Elec581 chapter 2 - fundamental elements of power eletronics

Chapter 2

Fundamental Elements of Power

Electronics

To understand the operation of electronic circuits, it is useful to

imagine that individual terminals have a potential level with

respect to a reference terminal.

The reference terminal is any convenient point chosen in a

circuit it is assumed to have zero electric potential.

The potential level of all other points is then measured with

respect to this zero reference.

2

IntroductionPotential level

Advanced Electric Machines and Drives

3Advanced Electric Machines and Drives

Potential level

Introduction

4

Voltage across some circuit elements


Sources

By definition, ideal ac and dc voltage sources have zero internal

impedance. We suppose that nothing that happens in a circuit

can modify these levels.

5



Potential across a switch

When a switch is open, the voltage across its terminals depends

exclusively upon the external elements that make up the circuit.

On the other hand, when the switch is closed the potential level

of both terminals.

This simple rule also applies to idealized transistors, thyristors and

diodes, because they behave like perfect switches

6



Potential across a resistor

If no current flows in a resistor. its terminals 3, 4 must be at the

same potential, because the IR drop is zero

On the other hand, if the resistor carries a current I, the IR drop

produces a corresponding potential difference between the

terminals.

The terminals of a coil are at the same potential only during

those moments when the current is not changing.

If the current varies, the potential difference is given by.

7



Potential across an inductance

The terminals of a capacitor are at the same potential only when

the capacitor is completely discharged.

the potential difference between the terminals remains

unchanged during those intervals when the current f is zero

8



Potential across an capacitor

A final rule regarding potential levels is worth remembering.

Unless we know otherwise. we assume the following initial

conditions:.

a) All currents in the circuit are zero and none are in the process

of changing.

b) All capacitors are discharged.

9



Initial Potential Level

A diode is an electronic device possessing two terminals,

respectively called anode (A) and cathode (K)

Although it has no moving parts, a diode acts like a high-speed

switch whose contacts open and close according to the following

rules:

10

The Diode and Diode Circuits

Diode


Rule 1. When no voltage is applied

across a diode. it acts like an open

switch. The circuit is therefore

open between terminals A and K

Rule 2. If we apply an inverse voltage

E2 across the diode so that the

anode is negative with respect to the

cathode, the diode continues to act

as an open switch. We say that the

diode is reverse biased.



Diode

Rule 3. If a momentary forward

voltage E1 of 0.7 V or more is

applied across the terminals so that

anode A is slightly positive with

respect to the cathode, the

terminals become short-circuited.

The diode acts like a closed switch

and a current I immediately begins

to flow from anode to cathode. We

say that the diode is forward biased.



Diode

Rule 3. In practice, while the diode

conducts, a small voltage drop

appears across its terminals.

However, the voltage drop has an

upper value of about 1.5V, so it can

be neglected in most electronic

circuits. It is precisely because the

voltage drop is small with respect

to other circuit voltages that we can

assume the diode is essentially a

closed switch when it conducts.



Diode

Rule 4. As long as current flows,

the diode acts like a closed switch.

However, if it stops flowing for

even as little as 10 µs, the ideal

diode immediately returns to its

original open state



Diode

Diodes have many applications, some of which are found

again and again, in one form or another, in electronic power.

15

Diode circuit- Battery charger circuit with series resistor



Circuit Waveforms

16

Diode circuit- Battery charger circuit with series inductor



WaveformsCircuit

17

Diode circuit- Single phase rectifier



CircuitWaveforms

The rectifier circuits we have studied so far produce pulsating

voltages and currents.

In some types of loads, we cannot tolerate such pulsations, and filters

must be used to smooth out the valleys and peaks.

The basic purpose of a dc filter is to produce a smooth power flow

into a load.

Consequently, a filter must absorb energy whenever the dc voltage

or current tends to rise, and it must release energy whenever the

voltage or current tends to fall.

In this way the filter tends to maintain a constant voltage and current

in the load.

18


Filters


The most common filters are

inductors and capacitors.

