Aspects of the study of power-electronic-rotating-electromechanical systems I

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Aspects of the study of

power-electronic-rotating-electromechanical systems I

Citation for published version (APA):

Wyk, van, J. D. (1968). Aspects of the study of power-electronic-rotating-electromechanical systems I. (Technische Hogeschool Eindhoven. Afdeling Elektrotechniek. Groep Elektromechanica : rapport; Vol. 68-4). Technische Hogeschool Eindhoven.

Document status and date: Published: 01/01/1968 Document Version:

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afdeling der elektrotechniek • groep elektromechanica rapport nr.

CON'I1_~NTS.

Summary

1. Introduction.

1

2. Syetematics of' PEREJ1-systems.

3. A discuesion of grou~-II PB~REM-systems. ₃₅

4. Practical examplea and investigations on group-II systems.

5.

Concerning the theory of :periodically switched electrical machines.

14/é

6. Experimental systems developed for the investigations.

161

1.

Problems encountered in the synthesis of maohine-electronio systems. 213

8. Experimental work conducted on the systems. ₃₁₂

9.

Conclusive remarks. 348

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SUMMA.RY

Fart of the investigations on the electronic control (regulation) of electrical machines in the sectien on machine-electronics is

d~voted to the study of systems employing other methods of control of induction machines than varying the angular frequency of the airgdp flux of the machine. The present report intende to present the progress of these investigations.

In order to approach the study of thes~ systems in a systemntic way, ohapter 2 atterm:ts the formulation of a generol olassifioation for the methods of regulation. Chapter 3 examines the possible methode of re~

lation in the specific systems of interest, i.e. of what is exposed in the text as G:roup II FEREM-systems. Inveetigation of the past and rrer;,~nt

state of the art for these syetems as reflected in the literature may be found in charter

4.

Combination of this chapter and the previous chapters lead::; to a choice of ~yst~ms to be investi,rsated experimentally. The

elec-'

trical machine as the energy converting oomronent constitutes an impor-tant part of the system - therefore chapter

5

is a starting point for theor,.,tical characteristics of the switched induction machine.

Experimental study is to be conducted on a selected grou.p of systems. The initial set-up and design of these units are treated in chapter six. Attention i~ devoted especially to the power and info~ation electronica.

'

DurinR' synthesis of the systems some t;y"Pical problems were encountered, and these are treated in charter

7,

whereas the e.xperimental work during set-up and ini tüü eperation is discussed in the following chapter. As was to be expected, this consisted mainly of tracing the complicated

sys-tems throur:h for eli:nination of incidental and spurious Malfunctioning, and determining the correspondence between theoretically expeoted and nractioally observed functionin~ of the power electronica.

This report presr:nts a record of current, unfinished research i·rork -therefore one cannot expect clear conclusions. The most important con-clusion is the olear indica~ion of the aspects still to be inveeti&ated that is obtained in this way.

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Introduction: Inveetigations on systems consisting of electrical machines controlled or regulated by power electronic means.

The-use of ~ower-electronics for centrolling electrical machines is by no means new, yet it hae had a restricted application in the past if one conaiders the power range in which it was mostly applied. This may be ascribed to various scientific, technica! and economical considerations. Due to the availability of new types of semiconductor switches, an ever increasing growth has been stimulated during the past f'ew yep.rs. The characteristics of these semiconductor

.

devices, chiefly thyristors, not only encourage the realisation of schemes dreamed up in .the past, but a! so 1 r;~d tf'l conception of a large

amount of new circuits and approaches to the control of electrical machines. In design of large systems it beoomes a necesrity to know the exact transfe'r function of the subsys tem formed by the power electranies in cascade with an electrical machine.

It appéars that with the growing interest in the characteristic of such systems a new subject, machine-electroni.cs, is growing. The

aim of an engineer desj,çrning mach1ne-electrcnie syetems is to change the traditional toroue-speed re1at.ionship of a particular type of

rota-ting electromechanical traneducer, to suit the requirem?nts of a par-ticular sleetrical driv8, b:r combin'ing i t wi th a power electronica

ting of power-electronica and rotating electromechanicfl.l transducers), and does not merely oomprise a combination of the classical knowledge

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- - - 1 ' - - - 1

of power electronios and eleotrioal machines.

It bas been pointed out previouely that the term "machine-eleo-tronies" may be misleading in some respeots, and the use of the acro-nymn PERSM-syste~ proposed.

(7,8).

This terminology and subdivision will be put to use in the present report.

Regarding p~vious work. and ~raotioal applipations:

When oommencing a study of a subject that is technically in-teresting, it is necessary to investigate two aspects of the ~1~blem

during the prel im•' ftary phase, i.e.

a. Reviww of the contributton of previous werkers. b. Practical applications.

Regarding the former a bibliography bas already been oompiled

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and is extended from time'to time. Some spaoe in the present report is also devoted to a furthér detailed evaluation of the exieting sub-ject matter. Concerning the sec0nd aspect one may take the following into account:

The variable speed system to be investigated will use induo-tion machines; the presently known systems of this type may be divided into drives fed by variable frequenoy solid state inverters and drives where the amplitude of stator voltaRe or rotor ourrent is ohanged by

means of solid state switches. In the secend instanc~ the variabie slip charactP-ristice of the induction machine are used. It is with tbis

last tJ~e that the present audy will be ooncerned (Group II PEREM-systems ( 7 ) ) •

Variabie slip drives have been applied extensively in the past in a power range from fraotional horsepower machines to drives of more tha.n 1 M~.f ( 1), (2). The loads to be driven by a variabie el ip

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drive are:

(i) loa4s reauiring an apnroximately constant torque through-out the speed range (oranes, minehoists, li~ts ~or instanee

(ii) loads requiring an inoreasing torque with increasing speed (blowers, ventilation loads).

(iii}loads for which the reduction in speed caused by the variable-slip characteristics-is essential {Ward-Leonard-Ilgner sets, mill drives.)

