phase current is built up to the reference current_ while the A phase current is PWM-controlled. The modes 901,) and lO(Vb) are the cases that phase B is magnetising and phase A is demagnetised to decrease the A phase current toward zero. In the modes from I, to V,, subscript 'a' notes the mode that the energy stored in the dump capacitor is transferred to the primary winding of the flyback transformer. Subscript 'b' notes the mode that the energy of the primary winding is returned to the DC link capacitor through the transformer.

Fig. 4u shows the mode I,, with TA and T, both on and DR off, where the DC-link voltage source magnetises phase A and the energy of the dump capacitor is transferred to thc primary winding of the transfonner. Assuming the transformer is not saturated, the current in the primary winding increases nearly linearly because the chopping frequency of T, is relatively higher than the resonant frequency of the dump capacitor and inductor of the primary winding. The governing equations for the A phase current and primary winding current of the transformer can

Modes TA T.9 0, 0, T'

1 llal 1 0 0 0 1 A magnetising 2 (Id 1 0 0 0 0 3 Illa) 0 0 1 0 1 A freewheeling 4 IIlbI 0 0 1 0 0 5 lIllgl 1 1 0 0 1 A.B: magnetising 6 (llld 1 1 0 0 0

7 IIV,l 0 0 1 1 1 A demagnetising

8 (IVd 0 0 1 1 0 B: freewheeling 9 (Val 0 1 1 0 1 A demagnetising 10 IVbI 0 1 1 0 0 B: magnetising

e m o d e I l la f mode Illb

Di

L,

g mode IV, h mode IV,

i mode V, j mode V,

Fig. 4

be expressed by ( I ) and (2), respectively,

Mode.? of opemion ofproposed com~ifer

where l,(tl) and [ A t l ) are the peak currents of the primary and secondary windings at r = r l , respectively. The current in the secondary winding is returned to the DC link capacitor through the diode Of and is also used to magnetise the conducting phase A. The secondary winding current decreases linearly because the DC link voltage is nearly constant during the mode lh. The governing equations for the A phase current and scconddry winding current of the transformer in the mode Ih is given by (1) and (4), respectively,

dim d" (0) Vk = Ri, +L,(H)-+wi,- dr dB ( I )

di dt i,dt =L,,--/l+ KO, ( 2 )

where V,, is the saturation voltage ofthe switch 5, VCc and uCdare the voltages of the DC link capacitor Cdc and dump cauacitor C,,. resoectivelv. When T< is turned off at f = 1 , . ... .

(4) the operating mode is changed from I , to Ib.

and DA off. When the auxiliary switch ?is tumed off at t = tl, the voltage :tcross the primary winding reverses its pola& because the current flowing in the primary winding cannot change instantaneously. As such, the dotted ends of the windings are negative with respect to the undotted ends. The diode 0,is now fonvard.hiased current flows in the secondary winding. Thc initial peak current in the I1h. secondary winding at t = is related to the peak current of the primary winding and turn ratios of the primary and secondary windings, and is given by (3):

1,

di, -V&=Lr-+Vo: l l stst* Fig. 4h shows the mode I,,, with TA on and dt

where VI] is the voltage drop of the diode Of The initial current of the secondary winding at f= ( 1 is &(rl), as given in (3). In the discontinuous current mode of operation, the secondary winding current is decreased to zero before the auxiliary switch is turned on and remains zero to the mode

Fig. 4c and Fig. 4d show the modes I f , and Ith. respectively. In the mode It,, TA is off and DA and T, are on. The current in phase A continues flowing through the freewheeling diode, while the energy stored in the dump

(3) capacitor is transferred to the primary winding of the transformer. The dump capacitor voltage depends on the

91

I V L(tl) = - - i ) lP( t l )

