Series

A Series-Resonant Single-Phase Step up/down AC Chopper

Chien-Ming Wang*, Maoh-Chin Jiang*, Chang-Hua Lin**, Chia-Hua Liu* and Deng-Jie Yang*

* Department of Electrical Engineering, National Ilan University, I-Lan, Taiwan ** Department of Electrical Engineering, Tatung University, Taipei, Taiwan

Abstract -- A series-resonant single-phase step up/down

ac chopper is presented. The main attribute of the ac chopper topology is the fact that it generates an output ac voltage larger or lower than the input ac one, depending on the instantaneous duty-cycle. This property is not found in the classical ac chopper, which produces an ac output instantaneous voltage always lower than the input ac voltage. The presented single-phase ac chopper is configured by a series-resonant conversion. The presented single-phase ac chopper is a series resonator to configure adaptively the resonant voltage robes. The synthesized sinusoidal waveform (SSW) before output filter is synthesized by a series of sinusoidal amplitude quasi-sinusoidal pulses (QSPs) following the input voltage amplitude. Because the synthesized SSW very closes sinusoidal waveform, the presented single-phase ac chopper can use a simple LC filter to filter the undesired harmonics and get the sinusoidal voltage with low total harmonic distortion (THD). The presented single-phase ac chopper is operated by constant frequency pulse width modulation control technique. Waveform syntheses for the output sinusoidal voltage are clearly analyzed and derived. A typical design example of a 600W series-resonant single-phase ac chopper is examined to assess the system performance. The power efficiency is over 90% when the output power is at maximum output rated power. The total harmonic distortion (THD) when the output power is at maximum output rated power is within 6%. Index Terms – series resonant, ac chopper

I. INTRODUCTION

The ac voltage regulators have become important equipment for obtain variable ac voltage from a fixed ac source. Because the phase-angle control technique and integral-cycle control technique of thyristors are simplicity, they are traditionally used in the ac voltage regulator. However, the retardation of firing angle causes high low-order harmonic in both output and input sides and a lagging power factor in input side [1]. For improving these problems, the pulse-width modulation control technique is widely used in the ac choppers [2]-[7]. However, there still exit lots of shortcomings including high switching loss, and large EMI. And, one of their characteristics is that the instantaneous average output voltage is always lower than the input ac voltage. It will result in the application range decreases. For overcoming these problems and increasing the power density of the ac chopper, a series-resonant single-phase step up/down ac chopper is presented in this paper with a simple and compact topology. A turn-on zero-current-switching (ZCS) for the power switch is achieved. The synthesized sinusoidal waveform (SSW) before output filter is synthesized by a series of sinusoidal amplitude quasi-sinusoidal pulses (QSPs) following the

input voltage amplitude. Because the synthesized SSW very closes sinusoidal waveform, the presented single-phase ac chopper can use a simple LC filter to filter the undesired harmonics and get the sinusoidal voltage with low total harmonic distortion (THD). The constant frequency pulse width modulation (PWM) control strategy is designed to achieve well dynamic regulation characteristic. The properly driving signal of the power switches and the resonant characteristic of LC tank are also achieved by it. System analysis for predicting and evaluating the proposed ac chopper performance are conducted. A 60Hz 600W ac chopper is designed and realized. The total harmonic distortion (THD) is under 6% before EMI filtering, and the power efficiency is over 90% when the power is maximum rated power.

vin

S1

S4

S2

S3

Lr Cr

Lf

Cf RL

Sm

D1 D2

D3D4

Dm

vin

S1

S4

S2

S3

Lr Cr

Lf

Cf RL

Sm

D1 D2

D3D4

Dm

Fig.1 Circuit topology of the proposed series-resonant single-phase step

up/down chopper

II. PRICIPLES OF THE SERIES-RESONANT SINGLE-PHASE STEP UP/DOWN AC CHOPPER

The proposed series-resonant single-phase step up/down ac chopper shown in Fig. 1, which primarily comprises a series-resonant power stage and a cycloconverter. The series-resonant power stage composed of a power switch Sm, a power diode Dm, a resonant inductance Lr, a resonant capacitance Cr, parallel-loaded with the cycloconverter. The power stage is inherently a parallel-loaded series resonant converter. The cycloconverter composed of power switches S1-S4 and an output filter Lf and Cf. It interlacedly inverts the series of half-period unipolar composite sinusoidal waveform into an alternately bipolar form in a desired period. For ease of analysis, the cycloconverter can be simply thought of a resistive load for the power stage. The equivalent circuit in the positive (negative) half-period of the line input voltage vin(t) is composed of D2 (D1), D4 (D3), Sm, Dm, S1 (S4), S3 (S2), Lr, Cr, Lf, and Cf//RL. In the positive (negative) half-period