Inductors store energy in their

magnetic field. They tend to maintain

a constant current; consequently. they

are placed in series with the load.

Capacitors store energy in their

electric field. They tend to maintain a

constant voltage; consequently, they

are placed in parallel with the load

19


Filters


Circuits

The greater the amount of energy stored in the filter, the better is the

filtering action. In the case of a bridge rectifier using an inductor, the

peak-to-peak ripple in percent is given by:

ripple peak-to-peak current as a percent of the dc current [%]

WL = dc energy stored in the smoothing inductor [J]

P = dc power drawn by the load [W]

f = frequency of the source [Hz]

20


Filters


We wish to build a 135 V, 20 A dc power supply using a single-phase

bridge rectifier and an inductive filter. The peak-to-peak current ripple

should be about 10%. If a 60 Hz ac source is available, calculate the

following:

a) The effective value of the ac voltage

b) The energy stored in the inductor

c) The inductance of the inductor

d) The peak-to-peak current ripple

21


Exercise


An example of a 3-phase rectifier composed of 3 diodes connected

in series with the secondary windings of a 3-phase, delta-wye

transformer is shown in the following figure.

The line-to-neutral voltage has a peak value Em. A filter inductance

L is connected in series with the load, so that current Id remains

essentially ripple-free.

22


Three phase rectifier


Circuit



Waveforms




The sudden switch over from one diode to another called

commutation. When the switchover takes place automatically, it is

called natural commutation, or line commutation because it is the line

voltage that forces the transfer of current from one diode to the

next.

Voltage EKN across the load and inductor pulsates between 0.5 and

Em. The ripple voltage is therefore smaller than that produced by a

single-phase bridge rectifier. Moreover, the fundamental ripple

frequency is three times the supply frequency, which makes it easier

to achieve good filtering.


Consider the circuit of a 3-phase rectifier

The 6 diodes constitute what is called a 3-phase, 6-pulse rectifier.

It is called 6-pulse because the currents flowing in the 6 diodes

start at 6 different moments during each cycle of the line

frequency. However, each diode still conducts for only 120°.


Three-phase, 6-pulse rectifier

Circuit







Waveforms


The average dc output voltage is given by

The approximate peak-to-peak current ripple in percent is given

by




A 3-phase bridge rectifier has to supply power to a 360 kW, 240

V dc load. If a 600 V, 3-phase, 60 Hz feeder is available, calculate

the following:

a) Voltage rating of the 3-phase transformer

b) DC current per diode

c) PIV across each diode

d) Peak-to-peak ripple in the output voltage and its frequency

e) Calculate the inductance of the smoothing choke required, if the

peak-to-peak ripple in the current is not to exceed 5 percent.

29


Exercise


A thyristor is an electronic switch, similar to a diode, but wherein

the instant of conduction can be controlled. Like a diode, a

thyristor possesses an anode and a cathode, plus a third terminal

called a gate.

To initiate conduction, two conditions have to be met:

30

The Thyristor and Thyristor Circuits

What is a thyristor?

a) The anode must be positive.

b) A current must flow into the gate for at least a

few microseconds. In practice, the current is

injected by applying a short positive voltage pulse

to the gate


As soon as conduction starts, the gate loses all further control.

Conduction will only stop when anode current I falls to zero,

after which the gate again exerts control.

Basically, a thyristor behaves the same way a diode does except

that the gate enables us to initiate conduction precisely when we

want to.

This enables us not only to convert ac power into dc power, but

also to do the reverse: convert dc power into ac power.

31




As soon as conduction starts, the gate loses all further control.

Conduction will only stop when anode current I falls to zero,

after which the gate again exerts control.

Basically, a thyristor behaves the same way a diode does except

that the gate enables us to initiate conduction precisely when we

want to.

This enables us not only to convert ac power into dc power, but

also to do the reverse: convert dc power into ac power.



Advanced Electric Machines and Drives32

Consider the circuit of a thyristor and a resistor connected in

series across an ac source. A number of short positive pulses Eg

is applied to the gate, of sufficient amplitude to initiate

conduction, provided the anode is positive. These pulses may be

generated by a manual switch or an electronic control circuit.



