Elements of Power Electronics PART II: Topologies and applications

Transcription

1 Elements of Power Electronics PART II: Topologies and applications Fabrice Frébel September 2 st, 207

2 PART II: Topologies and applications Chapter 6: Converter Circuits Applications

3 Chapter 6: Converter Circuits What is a topology? Why different topologies? The choice of a topology depends on the application:. voltage/current range/direction, 2. power direction, 3. number of inputs/outputs, 4. isolated vs. non-isolated, 5. input and output current ripple, 6. switches/transformer/inductor utilization, 7. soft switching vs. hard switching, 8. compactness (see Google interest million-little-box.html), 9. EMC considerations... Today s optimum topologies are not tomorrow s better topologies because of semiconductors evolution (storageless example). Topology selection is a first important decision when designing a power converter.

4 Second edition Robert W. Erickson Dragan Maksimovic University of Colorado, Boulder Chapter : Introduction

5 Chapter 6. Converter Circuits 6.. Circuit manipulations 6.2. A short list of converters 6.3. Transformer isolation 6.4. Converter evaluation and design 6.5. Summary of key points Where do the boost, buck-boost, and other converters originate? How can we obtain a converter having given desired properties? What converters are possible? How can we obtain transformer isolation in a converter? For a given application, which converter is best?

6 6.. Circuit Manipulations L 2 C R V Begin with buck converter: derived in Chapter from first principles Switch changes dc component, low-pass filter removes switching harmonics Conversion ratio is M = D 2

7 6... Inversion of source and load Interchange power input and output ports of a converter Buck converter example Port Port 2 L V 2 = DV V 2 V 2 Power flow 3

8 Inversion of source and load Interchange power source and load: Port Port 2 L V 2 V 2 Power flow V 2 = DV V = D V 2 4

9 Realization of switches as in Chapter 4 Reversal of power flow requires new realization of switches Transistor conducts when switch is in position 2 Interchange of D and D Port L Port 2 V V 2 Power flow V = D' V 2 Inversion of buck converter yields boost converter 5

10 6..2. Cascade connection of converters Converter Converter 2 V V V = M V (D) = M g V 2 (D) V D V = M (D) V Vg = M(D)=M (D)M 2 (D) V = M 2 (D)V 6

11 Example: buck cascaded by boost L L C V C 2 R V { { Buck converter Boost converter V = D V V = D V = V D g D 7

12 Buck cascaded by boost: simplification of internal filter Remove capacitor C L L C 2 R V Combine inductors L and L 2 L i L 2 2 V Noninverting buck-boost converter 8

13 Noninverting buck-boost converter L i L 2 2 V subinterval subinterval 2 i L V V i L 9

14 Reversal of output voltage polarity subinterval subinterval 2 i L noninverting buck-boost V i L V i L i L inverting buck-boost V V 0

15 Reduction of number of switches: inverting buck-boost Subinterval Subinterval 2 i L i L V V One side of inductor always connected to ground hence, only one SPDT switch needed: 2 i V L = D V Vg D

16 Discussion: cascade connections Properties of buck-boost converter follow from its derivation as buck cascaded by boost Equivalent circuit model: buck :D transformer cascaded by boost D : transformer Pulsating input current of buck converter Pulsating output current of boost converter Other cascade connections are possible Cuk converter: boost cascaded by buck 2

17 6..3. Rotation of three-terminal cell Treat inductor and SPDT switch as threeterminal cell: Three-terminal cell A a b B c C 2 v Three-terminal cell can be connected between source and load in three nontrivial distinct ways: a-a b-b c-c buck converter a-c b-a c-b boost converter a-a b-c c-b buck-boost converter 3

18 Rotation of a dual three-terminal network A capacitor and SPDT switch as a threeterminal cell: Three-terminal cell A a b B 2 c C v Three-terminal cell can be connected between source and load in three nontrivial distinct ways: a-a b-b c-c a-c b-a c-b a-a b-c c-b buck converter with L-C input filter boost converter with L-C output filter Cuk converter 4

