SINGLE-PHASE ACIAC CONVERTER BASED ON QUASI-Z

SOURCE TOPOLOGY

ABSTRACT

This paper deals with a new family of quasi-Z-source converters applying to AC/AC

power conversion called single phase quasi-Z-source AC/AC converter (q ZSAC). The proposed

q ZSAC inherits all the advantages of the traditional single-phase Z-source ACIAC converter

(ZSAC), which can realize buck-boost, reversing or maintaining phase angle. In addition, the

proposed q ZSAC has the unique features; namely that the input. Voltage and output voltage is

sharing the same ground; the operation IS In continuous current mode (CCM). Compared to the

conventional ZSAC, the proposed q ZSAC has a lower harmonic distortion input current and a

higher efficiency. The proposed q ZSAC can control to shape the input current to be sinusoidal

and in phase with the input voltage. The operating principles of the proposed q ZSAC are

described, and a circuit analysis is provided. Simulation results are shown in comparison to that

of the conventional SZAC. Experimentation is implemented to verify the operational concept.

INTRODUCTION

For AC/AC power conversion, the most popular topologies are indirect ACIAC

converters with DC link, matrix converters and direct pulse width modulation (PWM) ACIAC

converters. The indirect ACIAC converters and matrix converters can provide variable output

voltage and variable frequency. However, for the applications where only voltage regulation

needs, the direct PWM ACIAC converters are used to perform as AC choppers or power line

conditioners with following features: providing better a power factor and efficiency, low

harmonic current in line, single-stage conversion, simple topology, easiness to control, smaller

size and lower cost. It was reported that the use of safe-commutation switches with PWM control

can significantly improve the performance of ac-ac converter.

Traditional single-phase Z-source ACIAC converters (ZSAC) proposed in as shown in

Fig. 1 have merits such as providing a larger range of output voltage with buck boost mode,

reversing or maintaining phase angle. However, the conventional voltage-fed ZSAC has some

main drawbacks: the input voltage and output voltage is not sharing the same ground, thus the

feature that the output voltage reverses or maintains phase angle with the input voltage is not

supported well. In addition, the input current of the conventional ZSAC is operated in

discontinuous current mode (DCM). In general, the peak of input current in DCM which gives

rise to the device stress is higher than that in CCM. Moreover, the waveform of input current in

CCM is more sinusoidal than that in DCM. Recently, quasi-Z-source inverters (qZSI) proposed

in have applied to DCIAC voltage-fed inverters and DC/AC current-fed inverters. For DCIAC

power conversion, the q ZSI when compared to the traditional Z-source inverter, features lower

DC voltage on capacitor as well as continuous input current.

The q ZSI for photovoltaic (PV) applications is presented in When the q ZSI applies to

DC/DC converter, a family of quasi-Z source DC/DC converters is proposed in with minimal

number of switches and passive devices

Fig.1. Conventional single-phase Z-source ac-ac converter (ZSAC)

Fig.2. Proposed single-phase quasi-Z-source ac-ac converter (q ZSAC).

In this paper, a new family of quasi-Z-source converters applying to ACIAC power

conversion is presented. The proposed converter called single-phase quasi-Z-source ACIAC

converter (q ZSAC) inherits all the advantages of the traditional ZSAC, which can realize buck-

boost, reversing or maintaining phase angle.

In addition, the proposed q ZSAC has the unique features; namely that the input voltage

and output voltage is sharing the same ground; that the operation is in continuous current mode

(CCM). The proposed q ZSAC can control to shape the input current to be sinusoidal and in

phase with the input voltage. The operating principles, simulation and experimental results are

shown.

QUASI Z-SOURCE AC\AC CONVERTER

The qZSAC has following features: the input voltage and output voltage is sharing the

same ground; the operation is in continuous current mode (CCM). The proposed qZSAC can

control to shape the input current to be sinusoidal and in phase with the input voltage. The

operating principles, simulation results are presented. To verify these described performance

features, PSIM simulation and experimental results were performed with a low total harmonic

distortion of input current and high input power factor.

The proposed converter has the main features in that the output voltage can be bucked or

boosted and be both in-phase and out-of-phase with the input voltage. The input voltage and

output voltage share the same ground, the size of converter is reduced, and it operates in a

continuous current mode. A safe-commutation strategy for the modified single-phase quasi-Z-

source ac-ac converter is used instead of a snubber circuit. The operating principles and a steady-

state analysis are presented. A laboratory prototype, tested using a resistive load, a passive load,

and a non-linear load, was constructed that used an input voltage of 70 Vrms/60 Hz in order to

verify the performance of the modified single-phase quasi-Z-source ac-ac converter. The

experiment results verified that the converter has a lower input current total harmonic distortion,

a higher input power factor, and a higher efficiency in comparison to a conventional single-phase

Z-source ac-ac converter. In addition, the experimental results show that the use of the safe-

commutation strategy is a significant improvement, as it makes it possible to avoid voltage

spikes on the switches.

AC/AC CONVERTER

An AC/AC converter converts an AC waveform such as the mains supply, to another AC

waveform, where the output voltage and frequency can be set arbitrarily.

AC/AC converters can be categorized into

Converters with a DC-link.

Cycloconverters

Hybrid Matrix Converters.

Matrix Converters.

As shown in Fig 1. For such AC-AC conversion today typically converter systems with a

voltage (Fig. 2) or current (Fig. 3) DC-link are employed. For the voltage DC-link, the mains

coupling could be implemented by a diode bridge. To accomplish braking operation of a motor, a

braking resistor must be placed in the DC-link. Alternatively, an anti-parallel thyristor bridge

must be provided on the mains side for feeding back energy into the mains. The disadvantages of

this solution are the relatively high mains distortion and high reactive power requirements

(especially during inverter operation).

An AC/AC converter with approximately sinusoidal input currents and bidirectional

power flow can be realized by coupling a PWM rectifier and a PWM inverter to the DC-link.

The DC-link quantity is then impressed by an energy storage element that is common to both

stages, which is a capacitor C for the voltage DC-link or an inductor L for the current DC-link.

The PWM rectifier is controlled in a way that a sinusoidal mains current is drawn, which is in

phase or anti-phase (for energy feedback) with the corresponding mains phase voltage.

Due to the DC-link storage element, there is the advantage that both converter stages are

to a large extent decoupled for control purposes. Furthermore, a constant, mains independent

input quantity exists for the PWM inverter stage, which results in high utilization of the

converter’s power capability.

On the other hand, the DC-link energy storage element has a relatively large physical

volume, and when electrolytic capacitors are used, in the case of a voltage DC-link, there is

potentially a reduced system lifetime.

In order to achieve higher power density and reliability, it is makes sense to consider

Matrix Converters that achieve three-phase AC/AC conversion without any intermediate energy

storage element. Conventional Direct Matrix Converters (Fig. 4) perform voltage and current

conversion in one single stage.

A cycloconverter constructs an output, variable-frequency, approximately sinusoid

waveform by switching segments of the input waveform to the output; there is no intermediate

DC link. With switching elements such as SCRs, the output frequency must be lower than the

input. Very large cycloconverters (on the order of 10 MW) are manufactured for compressor and

wind-tunnel drives, or for variable-speed applications such as cement kilns.

There is the alternative option of indirect energy conversion by employing the Indirect

Matrix Converter (Fig. 5) or the Sparse Matrix Converter which was invented by Prof. Johann

W. Kolar from the ETH Zurich. As with the DC-link based systems (Fig. 2 and Fig. 3), separate

stages are provided for voltage and current conversion, but the DC-link has no intermediate

storage element. Generally, by employing matrix converters, the storage element in the DC-link

is eliminated at the cost of a larger number of semiconductors. Matrix converters are often seen

as a future concept for variable speed drives technology, but despite intensive research over the

decades they have until now only achieved low industrial penetration. The reason for this could

be the higher complexity in modulation and analysis effort.

AC /AC CONVERTER CLASSIFICATION

Three Phase AC -AC voltage DC

3PAC current DC

CYCLOCONVERTERS

In industrial applications, two forms of electrical energy are used: direct current (dc) and

alternating current (ac). Usually constant voltage constant frequency single-phase or three-phase

ac is readily available. However, for different applications, different forms, magnitudes and/or

frequencies are required. There are four different conversions between dc and ac power sources.

These conversions are done by circuits called power converters. The converters are classified as:

1-rectifiers: from single-phase or three-phase ac to variable voltage dc

2-choppers: from dc to variable voltage dc

3-inverters: from dc to variable magnitude and variable frequency, single-phase or three phase

ac

4-cycloconverters: from single-phase or three-phase ac to variable magnitude and variable

frequency, single-phase or three-phase ac

The first three classes are explained in other articles. This article explains what cyclo converters

are, their types, how they operate and their applications.

Traditionally, ac-ac conversion using semiconductor switches is done in two different

ways: 1- in two stages (ac-dc and then dc-ac) as in dc link converters or 2- in one stage (ac-ac)

cycloconverters (Fig. 1). Cycloconverters are used in high power applications driving induction

and synchronous motors.

They are usually phase-controlled and they traditionally use thyristors due to their ease of

phase commutation.

Fig.1 Block diagram of a cyclo converter

There are other newer forms of cyclo conversion such as ac-ac matrix converters and

high frequency ac-ac (hfac-ac) converters and these use self-controlled switches. These

converters, however, are not popular yet.

Some applications of cyclo converters are:

· Cement mill drives

· Ship propulsion drives

· Rolling mill drives

· Scherbius drives

· Ore grinding mills

· Mine winders

1. OPERATION PRINCIPLES:

The following sections will describe the operation principles of the cyclo converter

starting from the simplest one, single-phase to single-phase (1f-1f) cyclo converter.

1.1. SINGLE-PHASE TO SINGLE-PHASE (1F-1F) CYCLO CONVERTER:

To understand the operation principles of cyclo converters, the single-phase to single-

phase cycloconverter (Fig. 2) should be studied first. This converter consists of back-to-back

connection of two full-wave rectifier circuits. Fig 3 shows the operating waveforms for this

converter with a resistive load.

The input voltage, vs is an ac voltage at a frequency, fi as shown in Fig. 3a. For easy

understanding assume that all the thyristors are fired at a=0° firing angle, i.e. thyristors act like

diodes. Note that the firing angles are named as aP for the positive converter and aN for the

negative converter.

Consider the operation of the cyclo converter to get one-fourth of the input frequency at

the output. For the first two cycles of vs, the positive converter operates supplying current to the

load. It rectifies the input voltage; therefore, the load sees 4 positive half cycles as seen in Fig.

3b. In the next two cycles, the negative converter operates supplying current to the load in the

reverse direction. The current waveforms are not shown in the figures because the resistive load

current will have the same waveform as the voltage but only scaled by the resistance. Note that

when one of the converters operates the other one is disabled, so that there is no current

circulating between the two rectifiers.

Fig. 2 Single-phase to single phase cyclo converter

Fig. 3 Single-phase to single-phase cyclo converter waveforms

a) Input voltage

b) Output voltage for zero firing angle

c) Output voltage with firing angle p/3 rad.

d) Output voltage with varying firing angle

The frequency of the output voltage, vo in Fig. 3b is 4 times less than that of vs, the input

voltage, i.e. fo/fi=1/4. Thus, this is a step-down cycloconverter. On the other hand,

cycloconverters that have fo/fi>1 frequency relation are called step-up cycloconverters. Note that

step-down cycloconverters are more widely used than the step-up ones.