The ef~iciency of the drive will depend on the application and the type of regulation. The amount of heat generated due to rotor lossas (slip power not' ~ed back to the eupply) ie toa ~irst approxima-tion proporapproxima-tional te bo~h the required torqu& and the slip of the machine. This indioates that drives with type (i) loads will show decreasing ef-ficiency witb speed, and system design must allow for the extra heat

.

loss. Loads of type (ii) do not introduce this drawback, while with type (iii) loads the decrement in speed is such that the efficiency

re-' .

rnains competitive with other drives. Before the e~~ect of efficiency on ap,-,lication will be clear, many other factors have to be taken into consideration - the drive may only be required to operate at low speed fora short time o~ its operational cycle (hoists)for instance. Further-more questions such as the prioe of electrical energy, size of the drive, initial oost ~. influence the choice of a drive system, and det8rmine the relativa importance of any one ~actor, such as the efficiency for example. In fact, Laithwaite (1) bas indicated that in general an intri-cate and interrelated set of conditionw determine the applicability of a variabie speed electrical drive. Without analysing these conditions here for the present situation it will be stated that the renewed interest in variabie slip drives, and the continued production interest (3,4), indiCQ~e

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the necessary conditions are still fulfilled to aasure the future of these systems.

Conducting a study of the drive systems.

The fact that the subject is not entirely new, but hae been investigated previouely for other types of ewitching devices results in a bistorical bias, especially in the earlier stages, during inves-tigations with new types of switching elemênts. •fuether this histori-cal bias is an advantage or disadvantage is mostly not to be deter-mined during the first period of the life of a new deYioe. It is

con-side~d by th~l a.ut~:c1~ to be the best solution to eliminate the bias, and after having attained a certain level of study, re-apply the hie-torical bias in order to evaluate the pract~oal implications. Definition of the required level ie difficul t, and may be regarded as one of the most important parts experience plays in the solution of engineering problems.

In the course of the pr~>sent investigations i t was at t,empted to remove the bias by devisin~ a new classifica tion system ( Chapter 2). The theoretica! pos~ibilities resulting from this system are then

examined briefly in the following chaptPr. By discuseinp the work already done, thA situation ü, then evaluated .. 'I'his indicates that several espects of ~roun-II PBRE:M systems remain to be treat8d, and contrar.y to bistorical practica in this subject, sbould be done during the course of a compa,ri tive study. In order to conduct this study some systems were chosen, operatinp: on the same machine. 'Phis report also nescribes the first round desip;n and build-up of these systems.

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CHAPTER 2

SYSTEMATICS OF PEREM - SYSTEMS.

2.0 Synopsis

2.1 The system approach

2.2 Review of- the possibilities tor olassi~ication.

2.3 Systematic approach based on the power .relations.

2.3.1 Proposal ~or olassifioation.

2.3.2 Model used for systematics.

2.3.3 Power flow in the di~terent systems.

blz

s

v•

rapport nr.

2.3.4 DefinitiohN'of the different groups of Perem-eystems.

2.4 Subdivieion o~ the .different groups.

2.5 PEREK-systems in relation to other variable speed drives.

2.6 Evaluation.

2.0 Synopsis.

In this ohapter it is attempted to start some investigations trom the systoo-viewpoint. It is f'ound that machine-electronio systems

are d.:!..screte-time) time-invariant systems wi th a fini te memory. The

first objective is to define a way in which the study of PEREM-systems may be approaohed systematioally. To this end the most obvious ways

are shortly summarised, and the approach of olassifioa~ion aooording

to the power relations, ohosen. This model is then disoussed in more dètail, and the different groups found neoessary (Group I, II and III) are subdivided aooording to the known PEREM-systems at present. In or-der to relate this.wot.k to other types of controlled or regulated

eleo-trical variable speed drive systems, a ohart has been oompiled inolu-ding as many of the basic variante of this type of system as known.

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2.1 The system approach to the study of PEREM-aystems.

Power eleotronio rotating eleotromechanioal transduoer "systems" are

...

-

-employed as controlled or regulated drives, the former applioation referring to a oloeed loop system, and the last to an open loop system. The idea of "system" is purely a matter of definition and will be

de-fined in oonformity with present trends as a oolleotion of

interoonneo-ted oomponents, of whioh the

mutual

influenoes on ä ayatem input vector

[L]

F

(u]

Fig. 2.1

[iJ

resulting in an output vector [u] may be written as a transfer

tunetion F so that

i.e. [u]is the response of F to

(i] ,

where the input and output veetors

may be

r

and

1

dimensional respectively' being

i - r- u -1 1 i ' 2 ~

[i] ..

_~3

[u

J ..

_~3

I ' I I I I I I ' I _~ ip u q

....

-

L- _--I

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-[i.]

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It may be remarked that ~uestions ooncerning the eystem

bounda-ries, and transitions ~rom component to system, are tor a large part

purely philoaophioal, and irrelevant to the present inveetigation.

What preoisely constitutes a oomponent

ot

an input or output vector may

be regarded trom the same viewpoint, and will in this report be oonsi-dered to be a-matter of detinition.

..

Examine.an eleotrioal variable speed drive system as an example. Let the drive be a machine-electronic of PEHEM-system. Refer to system

bo~nr:AA'Y 8₁

-

_'

_...

_~

-

' ' "' _' '

,..._

'

""

(u]

n

_t.,. a.

-._.-

----

~--

---

----

·-1 • I I

-Cr-

F,

rb-n,.,r

• _F

P.~.

F

3 '

'

L

rcr

-'

I I I ' · ' ~"~..,.,.--- ~-.--- .,.

**... *Jl:**

-z

F

transfer funotions as followsa

F₁s speed contrailer F2s ourrent controller F

3

t "in.forma.tion-eleotronics" F pe : pow•r eleotronios Fmach.:electrioal machine

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rapport nr.

'l'he input vector

[i]

ha.e as only component the current that is

propor-tional to the desired speed, where~s [u] is two dimensional in its

components n abd T , the aotual speed and the eleotromagnetio torque

a e

ot the machine. The arbitrarinews of syetem boundary may be eucoeesfully

illustrated in thie case - B

1 ma.y have been ohosen so as to include the

driven load, resul ting in ether components of [u

J

Fora study ot PEREM-systems the boundar.f B

1 ie ehifted to B2, as

already remarked and indioated in fig. 2.2. This inoludes

information-eleotronios, power electronica and eleotromeohanical traneducer, and it will now be inveetigated what type of system this will be.

