Journal of ELECTRICAL ENGINEERING, VOL. 64, NO. 4, 2013, 201–211

PERFORMANCE OF CONVERTERS SUITABLE FORSWITCHED RELUCTANCE GENERATOR (SRG) OPERATION

Valeria Hrabovcova∗— Pavol Rafajdus

∗

Martin Liptak∗∗— Lorand Szabo

∗∗∗

The paper deals with various kinds of converter topologies and their performances suitable for SRG operation. For eachtopology the equivalent circuit, mathematical model and simulation waveforms of phase variables are given. At the end ofthe paper the performances of individual converter topologies are compared and recommendations for their employment aregiven.

K e y w o r d s: switched reluctance generator, converter, mathematical model, simulation

1 INTRODUCTION

Switched reluctance (SR) machines belong to the ma-chines which are obviously called electronically commu-tated machines. It means that they are not able to operateon the rigid grid with a constant voltage and frequency,but they need to cooperate with converters. Therefore itis very important to investigate how a converter topologyinfluences the performances of this machine operation [1].

At present various kinds of converter topologies areknown for switched reluctance motor (SRM) operation.Many of them are described in [2–4], but not all are suit-able for switched reluctance generator (SRG) operation.In this paper detailed analyses of those, which are suitablefor the SRG operation are given.

As it is known, a motoring torque is developed duringthe period of inductance increasing and generating torqueduring the period of inductance decreasing. However dur-ing the generating period in a generator operation thereare defined excitation and generation periods. The exci-

tation period is between the θon and θoff in Fig. 1, during

which the phase is excited from a dc source (or from a

capacitor), or in the next cycle the generated energy of

the SRG is utilized for its own excitation. Then there is

a generation period, between θoff and θext , during which

electrical energy is generated and delivered to the load

[5]. As it can be seen in Fig. 2, the values of θon and θoffare very important variables affecting output parameters

of the SRG.

The converters employed for SR machines are obvi-

ously divided according the number of switches, usu-

ally transistors, per phase. If the phase number is m ,

then there are converters with eg m , m + 1, 1.5m , 2m

switches. However there are more details which can be

important for the converter’s evaluation, and then con-

verters can be called as: converter with neutral point of

the source, converter with a capacitor, converter with bifi-

lar winding, and converter with controlled dc bus voltage.

All these converters are suitable for the SRG operation,

Unaligned

position

qmin0

Vphiph

qon qoff qexc

qgen

Vdc

-Vdc

q

Lph

qexc

Aligned

position

(a)

Lph

Vph

Vdc

-Vdcqoff1

qon0

qc

qexc

qext q,t

iph

qgen

tpwm

ton

toff

(b)

Fig. 1. SRG phase variables at a) – single pulse operation, b) – multi-pulse operation, current control

∗University of Zilina, Faculty of Electrical Engineering, Slovakia, pavol.rafajdus@fel.uniza.sk, valeria.hrabovcova@fel.uniza.sk

∗∗Treves s.r.o., 17. listopadu 341, 544 01 Dvur Kralove nad Labem, Czech Republic,

∗∗∗Technical University of Cluj-Napoca,

Department of Electrical Machines and Drives, Romania

DOI: 10.2478/jee-2013-0030, Printed ISSN 1335-3632, On-line ISSN 1339-309X, c© 2013 FEI STU

202 V. Hrabovcova — P. Rafajdus — M. Liptak — L. Szabo:PERFORMANCE OF CONVERTERS SUITABLE FOR SWITCHED . . .

Fig. 2. Input power, output power, iron losses and θoff vs θon

will be analyzed in greater details and their performances

will be compared.

2 MATHEMATICAL MODELS

AND SIMULATION WAVEFORMS

2.1 Mathematical model of the 2m converter

(C2m)

As it will be seen below, the 2m converter gives most

favorite performances, the equivalent circuit in single and

three phase configuration of which is shown in Fig. 3.