The frequency of vo can be changed by varying the number of cycles the positive and the

negative converters work. It can only change as integer multiples of fi in 1f-1f cyclo converters.

With the above operation, the 1f-1f cyclo converter can only supply a certain voltage at a certain

firing angle a. The dc output of each rectifier is:

Where V is the input rms voltage.

The dc value per half cycle is shown as dotted in Fig. 3d.

Then the peak of the fundamental output voltage is

Above equation implies that the fundamental output voltage depends on . For =0,

Where

If is increased to /3 as in Fig. 3d, then Thus varying , the fundamental

output voltage can be controlled.

Constant a operation gives a crude output waveform with rich harmonic content. The

dotted lines in Fig. 3b and c show a square wave. If the square wave can be modified to look

more like a sine wave, the harmonics would be reduced. For this reason a is modulated as shown

in Fig. 3d. Now, the six-stepped dotted line is more like a sine wave with fewer harmonics. The

more pulses there are with different a's, the less are the harmonics.

1.2. THREE-PHASE TO SINGLE-PHASE (3F-1F) CYCLO CONVERTER:

There are two kinds of three-phase to single-phase (3f-1f) cyclo converters: 3f-1f half-

wave Cyclo converter (Fig. 4) and 3f-1f bridge cyclo converter (Fig. 5).

Like the 1f-1f case, the 3f-1f cyclo converter applies rectified voltage to the load. Both

positive and negative converters can generate voltages at either polarity, but the positive

converter can only supply positive current and the negative converter can only supply negative

current. Thus, the cycloconverter can operate in four quadrants: (+v, +i) and (-v, -i) rectification

modes and (+v, -i) and (-v, +i) inversion modes. The modulation of the output voltage and the

fundamental output voltage are shown in Fig. 6. Note that a is sinusoidally modulated over the

cycle to generate a harmonically optimum output voltage.

Fig. 4 3-1half-wave cycloconverter

Fig. 5 3-1bridge cyclo converter

Fig. 6 3-1half-wave cycloconverter waveformsa) + Converter output voltage

b) Cosine timing wavesc) – Converter output voltage

The polarity of the current determines if the positive or negative converter should be

supplying power to the load. Conventionally, the firing angle for the positive converter is named

aP, and that of the negative converter is named aN. When the polarity of the current changes, the

converter previously supplying the current is disabled and the other one is enabled. The load

always requires the fundamental voltage to be continuous. Therefore, during the current polarity

reversal, the average voltage supplied by both of the converters should be equal. Otherwise,

switching from one converter to the other one would cause an undesirable voltage jump. To

prevent this problem, the converters are forced to produce the same average voltage at all times.

Thus, the following condition for the firing angles should be met.

The fundamental output voltage in Fig. 6 can be given as:

Where Vo is the rms value of the fundamental voltage

At a time to the output fundamental voltage is

The positive converter can supply this voltage if P satisfies the following condition.

Where (p=3 for half wave converter and 6 for bridge converter)

From the condition (3)

The firing angles at any instant can be found from above two equations

The operation of the 3f-1f bridge cyclo converter is similar to the above 3f-1f half-wave

Cyclo converter. Note that the pulse number for this case is 6.

1.3 THREE-PHASE TO THREE-PHASE (3F-3F) CYCLOCONVERTER:

If the outputs of 3 3f-1f converters of the same kind are connected in wye or delta and if

the output voltages are 2p/3 radians phase shifted from each other, the resulting converter is a

three phase to three-phase (3f-3f) cycloconverter. The resulting cycloconverters are shown in

Figs. 7 sand 8 with wye connections.

If the three converters connected are half-wave converters, then the new converter is

called a 3f-3f half-wave cycloconverter.

If instead, bridge converters are used, then the result is a 3f-3f bridge cyclo converter. 3f-

3f half-wave cyclo converter is also called a 3-pulse cyclo converter or an 18-thyristor cyclo

converter. On the other hand, the 3f-3f bridge cyclo converter is also called a 6-pulse cyclo

converter or a 36-thyristor cyclo converter. The operation of each phase is explained in the

previous section.

Fig. 7 3-3half-wave cyclo converter

Fig. 8 3-3bridge cycloconverter

The three-phase cycloconverters are mainly used in ac machine drive systems running

three phase synchronous and induction machines. They are more advantageous when used with a

synchronous machine due to their output power factor characteristics. A cycloconverter can

supply lagging, leading, or unity power factor loads while its input is always lagging. A

synchronous machine can draw any power factor current from the converter. This characteristic

operation matches the cycloconverter to the synchronous machine. On the other hand, induction

machines can only draw lagging current, so the cycloconverter does not have an edge compared

to the other converters in this aspect for running an induction machine. However,

cycloconverters are used in Scherbius drives for speed control purposes driving wound rotor

induction motors.

Cycloconverters produce harmonic rich output voltages, which will be discussed in the

following sections. When cycloconverters are used to run an ac machine, the leakage inductance

of the machine filters most of the higher frequency harmonics and reduces the magnitudes of the

lower order harmonics.

2. BLOCKED MODE AND CIRCULATING CURRENT MODE:

The operation of the cycloconverters is explained above in ideal terms. When the load

current is positive, the positive converter supplies the required voltage and the negative converter

is disabled. On the other hand, when the load current is negative, then the negative converter

supplies the required voltage and the positive converter is blocked. This operation is called the

blocked mode operation, and the cycloconverters using this approach are called blocking mode

cycloconverters.

However, if by any chance both of the converters are enabled, then the supply is short-

circuited.To avoid this short circuit, an intergroup reactor (IGR) can be connected between the

converters as shown in Fig. 9. Instead of blocking the converters during current reversal, if they

are both enabled, then a circulating current is produced. This current is called the circulating

current. It is unidirectional because the thyristors allow the current to flow in only one direction.

Some cycloconverters allow this circulating current at all times. These are called circulating

current cycloconverters.

Fig. 9 Circulating current and IGR

2.1 BLOCKING MODE CYCLOCONVERTERS:

The operation of these cycloconverters was explained briefly before. They do not let

circulating current flow, and therefore they do not need a bulky IGR.When the current goes to

zero, both positive and negative converters are blocked. The converters stay off for a short delay

time to assure that the load current ceases. Then, depending on the polarity, one of the converters

is enabled. With each zero crossing of the current, the converter, which was disabled before the

zero crossing, is enabled. A toggle flip-flop, which toggles when the current goes to zero, can be

used for this purpose. The operation waveforms for a three-pulse blocking mode cycloconverter

are given in Fig. 10.

The blocking mode operation has some advantages and disadvantages over the

circulating mode operation. During the delay time, the current stays at zero distorting the voltage

and current waveforms. This distortion means complex harmonics patterns compared to the

circulating mode cycloconverters. In addition to this, the current reversal problem brings more

control complexity.

However, no bulky IGRs are used, so the size and cost is less than that of the circulating

current case. Another advantage is that only one converter is in conduction at all times rather

than two this means less losses and higher efficiency.

Fig. 10 blocking mode operation waveformsa) + Converter output voltageb) – Converter output voltage

c) Load voltage

2.2 CIRCULATING CURRENT CYCLOCONVERTERS:

In this case, both of the converters operate at all times producing the same fundamental

output voltage. The firing angles of the converters satisfy the firing angle condition (Eq. 3), thus

when one converter is in rectification mode the other one is in inversion mode and vice versa. If

both of the converters are producing pure sine waves, then there would not be any circulating

current because the instantaneous potential difference between the outputs of the converters

would be zero. In reality, an IGR is connected between the outputs of two phase controlled

converters (in either rectification or inversion mode). The voltage waveform across the IGR can

be seen in Fig. 11d. This is the difference of the instantaneous output voltages produced by the

two converters. Note that it is zero when both of the converters produce the same instantaneous

voltage. The center tap voltage of IGR is the voltage applied to the load and it is the mean of the

voltages applied to the ends of IGR, thus the load voltage ripple is reduced.

Fig. 11 circulating mode operation waveformsa) + Converter output voltageb) – Converter output voltage

c) Load voltage d) IGR voltage

The circulating current cycloconverter applies a smoother load voltage with less

harmonics compared to the blocking mode case. Moreover, the control is simple because there is

no current reversal problem. However, the bulky IGR is a big disadvantage for this converter. In

addition to this, the number of devices conducting at any time is twice that of the blocking mode

converter. Due to these disadvantages, this cycloconverter is not attractive.

The blocked mode cycloconverter converter and the circulating current cycloconverter

can be combined to give a hybrid system, which has the advantages of both. The resulting

cycloconverter looks like a circulating mode cycloconverter circuit, but depending on the

polarity of the output current only one converter is enabled and the other one is disabled as with

the blocking mode cycloconverters. When the load current decreases below a threshold, both of

the converters are enabled. Thus, the current has a smooth reversal. When the current increases

above a threshold in the other direction, the outgoing converter is disabled. This hybrid

cycloconverter operates in the blocking mode most of the time so a smaller IGR can be used.

The efficiency is slightly higher than that of the circulating current cycloconverter but

much less than the blocking mode cycloconverter.

Moreover, the distortion caused by the blocking mode operation disappears due to the

circulating current operation around zero current. Moreover, the control of the converter is still

less complex than that of the blocking mode cycloconverter.

3. OUTPUT AND INPUT HARMONICS:

The cycloconverter output voltage waveforms have complex harmonics. Higher order

harmonics are usually filtered by the machine inductance, therefore the machine current has less

harmonics. The remaining harmonics cause harmonic losses and torque pulsations. Note that in a

cycloconverter, unlike other converters, there are no inductors or capacitors, i.e. no storage

devices. For this reason, the instantaneous input power and the output power are equal.

There are several factors affecting the harmonic content of the waveforms. Blocking

mode operation produces more complex harmonics than circulating mode of operation due to the

zero current distortion. In addition to this, the pulse number effects the harmonic content. A

greater number of pulses has less harmonic content. Therefore, a 6-pulse (bridge) cycloconverter

produces less harmonics than a 3-pulse (half-wave) cycloconverter. Moreover, if the output

frequency gets closer to the input frequency, the harmonics increase. Finally, low power factor

and discontinuous conduction, both contribute to harmonics.

For a typical p-pulse converter, the order of the input harmonics is "pn+1" and that of the

output harmonics is "pn", where p is the pulse number and n is an integer. Thus for a 3-pulse

converter the input harmonics are at frequencies 2fi, 4fi for n=1, 5fi, 7fi for n=2, and so on. The

output harmonics, on the other hand, are at frequencies 3fi, 6fi, …

The firing angle a in cycloconverter operation is sinusoidal modulated. The modulation

frequency is the same as the output frequency and sideband harmonics are induced at the output.

Therefore, the output waveform is expected to have harmonics at frequencies related to both the

input and output frequencies.