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of the line input voltage vin(t), the switches S2 (S1) and S4 (S3) are always off, the switch S1 (S2) and S3 (S4) are always on, and Sm performs the conversion function at high frequency switching. The equivalent circuits for describing their behavior are shown in Fig. 2. The complete synthesized resonant output voltage robes and switches drive signal are shown in Fig. 3. It is clearly seen that the output voltage vo(t) is synthesized by resonant voltage robes with sinusoidal amplitude and the resonant synthesized sinusoidal voltage waveform in resonant capacitor Cr very closes sinusoidal waveform. Thus, the presented ac chopper can use a simple LC filter to get the sinusoidal output voltage waveform with low THD. The working states include a linear charging and discharging state, a resonant state, and a linearly discharging state. Remarkably, the proposed single-phase ac chopper operates

in discontinuous conduction mode (DCM). For convenience in analysis, it is presumed that all devices are ideal and that the losses in Lr, Lf, Cr, and Cf are all neglected. They are assumed that the input voltage are approximated a stairway waveform and it is approximate a constant value in one switching period. Since the circuit operation at positive line input voltage is the same as the circuit operation at negative line input voltage. Only the resonant behaviors in positive line input voltage are described in the following. The initial states of the switch Sm is off. Before t=tk0, it is assumed that the circuit operation is in the linearly discharging state. There are three resonant states in one switching cycle. They are described in the following.

Linear charging and discharging state

vin

S1

S4

S2

S3

Lr

Cr

Lf

Cf RL

Sm

D1 D2

D3

D4

Dm

iLr(t)+

_vCr

iLf(t)+

_vovin

S1

S4

S2

S3

Lr

Cr

Lf

Cf RL

Sm

D1 D2

D3

D4

Dm

iLr(t)+

_vCr

+

_vCr

iLf(t)iLf(t)+

_vo

+

_vo

+

_vCr

iLr(t)

Lr

Vink ILfk

+

_vCr

+

_vCr

iLr(t)

Lr

VinkiLr(t)iLr(t)

Lr

Vink ILfk

(a) Resonant state Linear-discharging state

vin

S1

S4

S2

S3

Lr

Cr

Lf

Cf RL

Sm

D1 D2

D3

D4

Dm

iLr(t)+

_vCr

iLf(t)+

_vovin

S1

S4

S2

S3

Lr

Cr

Lf

Cf RL

Sm

D1 D2

D3

D4

Dm

iLr(t)+

_vCr

+

_vCr

iLf(t)iLf(t)+

_vo

+

_vo vin

S1

S4

S2

S3

Lr

Cr

Lf

Cf RL

Sm

D1 D2

D3

D4

Dm

iLr(t)+

_vCr

iLf(t)+

_vovin

S1

S4

S2

S3

Lr

Cr

Lf

Cf RL

Sm

D1 D2

D3

D4

Dm

iLr(t)+

_vCr

+

_vCr

iLf(t)iLf(t)+

_vo

+

_vo

+

_vCr

iLr(t)

Lr

ILfk

+

_vCr

+

_vCr

iLr(t)iLr(t)

Lr

ILfk

+

_vCr ILfk

+

_vCr

+

_vCr ILfk

(b) (c) Fig. 2 The equivalent circuits for describing the resonant robes of vCr(t) in the kth switching period

Stage I: Linear charging and discharging state, t in [tk0, tk1]:

This state begins as the power switch Sm turns on with

ZCS at t=tk0, the resonant inductor Lr is charged linearly energy by input voltage source and the resonant capacitor Cr discharges its energy to the load until t=tk1. Thus, the resonant current iLr(t) increases and the resonant voltage

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vCr(t) decreases. The portraits iLr(t) and vCr(t) with the initial conditions iLr(tk0)=0 (due to DCM) and vCr(tk0) are, respectively, represented by

)()( 0kr

inkLr tt

LVti −= (1)

)()()( 00 kr

LfkkCrCr tt

CI

tvtv −−= (2)

