# Chapter 4 AC to AC Converters ( AC Controllers and Frequency Converters )

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1 Chapter 4 AC to AC Converters ( AC Controllers and Frequency Converters )

2 Classification of AC to AC converters Same frequency variable magnitude AC power AC controllers AC power Frequency converters (Cycloconverters) Variable frequency AC power AC to AC converters 2

3 Classification of AC controllers AC controller Phase control: AC voltage controller (Delay angle control) Integral cycle control: AC power controller PWM control: AC chopper (Chopping control) n/off switch: electronic AC switch PWM: Pulse Width Modulation 3

4 Classification of frequency converters Frequency converter (Cycloconverter) Phase control: thyristor cycloconverter (Delay angle control) PWM control: matrix converter (Chopping control) Cycloconverter is sometimes referred to in a broader sense any ordinary AC to AC converter in a narrower sense thyristor cycloconverter 4

5 utline 4.1 AC voltage controllers 4.2 ther AC controllers 4.3 Thyristor cycloconverters 4.4 Matrix converters 5

6 4.1 AC voltage controllers Single-phase AC voltage controller Three-phase AC voltage controller Applications Lighting control Soft-start of asynchronous motors Adjustable speed drive of asynchronous motors Reactive power control 6

7 4.1.1 Single-phase AC voltage controller Power Electronics Resistive load u u o The phase shift range (operation range of phase delay angle): 0 α π io R u 1 u o i o u ωt ωt ωt ωt 7

8 Resistive load, quantitative analysis RMS value of output voltage U o 2 ( 2U sinωt) d( ωt) 1 π 1 π α = = α + π 1 U1 sin2 α 2π π RMS value of output current U o I o = R RMS value of thyristor current I T π 2 1 sinω U t U = 2π α d R R Power factor of the circuit 1 2 α π sin2α 2π ( ωt) = (1 + ) P U oi o U o 1 π α λ = = = = sin 2α + S U I U 2π π 1 o 1 (4-1) (4-2) (4-3) (4-4) 4) 8

9 Inductive (Inductor-resistor) resistor) load, operation principle Power Electronics u i o u o The phase shift range: ϕ α π R u 1 u G1 u G2 u o i o u 0.6 ωt ωt ωt ωt ωt ωt 9

10 Inductive load, quantitative analysis Differential equation dio L d t i o ω t=α Solution + Ri = 0 o = 2U sinωt Considering i o =0 when ωt=α+θ We have 1 (4-5) θ tg ϕ (4-6) θ /( ) sin( α + θ ϕ ) = sin( α ϕ ) e (4-7) ϕ = α /( ) The RMS value of output voltage, output current, and thyristor current can then be calculated. 10

11 Inductive load, when α < ϕ The circuit can still work. The load current will be continuous just like the thyristors are short-circuit, and the thyristors can no longer control the magnitude of output voltage. The start-up transient will be the same as the transient when a RL load is connected to an AC source at ωt =α (α < ϕ). u 1 i G1 i G2 i o α i T1 α θ π α+π i T2 ϕ Start-up transient ωt ωt ωt ωt 11

12 Harmonic analysis There is no DC component and even order harmonics in the current. The current waveform is half- wave symmetric. The higher the number of harmonic ordinate, the lower the harmonic content. α = 90 is when harmonics is the most severe. The situation for the inductive load is similar to that for the resistive load except that the corresponding harmonic content is lower and is even lower as ϕ is increasing. In/I * /% Fundamental α/( ) Current harmonics for the resistive load 12

13 4.1.2 Three-phase AC voltage controller Classification of three-phase circuits Y connection Line-controlled connection Branch-controlled controlled connection Neutral-point point-controlled connection 13

14 3-phase 3-wire 3 Y connection AC voltage controller i a u a 1 a 4 3 n b n' u b 6 5 c u c 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 the two conducting phases are half of the corresponding line to line voltage, while the load voltage of the other phase is 0. U a0' 14

15 3-phase 3-wire 3 Y connection AC voltage controller Resistive load, 0 α < 60 u ao' 5 u ab u a u ac 2 0 α π 2 π 4 π 5 π 2 π t 1 t 2 t 3 15

16 3-phase 3-wire 3 Y connection AC voltage controller Resistive load, 60 6 α < 90 u ao' u ab 2 u a u ac 2 4 π 3 5 π 3 0 π 2 π π α π t 1 t 2 t 3 16

17 3-phase 3-wire 3 Y connection AC voltage controller Power Electronics Resistive load, 90 9 α < 150 u ao' u 2 5 ab u a π 0 π 2 π π 4 π 2 π 3 α 3 3 u 2 ac

18 3-phase 3-wire 3 branch-controlled controlled connection AC voltage controller n The operation principle is the same as 3 independent single- phase AC voltage controllers. Application Thyristor Thyristor-controlled reactor (TCR) To control the effective current flowing through the reactor by controlling delay angle, therefore control the reactive power absorbed by the reactor. u a i a u b b a u c c a) b) c) 18

19 4.2 ther AC controllers Integral cycle control AC power controller Electronic AC switch Chopping control AC chopper 19

20 4.2.1 Integral cycle control AC power controller u i o u o R u o 2U 1 Conduction angle π M Line period = 2 πn M Control period = M *Line period =2π Circuit topologies are the same as AC voltage controllers. nly the control method is different. Load voltage and current are both sinusoidal when thyristors are conducting. 2π M 3π M u o,i o 4π M u1 ωt 20

