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) rectifier 2. 1 2.1 Single- phase controlled (controllable) rectifier 2.1.1 Single-phase half-wave controlled rectifier

Inductive (resistor-inductor) load

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

Average output (rectified) voltage: Average output current: For thyristor: For transformer:

Inductive load (L is large enough)

Electro- motive-force (EMF) load With resistor

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

2.1.3 Single- phase full- wave controlled rectifier

2.1.4 Single- phase bridge half-controlled rectifier

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, α= 30º

Resistive load, α= 60º

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

Inductive load, L is large enough

Thyristor voltage and currents, transformer current :

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.

Resistive load, α= 0º

Resistive load, α= 30º

Resistive load, α= 60º

Resistive load, α= 90º

Inductive load, α= 0º

Inductive load, α= 30º

Inductive load, α= 90º

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↑

Summary of the effect on rectifier circuits

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:

Single-phase bridge, RLC load

2.4.2 Capacitor- filtered three- phase uncontrolled rectifier Three-phase bridge, RC load

Three- phase bridge, RC load Waveform when ωRC≤1.732

Three- phase bridge, RLC 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

A typical gate triggering control circuit

Three- phase bridge fully-controlled rectifier

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.

2.5.4 Harmonic analysis of output voltage and current

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

Harmonics in the output current where

Conclusions for α = 0º Only mk (k is positive integer) order harmonics exist in the output voltage and current of m- pulse rectifiers Magnitude of harmonics decreases as harmonic order increases when m is 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

Effect of interphase reactor(inductor, transformer)

Quantitative analysis when α = 0º

Waveforms when α > 0º

2.6.2 Connection of multiple rectifiers

Phase-shift connection of multiple rectifiers Parallel connection

Series connection

Sequential control of multiple series-connected rectifiers

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.

Inverter mode operation of 3- phase bridge rectifier

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 continuous

Speed- torque (mechanic) characteristic when load current is discontinuous EMF at no load (taking 3- phase half-wave as example)

2.8.2 Inverter mode of operation

2.8.3 Reversible DC motor drive system(4-quadrant operation)

2.9 Gate triggering control circuit for thyristor rectifiers A typical gate triggering control circuit