To present how the procedure of the simulation will be

carried out, this converter is analyzed in greater details.

The equivalent circuit is a base for a mathematical

model, needed for simulation. In Fig. 3a there are sevenunknown variables for which seven equations have to be

written. Four of them, for current and voltage phase val-

ues, must be written extra for each phase

diphdt

=1

Lph

[

vph −

(

Rph +dLph

dθω)

iph

]

, (1)

iin =

iph , if S1 and S2 are switched on,

0 at least one of S1, S2 is switched off.(2)

iout =

iph , if S1 and S2 are switched off,

0 , at least one of S1, S2 is switched on.(3)

vph =

+vdc , if S1 and S2 are switched on,

−vdc , if S1 and S2 are switched off,

0 , if only one of S1, S2

is switched on or iph = 0 ,

(4)

where iin is a total current during the period of exci-

tation, and iout is a total current during the period of

generation.

The further three equations are common for all phases

or better to say for the whole generator, and are for

capacitor current ic , load current iL and dc voltage vdc .

ic =

m∑

j=1

iout j −

m∑

j=1

iin j − iL , (5)

iL =vdcRL

, (6)

dvdcdt

=1

Cic . (7)

The definitions of iin and iout are seen in Fig. 4 and in(8) and (9).

Iin =1

θT

∫ θoff

θon

iphdθ , (8)

Iout =1

θT

∫ θext

θoff

iphdθ , (9)

ε =IinIout

, (10)

Pout = m(Iout − Iin)Vdc . (11)

By means of iin and iout two important parameters (see(10) and 11)) which will be evaluated for all converters,are defined. The first is an excitation factor ε and thesecond power output Pout . It is seen that excitation factorshould be as small as possible by small value of Iin andbig value of Iout . Besides, the big difference between themwill give higher value of output power. Therefore bothvalues are important for the converter evaluation. Beforesimulation waveforms and the results will be given, thecontrol strategy, how to get a required torque and power,will be explained.

2.2 Simulation waveforms of the 2m converter(C2m)

The mathematical model from Section 2.1 was appliedand a block diagram (see Fig. 5) for SRG simulation wascreated. The simulations were done for a SRG, which wasoriginally manufactured as a SR motor with the followedrating: 3.7 kW, 3 000 rpm, 540 V. The input static pa-rameters of all SRG mathematical models are obtainedby means of FEM and they are verified by measure-ments. In greater details it can be found in [6, 7] andthe basic SRG parameters are as follows: Lmax = 40 mH,Lmin = 5.5 mH, Rph = 0.7Ω.

Input parameters for single-pulse operation are Vdc ,ω and θoff . The angle θon is generated by PI regulator,which compares the required and real value of the dc volt-age. If the power on the load pout L and output power poutis equal, the vdc is constant and generator is in steadystate condition. In Fig. 6 it is seen that the output powercan be the same at various values of excitation param-eters. In general, the power increases with increasing ofthe excitation period θexc = θoff − θon, but only to aspecific value corresponding to the RMS current limit. InFig. 7 there is seen excitation period and phase current vs

Journal of ELECTRICAL ENGINEERING 64, NO. 4, 2013 203

iph

One

phase

of SRG

RLVph

Vexc

D2

D1

S1

S2

iout ic

Vdc

iL

iin

C+

(a)

Vexc

iA

phase

A

VA

D2A

D1A

S1A

S2A

ioutA

iinA

RL

ic

Vdc

iL

C+iB

phase

B

VB

D2B

D1B

S1B

S2B

ioutB

iinB

iC

phase

C

VC

D2C

D1C

S1C

S2C

ioutC

iinC

(b)

Fig. 3. Equivalent circuit of 2m converter in (a) – single phase, (b) – three phase operation

Fig. 4. Definition of the input and output currents

θoff and Pout at 3 000min−1 and vdc = 300 V. The out-

put power was changed by the load resistance changing.