Principle of gate firing



Principle of gate firing

When a voltage pulse is applied to the gate, a certain gate current

flows. Because the pulses last only a few microseconds, the

average power supplied to the gate is very small, in comparison

to the average power supplied to the load.

The ratio of the two powers, called power gain, may exceed one

million. Thus, an average gate input of only I W may control a

load of 1000 k W.

An SCR does not, of course, have the magical property of

turning one watt into a million watts. The large power actually

comes from an appropriate power source, and the SCR gate only

serves to control the power flow.



Power gain of thyristor


A thyristor ceases to conduct and the gate regains control only

after the anode current falls to zero.

The current may cease flowing quite naturally at the end of each

cycle or we can force it to zero artificially. Such forced commutation

is required in some circuits where the anode current has to be

interrupted at a specific instant.

The availability of GTOs, MOSFETs, and IGBTs has largely

eliminated the need to use thyristors in such force-com mutated

applications. For this reason, in the following discussion of

thyristor power circuits, we consider only those involving line

commutation.


Current interruption and forced commutation

Consider a circuit in which a thyristor and a load

resistor R are connected in series across a dc source

E.

If we apply a single positive pulse to the gate, the

resulting dc load current I will flow indefinitely

thereafter.

We can stop conduction in the SCR in one of 3 ways:

a) Momentarily reduce the dc supply voltage E to zero.

b) Open the load circuit by means of a switch.

c) Force the anode current to zero for a brief period.




Another technique consists of using 2 thyristors.

A load R can be switched on and off by alternately firing

thyristors Q 1 and Q2.




Basic thyristor power circuits

Thyristors are used in many different ways.

However, in power electronics, six basic circuits cover about 90

percent of all industrial applications. These circuits, and some of

their applications, are:

1. Controlled rectifier supplying a passive load

2. Controlled rectifier supplying an active load

3. Line-commutated inverter supplying an active ac load

4. AC static switch

5. Cycloconverter

6. Three-phase converter



By definition, a passive load is one that

contains no inherent source of energy

(i.e., the resistor).

The following figure shows a resistive

load and a thyristor connected in series

across a single-phase source. The source

produces a sinusoidal voltage having a

peak value Em.

The gate pulses are synchronized with

the line frequency and, in our example.

they are delayed by an angle of 90°.

40


Controlled rectifier supplying a passive load


It is seen that the current lags behind the voltage because it only

flows during the final 90.

This lag produces the same effect as an inductive load.

Consequently, the ac source has to supply reactive power Q in

addition to the active power P.

If the SCR is triggered at zero degrees (the start of the cycle), no

reactive power is absorbed by the rectifier.


Controlled rectifier supplying a passive load


The following figure shows an ac source

Em and a dc load connected by an SCR

in series with an inductor.

The load (represented by a battery)

receives energy because when the

thyristor conducts, current I enters the

positive terminal.

Smoothing inductor L limits the peak

current to a value within the SCR rating.

Gate pulses Eg initiate conduction at an

angle θ1


Controlled rectifier supplying an active load


Using terminal 1 as a zero reference potential, it follows that the

potential of terminal 2 lies Ed volts above it.

Furthermore, the potential of terminal A oscillates sinusoidally

above and below the level of terminal 1.

If the SCR were replaced by a diode, conduction would begin at

angle θ0 because this is the instant when the anode becomes

positive.

In our example, conduction only begins when the gate is fired at

θ1 degrees.

43


Controlled rectifier supplying an active load


An inverter, by definition, changes dc power into ac power. It

performs the reverse operation of a rectifier, which converts ac

power into dc power. There are two main types of inverters:

1. Self-commutated inverters (also called force commutated inverters) in

which the commutation means are included within the power

inverter

2. Line-commutated inverters, wherein commutation is effected by

virtue of the line voltages on the ac side of the inverter


Line-commutated inverter


In this chapter we examine the operating principle of a line-

commutated inverter.

