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Parallel operation of bridge rectifiers without an

interbridge reactor

J.K. Hall, MSc(Eng), PhD, CEng, MIMechE,

FlEE

J.G. Kettleborough, MSc

A.B.M.J. Razak, MSc

Indexing terms: Power electronics

Abstract: Parallel connection of rectifier circuits is

needed for very high direct-current supplies such

as those for electrochemical plant. Appropriate

phase displacement of their AC supply voltages is

used to increase the pulse number, and an inter-

rectifier reactor, often known as an interphase

transformer (IPT), is connected on the DC side to

prevent circulating AC components between the

rectifiers and to allow them to operate indepen-

dently. At very high power levels, this component

is occasionally dispensed with on economic

grounds. The interactions between two six-pulse

bridge rectifiers operating without an IPT are

described and analysed comprehensively. The rec-

tifier, transformer winding and AC-system current

waveforms are computed, together with their har-

monic components, and some typical operating

characteristics are given. Computed results are

supported by practical measurements on a labor-

atory rectifier system. It is noted that removal of

the IPT will considerably influence the rectifier

transformer design.

List of symbols

C

=

connection matrix

E,

e

=

EMF

E d =

DC-load back EMF

I

i =

current

I d

= total direct current

I = direct current from bridge 1

I d ,

= direct current from bridge 2

L =

self or mutual inductance

N

=

number of turns

p = d /d t operator

R =

load resistance

r =

winding resistance

V =

voltage

Z

=impedance

a

= thyristor firing-delay angle

/3 = angle of cessation of thyristor condution

y

(discontinuous load current)

= angle at completion of interbridge commutation

Paper 6987B (P6), first received 27th January and in revised form 26th

July 1989

Dr. Hall and Mr. K ettleborough are with the Department of Electron ic

and Electrical Engineering, Loughborough University of Technology,

Loughb orough, Leicestershire, LEI

1

3TU, United Kingdom

Mr. Razak is w ith the U niversity of Bradford, Bradford, West Y ork-

shire, BD7 IDP, United K ingdom

I E E P R O C E E D I N G S , Vol. 137, P t .

B,

N o .

2,

M A R C H 1990

6

p

Y

=

angle at completion of interphase commutation

=

interphase commutation angle

( p = 6 - a)

=

angle at completion of overlapping of interphase

within a bridge

commutations, one in each bridge

1 Introduct ion

The increasing size of electrochemical and electrometal-

lurgical plant for manufacturing such products as chlo-

rine, aluminium and copper, requires AC-DC power

convertors capable of delivering direct currents of up to

100

kA, and sometimes higher. This necessitates multiple

paralleling of the semiconductor devices within the recti-

fier circuit and parallelling complete circuits.

It is usual to use as high a pulse number as is eco-

nomical to minimise both the ripple in the DC output

voltage and the harmonic content in the AC-supply

current waveform to the rectifier installation. For

example, 12-pulse operation is provided by supplying

two parallel six-pulse rectifiers with

30

displaced AC

voltages. A 24-pulse arrangement requires four six-pulse

rectifiers mutually phase displaced by 15 . A disadvan-

tage of a high pulse number is the increased size and cost

of the rectifier transformer arrangement to provide the

necessary phase displacement. In standard practice, the

transformer tank also encloses the centre-tapped induc-

tor, usually known as an interphase transformer (IPT),

connected between each pair of rectifier circuits, and

circuit pairs if appropriate, on the DC side. This device

prevents interaction between the rectifiers by sustaining

the instantaneous voltage difference in their outputs

caused by the phase displacement on the AC side. Nowa-

days, it is usually considered most economical to use a

12-pulse system.

The three possible six-pulse rectifier circuits for this

application are illustrated in Fig. 1. Each circuit may

have to provide direct current up to about

50

kA, and the

physical arrangements for liquid cooling the parallelled

diodes or thyristors often requires the use of a circuit

containing a common cathode connection, i.e. Fig. l a or

b. An advantage of the double three-phase star connec-

tion is that the semiconductor devices carry only half the

load current, but at the expense of an additional IPT.

Fig. 2 shows a typical electrochemical 48.5 kA rectifier

arrangement with parallelled devices, snubbers and

water-cooled busbars. Generally, parallelled circuits

of

the types in Fig. l a or b are used for higher currents at

voltages up to 400V. For higher voltages of about

lo00 V and lesser currents the three-phase bridge is

popular, owing to its considerably lower transformer

rating in relation to the DC output.

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For continuously variable control of the DC output

voltage, the choice lies between using thyristors, or diodes

D

D E

load

a b

A

load

C

Fig. 1

n

Six-phase, halfwave

b

Double three-phase star with IPT needed due to the

60

hase difference of the

two three-phase circuit

c

Three-p hase full-wave bridge

Some six-pulse rectifier configurations

with flux-reset transductors in the AC-supply lines to the

rectifier. The availability of diodes with higher ratings

than thyristors eases problems of device parallelling, but

has the added expense of magnetic components.

Fig. 2

126

Electrochemical plant 48.5 kA rectrJier

In this paper, the operation of two parallel three-phase

thyristor bridges with a

30

phase offset is considered.

The size and cost of an IPT connected between them in

electrochemical plant is such that, on economic grounds,

it has occasionally been omitted. As stated above, the

resulting penalty

is

the interaction between the bridge cir-

cuits and the consequent circulating AC flowing between

them. The ability to predict the transformer winding and

AC supply current waveforms and establish their harmo-

nic content with reasonable accuracy is obvious, and this

has provided the incentive for this investigation.

2

Operating modes

2.1 Circuit representation

Fig. 3 shows a schematic diagram of the parallel bridges

supplied by two separate transformer output windings

I

=I. .

I

I

%Firnary

I

three-phase

SUWlY

turns

l

''71

B1tertiary

I

load

bridges n parallel

Fig.

3

Three w inding rectifier transformers

Schematic diagram

of

the 12-pulse system

(the secondary and tertiary) with equal open-circuit volt-

ages, and with the AC voltage in bridge 2 lagging that of

bridge 1 by 30 . The number of turns per phase on the

star-connected secondary windings is

1/J3

times that on

the tertiary. The primary winding has a delta connection.

