Power electronic handbook

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17 Multilevel Power Converters 479

Multilevel Inverter

System

Induction

Motor

Feature

Extraction

System

Output Voltage Signals

Input

Output

Neural network fault

classification

Fault diagnosis

system

Switching pattern and

time calculation

system

Gate output signals

FIGURE 17.33 Structure of fault diagnosis system of a multilevel cascaded H-bridges inverter.

(a) (b)

bus

FIGURE 17.34 (a) Block diagram of the multilevel conﬁguration and (b) 6-level dc–dc converter connected with three-phase conventional inverter.

480 S. Khomfoi and L. M. Tolbert

supply a load or the ac grid without voltage balancing prob-

lems. Nevertheless, the intrinsic characteristics of renewable

energy sources might have some trouble with their energy

source utilization, for instance, fuel cell energy sources have

some problems associated with their V–I characteristics. The

static V–I characteristic of fuel cells illustrates more than 30%

difference in the output voltage between no load and full

load condition. This unavoidable decrease, caused by internal

losses reduces fuel cell utilization factor. Therefore, a multi-

level dc–dc converter might be used to overcome the problem

as shown in Fig. 17.34. To overcome the fuel cell voltage drop,

either voltage regulators have to be connected at the fuel cell

outputs or fuel cell voltages have to be monitored and the

control signals have to be modiﬁed accordingly.

Five different approaches for integrating numerous fuel cell

modules have been evaluated and compared with respect to

cost, control complexity, ease of modularity, and fault tol-

erance in [75]. In addition, the optimum fuel cell utilization

technique with a multilevel dc–dc converter has been proposed

in [76, 77].

17.7 Conclusion

This chapter has demonstrated the state of the art of mul-

tilevel power converter technology. Fundamental multilevel

converter structures and modulation paradigms including the

pros and cons of each technique have been discussed. Most of

the chapter focus has addressed modern and more practical

industrial applications of multilevel converters. A procedure

for calculating the required ratings for the active switches,

clamping diodes, and dc link capacitors with a design example

has been described. The possible future enlargements of mul-

tilevel converter technology such as fault diagnosis system and

renewable energy sources have been noted. It should be noted

that this chapter could not cover all multilevel power converter

related applications, however the basic principles of different

multilevel converters have been discussed methodically. The

main objective of this chapter is to provide a general notion to

readers who are interested in multilevel power converters and

their applications.

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482 S. Khomfoi and L. M. Tolbert

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pp. 1572–1576.

AC–AC Converters

A. K. Chattopadhyay, Ph.D.

Electrical Engg. Department, Bengal

Engineering & Science University,

Shibpur, Howrah, India

18.1 Introduction .......................................................................................... 483

18.2 Single-phase AC–AC Voltage Controller ..................................................... 484

18.2.1 Phase-controlled Single-phase AC Voltage Controller • 18.2.2 Single-phase AC–AC

Voltage Controller with On/Off Control

18.3 Three-phase AC–AC Voltage Controllers .................................................... 488

18.3.1 Phase-controlled Three-phase AC Voltage Controllers • 18.3.2 Fully Controlled

Three-phase Three-wire AC Voltage Controller

18.4 Cycloconverters ...................................................................................... 493

18.4.1 Single-phase to Single-phase Cycloconverter • 18.4.2 Three-phase Cycloconverters

• 18.4.3 Cycloconverter Control Scheme • 18.4.4 Cycloconverter Harmonics and Input

Current Waveform • 18.4.5 Cycloconverter Input Displacement/Power Factor

• 18.4.6 Effect of Source Impedance • 18.4.7 Simulation Analysis of Cycloconverter Performance

• 18.4.8 Power Quality Issues • 18.4.9 Forced Commutated Cycloconverter

18.5 Matrix Converter .................................................................................... 503

18.5.1 Operation and Control of the Matrix Converter • 18.5.2 Commutation and Protection

Issues in a Matrix Converter

18.6 High Frequency Linked Single-phase to Three-phase Matrix Converters ........... 509

18.6.1 High Frequency Integral-pulse Cycloconverter [48] • 18.6.2 High Frequency

Phase-controlled Cycloconverter [49]

18.7 Applications of AC–AC Converters ............................................................ 510

18.7.1 Applications of AC Voltage Controllers • 18.7.2 Applications of Cycloconverters

• 18.7.3 Applications of Matrix Converters

References ............................................................................................. 513

18.1 Introduction

A power electronic ac–ac converter, in generic form, accepts

electric power from one system and converts it for delivery

to another ac system with waveforms of different amplitude,

frequency, and phase. They may be single- or three-phase

types depending on their power ratings. The ac–ac converters

employed to vary the rms voltage across the load at constant

frequency are known as ac voltage controllers or ac regulators.