PE~-syetems, b~ing energy processing, emrloy switches as adjustors

in the system. By the ve~ nature

ot

a switch ~he proportionality

be-tween input and output disappears when the switch has been cloaed.

Pos-sibility ot control ie ragained only after the zero-current condition

has again been reaohed. Thie·means that PEREM-systems are discrete-time systems.

-

.

-11 ( td) .., i2( td) I I

'

I I i~( t4) "-

-t d' ( d • 1 ,2 ' - - -)

discrete time of ohanging input

In sorne PEREM-systems, i.e. in the system where the supply frequP-ncy of the electromechanical transduoer is changed, the input may approach a

continuous time f'unction, due to tbe use of filtering circuits or

qual\l:1zcd

levels. These sys.tems then apy)roach the oontinuous-time systems,

with

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This type of system is1not possible with switohed induction machines,

aince these systems employ the disere tE•-t~r.~e oharaoteristics

ot

non-linear elementa. It will be useful to ke~p this tact in mind in the

next seotion on a olassifioation o:f PEREM-systems.

For PEREM-systems in general it may be stated that at least to a first a.ppro::x:imation

FP

[i(td-rd>]

• lu (

~d

- td

)J

wi~h

li (

td)}

~p

_•

(u(

_td

>J

Tbe systems are therefore time-in~riant , and as they will also be

non-anticipatory are causal. •

It now remains to inves~igate whether the systems are instantaneous

or dynamio and linear or non linear. The PEREM-systems contemplated

contain mtmerous e~ergy-reservoirs, these in the sleetrical machine

lt is usatul to remark already at this stage that the time invarianc~

is an asaumption. Systems characterised

b.Y

linear differential

equQ-tions with constant ooeffioients are time-invariant. In general systems described by linear ditferential equations with time var.ying ooeffeoients are time varying. Eleotromechanical energy transduoers are descrined by

sets o:f non-linear dif~erential equations that may be reduoed to linear

sets with time varying coeff'icients under constrainta sutf'ioient f'or a

first round study of PEREM-systems. B,y coordinate transformations it is

furthermore posaible to transfer the seis to piece-wise linear equations

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---~---~

usually being the largest. This will have as a consequence that the

system will, at least in a certain sense, poesas a finite memory, making

the system non-instataneous or dYpamic.

Although the systems are non-linear, it is to be remembered that during a first round investigation, insight is more important than ao-curacy, and therefore pieoe-wise linear analysis will be assumed valid

in analyeis ~nd synthesis for the entire machine-eleotronics. To sum up,

PEREM-systems may beregardedas causal,discrete-time, time-invariant dynamio syetems on whioh piece-wise linear analysis will be employed tor the purpose of thie report.

2~2 R~iew of the poesibilities for classification of the systems.

A systematio olassifioation of PEREM-systems may employ a number of approaches to the subject. Some of the most obvious alter-natives are given below:

a. Classification aooor6ing to the type of energy supply needed to exoite the system.

b. Classificá~tion aocording to the different types of power-eleo-tronie circuits used as adjustors in the system.

o. Classifioation aocording to the parameters in the theoretica! torQue-speed relationship whioh are subject to changes due to the pressnee of the power electronica.

d. Classifioation acoording to the ~~e of electrical machine

ohosen as output unit for the syetem.

e. Classification acco:rd.ing to the fundamental po,rer relations in the system.

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2.2.1 In the past a powertul tradition bas grown in electrical engineer-ing with a view to tbe groupengineer-ing of eleetrical drives or eleotrical

machine!! into the two oa.tegories "a.c. drives" a.ndnd.c. drives"% • This may also be introduoed as regarde maohine-electronio systems or PEREM-systems, and sinoe the systems known at present are either fed from a direct voltage supply, obtained from ba.tteries or by

reotifioa-tion and filtering. To a oertain extent this has alrea.dy been oocurring, ae for instanee reflected in the types of names such as noolleotor-less

"

d.c. drives etc.

It is felt, however, that such a grouping of the systems will only lead to confusion by placing drives with totally different

charaoteris-tics in the same oatego~. (Example: An induction machine fed by a) a

cycloconverter, b) chopped voltage souroe of fundamental frequencyJ

2.2 .2 Recently some extensive attempts have been made to develop a

systematic approach to power electrcnic circuits,

(9),

(10), and this

may also be employed to systematise the machine electronica. Using

'

such a system will obscure the ·real intention of a PEREM-system, i.e. employment as part of an electrical drive, as it uses details of the power-electronio circuits to distinguish between the different systems.

This type of classification may be used to adv~ntage for subdivision

of the main types of machine-electronic systems, as will be evident later, but is not suited to setting up a general classification.

In fa.ct these drives ma.y better be termed "a. V • drives" and "d. V.

drives", since in practice machinesare almost always fed from a voJ:tage

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2.2

.3

Under the assumption that rotating electro-meohanical

trans-duoers operate under quasi-static conditions, have sinusoidal spatial current distributions on moving and stationa.l"'J members, 1!-ave a linear mag.netio circuit, and are excited by voltages and currents of simrle harmonie type , it is possib1e to characterise the ::1aobine b;y an equiva-lent circuit, -and the torque-speed relationship beoomes a 'funotion of

the lumped-elements in this equivalent ciro~it, and the voltages

impres-sed thereon. When one of these parameter~is ohanged, tbe

torque-speed charaoterietic is influenoed, and one may therefore speak of eystems with R , R , control f'or instanoe.

r s

This metbod of classifioation will not be suited to a general approach of' PEREM-eystems, however, since quite otten ,it is not possible to

re-present suoh a system by the lumped elements of one equivalent circuit

as discuseed a.bove, even under the same constraints used for the "nor-ma.l" system, sinoe barmonic'power flow bas to be taken into account.

2.2

·4

The same àrguments that plead against a division of PEREM

sys-tema into a.v. and d.v. categories, also plead against classification aocording to the output machine. Although suoh an approach may be

use-tul when it concerns choosing a system for given environmental oonditions,

it must be dismissed as a possibility ~or a general classification.

