Chapter 11 semi controlled bridge converters

Analysis of Electric Machinery and Drive Systems Editor(s): Paul Krause, Oleg Wasynczuk, Scott Sudhoff, Steven Pekarek

11.1 INTRODUCTION

A brief analysis of single- and three-phase semi-controlled bridge converters is sented in this chapter This type of converter is also commonly referred to as a line-commutated converter The objective is to provide a basic background in converter operation without becoming overly involved For this reason, only the constant-current operation is considered A more detailed analysis of these and other converters can be found in References 1–4 Finally, to set the stage for the analysis of dc and ac drive systems in later chapters, an average-value model of the three-phase semi-controlled bridge converter is derived This model can be used to predict the average-value per-formance during steady-state and transient operating conditions

11.2 SINGLE-PHASE LOAD COMMUTATED CONVERTER

A single-phase line-commutated full-bridge converter is shown in Figure 11.2-1 The

ac source voltage and current are denoted e ga and i ga , respectively The series inductance (commutating inductance) is denoted l c The thyristors are numbered T 1 through T 4, and the associated gating or fi ring signals are denoted e f 1 through e f 4 The converter

output voltage and current are v d and i d The following simplifying assumptions are

Analysis of Electric Machinery and Drive Systems, Third Edition Paul Krause, Oleg Wasynczuk,

Scott Sudhoff, and Steven Pekarek.

© 2013 Institute of Electrical and Electronics Engineers, Inc Published 2013 by John Wiley & Sons, Inc.

SEMI-CONTROLLED BRIDGE CONVERTERS

11

Figure 11.2-1 Single-phase full-bridge converter

made in this analysis: (1) the ac source contains only one frequency, (2) the output

current i d is constant, (3) the thyristor is an infi nite impedance device when in the

reverse bias mode (cathode positive) or when the gating signal to allow current fl ow has not occurred, and (4) when conducting, the voltage drop across the thyristor is negligibly small

Operation without Commutating Inductance or Firing Delay

It is convenient to analyze converter operation in steps starting with the simplest case where the commutating inductance is not present and there is no fi ring delay In this case, it can be assumed that the gating signals are always present, whereupon the thyris-tors will conduct whenever they become forward biased (anode positive) just as if they

were diodes Converter operation for constant i d with l c = 0 and without fi ring delay is

depicted in Figure 11.2-2 The thyristor in the upper part of the converter ( T1 or T3 ) that

conducts is the one with the greatest anode voltage Similarly, the thyristor that conducts

in the lower part of the converter ( T 2 or T 4) is the one whose cathode voltage is the

most negative In this case, the converter operates as a full-wave rectifi er

Let us begin our analysis assuming that the source voltage may be described by

where

In (11.2-2) , ω g and ϕ g are the radian frequency and phase of the source, respectively

We wish to compute the steady-state average-value of v d , which is defi ned as

It is noted that the output voltage is made up of two identical π intervals per cycle of

the source voltage For the interval − π /2 ≤ θ ≤ π /2

v d =e ga (11.2-4) Using symmetry and (11.2-1)–(11.2-4) , the average output voltage may be determined

by fi nding the average of (11.2-3) over the interval − π /2 ≤ θ g ≤ π /2 Thus, the value of v d may be expressed

2

212

Figure 11.2-2 Single-phase, full-bridge converter operation for constant output current

without l c and fi ring delay

Operation with Commutating Inductance and

without Firing Delay

When l c is zero, the process of “current switching” from one thyristor to the other in either the upper or lower part of the converter ( T 1 to T 3 to T 1 to , etc., and T 2 to

T 4 to T 2 to , etc.) takes place instantaneously Instantaneous commutation cannot

occur in practice since there is always some inductance between the source and the converter The operation of the converter with commutating inductance and without

fi ring delay is shown in Figure 11.2-3 During commutation, the source is

short-circuited simultaneously through T 1 and T 3 and through T 2 and T 4 Hence, if we consider the commutation from T 1 to T 3 and T 2 to T 4 and if we assume that the short- circuit current during commutation is positive through T 3, then

Figure 11.2-3 Single-phase, full-bridge converter operation for constant output current

with l and without fi ring delay

where i 3 is the current in thyristor T3 Substituting (11.2-1) into (11.2-6) and solving

