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Chapter 6 AC to AC Converters ( AC Controllers and Frequency Converters ) Classification of AC to AC converters Power Same frequency variable magnitude AC power AC power AC controllers Variable frequency AC power Frequency converters (Cycloconverters) AC to AC converters 2 Classification of AC controllers Phase control: AC voltage controller (Delay angle control) Integral cycle control: AC power controller Power AC controller PWM control: AC chopper (Chopping control) On/off switch: electronic AC switch PWM: Pulse Width Modulation 3 Classification of frequency converters Power 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 Outline 6.1 AC voltage controllers Power 6.2 Other AC controllers 6.3 Thyristor cycloconverters 6.4 Matrix converters 5 6.1 AC voltage controllers 6.1.1 Single-phase AC voltage controller 6.1.2 Three-phase AC voltage controller Power Applications Lighting control Soft-start of asynchronous motors Adjustable speed drive of asynchronous motors Reactive power control 6 6.1.1 Single-phase AC voltage controller Resistive load u1 VT1 io O wt uo VT2 uo Power u1 R O io wt O wt u VT The phase shift range (operation range of phase delay angle): O wt 0ap 7 Resistive load, quantitative analysis RMS value of output voltage Uo p 1 p a 2U 1 sin w t d w t U 1 2 1 p a (6-1) sin 2a 2p p RMS value of output current Power Uo Io R (6-2) RMS value of thyristor current 2 U1 1 2U1 sin w t IT d w t 2p a R R p 1 a sin 2a (1 ) 2 p 2p (6-3) Power factor of the circuit P UoIo Uo S U1 I o U1 1 p a sin 2a 2p p (6-4) 8 Inductive (Inductor-resistor) load, operation principle u1 VT1 Power u1 VT2 uo wt O io uG1 R The phase shift range: ap 0.6 O uG2 wt O uo wt O io wt O wt uVT O wt 9 Inductive load, quantitative analysis Differential equation d io L Rio 2U 1 sin w t dt (6-5) io w t a 0 2U 1 [sin(wt ) sin(a )e Z (6-6) a wt a q Considering io=0 when wt=a+q Power io sin(a q ) sin(a )e q tg a wt tg q/(°) 140 Solution We have ã 90¡ = ¡ã 75 ¡ã 60 ¡ã 45 ¡ã 30 ¡ã 15 ¡ã 0 180 ] 100 60 20 0 20 60 100 a/(°) 140 180 图4-3 (6-7) The RMS value of output voltage, output current, and thyristor current can then be calculated. 10 Inductive load, when a < The circuit can still work. Power u1 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 wt =aa < . wt O iG1 p Oa wt iG2 O io iT1ap Oa q wt wt iT2 图4-5 Start-up transient 11 Harmonic analysis There is no DC component and even order harmonics in the current. 100 80 The higher the number of harmonic ordinate, the lower the harmonic content. In/I*/% – The current waveform is halfwave symmetric. Fundamental 60 40 3 Power 20 5 7 a90 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 is increasing. 0 60 120 180 a/( °) Current harmonics for the resistive load 12 6.1.2 Three-phase AC voltage controller Power Classification of three-phase circuits Y connection Branch-controlled ∆ connection Line-controlled ∆ connection Neutral-point-controlled ∆ connection 13 3-phase 3-wire Y connection AC voltage controller ia U a0' VT 1 a ua VT 3 b n u b VT 5 Power VT 4 n' VT 6 c u 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 the two conducting phases are half of the corresponding line to line voltage, while the load voltage of the other phase is 0. 14 3-phase 3-wire Y connection AC voltage controller Resistive load, 0 a < 60 VT VT Power VT VT 4 1 VT 1 VT 3 6 VT 5 u ab 2 ua VT 6 VT 2 5 u ac 2 u ao' 0 p 3 a t 1 t 2 2p 4p 5p 3 t 3 3 2 p 3 15 3-phase 3-wire Y connection AC voltage controller Resistive load, 60 a < 90 VT VT 5 VT Power u u 2 u VT 6 ab VT 1 u a 2 a p 3 t 1 2p 3 t 2 VT 2 4 5 VT 6 ac 4p 3 ao' 0 VT 3 p t 5p 3 2p 3 16 3-phase 3-wire Y connection AC voltage controller Resistive load, 90 a < 150 VT VT 5 VT VT u 4 Power VT 5 ab 6 1 VT VT u 6u a VT 3 VT 2 VT 3 VT 2 VT 5 5 VT 4 VT 4 6 ac 2 u VT VT 1 5p 2 ao' 3 0 p 2p 3 3 a p 4p 2p 3 17 6.2 Other AC controllers 6.2.1 Integral cycle control—AC power controller Power 6.2.2 Electronic AC switch 6.2.3 Chopping control—AC chopper 18 6.2.1 Integral cycle control —AC power controller uo VT1 2 U1 io O Power u1 VT2 uo Conduction 2pN = M angle R p M 2p M u1 uo,io 3p M 4p M =M *Line period =2p wt Line period Control period 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. 