The circuit of such an inverter is identical to that of a controlled

rectifier, except that the battery terminals are reversed.

45


Line-commutated inverter


46

An ac static switch is composed of two

thyristors connected in anti parallel (back-

to-back), so that current can flow in both

directions.

The ac current flowing in the load resistor

R can be precisely controlled by varying the

phase angle α of gates g1 and g2. Thus, if

the gate pulses are synchronized with the

line frequency, a greater or lesser ac current

will flow in the load.


AC static switch


However, such delayed firing will draw reactive power from the

line, even if the load is purely resistive. The reason is that the

current is displaced behind the voltage.

If the gates are fired at 0° and 180° respectively, the static switch

is in the fully closed position.

On the other hand, if neither gate is fired, the switch is in the

open position.

Thus, a static switch ca n be used to replace a magnetic

contactor.

In contrast to magnetic contactors, an electronic contactor is

absolutely silent and its contacts never wear out.

47


AC static switch


A cycloconverter produces low-frequency ac power directly from

a higher-frequency ac source.

A simple cycloconverter is shown in the following figure

48


Cycloconverter


It consists of three groups of thyristors, mounted back-to-back

and connected to a 3-phase source. They jointly supply single-

phase power to a resistive load R.

49


Cycloconverter


Suppose all thyristors are initially blocked

Then, for an interval T, the gates of thyristors Q1, Q2, and Q3 are

triggered by 4 successive pulses g1, g2, g3, g1, in such a way that

the thyristors function as if they were ordinary diodes.



Cycloconverter

During the next interval T, thyristors Q4, Q5, Q6, are fired by 4

similar pulses g4, g5, g6, g4. This makes terminal 4 negative with

respect to N. The firing process is then repeated for the Q1, Q2, Q3

thyristors, and so on.



Cycloconverter

Compared to a sine wave, the low-frequency waveshape is rather

poor. It is flat-topped and contains a large 180 Hz ripple when

the 3-phase frequency is 60 Hz.

Assuming a 60 Hz source, we can show that each half-cycle

corresponds to 540º on a 60 Hz base. The duration of T is,

therefore, (540/360)x(1/60) =0.025s, which corresponds to a

frequency of 1/(2 x 0.025) = 20 Hz.



Cycloconverter

Obviously, by repeating the firing sequence g1, g2, g3, g1, ... , we

could keep terminal 4 positive for as long as we wish, followed

by an equally long negative period, when g4, g5, g6, g4 ... are fired.

In this way we can generate frequencies as low as we want.

This cycloconverter can supply a single-phase load from a 3-

phase system, without unbalancing the 3-phase lines.

53


Cycloconverter


The 3-phase, 6-pulse thyristor converter is one of the most

widely used rectifier/inverter units in power electronics.

Three-phase, 6-pulse converters have 6 thyristors connected to

the secondary winding of a 3-phase transformer


3-phase, 6-pulse controllable converter


Because we can initiate conduction whenever we want, the

thyristors enable us to vary the dc output voltage when the

converter operates in the rectifier mode.

The converter can also function as an inverter, provided that a

dc source is used in place of the load resistor R.




56

The converter is fed from a 3-phase transformer. The gates of

thyristors Q1 to Q6 are triggered in succession at 60-degree intervals.

The load is represented by a resistor in series with an inductor L.

The inductor is assumed to have a very large inductance, so that the

load current Id remains constant.

The two thyristors Q1, Q5 are conducting. A moment later, the

thyristors Q2, Q4 conduct. The other thyristors are similarly switched,

in sequence. When these steps have been completed, the entire

switching cycle repeats.

The switching sequence is similar to that of the diode bridge rectifier




57




58




Delayed triggering - rectifier mode





60





Exercise

The 3-phase converter of the following figure is connected to a

3-phase 480V, 60 Hz source. The load consists of a 500 V dc

source having an internal resistance of 2Ω. Calculate the power

supplied to the load for triggering delays of (a) ]5° and (b) 75°.


