Chapter 5 AC-to-AC Converters “Introduction to Modern Power Electronics”, 3rd Ed., John Wiley 2015 by Andrzej M. Trzynadlowski Chapter 5 AC-AC Converters 1 Content •5.1 AC Voltage Controllers 196 •5.1.1 Phase-Controlled Single-Phase AC Voltage Controller 196 •5.1.2 Phase-Controlled Three-Phase AC Voltage Controllers 203 •5.1.3 PWM AC Voltage Controllers 211 •5.2 Cycloconverters 215 •5.3 Matrix Converters 220 •5.3.1 Classic Matrix Converters 220 •5.3.2 Sparse Matrix Converters 227 •5.3.3 Z-Source Matrix Converters 230 •5.4 Device Selection for AC-to-AC Converters 234 •5.5 Common Applications of AC-to-AC Converters 235 Chapter 5 AC-AC Converters 2 Single-phase ac voltage controller T1 ii = io io T2 SOURCE vo vi LOAD Fig. 5.1 Chapter 5 AC-AC Converters 3 Waveforms of output voltage and current in a single-phase ac voltage controller (π = 30π ): (a) πΌπ = 45π , (b) πΌπ = 135π • RMS value of the output voltage • Depends on firing angleπΌπ and extinction angle πΌπ • Note: There is no close form solution for πΌπ Chapter 5 AC-AC Converters Fig. 5.2 4 Envelope of control characteristics, ππ = π(πΌπ ), of a single-phase ac voltage controller Fig. 5.3 Chapter 5 AC-AC Converters 5 Operation of the single-phase ac voltage controller with: (a) single-pulse gate signal, (b) multipulse gate signal Fig. 5.4 Chapter 5 AC-AC Converters 6 Fully controlled three-phase ac voltage controller SUPPLY LINE A B C iA iB TA va iC TB vb vc TC LOAD Fig. 5.7 Chapter 5 AC-AC Converters 7 Voltage and current distribution in a fully controlled three-phase ac voltage controller: (a) two triacs conducting, (b) three triacs conducting • In three-phase connection at least two switches need to conduct, otherwise there would not be a path for current • It can be shown that output voltages are vA vB vB vC vC -i B iA TA vA TB iB iA TC TA TB iC TC 1_ v 2 BA 1_ v 2 AB vA B vA (a) vB vC (b) Fig. 5.8 Chapter 5 AC-AC Converters 8 Phase-A output voltage waveform in a fully-controlled three-phase ac voltage controller with R load and small firing angles: (a) πΌπ = 0π , (b) πΌπ = 30π Fig. 5.9 Chapter 5 AC-AC Converters 9 Phase-A output voltage waveform in a fully-controlled three-phase ac voltage controller with R load and large firing angles: (a) πΌπ = 75π , (b) πΌπ = 120π Fig. 5.10 Chapter 5 AC-AC Converters 10 Three-phase ac voltage controllers connected before the load: (a) half-controlled, (b) delta-connected A A B B C C (a) (b) Fig. 5.13 Chapter 5 AC-AC Converters 11 Three-phase ac voltage controllers connected after the load: (a) wye-connected, (b) delta-connected A A B B C C (b) (a) Fig. 5.14 Chapter 5 AC-AC Converters 12 Three-phase four-wire ac voltage controller A B C N Fig. 5.15 Chapter 5 AC-AC Converters 13 Single-phase ac chopper with input filter S1 •Input filter is required to attenuate high-frequency current harmonics •Inductance of ac system is often enough •Ac choppers have been developed to improve input power factor, control characteristics and quality of output current i i' ii io S2 vi S3 S4 vo Fig. 5.16 Chapter 5 AC-AC Converters 14 Waveforms of voltages and currents in a single-phase ac chopper: (a) output voltage and current, (b) input voltage and current after the input filter, and the fundamental output current Fig. 5.17 Chapter 5 AC-AC Converters 15 Control characteristic of the ac chopper Fig. 5.18 Chapter 5 AC-AC Converters 16 Wye-connected three-phase ac chopper A B C S2 S1 S3 S4 Fig. 5.19 Chapter 5 AC-AC Converters 17 Delta-connected three-phase ac chopper A B C S1 S4 S2 S3 Fig. 5.20 Chapter 5 AC-AC Converters 18 5.2 Cycloconverters • Direct ac-ac converters without intermeadiate dc bus • Operation