N ,

r a P~OC-EIW~. POW ,+pi., I+,/. 150, hio. 1. J ~ , ~ ~ ~ ~ ~ z m

charging current. i.e. the freewheeling current of pliase A and discharging current to the primary winding of the transformer. The governing equations for the A phase current i,, and primary current i,, in the mode II;, arc given by ( 5 ) and (6):

d i ticd = VCd(fj) + - ( j a y ~ i,)df = L + KO! (6)

In the mode ]Ib. with TA and T, off and DA on, the energy of the sccondary winding of the transfomier is returned to the DC link capacitor vi3 the diode 0,; while the A phase current continues freewheeling through the diode DA and dump capacitor C,, Equations ( 5 ) and (4) givc thc governing equations for the A phase current i<,T and secondary current L(f) in the mode I Ih, respectivcly.

Fig. 4e shows the mode Illa, with TA> T, and T, on, where phase A and phase B currents are overlapped. The mode Ill , is similar to the mode I$,. where only pha:je A is conducting in the modc I , . Thc A phase current continues flowing and B phase current starts to he magnctised, while the energy of the dump capacitor is transferred to the primary winding of the transformer. The governing equatlons for the currents of phase A, phase B and primary current ip in the mode 111, are given by equations (I), (7) and (2) , respectively.

C'i l i . dr I ,

The mode HIb is shown in Fig. 4j; with TA and T, on and T, off, the currents or phasc A and phase B continue flowing and the energy of the secondary winding is rctumed to the D C link capacitor via the diode Of The governing equations for the currents of phase A; phase 13 and secondary current i.,(f) in the mode Illb arc given by (I), (7) and (4), respectively.

Fig. 4,) and Fig 4/1 show the mode IV, with TA, TH off and T, on, and the mode IVh with TA, To and 5 of, respectivcly. The operation of modes IV, and IVh are similar to that of the modes I&, and ]Ih, respectively, where the demagnetising current of phasc A in the modes 1V is still flowing through the freewheeling diode. The governing equations for the currcnts of phase A, phase B and primary current $, in the mode IV, are given by (9, (8) and (9). respectively,

di dr =L A+ K",

In this mode. the charging currents into the dump capacitor consist of the freewheeling currents from phase A and B, while the discharging current of the dump capacitor consists of the primary current of thc transformer. In a similar way, the govemine equations for the currents of phase A_ phase Band secondary current i,y in the mode lVb are given by (5), (8) and (4), respectively.

Fig. 4i and Fig. 4j show the mode V$,, with TA off. T , 5 and DA on. and the mode Vb with T, on and TA, T/ off, respectively, where the phase A is in the demagnetising mode and phase B is in the magnetising mode. The

92

operation of modes V, and Vb arc similar to that of the modes I;, and lh. respectively, where the demagnetising current of phase A in the modes V is still flowing through the freewheeliiig diode. The governing equations for the currents of phase A, phase B and primary current ip in the mode V, are given by (3, (7) and (6), respectively. 111 a similar way, those for the currents of phase A, phase B and secondary current i, in the inode Vh arc given by (9, (7) and (4). respectively. When the demagnetising current of phase A becomes zero, modes V;, and Vh will he changcd to the operating modes of I, and lb. respectively, where the phase B is chopping instead of the phase A.

3. I Transformer design The DC-DC coiivertcr plays a critical role in the operation of the proposed converter, because the efficiency and power ratings of the additional components depend on the duty ratio and chopping frequency of the auxiliary switch as well as inductance of the transfonner. The build-up time of the phasc currents depends on the DC-link voltage and dump capacitor voltage. The dcmagnetising time, where the off- going phase current decreases toward zero, depends on the dump capacitor voltage. For the given input powers and dump capacitor voltage, the transformer winding specifica- tion can be designed. The design guideline for the transformer is summarized as follows:

(i) Calculate the energy transferred from thc motor windings to the dump capacitor. The transferred cnergy depends on the transferred currents from the motor windings to the dump capacitor, which consists of the freewheeling current during conimutation and overlap and demagnetising current after commutation The frcewheeling currents flow into the dump capacitor, when the main switch is turned off during the chopping mode. Thc transferred energy of the demagnetising current may be detemiined by maximum phasc inductance and maximum phase current, because the main switch is turned off at the maximum phase inductance. The maximum power trans- ferred to the dump capacitor can be expressed as

I 4 ( 1 + ") 6o I,,, ' l a c d l - o,"~,,,)l,,,,,+ZL""If,Pf",

(10)

where a is the overlap angle between adjacent conducting phases and I,,,r., is the maximum phasc current.

