CHAPTER 12

A NEW POLYPHASE SWITCHING POWER AMPLIFIER

CHAPTER 12 CHAPTER 12

for the method which will be discussed in Chapter 14.

12.1 Polyphase Ope~ation

In the previous part, it was shown that the push-pull amplifier can be used as a single-phase inverter. The inverter may be extended for use in three-phase power generation by employing three separate inverters, one for each phase.

As customary with three-phase systems, one might want to put the outputs in a star or delta connection. However, because the outputs of the inverters may not be electrically isolated from the input, these connections are not possible in general and would cause uncontrollable currents to flow among the inverters. Nevertheless, there is a special case where the use of three separate inverters is possible. Three power amplifiers may be utilized as illustrated in Fig. 12.1 to generate a three-phase motor drive. The only requirement is that the three

reference voltages constitute a three-phase system with the usual 120°

phase displacement among them. The electrical isolation is provided by the windings of the motor, which are in this case used separately.

This scheme works, but its application is severely limited. Although it is a rather straightforward implementation of power amplifiers to three-phase systems, a major drawback is that this technique requires six bidirectional power converters, two per amplifier in Fig. 12.l.

The goal, then, is to find an inverter with fewer converters and a general form of output which permits regular three-phase load

connections. The general form of output connection, however, can be

sin (wt-120°)

Elg. 12.1

v₉ sin wt

POWER AMP

3-PHASE

MOTOR DRIVE

sin (wt -240°)

ThJLe.e.-phcue. mo-totL cl!U_ve employing -thJLe.e. Jte.gulaX.e.d .owi.:tc.hing pawe.Jt ampli6ie..46.

obtained by the same technique, but with the isolated version of the converters as demonstrated in Fig. 12.2. Each converter of the

amplifier behaves as a controlled quasi-voltage source which provides voltages according to its inherent gain.

A conventional amplifier is shown in Fig. 12.2a where the

converters are modelled as variable-voltage sources and share the same ground with the source Vg. Figure 12.2b models the isolated version in which the ground of vg and the converter's outputs are separated.

In order to provide the conventional load (3 or 4 wires), three isolated inverters may be put in a delta connection as shown in Fig. 12.2c,

where d₁, d₂, and d

3 are determined by a set of three-phase sine waves.

However, the outputs of the converters are all parallelled through the outer loop and, unless prevented by very accurate feedback systems, a large current can be generated between the converters.

Figure 12.2d, on the other hand, illustrates use of three isolated inverters in a star connection. This technique permits the general

form of the output and the common point of the amplifiers can be utilized as the neutral connection for the load. It can be noticed that the

linisolated version of the amplifiers, when employed in the star

connection as in Figo 12.2d, cause uncontrollably large currents since three semi-voltage sources are parallelled whose control signals are different. This is the result of control of six converters with three signals.

Next, we generalize the single-phase amplifier.

Fig. 12. 2

d)

~urce

Vo

1 ⁼

b)

~urce

Vg

T ⁼

c)

~urce

VgT ⁼

~urce

Vg

T ⁼

_I

I

I

d1

LOAD

0

_d ^I _d ^I,

N

I

I

I I I

d'1 d2 d'2 d3 d~

Gene.Jtal th!Lee-pha.oe eonnec;U,on: (a) a ~ingle-pha.oe powen amptibien, (b) ,0sofated ~ingle-phMe. inve!Lten, (e) delta eonnec;U,on

On

^invent~, (d) ~tan eonnec;U,on

On

invente.Jlll.

12.2 New Polyphase Amplifier

The key to operation of the push-pull amplifier of Fig. 6.9 is the cancellation of the de component of the output in the differential load.

This was automatically provided at duty ratio D = 0.5 in the original amplifier, but this cancellation effect can be assured at any steady state duty ratio and corresponding output voltage, provided that~two

independent modulators as in Fig. 12.3a are used.

If two equal voltages are applied to the modulator inputs, the outputs of the two converters will be at the same de potential, leading to zero voltage across the load. Therefore, even if the voltages of Fig. 12.3b (equal sine waves) are applied to the inputs, the differential output voltage remains at zero. This clearly illustrates that the

quiescent operating point of the amplifier can be set to values other than Oe5 as well.