19 6..4. Differential connection of load to obtain bipolar output voltage dc source load Converter V = M(D) D Converter 2 V V 2 V Differential load voltage is V = V V 2 The outputs V and V 2 may both be positive, but the differential output voltage V can be positive or negative. V 2 = M(D') D' 5

20 Buck converter } ELEC0055: Elements of Power Electronics - Fall 207 Differential connection using two buck converters 2 2 V V Converter # transistor driven with duty cycle D Converter #2 transistor driven with duty cycle complement D Differential load voltage is V = D D' V 2 Simplify: Buck converter 2{ 6 V =(2D )

21 Conversion ratio M(D), differentially-connected buck converters V =(2D ) M(D) D 7

22 Buck converter } ELEC0055: Elements of Power Electronics - Fall 207 Simplification of filter circuit, differentially-connected buck converters Original circuit Bypass load directly with capacitor 2 V V 2 V 2 2 V 2 Buck converter 2{ 8

23 Simplification of filter circuit, differentially-connected buck converters Combine series-connected inductors Re-draw for clarity 2 L V g i 2 L C V R 2 2 V H-bridge, or bridge inverter Commonly used in single-phase inverter applications and in servo amplifier applications 9

24 Differential connection to obtain 3ø inverter dc source Converter 3øac load With balanced 3ø load, neutral voltage is V = M(D ) V V n = 3 V V 2 V 3 D Converter 2 V 2 = M(D 2 ) D 2 Converter 3 V 3 = M(D 3 ) D 3 V 2 V 3 v bn v an v cn V n Phase voltages are V an = V V n V bn = V 2 V n V cn = V 3 V n Control converters such that their output voltages contain the same dc biases. This dc bias will appear at the neutral point V n. It then cancels out, so phase voltages contain no dc bias. 20

25 3ø differential connection of three buck converters dc source 3φac load V v an V 2 v bn v cn V n V 3 2

26 3ø differential connection of three buck converters Re-draw for clarity: dc source 3φac load v an v bn v cn V n Voltage-source inverter or buck-derived three-phase inverter 22

27 The 3ø current-source inverter dc source 3φac load v an v bn v cn V n Exhibits a boost-type conversion characteristic 23

28 6.2. A short list of converters An infinite number of converters are possible, which contain switches embedded in a network of inductors and capacitors Two simple classes of converters are listed here: Single-input single-output converters containing a single inductor. The switching period is divided into two subintervals. This class contains eight converters. Single-input single-output converters containing two inductors. The switching period is divided into two subintervals. Several of the more interesting members of this class are listed. 24

29 Single-input single-output converters containing one inductor Use switches to connect inductor between source and load, in one manner during first subinterval and in another during second subinterval There are a limited number of ways to do this, so all possible combinations can be found After elimination of degenerate and redundant cases, eight converters are found: dc-dc converters buck boost buck-boost noninverting buck-boost dc-ac converters bridge Watkins-Johnson ac-dc converters current-fed bridge inverse of Watkins-Johnson 25

30 Converters producing a unipolar output voltage. Buck M(D)=D M(D) 2 V D 2. Boost 2 M(D)= D M(D) 4 3 V D 26

31 Converters producing a unipolar output voltage 3. Buck-boost M(D)= D D 2 V M(D) D 4. Noninverting buck-boost M(D)= D D 2 2 V M(D) D 27

32 Converters producing a bipolar output voltage suitable as dc-ac inverters 5. Bridge M(D)=2D M(D) 2 V g V D 6. Watkins-Johnson 2 V g V or M(D)= 2D D 2 V M(D) D

33 Converters producing a bipolar output voltage suitable as ac-dc rectifiers 7. Current-fed bridge V 2 M(D)= 2D 2 M(D) D 8. Inverse of Watkins-Johnson 2 V M(D)= D 2D or V g 2 V M(D) D

34 Several members of the class of two-inductor converters. Cuk M(D)= D D 2 V M(D) D 2. SEPIC M(D)= D D M(D) V g V D 30

35 Several members of the class of two-inductor converters 3. Inverse of SEPIC M(D)= D D M(D) V D 4. Buck 2 M(D)=D 2 M(D) 2 2 V D 3