2.2

·5

Power electronic rotating electromeohanical transducer

sys-tems may always be oonsidered to be part of an electrical drive, and as st~h power considerations are of' prime importance. When one examines

the power flow in the different machine-electronic systems, it beoomes

apparent that there are groups of systems in which the power electronios

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tic to set up a claseitication should aid insight and the validity is

not affected by any internal change in the power electronica. In the

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2.3

Classifioation basedon the power-relations in PEREM-systems

2.3.1

Proposal for olassification.

The di:f":f'erent variable speed drives using

maohine-electro-nio systems ma~ be divided into the following classest

I Systems in which the funotion of the power-electronica is to

change the fundamental frequenoy of the rotàting magnetio field of the stator. These systems operate at an essentially constant slip for con-stant torque for no parameter changes in rotating or stationary members.

II Systems in which the function of the power electronica is to change the amplitude of. the fundamental of the rotating magnatie field

or

the amplitude and

/:J~

phase angle of the tnduoed rotor current. It is

essential that these systems operate at variable slip for constant to~

que.

III Systems in which the function of the power electronica is to

change tbe fundame~tal oomponent of either the rotor or the stator field,

while a machanical commutator ~unotions as frequenoy ohanger in order

to allow the system to operate at constant slip for constant torque.

These remarke are made relativa to the roodel disoussed in Sectien

2.2.2.

In the actual systems used in practica the "rotor" and "sta.tor" magne-tic fields are mostly stationa.ry, the last due to the conventional mechanica! oommutator on the rotating armature of the machine.

It

is proposed that these three types of machine electronio

sys-tema be called group

I,

group

II

and group

III

PEREM-systems

reepective-ly.

When classifjing the practical systems known at present, the

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Group I sys tems All types of synchronous machines having an

electronic commutator, such as the previous thyratron-commutator machines and the present thyristor and transistor commutator machines, as well as all induction machines fed by static frequency changers.

Group II systems All types of induction machines employing regula-tion of the stator voltage by means of anti~arallel thyristors, as well as all types of slipring inrluction motors having regulation of the ro-tor current by means of thyrisro-tors or previously thyratrons or igni-trons, whether the slip energy is fP-d back to the supply systèm or not.

Group _I,II systems All types of direct vol t'age machines having regula-tion of the armature voltage or field voltage by means of static thyris-tor or transisthyris-tor eQ.uipment, a.nd all types of d.v. machines fed by

• controlled rectifiers from an a.v. supply (electronic Ward - Leona~

aystems).Group III systems is the only group of aystems still retaining the conventional mechanioal commutator.

It may be remarked that the regulation of machines by non-electra---nic methode, such as rotor resistance-regulation of induction machines, series reactor •'egulation of induction machines, voltage regula'f;ion of induction machines and d.v. machines and all saturable reactor regu-lation systems may be aocomodated in the above proposed systematic classification.

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2.3.2 Description of model used for the systematio olassification.

In order to be able to apply the olassifioation eystematioally, all systems should be referred to one model. In addition to the aseump-tions mentioned under 2.2.3 tor the eleotrioal machine part of the sys-tem, the following points must be kept in mind.

It is asspmed that the PEREM-system may be divided into two

sub-systems - The power-eleotronios ~nd the rotating electrioal machine.

To-gather with the control oircuitry, the PEREM-system oomprises a oontrol-_ led electrical drive, as shown in fig. 1. The two subsystems will now

be considered separately..

...

_t

--•

I I I I I I I I I I I I I

•

I

'

-

,_---

~---

.

POWER

ELECTRON/CS

·---'

-ROTATING ELE.CTROME.t:I-IANIC/J.1 TRANSDUCE.R

I

-

..

-

...

I I I I I I I I I I I

•

I I I I I I I

'---

--- ë:n&;oiieJ

~-;;~,-cJ~,:e~-- J FIG 2·3

It is assumed that the power electronica perform the same funotion

as a mechanica! oommutatpr or meohanioal switch. The losseà in this

switching mode are negleoted to a first approxim~tion. Furthermore it

may be assumed thRt

it

is post=:ible to inoorporate energy reservoirs in

the power-electronica system, so that the output power may be of one freQuency only. This energy reservoirs are also aesumed lossless to a

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technische hogeschool eindhoven blz 11 VIlt afdeling der elektrotechniek • groep elektromechanica rapport nr.

first approximation, so that the power electronica as a whole ie taken to be lossless •.

The rotating eleotromeohnnical transduoer is taken to consist of a etator and a rotor, both containing magnetioally aotive material, this structure being subject to the oonditions already mentioned. (see 2.2.3)

.

FIG. 2·4

Consider that power P~

,

~ ars fed to the stator and rotor

respeo-'

tively. Let it be a symmetrical machine in steady state, i.e.

d\f

m dt

• 0 .. dW e

dt

where W and W are the meohanical and electrioal energy oontained

m

e

within the machine.

The power flow equation for the structure may now be set up as:

-

Ps

_cu

₊

Pr

_Ot!₊

Pa

_{Fe "" Fe}

Pr

₊

T

_{e "'m} 2·1

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compo-technische hogeschool eindhaven blz 111 v•

afdeling der elelctrotechniek • groep elelctromechonico ropport nr.

nents, and this may also be taken to hold ~or the torque:

and T e

...

p~r 1n (n) 2.·2

T

(n) e 2·3

For this structure (neglecting saliency) it may be shown that tor the

production of a nonzero average eleot~magnetio torque T , the frequen-_e

oies of rotor and stator eurrente must be related by (B1):

21T'n~

8 s ~· · 21t'n r r .f •

+

- P"fu .

2·4

Examining equation

4

it becomes·evident that this is the necessary

een-dition for a oontinuous conversion of eleotromagnetio energy into meoha-nioal energy in the rotating model assumed. One may n01v distinguieh

the two main familîes of transduoers employed in maohine-electronio systems by inspeetion of this equation.

(i) The stator and rotor frequenoies n ~ and n f are determined

s s r r

by the SUpply systems feeding the stator and rotor respeotively.

(ii)Only the stator frequenoies n8f

8 are determined by the supply

system, the rotor ~requencies being determined by induction

and non-linearities (switches) present in the rotor.