The position of a conventional IPT is shown in broken

lines, although in this investigation it is omitted. The 12-

pulse DC output is applied to the load, which comprises

resistance, inductance and a back EMF, as is typical for

electrochemical cells.

There are two basic transformer arrangements which

may be used for supplying three-phase bridges in the

required manner. These use either

(a)

two separate three-phase transformers having the

same primary winding connection (delta) supplied in

parallel, each with a secondary (one in star and the other

in delta) connected to a bridge or

(b) a single three-phase three-winding transformer with

the star-connected secondary supplying one bridge and

the delta-connected tertiary the other, as depicted in Fig.

3.

The latter is more complicated to deal with analytically,

owing to the larger number of mutual inductances, and is

the arrangement adopted here.

The complete equivalent circuit used for analysis is

given in Fig.

4.

Each of the transformer windings is rep-

resented by a designated branch impedance Z comprising

a resistance and self-inductance. Also included are the

mutual inductances between the windings in each phase

and between the phases, e.g. L,, and L respectively.

Inductances are included for the IPT for completeness,

although these values are zero for the present investiga-

tion. A conducting thyristor is represented by an imped-

I E E P R O C E E D I N G S ,

V o l . 137,

P t . B , N o .

2,

M A R C H

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ance in series with a constant voltage source. A DC load. Higher operating modes occur during overload

nonconducting thyristor is assumed to have infinite and short-circuit

[2].

In this study, the simplest condition

impedance. The simple conventional three-winding trans- occurs for large thyristor firing-delay angles, when the

L13

L14j L25.L36

424

/

233 L23

1

L39. L17. L28

Fig.

4

z , , =

I ,

+

p L , ,

and similarly for each winding

Equivalent circuit showing impedances

former equivalent circuit is shown in Fig.

5[l].

Although

helpful in showing the important reactances for limiting

circulating currents, it was not considered sufficiently

comprehensive for the analysis adopted here. However, it

is used later to obtain approximate results for compari-

son.

If

the AC side inductances are assumed to be zero and

with no IPT, only the bridge which experiences the

highest instantaneous voltages in any 12-pulse ripple

period of 30 will conduct. Thus the normal conduction

interval of

120

for a thyristor in one bridge is broken up

by the conduction of thyristors in the other bridge. With

the AC-side inductances present, instantaneous transfer

of load current between the bridges (and between phases

within a bridge) is impossible, and commutation effects

occur in various degrees of complexity.

When defining the operating modes of single rectifier

circuits it is conventional to consider as Mode

1

the con-

dition where the load-current flow is continuous and the

commutation angles are small, i.e. less than a pulsewidth,

this being typical of normal operation with an inductive

l t e z

primary branch

secondary branch

Fig. 5

Conventional equivalent circuit of

a

three-winding transformer

(per phase)

I E E P R O C E E D I N G S , V o l . 137, P t . B, N o . 2, M A R C H 1990

load current is discontinuous and therefore no com-

mutations occur. This condition is adopted as Mode

1.

As the firing-delay angle is reduced, the load current

becomes continuous and both the operation and analysis

becomes increasingly complicated, with simultaneous

conduction of first the two bridges and then the rectifier

phases as the firing delay is reduced and current

increases. At each change

of

operation the mode number

rises.

The assumptions made for consideration of these oper-

ating modes are

(i) the AC supply voltages to the transformer are sinus-

oidal

(ii) the thyristor firing-delay angles are all equal

(iii) the transformer reactances presented to the two

bridges are equal.

Thus the bridges operate perfectly symmetrically and

with the required

30

phase displacement.

2.2 M o d e

1

: i scont inuous load current and

discont inuou s br idge currents

Fig. 6 shows the conduction patterns for the five oper-

ating modes considered here and covers 150 of the oper-

ating cycle. The numbers of the conducting thyristors are

defined in Fig.

7.

In Mode

1

the load, bridge and thyris-

tor currents flow in short pulses having a conduction

interval less than 30 . The bridges conduct alternately

into the load, there being one load-current loop present

at a time, say

i,

in Fig.

7.

Typical waveforms are shown in Fig. 8.The conduc-

tion interval is B

- a),

with the firing-delay angle

a

mea-

sured from the zero-voltage crossing of the appropriate

bridge-supply line voltage. This reference is more conve-

nient than the usual definition of

a = 0

when the incom-

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ing thyristor becomes forward biased, which is 75 later

in a 12-pulse system as shown in this Figure.

bridge 2 4 4 R f 6 Y ' $28:

d 30 60

90

120

150

0

5 I

I I

I I

v/3Y +4R/A/2B*3Y//1/1R+2B//1

V/lR

+ 2BA v2B'+3YYA

-I

2

1

2

Fig.6

Bridge 2 conduction lags bridge

1

conduction by 30

Interbridge commutations are shown

i /b

Interphase commutations are show n by i / p

Overlapping interphase commutations between bridges are shown by

i /pb

Interphase commutation overlap interference within each bridge is shown by

Conduction patterns or various operating modes

m2

2.3

M o d e 2: Cont inuous load c urrent , d iscont inuous

bridge currents and interbridge com mutation s

Mode 2 occurs when the thyristor firing delay is reduced

and the load current rises so that the conduction angle

increases to between 30 and 60 . The transition between

Modes 1 and 2 occurs at a critical firing-delay angle aCl.

w5B

R

Ed

In Mode 2 a thyristor in one bridge is turned on before

that in the alternate bridge has ceased to conduct. This

7 E O

-1-

12v

a

n

Fig.

8 Mo d e

I

waveforms

a = DC output voltage

b = load current

c = bridge

1

current

d = bridge

2

current

e = bridge 2 supply line current 1;

fl = angle of cessation current flow (measured from voltage zero)

initiates the transfer of current from one bridge to the

other, i.e. an interbridge commutation takes place, as

shown in Fig.

6.