36 6.3. Transformer isolation Objectives: Isolation of input and output ground connections, to meet safety requirements Reduction of transformer size by incorporating high frequency isolation transformer inside converter Minimization of current and voltage stresses when a large step-up or step-down conversion ratio is needed use transformer turns ratio Obtain multiple output voltages via multiple transformer secondary windings and multiple converter secondary circuits 32

37 A simple transformer model Multiple winding transformer Equivalent circuit model v (t) i (t) n : n 2 i 2 (t) v 2 (t) i 3 (t) v 3 (t) v (t) i (t) i M (t) L M i '(t) v (t) n = v 2(t) n = v 3(t) 2 n = =n i '(t)n 2 i 2 (t)n 3 i 3 (t)... n : n 2 : n 3 i 2 (t) v 2 (t) i 3 (t) v 3 (t) : n 3 Ideal transformer 33

38 The magnetizing inductance L M Models magnetization of transformer core material Appears effectively in parallel with windings If all secondary windings are disconnected, then primary winding behaves as an inductor, equal to the magnetizing inductance At dc: magnetizing inductance tends to short-circuit. Transformers cannot pass dc voltages Transformer saturates when magnetizing current i M is too large Transformer core B-H characteristic B(t) v (t) dt saturation slope L M H(t) i M (t) 34

39 Volt-second balance in L M The magnetizing inductance is a real inductor, obeying di v (t)=l M (t) M dt integrate: v (t) i M (t)i M (0) = t v L (τ)dτ M 0 Magnetizing current is determined by integral of the applied winding voltage. The magnetizing current and the winding currents are independent quantities. Volt-second balance applies: in steady-state, i M (T s ) = i M (0), and hence 0= T T s v (t)dt s 0 i (t) i M (t) L M i '(t) n : n 2 : n 3 Ideal transformer i 2 (t) v 2 (t) i 3 (t) v 3 (t) 35

40 Transformer reset Transformer reset is the mechanism by which magnetizing inductance volt-second balance is obtained The need to reset the transformer volt-seconds to zero by the end of each switching period adds considerable complexity to converters To understand operation of transformer-isolated converters: replace transformer by equivalent circuit model containing magnetizing inductance analyze converter as usual, treating magnetizing inductance as any other inductor apply volt-second balance to all converter inductors, including magnetizing inductance 36

41 6.3.. Full-bridge and half-bridge isolated buck converters Full-bridge isolated buck converter Q D Q 3 D 3 i (t) : n D 5 i D5 (t) L i(t) v T (t) v s (t) C R v Q2 D 2 Q4 D 4 : n D 6 37

42 Full-bridge, with transformer equivalent circuit Q D Q 3 D 3 i (t) i '(t) i M (t) : n D 5 i D5 (t) i(t) L v T (t) L M v s (t) C R v Q2 D 2 Q4 D 4 : n Ideal D 6 i D6 (t) Transformer model 38

43 Full-bridge: waveforms i M (t) v T (t) i(t) v s (t) i D5 (t) I conducting devices: L M 0 0 n i 0 i L M n 0.5 i 0.5 i 0 0 DT s T s T s DT s 2T s Q D 5 Q 2 D 5 Q 4 D 6 Q 3 D 6 D 5 D 6 0 t During first switching period: transistors Q and Q 4 conduct for time DT s, applying voltseconds DT s to primary winding During next switching period: transistors Q 2 and Q 3 conduct for time DT s, applying voltseconds DT s to primary winding Transformer volt-second balance is obtained over two switching periods Effect of nonidealities? 39

44 Effect of nonidealities on transformer volt-second balance Volt-seconds applied to primary winding during first switching period: ( (Q and Q 4 forward voltage drops))( Q and Q 4 conduction time) Volt-seconds applied to primary winding during next switching period: ( (Q 2 and Q 3 forward voltage drops))( Q 2 and Q 3 conduction time) These volt-seconds never add to exactly zero. Net volt-seconds are applied to primary winding Magnetizing current slowly increases in magnitude Saturation can be prevented by placing a capacitor in series with primary, or by use of current programmed mode (Chapter 2) 40