21 Spectrum of the current in AC power controller There is N harmonics in the ordinary sense. There is harmonics as to the control frequency. As to the line frequency, these components become fractional harmonics. I n /I 0m Harmonic order as to control frequency Harmonic order as to line frequency 21

22 4.2.2 Electronic AC switch Circuit topologies are the same as AC voltage controllers. But the back-to to-back thyristors are just used like a switch to turn the equipment on or off. Application Thyristor Thyristor-switched switched capacitor (TSC) U I 22

23 TSC waveforms when the capacitor is switched in/out i C u s u 1 u C 1 C 2 u s u C u 1 i C t t t 1 t 2t1 t 2 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. 23

24 TSC with the electronic switch realized by a thyristor and an anti-parallel diode The capacitor voltage will be always charged up to the peak of source voltage. The response to switching-out command could be a little slower (maximum delay is one line-cycle). 24

25 4.2.3 Chopping control AC chopper Principle of chopping control The mean output voltage over one switching cycle is proportional to the duty cycle in that period. This is also called Pulse Width Modulation (PWM). Advantages Much better output waveforms, much lower harmonics For resistive load, the displacement factor is always 1. Waveforms when the load is pure resistor 25

26 AC chopper Modes of operation u o u o u o u o >0, i o >0: V 1 charging, V 3 freewheeling >0, i o <0: V 4 charging, V 2 freewheeling <0, i o >0: V 3 charging, V 1 freewheeling <0, i o <0: V 2 charging, V 4 freewheeling 26

27 4.3 Thyristor cycloconverters (Thyristor AC to AC frequency converter) Another name direct frequency converter (as compared to AC-DC DC-AC frequency converter which is discussed in Chapter 8) Can be classified into single-phase and three- phase according to the number of phases at output Single-phase thyristor-cycloconverter Three-phase thyristor-cycloconverter 27

28 4.3.1 Single-phase thyristor-cycloconverter Circuit configuration and operation principle P utput u o Z u α P =0 o α P = π voltage 2 N Average output voltage α P = π 2 ωt 28

29 Single-phase thyristor-cycloconverter Modes of operation u P i P u o i o i N u N u o,i o u o i o u P u N i P i N t 1 t 2 t 3 t 4 t 5 u o u o t t t t t P Rectifi cation Inver sion Blocking N Blocking Rectifi cation Inver sion 29

30 Single-phase thyristor-cycloconverter Typical waveforms u o i o ωt ωt

31 Modulation methods for firing delay angle Calculation method For the rectifier circuit u o = U d0 cos α For the cycloconverter output uo = Uom sinωot (4-16) Equating (4-15) and (4-16) U om cosα = sinω ot = γ sinω ot U d0 (4-17) Therefore α = cos 1 ( γ sinω t) Cosine wave-crossing method o (4-15) (4-18) u 2 u 3 u 4 u 5 u 6 u 1 α P3 α P4 u s2 u s3 u s4 u s5 u s6 u s1 u o Principle of cosine wave-crossing method ωt ωt 31

32 Calculated results for firing delay angle utput voltage ratio (Modulation factor) U om γ = (0 r U d0 1) α/( ) γ = 0 π 2 π γ = π π utput voltage phase angle ω 0 t 32

33 Input and output characteristics Maximum output frequency: 1/3 or 1/2 of the input frequency if using 6-6 pulse rectifiers Input power factor Harmonics in the output voltage and input current are very complicated, and both related to input frequency and output frequency. Input displacement factor γ = Load power factor Load power factor (leading) (lagging) 33

34 4.3.2 Three-phase thyristor-cycloconverter The configuration with common input line 34

35 Three-phase thyristor-cycloconverter The configuration with star-connected output 35

36 Three-phase thyristor-cycloconverter Typical waveforms utput voltage Input current with Single-phase output Input current with 3-phase output t/ms 200 t/ms 200 t/ms 36

37 Input and output characteristics The maximum output frequency and the harmonics in the output voltage are the same as in single- phase circuit. Input power factor is a little higher than single- phase circuit. Harmonics in the input current is a little lower than the single-phase circuit due to the cancellation of some harmonics among the 3 phases. To improve the input power factor: Use DC bias or 3k order component bias on each of the 3 output phase voltages 37

38 Features and applications Features Direct frequency conversion high efficiency Bidirectional energy flow, easy to realize 4-quadrant 4 operation Very complicated too too many power semiconductor devices Low output frequency Low input power factor and bad input current waveform Applications High power low speed AC motor drive 38

39 4.4 Matrix converter Circuit configuration Input utput 39

40 Matrix converter Usable input voltage U m U 1m U 1m 1 2U m a) b) c) a) Single-phase input voltage b) Use 3 phase voltages to construct output voltage c) Use 3 line-line voltages to construct output voltage

41 Features Direct frequency conversion high efficiency Can realize good input and output waveforms, low harmonics, and nearly unity displacement factor Bidirectional energy flow, easy to realize 4-quadrant 4 operation utput frequency is not limited by input frequency No need for bulk capacitor (as compared to indirect frequency converter) Very complicated too too many power semiconductor devices utput voltage magnitude is a little lower as compared to indirect frequency converter. 41

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