IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012 27
Cascade Three-Level AC/AC Direct ConverterLei Li, Member, IEEE, and Dongcai Tang
Abstract—This paper proposes a novel family of cascade three-level (TL) ac–ac direct converters based on ac switch cells, whichtransfer unsteady high ac voltage with distortion into regulatedsinusoidal voltage with low total harmonic distortion (THD). Thetopological family includes buck TL–boost, buck–boost TL, andbuck TL–boost TL modes. In order to achieve a reliable TL ac–acconversion, a double transient voltage feedback control strategyof the output voltage and the voltage across the flying capaci-tor is introduced in this paper. A 500-VA 220-V ±10% 50-Hzac/220-V 50-Hz ac prototype is presented with the experimentalresults to prove that the converters have four improved advantagessimultaneously, including lower voltage across power switches,bidirectional power flow, low THD of output voltage, and higherinput power factor.
Index Terms—AC switch cell, ac–ac direct converter, doubletransient voltage feedback control, three-level (TL).
I. INTRODUCTION
THE ac–ac converters have been widely used in variousindustrial domains in recent years. However, recent re-
search on the ac–ac converter technology mainly focuses ontwo-level ac–ac converters and ac–dc–ac-type multilevel ac–acconverters [1]–[4]. The former includes ac–ac converters withelectrical isolation and the ones without any electrical isolationsuch as ac choppers, thyristor phase-controlled cycloconverters,or matrix converters. The latter includes ac–ac converters withno electrical isolation as well as the ones with low or middlefrequency electrical isolation.
Nowadays, the ac–ac converters are required not only for thelow-voltage but also for the high-voltage input applications. Inthese fields, a multilevel technique is effective to reduce thevoltage across power switches with improved output voltage. Amultilevel technique was firstly proposed in inverters [5]–[13]and then developed in dc–dc converters and rectifiers [14]–[17].So far, a multilevel technique used in ac–ac converters has beenmainly limited to ac–dc–ac-type ac–ac converters, which havemany shortcomings such as more power stages, unidirectionalpower flow, low input power factor, and weak adaptability tovarious loads [18], [19]. Therefore, a cascade three-level (TL)
Manuscript received August 14, 2010; revised December 7, 2010 andFebruary 17, 2011; accepted March 29, 2011. Date of publication April 19,2011; date of current version October 4, 2011. This work was supported inpart by the Natural Science Foundation of China under Awards 50607008and 51177073, by the Natural Science Foundation of Jiangsu Province,China, under Award BK2009389, by the Outstanding Scholar Project, and bythe Nanjing University of Science and Technology Research Funding underAward 2010ZYTS043.
L. Li is with the College of Automation Engineering, Nanjing Univer-sity of Science and Technology, Nanjing 210094, China (e-mail: [email protected]).
D. Tang is with Emerson Electronics Company, Shenzhen 518057, China(e-mail: [email protected]).
Digital Object Identifier 10.1109/TIE.2011.2143376
Fig. 1. AC switch cells. (a) Two-level ac switch cell. (b) TL ac switch cell.
ac–ac direct converter was proposed in order to improve themultilevel ac–ac converters [20].
This paper proposes a novel family of cascade TL ac–acdirect converters based on ac switch cells. In order to achieve areliable TL ac–ac conversion, a strategy of the double transientvoltage feedback control is presented also. The convertersproposed in this paper have single-stage power conversion(low-frequency alternate-current LFAC-LFAC), bidirectionalpower flow, and higher input power factor compared with theac–dc–ac-type TL ac–ac converters. Moreover, the convertershave lower voltage across power switches compared with thetwo-level ac–ac converters. The converters are targeted to beused on a new type of regulated sinusoidal ac power sup-ply, electronic transformer, and ac regulator in which high-voltage input (output) and/or bidirectional power flow areneeded.
II. CONVERTER TOPOLOGY
As shown in Fig. 1, two-level (ui, 0) and TL (ui, ui/2, 0) acswitch cells are presented in this paper. A TL ac switch cell isproduced by two-level ac switch cells in series.