45 Operation of secondary-side diodes v s (t) i D5 (t) : n : n conducting devices: n i D 5 D 6 i D5 (t) 0 v s (t) L n C i(t) 0.5 i 0.5 i 0 t 0 DT s T s T s DT s 2T s Q D 5 Q 2 D 5 Q 4 D 6 Q 3 D 6 D 5 D 6 R 0 v During second (D ) subinterval, both secondary-side diodes conduct Output filter inductor current divides approximately equally between diodes Secondary amp-turns add to approximately zero Essentially no net magnetization of transformer core by secondary winding currents 4

46 Volt-second balance on output filter inductor : n D 5 i D5 (t) L i(t) i(t) I i v s (t) C R v v s (t) n n : n D 6 i D5 (t) i i 0.5 i 0 0 t V = v s V = nd M(D) = nd conducting devices: buck converter with turns ratio 0 DT s T s T s DT s 2T s Q D 5 Q 2 D 5 Q 4 D 6 Q 3 D 6 D 5 D 6 42

47 Half-bridge isolated buck converter Q D C a i (t) : n D 3 i D3 (t) L i(t) v T (t) v s (t) C R v Q2 D 2 C b : n D 4 Replace transistors Q 3 and Q 4 with large capacitors Voltage at capacitor centerpoint is 0.5 v s (t) is reduced by a factor of two M = 0.5 nd 43

48 Forward converter n : n 2 : n 3 D 2 L D 3 C R V Q D Buck-derived transformer-isolated converter Single-transistor and two-transistor versions Maximum duty cycle is limited Transformer is reset while transistor is off 44

49 Forward converter with transformer equivalent circuit n : n 2 : n 3 D 2 L i M i ' L M v v 2 v 3 D 3 v D3 C R V Q i i 2 i 3 D v Q 45

50 Forward converter: waveforms v i M v D3 n n 2 L n V g M n 2 L M 0 n 3 n 0 Magnetizing current, in conjunction with diode D, operates in discontinuous conduction mode Output filter inductor, in conjunction with diode D 3, may operate in either CCM or DCM Conducting devices: 0 0 DT s D 2 T s D 3 T s T s Q D D 3 D 2 D 3 t 46

51 Subinterval : transistor conducts i M n : n 2 : n 3 i ' D 2 on L L M v v 2 v 3 v D3 C R V i i i 2 3 Q on D off 47

52 Subinterval 2: transformer reset n : n 2 : n 3 L i M i ' L M v v 2 v 3 D 3 on v D3 C R V i i 3 i 2 = i M n /n2 Q off D on 48

53 Subinterval 3 n : n 2 : n 3 L i M = 0 L M v i ' v 2 v 3 D 3 on v D3 C R V i i i 3 2 Q off D off 49

54 Magnetizing inductance volt-second balance v 0 i M n n 2 L n V g M n 2 L M 0 v = D D 2 n /n 2 D 3 0 =0 50

55 Transformer reset From magnetizing current volt-second balance: Solve for D 2 : v = D D 2 n /n 2 D 3 0 =0 D 2 = n 2 n D D 3 cannot be negative. But D 3 = D D 2. Hence D 3 =D D 2 0 D 3 =D n 2 n 0 Solve for D D n 2 n for n = n 2 : D 2 5

56 What happens when D > 0.5 i magnetizing current M (t) waveforms, D < 0.5 for n = n 2 DT s D 2 T s D 3 T s t i M (t) D > 0.5 DT s D 2 T s t 2T s 52

57 Conversion ratio M(D) : n 3 D 2 L D 3 C R V v D3 n 3 n 0 0 DT s D 2 T s D 3 T s T s t v D3 = V = n 3 n D Conducting devices: Q D D 3 D 2 D 3 53