It is seen that by a given output power, θexc and mainly

IRMS achieve their local minimum on a specific range of

θoff and this is important for design of converter VA rat-

ing. The local minimum of the θexc is at θoff = 36÷ 40 ,

the local minimum of the current is at the θoff = 30÷34 .

The block diagram for the multi-pulse operation differs

from Fig. 5 only in the input parameters, where is also

θon . The PI regulator comparing the required and real

value of the voltage generates the required value of the

current. The both switches are switching simultaneously

on and off with hysteresis 2 A. Simulated waveforms of

inductance, current, voltage, switch pulses and DC volt-

age gained by the converter 2m , are in Fig. 8.

2.3 Converter with a neutral point of the source(Cnps)

In Fig. 9 there is a two-phase converter with a neutralpoint of the source (split DC supply converter-is its namefor the motoring operation), which is suitable for SRG op-eration because it enables energy regeneration to the DCsource. In fact, it is one switch per phase converter. Thisconverter must have an odd phase number. Its advantageis its possibility of current overlapping and employing ofthe whole torque zones. Its disadvantage is that it is notpossible to apply zero voltage, only either positive voltagefrom one capacitor, or negative from the other. It is con-trolled only by hard switching, what increases switchingfrequency and switching losses.

A complete mathematical model would consist of 14equations for 5 voltages and 9 currents from the circuit inFig. 9. Here only basic the differential equations for bothphases are given.

diadt

=1

La

[

va −(

Ra +dLa

dθω)

ia

]

, (12)

dibdt

=1

Lb

[

vb −(

Rb +dLb

dθω)

ib

]

(13)

with capacitors currents

ic1 = iD1 − iT1 − iL , (14)

ic2 = iD2 − iT2 − iL , (15)

Pout_L

SRG

Converter

SRG

Model

Vdc*

IL

qoff

qon

1

s

w

VA

VB

VCq

PI

1

s1/C

Io Ic+

+

+

*

*

1/R1

Pout

+

Vc(0)

-

-

Vdc

Fig. 5. Block diagram of the SRG model employed for one-pulse operation

204 V. Hrabovcova — P. Rafajdus — M. Liptak — L. Szabo:PERFORMANCE OF CONVERTERS SUITABLE FOR SWITCHED . . .

15

0

10

5

3530

40

40

30

20

10

25

I RMS (A)

q off (°) q on (°)

6

0

4

2

3530

40

40

30

20

10

25

Pout (kW)

q off (°) q on (°)

(a) (b)

Fig. 6. (a) – power output and, (b) – phase current vs excitation parameters at 3 000min−1 and vdc = 300 V

20

0

(a)

32

40

10

24

Pout (W)q off (°) 500

1500

1000

q exc (°)

10

0

(b)

32

40

10

24

Pout (W)q off (°) 500

1500

1000

I RMS (A)

Fig. 7. (a)– excitation period, and (b) phase current vs θoff and Pout at 3 000 rpm and vdc = 300 V

where transistor current iT1 , (iT2 ) is equal to the currentof the corresponding phase if the transistor is switchedon, otherwise is zero, diode current iD1 (iD2 ) is zeroif the transistor with the same symbol is switched on,otherwise is equal to the phase current. The voltages canbe expressed as follows

va =

+vc1 , if T 1 is switched on,

−vc2 , if T 1 is switched off and ia > 0 ,

0 , if T 1 is switched off, and ia = 0 .

(16)

vb =

+vc2 , if T 2 is switched on,

−vc1 , if T 2 is switched off and ib > 0 ,

0 , if T 2 is switched off, and ib = 0 .

(17)

The load current is determined by the voltage on the loadand its resistance

IL =vdcRL

(18)

where load voltage is given by the sum of the voltages ofboth capacitors

vdc = vc1 + vc2 . (19)

To be able to compare the simulated values and im-portant parameters with other converters, a four phaseversion will be introduced and analyzed. The capacitor

C1 excites two phases (A and B ) and accumulates theenergy from the other two phases (C and D ). The phasescan be excited in A-C - B -D sequence or A-B -C -D ,what is a case of the following simulations.