Based on ac switch cells, a novel family of cascade TL ac–acdirect converters shown in Fig. 2 is proposed. The topologicalfamily includes buck TL–boost, buck–boost TL, and buckTL–boost TL modes. According to different output voltages,pulsewidth modulation (PWM) controlled TL ac–ac converterschopper in different operation modes with three voltage levels.Therefore, the converters can directly transfer unsteady high acvoltage with distortion into regulated sinusoidal voltage withlow total harmonic distortion (THD).
III. OPERATING PRINCIPLES
To simplify the steady-state analysis, the following assump-tions are made: 1) Switching and conduction losses of thecomponents are neglected; 2) input and output voltages areconsidered constant during one switching period Ts; 3) parasiticparameters of inductor L for energy storage, flying capacitorCb, and filter capacitor Co are neglected; and 4) flying capacitorCb is large enough to be considered as a constant dc voltagesource with value ui/2. According to the polarities of inputvoltage ui and current of inductor L for energy storage iL, thebuck TL–boost mode cascade TL ac–ac direct converter canwork in four kinds of operation modes: A (ui > 0, iL > 0),B (ui > 0, iL < 0), C (ui < 0, iL < 0), and D (ui < 0, iL > 0).
A. Operation Mode A
Power switches S1 ∼ S6 chop with high frequency, andpower supply delivers power to the ac load. Topological statesduring one Ts in mode A are shown in Fig. 3.
State 1 [t0 ∼ t1] [refer to Fig. 3(a)]: S2, S4, and S5 are on.Cb and L are both charged by power supply, and voltage uTL =ui/2. Co transfers power to the ac load. The voltage across L isuL = ui − uCb, so inductor current iL increases linearly. Thechange of iL is given by
Δi1 =
t1∫
t0
ui − uCb
Ldt =
ui − uCb
L(t1 − t0) =
ui
2L(t1 − t0).
(1)
State 2 [t1 ∼ t2] [refer to Fig. 3(b)]: S1, S4, and S5 are on.S2 is off. L is still charged by power supply, and uTL = ui.Co delivers power to the ac load. Voltage uL = ui, so iL stillincreases linearly. The change of iL is obtained as
Δi2 =
t2∫
t1
ui
Ldt =
ui
L(t2 − t1). (2)
State 3 [t2 ∼ t3] [refer to Fig. 3(c)]: S1, S3, and S6 are on.S4 and S5 are off. Cb and L transfer power to Co and the acload, and uTL = ui/2. Voltage uL = uCb − uo, so iL startsto decrease linearly. The change of iL can be given by thefollowing:
Δi3 =
t3∫
t2
uCb − uo
Ldt =
ui/2 − uo
L(t3 − t2). (3)
State 4 [t3 ∼ t4] [refer to Fig. 3(d)]: S2, S3, and S6 are on.S1 is off. L supplies power to Co and the ac load, and uTL = 0.Voltage uL = −uo, so iL still decreases linearly. The change ofiL is
Δi4 =
t4∫
t3
−uo
Ldt =
−uo
L(t4 − t3). (4)
In the steady state, the change of iL during one Ts must bezero, i.e., Δi1 + Δi2 + Δi3 + Δi4 = 0. From (1)–(4), (5) isobtained as
Then, the ratio of the output root mean square (rms) voltage tothe input rms voltage of the converter in continuous conductionmode is given by
Uo
Ui=
(t2 − t0) + (t3 − t1)2 [(t4 − t0) − (t2 − t0)]
=D + D′
2(1 − D)(6)
where D = (t2 − t0)/(t4 − t0) is the duty cycle of S4,S5 (S ′
4, S′5) and D′ = (t3 − t1)/(t4 − t0) is the duty cycle of
S1 (S ′1).