(ii) Determine thc switching frequency and duty ratio of T,and Vcci by considcring the size and peak currents of the transformer. The choicc of chopping frequency of the auxiliary switch depends on a compromise between size and efficiency. The size of the transformer can he greatly reduced by operating at high frequencies, however switching losses and iron losses increase, reducing circuit cfficiency. The chopping frequency of Tj may he selected between 30-70kHz. The dump capacitor voltage is desired to be high for largc demagnetising voltage, hut low for low voltage rating of the auxiliary switch and dump capacitor. In this application, the maximum dump capacitor voltage is designed to he halrof the DC-link voltage. The duty ratio of the auxiliary switch depends on the motor speed. dump capacitor voltage and the energy transferred from the dump capacitor to the D C link capacitor. For a given dump capacitor voltage, the duty ratio has to he large at heavy loads condition, i.e. high speed and large phase currents.

(iii) The maximum power, P,,,<,, transferred to the dump capacitor from the phase windings as given by (IO) is

IEE Proc-Eiwil: Pi,ilrr Ai~iii . . l'd 150. Nu. 1. knirmur? XXJ3

equal to the power of the primary transformer winding. therefore, the maximum current of the primary winding and the primary inductance LIJ can he cxpressed as ( I I ) and (12), respectively,

(iv) The number of turns of the primary winding can be determined by considering the flux density of the transfor- mer and then the length of thc airgap can he obtained as shown in (13) and (14) respectively,

where A is the effective flux areas; /c, and B are the airgap and the flux density of the transformer. rcspectively.

The transformer currents can be operated in the discontinuous current mode (DCM) and continuous current mode (CCM). Under the given transformer powers, these modes depend on the duty ratio and the tums ratio of the primary and secondary windings of the transformer. CCM is suited for those applications that require constant output voltage. while DCM is suited for those applications that require constant output current. The boundary condition between CCM and DCM depcnds on the dump capacitor voltage, duty ratio of the auxiliary switch, and turns ratios of the transformer. For a givcn switching frequency of the auxiliary switch and inductance of the primary winding. the duty ratio of the auxiliary switch at the boundary condition can he given by

where N,$,> is the tums ratio of the secondary and primary windings, N,JN,>. Fig. 5 shows a set of curves with the duty ratio of the auxiliary switch according to the dump capacitor voltages, for some tums ratios. The currents are continuous in the upper region of the boundary curves and are discontinuous in the lower region. The duty ratio of the auxiliary switch at the boundary condition is inversely proportional to the dump capacitor voltage. For a given dump capacitor voltage, increasing turns ratio at the boundary conditions results in decreasing the duty ratio of the auxiliary switch. In this application, IV\~ of 2 is reasonable, because the duty ratio of 0.5 is in the boundary r e ~ o n when the maximum dump capacitor voltage is half

of the DC-link voltage. In CCM, the nonzcro offset current in the primary winding is transferred to the secondary winding when the auxiliary switch is turned off. 111 a similar way, the nonzero offset current in the secondary winding is transferred back to the primary winding when the auxiliary switch is turned on. These offset currents have no impact on the energy transfer from the dump capacitor to the DC-link capacitor. but they increase the conduction losses. If the transferred energy from thc phase windings to the dump capacitor increases when Dai,.y is set to be constant, then the dump capacitor voltage exceeds the value &en by ( IO) and D,,,,.v lies above the curve in Fig. 5. D,,,, should be reduced in order to make the transformer currents track the curves of boundary conditions. In this case, the additional circuit has to he added to detect the dump capacitor voltage or transformer currents.