Referring to the circuit of Fig.

9,

thyris-

tor 1R and 6Y, say, are conducting the falling current i

in the outgoing bridge and 1R' and

6 Y

carrying the

rising current i in the incoming bridge. The interbridge

commutation is completed when

i

falls to zero, after

which

i

flows alone until the next pair of thyristors in the

sequence (1R and 2B) are fired. A point to note is that

during a bridge 1-bridge 2 commutation, devices in the

same phases are coming into conduction, e.g 1R' and 6 Y

take over conduction for 1R and

6Y.

During a bridge

2-bridge 1 commutation the third phase is involved, e.g.

1R and 2B take over from

1R

and 6Y'. Hence the trans-

former current paths are different in the two com-

mutations.

Fig. 10shows typical waveforms. The continuous load

current is made up of two alternating parts

r~

Fig.

7

Secondary and tertiary windings shown

128

Typical current loop paths o r Mo de I

Fig.

9


Typical current loop paths o r mode 2

I E E P R O C E E D I N G S , Vol . 137, P t .

E,

N o .

2,

M A R C H 1990

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( a )

the sum of the two bridge currents, one rising, the

other falling, during the interbridge commutation interval

Y

-

a)

( b )

a single bridge current similar to Mode 1.

75

a

n

3Y+4R 4R+5B

C

I

e

- in bridge2

Fig.

10 M o d e

2

waveforms

a

= DC output voltage

b

=

load current

c = bridge 1 current

d = bridge 2 current

e =

bridge 2 supply line current 1;

y = angle at completion

of

interbridge commutation

2.4

M o d e 3: Cont inuous load current , cont inuou s

bridg e currents and separated interphase

com mutat ions a l ternate ly in each br idge

A reduction of the firing-delay angle to a second critical

value a,* , defined by the bridge conduction intervals

reaching

60 ,

results in the whole of each 30 output

voltage pulsewidth being taken up by an interbridge

commutation. Operation moves into Mode 3 when

a

is

less than

aC2

and the conduction intervals within each

bridge overlap. Fig.

6

shows the conduction pattern.

Referring to Fig. 11,the sequence of events is defined

as follows

:

(i) let an interbridge commutation occur with bridge 2

incoming and bridge 1 outgoing; loop currents

ib

and i,,

respectively, flow in the bridges

7 7

50

i

0

I

I

I

Fig.

11



Vol .

137, P t . B, N o . 2, M A R C H 1990

Typica l current loop paths fo r Mo de 3

(ii) before the interbridge commutation is completed,

the next thyristor is sequence 2B in the outgoing bridge is

fired and an interphase commutation commences,

6Y

current transferring to 2B with an additional loop

current

i,

flowing

(iii) on completion of the interphase commutation,

i,

has fallen to zero leaving an interbridge commutation

with the bridge roles reversed, i.e. the previous incoming

bridge now being the outgoing one and loop currents

i,

and

i,

remaining. The interphase commutation angle

< 30 .

Fig. 12 shows typical waveforms. Now the bridge cur-

rents are continuous, and the individual thyristors

75

a

n

b

C

0

I I

I

d

commutations

in bridge 2

-

Fig.12 M o d e 3 waveforms

a =

DC

output voltage

b

=

oad current

c = bridge 1 current

d

=

bridge 2 current

e

=

bridge 2 supply line current

ry

6 =

angle of completion

of

interphase commutation within a bridge

p

=

nterphase commutation angle

conduct for an angle of between 120 and

150 ,

as the

two pulses of Mode 2 have widened and merged. Since

commutations are taking place throughout the operating

cycle, the DC output voltage at no time follows the sinus-

oidal AC supply, but is at some intermediate value

between the appropriate phase voltages depending on the

commutation conditions.

2.5 M o d e

4:

Cont inuous load current , cont inuo us

br idge currents and in terphase commutat ions n

the br idges par t ly over lapping

With further reduction of firing delay and increased

current, the interphase commutation angles

p

in the

bridges increase to 30 at the third critical firing-delay

angle aC3.Operation then moves into Mode 4 f p

> 30,

with the individual bridge interphase commutations over-

lapping each other by an angle p

- 30) ,

as shown in

Fig.

6.

Again, a new loop current flows during this inter-

val, shown as id in Fig. 13. The stages of operation are as

follows:

(i) first, let an interphase commutation take place in

bridge 1 with current t ransferring from thyristor

6Y

to

2B;

i,

is rising and

i,

falling. Bridge 2 carries a single

current

ib

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(ii) before stage (i) is completed thyristor

2 B

in bridge

2 is fired, starting at

6Y'

to 2B' interphase commutation

with loop current

id

increasing and

i

decreasing

(iii) the interphase commutation is completed when i,

falls to zero, leaving the single current loop

i

in bridge

1

and the existing interphase commutat ion proceeding in

bridge

2.

R

L

Fig. 13

Secondary and tertiary windings

Typical current loop pathsfor M o d e

4

0

0

0

e

0

Fig.14 M o d e 4 w a v e f o r m

a =

DC output voltage

b = load current

c

= bridge

1

current

d = bridge

2

current

e

= bridge I supply line current

I

t

= angle

of

completion of coincidence of interphase com mutations between the

bridges

130

Typical waveforms are shown in Fig.

14.

The interphase

commutations overlap for an angle (I+

a) ,

and each

thyristor now conducts for an angle of between 150 and

180 .

An interesting feature is that the convetor can operate

with a thyristor firing-delay angle of less than 75

because the incoming thyristor becomes forward biased

earlier in the cycle than would occur with purely sinus-

oidal voltages applied to the bridges. The degree of such

firing 'advance' depends on the AC voltage distortion at

the bridge terminals and on the load current. This effect

was observed experimentally as results show later.

2.6 M o d e

5:

Cont inuous load current , cont inuous

br idge currents and comp lete over lapping of

br idge in terphase com mutat ions w i th o ver lap

interference in each b ridge

If the firing-delay angle is further reduced until the inter-

phase commutation in each bridge is

60,

both bridges

are permanently in a state of interphase commutation,

with three thyristors per bridge conducting. The critical

value

aC4

denotes the onset of Mode

5,

for which p is

greater than

60 .