Stage II: Resonant State, t in [tk1, tk2]:

During this state, Sm is turned off. The resonant operation of Lr and Cr is started. The series-resonant loop is then formed by Lr, Dm, Cr, S1, S3 and ILfk. The energy stored in Lr is then transferred to Cr until null at t=tk2. The resonant voltage vCr(t) increase and then decrease when arrive its peak values. The portraits iLr(t) and vCr(t) are, respectively, represented by

[ ])(cos))( 11 krLfkkLrLfkLr ttItiIi −−+= ω

)(sin)(1

1kr

o

kCr ttZ

tv −− ω (3)

)(cos)( 11 krkCrCr tttvv −= ω

[ ] )(sin)( 11 krLfkkLro ttItiZ −−+ ω (4)

where rrr CL/1=ω is resonant angular frequency,

rro CLZ /= is characteristic impedance.

Stage III: The Linearly Discharging State, t in [tk2, tk3]:

In this state, the resonant current iLr(t) still maintain at zero value. The energy stored in Cr is discharged linearly by the piecewise constant current ILfk. This state is end when this switching period is complete and next switching period is started. The portraits iLr(t) and vCr(t) are, respectively, represented by

0)( =tiLr , (5)

( )22 )()( kr

LfkkCrCr tt

CI

tvtv −−= . (6)

The composite profiles of the kth iLr(t) and vCr(t) in the kth switching period are simulated in Fig. 3. The SSW before and after the output filter are also simulated and shown in Fig. 3.

t

vCr(t)

vo(t)

iLr(t)

t

vCr(t)

iLr(t)vCr(tk0)

S1

S2

S3

S4

State I State II State IIITs

t

t

t

t

DTs D1Ts

tk0 tk1 tk2 tk3D2Ts

tSm

t

vCr(tk0)

S1

S2

S3

S4


t

t

t

t

DTs D1Ts

tk0 tk1 tk2 tk3D2Ts

vCr(t)

iLr(t)

tSm

t

vCr(t)

vo(t)

iLr(t)

t

vCr(t)

iLr(t)vCr(tk0)

S1

S2

S3

S4


t

t

t

t

DTs D1Ts

tk0 tk1 tk2 tk3D2Ts

tSm

t

vCr(t)

iLr(t)vCr(tk0)

S1

S2

S3

S4


t

t

t

t

DTs D1Ts

tk0 tk1 tk2 tk3D2Ts

tSm

t

vCr(tk0)

S1

S2

S3

S4


t

t

t

t

DTs D1Ts

tk0 tk1 tk2 tk3D2Ts

vCr(t)

iLr(t)

tSm

t

vCr(tk0)

S1

S2

S3

S4


t

t

t

t

DTs D1Ts

tk0 tk1 tk2 tk3D2Ts

vCr(t)

iLr(t)

tSm

Fig. 3 Sampled resonant robes of the resonant voltage vCr(t).

III. SYSTEM CONTROL AND SYNTHESIZED

SINUSOIDAL WAVEFORMS

Fig. 3 shows the formations of the sinusoidal output voltage vo(t) by combining the resonant robes of vCr(t) in

the continuous conduction mode (CCM). For convenient analysis, the control strategy is first described for generating the resonant robes on Cr. The control system of proposed single-phase step up/down ac chopper is constructed in Fig. 4. A fixed-frequency pulse width modulation (PWM) technique is used to regulate the system

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dynamics. The feedback circuit includes an isolated voltage sensor, a rectifier, a low-pass filter, a voltage error amplifier, a pulse width modulation generator, and a control logic circuit. First, the isolated voltage sensor samples the output voltage signal kovo. Then, the signal kovo is rectified and filtered to generate the average dc voltage Va. The voltage error amplifier is necessary to compare the the average dc voltage Va with the reference Vref and generate an error signal vc. The error signal is applied to the pulse width modulation generator. The pulse width modulation generator then generates a square waveform of necessary duty ratio of proposed ac chopper according to the error signal. The square waveform drives then control logic circuit. The gating pulse train for driving the power switches is generated. The gating pulse train is designed to have a fixed period time signal with duty ratio varied.