For blocking mode operation, the output harmonics are found at "pnfi+Nfo", where N is

an integer and pn+N=odd condition is satisfied. Then the output harmonics for a 3-pulse

cycloconverter in blocking mode will be found at frequencies

n=1 3fi, 3fi+2fo, 3fi+4fo, 3fi+6fo, 3fi+8fo, 3fi+10fo …

n=2 6fi, 6fi+1fo, 6fi+3fo, 6fi+5fo, 6fi+7fo, 6fi+9fo …

n=3 9fi, 9fi+2fo, 9fi+4fo, 9fi+6fo, 9fi+8fo, 9fi+10fo, …

n=4, 5,…

Some of the above harmonics might coincide to frequencies below fi. These are called

Sub harmonics. They are highly unwanted harmonics because the machine inductance cannot

filter these. For the circulating mode operation, the harmonics are at the same frequencies as the

blocking mode, but N is limited to (n+1). Thus, the output harmonics for a 3-pulse

cycloconverter in circulating mode will be found at frequencies

n=1 3fi, 3fi+2fo, 3fi+4fo

n=2 6fi+1fo, 6fi+3fo, 6fi+5fo, 6fi+7fo

n=3 9fi, 9fi+2fo, 9fi+4fo, 9fi+6fo, 9fi+8fo, 9fi+10fo

n=4, 5,…

With N limited in the circulating mode, there are fewer sub harmonics expected.

According to calculations done in sub harmonics in this mode exist for fo/fi>0.6.For the blocking

mode states that the sub harmonics exist for fo/fi>0.2.

The output voltage of a cycloconverter has many complex harmonics, but the output

current is smoother due to heavy machine filtering. The input voltages of a cycloconverter are

sinusoidal voltages. As stated before the instantaneous output and input powers of a

cycloconverter are balanced because it does not have any storage devices. To maintain this

balance on the input side with sinusoidal voltages, the input current is expected to have complex

harmonic patterns. Thus as expected, the input current harmonics are at frequencies

"(pn+1)fi+Mfo" where M is an integer and (pn+1)+M=odd condition is satisfied. Thus, a 3-pulse

cycloconverter has input current harmonics at the following frequencies:

n=0 fi, fi+6fo, fi+12fo, …

n=1 2fi+3fo, 2fi+9fo, 2fi+15fo …

4fi+3fo, 4fi+9fo, 4fi+15fo,…

n=2, 3,…

4. NEWER TYPES OF CYCLOCONVERTERS:

4.1 MATRIX CONVERTER:

The matrix converter is a fairly new converter topology, which was first proposed in the

beginning of the 1980s. A matrix converter consists of a matrix of 9 switches connecting the

three input phases to the three output phases directly as shown in Fig. 12. Any input phase can be

connected to any output phase at any time depending on the control. However, no two switches

from the same phase should be on at the same time, otherwise this will cause a short circuit of

the input phases. These converters are usually controlled by PWM to produce three-phase

variable voltages at variable frequency.

Fig. 12 Matrix Converter

This direct frequency changer is not commonly used because of the high device count,

i.e. 18 switches compared to 12 of a dc link rectifier-inverter system. However, the devices used

are smaller because of their shorter ON time compared to the latter.

4.2 SINGLE-PHASE TO THREE-PHASE (1F-3F) CYCLOCONVERTERS:

Recently, with the decrease in the size and the price of power electronics switches,

single-phase to three-phase cycloconverters (1f-3f) started drawing more research interest.

Usually, an H-bridge inverter produces a high frequency single-phase voltage waveform,

which is fed to the cycloconverter either through a high frequency transformer or not. If a

transformer is used, it isolates the inverter from the cycloconverter. In addition to this, additional

taps from the transformer can be used to power other converters producing a high frequency ac

link. The single-phase high frequency ac (hfac) voltage can be either sinusoidal or trapezoidal.

There might be zero voltage intervals for control purposes or zero voltage commutation. Fig. 13

shows the circuit diagram of a typical hfac link converter. These converters are not commercially

available yet. They are in the research state. Among several kinds, only two of them will be

addressed here:

4.2.1 INTEGRAL PULSE MODULATED (1F-3F) CYCLOCONVERTERS:

The input to these cycloconverters is single-phase high frequency sinusoidal or square

waveforms with or without zero voltage gaps. Every half-cycle of the input signal, the control for

each phase decides if it needs a positive pulse or a negative pulse using integral pulse

modulation. For integral pulse modulation, the command signal and the output phase voltage are

integrated and the latter result is subtracted from the former. For a positive difference, a negative

pulse is required, and vice versa for the negative difference. For the positive (negative) input

half-cycle, if a positive pulse is required, the upper (lower) switch is turned on; otherwise, the

lower (upper) switch is turned on.

Therefore, the three-phase output voltage consists of positive and negative half-cycle

pulses of the input voltage. Note that this converter can only work at output frequencies which

are multiples of the input frequency.

Fig. 13 High frequency ac link converter (1f hf inverter + (1f-3f) Cycloconverter)

4.2.2 PHASE-CONTROLLED (1F-3F) CYCLOCONVERTER:

This cycloconverter converts the single-phase high frequency sinusoidal or square wave

voltage into three-phase voltages using the previously explained phase control principles. The

voltage command is compared to a sawtooth waveform to find the firing instant of the switches.

Depending on the polarity of the current and the input voltage, the next switch to be turned on is

determined. Compared to the previous one, this converter has more complex control but it can

work at any frequency.

5. SUMMARY:

Cycloconverters are widely used in industry for ac-to-ac conversion. With recent device

advances, newer forms of cycloconversion are being developed. These newer forms are drawing

more research interest. In this article, the most commonly known cycloconverter schemes are

introduced, and their operation principles are discussed. For more detailed information, the

following references can be used.

BUCK CONVERTER

A buck converter is a step-down DC to DC converter. Its design is similar to the step-

up boost converter, and like the boost converter it is a switched-mode power supply that uses two

switches (a transistor and a diode), an inductor and a capacitor.

The simplest way to reduce a DC voltage is to use a voltage divider circuit, but voltage

dividers waste energy, since they operate by bleeding off excess power as heat; also, output

voltage isn't regulated (varies with input voltage). Buck converters, on the other hand, can be

remarkably efficient (easily up to 95% for integrated circuits) and self-regulating, making them

useful for tasks such as converting the 12–24 V typical battery voltage in a laptop down to the

few volts needed by the processor.

sTheory of operation

Fig: Buck converter circuit diagram.

Fig: The two circuit configurations of a buck converter: On-state, when the switch is closed, and

Off-state, when the switch is open.

Fig: Naming conventions of the components, voltages and current of the buck converter.

Fig: Evolution of the voltages and currents with time in an ideal buck converter operating in

continuous mode.

The operation of the buck converter is fairly simple, with an inductor and two switches

(usually a transistor and a diode) that control the inductor. It alternates between connecting the

inductor to source voltage to store energy in the inductor and discharging the inductor into the

load.

Continuous mode

A buck converter operates in continuous mode if the current through the inductor (IL) never

falls to zero during the commutation cycle. In this mode, the operating principle is described by

the chronogram in figure:

When the switch pictured above is closed (On-state, top of figure 2), the voltage across the

inductor is VL = Vi − Vo. The current through the inductor rises linearly. As the diode is

reverse-biased by the voltage source V, no current flows through it;

When the switch is opened (off state, bottom of figure 2), the diode is forward biased. The

voltage across the inductor is VL = − Vo(neglecting diode drop). Current IL decreases.

The energy stored in inductor L is

Therefore, it can be seen that the energy stored in L increases during On-time (as IL increases)

and then decreases during the Off-state. L is used to transfer energy from the input to the output

of the converter.

The rate of change of IL can be calculated from:

With VL equal to Vi − Vo during the On-state and to− Vo during the Off-state. Therefore, the

increase in current during the On-state is given by:

Identically, the decrease in current during the Off-state is given by:

If we assume that the converter operates in steady state, the energy stored in each component at

the end of a commutation cycle T is equal to that at the beginning of the cycle. That means that

the current IL is the same at t=0 and at t=T (see figure 4). Therefore,

So we can write from the above equations:

It is worth noting that the above integrations can be done graphically: In figure 4,   

is proportional to the area of the yellow surface, and   to the area of the orange surface, as

these surfaces are defined by the inductor voltage (red) curve. As these surfaces are simple

rectangles, their areas can be found easily:   for the yellow rectangle

and − Votoff for the orange one. For steady state operation, these areas must be equal.

As can be seen on figure 4,   and . D is a scalar called the duty cycle with a

value between 0 and 1. This yields

From this equation, it can be seen that the output voltage of the converter varies linearly

with the duty cycle for a given input voltage. As the duty cycle D is equal to the ratio between

tOn and the period T, it cannot be more than 1. Therefore,  . This is why this converter is

referred to as step-down converter.

So, for example, stepping 12 V down to 3 V (output voltage equal to a fourth of the input

voltage) would require a duty cycle of 25%, in our theoretically ideal circuit.

Discontinuous mode

In some cases, the amount of energy required by the load is small enough to be

transferred in a time lower than the whole commutation period. In this case, the current through

the inductor falls to zero during part of the period. The only difference in the principle described

above is that the inductor is completely discharged at the end of the commutation cycle. This has,

however, some effect on the previous equations.

Fig: Evolution of the voltages and currents with time in an ideal buck converter operating in

discontinuous mode.

We still consider that the converter operates in steady state. Therefore, the energy in the

inductor is the same at the beginning and at the end of the cycle (in the case of discontinuous

mode, it is zero). This means that the average value of the inductor voltage (VL) is zero; i.e., that

the area of the yellow and orange rectangles in figure are the same. This yield:

So the value of δ is:

The output current delivered to the load (Io) is constant; as we consider that the output capacitor

is large enough to maintain a constant voltage across its terminals during a commutation cycle.

This implies that the current flowing through the capacitor has a zero average value. Therefore,

we have:

Where   is the average value of the inductor current. As can be seen in figure, the inductor

current waveform has a triangular shape. Therefore, the average value of IL can be sorted out

geometrically as follow:

The inductor current is zero at the beginning and rises during ton up to ILmax. That means that

ILmax is equal to:

Substituting the value of ILmax in the previous equation leads to:

And substituting δ by the expression given above yield:

This latter expression can be written as:

It can be seen that the output voltage of a buck converter operating in discontinuous

mode is much more complicated than its counterpart of the continuous mode. Furthermore, the

output voltage is now a function not only of the input voltage (V i) and the duty cycle D, but also

of the inductor value (L), the commutation period (T) and the output current (Io).

From discontinuous to continuous mode (and vice versa)

Fig: Evolution of the normalized output voltages with the normalized output current.

As told at the beginning of this section, the converter operates in discontinuous mode when low

current is drawn by the load, and in continuous mode at higher load current levels. The limit

between discontinuous and continuous modes is reached when the inductor current falls to zero

exactly at the end of the commutation cycle. with the notations of figure, this corresponds to :

Therefore, the output current (equal to the average inductor current) at the limit between

discontinuous and continuous modes is:

Substituting ILmax by its value:

On the limit between the two modes, the output voltage obeys both the expressions given

respectively in the continuous and the discontinuous sections. In particular, the former is

Vo = DVi

So Iolim can be written as:

Let's now introduce two more notations:

The normalized voltage, defined by  . It is zero when Vo = 0, and 1 when Vo = Vi ;

The normalized current, defined by  .

The term   is equal to the maximum increase of the inductor current during a cycle; i.e.,

the increase of the inductor current with a duty cycle D=1. So, in steady state operation of the

converter, this means that   equals 0 for no output current, and 1 for the maximum current

the converter can deliver.

