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
2.1 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
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.
load (L is large enough) Inductive
–Only single pulse in one line cycle
–DC component in the transformer current
Average output current:
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
Comparison with previous circuit:
–No need for additional freewheeling diode
–Isolation is necessary between the drive circuits of the two thyristors
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
2.2.1 Three- phase half- wave controlled rectifier
Resistive load, α= 0º
When α≤ 30º , load current id is continuous.
When α > 30º , load current id is discontinuous.
Average load current
Common- cathode group and common- anode group of thyristors
Numbering of the 6 thyristors indicates the trigger sequence.
Average output voltage:
For resistive load, When a > 60º, load current id is discontinuous.
everage output current (load current):
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.
Circulating current ik during commutation
Output voltage during commutation
Reduction of average output voltage due to the commutation process
Calculation of commutation angle
– Id ↑,γ↑
– XB↑, γ↑
– For α ≤ 90۫ , α↓, γ↑
–Commutation process actually provides additional working states of the circuit.
–di/dt of the thyristor current is reduced.
–The average output voltage is reduced.
– Notching in the AC side voltag
2.4.1 Capacitor- filtered single- phase uncontrolled rectifier
Single-phase bridge, RC load:
Three-phase bridge, RC load
2.5.1 Basic concepts of harmonics and reactive power
For pure sinusoidal waveform
For periodic non-sinusoidal waveform
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.
Distortion factor (fundamental- component factor):
Displacement factor (power factor of fundamental component):
Definition of reactive power is still in dispute
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.
–Only odd order harmonics exist
– In / I1 = 1/n
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.
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
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
2.6.1 Double- star controlled rectifier
Circuit Waveforms When α= 0º
Rectifier and inverter mode operation of single- phase full- wave converter
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 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）
2.8.1 Rectifier mode of operation
EMF at no load (taking 3- phase half-wave as example)
A typical gate triggering control circuit