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Chapter 2 AC to DC Converters

Outline

2.1 Single-phase controlled rectifier

2.2 Three-phase controlled rectifier

2.3 Effect of transformer leakage inductance on rectifier circuits

2.4 Capacitor-filtered uncontrolled rectifier

2.5 Harmonics and power factor of rectifier circuits

2.6 High power controlled rectifier

2.7 Inverter mode operation of rectifier circuit

2.8 Thyristor-DC motor system

2.9 Realization of phase-control in rectifier

2.1 Single- phase controlled (controllable) rectifier2.1.1 Single-phase half-wave controlled rectifier

Basic thought process of time-domain analysis for power electronic circuits

The time- domain behavior of a power electronic circuit is actually the combination of consecutive transients of the different linear circuits when the power semiconductor devices are in different states.

Single- phase half- wave controlled rectifier with freewheeling diode

load (L is large enough) Inductive

Maximum forward voltage, maximum reverse voltage

Disadvantages:

–Only single pulse in one line cycle

–DC component in the transformer current

2.1.2 Single- phase bridge fully-controlled rectifier

- Resistive load

With resistor and inductor

When L is large enough, the output voltage and current waveforms are the same as ordinary inductive load.

When L is at a critical value

Another single- phase bridge half-controlled rectifier

Comparison with previous circuit:

–No need for additional freewheeling diode

–Isolation is necessary between the drive circuits of the two thyristors

Summary of some important points in analysis

When analyzing a thyristor circuit, start from a diode circuit with the same topology. The behavior of the diode circuit is exactly the same as the thyristor circuit when firing angle is 0.

A power electronic circuit can be considered as different linear circuits when the power semiconductor devices are in different states. The time- domain behavior of the power electronic circuit is actually the combination of consecutive transients of the different linear circuits.

Take different principle when dealing with different load

– For resistive load: current waveform of a resistor is the same as the voltage waveform

–For inductive load with a large inductor: the inductor current can

be considered constant

2.2 Three- phase controlled (controllable) rectifier

2.2.1 Three- phase half- wave controlled rectifier

Resistive load, α= 0º

Resistive load, quantitative analysis

When α≤ 30º , load current id is continuous.

When α > 30º , load current id is discontinuous.

Average load current

Thyristor voltages

2.2.2 Three- phase bridge fully-controlled rectifier

Circuit diagram

Common- cathode group and common- anode group of thyristors

Numbering of the 6 thyristors indicates the trigger sequence.

Quantitative analysis

Average output voltage:

For resistive load, When a > 60º, load current id is discontinuous.

everage output current (load current):

Transformer current:

2.3 Effect of transformer leakage inductance on rectifier circuits

In practical, the transformer leakage inductance has to be taken into account.

Commutation between thyristors, thus can not happen instantly,but with a commutation process.

Commutation process analysis

Circulating current ik during commutation

Output voltage during commutation

Quantitative calculation

Reduction of average output voltage due to the commutation process

Calculation of commutation angle

– Id ↑,γ↑

– XB↑, γ↑

– For α ≤ 90۫ , α↓, γ↑

Conclusions

–Commutation process actually provides additional working states of the circuit.

–di/dt of the thyristor current is reduced.

–The average output voltage is reduced.

–Positive du/dt

– Notching in the AC side voltag

2.4 Capacitor- filtered uncontrolled (uncontrollable) rectifier

2.4.1 Capacitor- filtered single- phase uncontrolled rectifier

Single-phase bridge, RC load:

2.4.2 Capacitor- filtered three- phase uncontrolled rectifier

Three-phase bridge, RC load

2.5 Harmonics and power factor of rectifier circuits

2.5.1 Basic concepts of harmonics and reactive power

For pure sinusoidal waveform

For periodic non-sinusoidal waveform

where

Harmonics-related specifications

Take current harmonics as examples

Content of nth harmonics

In is the effective (RMS) value of nth harmonics.

I1 is the effective (RMS) value of fundamental component.

Total harmonic distortion

Ih is the total effective (RMS) value of all the harmonic components.

