# Chapter 4 AC to AC Converters Outline 4.1

Chapter 4 AC to AC Converters Outline 4.1 AC voltage controllers 4.2 Other AC controllers 4.3 Thyristor cycloconverters 4.4 Matrix converters 4.1.1 Single-phase AC voltage controller VT 1 VT2 u1 io u1 O uo R uo O io The phase shift range (operation range of phase delay angle): O u VT t t t 0 O t

Resistive load, quantitative analysis RMS value of output voltage Uo 2 1 1 2 U sin t d t U sin 2 1 1 2 (4-1)

RMS value of output current U o I o R RMS value of thyristor current ( 4 2 ) 2 U1 1 sin2 1 2U1 sint IT d t (1 ) 2 R R 2 2

(4-3) Power factor of the circuit P UoIo Uo 1 sin2 S U1Io U1 2 (4-4) Inductive (Inductor- resistor) load , operation principle u1 VT 1 VT2 O io uG1 R u1 uo The phase shift range: t L

O uG2 O uo t O io t O uVT O t t t Inductive load, quantitative analysis Differential equation d io Ri d t i o t 0 L o 180 2 U 1 sin t

140 (4 -5 ) 2U io Z 1 t tg sin( t ) sin( ) e C o n s id e r in g io = 0 w h e n t= + W e have sin( ) sin( ) e /( ) S o lu tio n t (4 -6 ) 100 60 20 0 tg

(4 -7 ) 20 60 100 / ( ) 140 180 4-34-3 The RMS value of output voltage, output current, and thyristor current can then be ca lculated. 4.1.2 Three-phase AC voltage controller Classification of three- phase circuits ia VT1 a u a VT 3 n ub Ua0' ia VT4 b VT5 uc

ua n' VT6 c n n Line- controlled connection n ub ub uc c Branch-controlled connection ia ua a b uc ub uc Y connection ia

b c VT2 ua a a b c Neutral-point controlled connection 3- phase 3- wire Y connection AC voltage controller i a VT 1 ua n ub uc VT3 VT5 a VT4 b Ua0' n' VT6 c

VT 2 For a time instant, there are 2 possible conduction states: Each phase has a thyristor conducting. Load voltages are the same as the source voltages. There are only 2 thyristors conducting, each from a phase. The load voltages of t he two conducting phases are half of the corresponding line to line voltage, wh ile the load voltage of the other phase is 0. 4.2 Other AC controllers 4.2.1 Integral cycle controlAC power controller VT 1 VT2 u1 io Conduction uo angle = 2 U1 uo R O M 2 M 2N M u1 uo,io 3 M 4

M t Line period Control period = M *Line period = 2 Circuit topologies are the same as AC voltage controllers. Only the control method is different. Load voltage and current are both sinusoidal when thyristors are conducting. Spectrum of the current inAC po wer controller 0.6 There is NO harmonics in the ordinary sense. There is harmonics as to the control frequency. As to the line frequency, these components become fractional harmonics. 0.5 0.4 IO/I0m 0.3 0.2 0.1

2 0 4 6 8 10 12 14 Harmonic order as to control frequency 0 1 2 3 4 Harmonic order as to line frequency 5 4.2.2 Electronic AC switch Circuit topologies are the same as AC voltage controllers. But the back- to- back t hyristors are just used like a switch to turn the equipment on or off. ApplicationThyristor-switched capacitor (TSC) I U TSC waveforms when the capacitor is switched in/out uVT 1

uC iC VT1 us VT2 us t uC C t uVT 1 t VT1 iC VT2 t1 t t2 The voltage across the thyristor must be nearly zero when switching in the capacitor, and the current of the thyristor must be zero when switching out the capacitor. TSC with the electronic switch realized by a thyristor and an antiparallel diode uVT

uC iC VT us VD C us t uC t uVT t VD iC VT t t 1 t2 t 3 t 4 The capacitor voltage will be always charged up to the peak of source volt age. The response to switching- out command could be a little slower (maximu m delay is one line-cycle). 4.2.3 Chopping controlAC chopper AC chopper

Modes of operation VD V 1 1 i1 u V 1 2 VD 2 V VD R VD 3 3 u>0, io >0: V 1 charging, 4-34-7V 3 freew heeling u>0, io <0: V 4 charging, V 2 freew heeling u<0, io >0: V 3 charging, V 1 freew heeling u<0, io <0: V 2 charging, V 4 freew heeling

4 u V 4 o L 4.3 Thyristor cycloconverters 4.3.1 Single- phase thyristor-cycloconverter Circuit configuration and operation principle P N Z uo a p= 2 Output voltage Average ap=0 output voltage ap= 2

t Single- phase thyristor-cycloconverter Modes of operation uo u o,io O t1 uP iP uo t2 t4 t3 t5 t O iN uN t uo uP io io

uN t uo O iP P N O iN t O t Rectifi Inver cation sion bl ocki ng bl ocki ng Rectifi Inver cation sion

Typical waveforms uo O t io O t 1 3 2 4 6 5 Modulation methods for firing delay angle Calculation method For the rectifier circuit u o U cos d0 (4 -1 5 ) u2 u3 u4 u5 u6

u1 t F o r th e c y c lo c o n v e rte r a p3 a p4 o u tp u t uo U sin o t om (4 -1 6 ) E q u a tin g (4 - 1 5 ) a n d (4 -1 6 ) U cos U om d0 th e re fo re cos 1 u s2 u s3 u s4 u s5 u s6 u s1 uo t sin o t sin o t (4 -1 7 ) ( sin o t )

(4 -1 8 ) P rin c ip le o f c o s in e w a v e -c ro s s in g m e th o d O u tp u t v o lta g e ra tio (M o d u la tio n fa c to r) 150 U om 120 (0 1) /( ) U d0 90 60 30 0 3

2 t 2 2 Ou t p u t v o l t a g e p h a s e a n g l e 4.3.2 Three- phase thyristor-cyclo converter The configuration with common input line 4-34-24 The configuration with star-connected output Typical waveforms Output voltage 200 t/ms Input current with Single-phase output Input current with 3-phase output 200 t/ms 200 t/ms Input and output characteristics The maximum output frequency and the harmonics in the output voltage a re the same as in single-phase circuit. Input power factor is a little high er than single-phase circuit. Harmonics in the input current is a little lo wer thanthe single- phase circuit due to the cancellation of some harm onics among the 3 phases. To improve the input power factor: Use DC bias or 3k order component bias on each of the 3 output phas

e voltages Features and applications Features: Direct frequency conversionhigh efficiency Bidirectional energy flow, easy to realize 4- quadrant operation Very complicatedtoo many power semiconductor devices Low output frequency Low input power factor and bad input current waveform Applications: High power low speed AC motor drive 4.4 Matrix converter Circuit configuration i nput b a c S1 S1 S1 1 2 3 S2 S2

S2 1 2 3 S3 S3 S3 1 2 3 a) u S ij v output w b) Usable input voltage U1m 1 Um 2 Um

a) 3 U1m 2 b) a) Single-phase input b) Use 3 phase voltages voltage to construct output voltage c) c) Use 3 line-line voltages to construct output voltage Features Direct frequency conversionhigh efficiency can realize good input and output waveforms, low harmonics, and nearly unity displacement factor Bidirectional energy flow, easy to realize 4- quadrant operation Output frequency is not limited by input frequency No need for bulk capacitor (as compared to indirect frequency converter) Very complicatedtoo many power semiconductor devices Output voltage magnitude is a little lower as compared to indirect frequency converter.

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