In this mode, when the next (fourth) thyristor is gated,

this must necessarily be associated with the same phase

as that carrying the outgoing interphase commutation

current,

i,

in phase

Y

shown in Fig.

15.

As long as

i

flows in thyristor

6Y,

the newly gated thyristor

3Y

cannot conduct since its anode is negative with respect to

its cathode. A period of interphase overlap interference

follows until the outgoing thyristor

6Y

current

i,

falls to

zero. Then the incoming thyristor

3Y

commences to

conduct current i giving the start of a new interphase

Commutation. Hence all interphase commutations are

constrained to be

60

in Mode

5.

Such commutation

overlap interference is well known in single bridges [2].

Fig.

6

again gives the conduction pattern, with each thy-

ristor conducting for

180 .

For

typical values of AC-side inductances, interphase

commutations approaching

60

only occur under abnor-

mally high overload conditions and Mode 5 will not be

considered further.

Table 1 summarises the conduction conditions in the

various modes.

Fig.

15


Typical current

loop

paths

for

projected Mode 5

I E E P R O C E E D I N G S , Vol. 137, P t .

B,

N o . 2, M A R C H 1990

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Table 1 Showin g commutat ion angles and interact ion between br idges

~~

Mode Device Bridge Interphase Overlapping of Interphase commutation

conduction conduction commutation bridge interphase overlap interference

within a bridge, commutation within each bridge

angle p between bridges

1 2 x

0 -+

30 Independent -

2

2 ~ 3 0 + 6 0 - - -

B

- 0

pulses

Y

a

bridges

I

Ibridges

bridges

3 1 x

120

-+ 150 Continuous

0

-+

30

-

pulse overlapping

(p

=

6

U)

between

150 +180 Continuous 30 + 60 0 --+ 30

overlapping ( p )

( w -

a) =

(p

- 30 )

between

5

180 Continuous 60

-+ 90

30 0

-+

30

overlapping

(p)

Continuous

between

3

Outl ine of analysis

3.1 In t roduct ion

The analysis is based on Kron's tensor methods, modified

to assist in the handling of the device conduction patterns

[3],

and it incorporates all circuit elements without any

simplifying assumptions such as infinite DC-load induc-

tance. The description of the model is limited to an

outline of the technique, which is covered fully in Refer-

ence 4. The only assumptions made are those stated in

Section 2.1, which provide symmetrical operation of the

bridges. The equivalent circuit adopted is tha t of Fig.

4.

3.2 Method

The technique uses tensor analysis with the circuit mesh

currents defined as the system state variables. The con-

nection tensors, expressed in relation to the conducting

thyristors, are used to assemble the mesh state variable

equations.

The analysis involves an algorithm, which

(a) assembles automatically, for any thyristor conduc-

tion pattern, the closed-path or mesh (loop) equations in

state variable form

e15

_ -

e2

V21

e 2 1

2

I21

1%

--

Fig. 16 Primitive referenceframe

(b )

solves the equations using a numerical integration

method

(c)

determines the individual branch currents and volt-

ages from the mesh values.

Assembly of the mesh contour equations requires three

references frames

(i) the primitive

or

branch reference frame

(ii) the intermediate reference frame

(iii) the mesh reference frame.

3.3 Primitive reference frame

The primitive reference frame is concerned with individ-

ual branches of the network, as shown in Fig. 16. The

system-voltage equation in abbreviated matrix form is

v b Eb

=

Z b b I ,

(1)

The elements of the separate matrices for the transformer,

thyristors, IPT and load are given in Appendix 11.1,

(eqns.

9,

10 and 11). The main diagonal terms contain the

branch resistances and self-inductances defined in Fig.

4,

and the

off

diagonal terms contain mutual inductances. I t

should be noted that the laboratory transformers used in

this study were single-phase three-winding units and the


V o l . 137,

P t . B , N o . 2, M A R C H 1990

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mutual inductance terms in the I,,,

, L14 L7,

groups of

Fig. 4are zero.

-

0 1

0 0

0 0

1 0

-1

0

O 0

1

0

0 1

1 0

1 1

-

3.4 intermediate reference frame

Fig. 17 shows the branches of the primitive reference

frame connected together to form the circuit defined by

the intermediate reference frame. Applying Kirchhoff

s

current law to the nodes defines a current transformation

between the branch and intermediate reference frame cur-

rents reflected into the secondary and tertiary windings,

to give the relationship

b

= (2)

The complete form of

Cbi

s given in eqn. 12 in Appendix

11.1. The intermediate branch currents are related by

E, +

Vi

= ZiiZi

(3)

Assuming power invariance, the following relationships

apply:

(4)

b = cbIzI

vi

=

CLi

v

E, = cL,E,

ziI = CL zbb

noting that matrix CL, is the transpose of matrix C,,

.

[ I

b

tion in which thyristors l R ,

6Y, R

and

6Y

are conduct-

ing. Three mesh currents

i, i,

and ib are required, as

shown in Fig. 9.The intermediate reference frame cur-

rents (Fig. 17)

Z

are related to the mesh currents

Z

by

the transformation tensor

C,,

as follows:

The complete master conduction transformation tensor

C,,, of which the above forms part, is given in eqn. 13 in

Appendix 11.1. It contains the twelve meshes which

describe all practical thyristor conduction patterns, with

positive mesh current defined such that thyristor extinc-

tion is indicated when the current becomes negative.

T

T I

10

I10

11

=Id

6 14

122-110-112=114 v2

11

3.5

Mesh reference frame

The mesh reference frame is concerned with the meshes

formed when individual thyristors are conducting. Kron's

'equation of constraint' technique [ S ,

6 ,

71 is used used,

whereby the currents of nonconducting devices are set to

zero. A new transformation tensor is defined, which

relates the intermediate reference frame to the mesh refer-

ence frame currents and introduces the changes in circuit

topology produced by switching. This new matrix

C,,

is

a reduction of

c b , .