LI AND TANG: CASCADE THREE-LEVEL AC/AC DIRECT CONVERTER 29
Fig. 3. Topological states during one switching period Ts in mode A. (a) State1 [t0 ∼ t1]. (b) State 2 [t1 ∼ t2]. (c) State 3 [t2 ∼ t3]. (d) State 4 [t3 ∼ t4].
B. Operation Mode B
Power switches S ′1 ∼ S ′
6 chop with high frequency, and theload delivers power to the power supply. Voltage uTL varieswith ui/2, ui, ui/2, and 0. Topological states during one Ts
in mode B are shown in Fig. 4. Operation modes C and D aresimilar to A and B, respectively, and we do not provide detailedanalysis in this paper.
IV. DESIGN CONSIDERATIONS
Design specifications of the buck TL–boost mode cas-cade TL ac–ac direct converter are defined as follows: inputvoltage Ui = 198–242 V (50 Hz) ac, output voltage Uo =220 V (50 Hz) ac, rated capacity S = 500 VA, switchingfrequency fs = 100 kHz, Δuo ≤ 2%uo, ΔuCb ≤ 5%uCb, andΔiL ≤ 20%iL. To ensure the operation of the converter, cir-cuit parameters, including D, Co, Cb, L, and S1 ∼ S ′
6, aredetermined.
A. Designing Duty Cycle D
In order to simplify the design of D, Co, and Cb, the currentiL of inductor L and current iCo of filter capacitor Co areconsidered as constant during one switching period Ts. Keywaveforms of the converter during one Ts are shown in Fig. 5,where uCb, iCb, and uCo are the voltage across flying capacitorCb, the current of Cb, and the voltage across filter capacitor Co,respectively.
During t0 ∼ t2, uCo decreases linearly, and then, the decre-ment ΔuCo− is
ΔuCo− = Δuo =
t2∫
t0
ioCo
dt =ioCo
(t2 − t0) =ioCo
· Ts · D.
(7)
During t2 ∼ t4, uCo increases linearly, and the incrementΔuCo+ can be derived as
ΔuCo+ =
t4∫
t2
iCo+
Codt =
iCo+
Co· Ts · (1 − D). (8)
However, ΔuCo− = ΔuCo+ in one Ts, and then, iCo+ =Dio/(1 − D), and iL = iCo+ + io = io/(1 − D).
During t0 ∼ t1, uCb increases linearly, and the increment ofuCb is given by
ΔuCb+ =
t1∫
t0
iLCb
dt =io
Cb(1 − D)· (t1 − t0). (9)
During t2 ∼ t3, uCb decreases linearly, and the decrement ofuCb can be obtained
ΔuCb− =
t3∫
t2
iLCb
dt =io
Cb(1 − D)· (t3 − t2). (10)
30 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012
Fig. 4. Topological states during one Ts in mode B. (a) State 1. (b) State 2.(c) State 3. (d) State 4.
LI AND TANG: CASCADE THREE-LEVEL AC/AC DIRECT CONVERTER 31
Fig. 7. Control structure block diagram of the presented control strategy.
B. Designing Filter Capacitor Co
From (7), (12), and Δuo ≤ 2%uo, Co must satisfy
Co ≥ Io · Ts · Dmax
2%Uo=
S · Ts · Dmax
0.02U2o
=500 × 10 × 10−6 × 0.526
0.02 × 2202= 2.72 (μF). (14)
The maximum voltage across Co is√
2Uo =√
2 × 220 =311 (V), so Co is chosen as 4.7 μF/630 V.
C. Designing Flying Capacitor Cb
To simplify the control, let (t1 − t0)/Ts = 0.25. Accordingto (9), (11), uCb = ui/2, and ΔuCb ≤ 5%uCb, Cb must besatisfied with the following expression:
Cb ≥io · (t1 − t0)
(1 − D) · 5% · ui/2=
40S · (t1 − t0) · Dmax
(1 − Dmax)2 · U2o
=40 × 500 × 10 × 10−6× 0.25 × 0.526
(1 − 0.526)2 × 2202= 2.42 (μF).