If triggering is delayed by more than 90°, the voltage Ed

developed by the converter becomes negative.

This does not produce a negative current because SCRs conduct

in only one direction. Consequently, the load current is simply

zero.

62

Delayed triggering – inverter mode


Triggering

sequence and

waveforms

with a delay

angle of 105°.


However, we can force a current to flow by connecting a dc

voltage of proper magnitude and polarity across the converter

terminals. This external voltage E0 must be slightly greater than

Ed in order for current to flow.

The load current is given by



Because current flows out of the positive terminal of E0, the load

is actually a source, delivering a power output P= E0Id.

Part of this power is dissipated as heat in the circuit resistance R

and the remainder is delivered to the secondaries of the 3-phase

transformer.

64




The original rectifier has now become an inverter, converting dc

power into ac power. The transition from rectifier to inverter is

smooth, and requires no change in the converter connections.

In the rectifier mode, the firing angle lies between 0° and 90°,

and the load may be active or passive. In the inverter mode, the

firing angle lies between 90° and 180°, and a dc source of proper

polarity must be provided.

65




Semiconductor switches

Apart from their important gate

turn-off feature, GTOs are very

similar to ordinary thyristors. The

characteristics of both these

devices in the on and off states are

illustrated in the following figures.

Thus, in the off state, when the

current is zero the thyristor can

withstand both forward and

reverse blocking voltages EAK, up

to the maximum limits bounded

by the cross-hatched bands

66

Thyristor and GTO Basic Characteristics


67


During the on state, when the

thyristor conducts, the figure

shows that the EAK voltage drop is

about 2 V, and the upper limit of

the anode current IAK is again

indicated by the crosshatched

band. These bands merely indicate

the broad-brush maximum values

that are currently available.



68


The figure shows that GTOs are able

to withstand forward voltages but not

reverse blocking voltages.

Furthermore, the voltage drop is

about 3 V compared to 2 V for

thyristors.

As in the case of a thyristor,

conduction in a GTO is initiated by

injecting a positive current pulse into

the gate. In order to keep conducting,

the anode current must not fall below

the holding current of the GTO.




However, the GTO is a device in

which the anode current can be

blocked by injecting a strong negative

current into the base for a few

microseconds. To ensure extinction,

the amplitude of the gate pulse has to

be about one third the value of the

anode current.

GTOs are high-power switches, some

of which can handle currents of

several thousand amperes at voltages

of up to 4000 V.



70


The transistor has three terminals

named collector C, emitter E, and

base B.

BJT Basic Characteristics

The collector current IC that flows from collector to emitter is

initiated and maintained by causing a sustained current IB to flow

into the base. When operated as a switch, the base current must be

large enough to drive the BJT into conduction.


71


Under these conditions, the voltage

between the collector and emitter is

about 2 to 3 volts, at rated collector

current. Conduction ceases as soon as

the base current is suppressed.


The characteristics of the BJT in the on and off states are shown in

the upper figure. together with the approximate limits of the

collector-emitter voltage ECE and collector current Ic. Note that the

transistor cannot tolerate negative values of ECE. Power transistors

can carry currents of several hundred amperes and withstand ECE

voltages of about 1kV. To establish collector currents of 100A the

corresponding base current is typically about 1A.


72


The power MOSFET is a

voltage-controlled three-terminal

device having an anode and

cathode, respectively called drain

D, source S, and gate G.

MOSFET Basic Characteristics

The drain current ID is initiated by applying and maintaining a

voltage EGS of about 12V between the gate and the source.

Conduction stops whenever EGS falls below a threshold limit

(about 1 V).


73


The gate currents are extremely

small; consequently, very little power

is needed to drive this electronic

switch. The characteristics in the on

and off states are shown in the

following figure, together with

typical maximum


limits of drain voltage EDS and drain current ID.

The MOSFET cannot tolerate negative values of EDS To meet this

requirement. it has incorporated within it a reverse-biased diode, as

shown in the symbol for the device.


