Chapter 11 semi controlled bridge converters

434

11.1. INTRODUCTION

A brief analysis of single- and three-phase semi-controlled bridge converters is pre￾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 f1 through e f4 . 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

SINGLE-PHASE LOAD COMMUTATED CONVERTER 435

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

e E ga g = 2 cosθ (11.2-1)

where

θω φ ggg = +t (11.2-2)

In (11.2-2) , ωg and ϕg 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

V vd d dg =

−

∫ 1

2π

θ

π

π

(11.2-3)

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 ≤ θg ≤ π /2