In Fig. 11 there are waveforms of four phase converterwith neutral point of the source. Its further importantperformances will be compared with other kinds of con-verters below.

2.4 Converter with dump-capacitor (Cdc)

A model of a single phase converter with dump- ca-pacitor Cd is in Fig. 12 and its complete mathematicalmodel is as follows

diadt

=1

La

[

va −(

Ra +dLa

dθω)

ia

]

, (20)

iT1 =

ia , if T 1 is switched on,

0 , if T 1is switched off,(21)

iD1 =

ia , if T 1is switched off,

0 , if T 1 is switched on,(22)

vph =

+vdc , if T 1 is switched on,

−vdc − vcd , if T 1 is switched off, ia > 0 ,

0 , if T 1 is switched off, ia = 0 .

(23)

Journal of ELECTRICAL ENGINEERING 64, NO. 4, 2013 205

Lb

Vdc

302

q , t

Lc La

Vb

ib

Vc

ic

Va

ia

Lph

iph

vph

T1,T2

T3,T4

T5,T6

300

298

0

0

0

0

0

0

1

1

1

+

Fig. 8. Converter 2m , simulated waveforms of the investigatedthree-phase SRG at 1000 rpm, RL = 2000Ω, vDC = 300 V, i∗ =

10 A, hysteresis control, hard switching

Fig. 9. Two-phase converter with a neutral point of the source

Vc1

Vc2

C1

C2

Vdc

T1

T3D3

D1

Phase A

Phase C

T2

T4D4

D2

Phase B

Phase D

RL

+

+

Fig. 10. Four phase version of the converter with neutral point ofthe source

150

q , t

Lph

iph

vph

T1

300

0

0

0

0

1

1

1

LcLbLa Ld

icibiaid

VcVbVa Vd

iph = 10A*

Vdc = Vc1+Vc2

Vc1Vc2

T2

T3

(V)

Vdc ,Vc

0

Fig. 11. Waveforms of four phase version of the converter withneutral point of the source at 1000 rpm, RL = 150Ω

A model for multiphase version would content four such

equations for each phase. Further equations are current

and voltages of capacitor Cd

icd = iD1 − iTr , (24)

dvcddt

=icdCd

. (25)

And currents of elements of pulse converter

iTr =

iLr , if Tr is switched on,

0 , if Tr is switched off,(26)

iDr =

iLr , if Tris switched off,

0 , if Tr is switched on,(27)

diLr

dt=vLr

Lr

(28)

206 V. Hrabovcova — P. Rafajdus — M. Liptak — L. Szabo:PERFORMANCE OF CONVERTERS SUITABLE FOR SWITCHED . . .

Va

+

Dr

Phase A

Vdc

Vcd

C

icd

icLr VLr

iLr Tr

iDr

iTr

CdT1

iT1

D1iD1ia

iL

RL

Fig. 12. Single phase version of the converter with capacitor

600

q , t

La Lb Lc

Vcd

iph

vph

T1

300

0

0

0

0

0

1

1

1

ia ib ic

Va Vb Vc

*iph

T2

iTr-

iLr-

Tr

v(V)

Vdc

icd

Vdc-Vcd

Ujs

0

Fig. 13. Simulated waveforms of the important variables of theconverter with capacitor

where

vLr =

+vcd − vdc , if Tr is switched on,

−vdc , Tr is switched off, iLr > 0 ,

0 , otherwise.

(29)

The last three equations describe capacitor current, loadand DC voltage and are derived from Fig. 12.

ic = iLr − ia − iL , (30)

iL =vdcRL

, (31)

dvdcdt

=icC. (32)

In Fig. 13 there are simulated waveforms of the importantvariables. It is seen that the currents are overlapped. The

voltage has been controlled on the 600 V with hysteresis±10 V, what is double of vdc = 300 V.