The number of mesh currents needed for a particular

topology [7] is

M = B - N + S 5 )

where

M

is the minimum number

of

independent meshes,

B is the number of branches, N is the number of nodes

and S is the number of electrically isolated subnetworks

S=

1 here). As an example, consider the Mode

2

condi-

132

The transformation tensor C,, is dynamic, since its

elements vary with thyristor switching, and is assembled

automatically by the computer program. The matrix

equation relating the mesh currents and voltages is

E , + v = z,,z,

(7)

From Kirchhoffs voltage law

V ,

=

0.

the mesh and intermediate reference frames

Similar relationships to those of eqn. 4 apply between

(8)

=

C i m

1,

v = c:, vi

E , = C:, E,

z,, = CILZrrC,,

The mesh equation is solved numerically using a 4th-

order Runge-Kutta routine.


Vol . 137,

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4 AC side-current waveforms

This section presents computed results which are com-

pared with experimental results to validate the program,

and to confirm the waveshapes of the operating modes

described in Section 2.

The circuit parameters used in the computer program

are given in Tables

4,

5 and 6 in Appendix 11.2, obtained

from measurements on the laboratory convertor. Reason-

able balance of the voltages and inductances of the three

single-phase transformer units was achieved and averages

values used as data. The conventional three-branch per

phase equivalent circuit (Fig. 5) data is included in Table

7.

The importance of the values of the secondary and ter-

tiary branch impedances will be referred to later.

Figs. 18, 19 and 20 show for Modes 2, 3 and

4,

respec-

tively, predicted and experimental waveforms for the

bridge-supply line (transformer secondary phase) and

transformer tertiary-phase currents. In addition, the

transformer primary side currents are included for Mode

3. The correlation is quite acceptable in view of the

experimental equipment limitations and confirms the

waveforms given in Figs. 10, 12 and 14. It is interesting to

note that the firing-delay angle for Mode

4

operation was

60 ,

which is less than the minimum

75

expected, due to

the bridge AC terminal-voltage distortion described in

Section 2.5.

Table 2 gives the predicted and the extremes of mea-

sured values for the first six characteristic harmonics in

the bridge 1 supply line-current waveforms for the four

operating modes. Again correlation is generally accept-

able, although there is considerable deviation in a few

cases. This is due to slight differences between the com-

puted and measured conduction periods of the thyristors

caused by inaccuracy in the measured parameters, phase

*

O

a

-5-

5 t

oo

b.kd

1.b?o-l.h

time,s

x10-2

a

-5-

-15 I

O-O.;o bo

100 1z 5 0 time,s

x10-2

a

5

-lo[

15

b

-

1

1

1

6

'able

2:

Computed bridge

1

supply l ine-current harmonics

ixpressed as p.u. of the fund amental w i t h th e t w o extreme

neasured values fr om the t hree phases shown in br ackets

irin g-delay Harmonic order

ingle a

5th 7th 11th 13th 17th 19th

65

node 1

50

node 2

20

Aode 3

io

Aode 4

0.860

(0.863)

(0.795)

0.640

(0.630)

(0.059)

0.290

(0.260)

(0.240)

0.085

(0.1 02)

(0.095)

0.735

(0.685)

(0.614)

0.380

(0.460)

(0.405)

0.030

(0.022)

(0.021

0.049

(0.050)

(0.046)

0.430

(0.508)

(0.455)

0.009

(0.080)

(0.081)

0.069

(0.056)

(0.060)

0.036

(0.020)

(0.023)

0.280

(0.355)

(0.318)

0.056

(0.031

(0.030)

0.040

(0.034)

(0.036)

0.030

(0.024)

(0.021)

0.046

(0.173)

(0.168)

0.01 9

(0.066)

(0.73)

0.039

(0.047)

(0.037)

0.006

(0.020)

(0.017)

0.031

(0.069)

(0.082)

0.01 4

(0.046)

(0.041

0.026

(0.023)

(0.025)

0.008

(0.017)

(0.016)

imbalance and imprecise adjustment of the firing-delay

angles.

The characteristic harmonics present in each six-pulse

bridge-supply current waveform (5th, 7th, 17th, 19th etc.)

are absent in the transformer supply current for the

'perfect' 12-pulse convertor system with commutation

angle neglected. Here the computed characteristic and

uncharacteristic harmonics for the supply line current are

shown in Fig. 21a and

b

with perfect phase voltage,

impedance and firing balance assumed. The experimental

transformer impedances are slightly unbalanced, resulting

in the presence of additional uncharacteristic harmonic

levels which are, however, too low to be distinguishable.

5

System operating ch aracteristics

Various system operating characteristics are shown in

Figs. 22 to 26. The DC output-voltage regulation charac-

Fig. 18

Frequency

= 50 Hz

Computed and observed waveforms od e 2

a Bridge supply line current

a = 150

I = 0.75 A

R = 5 . 1 n

I =

0.75

A

L = 0.0174H

I

= 1.5

A

E,

=

24 V

V,

= 32.4

V

IEE PROCEEDINGS, Vol.

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P t . E ,

No. 2,

M A R C H

1990

b Tertiary w inding current

Oscillogram scale

Horizontal ms/div

Vertical A/div

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teristic with increasing load current (Fig.

22)

is obtained

by reducing the load resistance for three set values of

firing delay, to give operation in Modes

2 ,

3 and 4.The

knee in the lower characteristic may be attributed to the

load conduction becoming continuous and interbridge

commutation effects commencing. The voltage drops are

mainly due to commutation and amount to 20% or less

for the two higher modes.

The increase in thyristor conduction interval with

reduction of the firing-delay angle for a set load imped-

15-

10

5-

-10

-15-

15

tirne,s

i=

-5 x10-2

-

-;Lx-hm+l~o.2

irne,s

-

-lot1

5

tirne,s

x10-2

-lo[

15

b

C

time,s

2 -5

-101

-1 5L

Fig.