58 Maximum duty cycle vs. transistor voltage stress Maximum duty cycle limited to which can be increased by decreasing the turns ratio n 2 / n. But this increases the peak transistor voltage: For n = n 2 D n 2 n max v Q = n n 2 D 2 and max(v Q ) = 2 54

59 The two-transistor forward converter D Q : n D 3 L D 4 C R V D 2 Q 2 V = nd D 2 max(v Q ) = max(v Q2 ) = 55

60 Push-pull isolated buck converter Q v T (t) : n i D (t) D i(t) L v s (t) C R V v T (t) D 2 Q 2 V = nd 0 D 56

61 Waveforms: push-pull i M (t) v T (t) i(t) v s (t) i D (t) I Conducting devices: L M 0 0 n i 0 i L M n 0.5 i 0.5 i 0 0 DT s T s T s DT s 2T s Q D Q 2 D D D 2 D 2 D 2 0 t 57 Used with low-voltage inputs Secondary-side circuit identical to full bridge As in full bridge, transformer volt-second balance is obtained over two switching periods Effect of nonidealities on transformer volt-second balance? Current programmed control can be used to mitigate transformer saturation problems. Duty cycle control not recommended.

62 Flyback converter buck-boost converter: Q D L V construct inductor winding using two parallel wires: L Q D : V 58

63 Derivation of flyback converter, cont. Isolate inductor windings: the flyback converter L M Q D : V Flyback converter having a :n turns ratio and positive output: L M :n D C V Q 59

64 The flyback transformer i g L M Transformer model i v L :n Q D C i C R v A two-winding inductor Symbol is same as transformer, but function differs significantly from ideal transformer Energy is stored in magnetizing inductance Magnetizing inductance is relatively small Current does not simultaneously flow in primary and secondary windings Instantaneous winding voltages follow turns ratio Instantaneous (and rms) winding currents do not follow turns ratio Model as (small) magnetizing inductance in parallel with ideal transformer 60

65 Subinterval Transformer model i g i :n i C v L = L M v L C R v i C = v R i g = i CCM: small ripple approximation leads to Q on, D off v L = i C = V R i g = I 6

66 Subinterval 2 i g = 0 Transformer model i v L v/n :n i/n C i C R v v L = v n i C = i n v R i g =0 CCM: small ripple approximation leads to Q off, D on v L = V n i C = I n V R i g =0 62

67 CCM Flyback waveforms and solution v L Volt-second balance: i C V/n I/n V/R v L = D D' V n =0 Conversion ratio is M(D)= V V = n D g D' Charge balance: i g V/R I DT s 0 D'T s t i C = D V R D' I n V R =0 Dc component of magnetizing current is I = D'R nv Dc component of source current is I g = i g = DI D' 0 Conducting devices: T s Q D 63

68 Equivalent circuit model: CCM Flyback v L = D D' V n =0 I g I i C = D V R D' I n V R =0 I g = i g = DI D' 0 DI D'V D'I n R D n V : D D' : n I g I R V 64

69 Discussion: Flyback converter Widely used in low power and/or high voltage applications Low parts count Multiple outputs are easily obtained, with minimum additional parts Cross regulation is inferior to buck-derived isolated converters Often operated in discontinuous conduction mode DCM analysis: DCM buck-boost with turns ratio 65

70 Obtaining isolation in the Cuk converter Nonisolated Cuk converter L C Q D L 2 C 2 R v L L 2 Split capacitor C into series capacitors C a and C b C a C b Q D C 2 R v 75

71 Isolated Cuk converter L L 2 Insert transformer between capacitors C a and C b Q C a C b D C 2 R v M(D)= V = nd D' : n Discussion Capacitors C a and C b ensure that no dc voltage is applied to transformer primary or secondary windings Transformer functions in conventional manner, with small magnetizing current and negligible energy storage within the magnetizing inductance 76

72 6.4. Converter evaluation and design For a given application, which converter topology is best? There is no ultimate converter, perfectly suited for all possible applications Trade studies Rough designs of several converter topologies to meet the given specifications An unbiased quantitative comparison of worst-case transistor currents and voltages, transformer size, etc. Comparison via switch stress, switch utilization, and semiconductor cost Spreadsheet design 77

