Malcolm Barnes. Practical Variable Speed Drives and Power Electronics

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Power electronic converters 79

• Current (I

) through the diode that is turning off decreases in value

= I – I

decreasing

Figure 3.7:

The currents in each branch during commutation

For this special example, it can be assumed that the commutation voltage V

is constant

during the short period of the commutation. At time t the integration yields the following

value of I

, which increases linearly with time.

)(

t t

−

When I

has increased to a value equal to the load current I at time t

, then all the

current has been transferred from branch 1 to branch 2 and the current through the switch

that is turning off has decreased to zero. The commutation is then over.

Consequently, at time t2

= 0

= I

At the end of commutation when t = t2, putting I

equal to I in the above equation, the

time taken to transfer the current from one circuit branch to the other (commutation time),

may be calculated.

)

(

= I

12c

−

= I

L I

It is clear from this equation that the commutation time t

depends on the overall circuit

inductance (L

+ L

) and the commutation voltage.

80 Practical Variable Speed Drives and Power Electronics

From this we can conclude that:

• A large circuit inductance will result in a long commutation time.

• A large commutation voltage will result in a short commutation time.

In practice, a number of deviations from this idealized situation occur.

• The diodes are not ideal and do not turn off immediately when the forward

voltage becomes negative. When a diode has been conducting and is then

presented with a reverse voltage, some reverse current can still flow for a few

microseconds as indicated in Figure 3.7. The current I

continues to decrease

beyond zero to a negative value before returning to zero. This is due to the

free charges that must be removed from the PN junction before blocking is

achieved.

• Even if the commutation time is very short, the commutation voltage of an

AC fed rectifier bridge does not remain constant but changes slightly during

the commutation period. An increasing commutation voltage will tend to

reduce the commutation time.

In practical power electronic converter circuits, commutation follows the same basic

sequence outlined above. The figure below shows a typical 6-pulse rectifier bridge circuit

to convert 3-phase AC currents I

, I

and I

, to a DC current I

Figure 3.8:

3-Phase commutation with a 6-pulse diode bridge

This type of circuit is relatively simple to analyze because only 2 of the 6 diodes

conduct current at any one time. The idealized commutation circuit can easily be

identified. In this example, commutation is assumed to be taking place from diode D

in the positive group, while D

conducts in the negative group.

In power electronic bridge circuits, it is conventional to number the diodes D

to D

the sequence in which they turned ON and OFF. When V

is the highest voltage and V

the lowest, D

and D

are conducting.

In a similar way to the idealized circuit in Figure 3.6, when V

rises to exceed V

, D

turns on and commutation transfers the current from diode D

to D

. As before, the

Power electronic converters 81

commutation time is dependent on the circuit inductance (L) and the commutation voltage

– V

As can be seen from the 6-pulse diode rectifier bridge example above in Figure 3.8,

commutation is usually initiated by external changes. In this case, commutation is

controlled by the 3-phase supply line voltages. In other applications, commutation can

also be initiated or controlled by other factors, depending on the type of converter and the

application. Therefore, converters are often classified in accordance with the source of the

external changes that initiate commutation.

• In the above example, the converter is said to be line commutated because

the source of the commutation voltage is on the mains supply line.

• A converter is said to be self-commutated if the source of the commutation

voltage comes from within the converter itself. Gate-commutated converters

are typical examples of this.

3.6.1 Line commutated diode rectifier bridge

One of the most common circuits used in power electronics is the 3-phase line

commutated 6-pulse rectifier bridge, which comprises 6 diodes in a bridge connection.

Single-phase bridges will not be covered here because their operation can be deduced as a

simplification of the 3-phase bridge.