19

Frequency = 50 Hz

Computed and observed waveforms ode 3

a

Bridge supply line current

a

=

120

R = 5.1 R

L = 0.0174 H

E ,

= 24 V

I = 4.78 A

I

= 5.46 A

I

= 10.24 A

V,

=

76.8 V

b Tertiary winding current

c Supply line current

d Primary phase current

Oscillogram scale:

Horizontal ms/div

Vertical A/div

134

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ance is evident in Fig. 23, as is the sharp jump from 60

to

120

at the Mode 2-Mode 3 change when the two 60

current pulses/cyc le merge.

-

0 .6 -

2

0 4 -

u

U

E

5

c

time,s

U

-10

L.

10-2

-201

-30L

t ime,s

J -10 x10-2

- O I

30

Fig. 20

Frequency = 50 Hz

Computed and observed waveforms

~

Mode 4

a Bridge supply line current

a = W I = 12.17 A

R

=

5.1 R I = 12.25 A

L = 0.0174 H

I

= 24.42 A

V, = 150.1 V

= 24 V

The increase of interbridge commutation angle from

zero 30

is shown in Fig. 24, and the bridge interphase

b

60 80 100 120 140 160 180

firing delay angle, degree

a

b

Tertiary winding current

Oscillogram scale:

Horizontal

~

2 ms/div

Vertical

~

10 Aidiv

Fig.

21

a

Characteristic a 1 lth component b A 5th component

b Uncharacteristic x 13th component x 7th component

Computed AC-supply line-current harmonics

17th component

firing delay angle,

degrees

b

Load data:

R = 5.1 R

L

=

0.0174

H

E , = O V

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commutation angles within the bridges and the overlap-

ping of these between the bridges are given in Figs. 25

and 26, respectively. The critical firing-delay angles at

which mode changes occur are well defined by these

characteristics. A load EM F of 0 V was chosen for these

simulations, to allow the highest safe load current of 30A

to flow.

It is evident that differences exist in the computed

values of thyristor conduction and commutation angles

for the two bridges, which is surprising since balanced

(averaged) voltage and impedance values were used as

data. The differences are due to the fact that, for a per-

fectly symmetrical transformer, the resistance and self-

inductance values of the delta output winding should be

three times those of the star output winding and,

assuming the same coupling coefficient, the mutual

inductances between primary and delta output winding

should be

,/3

times those between the primary and the

star output winding. The adjustment of the experimental

transformer inductance and resistance balance to these

relationships was not perfect, with the deviation of the

resistance values being greatest, as can be seen by com-

paring the relative values in Table 5 (Appendix

11.2).

Computed results with suitably adjusted resistances

values show identical operation for the two bridges.

160-

140

v1

;

20-

ul

U

-

9

100-

t

.e

8 0 -

-

C

U

D

.-

-

60-

4

20-

6

With an interphase transformer present between the

bridges on the

DC

side, they operate without interaction

or specifically with very little circulating current between

them, depending on the value of the IPT inductance and

the firing-delay angle

a.

The circulating current is highest

Comparison wi th parallel bridges having an

IPT

-

-

140

>

*

3

a

3 100-

80

60-

4

0

10

20 30

40

0

load current, A

Fig.

22 Load characteristic

A computed a = 60 Load data:

x

experimental a = 60 L = 0.0174

H

computed a = 75 E , = O V

experimental

a = 75

R

=

variable

A computed a

=

120

experimental a

=

120

136

at larger firing-delay angles. Industrial installations nor-

mally operate in Mode

3

without an IPT, so the condi-

mode

1

two

pulsesof current

?-

9 0

$0 i o

lb 1o

i o + l k O lb

firing delay angle degrees

Fig.

23

A bridge

1

Load data:

x

bridge 2 ]computed R = 5.1 R

L

=

0.0174 H

bridge

1

-experimental

E , = O V

Thy risto r conduction interval characteristic

Ln

U

-

2

C

C

.-

._

c

c

i

E

8

firing del ay angle, degrees

Fig.

24

Interbridge commutation characteristic ode 2

Load data:

: Lzgi ] omputed

bridge 1 -experimental L = 0.0174 H

R = 5.1 R

E , = O V

delay

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tions shown in Fig. 19with

U =

120 will be adopted for

consideration with an IPT present, each half winding of

p

ritical firing angle uc3

firing delay angle, degrees

Interphase commutation characteristic ode 3

ig.

25

: ]

omputed

bridge

1

-

xperimental

L = 0.0174

H

Load data:

R

=

5.1

R

E , = O V

;a

critical firing delay

75 80

firing delay angle, degrees

Fig. 20

Overlapping interphase commutation characteristic - o d e

4

Load data:

: iz

]computed

R = 5 . 1 R

bridge 1 -experimental L = 0.0174

H

E , = O V

I E E P R O C E E D I N G S , Vol .

137,

P t . B , N o .

2,

M A R C H

1990

which will be assumed to have a self-inductance of

200 mH.

Fig. 27 shows the waveform of the bridge supply

current calculated by conventional methods with the rec-

tifier transformer commutating inductances obtained

from the averaged values quoted in Table 7. The com-

mutation angle is

5.9 .

The relatively small components

of the load-current ripple 0.24 A peak) and circulating

current

(0.13

A peak) are not shown.

Fig.

27 Calculated bridge supply current waveform with IPT present

Typical values of the first six harmonic components of

this waveform are given in Table

3.

Table 3: Predicted bridge-supply l ine-current harmonics as

a fraction of t he fundamental wit h IPT present

Firing delay- Harmonic order

angle a

5th 7th 11th 13th 17th 19th

120

0.198 0.141 0.086 0.071 0.050 0.045

It is evident from comparing these harmonic levels with

those of Table

2

for

U =

120

that omission of the IPT

results in considerably reduced values for all orders

except the 5th, which increases by about

50%.

Compari-

son of the waveforms (Figs.

19a

and 27) clearly demon-

strates the heavy circulating-current component with no

IPT, resulting in this substantially higher 5th harmonic.