74


Power MOSFETs can carry

drain currents of about a

hundred amperes and withstand

ECE voltages of about 500 V. At

rated current, when driven into

saturation, the EDS voltage drop

ranges from about 2 V to 5 V.



75


The IGBT is also a voltage-

controlled switch whose terminals

are identified the same way as those

in a transistor, namely collector.

emitter, and base. The characteristics

in the on and off states are shown in

the following figure together with

the limiting voltages and current.

The collector current in an IGBT is

much higher than in a MOSFET.

Consequently, the IGBT can handle

more power.

IGBT Basic Characteristics


Compared to GTOs, an important feature of BJTs, MOSFETs,

and IGBTs is their fast turn-on and turn-off times. This enables

these switches to be used at much higher frequencies. As a result,

the associated transformers. inductors, and capacitors are smaller

and cheaper. Typical maximum frequencies are shown in Figs.

The following. Another advantage of high-speed switching is

that the semiconductor switches can generate lower-frequency

voltages and currents whose waveshapes and phase can be

tailored to meet almost any requirement.

76




77

In some power systems there is a need to transform DC power

from one DC voltage level to either a higher or lower dc level.

In alternating current systems the voltage step-up or step-down

can easily be done with a transformer.

In DC systems, an entirely different approach is required. It

involves the use of a dc-to-dc switching converter.

sometimes called a chopper.




DC-to-DC Switching Converter

Suppose that power has to be transferred from a high-voltage dc

source Es to a lower-voltage dc load E0.

One solution is to connect an inductor between the source and

the load and to open and close the circuit periodically with a

switch





When the switch is closed, the voltage across the inductor is

eL=ES-E0.

The inductor accumulates volt-seconds, and the resulting current

i increases at a constant rate given by:

After time T1, the current is:

The corresponding magnetic energy stored in the inductor is

80

81

When the switch opens the current collapses and all the stored

energy is dissipated in the arc across the switch. At the same

time, a high voltage eL is induced across the inductor because the

current is collapsing so quickly.

The polarity of this voltage is opposite to what it was when the

current was increasing.

The high negative voltage indicates that the inductor is rapidly

discharging the volt-seconds it had previously accumulated. As a

result, the current decreases very quickly.



82

We can prevent the energy loss every time the switch opens and

closes by adding a diode to the circuit.

When the switch closes, the current rises to Ia as before. The

diode has no effect because its cathode is positive with respect to

the anode and so the diode does not conduct. When the switch

opens, current i again begins to fall, inducing a voltage eL.

The current eventually becomes zero after a time T2. We can

calculate T2 because the volt-seconds accumulated during the

charging period T1 must equal the volt-seconds released during

the discharge interval Referring



83




When the current is zero, the inductor will have delivered all its

stored energy to load E0. Simultaneously, the diode will cease to

conduct. We can therefore reclose the switch for another interval

T1 and repeat the cycle indefinitely.

Consequently, this circuit enables us to transfer energy from a

high voltage dc source to a lower-voltage dc load without

incurring any losses.

In effect, the inductor absorbs energy at a relatively high voltage

(ES-E0) and delivers it at a lower voltage E0.



The diode is sometimes called a freewheeling diode because it

automatically starts conducting as soon as the switch opens and

stops conducting when the switch closes.

The switch is actually a GTO, MOSFET, or IGBT, whose

on/off state is controlled by a signal applied to the gate. The

combination of the electronic switch, inductor, and diode

constitutes what is known as a step-down dc-to-dc converter, or

buck chopper.



Referring to the following figure, the switch is closed for an

interval Ta and open during an interval Tb.

When the switch is open, the load current falls from its peak

value Ia to a lower value Ib.

During this interval, current flows in the inductor, the load, and

the freewheeling diode.



When the current has fallen to a value Ib, the switch recloses.

Because the cathode of the diode is now (+), the current in the

diode immediately stops flowing, and the source now supplies

current Ia. The current then builds up and when it reaches the

value Ia (after a time Ta ), the switch reopens.

The freewheeling diode comes into play and the cycle repeats.