Using these notations, we have:

In continuous mode:

In discontinuous mode:

The current at the limit between continuous and discontinuous mode is:

Therefore, the locus of the limit between continuous and discontinuous modes is given by:

These expression have been plotted in figure 6. From this, it is obvious that in continuous mode,

the output voltage does only depend on the duty cycle, whereas it is far more complex in the

discontinuous mode. This is important from a control point of view

Non ideal circuit

Fig: Evolution of the output voltage of a buck converter with the duty cycle when the

parasitic resistance of the inductor increases.

The previous study was conducted with the following assumptions:

The output capacitor has enough capacitance to supply power to the load (a simple

resistance) without any noticeable variation in its voltage.

The voltage drop across the diode when forward biased is zero

No commutation losses in the switch nor in the diode

These assumptions can be fairly far from reality, and the imperfections of the real components

can have a detrimental effect on the operation of the converter.

Output voltage ripple

Output voltage ripple is the name given to the phenomenon where the output voltage rises during

the On-state and falls during the Off-state. Several factors contribute to this including, but not

limited to, switching frequency, output capacitance, inductor, load and any current limiting

features of the control circuitry. At the most basic level the output voltage will rise and fall as a

result of the output capacitor charging and discharging:

During the Off-state, the current in this equation is the load current. In the On-state the current is

the difference between the switch current (or source current) and the load current. The duration

of time (dT) is defined by the duty cycle and by the switching frequency.

For the On-state:

For the Off-state:

Qualitatively, as the output capacitor or switching frequency increase, the magnitude of the

ripple decreases. Output voltage ripple is typically a design specification for the power supply

and is selected based on several factors. Capacitor selection is normally determined based on

cost, physical size and non-idealities of various capacitor types. Switching frequency selection is

typically determined based on efficiency requirements, which tends to decrease at higher

operating frequencies, as described below in Effects of non-ideality on the efficiency. Higher

switching frequency can also reduce efficiency and possibly raise EMI concerns.

Output voltage ripple is one of the disadvantages of a switching power supply, and can also be a

measure of its quality.

Effects of non-ideality on the efficiency

A simplified analysis of the buck converter, as described above, does not account for non-

idealities of the circuit components nor does it account for the required control circuitry. Power

losses due to the control circuitry are usually insignificant when compared with the losses in the

power devices (switches, diodes, inductors, etc.) The non-idealities of the power devices account

for the bulk of the power losses in the converter.

Both static and dynamic power losses occur in any switching regulator. Static power losses

include I2R(conduction) losses in the wires or PCB traces, as well as in the switches and

inductor, as in any electrical circuit. Dynamic power losses occur as a result of switching, such

as the charging and discharging of the switch gate, and are proportional to the switching

frequency.

It is useful to begin by calculating the duty cycle for a non-ideal buck converter, which is:

Where:

VSWITCH is the voltage drop on the power switch,

VSYNCHSW is the voltage drop on the synchronous switch or diode, and

VL is the voltage drop on the inductor.

The voltage drops described above are all static power losses which are dependent primarily on

DC current, and can therefore be easily calculated. For a transistor in saturation or a diode drop,

VSWITCH and VSYNCHSW may already be known, based on the properties of the selected device.

VSWITCH = ISWITCHRON = DIoRON

VSYNCHSW = ISYNCHSWRON = (1 − D)IoRON

VL = ILRDCR

where:

RON is the ON-resistance of each switch (RDSON for a MOSFET), and

RDCR is the DC resistance of the inductor.

The careful reader will note that the duty cycle equation is somewhat recursive. A rough analysis

can be made by first calculating the values VSWITCH and VSYNCHSW using the ideal duty cycle

equation.

Switch resistance, for components such as the power MOSFET, and forward voltage, for

components such as theinsulated-gate bipolar transistor (IGBT) can be determined by referring to

datasheet specifications.

In addition, power loss occurs as a result of leakage currents. This power loss is simply

PLEAKAGE = ILEAKAGEV

where:

ILEAKAGE is the leakage current of the switch, and

V is the voltage across the switch.

Dynamic power losses are due to the switching behavior of the selected pass devices

(MOSFETs, power transistors, IGBTs, etc.). These losses include turn-on and turn-off switching

losses and switch transition losses.

Switch turn-on and turn-off losses are easily lumped together as

where:

V is the voltage across the switch while the switch is off,

tRISE and tFALL are the switch rise and fall times, and

T is the switching period.

But this doesn't take into account the parasitic capacitance of the MOSFET which makes

the Miller plate. Then, the switch losses will be more like:

When a MOSFET is used for the lower switch, additional losses may occur during the time

between the turn-off of the high-side switch and the turn-on of the low-side switch, when the

body diode of the low-side MOSFET conducts the output current. This time, known as the non-

overlap time, prevents "shootthrough", a condition in which both switches are simultaneously

turned on. The onset of shootthrough generates severe power loss and heat. Proper selection of

non-overlap time must balance the risk of shootthrough with the increased power loss caused by

conduction of the body diode.

Power loss on the body diode is also proportional to switching frequency and is

PBODYDIODE = VFIotNOfSW

Where:

VF is the forward voltage of the body diode, and

tNO is the selected non-overlap time.

Finally, power losses occur as a result of the power required to turn the switches on and off.

For MOSFET switches, these losses are dominated by the gate charge, essentially the energy

required to charge and discharge the capacitance of the MOSFET gate between the threshold

voltage and the selected gate voltage. These switch transition losses occur primarily in the gate

driver, and can be minimized by selecting MOSFETs with low gate charge, by driving the

MOSFET gate to a lower voltage (at the cost of increased MOSFET conduction losses), or by

operating at a lower frequency.

PGATEDRIVE = QGVGSfSW

Where:

QG is the gate charge of the selected MOSFET, and

VGS is the peak gate-source voltage.

It is essential to remember that, for N-MOSFETs, the high-side switch must be driven to a higher

voltage than Vi. Therefore VG will nearly always be different for the high-side and low-side

switches.

A complete design for a buck converter includes a tradeoff analysis of the various power losses.

Designers balance these losses according to the expected uses of the finished design. A converter

expected to have a low switching frequency does not require switches with low gate transition

losses; a converter operating at a high duty cycle requires a low-side switch with low conduction

losses.

Specific structures

Synchronous rectification

Fig: Simplified schematic of a synchronous converter, in which D is replaced by a

second switch, S2

A synchronous buck converter is a modified version of the basic buck converter circuit

topology in which the diode, D, is replaced by a second switch, S 2. This modification is a

tradeoff between increased cost and improved efficiency.

In a standard buck converter, the freewheeling diode turns on, on its own, shortly after the switch

turns off, as a result of the rising voltage across the diode. This voltage drop across the diode

results in a power loss which is equal to

PD = VD(1 − D)Io

Where:

VD is the voltage drop across the diode at the load current Io,

D is the duty cycle, and

Io is the load current.

By replacing diode D with switch S2, which is advantageously selected for low losses, the

converter efficiency can be improved. For example, a MOSFET with very low RDSON might be

selected for S2, providing power loss on switch 2 which is

By comparing these equations the reader will note that in both cases, power loss is

strongly dependent on the duty cycle, D. It stands to reason that the power loss on the

freewheeling diode or lower switch will be proportional to its on-time. Therefore, systems

designed for low duty cycle operation will suffer from higher losses in the freewheeling diode or

lower switch, and for such systems it is advantageous to consider a synchronous buck converter

design.

Without actual numbers the reader will find the usefulness of this substitution to be

unclear. Consider a computer power supply, where the input is 5 V, the output is 3.3 V, and the

load current is 10A.

In this case, the duty cycle will be 66% and the diode would be on for 34% of the time. A

typical diode with forward voltage of 0.7 V would suffer a power loss of 2.38 W. A well-selected

MOSFET with RDSON of 0.015 Ω, however, would waste only 0.51 W in conduction loss. This

translates to improved efficiency and reduced heat loss.

Another advantage of the synchronous converter is that it is bi-directional, which lends

itself to applications requiring regenerative braking. When power is transferred in the "reverse"

direction, it acts much like a boost converter.

The advantages of the synchronous buck converter do not come without cost. First, the

lower switch typically costs more than the freewheeling diode. Second, the complexity of the

converter is vastly increased due to the need for a complementary-output switch driver.

Such a driver must prevent both switches from being turned on at the same time, a fault

known as "shootthrough." The simplest technique for avoiding shootthrough is a time delay

between the turn-off of S1 to the turn-on of S2, and vice versa. However, setting this time delay

long enough to ensure that S1 and S2 are never both on will itself result in excess power loss. An

improved technique for preventing this condition is known as adaptive "non-overlap" protection,

in which the voltage at the switch node (the point where S1, S2 and L are joined) is sensed to

determine its state. When the switch node voltage passes a preset threshold, the time delay is

started. The driver can thus adjust to many types of switches without the excessive power loss

this flexibility would cause with a fixed non-overlap time.

Multiphase buck

Fig: Schematic of a generic synchronous n-phase buck converter.

Fig: Closeup picture of a multiphase CPU power supply for an AMD Socket 939

processor. The three phases of this supply can be recognized by the three black toroidal

inductors in the foreground. The smaller inductor below the heat sink is part of an input

filter.

The multiphase buck converter is circuit topology where the basic buck converter circuit

are placed in parallel between the input and load. Each of the n "phases" is turned on at equally

spaced intervals over the switching period. This circuit is typically used with the synchronous

buck topology, described above.

The primary advantage of this type of converter is that it can respond to load changes as

quickly as if it switched at n times as fast, without the increase in switching losses that that

would cause. Thus, it can respond to rapidly changing loads, such as modern microprocessors.

There is also a significant decrease in switching ripple. Not only is there the decrease due

to the increased effective frequency, but any time that n times the duty cycle is an integer, the

switching ripple goes to 0; the rate at which the inductor current is increasing in the phases

which are switched on exactly matches the rate at which it is decreasing in the phases which are

switched off.

Another advantage is that the load current is split among the n phases of the multiphase

converter. This load splitting allows the heat losses on each of the switches to be spread across a

larger area.

This circuit topology is used in computer power supplies to convert the 12 VDC power

supply to a lower voltage (around 1 V), suitable for the CPU. Modern CPU power requirements

can exceed 200W, can change very rapidly, and have very tight ripple requirements, less than

10mV. Typical motherboard power supplies use 3 or 4 phases, although control IC

manufacturers allow as many as 6 phases.

One major challenge inherent in the multiphase converter is ensuring the load current is

balanced evenly across then phases. This current balancing can be performed in a number of

ways. Current can be measured "losslessly" by sensing the voltage across the inductor or the

lower switch (when it is turned on). This technique is considered lossless because it relies on

resistive losses inherent in the buck converter topology. Another technique is to insert a small

resistor in the circuit and measure the voltage across it. This approach is more accurate and

adjustable, but incurs several costs—space, efficiency and money.

Finally, the current can be measured at the input. Voltage can be measured losslessly, across the

upper switch, or using a power resistor, to approximate the current being drawn.

This approach is technically more challenging, since switching noise cannot be easily

filtered out. However, it is less expensive than emplacing a sense resistor for each phase.

EFFICIENCY FACTORS

Conduction losses that depend on load:

Resistance when the transistor or MOSFET switch is conducting.