4 Experimental results

Table 2 shows the specifications of the switched reluctance motor uscd in the simulation and experiment. An SRM is designed for the blower of HVAC and the teeth for the stator and rotor are 12 and 8, respectivcly. The DC-link capacitor voltage V,/< is 310V and the chopping frequency of main switches is 12 kHz. The maximum phase inductance is l500mH, when the phase current is 0.4A, and it is decrcased to 1400mH at 0.6A and 1200mH at 0.8A due to the saturation of the stator and rotor cores. The minimum phasc inductance has small variation for various phase currents. The transformer core type is E128 lamination corc with O.jnlm airgap and ferrite core, wherc the flux density B,sc,,=0.3T. The peak current is 2.5 and the primary inductance and secondary inductance of the transfoimer are 0.26mH and 1.04niH, rcspcctively. The numbers of tums for the primary and secondary windings are 25 and SO. respectively.

Table 2 Specifications of switched reluctance motoi

Parameters Value

Number of statorlrotor poles 1 2 1 8

DC link voltage 310 V Output torque Phase resistance 133!2

Minimum inductance 400 mH

Maximum inductance 1.500mH

Moment of inettia 0.002 kgmz

8 kgfcm at 330 revlmin

Fig. 6 shows the phase currents when the motor speed is 330rev/min. The conduction angle of each phasc is 72 electrical degrccs to increase the motor torque by over- lapping thc currents of adjacent phases. This results in 12 electrical degrees overlapping between adjacent phase currents. The phase currents have an overshoot, due to the voltage control of the phase windings, and it can be reduced and flattened if the phase currents are controlled.

Fig. 7 shows the primary and secondary currents of the transformer. The chopping frequency of the auxiliary switch Tfis 58 kHz and duty ratio is 50%. The secondary current of the transformer falls to zero within turn off time of the auxiliary switch, because the dump capacitor voltage is a quarter of the DC-link voltage. The peak current of the secondary winding is half that of the primary winding. because the turns ratio of the primary and secondary windings is 1 2 The rising slope of the primary current and

93

time. 10 msldiv

Fig. 6 it Gating signal of phase A h A phast current. O.ZA/divisiun c B phase current. 0.2A/division .x-axis: time. lOnis/division

P1ro.s~ curretits UI 330retilrr?in

( i l

time. 5 sldiv

Pririmry orid seconhy (“wnf.s of t~rmsfbrmer. Fig, 7

b Primary winding current, 1 A/division c Secondary winding currenl. I Aldivision .y-axis: time. 5 psldivision

falling slope of the secondary current are nearly equal because L, = 4L,, and Klc = 4 Vca. Hence, the falling time of the secondary current is half the rising time of the primary current as thc peak of the secondary current is half that of the primary current. The leakage inductance and stray capacitance of the transformer cause the ringing currents of high frequency in the primary and secondary currents. This causes an additional r i n p g voltage when vis tumed off. so that the additional voltage stresses on the switch Tland diode 0, have to be considered. Increasing the chopping frequency and inductance of the transformer can reduce the peaks of the primary and secondary currents of the transformer. but this increases the switching losses of the auxiliary switch and the size of the transformer.

Fig. 8 shows the dump capacitor voltage and transferred current to the dump capacitor through the freewheeling diodes. The transferred current consists of the demagnetis-

Gating signal of 7 j

. . . ’ ‘.I i A: 20*mr

8 . t @:186m. .... . . I . . . . . . . . . . . . . . . . . . . . . . . , . . . , I . . . . --

’ ! a : 7 5 4 m s . . . . . . . . . - ; - ! 5 0 : s

. . . . . . . I 4

time, 1 msldiv

Fig. 8 U Voltage, 50Vldivision h Current. 0.2A/division \;axis: time. 1 ms/di\,ision

94

Dump cupocitoi. uolrrrye m d trm.$&wil C U ~ C I I I

ing current of the off-going phase and freewheeling current of the conducting phase with PWM chopping. The pulsating current with high frequency shows the free- wheeling current of the conducting phase and it starts to flow before Lhc beginning of the next demagnetising currents flow due to the conduction overlap in two phases. The frequency of the pulsating current corresponds to the chopping frequency of main switches, i.e. 12 kHz.