A disadvantage of this converter is fact that the com-

mutation of the currents depend on the difference be-tween vdc and vcd . A fast commutation requires highervcd and hence higher voltage rating of semiconductor el-

ements and capacitor Cd . Further, there are losses at thepulse converter and hence lower efficiency. This converteris not able to create zero voltage in the circuit therefore

is possible to control it only with hard switching.

2.5 Converter for the SRG with bifilar winding

(Cbw)

In Fig. 14 there is an equivalent circuit of the converter

with bifilar winding.

A mathematical model must take into account that aratio of the number of turns of both parts of the bifilar

winding is in general “a”. An equation for primary partof the bifilar winding (subscript ”p”)

diapdt

=1

Lbif

[

vap −(

Rbp +dLbif

dθω)

iap

]

(33)

where Lbif is self-inductance of the primary part of the

bifilar winding. In the equation for secondary winding(subscript “s”) of the bifilar winding is taken into accountthat its phase inductance is inversely proportional to thea2

diasdt

=a2

Lbif

[

vas −(

Rbs +1

a2dLbif

dθω)

ias

]

. (34)

Voltage equations are

vap =

vdc , if T1is switched on,

−avdc , if T1is switched off and ias > 0 ,

0 , otherwise,

(35)

vas =

vdca, if T1is switched on,

−vdc , if T1 is switched off and ias > 0 ,

0 , otherwise.

(36)

The ratio of the number of turns of primary and sec-

ondary winding a has a significant influence on the cur-rent values in both parts of bifilar winding at the T1switching. If T1 is switched on, ias is zero, at the in-

stant of the T1 switching off, the value of ias is changingfrom zero to the value of iapa , and at the instant of theT1 switching on is changing to zero. If T1 is switched off,

the iap is zero and at the T1 switching on is iap chang-ing from zero to ias/a and ias is changing to zero (see

Fig. 15). Then it can be written shortly:

Journal of ELECTRICAL ENGINEERING 64, NO. 4, 2013 207

Fig. 14. Equivalent circuit of the converter with bifilar winding

La

q , t

Lbs

*is =5A

300

iph

T1

0

0

1

(V)Vdc,Vph

0

Lbp

iap ias ibp ibs icp ics

Vas

Vdc

Vap

VT1(ds) VD1

Lph

-300

(V)VD ,VT

900

600

300

301

300

299

Vdc (V)

Fig. 15. Simulated waveforms of a three phase converter for SRGwith bifilar winding

Fig. 16. Equivalent circuit of one phase of the converter with

variable DC link

If T1 is switched off, then ias = a iap and iap = 0.If T1 is switched on, then iap = ias/a and ias = 0.

A capacitor current will be a difference between thecurrents of both parts of winding and load current

ic = ias − iap − iL . (37)

At the end, the equations for load current and DC voltageare as before

iL =vdcRL

, (38)

dvdcdt

=1

Cic . (39)

In Fig. 15 there are simulated variables of the three phaseSRG with bifilar winding, if the ratio of the turns num-ber is a = 0.5. The DC voltage was kept at 300 V. Thephase currents can be overlapped because this converterhas no common switch and current control is indepen-dent. On the waveforms of the inductances is seen thatself inductance of the primary winding Lbp , when T1 is

conducting is 14

of the self inductance of the secondarywinding Lbs , when D1 is conducting. There is also seenthat at the switching over T1 are currents and voltagesalways in the ratio of “a”. Preferable is a < 1, becausethe primary winding is excited in very short time, whatresults in reduction of losses and excitation factor ε . Onthe other side there is a higher voltage loading of a diodeand secondary winding.

2.6 Converter with variable DC link (CvDC)

In Fig. 16, there is a simplified equivalent circuit ofone phase of a converter with variable DC link. The basicprinciples of operation can be explained on the base ofthis figure.