Diode forward voltage drop (usually 0.7 V or 0.4 V for schottky diode)

Inductor winding resistance

Capacitor equivalent series resistance

Switching losses:

Voltage-Ampere overlap loss

Frequencyswitch*CV2 loss

Reverse latence loss

Losses due driving MOSFET gate and controller consumption. Transistor leakage current losses,

and controller standby consumption.

Impedance matching

A buck converter can be used to maximize the power transfer through the use of impedance

matching. An application of this is in a "maximum power point tracker" commonly used

in photovoltaic systems.

By the equation for electric power:

Where:

Vo is the output voltage

Io is the output current

η is the power efficiency (ranging from 0 to 1)

Vi is the input voltage

Ii is the input current

By Ohm's Law:

where:

Zo is the output impedance

Zi is the input impedance

Substituting these expressions for Io and Ii into the power equation yields:

As was previously shown for the continuous mode, (where IL > 0):

where: D is the duty cycle

Substituting this equation for Vo into the previous equation, yields:

which reduce to:

and finally:

This shows that it is possible to adjust the impedance ratio by adjusting the duty cycle. This is

particularly useful in applications where the impedance(s) are dynamically changing.

BOOST CONVERTER

A boost converter (step-up converter) is a power converter with an output DC voltage

greater than its input DC voltage. It is a class of switching-mode power supply

(SMPS) containing at least two semiconductor switches (a diode and a transistor) and at least

one energy storage element. Filters made of capacitors (sometimes in combination

with inductors) are normally added to the output of the converter to reduce output voltage ripple.

Power can also come from DC sources such as batteries, solar panels, rectifiers and DC

generators. A process that changes one DC voltage to a different DC voltage is called DC to DC

conversion. A boost converter is a DC to DC converter with an output voltage greater than the

source voltage. A boost converter is sometimes called a step-up converter since it “steps up” the

source voltage. Since power (P = VI or P = UI in Europe) must be conserved, the output current

is lower than the source current.

A boost converter may also be referred to as a 'Joule thief'. This term is usually used only

with very low power battery applications, and is aimed at the ability of a boost converter to 'steal'

the remaining energy in a battery. This energy would otherwise be wasted since a normal load

wouldn't be able to handle the battery's low voltage.*

This energy would otherwise remain untapped because in most low-frequency applications,

currents will not flow through a load without a significant difference of potential between the

two poles of the source (voltage.)

BLOCK DIAGRAM

The basic building blocks of a boost converter circuit are shown in Fig.

Fig. Block diagram

The voltage source provides the input DC voltage to the switch control, and to the magnetic field

storage element. The switch control directs the action of the switching element, while the output

rectifier and filter deliver an acceptable DC voltage to the output.

OPERATING PRINCIPLE

The key principle that drives the boost converter is the tendency of an inductor to resist

changes in current. When being charged it acts as a load and absorbs energy (somewhat like a

resistor), when being discharged, it acts as an energy source (somewhat like a battery). The

voltage it produces during the discharge phase is related to the rate of change of current, and not

to the original charging voltage, thus allowing different input and output voltages.

Fig: Boost converter schematic

Voltage

Source

MagneticField Storage

Switch Control

SwitchingElement

Output

Rectifier and

Fig. The two configurations of a boost converter, depending on the state of the switch S.

The basic principle of a Boost converter consists of 2 distinct states (see figure ):

in the On-state, the switch S (see figure) is closed, resulting in an increase in the inductor

current;

In the Off-state, the switch is open and the only path offered to inductor current is through

the flyback diode D, the capacitor C and the load R. This result in transferring the energy

accumulated during the On-state into the capacitor.

The input current is the same as the inductor current as can be seen in figure. So it is not

discontinuous as in the buck converter and the requirements on the input filter are relaxed

compared to a buck converter.

CONTINUOUS MODE

When a boost converter operates in continuous mode, the current through the inductor

(IL) never falls to zero. Figure shows the typical waveforms of currents and voltages in a

converter operating in this mode. The output voltage can be calculated as follows, in the case of

an ideal converter (i.e. using components with an ideal behavior) operating in steady conditions:

Fig: Waveforms of current and voltage in a boost converter operating in continuous mode.

During the On-state, the switch S is closed, which makes the input voltage (Vi) appear across the

inductor, which causes a change in current (IL) flowing through the inductor during a time period

(t) by the formula:

At the end of the On-state, the increase of IL is therefore:

D is the duty cycle. It represents the fraction of the commutation period T during which the

switch is on. Therefore D ranges between 0 (S is never on) and 1 (S is always on).

During the Off-state, the switch S is open, so the inductor current flows through the load. If we

consider zero voltage drop in the diode, and a capacitor large enough for its voltage to remain

constant, the evolution of IL is:

Therefore, the variation of IL during the Off-period is:

As we consider that the converter operates in steady-state conditions, the amount of energy

stored in each of its components has to be the same at the beginning and at the end of a

commutation cycle. In particular, the energy stored in the inductor is given by:

So, the inductor current has to be the same at the start and end of the commutation cycle. This

means the overall change in the current (the sum of the changes) is zero:

Substituting   and   by their expressions yields:

This can be written as:

Which in turns reveals the duty cycle to be

From the above expression it can be seen that the output voltage is always higher than the input

voltage (as the duty cycle goes from 0 to 1), and that it increases with D, theoretically to infinity

as D approaches 1. This is why this converter is sometimes referred to as a step-up converter.

DISCONTINUOUS MODE

In some cases, the amount of energy required by the load is small enough to be transferred in a

time smaller than the whole commutation period. In this case, the current through the inductor

falls to zero during part of the period.

The only difference in the principle described above is that the inductor is completely

discharged at the end of the commutation cycle (see waveforms in figure ). Although slight, the

difference has a strong effect on the output voltage equation. It can be calculated as follows:

Fig:Waveforms of current and voltage in a boost converter operating in discontinuous mode.

As the inductor current at the beginning of the cycle is zero, its maximum value   (at

t = DT) is

During the off-period, IL falls to zero after δT:

Using the two previous equations, δ is:

The load current Io is equal to the average diode current (ID). As can be seen on figure 4,

the diode current is equal to the inductor current during the off-state. Therefore the output current

can be written as:

Replacing ILmax and δ by their respective expressions yields:

Therefore, the output voltage gain can be written as flow:

Compared to the expression of the output voltage for the continuous mode, this expression is

much more complicated. Furthermore, in discontinuous operation, the output voltage gain not

only depends on the duty cycle, but also on the inductor value, the input voltage, the switching

frequency, and the output current.

APPLICATIONS:

Battery powered systems often stack cells in series to achieve higher voltage. However,

sufficient stacking of cells is not possible in many high voltage applications due to lack of space.

Boost converters can increase the voltage and reduce the number of cells. Two battery-powered

applications that use boost converters are hybrid electric vehicles (HEV) and lighting systems.

The NHW20 model Toyota Prius HEV uses a 500 V motor. Without a boost converter,

the Prius would need nearly 417 cells to power the motor. However, a Prius actually uses only

168 cells and boosts the battery voltage from 202 V to 500 V. Boost converters also power

devices at smaller scale applications, such as portable lighting systems. A white LED typically

requires 3.3 V to emit light, and a boost converter can step up the voltage from a single 1.5 V

alkaline cell to power the lamp. Boost converters can also produce higher voltages to

operate cold cathode fluorescent tubes (CCFL) in devices such as LCD backlights and

some flashlights.

BUCK-BOOST CONVERTER

Schematic for buck-boost converter

With continuous conduction for the Buck-Boost converter Vx =Vin when the

transistor is ON and Vx =Vo when the transistor is OFF. For zero net current

change over a period the average voltage across the inductor is zero

Waveforms for buck-boost converter

………….. (21)

Which gives the voltage ratio

………… (22)

And the corresponding current

……….. (23)

Since the duty ratio "D" is between 0 and 1 the output voltage can vary between

lower or higher than the input voltage in magnitude. The negative sign indicates a

reversal of sense of the output voltage.

 CONVERTER COMPARISON

The voltage ratios achievable by the DC-DC converters is summarised in Fig. 10.

Notice that only the buck converter shows a linear relationship between the control

(duty ratio) and output voltage. The buck-boost can reduce or increase the voltage

ratio with unit gain for a duty ratio of 50%.

Comparison of Voltage ratio

 

CUK CONVERTER

The buck, boost and buck-boost converters all transferred energy between input

and output using the inductor, analysis is based of voltage balance across the

inductor. The CUK converter uses capacitive energy transfer and analysis is based

on current balance of the capacitor. The circuit in Fig. below(CUK converter) is

derived from DUALITY principle on the buck-boost converter.

CUK Converter

If we assume that the current through the inductors is essentially ripple free we can

examine the charge balance for the capacitor C1. For the transistor ON the circuit

becomes

CUK "ON-STATE"

And the current in C1 is IL1. When the transistor is OFF, the diode conducts and the

current in C1 becomes IL2.

CUK "OFF-STATE"

Since the steady state assumes no net capacitor voltage rise ,the net current is zero

…………… (24)

which implies

…….. (25)

The inductor currents match the input and output currents, thus using the power

conservation rule

………… (26)

Thus the voltage ratio is the same as the buck-boost converter. The advantage of

the CUK converter is that the input and output inductors create a smooth current at

both sides of the converter while the buck, boost and buck-boost have at least one

side with pulsed current.

PULSE WIDTH MODULATION

Pulse Width Modulation (PWM) is the most effective means to achieve constant voltage

battery charging by switching the solar system controller’s power devices. When in PWM

regulation, the current from the solar array tapers according to the battery’s condition and

recharging needs .Consider a waveform such as this: it is a voltage switching between 0v and

12v. It is fairly obvious that, since the voltage is at 12v for exactly as long as it is at 0v, then a

'suitable device' connected to its output will see the average voltage and think it is being fed 6v -

exactly half of 12v. So by varying the width of the positive pulse - we can vary the 'average'

voltage.

Similarly, if the switches keep the voltage at 12 for 3 times as long as at 0v, the average

will be 3/4 of 12v - or 9v, as shown below

and if the output pulse of 12v lasts only 25% of the overall time, then the average is

By varying - or 'modulating' - the time that the output is at 12v (i.e. the width of the

positive pulse) we can alter the average voltage. So we are doing 'pulse width modulation'. I said

earlier that the output had to feed 'a suitable device'. A radio would not work from this: the radio

would see 12v then 0v, and would probably not work properly. However a device such as a

motor will respond to the average, so PWM is a natural for motor control.

PULSE WIDTH MODULATOR

So, how do we generate a PWM waveform? It's actually very easy, there are circuits

available in the TEC site. First you generate a triangle waveform as shown in the diagram below.

You compare this with a d.c voltage, which you adjust to control the ratio of on to off time that

you require. When the triangle is above the 'demand' voltage, the output goes high. When the

triangle is below the demand voltage, the

When the demand speed it in the middle (A) you get a 50:50 output, as in black. Half the

time the output is high and half the time it is low.

Fortunately, there is an IC (Integrated circuit) called a comparator: these come usually 4

sections in a single package. One can be used as the oscillator to produce the triangular

waveform and another to do the comparing, so a complete oscillator and modulator can be done

with half an IC and maybe 7 other bits.

The triangle waveform, which has approximately equal rise and fall slopes, is one of the

commonest used, but you can use a saw tooth (where the voltage falls quickly and rinses slowly).

You could use other waveforms and the exact linearity (how good the rise and fall are) is not too

important.