The voltage ripple of the dump capacitor depends on the capacitance of the dump capacitor. Fig. 9r1 shows the dump capacitor voltage and phase current when C, is 10pF and the motor speed is 330rev/min. Similar waveforms when C, is 40pF are shown in Fig. 96. The capacitor voltage begins to increase at the beginning of the commutation because the demagnetising current of the off-going phase starts to he dumped into the dump capacitor C,l. The ripple frequency of the dump capacitor voltage can he expressed as

,fr = NP . h. (16) where N is the number of phases. The average voltage of the dump capacitor is 73 V and the peak-to-peak voltage ripples when Cd= 10pF and C,=40pF are 23 V and 6V, respectively.

I i t I

time, 5 mddiv b

Fig. 9 a C,, = 10pF h C,, = 40pF (i) Voltage. 50 V/division (ii) Current. O.ZA/division x-axis: time. 5 ms/division

Dwiip cuparitor aolroge rind phme current

Fig. I O shows the ripple voltages across the dump capacitor, according to the dump capacitor. when the duty ratio is 50%. The voltage ripple is inversely proportional to the capacitance of the dump capacitor. The voltage ripple

60

W : 330ipm (experiment) L

D

25

a a

=

- oi 40 .-

z’ 20 4

0 0 20 40 60 80 100 120

capacitance. C,,

Vo/tuge ~ipples o/dunp cupmiroi Fig. 10

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and average voltage of the dump capacitor is proportional to the motor speeds, because the demagnetising current a t the beginning of commutation becomes large as the motor speed increases. The average voltages at 330 rev/niin and 410 rev/min are 73 V and 87 V, respectively. The normalised voltage ripples based on the average voltages of the dump capacitor are nearly equal for various motor speeds. The nonnalised voltage ripples for 330 revjinin and 410 rev/min when C,,= 10pF are 32% and 34%, respectively. Those for 330 rev/min and 410 rev/min when C , = 40 pF are 8% and 9%. respectively. The choice of the capacitance of C, should be determined by considering the lifetime and the performance of the flyback converter. The lifetime of the capacitors depend on the current ripple (voltage ripple) of the capacitors and ambient temperature around the capacitor. In this application of the blowers, 40pF of C , may be appropriate. The voltage ripple of the DC-link capacitor increases as C,, decreases. but its average voltage decreases. The average voltage and voltage ripples of the dump capacitor are not dependent on the DC-link capacitors. Thc peak currents of the primary and secondary windings also remain constant because the peak current of the primary winding is proportional to the dump capacitor voltage.

Fig. 1 I shows the dump capacitor voltage and demagne- tising degrees according to the duty ratio of the auxiliary switch. The transferred energy from the dump capacitor to DC-link capacitor increases a s the duty ratio increases_ so that the dump capacitor voltage is inversely proportional to the duty ratio. The demagnetising degree, however, is proportional to the duty ratio. For the given duty ratios, the dump capacitor voltages and demagnetising degrees at high speeds are larger than those at low speeds, duc to the increased demagnetising current and coinmutation fre- quency. Large demagnetising degrees may cause severe problems in the motor efficiency at high speeds, so that it is desirable to reduce the duty ratio with suffering the increased peak ciirreiits in the transformer. Large advance angle is one of the methods for high efficiency at high speeds.