vin

S1

S4

S2

S3

Lr Cr

Lf

Cf RL

Sm

D1 D2

D3

D4

Dm

vin

S1

S4

S2

S3

Lr Cr

Lf

Cf RL

Sm

D1 D2

D3

D4

Dm

PWM

Control Logic and Drive Circuit

Controller

Vref

+

_PID

Voltage error amplifier

Isolated VoltageSensorRectifier

Low PassFilter

S1 S2 S3 S4Sm

vin

S1

S4

S2

S3

Lr Cr

Lf

Cf RL

Sm

D1 D2

D3

D4

Dm

vin

S1

S4

S2

S3

Lr Cr

Lf

Cf RL

Sm

D1 D2

D3

D4

Dm

PWMPWM

Control Logic and Drive Circuit

Controller

Vref

+

_PID

Voltage error amplifier

Isolated VoltageSensor

Isolated VoltageSensorRectifierRectifier

Low PassFilter

Low PassFilter

S1 S2 S3 S4Sm S1 S2 S3 S4Sm

Fig. 4 Control system of the presented single-phase AC chopper.

In proposed ac chopper, iLr(t) is in DCM but iLf(t) is continuous. Thus, the steady-state description in the kth switching period can then be determined by the average method. The average resonant inductor current can be described as following.

⎩⎨⎧

+′+= skLfksr

ink

savgLrk TDITD

LV

TI 1

22, 2

1

skrr

Lfk

o

inks TDI

ZVDT

1sinωω ⎟⎟

⎠

⎞⎜⎜⎝

⎛−+

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+−+ Lfks

r

inkLfk

skrr

skr IDTL

VITD

TD

1

1

sin1cos

ωωω

]skr TD1cosω• (7) where

s

kk

TttD 01 −= (8)

DVVD

Crk

inkk =1 (9)

and

avgLrkkLfkL

ok IDIRV

,1== (10)

okCrk VV = (11)

where

⎩⎨⎧

+=L

skoks

r

ink

s

Lkok R

TDVTDL

VT

RDV 1221

2

TDRV

ZVDT

krrL

ok

o

inks1sinω

ω ⎟⎟⎠

⎞⎜⎜⎝

⎛−+

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+−+

L

oks

r

ink

L

ok

skrr

skr

RVDT

LV

RV

TDTD

1

1

sin1cos

ωωω

]skr TD1cosω• (12)

Thus, the conversion ratio M(D) can be described as

follow.

ink

ok

VVDM =)( (13)

The conversion ratio M(D) versus the duty ratio D with different loads RL is shown in Fig. 5.

RL=60Ω

RL=40Ω

RL=30ΩRL=24ΩRL=20Ω

RL=10Ω

Duty ratio D

Conversion R

atio M(D

)

RL=60Ω

RL=40Ω

RL=30ΩRL=24ΩRL=20Ω

RL=10Ω

Duty ratio D

Conversion R

atio M(D

)

Fig. 5 The conversion ratio M(D) versus duty ratio D with different loads.

Since vin(t)=Vmsinωint, the output voltage Vok in the kth switching period can be obtained as

sinminkok kTVDMVDMV ωsin)()( == )]()([ )1( +−−−• kk ttuttu (14)

We assume that there are the number of n discrete Von in one period of the desired vo(t). Thus, the complete output voltage can be expressed as

]()([sin)( )1(1

+=

−−−•==∑ kksinm

n

koko ttuttukTVDMVv ω

(15) In reality, if fs>>fin and n is so large, we can approximately obtain

)sin()()( tVDMtv inmo ω≅ (16) (16) is truly a sinusoidal waveform of the desired output voltage vo(t).

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IV. DESIGN CONSIDERATIONS AND REALIZATION

An example of a single-phase soft-switching ac chopper is designed and realized. The design procedure is described as follows:

Step 1—Input and output data specification.

The input voltage vin(t)=Vin,maxsinωint= 155sin(2π×60)t;

The output voltage vo(t)=Vo,maxsinωint=220sin(2π×60)t; The maximum output power Po,max=600W. The switching frequency fs=40kHz The resonant frequency fr=20kHz.

Step 2—Decision of the duty cycle D.

With the parameters shown in Step 1, the duty cycle D can be obtained from Fig. 5 under the condition of Po,max=600W, Vo,max=220V, 402/ max,

2max, == ooL PVR ,

Vo,max/Vin,max=1.42. Thus, D=0.3. Substituting D=0.3 into (9) yield D1k=0.21.

Step 3—Calculation of the resonant parameters.