73 6.4.. Switch stress and switch utilization Largest single cost in a converter is usually the cost of the active semiconductor devices Conduction and switching losses associated with the active semiconductor devices often dominate the other sources of loss This suggests evaluating candidate converter approaches by comparing the voltage and current stresses imposed on the active semiconductor devices. Minimization of total switch stresses leads to reduced loss, and to minimization of the total silicon area required to realize the power devices of the converter. 78

74 Total active switch stress S In a converter having k active semiconductor devices, the total active switch stress S is defined as S = k Σ j = V j I j where V j is the peak voltage applied to switch j, I j is the rms current applied to switch j (peak current is also sometimes used). In a good design, the total active switch stress is minimized. 79

75 Active switch utilization U It is desired to minimize the total active switch stress, while maximizing the output power P load. The active switch utilization U is defined as U = P load S The active switch utilization is the converter output power obtained per unit of active switch stress. It is a converter figure-of-merit, which measures how well a converter utilizes its semiconductor devices. Active switch utilization is less than in transformer-isolated converters, and is a quantity to be maximized. Converters having low switch utilizations require extra active silicon area, and operate with relatively low efficiency. Active switch utilization is a function of converter operating point. 80

76 Comparison of switch utilizations of some common converters Table 6.. Active switch utilizations of some common dc-dc converters, single operating point. Converter U(D) max U(D) max U(D) occurs at D = Buck Boost Buck-boost, flyback, nonisolated SEPIC, isolated SEPIC, nonisolated Cuk, isolated Cuk Forward, n = n 2 Other isolated buck-derived converters (fullbridge, half-bridge, push-pull) Isolated boost-derived converters (full bridge, push-pull) D D' 0 D D' D 2 D D 2 2 D' 2 D = = =

77 Switch utilization : Discussion Increasing the range of operating points leads to reduced switch utilization Buck converter can operate with high switch utilization (U approaching ) when D is close to Boost converter can operate with high switch utilization (U approaching ) when D is close to Transformer isolation leads to reduced switch utilization Buck-derived transformer-isolated converters U should be designed to operate with D as large as other considerations allow transformer turns ratio can be chosen to optimize design 85

78 Switch utilization: Discussion Nonisolated and isolated versions of buck-boost, SEPIC, and Cuk converters U Single-operating-point optimum occurs at D = /3 Nonisolated converters have lower switch utilizations than buck or boost Isolation can be obtained without penalizing switch utilization 86

79 Active semiconductor cost vs. switch utilization semiconductor cost per kw output power = semiconductor device cost per rated kva voltage derating factor current derating factor converter switch utilization (semiconductor device cost per rated kva) = cost of device, divided by product of rated blocking voltage and rms current, in $/kva. Typical values are less than $/kva (voltage derating factor) and (current derating factor) are required to obtain reliable operation. Typical derating factors are Typical cost of active semiconductor devices in an isolated dc-dc converter: $ - $0 per kw of output power. 87

80 Summary of key points. The boost converter can be viewed as an inverse buck converter, while the buck-boost and Cuk converters arise from cascade connections of buck and boost converters. The properties of these converters are consistent with their origins. Ac outputs can be obtained by differential connection of the load. An infinite number of converters are possible, and several are listed in this chapter. 2. For understanding the operation of most converters containing transformers, the transformer can be modeled as a magnetizing inductance in parallel with an ideal transformer. The magnetizing inductance must obey all of the usual rules for inductors, including the principle of volt-second balance. 99

81 Summary of key points 3. The steady-state behavior of transformer-isolated converters may be understood by first replacing the transformer with the magnetizing-inductance-plus-ideal-transformer equivalent circuit. The techniques developed in the previous chapters can then be applied, including use of inductor volt-second balance and capacitor charge balance to find dc currents and voltages, use of equivalent circuits to model losses and efficiency, and analysis of the discontinuous conduction mode. 4. In the full-bridge, half-bridge, and push-pull isolated versions of the buck and/or boost converters, the transformer frequency is twice the output ripple frequency. The transformer is reset while it transfers energy: the applied voltage polarity alternates on successive switching periods. 00