In the analysis of the various types of converter that follow, the procedure will be to

assume initially that the conditions and components are ideal. Once the principles have

been established, any deviations from the ideal will be discussed. The following ideal

assumptions are made:

• The supply voltages are ‘stiff’ and completely sinusoidal

• Commutations are instantaneous and have no recovery problems

• Load currents are completely smooth

• Transformers and other line components are linear and ideal

• There is no volt drop in power electronic switches

These assumptions are made to gain an understanding of the circuits and to make

estimates of currents, voltages, commutation times, etc. Thereafter, the limiting

conditions that affect the performance of the practical converters and their deviation from

the ideal conditions will be examined to bridge the gap from the ideal to the practical.

In the diode bridge, the diodes are not controlled from an external control circuit.

Instead, commutation is initiated externally by the changes that take place in the supply

line voltages, hence the name line commutated rectifier.

According to convention, the diodes are labeled D

to D

in the sequence in which they

are turned ON and OFF. This sequence follows the sequence of the supply line voltages.

82 Practical Variable Speed Drives and Power Electronics

Figure 3.9:

Line commutated diode rectifier bridge

The 3-phase supply voltages comprise 3 sinusoidal voltage waveforms 120° apart

which rise to their maximum value in the sequence A – B – C. According to convention,

the phase-to-neutral voltages are labeled V

, V

and V

and the phase-to-phase voltages

are V

, V

and V

, etc.

These voltages are usually shown graphically as a vector diagram, which rotates

counter-clockwise at a frequency of 50 times per second. A vector diagram of these

voltages and their relative positions and magnitudes is shown below. The sinusoidal

voltage waveforms of the supply voltage may be derived from the rotation of the vector

diagram.

Figure 3.10:

Vector diagram of the 3-phase mains supply voltages

The output of the converter is the rectified DC voltage V

, which drives a DC current I

through a load on the DC side of the rectifier. In the idealized circuit, it is assumed that

the DC current I

is constant and completely smooth and without ripple.

Power electronic converters 83

The bridge comprises two commutation groups, one connected to the positive leg,

consisting of diodes D

–D

, and one connected to the negative leg, consisting of

diodes D

–D

. The commutation transfers the current from one diode to another in

sequence and each diode conducts current for 120° of each cycle as shown in Figure 3.11.

In the upper group, the positive DC terminal follows the highest voltage in the sequence

–V

via diodes D

–D

. When V

is near its positive peak, diode D

conducts

and the voltage of the +DC terminal follows V

. The DC current flows through the load

and returns via one of the lower group diodes. With the passage of time, V

reaches its

sinusoidal peak and starts to decline. At the same time, V

is rising and eventually reaches

a point when it becomes equal to and starts to exceed V

. At this point, the forward

voltage across diode D

becomes positive and it starts to turn on. The commutating

voltage in this circuit, V

–V

starts to drive an increasing commutation current though the

circuit inductances and the current through D

starts to increase as the current in D

decreases. In a sequence of events similar to that described above, commutation takes

place and the current is transferred from diode D

to diode D

. At the end of the

commutation period, diode D

is blocking and the +DC terminal follows V

until the next

commutation takes place to transfer the current to diode D

. After diode D

, the

commutation transfers the current back to D

and the cycle is repeated.

In the lower group, a very similar sequence of events takes place, but with negative

voltages and the current flowing from the load back to the mains. Initially, D

is assumed

to be conducting when V

is more negative than V

. As time progresses, V

becomes

equal to V

and then becomes more negative. Commutation takes place and the current is

transferred from diode D

to D

. Diode D

turns off and D

turns on. The current is later

transferred to diode D

, then back to D

and the cycle is repeated.

In Figure 3.11, the conducting periods of the diodes in the upper and lower groups are

shown over several cycles of the 3-Phase supply. This shows that only 2 diodes conduct

current at any time (except during the commutation period, which is assumed to be

infinitely short!!) and that each of the 6 diodes conducts for only one portion of the cycle

in a regular sequence. The commutation takes place alternatively in the top group and the

bottom group.