The voltage control is accomplished either by (i) phase control

under natural commutation using pairs of silicon controlled

rectiﬁers (SCRs) or triacs or (ii) by on/off control under forced

commutation/ self-commutation using fully controlled self-

commutated switches like gate turn-off thyristors (GTOs),

power transistors, integrated gate bipolar transistor (IGBTs),

MOS controlled thyristors (MCTs), integrated gate commu-

tated thyristor (IGCTs), etc. The ac–ac power converters

in which ac power at one frequency is directly converted to

ac power at another frequency without any intermediate dc

conversion link (as in the case of inverters) are known as cyclo-

converters, the majority of which use naturally commutated

SCRs for their operation when the maximum output frequency

is limited to a fraction of the input frequency. With rapid

advancements of fast-acting fully controlled switches, forced

commutated cycloconverters, or recently developed matrix

converters with bi-directional on/off control switches provide

independent control of the magnitude and the frequency of

the generated output voltage as well as sinusoidal modulation

of output voltage and current.

While typical applications of ac voltage controllers include

lighting and heating control, online transformer tap changing,

soft-starting and speed control of pump and fan drives, the

cycloconverters are mainly used for high power low speed large

ac motor drives for application in cement kilns, rolling mills,

483

484 A. K. Chattopadhyay

and ship propellers. The power circuits, control methods and

the operation of the ac voltage controllers, cycloconverters,

and matrix converters are introduced in this chapter. A brief

review is also made regarding their applications.

18.2 Single-phase AC–AC Voltage

Controller

The basic power circuit of a single-phase ac–ac voltage con-

troller, as shown in Fig. 18.1a, comprises a pair of SCRs

connected back-to-back (also known as inverse-parallel or

anti-parallel) between the ac supply and the load. This con-

nection provides a bi-directional full-wave symmetrical control

and the SCR pair can be replaced by a triac (Fig. 18.1b) for low-

power applications. Alternate arrangements are as shown in

= 2V

sinωt

−

−−

(a)

(e)

(b)

TRIAC

−

= 2V

sinωt

= 2V

sinωt

= 2V

sinωt

= 2V

sinωt

FIGURE 18.1 Single-phase ac voltage controllers: (a) full wave, two SCRs in inverse-parallel; (b) full wave with triac; (c) full wave with two SCRs

and two diodes; (d) full wave with four diodes and one SCR; and (e) half wave with one SCR and one diode in anti-parallel.

Fig. 18.1c with two diodes and two SCRs to provide a common

cathode connection for simplifying the gating circuit without

needing isolation, and in Fig. 18.1d with one SCR and four

diodes to reduce the device cost but with increased device

conduction loss. An SCR and diode combination, known

as thyrode controller, as shown in Fig. 18.1e provides a uni-

directional half-wave asymmetrical voltage control with device

economy, but introduces dc component and more harmonics

and thus is not so practical to use except for very low power

heating load.

With phase control, the switches conduct the load current

for a chosen period of each input cycle of voltage and with

on/off control, the switches connect the load either for a few

cycles of input voltage and disconnect it for the next few cycles

(integral cycle control) or the switches are turned on and off

several times within alternate half cycles of input voltage (ac

chopper or pulse width modulated (PWM) ac voltage controller).

18 AC–AC Converters 485

18.2.1 Phase-controlled Single-phase

AC Voltage Controller

For a full wave, symmetrical phase control, the SCRs T

and

in Fig. 18.1a are gated at α and π + α, respectively from

the zero crossing of the input voltage and by varying α, the

power ﬂow to the load is controlled through voltage control

in alternate half cycles. As long as one SCR is carrying cur-

rent, the other SCR remains reverse biased by the voltage drop

across the conducting SCR. The principle of operation in each

half cycle is similar to that of the controlled half-wave rectiﬁer,

and one can use the same approach for analysis of the circuit.

Operation with R-load: Figure 18.2 shows the typical volt-

age and current waveforms for the single-phase bi-directional

phase-controlled ac voltage controller of Fig. 18.1a with a

resistive load. The output voltage and current waveforms have

half-wave symmetry and so no dc component.

If v

√

sin ωt is the source voltage, the rms output

voltage with T

triggered at α can be found from the half-wave

2π

ωt

απ

(a)

(b)

π+α

2ππ

π+α

2ππ

FIGURE 18.2 Waveforms for single-phase ac full-wave voltage con-

troller with R-load.

symmetry as







sin

ωt d(ωt)







1−

sin2α

2π



(18.1)

Note that V

can be varied from V

to 0 by varying α from

0toπ.