(15)
The maximum voltage across Cb is√
2Ui,max/2 =√
2 ×242/2 = 171 (V), so Cb is selected as 4.7 μF/630 V.
D. Designing Inductor L for Energy Storage
During t0 ∼ t2, current iL of inductor L increases. From(11), uCb = ui/2, D = (t2 − t0)/Ts, and (t1 − t0)/Ts =0.25, the maximum change of iL is
ΔiL =ui − uCb
L(t1 − t0) +
ui
L(t2 − t1)
=(2D − 0.25) · (1 − D)
2D · L Ts · uo. (16)
Fig. 8. Prototype of cascade TL ac–ac direct converter.
According to (16), ΔiL ≤ 20%iL, and iL = io/(1 − D), Lmust satisfy
32 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012
Fig. 9. Experimental waveforms with resistive load (R = 96 Ω). (a) Input voltage ui and output voltage uo. (b) Voltage across CbuCb and ui. (c) Voltageacross S1uds and ui. (d) Voltage uTL. (e) Voltage uTL. (f) Current iL of inductor for energy storage.
The maximum rms current of S1 ∼ S ′6 is given by
IL,max =Io,max
1 − Dmax=
500198 × (1 − 0.526)
= 5.33 (A). (20)
Then, MOSFET IRFP460 (500 V/20 A) is chosen for S1 ∼ S ′6.
V. MECHANISM FOR CONTROLLING VOLTAGE
ACROSS FLYING CAPACITOR
A strategy of the transient output voltage feedback control,shown in Fig. 6, is introduced for the converters. According tothe polarity of ui and iL, the converter will work in four modes:A, B, C, and D.
If voltage uCb across flying capacitor Cb is out of control, TLwaveforms of uTL cannot be achieved. Therefore, a new doubletransient voltage feedback control strategy of uo and uCb ispresented, whose control structure block diagram is shown inFig. 7. EA represents the error amplifier. Sample signal ucf ofuCb is compared with sample signal uif of ui, and then, error-
amplified signal uEA−c can be obtained. Meanwhile, samplesignal uof of uo is compared with reference voltage uref , andthen, another error-amplified signal uEA−o can be got. VoltageuEA1 can be gained by adding uEA−c to uEA−o. By comparinguEA1 and −uEA1 with carrier waves uRAMP, PWM signalsu3 ∼ u′
6 can be obtained. Similarly, uEA2 can be gained byadding −uEA−c to uEA−o. By comparing uEA2 and −uEA2
with uRAMP, PWM signals u1 ∼ u′2 can be got.
In the positive (negative) half cycle of uo, once uCb <ui/2, uEA−c is positive; then, uEA1 (−uEA1) increases, anduEA2 (−uEA2) decreases. As the results, the pulses of S4 andS5 (S ′
4 and S ′5) turn wider, and the pulse of S1 (S ′
1) turnsnarrower. The charge time and the discharge time of Cb turnlonger and shorter, respectively, so uCb can be controlled to beui/2. On the other hand, if sample signal uof of uo is less thanreference voltage uref , uEA−o is positive, and then, uEA1 anduEA2 (−uEA1 and −uEA2) rise. Therefore, the pulses of S1,S4, and S5 (S ′
1, S ′4, and S ′
5) turn wider, so uo can be increasedto be the expected value.
LI AND TANG: CASCADE THREE-LEVEL AC/AC DIRECT CONVERTER 33
Fig. 10. Experimental waveforms with RL (R = 72 Ω, L = 200 mH) andRC load (R = 72 Ω, C = 50 μF). (a) Output voltage uo and output currentio. (b) Output voltage uo and output current io.