7 Implications for transformer design

It is evident that, from the current-harmonic viewpoint,

omission of the IP T is beneficial except for the 5th har-

monic. With greater firing-delay angles, this can be

increased by more than the

50

demonstrated here, 75%

being observed with transformers having low-leakage

reactance.

The 5th and 7th harmonic components flowing in the

star and delta output windings of the transformer are in

antiphase, and

so

therefore are the associated flux com-

ponents. These are at

90 to

the preferred direction

of

the

main fundamental leakage flux relative to the winding

conductors. The much lower 7th harmonic component

gives no difficulty, but the increased 5th harmonic flux

can cause severe localised eddy-current heating in the

windings.

The transformer design must therefore be adapted, if

the IPT is omitted,

so

that the circulating current, and

thus the 5th harmonic winding current components, are

10%

a b

Fig.

28

three-winding equivalent circuit

B WithIPT

b Without IPT

Typ ical percentage reactance values for the conventional

137

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restricted. This takes the form of reconfiguring the wind-

ings to give relatively high leakage between the two

output windings on each phase. The change in leakage

flux distribution is well illustrated by the different reac-

tance values in the conventional three-winding equivalent

circuit. Fig.

28

illustrates percentage reactances which are

typical for an industrial transformer supplying parallel

bridge rectifiers. For

a,

each transformer phase may have

a single primary winding and multiple flat coils in alter-

nate layered sandwich form for the two output windings

to give low leakage between the latter. For

b ,

a primary

winding in two parallel-connected halves may be used,

with separate single output windings positioned end to

end for increased flux leakage between them.

8 Conclusions

Four operating modes for two 6-pulse bridge rectifiers

connected in parallel, without a DC side interbridge

reactor (IPT), have been described and analysed. A fifth

mode is postulated. The interbridge and interphase com-

mutation effects are defined, and the AC side current

waveforms and rectifier characteristics are predicted, by

the mathematical model, and verified experimentally

using a laboratory converter. Good correlation is evident

between computed and measured results, thereby con-

firming the analysis and computer program. Small dis-

crepancies are explained by imperfections in the balance

and symmetry of the laboratory equipment. Large-scale

industrial plant is expected to be much better in this

respect.

A rigorous modelling technique using tensors has been

adopted, which has the following features

:

( a )

all circuit impedance components are included and

have finite values

( b )

he DC load has all the typical elements of electro-

chemical plant ; resistance, inductance and back EM F

(c)

the analysis has been developed from first prin-

ciples

:

no separately derived equivalent circuit is used

(d)

the mathematical model includes all mutual induc-

tance terms, including those for a three-phase trans-

former and an IPT, and is therefore complete, although

three single-phase transformers and no IPT were used

here

(e )

perfect balance between the three phases and sym-

metrical firing of the thyristors are assumed.

The requirement for transformer da ta which include self-

and mutual-inductance values and not p.u. or percentage

winding leakage reactances is unconventional in terms of

industrial practice, where the three-branch equivalent

circuit per phase is more usual. The latter, however, is

not sufficiently comprehensive, since it neglects the inter-

phase coupling of a three-phase transformer unit.

The bridge-supply current waveform for typical oper-

ating conditions is predicted by conventional methods for

the case with an IPT included to compare the waveform

harmonic contents.

It is demonstrated that the absence of an IPT need not

be a handicap to the successful operation of two parallel

bridge rectifiers. However, it is necessary to modify the

rectifier transformer design to provide high-leakage reac-

tance between the two output windings to limit the inter-

bridge circulating current and hence the troublesome 5th

harmonic fluxes in the transformer. In simple terms, it

can be said that these high-leakage reactances act like an

IPT in this respect.

0

0

r +PL33

0

0 r4 +p L 4 4

0 0

0

PL47

0 0

PL36 0

PL39 0

9 Acknowledgments

Acknowledgments are made to the Department of Elec-

tronic and Electrical Engineering and the Computer

Centre of Loughborough University of Technology for

the provision of facilities, and to GEC TDPL, Stafford,

and Mr G. E. Snazell in particular for financial support,

helpful discussions and permission to reproduce Fig.

2.

10 References

1 LANGLOIS-BERTHELOT, R.

:

Transformers and generators for

power systems (Macdonald, London, 1960)

2 RAMAMOORTY, M.: An introduction to thyristors and their

applications (Macmillan Press Ltd., London, 1978)

3 KETTLE BOROUG H, J.G., SMITH, I.R., and FANTHO ME, B .A.:

Simulation of a transformer/rectifier unit for aircraft power supply

systems,

IEE P roc . B,

1982,

129,

(6), pp. 323-329

4 RAZAK, A.B.M.J.: Parallel operation of bridge rectifiers without an

interbridge reactor. MSc T hesis, Loughborough University of Tech-

nology, 1985

5

KRON, G .: Tensors

for

circuits (Dove r, 1959)

6 WILLIAMS,

S.,

and S MIT H, I.R .: SCR bridge converter computa-

tion using tensor methods, IEEE

Trans.,

1976, C-25 pp. 1-6

7 HAP P, H .H.: Diakoptics and networks (Academic Press, 1971)

11 Appendix

1 1 . 1

Matrices develop ed in the analysis

(a ) Primitive reference fram e:

the following are the

primitive reference frame matrices containing the branch

equations for the network components of the transformer

(eqn.

9),

thyristor branches (eqn.

10)

and IPT (if present)

with load (eqn. 11)

b)

Transformation matrix

C,,

for primitive to interme-

diate reference frame:

this matrix (eqn. 12) is used in eqn.

4

for transforming the primitive branch matrices into the

complete network (intermediate) frame

( c ) Intermediate branch to mesh transformation matrix

C,,,,:This matrix is used in eqn.

8

to transform the

network frame into the final mesh frame for solution and

it incorporates the sequential switching of the thyristors

0 0

PL17 0

0

0

0

0

0

PL36

r6 PL66

PL69

0

0

0

0

0

0

PL47

r7 +PL77

138

(9)

I E E P R O C E E D I N G S , Vol. 137,Pt. B, No .