Nevertheless, it is easy to produce some useful ac power by

implementing waveforms of Fig. 12.3c as inputs to the modulators - that is, by shifting the sinusoidal components of the signals to be 180° out of phase. As in the original push-pull amplifier, the output is the difference between two out-of-phase sine waves with equal de components.

Hence, a pure sine wave can be obtained and the previous push-pull output reproduced (fig. 6.9), but now with an arbitrary quiescent operating point and arbitrary de component.

Even the special 180° phase shift can be dispensed with. With the two separate modulators, an arbitrary phase shift between the two

reference sine waves may be implemented and still result in a sine wave

GENERALIZED POWER AMPLIFIER

I

DC CONVERTER

111---

< >

LOAD

2

DC CONVERTER

111---

< >

MODULATORS

INPUT 2

INPUT I

(b)

Vo ^~ _~ ^~ _~

INPUT I 0

Vo ^~ ...__... ^~ ""---""

INPUT 2 0

( c)

v, ^~ ,...__... ^~ ...___...

INPUT 0

V1 _~ ^~ _~ ^~

INPUT 2 0

Fig. 12. 3 Gen.Vl..alized pttoh-pull. amput)ieJt: (a.) ea.c.h c.on.vviXeA ha.o

w

own. modulat.oh.., ( b} equal in.pu,to gen.eJl.Ltt.e zeAo output and ( c.} a. ,oin.e wa.v e i6 g en.eJl..Ctted wdh the ^-6 et

an

^{in.puU .}

output. This is, of course, owing to the unique nature of sinusoidal quantities, whose addition even when phase-shifted, yields sinusoidal outputs. A non-sinusoidal quantity, when phase shifted and subtracted from the original, can result in output changed in its form, although

the de parts are still eliminated.

For the sinusoidal case, there is a particular phase shift which is of more interest than any other. Consider the case where the sine waves are 120° out of phase and nonlinearities of the converters are neglected.

The load voltage becomes:

fDC + sinwt] - {DC+ sin(wt - 120°}] = sinwt - sin(wt - 120°) =

=f3

sin (wt + 30°) (12.1)

It now seems quite natural to add a third converter with its own modulator, driven with a 240° phase-shifted sine wave, to the circuit as shown in Fig. 12o4. This is the new polyphase sine amplifier [13,22].

The modulators are driven by a set of three-phase sine waves:

input l

= vl

⁺

v2

^sinwt

input 2 = V

1 + V

2 sin (wt - 120 °) (12.2)

input 3 =

vl

+

v2

sin(wt - 240°)

Elg. JZ.4

NEW POLYPHASE AMPLIFIER

I DC CONVERTER I A

< > ~ - - -

2 DC CONVERTER

I

B

<: :>

I I ~

VgI

I I r I I

- - - -

- 3 DC CONVERTER

I c < > I - - NV1

New t.lvtee-phMe ,owi;tc./Ung ampufi,[eJL. ThJtee biclUtec;tfonal dc.-dc. c.onvvitetU>, wit.h t.heilt own modulat.oM, dfliven btj a ,oet. at) t.hJtee-phMe ,oine wavu, c.on,6.ti.tu;t.e t.hJtee pha,oe voLtage..-6 aJtound t.he clLt)t)eJten:tlal load.

This set of inputs results in the following output voltages (with respect to ground):

v

₈₈ =

v

_0e + Vm sin(wt - 120° + y)

VeG = Voe + vm sin(wt - 240° + y)

(12.3)

where G refers to ground and y is the phase of the control transfer function at the frequency w. The voltage

v

₀e corresponds to a steady- state duty ratio (representing V

1). Figure 12.5a shows these line-to- ground voltages. The differential load actually receives the difference of these voltages which are line-to-line voltages and again constitute a balanced three-phase system:

VAB

=Vi

^V₁₁₁ ^{sin(wt + 30° + y)}

v

₈

e ='\/3

Vm sin (wt - 90° + y) (12.4)

VeA

=Vi

Vm sin(wt - 210° + y)

The line-to-line voltages are shown in Fig. 12.5b.