The average resonant current ILrk,avg and the filter current ILfk can be obtained from (12) as ILfk,max=5.5A, ILrk,avg,max=26.2A. According to the resonant frequency and from (7), the characteristic impedance Zo can be obtained as Zo=1.45Ω in this example. Thus,

FZC ror μω 5.5)/(1 == and FCL rrr μω 5.11)/(1 2 == .

Step 4—Calculation of the output filter inductor and capacitor.

For minimizing unnecessary harmonics, the output filter inductor Lf=1mH and capacitor Cf=4.7μF are selected. In hardware realization, IGBT’s IRG4PC50UD and diode’s S30L60 are as power switches and power diodes, respectively. The commutation phenomenon of power switches are measured and shown in Fig. 6, in which the

main power switche Sm turns on at ZCS and the switch S1 of cycloconverter turn on and of at ZVS and ZCS. The experimental results shown in Fig. 6, demonstrate that soft-switching function is achieved. The waveforms of resonant voltage vCr(t) and resonant current iLr(t) are measured and shown in Fig. 7, which exactly meets the simulation result. The waveforms of input voltage and output voltage are simultaneously measured and shown in Fig. 8. The efficiency of the presented single-phase soft-switching ac chopper is also measured, in which the efficiency is over 90% when the output power is at maximum output power 600W.

V. CONCLUSION

A high performance single-phase step up/down ac chopper by a simple and compact characteristic with series-resonant conversion is presented. The main attribute of the ac chopper topology is the fact that it generates an output ac voltage larger or lower than the input ac one, depending on the instantaneous duty-cycle. This property is not found in the classical ac chopper, which produces an ac output instantaneous voltage always lower than the input ac voltage. The active switches are operated at a fixed frequency with the pulse width modulation technique. A resonant cell is built in the power stage to build ZCS for turning on the power switches. Thus, lower switching losses, lower electromagnetic interference noises, and higher power efficiency can be achieved. Because the synthesized SSW very closes sinusoidal waveform, the presented single-phase ac chopper can use a simple LC filter to filter the undesired harmonics and get the sinusoidal voltage with low total harmonic distortion (THD). Total harmonic distortion (THD) at maximum output rated power is within 6%. The power efficiency is over 90% when the output power is at maximum output rated power can be obtained. The analysis and design of circuit has been verified by realization of practical circuit in laboratory.

iDSm

vDSm

iDSm

vDSm

iDS1vDS1

iDS1vDS1

(a) (b) Fig. 6 Commutation waveforms of the main power switch.

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vCr

iLr

vCr

iLr iLr

vCr

iLr

vCr

(a) (b) Fig. 7 The waveforms of resonant voltage vCr(t) and resonant current iLr(t).

vo

vin

vo

vin

Fig. 8 Experimental waveforms of vo(t) and vin(t).

REFERENCES [1] E. El-Bidweihy, K. Al-Badwaihy, M. S. Metwally, and M.

El-Eedweihy, ”Power factor of ac controllers for inductive loads” IEEE Trans. Industrial Electron. Contr. Instrumentation, vol. 27, no. 3, pp. 210-212, 1980.

[2] B. W. Williams, “Asymmetrically modulated AC choppers,” IEEE Trans. Ind. Electron., vol. IE-29, pp. 181–185, Aug. 1982.

[3] S. A. Bhat and J. Vithayathil, “A simple multiple pulse width modulated AC chopper,” IEEE Trans. Ind. Electron., vol. IE-29, pp. 185–189, Aug. 1982.

[4] G. Roy, P. Poitevin, and G. Olivier, “A Comparative study of singlephase modulated AC choppers,” IEEE Trans. Ind. Applicat., vol. IA-20, pp. 1498–1506, Nov./Dec. 1984.

[5] G. H. Choe, A. K. Wallace, and M. H. Park, “An improved PWMtechnique for AC choppers,” IEEE Trans. Power Electron., vol. 4, pp. 496–505, Oct. 1989.

[6] D. H. Jang and G. H. Choe, “Improvement of Input Power Factor in AC Choppers Using Asymmetrical PWM Technique,” IEEE Trans. Ind. Electron., vol. 42, no. 2, pp. 179–185, April 1995.

[7] N. A. Ahmed, K. Amei, and M. Sakui, ,” A New Configuration of Single-Phase Symmetrical PWM AC Chopper Voltage Controller,” IEEE Trans. Ind. Electron., vol. 46, no. 5, pp. 942-951, Oct. 1999.

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