During an excitation T1 is switched on, current flowsthrough phase winding A , T1 and Cb . Equations for cur-rents iT1 , iD1 and a differential equation for the currentiph are identical with (1), (2), (3) in Section 2.4. Aftera commutation of the T 1 the current flows through thewinding of the phase A , and D1 and charges the capac-itor C , therefore the voltage on the phase A can be

Vph =

+vi , if T 1 is switched on,

−vdc , if T 1 is switched off and ia > 0 ,

0 , if T 1is switched off, and ia = 0 .

(40)

Equation for load current and voltage are again identicalwith Section 2.5, see (38) and (39).

Energy for repeated excitation is transmitted from ca-pacitor C by means of switching Tb , therefore

ic = iD1 − iTb − iL , (41)

where

ITb =

iLb , if Tb is switched on,

0 , if Tb is switched off.(42)

208 V. Hrabovcova — P. Rafajdus — M. Liptak — L. Szabo:PERFORMANCE OF CONVERTERS SUITABLE FOR SWITCHED . . .

PI

Db

+

Cb

Vi

Tb

LbVdc

PWM+

-

Fig. 17. Control of the converter with variable DC link

Fig. 18. Simulated waveforms of the three phase 12/8 SRG con-verter with variable DC link, vi = 2Vdc = 600 V and n =

10 000 rpm.

Fig. 19. Output power vs speed for investigated SRG converters

Fig. 20. Apparent power vs speed for investigated SRG converters

Fig. 21. Apparent power vs output power for investigated SRGconverters

Energy is transmitted from DC circuit through the tran-

sistor Tb , inductance Lb to the capacitor Cb . The voltage

and current of the Lb are as follows

vLb =

+vdc , if Tb is switched on,

−vi, if Tb is switched off and iLb > 0 ,

0 otherwise,

(43)

diLb

dt=vLb

Lb

. (44)

The first derivation of the of the Cb voltage is directlyproportional to its current

dvidt

=iCb

Cb

(45)

which is a sum of the currents through the inductanceLb , capacitor C , load and phase winding

icb = iLb − ic − iL − ia , (46)

Simulations have been carried out at the voltage vdc =300 V, as before. The transistor Tb of the pulse converter

Journal of ELECTRICAL ENGINEERING 64, NO. 4, 2013 209

Fig. 22. Excitation factor vs speed for investigated SRG converters Fig. 23. Power factor vs speed for investigated SRG converters

Table 1. Comparison of the analyzed SRG converters

Advantages Disadvantages

Converter – independent current conduction

2m (C2m) by (+Vdc, 0,−Vdc) – more switches

– voltage stress of components ⇐ Vdc

Converter – phase is excited by lower voltage (Vdc/2),with neutral – less switches and diodes but voltage stress of components = Vdc

point of – voltage stress of components ⇐ Vdc – Suitable only for SRG withthe source – independent control of phase currents even number of phases(Cnps) – hard chopping only

Converter – less switches and diodes (m+ 1) – higher voltage stress of components (commonly 2Vdc )with – possibility to generate the power – additional losses on the pulse converter elementsdump by various voltage (Vph <> Vdc) – voltage Vdc must be controlled independently from Vcd

capacitor – hard chopping only(Cdc)

Converter – more complicated bifilar windingwith – less switches and diodes (m) – higher voltage stress of switches and/or diodesbifilar – possibility of rapid excitation – air gap should be as small as possible,bifilar and slow generating by a < 1, otherwise magnetic linkage get worsewinding advantage by higher speeds – the both primary and secondary(Cbw) winding current is to be sensed

– only hard chopping

Converter - less switches and diodes (m+1) – additional losses on thewith - possibility of excitation with higher voltage pulse converter elementsvariable (Vph > Vdc ) advantage by higher speed – voltage Vi must be controlledDC link – less apparent power of pulse converter in independently from Vdc

(CvDC) comparison with converter – only hard chopping

with dump capacitor

has been controlled on the base of PWM modulation

to the output voltage vi = 600 V, to be able to see a

difference to asymmetrical converter (Fig. 17). In Fig. 18

there are simulated waveforms for the investigated SRG

at 10 000 rpm. The speed is higher than its rated speed

3 000 rpm to show its advantage in this speed region. It is

seen that the phase is active during the whole period of

the phase current. Because magnetic flux arises faster atthe higher excitation voltage vi , the ratio of the θgen

/

θexcis approximately 2 and is identical with the ratio of thevi/

vdc .