Fig. 12 shows the demagnetising degrees. motor efficiency and losses for three types of the converters. The efficiency or

01 I 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

duty ratio 01 auxiiary Switch T, a

J 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

duty ratio of auxilary switch T, b

200

a 50

0

E 0, 6or

A inputpower a motor power

E 0 100 200 300 400 500

2 600

I

60 r

0 100 200 300 400 500 GOO c

100,

480 revimin d

Fig. 12 Compuri.sm of " x r e r s U Powers of proposcd converter h Dcmagnetising degrees (. Efficiency d Losses ( I ) Asymmetric, (2) modified C-dump, (3) proposed

the switched reluctance motor with the converter was measured on the dynamo system. The load torque corresponding to the blowers is applied. which is npproxi- mately proportional to the square of the motor speeds. The load torque was 8.0 kgfcm at 330rev/min, and 2.5 kgfcm and 16.5 kgfcni at 180 rev/min and 480rev/min_ respectively. The output power is approximately a third power of the motor speed as shown in Fig 12u. The duty ratio of the main switches for the proposcd converter is 60% at 330 rev/ min and 95% at 480 rev/min.The dump capacitor voltage of the modified C-dump converter is nearly equal to the DC- link voltage with sinall hysteresis band. In the proposed converter, the dump capacitor voltage is half of the DC-link voltage with hysteresis band by controlling the duty ratio of the auxiliary switch. The demagnetising degree of the modified C-dump converter is nearly equal to that of the asymmetric bridge converter at low speeds. To regulate the dump capacitor voltage under the increased energy transfer at high speeds, turn on and off of the auxiliary switch occurs frcquently during the demagnetising periods, so that the demagnetising degree in the modified C-dump converter becomes larger than that of the asymmetric bridge

Y5

Table 3 Comparison of the converter circuits

Main Freewheel Photo Auxiliary switch Inductor Dump ReC0"ely <:o"pler ITransl capacitor Diode switches diodes

Asymmetric 2N 2N Irl

C-dump N N 1 1 1 1

Modified C-dump N N 1 1 1 2

Proposed N N 1 1 1 1

I VdA I V d J

12 V*I 12 VdJ 12 V,) 12 v,) 12 Vel

12 V d 12 V,I ( V*I ( vdc) 1 v d m 2 vdc)

I v,+ VCd) I V&+ VCdI I vdNso+VcJ 1 VCd) I Vdc+NsoVcJ

l1.5Vfdl 11.5l&I (GI 10.5!&) 12L&

' V,= Vdc/2, N,=2, N: Number of phases

converter. The demagnetising degree of the proposed converter is larger compared with that of other converters, because the dump capacitor voltage (as shown in Fig. 12h) is low. Figs. 12c and 12d show the efficiency and lo:ises of the motor including the converter, respectively. The converter losses include the losses of the rectifier, SMPS (switched mode power supply), transformer a s well as the conduction and switching losses of the switching devices and diodes. The core losses consist of the hysteresis losses and the eddy current losses of the stator and rotor cores. The core losses and stator winding losses have large portions in the input power at low speeds, as the load torque is considerably low at low spccds. Hence, the efficiency at low speeds is much lower than that at high speeds. The motor efficiency of the asymmetric bridge converter is higher than that of other converters by 2.-5% for entire operating ranges. For the modified C--dump converter, the switching losses of the auxiliary switch and conduction losses by the large peak currents flowing in the inductor and auxiliary switch deteriorate the motor efficiency. These losses become more serious at high speeds, under small DC-link capacitor as well as sinall dump capacitor. The efficicncy of the proposed converter is lower than that of the asymmetric bridge converter, due to the large demagnetising degrees and losses in the auxiliary switch and transformer. The transformer current in the proposed converter, however. is smaller than the inductor current of the modified C-dump converter; so that the motor efficiency is lower than that of the modified C-.dump converter by I-2% for entire operating ranges.