is based on line-commutation, i.e. thyristors • Control angle of the thyristor bridge is controlled continuously => variable dc-voltage, which is actually ac • Can be built for high powers • Output frequecy must be much lower than input, nominal frequency typically one fith on linefrequency (< 10 Hz) and maximum around 20 Hz silta 1 silta 2 kuormitus R S T Chapter 5 AC-AC Converters 19 Single-phase cycloconverter Ouput voltage •Resistive+inductive load •Average of dc controlled sinusoidally • ƒ1 = 50, ƒ2 =16,5 Hz •Phase-shift in load can be plus, minus or zero •Power flow can be in both directions Ouput current Control angle of the conduction bridge Bridge 1 Bridge 2 TS= rectifier mode, VS=inverter mode Chapter 5 AC-AC Converters 20 Three-phase cycloconverter • Three separate converters • All phases are indepent, i.e. no star or delta connection used • Does’t quarantee the cancellation of zero sequency components as in normal threephase connection • No transformer in the input needed, i.e. cheaper Chapter 5 AC-AC Converters 21 Three-phase cycloconverter •Load is connected either in star or delta •Transformer is needed in the input side! •Why? if Chapter 5 AC-AC Converters 22 Three-phase three-pulse cycloconverter Fig. 5.21 Chapter 5 AC-AC Converters 23 Three-phase six-pulse cycloconverter with isolated phase loads Fig. 5.22 Chapter 5 AC-AC Converters 24 Three-phase six-pulse cycloconverter with interconnected phase loads Fig. 5.23 Chapter 5 AC-AC Converters 25 Waveforms of the firing angle in a cycloconverter • Output voltage depends on the control angle • On the other hand, output needs to change sinusoidally • Therefore the output angle dependent change of the control angle is πΌπ ππ π‘ = πππ −1 [π π ππ ππ π‘ ] Fig. 5.24 Chapter 5 AC-AC Converters 26 Output voltage waveforms in a six-pulse cycloconverter (ππ π = 0.2): (a) M = 1, (b) M = 0.5 Fig. 5.25 Chapter 5 AC-AC Converters 27 5.4 Matrix converter SUPPLY LINE A B C iA iB vA SAc MATRIX CONVERTER S Ab SAa iC vB SBc SBb SBa vC SCc SCb SCa LOAD a b c ia ib ic va vb vc vn Fig. 5.26 Chapter 5 AC-AC Converters 28 The voltages va, vb, and vc, at the output terminals are given by π£π π₯π΄π π£π = π₯π΄π π£π π₯π΄π π₯π΅π π₯π΅π π₯π΅π π₯πΆπ π₯πΆπ π₯πΆπ π£π΄ π£π΅ π£πΆ As 1 π£π = (π£π + π£π + π£π ) 3 then π£ππ 2 −1 −1 π£π 1 π£ππ = −1 2 −1 π£π 3 π£ππ −1 −1 2 π£π The input currents, iA, iB, and iC, are related to the output currents, ia, ib, and ic, as π₯π΄π ππ΄ ππ΅ = π₯π΅π π₯πΆπ ππΆ π₯π΄π π₯π΅π π₯πΆπ π₯π΄π π₯π΅π π₯πΆπ Chapter 5 AC-AC Converters ππ ππ ππ 29 Arrangement of 3ο-1ο and 1ο-3ο matrix converters equivalent to a 3ο-3ο matrix converter • Full matrix converter can be seen as combination of two virtual converters • CONV1 A B C • Virtual rectifier • CONV2 • Virtual inverter • P and N virtual dc bus a Idc CONV 1 SAP SAN SBP SBN SCP SCN Vdc c b CONV 2 SPa SNa SPb SNb P SPc SNc N Fig. 5.27 Chapter 5 AC-AC Converters 30 State AAB as realized by activation od switches in (a) virtual rectifier and inverter, (b) matrix converter A B C P SAP SBP SCP SAN SBN SCN N SPa SPb SPc SNa SNb SNc b a c (a) A B C SAa SBa SCa SAb SBb SCb SAc SBc SCc a b c (b) Fig. 5.28 Chapter 5 AC-AC Converters 31 Reference current vector in the vector space of input currents of the virtual rectifier jq j 3 IDC I 0PN • E.g. when virtual rectifier is in state PN0 input currents are Idc, -Idc and 0 and the corresponding input current space vector is III i* I PON ο‘ I* INP0 3 3 πΌPNO = πΌdc − π πΌ 2 3 dc • In the same way the other five vectors can be obtained • Current reference is shown in Fig. 5.29 too. • Input current should be alligned with input voltage vector in order