19 Spectrum of the current in AC power controller Power There is NO harmonics in the ordinary sense. In/I0m There is harmonics as to the control frequency. As to the line frequency, these components become fractional harmonics. 0.6 0.5 0.4 0.3 0.2 0.1 0 0 2 4 6 8 10 12 14 Harmonic order as to control frequency 1 2 3 4 5 Harmonic order as to line frequency 20 6.2.2 Electronic AC switch Power Circuit topologies are the same as AC voltage controllers. But the back-to-back thyristors are just used like a switch to turn the equipment on or off. 21 6.2.3 Chopping control—AC chopper Principle of chopping control Power 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 22 AC chopper Power Modes of operation u o>0, io>0: u o>0, io<0: u o<0, io>0: u o<0, io<0: V1 charging, V3 freewheeling V4 charging, V2 freewheeling V3 charging, V1 freewheeling V2 charging, V4 freewheeling 23 6.3 Thyristor cycloconverters (Thyristor AC to AC frequency converter) Another name—direct frequency converter (as compared to AC-DC-AC frequency converter which is discussed in Chapter 8) Power Can be classified into single-phase and threephase according to the number of phases at output 6.3.1 Single-phase thyristor-cycloconverter 6.3.2 Three-phase thyristor-cycloconverter 24 6.3.1 Single-phase thyristor-cycloconverter Circuit configuration and operation principle N P Power uo uo O aP= p 2 Output voltage Z a P=0 Average output voltage aP= p 2 wt 25 Single-phase thyristor-cycloconverter uo,io Modes of operation uo O t1 uP io iP Power uP uo iN io t3 t2 t4 t uo t O uN t5 uN O uo t iP O iN t O t P Rectifi cation Inver sion N Blocking Blocking Rectifi Inver cation sion 26 Single-phase thyristor-cycloconverter Typical waveforms uo Power O wt io O wt 1 3 4 6 5 2 图4-20 27 Modulation methods for firing delay angle Calculation method – For the rectifier circuit uo U d0 cosa (6-15) Power – For the cycloconverter output uo U om sin w o t (6-16) – Equating (6-15) and (6-16) U cosa om sin w o t sin w o t U d0 (6-17) – Therefore u2 u3 u4 u5 u6 u1 wt aP3 us2 us3 aP4 us4 us5 us6 us1 uo wt a cos1 ( sin wo t ) (6-18) 图4-21 Cosine wave-crossing method Principle of cosine wave-crossing method 28 Calculated results for firing delay angle Power U om (0 r 1) U d0 a/(°) Output voltage ratio (Modulation factor) 180 1.0 0.9 0.8 0.3 0.2 0.1 150 120 =0 90 = 0.1 0.2 0.3 0.8 0.9 1.0 60 30 0 p 2 p 3p 2 2p w0t Output voltage phase angle 29 Input and output characteristics Maximum output frequency: 1/3 or 1/2 of the input frequency if using 6pulse rectifiers Power 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 0.8 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1.0 0.8 0.6 0.4 0.2 0 Load power factor Load power factor (lagging) (leading) 30 6.3.2 Three-phase thyristor-cycloconverter Power The configuration with common input line 31 Three-phase thyristor-cycloconverter Power The configuration with star-connected output 32 Three-phase thyristor-cycloconverter Typical waveforms Power Output voltage Input current with Single-phase output 0 200 t/ms 0 200 t/ms 0 200 t/ms Input current with 3-phase output 33 Input and output characteristics The maximum output frequency and the harmonics in the output voltage are the same as in singlephase circuit. Power Input power factor is a little higher than singlephase 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 34 Features and applications Power Features – Direct frequency conversion—high efficiency – Bidirectional energy flow, easy to realize 4-quadrant operation – Very complicated—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 35 6.4 Matrix converter Circuit configuration Input a b c Power u S11 S12 S13 v S21 S22 Sij Output S23 w S31 S32 a) S33 b) 36 Matrix converter Usable input voltage U1m Power Um a) a) Single-phase input voltage 3 2 1 2 Um b) b) Use 3 phase voltages to construct output voltage U1m c) c) Use 3 line-line voltages to construct output voltage 37 Power 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 operation Output frequency is not limited by input frequency No need for bulk capacitor (as compared to indirect frequency converter) Very complicated—too many power semiconductor devices Output voltage magnitude is a little lower as compared to indirect frequency converter. 38