The current supplied to the load fluctuates between Ia and Ib. Its

average or DC value I0 is given by:

The average current Is during one cycle (time T) is:

That is,



Turning our attention to the power aspects, the de power drawn

from the source must equal the dc power absorbed by the load

because, ideally, there is no power loss in the switch, the

inductor, or the freewheeling diode. We can, therefore, write:

E0 can be controlled simply by varying the duty cycle D. Thus,

the converter behaves like a highly efficient DC transformer in

which the "turns ratio" is D.



For a given switching frequency, this ratio can be changed as

needed by varying the on time of the switch.

In practice, the mechanical switch is replaced by an electronic

switch, such as an IGBT. It can be turned on and off at a

frequency that may be as high as 50 kHz.

If more power is required. a OTO is used, wherein the frequency

could be of the order of 300 Hz.


Exercise1

The switch in the figure below opens and closes at a frequency

of 20 Hz and remains closed for 3ms per cycle. A dc ammeter

connected in series with the load E0 indicates a current of 70 A.

a) If a dc ammeter is connected in series with the source. what

current will it indicate?

b) What is the average current per pulse?


92

Exercise2

We wish to charge a 120 V battery from a 600 V dc source using a

dc chopper. The average battery current should be 20 A, with a

peak-to-peak ripple of 2 A. If the chopper frequency is 200 Hz,

calculate the following:

a) The dc current drawn from the source

b) The duty cycle

c) The inductance of the inductor


Basic 2-quadrant dc-to-dc converter

Consider the following figure in which two

mechanical switches S1 to S2 are connected across

a dc voltage source EH .

The switches open and close alternately in such a

way that when S1 is closed, S2 is open and vice

versa.

The time of one cycle is T, and S1 is closed for a

period Ta

It follows that the duty cycle of S1 is D = Ta/T,

while that of S2 is (1-D).



When S1 is closed, EL=E12=EH

When S2 is closed, E12=0.

The output voltage oscillates,

therefore, between EH and zero and

its average dc value E1 is given by

By varying D from zero to 1, we

can vary the magnitude of EL from

zero to EH



Suppose we want to transfer dc power from terminals E12 to a

load such as a battery, whose dc voltage E52 has a value E0

An inductor is used as filter

We assume that the load has a small internal resistance R.

Suppose that both the voltage source EH and the duty cycle D

are fixed. Consequently, the dc component EL between points 1

and 2 is constant.



If E0 is less than EL, a dc current IL will flow from terminal 1 into

terminal 5. Its magnitude is given by

In this mode of operation, with less than EL , the converter acts

like the step-down (buck) chopper.

On the other hand, if E0 is greater than EL , a dc current IL will

flow out of terminal 5 and into terminal 1.

Its magnitude is:

Power now flows from the low-voltage battery side E0 to the

higher voltage side EH.

In this mode of operation, with E0 greater than EL, the converter

acts like a step-up (boost) chopper


Four-quadrant dc-to-dc converter

A four quadrant converter consists of two identical 2-quadrant

converters arranged as shown in the following figure.

Switches Q1, Q2 in converter arm A open and close alternately,

as do switches Q3, Q4 in converter arm B.

The switching frequency (assumed to be 100 kHz) is the same

for both.



The switching sequence is such that Q1 and Q4 open and close

simultaneously.

Similarly, Q2 and Q3 open and close simultaneously.

Consequently, if the duty cycle for Q1 is D, it will also be D for Q4.

It follows that the duty cycle for Q2 and Q3 is (1 - D).



The dc voltage appearing between terminals A, 2 is given by

The dc voltage EB, between terminals B, 2 is

The dc voltage EB between terminals A and B is the difference

between EA and EB,:

thus



the dc voltage is zero when D is 0.5. Furthermore, the voltage

changes linearly with D, becoming + EH when D = I, and –EH

when D = O.

The polarity of the output voltage can therefore be either

positive or negative.

Moreover, if a device is connected between terminals A, B, the

direction of dc current flow can be either from A to B or from B

to A.