The DC output voltage V

is not a smooth voltage and consists of portions of the phase-

to-phase voltage waveforms. For every cycle of the 50 Hz AC waveform (20 msec), the

DC voltage V

comprises portions of the 6 voltage pulses, V

, V

etc, hence the name 6-pulse rectifier bridge.

The average magnitude of the DC voltage may be calculated from the voltage

waveform shown above. The average value is obtained by integrating the voltage over

one of the repeating 120

portions of the DC voltage curve. This integration yields an

average magnitude of the voltage V

as follows.

= 1.35 × (RMS – Phase Voltage)

= 1.35 × V

RMS

For example, if V

RMS

= 415 volts, V

= 560 volts DC

If there is sufficient inductance in the DC circuit, then the DC current I

will be fairly

steady and the AC supply current will comprise segments of DC current from each diode

in sequence. As an example, the current in the A-phase is shown in Figure 3.9. The non-

sinusoidal current that flows in each phase of the supply mains can affect the performance

of other AC equipment connected to the supply line that are designed to operate with

84 Practical Variable Speed Drives and Power Electronics

sinusoidal waveforms. The effects of the non-sinusoidal currents is fully covered in

Chapter 4: Electromagnetic compatibility (EMC).

In practice, to ensure that the diode reverse blocking voltage capability is properly

specified, it is necessary to know the magnitude of the reverse blocking voltage which

appears across each of the diodes. Theoretically, the maximum reverse voltage across a

diode is equal to the peak of the phase–phase voltage. For example, the reverse voltage

and V

appears across diode D

during the blocking period. In practice, a factor of

safety of 2.5 is commonly used for specifying the reverse blocking capability of diodes

and other power electronic switches. On a rectifier bridge fed from a 415 V power supply,

the reverse blocking voltage V

of the diode must be higher than 2.5 × 440 V = 1100 V.

Therefore, it is common practice to use diodes with a reverse blocking voltage of 1200 V.

Figure 3.11

Voltage and current waveforms during commutation

Power electronic converters 85

3.6.2 The line commutated thyristor rectifier bridge

The output DC voltage and operating sequence of the diode rectifier above is dependent

on the continuous changes in the supply line voltages and is not dependent on any control

circuit. This type of converter is called an uncontrolled diode rectifier bridge because the

DC voltage output is not controlled and is fixed at 1.35 × V

RMS

If the diodes are replaced with thyristors, it then becomes possible to control the point

at which the thyristors are triggered and therefore the magnitude of the DC output voltage

can be controlled. This type of converter is called a controlled thyristor rectifier bridge

and requires an additional control circuit to trigger the thyristor at the right instant. A

typical 6-pulse thyristor converter is shown in Figure 3.12.

From the previous chapter, the conditions required before a thyristor will conduct

current in a power electronic circuit are:

• A Forward Voltage must exist across the thyristor

AND

• A Positive Pulse must be applied to the thyristor gate

Figure 3.12:

6-pulse controlled thyristor rectifier bridge

If each thyristor were triggered at the instant when the forward voltage across it tends to

become positive, then the thyristor rectifier operates in the same way as the diode rectifier

described above. All the voltage and current waveforms of the diode bridge apply to the

thyristor bridge. A thyristor bridge operating in this mode is said to be operating with a

zero delay angle and gives a voltage output of:

= 1.35 × V

RMS

The output of the rectifier bridge can be controlled by delaying the instant at which the

thyristor receives a triggering pulse. This delay is usually measured in degrees from the

point at which the switch CAN turn on, due to the forward voltage becoming positive.

86 Practical Variable Speed Drives and Power Electronics

The angle of delay is called the delay angle, or sometimes the firing angle, and is desig-

nated by the symbol α. The reference point, for the angle of delay, is the point where a

phase voltage wave crosses the voltage of the previous phase and becomes positive

relative to it. A diode rectifier can be thought of as a converter with a delay angle of

0°.