The first type oomprises the so-called synchronous machines, where in

praotiàe mostly n f •

o,

the rotor oarrying a.d.c. magnetising current

r r

or being made of permanent magnet ie ma te rial. The seoond type of trans-duoer is the socalied asynchronous machines, these types of transtrans-duoers having inherently the possibility of variable slip operation.

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technische hogeschool eindhoven blz /9 v ..

(c:t)

(1/tf)

IZ.C.

Fig. 2.5

PEREM-systeme of Group I employing a synchronous or a.n induotion trans-duoer are sï:mm sohematically in f'ig 2 .5(a) and (b). F:t·çr- thE!sP. sohe-matio drawinga it ia already evident how the ~odel will be used.

SM

' (A)M

·-

... -

--

-

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afdeling der elektrotechniek • groep elelctromechanica rapport nr.

This will tollew subeequently, however. When the synchronous

trans-ducer of tig. 2.5(a) is fed by a f'requency ohanger tor which the

frequen-cy

r

1 is zero, and the angular speed of the rotor is coupled back te the

frequenoy ohanger in order to determine the frequenoy, the special case

of an eleotronic version of the ordinary d.v. machine bas been obtained,

(fig.2.6) as has already been pointed out by Niesten (11). In order to

extend the applioation of tbs systematics to systemscontaining d.v.

machines with meohanical oommutators (Group

III),

this model will also

be manipulated with in the following to repreeent tbe conventional d.v.

machines.

From the r~marks made conoerning Group

II

PEREM-eystems, the

appli-cation of the model as in fig.2.7 for systems with an electronic switch

(E.s.)

in the etator or in the rotor respectively fellows immediately.

One may speculate on a tbird possible variant of Oroup-II eystems, i.e.

with an eleotronio switch oparating in etator and rotor eimultaneously.

Poseibilities tor oross-substitution among the groupe alè6 exist, tor

IM.

c.c

*

..

_••

E.S.

-{}-

_..

..

E.S.

e.c. Fig. 2.7

JM.

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technische hogeschool eindhoven blz 2.1 v•

instanee tbe system of fig. 2.6(a) with an electronic switch added in the rotor. These versions are f'ound so seldom, and are of' euoh a degree of' sophistieation, tbat it is judged inopportune to introduce them at pre-sent.

As alrea.dy mentioned, in some oases PEREM-systems are constructed by

retaining tbe mecbanical commutator, (i.e. using a oonventional d.v.

machine) and adj.usting the amplitude of the stator or rotor voltage

(ma.gnetio field) electronioally (choppers). Taking into account the re-marks of the previous paragraph, these Group Ill systems are shown sohematioally in fig. 2.B(a) and (b). The mechanicaloommutator impartw to these systems their variabie speed characteristio. When this is not desired, it may be omitted.

c.. c:.

SN.

*

..

_..

E..S (A)

-4i;l-

_.,

E:.S. ll.C. Fig 2 ,.8

It may be rematked that in tbe case of group I P~REM-systems

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at-technische hogeschool eindhoven blz 22 VIII afdeling der elektrotechniek • groep elektromechanica rapport nr.

tempted to reduce the harmonies to a minimum by incorporation of energy reservoirs and freewheel diodes. In the case of Group II PEHEM -.ystems the eleotronic switches ueusally do not contain energy reservoirs of large capacity, eo that the harmonie content of ourrents and voltages is in relation larger.

Examinatien of power flow in the different aystems.

- - -

·-···~---Sinoe it bas been claimed that the olassification was

eet up on grounds of the differenoe in power flow amongst the syetems,

thia aspect will now be oonsidered.

With relation to equation 1, negleoting stator oopper and iron lossea, oonsider a syetem of group I. Th• torque-speed relationsbip

is influenoed·by changing the stator fundamental frequenoy from f

S

I

to t (fig. 2.9) having the arbitrary relationship fora constant

s

stator frequency shown. If the harmonies of the stator and rotor cur-rente are neglected momentarily, it follows through equation 4 that

21ff

8

+

- 27ft

r

.. +

pw m 2·5

whioh indioate that in these syste~s the speed-torque relationship ie

influenced by a horisontal tranelation.

Ta.king the harmonies into consideration, and negleoting stator lees and the power fed externally to the rotor ( synchronous machines)

(26)

technische hogeschool eindhoven blz 23 VM

T

r

_s

_.\fs

T

_e

--- -- --

I

-

- -

-I _I I I I I I I I I I I I I j

l

I I

w

,... Fig. 2

.9

..

+

w

_m T e (n) 1

...

₊

Ta:(n) 1 OQ """0

Te1 • 00 s1

+I

Te(n)Wsn .. p:IA;+ p;e1

+

Te1 (J.)m tu.:>mL Te(n)

+

z~ulf!

2 2

In these types ~achine-electronics systems the voltage is lowered

in :fixed linear ratio to the :frecw~ncy so that currents and torques

re-main constant, since the system has been assumed linear :for continuous conduction o:f the switcbing elements. One may therefcre expect that

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technische hogeschool eindhoven blz 24 Yill

afdeling der elektrotechniek - groep elektromechanica ropport nr.

all the harmonie torques will remain constant when the waveferm of the primar.r voltage remain constant. Negleoting the rotor iron losses, the power balanoe beoomes

<IQ -o

Te1 • C.Ve1 +

L

Te(n)W sn • Pcu1 +

'2:

Pou(n) +Tel

...-c:::l

.w

_{m m.L}

+c.?

"!T ( )

en

2 2 2

When the fre~uency of the fundamental harmonie is now deoreaeed by a

'

factor &f i.e.

w

81 ""

1

l.O 81 ~ and s remains constant a

-

~ -co 1

L

2

I ₁

·L

T (n)

-

a Te(n) •

w

s(n) "" p

-- w

4u(n) a m e 1 1 1

~

00 1 t

z:

-

p

-

p ou(n) a ou(n) 1 1

This means that with the slip remaining the same, and the fre-quency ohanged by a faotor a, the rotor losses relativa to the input remain constant - these remain proportional to the slip.