3

122

where γ is the commutation angle (Fig 11.2-3 ) The uppercase ( I d ) is used to denote

constant or steady-state quantities During commutation, the converter output voltage

v d is zero Once commutation is completed, the short-circuit paths are broken, and the output voltage jumps to the value of the source voltage since i d , and hence i ga , are assumed constant after commutation Since i ga is constant, zero voltage is dropped across the inductance l c It is recalled that V d 0 given by (11.2-5) is the average converter

output voltage when l c is zero When l c is considered, the output voltage is zero during

commutation Hence, the average output voltage decreases due to commutation The average converter output voltage may be determined by

If (11.2-10) is solved for cos γ and the result substituted into (11.2-11) , the average

converter output voltage with commutating inductance but without fi ring delay becomes

V d V d l I

g c d

ω

It is interesting to note that commutation appears as a voltage drop as if the converter

had an internal resistance of ω g l c / π However, this is not a resistance in the sense that

it does not dissipate energy

Operation without Commutating Inductance and

with Firing Delay

Thus far, we have considered the thyristor as a diode and hence have only considered rectifi er operation of the converter However, the thyristor will conduct only if the anode voltage is positive and it has received a gating signal Hence, the conduction of a thy-ristor may be delayed after the anode has become positive by delaying the gating signal (fi ring signal) Converter operation with fi ring delay but without commutating induc-tance is shown in Figure 11.2-4

We can determine the average output by

E V

/ /

where α is the fi ring delay angle (Fig 11.2-4 ) If the current is maintained constant,

the average output voltage will become negative for α greater than π /2 This is referred

to as inverter operation, wherein average power is being transferred from the dc part

of the circuit to the ac part of the circuit

Operation with Commutating Inductance and Firing Delay

Converter operation with both commutating inductance and fi ring delay is shown

in Figure 11.2-5 The calculation of i 3 and V d are identical to that given by (11.2-6)– (11.2-12) , except that the intervals of evaluation are different In particular, (11.2-7)

applies, but it is at θ g = π /2 + α , where i 3 = 0, thus

Figure 11.2-4 Single-phase, full-bridge converter operation for constant output current

without l c and with fi ring delay

Solving (11.2-15) for cos ( α + γ ) and substituting the results into (11.2-16) yields the

following expression for the average output voltage with commutating inductance and

fi ring delay

Figure 11.2-5 Single-phase, full-bridge converter operation for constant output current

with l c and fi ring delay

g c d

= 0cosα−ω

The equivalent circuit suggested by (11.2-17) is shown in Figure 11.2-6

The average-value relations and corresponding equivalent circuit depicted in Figure 11.2-6 were developed based upon the assumptions that (1) the rms amplitude

of the ac source voltage, E , is constant, and (2) the dc load current i d is constant and hence denoted I This equivalent circuit provides a reasonable approximation of the

average dc voltage even if E and i d vary with respect to time provided that the

varia-tions from one conduction interval to the next are small

Modes of Operation

Various modes of operation of a single-phase, full-bridge converter are illustrated by simulation results in Figure 11.2-7 , Figure 11.2-8 , and Figure 11.2-9 The source voltage

is 280 V (rms) and the commutating inductance in 1.4 mH In each case, e ga , i ga , i 1 , i 3 ,

v d , and i d are plotted, where i 1 and i 3 are the currents through thyristors T 1 and T 3,

respectively In Figure 11.2-7 , the converter is operating with a series RL load

con-nected across the output terminals, where R = 3 Ω and L = 40 mH In Figure 11.2-7 a,

Figure 11.2-8 Single-phase, full-bridge converter operation with RL and an opposing dc

source connected in series across the converter terminals (a) α = 0°; (b) α = 60°

Figure 11.2-9 Single-phase, full-bridge converter operation with RL and an aiding dc source

connected in series across the converter terminals (a) α = 108°; (b) α = 126°

the converter is operating without fi ring delay In Figure 11.2-7 b, the fi ring delay angle

is 45° In Figure 11.2-7 c, the fi ring delay is slightly less than 90°; the current i d is

discontinuous The output current is nearly constant when the converter is operating without fi ring delay due to the large-load inductance

In the case shown in Figure 11.2-8 , the combination of a series RL ( R = 3 Ω ,

L = 40 mH) connected in series with a constant 200-V source is connected across the output terminals of the converter The dc source is connected so that it opposes a posi-

tive v d In Figure 11.2-8 a, the converter is operating without fi ring delay, while in Figure 11.2-8 b, the fi ring delay angle is 60° During the zero-current portion of operation, v d

is equal to 200 V, the magnitude of the series-connected dc source

Inverter operation is depicted in Figure 11.2-9 In this case, the combination of the