The main purpose of controlling a converter is to control the magnitude of the DC

output voltage. In general, the bigger the delay angle, the lower the average magnitude of

the DC voltage. Under steady state operation of a controlled thyristor converter, the delay

angle for each switch is the same. Figure 3.13 shows the voltage waveforms where the

triggering of the switches has been delayed by an angle of α degrees.

Figure 3.13:

Voltage waveforms of a controlled rectifier

In the positive switch group, the positive DC terminal follows the voltage associated

with the switch that is in conduction in the sequence V

–V

. Assume, initially, that

thyristor S

associated with voltage V

is conducting and S

is not yet triggered. The

voltage on the + bus on the DC side follows the declining voltage V

because, in the

absence of S

conduction, there is still a forward voltage across S

and it will continue to

conduct. When S

is triggered after a delay angle = α, the voltage on + bus jumps to V

whose value it then starts to follow. At this instant, with both S

and S

conducting, a

negative commutation voltage equal to V

–V

appears across the switch S

for the

commutation period, which then starts to turn off. With the passage of time, V

reaches its

Power electronic converters 87

sinusoidal peak and starts to decline, followed by + DC terminal. At the same time, V

rising and when S

is triggered, the same sequence of events is repeated and the current is

commutated to S

As with the diode rectifier, the average magnitude of the DC voltage V

can be

calculated by integrating the voltage waveform over a 120

period representing a

repeating portion of the DC voltage. At a delay angle α, the DC voltage is given by:

= 1.35 × (RMS – Phase Voltage) × Cos α

= 1.35 × V

RMS

× Cos α

This formula shows that the theoretical DC voltage output of the thyristor rectifier with

a firing angle α = 0 is the same as that for a diode rectifier. It also shows that the average

value of the DC voltage will decrease as the delay angle is increased and is dependent on

the cosine of the delay angle. When α = 90

, then Cosα = 0 and V

= 0, which means that

the average value of the DC voltage is zero. The instantaneous value of the DC voltage is

a saw-tooth voltage as shown in the figure below.

Figure 3.14:

DC output voltage for delay angle

= 90

If the delay angle is increased further, the average value of the DC voltage becomes

negative. In this mode of operation, the converter operates as an inverter. It is interesting

to note that the direction of the DC current remains unchanged because the current can

only flow through the switches in the one direction. However, with a negative DC

voltage, the direction of the power flow is reversed and the power flows from the DC side

to the AC side. Steady state operation in this mode is only possible if there is a voltage

source on the DC side. The instantaneous value of the DC voltage for α > 90

is shown in

Figure 3.15.

In practice, the commutation is not instantaneous and lasts for a period dependent on

the circuit inductance and the magnitude of the commutation voltage. As in the idealized

88 Practical Variable Speed Drives and Power Electronics

case, it is possible to estimate the commutation time from the commutation circuit

inductance and an estimate of the average commutation voltage.

Figure 3.15:

DC voltage when the delay angle

> 90

As in the diode rectifier, the steady DC current I

comprises segments of current from

each of the 3 phases on the AC side. On the AC side, the current in each phase comprises

non-sinusoidal blocks, similar to those associated with the diode rectifier and with similar

harmonic consequences. In the case of the diode bridge, with a delay angle of α = 0, the

angle between the phase current and the corresponding phase voltage on the AC side is

roughly zero. Consequently, the power factor is roughly unity and converter behaves

something like a resistive load.

For the controlled rectifier, with a delay angle of α, the angle between the phase current

and the corresponding phase voltage is also roughly α, but normally called the power

factor angle ∅. This angle should be called the displacement factor because it does not

really represent power factor (see later). Consequently, when the delay angle of the

thyristor rectifier is changed to reduce the DC voltage, the angle between the phase

current and voltage also changes by the same amount. The converter then behaves like a

resistive-inductive load with a displacement factor of Cos∅. It is well known that the

power factor associated with a controlled rectifier falls when the DC output voltage is

reduced.

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