The rms value of load current, I

(18.2)

The input power factor =



1 −

sin2α

2π



(18.3)

The average SCR current, I

A,SCR

2πR



√

sin ωt d(ωt )

(18.4)

Since each SCR carries half the line current, the rms current

in each SCR is

o,SCR

√

(18.5)

Operation with RL Load: Figure 18.3 shows the voltage and

current waveforms for the controller in Fig. 18.1a with RL

load. Due to the inductance, the current carried by the SCR

may not fall to zero at ωt = π when the input voltage goes

negative and may continue till ωt = β, the extinction angle,

as shown. The conduction angle,

θ = β −α (18.6)

of the SCR depends on the ﬁring delay angle α and the load

impedance angle φ.

The expression for the load current I

(ωt) when conducting

from α to β can be derived in the same way as that used for a

phase-controlled rectiﬁer in a discontinuous mode by solving

the relevant Kirchoff’s voltage equation:

(ωt )=

√

[sin(ωt −φ)

−sin(α−φ)e

(α−ωt )/tanφ

], α<ωt <β (18.7)

where Z = (R

+ ω

)

= load impedance and φ = load

impedance angle = tan

−1

(ωL/R)

486 A. K. Chattopadhyay

2π

π+α

2π

π+α

(b)

FIGURE 18.3 Typical waveforms of single-phase ac voltage controller

with an RL load.

The angle β, when the current i

falls to zero, can be deter-

mined from the following transcendental equation resulted by

putting i

(ωt = β) = 0 in Eq. (18.7)

sin

(

β − φ

)

= sin

(

α −φ

)

−sin

(

α −φ

)

(

α−β

)

/ tan φ

(18.8)

From Eqs. (18.6) and (18.8) one can obtain a relationship

between θ and α for a given value of φ as shown in Fig. 18.4

which shows that as α is increased, the conduction angle θ

decreases and the rms value of the current decreases.

180

120

0306090

α°

Φ=0°

30° 6060° 90°

120 150 180

30° 60°

FIGURE 18.4 θ vs α curves for single-phase ac voltage controller with

RL load.

The rms output voltage







2 V

sin

ωt d(ωt)







β − α +

sin 2α

−

sin 2β



(18.9)

can be evaluated for two possible extreme values of φ = 0

when β = π, and φ = π/2 when β = 2π − α and the enve-

lope of the voltage control characteristics for this controller is

shown in Fig. 18.5.

1.0

R-LOAD (R-LOAD (Φ=0=0°) L-LOAD (Φ=90°)

0.8

0.6

0.4

0.2

0.0

0306090

Firing Angle (α°)

120 150 180

R-LOAD (Φ=0°)

FIGURE 18.5 Envelope of control characteristics of a single-phase ac

voltage controller with RL load.

The rms SCR current can be obtained from Eq. (18.7) as:

o,SCR





2π



d(ωt)





(18.10)

The rms load current, I

√

2 I

o,SCR

(18.11)

The average value of SCR current, I

A,SCR

2π



d(ωt)

(18.12)

Gating Signal Requirements: For the inverse-parallel SCRs

as shown in Fig. 18.1a, the gating signals of SCRs must be

isolated from one another since there is no common cathode.

For R-load, each SCR stops conducting at the end of each half

cycle and under this condition, single short pulses may be used

for gating as shown in Fig. 18.2. With RL load, however, this

single short pulse gating is not suitable as shown in Fig. 18.6.

When SCR T

is triggered at ωt = π + α, SCR T

is still

conducting due to the load inductance. By the time the SCR T

stops conducting at β, the gate pulse for SCR T

has already

18 AC–AC Converters 487

(a)

(b)

(c)

2π

ωt

αβα+π

ωt

π+α

2π

π 2π 2π+α

2π 2π+α

π+α

2π

ππ+α

FIGURE 18.6 Single-phase full-wave controller with RL load: gate pulse

requirements.

ceased and T

will fail to turn on resulting the converter to

operate as a single-phase rectiﬁer with conduction of T

only.

This necessitates the application of a sustained gate pulse either

in the form of a continuous signal for the half cycle period

which increases the dissipation in SCR gate circuit and a large

isolating pulse transformer or better a train of pulses (carrier

frequency gating) to overcome these difﬁculties.