VI. PROTOTYPE
The designed and developed prototype is as follows: BuckTL–boost mode circuit topology, double transient voltage feed-back control strategy, rated capacity S = 500 VA, input voltageUi = 198–242 V (50 Hz) ac, output voltage Uo = 220 V(50 Hz) ac, duty cycle D = 0.476 ∼ 0.526, switching fre-quency fs = 100 kHz, inductance for energy storage L =1.2 mH, flying capacitance Cb = 4.7 μF/630 V, filter capac-itance Co = 4.7 μF/630 V, MOSFET IRFP460 (500 V/20 A)for S1 ∼ S ′
6, and load power factor cos ϕL = −0.75 ∼ +0.75.The prototype shown in Fig. 8 has the following good
performances: rated capacity S = 500 VA, input voltage Ui =198–242 V (50 Hz) ac, precision of output voltage ≤ 1.5 V,load power factor cos ϕL = −0.75 ∼ +0.75, output voltageTHD < 3.5%, conversion efficiency at rated power for differenttypes of loads η ≥ 80.7 ∼ 85.8%, line power factor at rateddifferent nature load cos ϕ ≥ 0.66 ∼ 0.94, operational time of120 min at 110% rated load, weight < 2.5 kg, and bulk <175 mm ∗ 170 mm ∗ 130 mm.
Experimental waveforms of the converter are shown inFigs. 9 and 10. The experimental results have verified that theconverter has the following advantages such as low THD of uo,symmetrical voltage uCb and uCb be controlled as ui/2, lowervoltage across the power switches in the buck TL stage (ui/2),TL (ui, ui/2, 0) in voltage uTL, strong adaptability to variousloads, etc.
Fig. 11 illustrates how the curves of the line power factor,THD of uo and ui, and conversion efficiency vary with the load.According to the results, the converter achieves high conversion
Fig. 11. Line power factor, THD, and conversion efficiency versus the load.(a) Line power factor versus output power. (b) THD of input and output voltagesversus output power at Ui = 220 V. (c) Conversion efficiency versus outputpower.
efficiency, higher line power factor, and low THD of outputvoltage.
VII. CONCLUSION
In this paper, a novel family of cascade TL ac–ac directconverters has been proposed based on ac switch cells. Theconverters directly transfer unsteady high ac voltage with dis-tortion into regulated sinusoidal voltage with low THD. The
34 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 1, JANUARY 2012
topological family includes buck TL–boost, buck–boost TL,and buck TL–boost TL modes. By introducing the doubletransient voltage feedback control strategy, the TL ac–ac con-version and lower voltage across power switches can be reliablyachieved.
This paper also describes the design and the development ofa 500-VA 220-V ±10% 50-Hz ac/220-V 50-Hz ac prototype.Experimental results show that the converters reduce the volt-age across the power switches in the TL stage to ui/2, whichis only a half of the traditional two-level ac–ac converters. Theinput power factor is higher than 0.66 ∼ 0.94 at rated capacity,which is better than the ac–dc–ac-type TL ac–ac converters.Furthermore, low THD of output voltage and the function ofbidirectional power flow are also demonstrated in this paper.
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Lei Li (M’09) received the B.S. degree from the De-partment of Electrical Engineering, Shandong Uni-versity of Science and Technology, Qingdao, China,in 1997, and the Ph.D. degree from the Depart-ment of Electrical Engineering, Nanjing Universityof Aeronautics and Astronautics, Nanjing, China,in 2004.
He is currently an Associate Professor with theCollege of Automation Engineering, Nanjing Uni-versity of Science and Technology, Nanjing. He haspublished more than 50 technical papers. His re-
search interests include multilevel technique, high-frequency power conversion,and control technique.
Dr. Li was the recipient of one first class reward production of science andtechnology of Jiangsu Province and is the holder of three China patents.
Dongcai Tang received the B.S. degree from the De-partment of Electrical Engineering, Xuzhou Teach-ers College, Xuzhou, China, in 2007, and the M.S.degree from the College of Power Engineering,Nanjing University of Science and Technology,Nanjing, China, in 2009.
He is currently an Engineer with the EmersonElectronics Company, Shenzhen, China. He has pub-lished several technical papers. His research interestsinclude multilevel technique and ac/ac converters.
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