82 Summary of key points 5. In the conventional forward converter, the transformer is reset while the transistor is off. The transformer magnetizing inductance operates in the discontinuous conduction mode, and the maximum duty cycle is limited. 6. The flyback converter is based on the buck-boost converter. The flyback transformer is actually a two-winding inductor, which stores and transfers energy. 7. The transformer turns ratio is an extra degree-of-freedom which the designer can choose to optimize the converter design. Use of a computer spreadsheet is an effective way to determine how the choice of turns ratio affects the component voltage and current stresses. 8. Total active switch stress, and active switch utilization, are two simplified figures-of-merit which can be used to compare the various converter circuits. 0

83 Applications Isolation Uninteruptible power supplies (UPS) Motor drive Heating, Welding Wireless power transfer Energy generation (solar, wind) Active filtering, power factor correction (PFC)

84 Utility grid adapter Excerpt of [] (fig 0-2), typical wall adapter with isolation, including feedback for proper DC regulated voltage.

85 Multiple outputs power supply Excerpt of [] (fig 0-3), multiple outputs isolated power supply with cross-regulated outputs.

86 Isolating feedback (solution ) Excerpt of [] (fig 0-34a), PWM controller on the output side.

87 Isolating feedback (solution 2) Excerpt of [] (fig 0-34b), PWM controller on the input side.

88 Uninterruptible power supply (classical solution) Excerpt of [] (fig -4), classical UPS for powering critical load.

89 Uninterruptible power supply (optimized solution) Excerpt of the CET web site, high efficiency UPS solution.

90 Motor drive application Excerpt of [] (fig 2-3), air conditioner that takes benefit of a converter (inverter) to control the temperature.

91 Servo drive control and current limiting Excerpt of [] (fig 2-8a), speed control block diagram (method a).

92 Servo drive control and current limiting Excerpt of [] (fig 2-8b), speed control block diagram (method b).

93 DC servo drive Excerpt of [] (fig 3-6), closed loop position/speed DC servo drive.

94 DC servo drive Excerpt of [] (fig 3-0), drive with four-quadrant operation.

95 Induction motor drive Excerpt of [] (fig 4-9), PWM-VSI inverter.

96 Synchronous motor servo drive Excerpt of [] (fig 5-5), synchronous motor servo drive.

97 Induction heating Excerpt of [] (fig 6-7), voltage source resonant induction heating.

98 Electric welding Excerpt of [] (fig 6-9), switch-mode welder.

99 Wireless power transfer Excerpt of the Qi standard, basic system overview.

100 Wireless power transfer Excerpt of the Qi standard, example of power TX and RX devices.

101 Solar inverter Excerpt of [2], H5 topology from SMA (implemented in their commercial inverters).

102 Wind inverter Excerpt of [3], example of wind energy converter implementing MPPT with optimal torque control of wind turbines.

103 Active filters Excerpt of [], utility grid parallel active filter.

104 Power factor corrector Excerpt of [], power factor correction problem.

105 Power factor corrector Excerpt of [], the typical solution.

106 Power converters find more and more applications... ELEC0055: Elements of Power Electronics - Fall 207

107 References [] Mohan, Undeland, and Robbins, POWER ELECTRONICS: Converters, Applications and Design. Wiley, third ed., [2] J. Wang, B. Ji, J. Zhao, and J. Yu, From h4, h5 to h6 - standardization of full-bridge single phase photovoltaic inverter topologies without ground leakage current issue, in 202 IEEE Energy Conversion Congress and Exposition (ECCE), pp , Sept 202. [3] B. Wu, Y. Lang, N. Zargari, and S. Kouro, Power Conversion and Control of Wind Energy Systems. Wiley-IEEE Press, first ed., 20. [4] R. W. Erickson and D. Maksimović, Fundamentals of Power Electronics. Kluwer Academic Publishers, second ed., 200.