Operation with α<φ: If α = φ, then from Eq.(18.8),

sin(β −φ) = sin(β −α) = 0 (18.13)

and β −α = θ = π (18.14)

As the conduction angle θ cannot exceed π and the load cur-

rent must pass through zero, the control range of the ﬁring

angle is φ ≤ α ≤ π. With narrow gating pulses and α<φ,

only one SCR will conduct resulting in a rectiﬁer action as

shown. Even with a train of pulses, if α<φ, the changes in

the ﬁring angle will not change the output voltage and cur-

rent but both the SCRs will conduct for the period π with T

becoming on at ωt = π and T

at ωt + π.

This dead zone (α = 0toφ) whose duration varies with the

load impedance angle φ is not a desirable feature in closed-

loop control schemes. An alternative approach to the phase

control with respect to the input voltage zero crossing has been

visualized in which the ﬁring angle is deﬁned with respect to

the instant when it is the load current, not the input voltage,

that reaches zero, this angle being called the hold-off angle (γ)

or the control angle (as marked in Fig. 18.3). This method needs

1.0

0.8

0.6

0.4

0.2

04080

Firing Angle α°

120 160

Per unit Amplitude

n = 1

n = 3

n = 5

n = 7

FIGURE 18.7 Harmonic content as a function of the ﬁring angle for a

single-phase voltage controller with RL load.

sensing the load current – which may otherwise be required

anyway in a closed-loop controller for monitoring or control

purposes.

Power Factor and Harmonics: As in the case of phase-

controlled rectiﬁers, the important limitations of the phase-

controlled ac voltage controllers are the poor power factor

and the introduction of harmonics in the source currents. As

seen from Eq.(18.3), the input power factor depends on α and

as α increases, the power factor decreases.

The harmonic distortion increases and the quality of the

input current decreases with increase of ﬁring angle. The

variations of low-order harmonics with the ﬁring angle as

computed by Fourier analysis of the voltage waveform of

Fig. 18.2 (with R-load) are shown in Fig. 18.7. Only odd

harmonics exist in the input current because of half-wave

symmetry.

18.2.2 Single-phase AC–AC Voltage Controller

with On/Off Control

Integral Cycle Control: As an alternative to the phase con-

trol, the method of integral cycle control or burst-ﬁring is

used for heating loads. Here, the switch is turned on for a

time t

with n integral cycles and turned off for a time t

with

m integral cycles (Fig. 18.8). As the SCRs or triacs used here

are turned on at the zero crossing of the input voltage and

turn off occurs at zero current, supply harmonics and radio

488 A. K. Chattopadhyay

(a)

0.2

0.8

0.6

0.4

0.2

0.4 0.6

(b)

0.8 1.0

Power factor = k

1.0

Power factor

FIGURE 18.8 Integral cycle control: (a) typical load voltage waveforms and (b) power factor with the duty cycle k.

frequency interference are very low. However, sub-harmonic

frequency components may be generated which are undesir-

able as they may set up sub-harmonic resonance in the power

supply system, cause lamp ﬂicker and may interfere with the

natural frequencies of motor loads causing shaft oscillations.

For sinusoidal input voltage, v =

√

sin ωt , the rms

output voltage,

= V

√

k where k = n/(n +m) = duty cycle (18.15)

and V

= rms phase voltage

The power factor =

√

k (18.16)

which is poorer for lower values of the duty cycle k.

PWM AC Chopper: As in the case of controlled rectiﬁer,

the performance of ac voltage controllers can be improved

in terms of harmonics, quality of output current, and input

power factor by PWM control in PWM ac choppers, the cir-

cuit conﬁguration of one such single phase unit being shown in

Fig. 18.9. Here, fully controlled switches S

and S

connected

in anti-parallel are turned on and off many times during the

S′

FIGURE 18.9 Single-phase PWM ac chopper circuit.

2π 4π

FIGURE 18.10 Typical output voltage and current waveforms of a

single-phase PWM ac chopper.

positive and negative half cycles of the input voltage, respec-

tively. S



and S



provide the freewheeling paths for the load

current when S

and S

are off. An input capacitor ﬁlter may

be provided to attenuate the high switching frequency currents

drawn from the supply and also to improve the input power

factor. Figure 18.10 shows the typical output voltage and load

current waveform for a single-phase PWM ac chopper. It can

be shown that the control characteristics of an ac chopper

depend on the modulation index, M which theoretically varies

from0to1.

Three-phase PWM choppers consist of three single-phase

choppers either connected in delta or four-wire star.

18.3 Three-phase AC–AC Voltage

Controllers

18.3.1 Phase-controlled Three-phase AC

Voltage Controllers

Various Conﬁgurations: Several possible circuit conﬁgura-

tions for three-phase phase-controlled ac regulators with star

or delta connected loads are shown in Fig. 18.11a–h.