RL load and dc source is still connected across the output terminals of the converter, but the polarity of the dc source is reversed In Figure 11.2-9 a, the fi ring delay angle

is 108° In Figure 11.2-9 b, the fi ring delay angle is 126°

Although (11.2-17) was derived for a constant output current, it is quite accurate for determining the average values of converter voltage and current, especially if the current is not discontinuous The reader should take the time to compare the calculated converter output voltage and current using (11.2-17) with the average-values shown

in Figure 11.2-7 , Figure 11.2-8 , and Figure 11.2-9 , and to qualitatively justify any ferences that may occur

11.3 THREE-PHASE LOAD COMMUTATED CONVERTER

A three-phase, line-commutated, full-bridge converter is shown in Figure 11.3-1 The

voltages of the three-phase, ac source are denoted e ga , e gb , and e gc , and the phase rents i ag , i bg , and i cg The ac source voltages may be expressed as

T 1 through T 6 in the order in which they are turned on and the gating or fi ring signals for the thyristors are e f 1 through e f 6 The converter output voltage and current are

denoted v d and i d , respectively This circuit also includes a dc inductor and resistor, L dc and r dc , that may represent the armature inductance and resistance of a dc machine or the inductance and resistance of a fi ltering circuit Likewise, the voltage e d may repre-

sent the back emf of a dc machine or the capacitor voltage in a dc fi lter

Modes of Operation

Before analyzing the converter, it is instructive to consider several modes of operation

of a three-phase, full-bridge converter illustrated in Figure 11.3-2 , Figure 11.3-3 , and Figure 11.3-4 by simulation results The line-to-line ac source voltage is 208 V (rms)

and the commutating inductance is 45 μ H In each case, e ga , i ga = − i ag , i 1 , i 3 , v d , and i d are plotted where the currents i 1 and i 3 are the currents through thyristors T 1 and T 3,

respectively

In Figure 11.3-2 , the converter is operating with r dc = 0.5 Ω , L dc = 1.33 mH, and

e = 0 In Figure 11.3-2 a, the converter is operating without fi ring delay It is interesting

Figure 11.3-1 Three-phase full-bridge converter

+ -

+ -

Figure 11.3-2 Three-phase, full-bridge converter operation with RL load (a) α = 0°; (b) α = 45°; (c) α = 90°

to note that the output current is nearly constant In this study, there are alternately two

or three thyristors conducting; hence, this will be referred to as 2-3 mode, which is the normal mode of operation The fi ring delay angle is 45° in Figure 11.3-1 b (again 2-3

mode) and 90° in Figure 11.3-1 c where the output current i d is discontinuous Note, when i d is zero, v d is also zero In this case, there are alternately 2 and 0 thyristors

conducting; hence, this will be referred to as 2-0 mode

In the case depicted in Figure 11.3-3 , the combination of a r dc = 50 m Ω and

L dc = 133 μ H is connected in series with a e d = 260 V dc source is connected across the output terminals of the converter In Figure 11.3-2 a (2-3 mode), the converter is

Figure 11.3-3 Three-phase, full-bridge converter operation with RL and an opposing dc

source connected in series across the converter terminals (a) α = 0°; (b) α = 35°

operating without fi ring delay In Figure 11.3-2 b, the fi ring delay angle is 35°, and the

output current is discontinuous (2-0 Mode) Note that when i d is zero, v d is 260 V

Inverter operation is illustrated in Figure 11.3-4 In this case, r dc = 50 m Ω ,

L dc = 133 μ H, and e d = − 260 V In Figure 11.3-4 a, the fi ring delay angle is 140° (2-3 mode) The fi ring delay angle in Figure 11.3-4 b is 160° where discontinuous output

current occurs (2-0 mode) Clearly, when i d is zero, v d is − 260 V

Note that while these studies depict 2-3 and 2-0 modes, other modes exist In 3-3 mode, which we will consider later, there are always three thyristors conducting In 3-4 mode, which occurs under heavy rectifi er loads, there are alternately three and four thyristors conducting In this case, the dc link becomes periodically shorted as in the single-phase case

Figure 11.3-4 Three-phase, full-bridge converter operation with RL and an aiding dc source

connected in series across the converter terminals (a) α = 140°; (b) α = 160°