3 THE COMPARISON OF THE

ANALYSED SRG CONVERTERS

A comparison can be made in a table (see Table. 1) orin graphs (see Figs. 19–23).

In Fig. 19 there is output power vs speed for inves-tigated SRG converters, in Fig. 20 apparent power vs

speed, in Fig. 21 apparent power vs output power, inFig. 22 excitation factor vs speed and in Fig. 23 powerfactor vs speed.

As it is seen in Fig. 19 the output power increaseslinearly up to the base speed what is around 3 000 rpm.This is in coincidence with the theory of operation on theconstant torque and constant power. Then the SRG is in

210 V. Hrabovcova — P. Rafajdus — M. Liptak — L. Szabo:PERFORMANCE OF CONVERTERS SUITABLE FOR SWITCHED . . .

single-pulse operation where the region of constant poweris quite narrow and the output power decreases with thespeed.

In Figs. 20 and 21 there is apparent power vs speedand vs output power, respectively. At the first one thereis seen that the apparent power decreases with the speedbut there are big differences between particular topolo-gies. The higher power is required at the topologies whereonly one common switch transmits energy, excited or gen-erated one, or if its voltage is higher than vdc . The higherapparent power is caused also by multi-pulse operationbecause it increases effective current through switches. Atthe second one there is apparent power vs. active power.As it is known, the better is lower ratio of the S/Pout .Therefore more suitable converters have their curves onthe right side on the bottom. The most unsuitable con-verter is that with a capacitor, the power of which is 2times more than that of 2m converter. The converter withvariable DC link is suitable for increasing of the power atspeed higher than base one. If the active power is in-creased by some tens of percent, the apparent power isincreased by many times more because of higher voltageloading of the switches.

In Fig. 22 there is a factor of excitation ε , which ex-presses the reactive power in the circuit of SRG. There-fore it will have a big influence on the winding losses.The higher ε , the higher magnetizing power is needed fora phase to be able to get the same output power. Thisdefinition is generalized for all converters, also for thosewhich have different voltage during excitation Vexc andduring generation Vgen . Then the factor will be definedas follows

ε =IinVexcIoutVgen

. (47)

In Fig. 22 there is seen that ε decreases with the speedand in one-pulse operation has the values around 0.26 till0.3 (it is not true for the converter with the lower numberof switches than 2m , because there exist mutual influencebetween the currents). The values of ε in single-pulseoperation in fact do not depend on the kind of converter,only on the geometrical dimensions of the SRG, such asair gap, material of the magnetic system, and inductanceratio.

In Fig. 23 there is power factor vs speed for investi-gated SRG converters. The power factor (PF) is evaluatedon the base of the next expression

PF =Pout

mVrmsIrms

. (48)

It is seen that the PF approaches the values of 0.45.

4 A CHOICE OF THE SUITABLE

CONVERTER TOPOLOGY

On the base of findings given in this paper some rec-ommendation can be made for the choice of suitable SRG

converter topology. Criterion for the choice could be: out-put power, speed, price of the converter (according theapparent power), or efficiency of the operation (accord-ing the PF). The classical 2m converter is most suitablefor the lower speed till the base speed with regard tothe power and efficiency. If the phase number is even, itwould be enough also the converter with neutral point ofthe source.