1U tb raferenee to fig. 2 •

9

i t may be said tha t when i t is possi-ble for a PEREM-system belonging to group I to deliver a torque T at

e

~ _m, it is oapable of dalivering the same torque at a another

meeha-'

nioal speed ~ with nc change in the relativa rotor los~es. In

m

these types of systems the funotion of the power electronica is

there-fore to change the amount of po1-rer flowing into the ;,~acJ::ine when tbe

(28)

technische hogeschool eindhoven blz 25 v111

A system belonging to group II PEREM-systems may now also

be examined. Taking into account equation 1, and under the same assumptions used previously, we bavet

1

...0

po);l(n)

+

wm2:'

Te(n)

1

The T-c.J _mrelationship is changed by a more oomplicated

geomet:M.-cal operatien than in the previous oase. For the new power ~low

con-Wm

dition we have, when

w

...

-1 m a • Wm p~ cu(n)

+

a 1 1 t T e(n)

Assume the spectrum of

G0

(n) to remain constant.

B T

--ç ---

r

!_

L---~----~---~~m

W' _~ 1.0"' Fig. 2.10

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technische hogeschool eindhoven

Sinoe the torque has been assumed constant,

!

..

1 1

amount of meehanieal po~er flowing out of the system is less by a

faotor a. The losses in the rotor will have increaaed by the same

factor. The restrietion that the spectrum of ~s(n) remain constant

is too restrietive, and will not normally be valid. In general the

difference between the input and output has proportiona.l

to the dewreaee in output, and

..

- ()<)

2:

Te(n)

·~s(n)

-U):

Z

-ç(n)

'

p ou(n) 1 1 1

beoomes mueh· larger. It may therefore be said that these systems are not oapable of dalivering two identieal torques at two mechanica! speeds

with the snme relative po~er loss. The power leas always increases

wi th deerease in speed sinee the pmfer tlov; aaraas the airgap is not

adjusted aaeordingly. The power electronica employs the variable slip charaoteristias of the machine to obtain a variable speed drive, and intlusnoes the to:rque-speed relationship by changing the phase-angle

and ;lor th~ amplitude

o:

the voltage and current components of eaoh

trequency in the syetem.

It is pos~ible to alter group II systems in such a way that they

do not operate with such a high loss ~t low speed by feeding baok

some of the difference between the machanical power and the electrical input power to the supply. Thie extra pieae of power electronica

ne-~e

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afdeling der elektrotechnielc • groep elelctromechanica rapport nr.

do not adjust the power flow aoross the air gap, nor is there a

meohanioal freq~noy ohanger fulfilling this function as in group III

systems.

Lastly, the power flow in group III PEREM-systems may be dis-oussed. Considar the pöwer balanoet

Te(n) • lO s(n)

..

n=1

p

ou(n)

-In systems of group I, the power flow may be ohanged by ohanging

either the torque ~mplitude or by ohanging the frequenoy. As this

change in torque ~mplitude was not taken to bé oharacteristio of

these systems, the main distinguishing faotor was the change of

2·6

power flow aoross the air gap by ohanging the fundamental frëquenoy. In group III systems the r.ower flow is a:f'fec~ ,": by ohanging the

a.m:pli-, ":.··

tuèe of the to:rque. The meoht::nicD.l frequency changer M.djusts the power flow by chan[;ing the frequenoy. In these systems the funotion of tha

power electronica of group I PEREM-systems bas been split into two

parts, the one baing exeouted by a power electronic circuit, and the

other by a meohanical frequenoy ohanger. For Oroup III systams the

possibility tharofore also exists for dalivering tha same torqua at two different machanical speeds without a change in relatiV( power

loss. As the normal d.v. machine m~y be conneoted to apnroaoh this

perfomanoa, it immediately again explains the above remark that good power charaoteristios of th$ systeo are not due to the pm·rer eleotro-nies in this instancA.

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technische hogeschool eindhoven blz 211 v•

afdeling der elektrotechniek • groep eleidromechanico rapport nr.

T

-Fig. 2 .11

mecharuc-of {re'luency

chonsc.r.

2

.3.4

An attempt at definition of thc diffc.re11t ~ypes of EIB.M-systems.

Group I - systems.

Oroup I PEREM-systems or machine-electronio systems are those syetems in which the constant torque power flow acrosc the air gap of the electromecbanioal transducer is cbanged by the power electro-nies wben the mechanica! speed at which the torqua is to be delivered,

-changes, by cbanging the fundamental speed of rotatien of the electra-magnatie field in the air gap. Due to this characteristic of the sys-tem it is oapable of delivering a torque of the same magnitude at

two different mechanica! speeds without in principle changing the

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technische hogeschool eindhoven

afdeling der elektrot•chniek o groep elektromechanica rapport nr.

Group 11 s:stems.

Group I I PEREM-systems or machine-electronic systems are those

systems in which the power-electronica need not in principle affect

the constant torqua power flow across the air gap of the

electromecha-nical tranducer, and due to the absence of a machaelectromecha-nical fre~uenc7

ohan-ger the power .input for all machanical output powers is

approximate-ly constant. Due to this characte~ietic of the system it is incapable

of dalivering the eame torqua at two è.i:fferent machanical speeds with-out ohanging the relative power loss in the system.

Grou:E ! I ! s:stems.

Oroup ! ! I PEREM systems or machine-electronio systems are

those systems in which the power eleotronics do not affect the con~

stant torque power flow aoross the air gap, but due to the pressnee of a mechanica! commutator the fundamental power flow across the air gap is changed when the mechanica! speed changes. Due to this oharac-teristio of the system it is again possible to deliver the snme torqua at two mechanica! speeds without increasing the relativa power losa in the electromechanical transducer. It must be stressed that thia ia not due to the power-electronica, but to the mechanioal frequency changer. Wh-en no variabie speed characteristics are desired, the machanical f'requency changer ma.y be omitted.

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technische hogeschool eindhoven lilz 30 VIII

afdeling der elektrotechniek • troep elektromechanica rapport nr.

2.4 Subdivision of the different machine-eleotronio groups.

In ordtar to acoomodate the dif+'erent types o:f system :found in eaoh group of PEREM-systems, a further subdivision is neoessary. It will not be attempted to discus!" all the variante o:f eaoh subdiv1sion

of the three different groups. The variante of group II will be

dis-cussed further later in this report.