Traditional solenoid driver electronics rely on linear control, which is the application of a

constant voltage across a resistance to produce an output current that is directly proportional to

the voltage. Feedback can be used to achieve an output that matches exactly the control signal.

However, this scheme dissipates a lot of power as heat, and it is therefore very inefficient.

A more efficient technique employs pulse width modulation (PWM) to produce the

constant current through the coil. A PWM signal is not constant. Rather, the signal is on for part

of its period, and off for the rest. The duty cycle, D, refers to the percentage of the period for

which the signal is on. The duty cycle can be anywhere from 0, the signal is always off, to 1,

where the signal is constantly on. A 50% D results in a perfect square wave. (Figure 1)

A solenoid is a length of wire wound in a coil. Because of this configuration, the solenoid

has, in addition to its resistance, R, a certain inductance, L.

When a voltage, V, is applied across an inductive element, the current, I, produced in that

element do not jump up to its constant value, but gradually rises to its maximum over a period of

time called the rise time (Figure 2). Conversely, I do not disappear instantaneously, even if V is

removed abruptly, but decreases back to zero in the same amount of time as the rise time.

Therefore, when a low frequency PWM voltage is applied across a solenoid, the current

through it will be increasing and decreasing as V turns on and off. If D is shorter than the rise

time, I will never achieve its maximum value, and will be discontinuous since it will go back to

zero during V’s off period (Figure 3).* In contrast, if D is larger than the rise time, I will never

fall back to zero, so it will be continuous, and have a DC average value. The current will not be

constant, however, but will have a ripple (Figure 4).

At high frequencies, V turns on and off very quickly, regardless of D, such that the

current does not have time to decrease very far before the voltage is turned back on. The

resulting current through the solenoid is therefore considered to be constant. By adjusting the D,

the amount of output current can be controlled. With a small D, the current will not have much

time to rise before the high frequency PWM voltage takes effect and the current stays constant.

With a large D, the current will be able to rise higher before it becomes constant. (Figure 5)

Dither

Static friction, stiction, and hysteresis can cause the control of a hydraulic valve to be

erratic and unpredictable. Stiction can prevent the valve spool from moving with small input

changes, and hysteresis can cause the shift to be different for the same input signal. In order to

counteract the effects of stiction and hysteresis, small vibrations about the desired position are

created in the spool. This constantly breaks the static friction ensuring that it will move even

with small input changes, and the effects of hysteresis are average out.

Dither is a small ripple in the solenoid current that causes the desired vibration and there

by increases the linearity of the valve. The amplitude and frequency of the dither must be

carefully chosen. The amplitude must be large enough and the frequency slow enough that the

spool will respond, yet they must also be small and fast enough not to result in a pulsating

output.

The optimum dither must be chosen such that the problems of stiction and hysteresis are

overcome without new problems being created. Dither in the output current is a byproduct of low

frequency PWM, as seen above. However, the frequency and amplitude of the dither will be a

function of the duty cycle, which is also used to set the output current level. This means that low

frequency dither is not independent of current magnitude. The advantage of using high frequency

PWM is that dither can be generated separately, and then superimposed on top of the output

current.

This allows the user to independently set the current magnitude (by adjusting the D), as

well as the dither frequency and amplitude. The optimum dither, as set by the user, will therefore

be constant at all current levels.

WHY THE PWM FREQUENCY IS IMPORTANT:

The PWM is a large amplitude digital signal that swings from one voltage extreme to the

other. And, this wide voltage swing takes a lot of filtering to smooth out. When the PWM

frequency is close to the frequency of the waveform that you are generating, then any PWM

filter will also smooth out your generated waveform and drastically reduce its amplitude. So, a

good rule of thumb is to keep the PWM frequency much higher than the frequency of any

waveform you generate.

Finally, filtering pulses is not just about the pulse frequency but about the duty cycle and

how much energy is in the pulse. The same filter will do better on a low or high duty cycle pulse

compared to a 50% duty cycle pulse. Because the wider pulse has more time to integrate to a

stable filter voltage and the smaller pulse has less time to disturb it the inspiration was a request

to control the speed of a large positive displacement fuel pump. The pump was sized to allow full

power of a boosted engine in excess of 600 Hp.

At idle or highway cruise, this same engine needs far less fuel yet the pump still normally

supplies the same amount of fuel. As a result the fuel gets recycled back to the fuel tank,

unnecessarily heating the fuel. This PWM controller circuit is intended to run the pump at a low

speed setting during low power and allow full pump speed when needed at high engine power

levels.

MOTOR SPEED CONTROL (POWER CONTROL)

Typically when most of us think about controlling the speed of a DC motor we think of

varying the voltage to the motor. This is normally done with a variable resistor and provides a

limited useful range of operation. The operational range is limited for most applications

primarily because torque drops off faster than the voltage drops.

Most DC motors cannot effectively operate with a very low voltage. This method also

causes overheating of the coils and eventual failure of the motor if operated too slowly. Of

course, DC motors have had speed controllers based on varying voltage for years, but the range

of low speed operation had to stay above the failure zone described above.

Additionally, the controlling resistors are large and dissipate a large percentage of energy

in the form of heat. With the advent of solid state electronics in the 1950’s and 1960’s and this

technology becoming very affordable in the 1970’s & 80’s the use of pulse width modulation

(PWM) became much more practical. The basic concept is to keep the voltage at the full value

and simply vary the amount of time the voltage is applied to the motor windings. Most PWM

circuits use large transistors to simply allow power On & Off, like a very fast switch.

This sends a steady frequency of pulses into the motor windings. When full power is

needed one pulse ends just as the next pulse begins, 100% modulation. At lower power settings

the pulses are of shorter duration. When the pulse is on as long as it is off, the motor is operating

at 50% modulation. Several advantages of PWM are efficiency, wider operational range and

longer lived motors. All of these advantages result from keeping the voltage at full scale

resulting in current being limited to a safe limit for the windings.

PWM allows a very linear response in motor torque even down to low PWM% without

causing damage to the motor. Most motor manufacturers recommend PWM control rather than

the older voltage control method. PWM controllers can be operated at a wide range of

frequencies. In theory very high frequencies (greater than 20 kHz) will be less efficient than

lower frequencies (as low as 100 Hz) because of switching losses.

The large transistors used for this On/Off activity have resistance when flowing current, a

loss that exists at any frequency. These transistors also have a loss every time they “turn on” and

every time they “turn off”. So at very high frequencies, the “turn on/off” losses become much

more significant. For our purposes the circuit as designed is running at 526 Hz. Somewhat of an

arbitrary frequency, it works fine.

Depending on the motor used, there can be a hum from the motor at lower PWM%. If

objectionable the frequency can be changed to a much higher frequency above our normal

hearing level (>20,000Hz).

PWM CONTROLLER FEATURES:

This controller offers a basic “Hi Speed” and “Low Speed” setting and has the option to

use a “Progressive” increase between Low and Hi speed. Low Speed is set with a trim pot inside

the controller box. Normally when installing the controller, this speed will be set depending on

the minimum speed/load needed for the motor. Normally the controller keeps the motor at this

Lo Speed except when Progressive is used and when Hi Speed is commanded (see below). Low

Speed can vary anywhere from 0% PWM to 100%.

Progressive control is commanded by a 0-5 volt input signal. This starts to increase PWM

% from the low speed setting as the 0-5 volt signal climbs. This signal can be generated from a

throttle position sensor, a Mass Air Flow sensor, a Manifold Absolute Pressure sensor or any

other way the user wants to create a 0-5 volt signal. This function could be set to increase fuel

pump power as turbo boost starts to climb (MAP sensor). Or, if controlling a water injection

pump, Low Speed could be set at zero PWM% and as the TPS signal climbs it could increase

PWM%, effectively increasing water flow to the engine as engine load increases. This controller

could even be used as a secondary injector driver (several injectors could be driven in a batch

mode, hi impedance only); with Progressive control (0-100%) you could control their output for

fuel or water with the 0-5 volt signal.

Progressive control adds enormous flexibility to the use of this controller. Hi Speed is

that same as hard wiring the motor to a steady 12 volt DC source. The controller is providing

100% PWM, steady 12 volt DC power. Hi Speed is selected three different ways on this

controller: 1) Hi Speed is automatically selected for about one second when power goes on. This

gives the motor full torque at the start. If needed this time can be increased (The value of C1

would need to be increased). 2) High Speed can also be selected by applying 12 volts to the High

Speed signal wire. This gives Hi Speed regardless of the Progressive signal.

When the Progressive signal gets to approximately 4.5 volts, the circuit achieves 100%

PWM – Hi Speed.

How does this technology help:

The benefits noted above are technology driven. The more important question is how the PWM

Technology jumping from a 1970’s technology into the new millennium offers:

• Longer battery life:

– reducing the costs of the solar system

– reducing battery disposal problems

• More battery reserve capacity:

– increasing the reliability of the solar system

– reducing load disconnects

– Opportunity to reduce battery size to lower the system cost

• Greater user satisfaction:

– get more power when you need it for less money!!

SPACE VECTOR PWM

The Space Vector PWM generation module accepts modulation index commands and

generates the appropriate gate drive waveforms for each PWM cycle. This section describes the

operation and configuration of the SVPWM module.

A three-phase 2-level inverter with dc link configuration can have eight possible

switching states, which generates output voltage of the inverter. Each inverter switching state

generates a voltage Space Vector (V1 to V6 active vectors, V7 and V8 zero voltage vectors) in

the Space Vector plane (Figure: space vector diagram). The magnitude of each active vector

(V1to V6) is 2/3 Vdc (dc bus voltage).

The Space Vector PWM (SVPWM) module inputs modulation index commands

(U_Alpha and U_Beta) which are orthogonal signals (Alpha and Beta) as shown in Figure. The

gain characteristic of the SVPWM module is given in Figure . The vertical axis of Figure

represents the normalized peak motor phase voltage (V/Vdc) and the horizontal axis represents

the normalized modulation index (M).

The inverter fundamental line-to-line Rms output voltage (Vline) can be approximated (linear

range) by the following equation:

………….. (1)

Where dc bus voltage (Vdc) is in volts

SPACE VECTOR DIAGRAM

This document is the property of International Rectifier and may not be copied or

distributed without expressed consent

Transfer Characteristics

The maximum achievable modulation (Umag_L) in the linear operating range is given

by:

………….. (2)

Over modulation occurs when modulation Umag > Umag_L. This corresponds to the

condition where the voltage vector in (Figure: voltage vector rescaling) increases beyond the

hexagon boundary. Under such circumstance, the Space Vector PWM algorithm will rescale the

magnitude of the voltage vector to fit within the Hexagon limit. The magnitude of the voltage

vector is restricted within the Hexagon; however, the phase angle (θ) is always preserved. The

transfer gain (Figure: Transfer characteristics) of the PWM modulator reduces and becomes non-

linear in the over modulation region.

VOLTAGE VECTOR RESCALING

This document is the property of International Rectifier and may not be copied or

distributed without expressed consent.