For the high power at the speed above the base one,it is suitable to employ the converter with variable DClink, at the price of increasing of apparent power and de-creasing of efficiency by adding some other elements. Ifthe speed is some multiple of the base speed, the con-verter with bifilar winding is more suitable. But this con-verter is more demanding for the manufacturing becauseit requires a high quality of a magnetic link between theprimary and secondary windings.

The converter with variable DC link has an advan-tage in comparison with the 2m converter because itselectromotive force (induced voltage vi ) can be adjustedwith speed what enables to adjust the output power. Thepower is at the constant speed directly proportional tothe torque and this is proportional to the magnitude ofmagnetic flux linkage ψ . This magnitude is proportionalto vi and the instant of switch on, it means at the con-stant speed to the θexc .

In Fig. 24 there is seen magnetic flux linkage of theconverter with variable DC link at vi = vdc (ψ1), andvi = 2Vdc (ψ2).

In Fig. 25a there is comparison of simulated energyconversion loops of the three phase 2m converter andconverter with variable DC link at Vdc = 300 V, Irms ≤

10 A, and vi = 2Vdc and vi = 3Vdc . At each curve isput also the output power. It is seen that at 10 000 rpmthe power does not increase very much if vi changesfrom 2Vdc to 3Vdc because the current was limited to10 A. But the apparent power has been increased by30.7%. In Fig. 25b, at the 20 000 rpm the power hasbeen increased by 23.3% and apparent power by the57%. The conclusion is that it is not suitable to increasethe vi to the higher value because the apparent power isenormously increased.

5 CONCLUSION

On the base of the analysis and discussions made inthis chapter it can be observed that most favorite is2m converter (C2m), because it has universal advantagefrom the point of view of output power, efficiency, phasenumber and controllability and has not very distinctivedisadvantage.

On the other hand it can be concluded that it is notvery suitable to employ the converter with capacitor, be-cause it has very high apparent power. This kind of con-verter is very favorable at motoring operation at highspeeds, at which its advantage is the controllable phasevoltage at the decay of phase current (at regeneration).

Journal of ELECTRICAL ENGINEERING 64, NO. 4, 2013 211

Fig. 24. Waveforms of linkage magnetic flux of the SRG with con-verter with variable DC link at vi = vdc (ψ1) , and vi = 2vdc(ψ2)

Fig. 25. Energy conversion loops of the SRG with 2m con-verter and converter with variable DC link a) – 10 000 rpm, b) –

20 000 rpm

Acknowledgements

This work was supported by R&D operational program

Centre of excellence of power electronics systems and

materials for their components No. ITMS II-2622012003

and by the Slovak Research and Development Agency

under the Contract No. SK-RO-0028-12.

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Received 3 July 2012

Valeria Hrabovcova graduated in electrical engineering

from the University of Zilina and gained her PhD in electricalengineering from Slovak University of Technology in Bratislavain 1985. She is a professor of electrical machines at University

of Zilina, Faculty of Electrical Engineering. Her professionaland research interests include classical, permanent magnetsand electronically commutated electrical machines.

Pavol Rafajdus was born in Trnava, Slovakia, in 1971.He received the MSc and PhD degree in electrical engineering

from University of Zilina, Slovakia, in 1995 and 2002, respec-tively. At present he is an associate professor at the Faculty

of Electrical Engineering, University of Zilina. His research isfocused on the electrical machines, mainly switched reluctancemotors and other electrical machine properties.

Martin Liptak (MSc, PhD) received his MSc degree in

Electrical engineering from the University of Zilina in 2002.Between 2002 and 2005 he was a PhD student at the Univer-sity of Zilina. Currently he is with Treves s.r.o., Czech Repub-lic

Lorand Szabo was born 1960 in Oradea (Romania). Hereceived the BSc and PhD degree from Technical Universityof Cluj (Romania) in electrical engineering in 1985 and 1985,respectively5. Currently, he is a professor in the Departmentof Electrical Machines of the same university. His researchinterests are in the areas of variable reluctance machines, faultdetection, etc. He published over 170 scientific papers andbooks in these fields.