to obtain unity input power factor II ο’ IV IN0P Fig. 5.29 Chapter 5 AC-AC Converters _ 3 I 2 DC d I VI V IPN0 I0NP 32 Reference voltage vector in the vector space of line-to-neutral output voltages of the virtual inverter jq • Virtual converter 2 can be analyzed in a similar way • E.g. state PNN means that output voltages are vP, vP and VN where vP and vN are potentials of line P and N • Space-vector of the corresponding output voltage is • All the six space vectors are shown in Fig 5.30 VNPN III VNPP v* _ V3 j_ 2 VDC ο‘ VPPN II ο’ I V* VDC VI IV d VPNN V VNNP VPNP Fig. 5.30 Chapter 5 AC-AC Converters 33 Modulation index, mrec, of the virtual rectifier is defined as and that of the virtual inverter as ππππ ≡ ππππ£ πΌπ,π πΌππ ππ,π ≡ πππ yielding the modulation index (and magnitude control ratio), m, of the whole matrix converter: π= 3 π π πππ ππ 2 πππ πππ£ where πππ ππ is the power factor of the virtual rectifier, usually set to 1. TABLE 5.1 Switching Pattern for 3Φ-3Φ Matrix Converter with Space Vector PWM Switching Subcycle 1 2 3 4 5 6 7 8 9 Rectifier State XI XI YI YI ZI YI YI XI XI Inverter State XV YV YV XV ZV XV YV YV XV ππ π»ππ dXIdXV/2 dXIdYV/2 dYIdYV/2 dYIdXV/2 1 – (dXI + dYI )( dXV + dYV) dYIdXV/2 dYIdYV/2 dXIdYV/2 dXIdXV/2 ππ = π sin 60o − πΌ ππ = π sin πΌ ππ = 1 − ππ − ππ Chapter 5 AC-AC Converters 34 Output voltage and current waveforms in a 3ο-3ο matrix converter: (a) m = 0.75, ππ π = 2.8 , (b) m = 0.35, ππ π = 0.7 Fig. 5.31 Chapter 5 AC-AC Converters 35 Bidirectional semiconductor power switches: (a) two IGBTs and two diodes, (b) one IGBT and four diodes (b) (a) Fig. 5.32 Chapter 5 AC-AC Converters 36 Circuit diagram of the classic 3ο-3ο matrix converter A a B b C c Fig. 5.33 Chapter 5 AC-AC Converters 37 Indirect matrix converter RECTIFIER P INVERTER A a B b C c N Fig. 5.34 Chapter 5 AC-AC Converters 38 Sparse matrix converter • Polarity of the intermediate voltage is fixed to be only positive • Rectifier is simpler, i.e. less components A a B b C c Fig. 5.35 Chapter 5 AC-AC Converters 39 Ultra-sparse matrix converter • Power flow is only towards the load • Further simplication of the rectifier A a B b C c Fig. 5.36 Chapter 5 AC-AC Converters 40 Z-source dc link L1 • In matrix converters ouput voltage amplitude is smaller than input voltage D • Output is less than √3/2 C2 vi vs CONVERTER D DC SOURCE • Z-source converters can be used to boost up the output voltage C1 S VDC L2 Fig. 5.37 Chapter 5 AC-AC Converters 41 Z-source during the non-shoot-through converter state A B vL VC VC VDC vi vs vL D C Fig. 5.38 Chapter 5 AC-AC Converters 42 Z-source during the shoot-through converter state A B vL VC VDC VC vs vi vL D C Fig. 5.39 Chapter 5 AC-AC Converters 43 Z-source matrix converter A a B b C c Fig. 5.40 Chapter 5 AC-AC Converters 44 TABLE 5.2 Switching Pattern for the Example Matrix Converter Switching Subcycle 1 2 3 4 5 6 7 8 9 Rectifier State 0PN 0PN NP0 NP0 Z00 or 0Z0 NP0 NP0 0PN 0PN Inverter State PPN NPN NPN PPN PPP PPN NPN NPN PPN ππ π»ππ 0.156 0.035 0.009 0.057 0.486 0.057 0.009 0.035 0.156 TABLE 5.3 Activation of Switches in the Example Matrix Converter Switching Subcycle 1 2 3 4 5 6 7 8 9 State of Matrix Converter BBC CBC ABA BBA BBB BBA ABA CBC BBC Activated Switches SBa, SBb, SCc SCa, SBb, SCc SAa, SBb, SAc SBa, SBb, SAc SBa, SBb, SBc SBa, SBb, SAc SAa, SBb, SAc SCa, SBb, SCc SBa, SBb, SCc Chapter 5 AC-AC Converters Duration (µs) 31.2 7.0 1.8 11.4 97.2 11.4 1.8 7.0 31.2 45 Switching signals for individual switches in the matrix converter in Example 5.4 SAa SAb SAc S Ba SBb SBc SCa SCb SCc 0 50 100 150 200 TIME, s Fig. 5.41 Chapter 5 AC-AC Converters 46