As may be oonoluded from the remarke in sectien 2.3.2, the

group I-systems may be divided into selfdirected and externally

direo-ted systems. (:fig. 2.5 (a) and (b) and fig. 2.6) An example of the

first is the various types of thyristor commutator machines under inves-tigation today, while an example of the secend is the different

sys-1"

tema of static frequency changes feeding induotion or synchronous

_,.

machines.

From the preceding remarks it also fellows that sinoe systems

belonging to group II are dependent on variable slip ohara.oteris.ticA

of the

e!f::~ctrÏ;lechanioal

transtlucer, induction rnaobines will be used.

Tbis gives the pocLibility of eithf,r centrolling thc stator volté..t,;e,

or centrolling tbe rotor curl'fmt. Subdivision ha.s therefore been made

for these tvro types.

The ~m::::.lo€Y existing between the two subdivisions for group II

and group iii systermJ, a.2· lrell as tbe fact that in bcth these systems

the J-Ol-ier-electronics do net change. 't,be const.::~nt torque poNï"r ~cross

the air gap} were theforevious raasons for classifying

thes~

systems

in one main group

(7).

It is telt that olarity is served by

separa-ting these two types of systems. From the examples cited in fig. 2.12

it is evident that the practical systems do not intheleast resemble ea.ch other.

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(35)

afdeling dar elektrotechnielc • groep elelctromec:honiea _{rapport nr.}

2.5

PEREM-systems in reiation to other eieotromechanioai variabie

speed drives.

A PEREM~syatem is but one of the possible solutiona to the control-led or regulated variabie speed drive problem. Although only these

types of systems will be discus' ed. in the r-resent report, and a spe-cific type at tbat (Group Il), it is advisable to see the problem againat the general background. This is always important, as the

merite of such a controlled or regulated variabie speed drive is

u~-fluenoed to a large r,:;::tent by tbe electrical, meoh&nioal and eoono-mical characteristios obtainable with other electrioal drives.

lt bas been remarked previously (section 2.2) that a traditio-nal way to classif;r eleotrioal drives is by tbe supply system needed, i.e. alternating or direct voltage. Many past workers have used tbis as a starting point (1). ln order to keep contact witlipast practica

this approach may be found in ~ig. 2.13. ln order to be able to

se-leot drives witb a specific machine type, the olassitioation by

machine type referred to previously, bas been introduoed in an

in-direct way. From an inspeetion of the possible variations it is appa-rent that at preeent only the variabie pole-pitob have no exact

sta-tic (electronic) equivalent₉ while it is aiso evident that

PEREM-syetems form a relatively small fraction of all the possibilities.

2.6 Evaiuation

ln thia ohapter it has been found, after examinatien

ot

the

various possible methode to approach the study of PEREM-syatems sys-ematioally, that a classification aoccrding to the role the power-electronica plays in the power flow in the system include all the

(36)

(37)

afdeling der elektrotechnielc • groep elektroaechanieo rapport nr.

variations known at present. The approach of the power relations have been ohosen with the argument that a drive is an energy processing system, and. therefore the power relations are of prime importanoe. In choosing this approach it was not possible to consider the over-all system characteristics, as these are almost unknown for the con-sidered system&. As pointed out in the eection on the system approach however, one may expect a system difference between the different categories, as in Group I and Group III the non-linearities are eli-mated as far as possible, while Group II systeme exist by the swit-ohing action.

(38)

afdeling der elektrotechnl.k • groep elelctromechanica rGpport nr.

CHAPTER

3

A DISCUSSION OF GROUP Il PEREJ.1-SYSTEMS.

3.0 Synopsis.

3.1 Theoretica! possibilities for Group II systems.

3.2 Stator regulation systems. Regulation of the voltage by:

3.2.1 High frequeney pulse-modulation. 3.2.2 Switehing supply- synchronous

3.2.3

Switohing at a frèqueney much lower than the supply frequency 3.2.4 General remarke eoncerning the stator regulated systems.

3.3

Rotor regulation systems

Regulation of the rotor action by: 3.3.1 High-frequency pulse modulation.

3.3.2

Switching rotor- synohronous

3.3.3

Svitching at a frequency much lower than the fotor frequenoy.

3.4

Evaluation.

3.0 Synopsis

~'h.:m :::-ons.i.dering the system• that may :po~:wibly be construoted

by using induction machines, a number of alternatives appear. This

chapter attempt to discues these possibilities in as simple and brief a way as possible.

A switching function is defined as well as driving voltages for stator and rotor circuits. According to whether this switching tunetion

(39)

technische hogeschool eindhoven IIIZ.3b

van

afdeling der elektrotechniek • groep elelc:tromechonico rapport nr.

has a frequenoy muoh higher, equal to, or muoh loweP, than the stator

or rotor fre~uencies, these possible systerns are discussed. In drives

employing a li.igh or a low switching fre~uenoy the a.dditional

possibi-lity of rela.ting the switohing tunetion to the driving tunetion or not exists. In rotor regulation systems one finds the posnibility of feed-ing back slip power to the supply system.

3.1 Theoretica! EOSsibilities for Group II syste~

No attention has been devoted to the different possibilities of eleotronic stator regulation or rotor regulation of induotion machines thus far in this report. As may be conoluded from chapter 2 the fundamental :f'req.uency of neither rotor nor stator is changed du-ring the process. The general idea is to use the non-linear action of a switch in these circuits 'to influence the torque-speed relationship of the electromechanioal transducer by

(i) Changing the mean amplitude of the applied stator voltage.

(ii) Changing the mean amplitude of the rotor current

(iii) Changing the phase angle between rotor current and air gap flux. (iv) Changing the phase angle between applied stator voltage and

stator current.

Since these influences do not always exist alone in a specific situa-tion, and are therefore difficult to be judged according to effectivity, it will be noted that in the subdivision of sectien 2.4 they had not been employed as criteria for eubdivision.

By studying the possibilities of oparating with a switohing tunetion on the rotor or stator voltage it is the intention to discern

(40)

(41)

technische hogeschool eindhoven blz 38 van afdeling der elektrotechniek ~ groep elelctromechaniea rapport nr.

group II systems that have been already realised experimentally in

the past by other workers and by the author are diecussed in subse-quant ohaptere, these theoretically possible variante will be kapt in mind. This should point out the alternatives that had not been given experimental attention, or that had been given inèufficient attention. As in the previous ohapters, an ideal switohing oharaoteristic of the

eleotronio switches will be assumed.

