Chapter 12 fully controlled three phase bridge converters

460

12.1. INTRODUCTION

In our study of induction, synchronous, and permanent-magnet ac machines, we set

forth control strategies that assumed the machine was driven by a three-phase, variable￾frequency voltage or current source without mention of how such a source is actually

obtained, or what its characteristics might be. In this chapter, the operation of a three￾phase fully controlled bridge converter is set forth. It is shown that by suitable control,

this device can be used to achieve either a three-phase controllable voltage source

or a three-phase controllable current source, as was assumed to exist in previous

chapters.

12.2. THE THREE-PHASE BRIDGE CONVERTER

The converter topology that serves as the basis for many three-phase variable speed

drive systems is shown in Figure 12.2-1 . This type of converter is comprised of six

controllable switches labeled T1–T6. Physically, bipolar junction transistor s ( BJT s),

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.

FULLY CONTROLLED THREE￾PHASE BRIDGE CONVERTERS

12

THE THREE-PHASE BRIDGE CONVERTER 461

metal–oxide–semiconductor fi eld-effect transistor s ( MOSFET s), insulated-gate bipolar

junction transistor s ( IGBT s), and MOS controlled thyristor s ( MCT s) are just a few of

the devices that can be used as switches. Across each switch is an antiparallel diode

used to ensure that there is a path for inductive current in the event that a switch which

would normally conduct current of that polarity is turned off. This type of converter is

often referred to as an inverter when power fl ow is from the dc system to the ac system.

If power fl ow is from the ac system to the dc system, which is also possible, the con￾verter is often referred to as an active rectifi er.

In Figure 12.2-1 , v dc denotes the dc voltage applied to the converter bridge, and i dc

designates the dc current fl owing into the bridge. The bridge is divided into three legs,

one for each phase of the load. The line-to-ground voltage of the a -, b- , and c- phase

legs of the converter are denoted v ag , v bg , and v cg respectively. In this text, the load

current will generally be the stator current into a synchronous, induction, or permanent￾magnet ac machine; therefore, i as , i bs , and i cs are used to represent the current into each

phase of the load. Finally, the dc currents from the upper rail into the top of each phase

leg are designated i adc , i bdc , and i cdc .

To understand the operation of this basic topology, it must fi rst be understood that

none of the semiconductor devices shown are ever intentionally operated in the active

region of their i–v characteristics. Their operating point is either in the saturated region

(on) or in the cutoff region (off). If the devices were operated in their active region,

then by applying a suitable gate voltage to each device, the line-to-ground voltage of

each leg could be continuously varied from 0 to v dc . At fi rst, such control appears

advantageous, since each leg of the converter could be used as a controllable voltage

source. The disadvantage of this strategy is that, if the switching devices are allowed

to operate in their active region, there will be both a voltage across and current through

each semiconductor device, resulting in power loss. On the other hand, if each semi￾conductor is either on or off, then either there is a current through the device but no

voltage, or a voltage across the device but no current. Neither case results in power

Figure 12.2-1. The three-phase bridge converter topology.

462 FULLY CONTROLLED THREE-PHASE BRIDGE CONVERTERS

loss. Of course, in a real device, there will be some power losses due to the small

voltage drop that occurs even when the device is in saturation (on), and due to losses

that are associated with turning the switching devices on or off (switching losses);

nevertheless, inverter effi ciencies greater than 95% are readily obtained.

In this study of the operation of the converter bridge, it will be assumed that either

the upper switch or lower switch of each leg is gated on, except during switching

transients (the result of turning one switch on while turning another off). Ideally, the

leg-to-ground voltage of a given phase will be v dc if the upper switch is on and the

lower switch is turned off, or 0 if the lower switch is turned on and the upper switch

is off. This assumption is often useful for analysis purposes, as well as for time–domain

simulation of systems, in which the dc supply voltage is much greater than the semi￾conductor voltage drops. If a more detailed analysis or simulation is desired (and hence

the voltage drops across the semiconductors are not neglected), then the line-to-ground

voltage is determined both by the switching devices turned on and the phase current.

To illustrate this, consider the diagram of one leg of the bridge as is shown in

Figure 12.2-2 . Therein, x can be a , b , or c , to represent the a -, b- , or c- phase, respec￾tively. Figure 12.2-3 a illustrates the effective equivalent circuit shown in Figure 12.2-2

if the upper transistor is on and the current i xs is positive. For this condition, it can be

seen that the line-to-ground voltage v xg will be equal to the dc supply voltage v dc less

the voltage drop across the switch v sw . The voltage drop across the switch is generally

in the range of 0.7–3.0 V. Although the voltage drop is actually a function of the switch

current, it can often be represented as a constant. From Figure 12.2-3 a, the dc current

into the bridge, i xdc , is equal to the phase current i xs .

If the upper transistor is on and the phase current is negative, then the equivalent

circuit is as shown in Figure 12.2-3 b. In this case, the dc current into the leg i xdc is again

equal to the phase current i xs . However, since the current is now fl owing through the

diode, the line-to-ground voltage v xg is equal to the dc supply voltage v dc plus the diode

forward voltage drop v d . If the upper switch is on and the phase current is zero, it seems

Figure 12.2-2. One phase leg.

THE THREE-PHASE BRIDGE CONVERTER 463

reasonable to assume that the line-to-ground voltage is equal to the supply voltage as

indicated in Figure 12.2-3 c. Although other estimates could be argued (such as averag￾ing the voltage from the positive and negative current conditions), it must be remem￾bered that this is a rare condition, so a small inaccuracy will not have a perceptible

effect on the results.

The positive, negative, and zero current equivalent circuits, which represent the

phase leg when the lower switching device is on and the upper switching device is off,

Figure 12.2-3. Phase leg equivalent circuits. (a) Upper switch on; i xs > 0. (b) Upper switch on;

i xs < 0. (c) Upper switch on; i xs = 0. (d) Lower switch on; i xs > 0. (e) Lower switch on; i xs < 0. (f)

Lower switch on; i xs = 0. (g) Neither switch on; i xs > 0. (h) Neither switch on; i xs < 0. (i) Neither

switch on; i xs = 0.