PWM OPERATION

Upon receiving the modulation index commands (UAlpha and UBeta) the sub-module

SVPW M_Tm starts its calculations at the rising edge of the PWM Load signal. The SVPWM

_Tm module implements an algorithm that selects (based on sector determination) the active

space vectors (V1 to V6) being used and calculates the appropriate time duration (w.r.t. one

PWM cycle) for each active vector. The appropriated zero vectors are also being selected. The

SVPWM _Tm module consumes 11 clock cycles typically and 35 clock cycles (worst case Tr) in

over modulation cases. At the falling edge of nSYNC, a new set of Space Vector times and

vectors are readily available for actual PWM generation (PhaseU, PhaseV, PhaseW) by sub

module Pwm Generation. It is crucial to trigger pwm load at least 35 clock cycles prior to the

falling edge of nSYNC signal; otherwise new modulation commands will not be implemented at

the earliest PWM cycle.

The above Figures voltage vector rescaling illustrates the PWM waveforms for a voltage

vector locates in sector I of the Space Vector plane (shown in Figure). The gating pattern outputs

(PWMUH … PWMWL) include dead time insertion

3-PHASE SPACE VECTOR PWM

2-phase (6-step PWM) Space Vector PWM

PWM CARRIER PERIOD:

Input variable PwmCval controls the duration of a PWM cycle. It should be populated

by the system clock frequency (Clk) and Pwm frequency (PwmFreq) selection. The variable

should be calculated as:

……….. (3)

The input resolution of the Space Vector PWM modulator signals U_Alpha and U_Beta

is 16-bit signed integer. However, the actual PWM resolution (PwmCval) is limited by the

system clock frequency.

Dead time Insertion Logic Dead time is inserted at the output of the PWM Generation

Module. The resolution is 1 clock cycle or 30nsec at a 33.3 MHz clock and is the same as those

of the voltage command registers and the PWM carrier frequency register.

The dead time insertion logic chops off the high side commanded volt*seconds by the

amount of dead time and adds the same amount of volt*seconds to the low side signal. Thus, it

eliminates the complete high side turn on pulse if the commanded volt*seconds is less than the

programmed dead time.

DEAD TIME INSERTION

The dead time insertion logic inserts the programmed dead time between two high and

low side of the gate signals within a phase. The dead time register is also double buffered to

allow “on the fly” dead time change and control while PWM logic is inactive.

SYMMETRICAL AND ASYMMETRICAL MODE OPERATION

There are two modes of operation available for PWM waveform generation, namely the

Center Aligned Symmetrical PWM (Figure) and the Center Aligned Asymmetrical PWM

(Figure)The volt-sec can be changed every half a PWM cycle (Tpwm) since Pwm Load occurs

every half a PWM cycle (compare Figure :symmetrical pwm and Figure :asymmetrical PWM).

With Symmetrical PWM mode, the inverter voltage Config = 0), the inverter voltage can be

changed at two times the rate of the switching frequency. This will provide an increase in voltage

control bandwidth, however, at the expense of increased current harmonic

Asymmetrical PWM Mode

Three-Phase and Two-Phase Modulation

Three-phase and two-phase Space Vector PWM modulation options are provided for the

IRMCx203. The Volt-sec generated by the two PWM strategies are identical; however with 2-

phase modulation the switching losses can be reduced significantly, especially when high

switching frequency (>10Khz) is employed. Figure: three-phase and two phase modulation

shows the switching pattern for one PWM cycle when the voltage vector is inside sector 1

THREE PHASE AND TWO PHASE MODULATION

The field Two Phase PWM of the PWM Config write register group provides selection of

three-phase or two-phase modulation. The default setting is three-phase modulation. Successful

operation of two-phase modulation in the entire speed operating range will depend on hardware

configuration. If the gate driver employs a bootstrap power supply strategy, disoperation will

occur at low motor fundamental frequencies (< 2Hz) under two-phase modulation control.

SINUSOIDAL PULSE WIDTH MODULATION

In many industrial applications, Sinusoidal Pulse Width Modulation (SPWM), also called

Sine coded Pulse Width Modulation, is used to control the inverter output voltage. SPWM

maintains good performance of the drive in the entire range of operation between zero and 78

percent of the value that would be reached by square-wave operation. If the modulation index

exceeds this value, linear relationship between modulation index and output voltage is not

maintained and the over-modulation methods are required

SPACE VECTOR PULSE WIDTH MODULATION

A different approach to SPWM is based on the space vector representation of voltages in

the d, q plane. The d, q components are found by Park transform, where the total power, as well

as the impedance, remains unchanged.

Fig: space vector shows 8 space vectors in according to 8 switching positions of inverter,

V* is the phase-to-center voltage which is obtained by proper selection of adjacent vectors V1

and V2.

Inverter output voltage space vector

Determination of Switching times

The reference space vector V* is given by Equation (1), where T1, T2 are the intervals of

application of vector V1 and V2 respectively, and zero vectors V0 and V7 are selected for T0.

V* Tz = V1 *T1 + V2 *T2 + V0 *(T0/2) + V7 *(T0/2)……….(4)

SPACE VECTOR PULSE WIDTH MODULATION (CONTINUED)

Fig. below shows that the inverter switching state for the period T1 for vector V1 and for

vector V2, resulting switching patterns of each phase of inverter are shown in Fig. pulse pattern

of space vector PWM.

Inverter switching state for (a)V1, (b) V2

Pulse pattern of Space vector PWM

Comparison

In Fig:- comparison, U is the phase to- center voltage containing the triple order

harmonics that are generated by space vector PWM, and U1 is the sinusoidal reference voltage.

But the triple order harmonics are not appeared in the phase-to-phase voltage as well. This leads

to the higher modulation index compared to the SPWM.

COMPARISON OF SPWM AND SPACE VECTOR PWM

As mentioned above, SPWM only reaches to 78 percent of square wave operation, but the

amplitude of maximum possible voltage is 90 percent of square-wave in the case of space vector

PWM. The maximum phase-to-center voltage by sinusoidal and space vector

PWM are respectively

Vmax = Vdc/2 : Sinusoidal PWM

Vmax = Vdc/√3 : Space Vector PWM

Where, Vdc is DC-Link voltage.

This means that Space Vector PWM can produce about 15 percent higher than

Sinusoidal PWM in output voltage.

SVM PWM TECHNIQUE

The Pulse Width modulation technique permits to obtain three phase system voltages,

which can be applied to the controlled output. Space Vector Modulation (SVM) principle differs

from other PWM processes in the fact that all three drive signals for the inverter will be created

simultaneously. The implementation of SVM process in digital systems necessitates less

operation time and also less program memory.

The SVM algorithm is based on the principle of the space vector u*, which describes all

three output voltages ua, ub and uc :

u* = 2/3 . ( ua + a . ub + a2 . uc ) ………(5)

Where a = -1/2 + j . v3/2 We can distinguish six sectors limited by eight discrete vectors

u0…u7 (fig:- inverter output voltage space vector), which correspond to the 23 = 8 possible

switching states of the power switches of the inverter.

SPACE VECTOR MODULATION

The amplitude of u0 and u7 equals 0. The other vectors u1…u6 have the same amplitude

and are 60 degrees shifted.

By varying the relative on-switching time Tc of the different vectors, the space vector u*

and also the output voltages ua, ub and uc can be varied and is defined as:

ua = Re ( u* )

ub = Re ( u* . a-1)

uc = Re ( u* . a-2) …………(6)

During a switching period Tc and considering for example the first sector, the vectors u0,

u1 and u2 will be switched on alternatively.

DEFINITION OF THE SPACE VECTOR

Depending on the switching times t0, t1 and t2 the space vector u* is defined as:

u* = 1/Tc . ( t0 . u0 + t1 . u1 + t2 . u2 )

u* = t0 . u0 + t1 . u1 + t2 . u2

u* = t1 . u1 + t2 . u2 ………….. (7)

Where

t0 + t1 + t2 = Tc and

t0 + t1 + t2 = 1

t0, t1 and t2 are the relative values of the on switching times.

They are defined as: t1 = m . cos ( a + p/6)

t2 = m . sin a

t0 = 1 - t1 - t2

Their values are implemented in a table for a modulation factor m = 1. Then it will be

easy to calculate the space vector u* and the output voltages ua, ub and uc. The voltage vector

u* can be provided directly by the optimal vector control laws w1, vsa and vsb. In order to

generate the phase voltages ua, ub and uc corresponding to the desired voltage vector u* the

following SVM strategy is proposed.

MODELING OF CASE STUDY

Fig. I shows the conventional voltage-fed SZAC in with input and output not sharing the

ground, and operating in DCM. Fig. 2 shows the proposed voltage-fed q ZSAC in which the

components used are the same as those shown in Fig l. It consists of a Z-source network with

two inductors LI, L], two capacitors CI, C], two bidirectional switches SI, S2 which are

implemented by connection of two diodes, two IGBTs in anti parallel (common back-to-back), a

LC filter and a R load. In the same manner as the conventional SZAC, the q ZSAC has two types

of operation states: active stave and shoot-through state. The equivalent circuits of the two states

are shown in Figs. 3a and 3b. According to the q ZSAC topology shown in Fig. 2, the output

shares the same ground with the input. In addition, the input current is continuous due to

connecting inductor LI directly to the input. Therefore, the main differences between the ZSAC

and q ZSAC are

(1) The input voltage and the output voltage is sharing the same ground and

(2) The q ZSAC draws a continuous AC current from source or input side while the ZSAC draws

a discontinuous AC current. In general, the peak of input current in DCM which gives rise to the

device stress is higher than that in CCM. Moreover, the waveform of input current in CCM is

more sinusoidal than that in DCM. Fig. 4 shows the PWM control scheme for proposed system.

As shown in Fig. 4, D is an equivalent duty-ratio; T is a switching period.

CIRCUIT ANALYSIS

The q ZSAC has two operating states in one switching period: state I and state 2 as

shown in Figs. 3a and 3b, respectively. In state I as shown in Fig. 3(a), the time interval in this

state is (1-D)T; T is the switching period as shown in Fig. 4. In state 2 as shown in Fig. 3(b), the

time interval in this state is DT. In state I, SI is turned on and S2 is turned off as shown in Fig.

3(a). The time interval in this state is (1-D)T.

We can get

Fig3. Equivalent circuit of the proposed system (a) State I; (b) State 2

Fig.4. Duty ratio control of switches

Fig.5. Voltage gains versus duty cycle of q ZSAC.

In state 2, SI is turned off and S2 is turned on as shown in Fig. 3(b). The time interval in

this state is DT. We can get

From (1) and (2), we get the averaged equation

TABLE I

VOLTAGEOF THE CONVENTIONAL SZAC ANDTHE PROPOSED QZSAC

In steady-state, we get

Thus, we have

The voltage gains can be defined as

Where Kc1, Kc2 and K; are voltage gain of C1, C2 and output, respectively.

Fig. 5 shows the voltage gains versus the duty cycle, D. The output voltage gain K; and

Z-network capacitor C, voltage gain Kc have features the same as those presented in while the

capacitor voltage gains Ke2 is different from those presented in it clearly shows in Fig. 5 that

there are two operation regions. When duty cycle is less than 0.5, the output voltage and Z-

network capacitor C, voltage are boosted and in phase with the input voltage while the Z-

network capacitor C2voltage is bucked/boosted and in-phase with the input voltage. When duty

cycle is greater than 0.5, the output voltage and Z network capacitor C, voltage are bucked

/boosted and out-of phase with the input voltage while the Z-network capacitor C2 voltage is

boosted and out-of-phase with the input voltage. In summary, the voltage of the conventional

SZAC proposed in and the proposed qZSAC is shown in Table 1.