It will be assumed that all the systems to be investigated are

fed by a sinusiodàl voltage:

1T

s

..

v

sin ( (.LJ t ...

e )

s s s

o,. hove induceci l"'obor voltose:

..

e == E sin ( t.V t

+

e )

r r r r

On this voltage a swi te hing flmction of the follo•ring form

opera.tes:

so that the equation for the switohed voltage beoomes

(W₈, rt

+

es, r .. 2n'iö

>[.~:

u(

t-t

_1+ktl-u(

t-~

2 +1tf ~}

k~o

•

Depending on the period

2îr

of the ~witohing funotion in relation to

2'1f

I

(1.'1 · the period

s,r of the voltage, ons may distinguish saveral cases,

(42)

technische hogeschool eindhoven lllz 39 v• afdeling der elektrotechniek • groep elektromechanica rapport nr •

•

_~ (i)

2c

<<.

0 s,r

•

2'lr ( ii)

2l

-

_-

_~ cvs,r

..

_21!

( iii)2

't

>>

ws,r _I

This division has been executed in fig. 3.1. The ma.in branches

have been set up aocording to rrhether the stator input vol ta.ge or the

induoed rotor voltage of the induction machine is switohed.

A summary of the static switching elements that may be employed to build the power-electronic switches has also been included in the fi-gure. It remains disputable whether the magnatie amplifiers should be classed with the electronic devices. They also exhibit limited switching characteristics, as may be seen from the limited amount of

regulation-systems possible with them •. In the experimental syst~ms built-up for

rotor and stator regulation semiconductor controlled reotifiers have been employed as switching elements{ forced oommutation being employed

to interrupt ourrents~. The reaeon for use of these elements in the

systems is their present extensive employment in rractice, raasons for

this will not be discus~ed at the present stage.

J.2 Stator re~ation &ystem~.

,l.2 .1 Reéffil~tion of the stator voltage by high freouenc;y; cho;pping.

It is theoretically poscible to regulate the amplitude of the stator voltage by employing a high-frequency pulse-width modulation of

the supply voltage. It is also possible to

kt(p

the pulee-width

(43)

afdeling der elektrotechniek • groep elektromechanica

(.U(; :o. s, I.D (t+'l) S I l

~

(4.+1).

s

R_L,C.

Fig. 3.2

{IMJ

blz 40

v•

ropport nr.

pulse-width in order to obtain a regulation range as wide as possible. In practica thie system will have saveral serioue drawbacks, the moet important being that the high switching frequency will inorease the switohing and iron lossêe in the eystem beyond all proportions. This alternative will therefore not be oonsidered further. Coneider the re-maining alternative of puJse-width modulation with a frequency of euoh a VJ,lue that the a.bove argu.":'lente apply to a leseer dfllgree.

(44)

afdeling der elektrotechnl.k • groep elektromec::honic:a

•

V₈SÎI"tc.V t

e b •

Vsup= Vs

and therefore from

3.3

the stator voltage will be

blz 41 v~~t ropport nr •

a,b

V

8

. V.L

~!:(oo

8 t

T

2n'il'J[L

u(t- t

1

+

k'lj,)-

u(t-\+~<T.:l3·4

n · k

It is now possible to make a fundamental distinction between th& pos-sibilities Th _~ 1

-

7r oh !..Ss a..nd t'h 1 1r

(ob

t'ractional)

..

-

non eh _Ws

>>

1

In fig. ).1 distinction between these two modes of oparation have been made, although it may not be of graat practical significance.

Theore-tically synchronization of the chopning fre~uenoy with the supply

frequency may be employed to build fre~uency-analogue drives

(51),

as will be discue<>ed later under rotor pulse-modulati.on. As the sii:ff-ness of the system increases with decrease in switching period, and one may therefore expect stability problems, the synohronized stator switchi~ frequency will usually not be ohosen so much different from the supply frequency.

(45)

afdeling der elektrotechniek • groop elelctromechanica rapport nr.

---~---;

In the region where the two freJuencies do not differ much,the beat frequencies resul ting from a random relation between the two may

influence thè oharaoteristics of the system adversely, and synohroni-zation beoomes necessarJ. On the ether hand one may construct a sys-tem with nevel charaoteristics by employing the beat frequencies, as will be disoussed under chapter 4·

By analysing the choppad stator voltage, it is found that the fundamental amplitude is:

A

Vst.Uh(t2-t1) =

211

(see app. 11) clearly indioating the two possihilities for pulse-width-modulation and freQuency modulation to increase or deorease the magnitude of V

81 • One of t~e advantages for this type of regulation may be noted here. The voltage equation indicates that the actua.l driving supply •oltage applied will have nc phase shift for the funda-mental component relative to the supply. Taking into account that the rotor time constant is much longer than the swi tching frequenoy, the current drawn from the supply will have more or lees the same power factor, even when eperating at low torn.ues, than current drawn in the case of no switching. The amplitude of the higher harmonies in the voltage waveferm may be found frorn A11.5 and the order of the switching f'rectuency as

A

(46)

afdeling der elektrotechniek • groep elektromechanica ropport nr.

indioating that this amplitude will be inversely proportional to the order, as is k:nown.

The ma~n disadvantage of the system is the high -frequency oom-ponents superposed on the stator. When the relation descrihing the

iron lossns as a f'unction of frequency and flux density in th•:. normal magnatie ma te rial used in the .::•)uz tJ.'L<C"' · 1. ' "" eleotromechHnioal

trans-duoers is eensidared , this is evident

(B8).

Again due to the rotor time constant, the

hig~rèquency

effects in the rotor circuits will be largely suppressed.

From tbc J)Oint of vie•• of ~jhe power switch i t mt>.y be oomsidared a serious drawback tha t the magnet ie enerQr conta ined irl ';he stE>. tor

leakae;e' fields must be taken up and ctored in the switch during the

11 11

off cycle. Thie impairs efficiency, and increases the switch dimensions due to the neoessary capaoitive storage. Recuperation of this energy during conduction is diffioult.

In summing UD, it may be said that chiefly due to the magnatie and commutation los~es this type of control or regulation 1-1il1 be of

",...