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r10 10

+PLlO 10

_ _

r20

20

+PLZO 20

r 2 1 2 1

PL2121 - -

r 1 2

12

+

PL12 12

...

'10 -

'1 1

I 2

'1 3

4

115

'1 6

1

7

'1

8

'1

9

1 20

1 2 1

-

...

..

..

...

...

...

r 2 2

22

+ P L 2 2 22 PL 2 2 2 3 0

P L 2 2

23 r23 23 + PL23 23 0

0 0

4

5

6 7

8

10 12 16 18 22 23 24

1

- -

0 0

- -

7 0 0

0 0 0 0 0 0

Nl

l

2

0 --

0

0 - -7 0 0 0 0 0 0 0

Nl

l

3

0 0 - - 3

3

0 0

0 0 0 0 0

NI NI

Nl

4

1 0

0

0

0

0 0

0

0 0 0 0

5 0

1

0 0

0

0

0

0

0 0 0 0

6 0

0 1

0

0

0

0

0 0 0 0 0

7

0

0 0 1

0

0

0 0 0 0 0 0

8 0

0 0

0

1 0

0

0

0 0 0 0

9

0

0 0

-1

-1 0

0 0

0 0 0 0

10

0

0

0 0 0

1 0

0 0 0 0 0

c,,= 11

-1 0

1 0 0

1 0

0 0 0 0 0

12

0 0

0 0 0 0

1 0

0 0 0 0

13

1 -1

0 0 0 0

1 0

0 0 0 0

14

0

0

0

0

0 - 1 - 1

0

0 1 0 0

15

0

1

-1 0

0 - 1 - 1

0

0 1 0 0

16

0

0

0

0 0 0 0

1 0 0 0 0

17

0 0

0 -1

0

0 0

1 0 0 0 0

18

0 0

0 0 0 0 0 0

1 0 0 0

19

0

0 0

0 -1 0 0 0

1 0 0

20

0

0 0

0 0 0

0 - 1 - 1 0 1 0

21

0

0 0

1

1 0 0 - 1 - 1 0 1 0

22

0

0 0

0 0 0 0 0

0 1 0 0

23 0

0 0

0

0 0 0 0 0 0 1 0

24

0

0 0

0

0 0 0 0

0 0 0 1


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Conduction path

10 10 12 12

14

14 16 16 18 18

20

20

thyristors

13 15 15 11 11 13 19 21 21 17 17 19

loop +

a b

c d

e

f g h i j k

Branch

number

4 1 0 0 - 1 0 0

0 0 0

0 0 0

5 0 0 1 0 0 - 1 0 0 0 0 0 0

6 0 - 1 0 0 1

0 0 0 0

0 0 0

7

0 0 0 0 0 0

1 1 0 - 1 - 1

0

8 0

0 0

0 0

0 - 1 0 1 1 0 - 1

c,,

=

10 1 1 0 0 0

0

0 0 0 0 0 0

12

0

0 1 1 0 0 0 0 0 0 0 0

16 0 0 0

0 0 . 0

1 1 0 0 0

0

18

0 0 0

0 0 0

0 0 1 1 0

0

22 1 1 1

1 1 1 0 0 0

0

0 0

23

0

0 0

0 0 0

1 1 1 1 1 1

24 1 1 1

1 1 1 1 1 1 1 1 1

Note: Other branches

are

omitted

here

as their effect

i s

included

in

the electrical connections transformation matrix.

(13)

1 1.2Experimental equipment data

(a) Transformer: Measured values of transformer

open-circuit voltages, turns ratios, resistances and induc-

tances, together with other circuit data are as below

Table 4: Measured transformer open-circuit voltages and

turns ratios

Primary winding (delta) line voltages

Secondary winding (star) line voltages

50 H z

R -Y

Y - B

Average

R -Y

B -R

Average

B R

Tertiary winding (delta) line voltages

Y - B

Turns ratios

NJN

Turns ratios

N , / N ,

240.0

V

129.5

V

129.8

V

129.0

V

129.4 V

129.0 V

129.8

V

129.5 V

129.4 V

0.539

0.31

1

Table 5 : Average measured transfor mer d ata used (Fig. 4)

Resistances, Q Self-inductances, H Mutual inductances, H

r ,

=r,=r ,=0.708 L,, L2,=L3,= 1.66 L,,= L,,=L,,=0.901

r 4 = r 5

= r ,

=0.289 L,,= L,,

=

L,, =0.5 06 L,,=L,,=L,, =0 .523

r 7 = r , = r 9

=0.307

L,,

=

L,,

=

L,, =0.279

,,= L,,

=

L,, =0.170

Table 6 : Measured thyristor branch and load data used (Fig.

4)

Thyristor model Load

No

IPT

e thv =

E

=

24.0 V

or

0 V

Z,,,, =

0

L?hv

=

L

=

0.01 74 H Z,,,,

=

0

R,,, =

0.1

Q

R

=

5.1

Zn,,

=

0

Table

7:

Measured transformer equivalent circuit param-

eters referred to the rectif ier side (Fig.

5)

Branch Transformer

A

Transformer B Transformer C

parameters

r , ,

-0.266

-0.207 -0.237

L,,

mH -3.075

-3.024 -3.1 77

r,,

Q

1.096

0.962 0.895

L,,

mH 8.321

8.270 8.203

r,,

0.994

0.895 0.949

L,,

mH

8.407

8.270 8.270

Erratum

AL ZAHAWI, B.A.T.,

JONES,

B.L., and DRURY,

W . :

Analysis and simulation of static Kramer drive under

steady-state conditions,

ZEE Proc. B,

1989, 136,

(6),

pp.

In this paper, the following correction should be made to

the text:

On page 285, eqn. 23 should read:

T = p{i,[-LL,i,

-

? M ( i , c ) / 2 ]

+

i , [ L , i ,

+

M i ,

-

M ( i ,

+

i c ) / 2 ] }

The results and conclusions of the paper are in no way

affected by this correction.

28 1-29 1

140

I E E P R O C E E D I N G S , Vol .

137,

P t . B , N o . 2, M A R C H 199

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