Definition of power and power factor for sinusoidal circuits

Active power

Reactive power

Apparent power

Power factor

Definition of power and power factor For non- sinusoidal circuit

Active power:

Power factor:

Distortion factor (fundamental- component factor):

Displacement factor (power factor of fundamental component):

Definition of reactive power is still in dispute

Review of the reactive power concept

The reactive power Q does not lead to net transmission of energy between the source and load. When Q ≠ 0, the rms current and apparent power are greater than the minimum amount necessary to transmit the average power P.

Inductor: current lags voltage by 90°, hence displacement factor is zero. The alternate storing and releasing of energy in an inductor leads to current flow and nonzero apparent power, but P = 0. Just as resistors consume real (average) power P, inductors can be viewed as consumers of reactive power Q.

Capacitor: current leads voltage by 90°, hence displacement factor is zero. Capacitors supply reactive power Q. They are often placed in the utility power distribution system near inductive loads. If Q supplied by capacitor is equal to Q consumed by inductor, then the net current (flowing from the source into the capacitor- inductive- load combination) is in phase with the voltage, leading to unity power factor and minimum rms current magnitude.

2.5.2 AC side harmonics and power factor of controlled rectifiers with inductive load

- Single- phase bridge fully-controlled rectifier

AC side current harmonics of single- phase bridge fully-controlled rectifier with inductive load

Where

Conclusions

–Only odd order harmonics exist

– In∝1/n

– In / I1 = 1/n

AC side current harmonics of three- phase bridge fully- controlled rectifier with inductive load

where

2.5.3 AC side harmonics and power factor of capacitor- filtered uncontrolled rectifiers

Situation is a little complicated than rectifiers with inductive load.

Some conclusions that are easy to remember:

–Only odd order harmonics exist in single- phase circuit, and only 6k±1 (k is positive integer) order harmonics exist in three- phase circuit.

–Magnitude of harmonics decreases as harmonic order increases.

–Harmonics increases and power factor decreases as capacitor increases.

–Harmonics decreases and power factor increases as inductor increases.

Ripple factor in the output voltage

Output voltage ripple factor

where UR is the total RMS value of all the harmonic components in the output voltage

and U is the total RMS value of the output voltage

Conclusions

for α = 0º

Only mk (kis positive integer) order harmonics exist in the output voltage and current of m-pulse rectifiers

Magnitude of harmonics decreases as harmonic order increases when mis constant.

The order number of the lowest harmonics increases as m increases. The corresponding magnitude of the lowest harmonics decreases accordingly.

For α ≠ 0º

Quantitative harmonic analysis of output voltage and current is very

complicated for α ≠ 0º.

As an example,for 3- phase bridge fully- controlled rectifie

2.6 High power controlled rectifier

2.6.1 Double- star controlled rectifier

Circuit Waveforms When α= 0º

Phase-shift connection of multiple rectifiers

Parallel connection

2.7 Inverter mode operationof rectifiers

- Review of DC generator- motor system

Inverter mode operation of rectifiers

Rectifier and inverter mode operation of single- phase full- wave converter

Necessary conditions for the inverter mode operation of controlled rectifiers

There must be DC EMF in the load and the direction of the DC EMF must be enabling current flow in

thyristors. (In other word EM must be negative if taking the ordinary output voltage direction as positive.)

α >90º so that the output voltage Ud is also negative.

Inversion angle (extinction angle) β

α+ β=180º

Inversion failure and minimum inversion angle

Possible reasons of inversion failures

–Malfunction of triggering circuit

–Failure in thyristors

–Sudden dropout of AC source voltage

–Insufficient margin for commutation of thyristors

Minimum inversion angle (extinction angle)

βmin= δ + γ+ θ′（2-109）

2.8 Thyristor- DC motor system

2.8.1 Rectifier mode of operation

Speed- torque (mechanic) characteristic when load current is discontinuous

EMF at no load (taking 3- phase half-wave as example)

2.9 Gate triggering control circuit for thyristor rectifiers

A typical gate triggering control circuit

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