The following figure shows the wave shape when D =0.5



102

The following figure shows the wave shape when D =0.8


All semiconductor switches such as GTOs, MOSFETs, and

IGBTs have losses that affect their temperature rise and switching

efficiency. The switches all function essentially the same way, but

to focus our analysis we assume the switching device is a GTO.

The switching operation involves four brief intervals:

Turn-On time T1

On-state time T2

Turn-off time T3

Off-state time T4

The sum of T1 + T2 + T3 + T4 is equal to the period T of one

cycle which, in turn, is equal to fc where fc is the switching

frequency.

Switching losses


Switching losses

During each interval the instantaneous power dissipated in the

GTO is equal to the product of the instantaneous voltage across

it times the instantaneous current that flows through it.

The average power is equal to the energy dissipated in the GTO

during one complete cycle, divided by T


105

Switching losses

Turn-On time T1

On-state time T2

Turn-off time T3

Off-state time T4


Switching losses

The following figure shows a GTO with its

anode, cathode, and gate. In addition to the

circuit that is being switched (not shown), a

snubber is connected to the GTO.

A snubber is an auxiliary circuit composed of

R, L, C components (usually including

semiconductor devices) that control the

magnitude and rate of rise of the anode

voltage EAK as well as the anode current I.

The purpose of a snubber is to aid

commutation and to reduce the losses in the

GTO.


Switching losses

It can be seen that the dissipation increases with the switching

frequency fc and the duty cycle D.

It can be seen also that the dissipation can be reduced if the

turn-on and turn-off times are shorter.


DC-TO-AC SWITCHING CONVERTERS

We have studied the 2-quadrant and 4-quadrant dc-to-dc

switching converters. In this following, we will examine the 4-

quadrant converter as a dc-to-ac converter.

We have seen that the converter is able to transform the dc

voltage into a rectangular ac voltage.

The rectangular wave can have any frequency


Dc-to-ac rectangular wave converter

109


Consider the 4-quadrant dc-to-dc converter of the following

figure, which is operating at a constant switching frequency, fc of

several kilohertz.

Fc is called carrier frequency.


Dc-to-ac converter with pulse with modulation


Suppose that the duty cycle is set at

0.8. The average value of ELL. is,

therefore,

If D is set to 0.5, the average output

voltage ELL becomes zero

if D = 0.2, we find that the average

value of ELL is -0.6 EH


Dc-to-ac converter with pulse

with modulation


Suppose now, that D is varied

periodically, switching suddenly

between D = 0.8 and D = 0.2 at a

frequency f that is much lower than

the carrier frequency fc.

As a result, the output voltage ELL

will fluctuate continually between

+0.6 EH and -0.6 EH.

The filtered output voltage is

therefore a rectangular wave having a

frequency f



The big advantage over the rectangular

wave of slide 108 is that the magnitude

of Eo, as well as its frequency f can be

controlled at will.



Consider now the following figure

wherein the duty cycle is varied

gradually between 0.8 and 0.2,

following a triangular pattern. This

causes the filtered output voltage

ELL to vary between +0.6 EH and

-0.6 EH, faithfully reproducing the

triangular wave.



We need to determine the duty cycle pattern to generate a

desired output voltage

We already know that

from which we immediately deduce


Dc-to-ac converter with pulse with modulation


Consequently, knowing EH (whose value is fixed) and knowing.

the desired value of ELL as a function of time, the pattern of D

can be programmed.

For example, suppose we want to generate an output voltage E

given by

D is given by

The ratio EmlEH is called amplitude modulation ratio, designated by

the symbol m. Consequently, the duty cycle pattern to generate a

sine wave can be expressed as:


Exercise

A 200 V dc source is connected to a 4-quadrant switching

converter operating at a carrier frequency of 8 kHz. It is desired

to generate a sinusoidal voltage having an effective value of 120

V at a frequency of 97 Hz and phase angle of 35° lagging.

Calculate the value of the amplitude modulation ratio and derive

an expression for the duty cycle .


Engineering

Elec581 chapter 2 - fundamental elements of power eletronics