Table 3 lists the number of switches and voltage ratings of the components for the conventional and proposed converters. The maximum dump capacitor voltage is half of the DC-link voltage. so that the voltage rating of main switches for the proposed converter can be about 75% of that of the conventional converter. Similarly, the voltage rating of the dump capacitor in the proposed converter can be 50% of that of the modified C-dump converter, and also one recovery diode can be reduced.

5 Conclusion

A converter circuit for a switched reluctance motor with a flyback transformer is proposed. It consists of one switch per phase, an auxiliary switch, transformer and dump

capacitor. The energy of the off-going phase is returned to the DC-link capacitor through the transformer, with appropriate chopping of the auxiliary switch. The dump capacitor voltage can be controlled according to operating conditions and it can be maintained at a lower level than the DC-link voltage. This allows lowcr voltage rating of main switches, auxiliary switch and dump capacitor compared to the C-dump and modified C-dump converters. The drive efficiency of the proposed converter is lower than that of the asymmetric converter_ due to the low demagnetising voltages and switching losses or the auxiliary switch. The modes of operation are described and the operating characteristics are verified through simulation and experi- ment.

6 References

I MILLER. T.J.E.: 'Switched reluctance motors and thcir c0111roI. (Magna Physics. Chrendon. London. UK; 1993)

2 LAWRENSON. P.J.. S-TEPHENSON. J.M.. BLENKINSOP. P.T.. clancc motors'.

pp. IIU0-IIIl 4 POLLOCK. C.. and WILLIAMS, B.W.: 'Power ~~nve~ter~ircui ts for

switched reluctance ~nmtors with the minimum number of switches'. IFF Ploc.. Elictr Puww Appl. 1990. 137. (6). pp. 373-384

5 BASS, J.T.. EHSANI. M.. and MILLER. T.J.E.: 'Oevclopmenl ora iinipolarconvcncr for variable reluctance motor drives'. Conf. Record uf IEEE lndiistiy Appl. Soc. Annual Meeting. 1985. pp. 1062-1068

6 VULKOSAVIC. S.. and STEFANOVIC. V.R.: 'SRM inverter topologies: A comparative cvalmtion'. IEEE Trum Ind. Appl.. ,U41 7, ,a "" ln2L lM7 ., , ., ~",, Fr. .-- . ." . .

7 MIR, S., HUSAIN. I.. and ELBULUK. M E Xnergy efficient C- diimn cnnvcrters for switched ~elucLance motmt'. IEEE Tranr. ltrl. ~~ ~~

i997. 12. (5 ) . pp. Y I ~ - Y ~ I 8 HAVA. A.M.. HLASKO. V.. and LIPO. T.A.: 'A modified C-dump

converter for vaiablc reluctance machines'. IEEE Trcm~. lnd Appl., 1992. 2R. (5). pp. 1017-1022 KRISHNAN. R.: -A novel converter topology far wilcbrd reluctance motor drivcs'. Power Elrctronim Specialist Conference Record. 1996.

9

(2). pp. 1811-1816 TSENC. K.J.. CAO, S., and WANG. J.: 'A new hybnd C-dump and huck-fronted converter for switched ~ C I U C P ~ C C niotors'. IEEE Twnr /,id. Elemur , 2000, 47, (61, pp. 1228-1236 POLLOCK. C., and WILLIAMS, B.W.: 'A unipolar convener for a switched r r l ~ ~ t i l i i ~ e motor'. /ERR T w m h d Appl.. 1990. 26. (2). pp. 222-228 KRISHNAN. R.. and MATERU. P.: 'Analysis and dcsign ofa low- cost converter for switched rcliictancc i m t ~ r dives'. IEEE Twi.s. /tu/. Appi. 1993. 29. (2). pp. 32S327 DESSOUKY, Y.C., WILLIAMS. B.W., and FLETCHER. LE.: 'A novel converter with valtagc-boosting capacitors for a four-phax SRM dive'. IEEE Tram hzd. &.clron. 1998. 45. (5). pp. 815-823

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