MATLAB

Matlab is a high-performance language for technical computing. It integrates

computation, visualization, and programming in an easy-to-use environment where problems and

solutions are expressed in familiar mathematical notation. Typical uses include Math and

computation Algorithm development Data acquisition Modeling, simulation, and prototyping

Data analysis, exploration, and visualization Scientific and engineering graphics Application

development, including graphical user interface building.

Matlab is an interactive system whose basic data element is an array that does not require

dimensioning. This allows you to solve many technical computing problems, especially those

with matrix and vector formulations, in a fraction of the time it would take to write a program in

a scalar no interactive language such as C or Fortran.

The name matlab stands for matrix laboratory. Matlab was originally written to provide

easy access to matrix software developed by the linpack and eispack projects. Today, matlab

engines incorporate the lapack and blas libraries, embedding the state of the art in software for

matrix computation.

Matlab has evolved over a period of years with input from many users. In university

environments, it is the standard instructional tool for introductory and advanced courses in

mathematics, engineering, and science. In industry, matlab is the tool of choice for high-

productivity research, development, and analysis.

Matlab features a family of add-on application-specific solutions called toolboxes. Very

important to most users of matlab, toolboxes allow you to learn and apply specialized

technology. Toolboxes are comprehensive collections of matlab functions (M-files) that extend

the matlab environment to solve particular classes of problems. Areas in which toolboxes are

available include signal processing, control systems, neural networks, fuzzy logic, wavelets,

simulation, and many others.

The matlab system consists of five main parts:

DEVELOPMENT ENVIRONMENT This is the set of tools and facilities that help you

use matlab functions and files. Many of these tools are graphical user interfaces. It includes the

matlab desktop and Command Window, a command history, an editor and debugger, and

browsers for viewing help, the workspace, files, and the search path.

THE MATLAB MATHEMATICAL FUNCTION LIBRARY This is a vast collection

of computational algorithms ranging from elementary functions, like sum, sine, cosine, and

complex arithmetic, to more sophisticated functions like matrix inverse, matrix eigen values,

Bessel functions, and fast Fourier transforms.

THE MATLAB LANGUAGE This is a high-level matrix/array language with control

flow statements, functions, data structures, input/output, and object-oriented programming

features. It allows both "programming in the small" to rapidly create quick and dirty throw-away

programs, and "programming in the large" to create large and complex application programs.

Matlab has extensive facilities for displaying vectors and matrices as graphs, as well as

annotating and printing these graphs.

It includes high-level functions for two-dimensional and three-dimensional data

visualization, image processing, animation, and presentation graphics. It also includes low-level

functions that allow you to fully customize the appearance of graphics as well as to build

complete graphical user interfaces on your matlab applications.

THE MATLAB APPLICATION PROGRAM INTERFACE (API) This is a library

that allows you to write C and Fortran programs that interact with matlab. It includes facilities

for calling routines from matlab (dynamic linking), calling matlab as a computational engine,

and for reading and writing MAT-files.

SIMULINK:

INTRODUCTION:

Simulink is a software add-on to matlab which is a mathematical tool developed by The

Math works,(http://www.mathworks.com) a company based in Natick. Matlab is powered by

extensive numerical analysis capability. Simulink is a tool used to visually program a dynamic

system (those governed by Differential equations) and look at results. Any logic circuit, or

control system for a dynamic system can be built by using standard building blocks available in

Simulink Libraries. Various toolboxes for different techniques, such as Fuzzy Logic, Neural

Networks, dsp, Statistics etc. are available with Simulink, which enhance the processing power

of the tool. The main advantage is the availability of templates / building blocks, which avoid the

necessity of typing code for small mathematical processes.

CONCEPT OF SIGNAL AND LOGIC FLOW:

In Simulink, data/information from various blocks are sent to another block by lines

connecting the relevant blocks. Signals can be generated and fed into blocks dynamic /

static).Data can be fed into functions. Data can then be dumped into sinks, which could be

scopes, displays or could be saved to a file.

Data can be connected from one block to another, can be branched, multiplexed etc. In

simulation, data is processed and transferred only at Discrete times, since all computers are

discrete systems. Thus, a simulation time step (otherwise called an integration time step) is

essential, and the selection of that step is determined by the fastest dynamics in the simulated

system.

Fig 4.1 Simulink library browser

CONNECTING BLOCKS:

fig 4.2 Connecting blocks

To connect blocks, left-click and drag the mouse from the output of one block to the input of another block.

SOURCES AND SINKS:

The sources library contains the sources of data/signals that one would use in a dynamic

system simulation. One may want to use a constant input, a sinusoidal wave, a step, a repeating

sequence such as a pulse train, a ramp etc. One may want to test disturbance effects, and can use

the random signal generator to simulate noise. The clock may be used to create a time index for

plotting purposes. The ground could be used to connect to any unused port, to avoid warning

messages indicating unconnected ports.

The sinks are blocks where signals are terminated or ultimately used. In most cases, we

would want to store the resulting data in a file, or a matrix of variables.

The data could be displayed or even stored to a file. the stop block could be used to stop

the simulation if the input to that block (the signal being sunk) is non-zero. Figure 3 shows the

available blocks in the sources and sinks libraries. Unused signals must be terminated, to prevent

warnings about unconnected signals.

fig 4.3 Sources and sinks

CONTINUOUS AND DISCRETE SYSTEMS:

All dynamic systems can be analyzed as continuous or discrete time systems. Simulink

allows you to represent these systems using transfer functions, integration blocks, delay blocks

etc.

Fig .continous and descrete systems

NON-LINEAR OPERATORS:

A main advantage of using tools such as Simulink is the ability to simulate non-linear

systems and arrive at results without having to solve analytically. It is very difficult to arrive at

an analytical solution for a system having non-linearities such as saturation, signup function,

limited slew rates etc. In Simulation, since systems are analyzed using iterations, non-linearities

are not a hindrance. One such could be a saturation block, to indicate a physical limitation on a

parameter, such as a voltage signal to a motor etc. Manual switches are useful when trying

simulations with different cases. Switches are the logical equivalent of if-then statements in

programming.

Fig . simulink blocks

MATHEMATICAL OPERATIONS:

Mathematical operators such as products, sum, logical operations such as and, or,

etc. .can be programmed along with the signal flow. Matrix multiplication becomes easy with the

matrix gain block. Trigonometric functions such as sin or tan inverse (at an) are also available.

Relational operators such as ‘equal to’, ‘greater than’ etc. can also be used in logic circuits.

Fig. Simulink math blocks

SIGNALS & DATA TRANSFER:

In complicated block diagrams, there may arise the need to transfer data from one portion

to another portion of the block. They may be in different subsystems. That signal could be

dumped into a goto block, which is used to send signals from one subsystem to another.

Multiplexing helps us remove clutter due to excessive connectors, and makes

matrix(column/row) visualization easier.

Fig. Signals and systems

MAKING SUBSYSTEMS

Drag a subsystem from the Simulink Library Browser and place it in the parent block

where you would like to hide the code. The type of subsystem depends on the purpose of the

block. In general one will use the standard subsystem but other subsystems can be chosen. For

instance, the subsystem can be a triggered block, which is enabled only when a trigger signal is

received.

Open (double click) the subsystem and create input / output PORTS, which transfer

signals into and out of the subsystem. The input and output ports are created by dragging them

from the Sources and Sinks directories respectively. When ports are created in the subsystem,

they automatically create ports on the external (parent) block. This allows for connecting the

appropriate signals from the parent block to the subsystem.

SETTING SIMULATION PARAMETERS:

Running a simulation in the computer always requires a numerical technique to solve a

differential equation. The system can be simulated as a continuous system or a discrete system

based on the blocks inside. The simulation start and stop time can be specified. In case of

variable step size, the smallest and largest step size can be specified. A Fixed step size is

recommended and it allows for indexing time to a precise number of points, thus controlling the

size of the data vector. Simulation step size must be decided based on the dynamics of the

system. A thermal process may warrant a step size of a few seconds, but a DC motor in the

system may be quite fast and may require a step size of a few milliseconds.

MATLAB DESIGN OF CASE STUDY

FIGURE:QUASI CONVENTIONAL

FIGURE:QUASI PROPOSED

FIGURE:QUASI PROPOSED GRAPHR

FIGURE:QUASI PROPOSED GRAPHR

SIMULATION RESULTS

Duty ratio control of switches.

Voltage gains versus duty cycle of conventional ZSAC

Voltage gains versus duty cycle of Proposed qZSAC

Simulation results of proposed qZSAC when D = 0.25.

Simulation results of proposed qZSAC when D = 0.7.

(a)

(b)

Simulation result input current when D = 0.25. (a) Conventional ZSAC in (b) Proposed qSZAC.

(a)

(b)

Simulation result input current when D = 0.7. (a) ConventionalZSAC (b) Proposed qSZAC.

FFT analysis of conventional ZSAC at D=0.25

FFT analysis of conventional ZSAC at D=0.7

FFT analysis of Proposed qSZAC at D=0.25

FFT analysis of Proposed qSZAC at D=0.7

PF versus duty cycle of Proposed qZSAC

CONCLUSION

A new family of single-phase ACIAC converter called single-phase quasi-Z-source

ACIAC converter (q ZSAC) has been presented in this paper. The proposed q ZSAC inherits all

the advantages of the traditional single-phase Z-source ac-ac converter (ZSAC), which can

realize buck-boost, reversing or maintaining phase angle. In addition, the proposed q ZSAC has

the unique advantages; namely that the input voltage and the output voltage are sharing the same

ground; the operation is in continuous current mode (CCM). The operating principles and

simulation results in comparison to that in conventional SZAC are presented. The experimental

results show that the proposed q ZSAC has a high efficiency, low harmonic distortion input

current and high input power factor.

REFERENCES

[I] X. P. Fang, Z. M. Qian, and F. Z. Peng, "Single-phase Z-source PWM AC-AC converters,"

IEEE Power Electronics Letters, Vol. 3, No.4, pp. 121-124,2005.

[2] Y. Tang, S. Xie and C. Zhang, "Z-source AC-AC converters solving commutation problem,"

IEEE Trans. Power Electron., Vol. 22, No. 6, pp. 2146-2154,2007.

[3] 1. 1-1. Youm and B. H. Kwon, "Switching technique for current-controlled ac-to-ac

converters," IEEE Trans. Ind. Electron., vol. 46, no. 2, pp. 309318, 1999.

[4] 1. Anderson, and F. Z. Peng, "Four quasi-Z-source inverters," in Proc. IEEE PC--SC '08,

2008, pp. 2743-2749.

[5] 1. Anderson, and F. Z. Peng, "A class of quasi-Z-source inverters," in Proc. IEEE lAS '08,

2008.

[6] Y. Li, J. Anderson, F. Z. Peng, and D. Liu, "Quasi-Z-source inverter for photovoltaic

systems," in Proc. IEEE APEC'09, 2009, pp. 918-924.

[7] 1. Park, H. Kim, T. Chun, E. Nho, H. Shin, and M. Chi, "Grid-connected PV system using a

qZ-source inverter," in Proc. IEEE APEC09, 2009, pp.925-929.

[8] D. Cao, and F. Z. Peng, "A family of Z-source and quasi-Z-source DCDC converter," in

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