Space Vector Modulation Control of an AC–DC–AC061

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1470 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 21, NO. 5, SEPTEMBER 2006

Space Vector Modulation Control of an AC–DC–ACConverter With a Front-End Diode Rectifier and

Reduced DC-link CapacitorXiyou Chen and Mehrdad Kazerani , Senior Member, IEEE

Abstract—In this paper, the control of an ac–dc–ac converterwith a front-end diode rectifier and reduced dc-link capacitorbased on the space vector modulation strategy is investigated. Themodulation index is time-varying and determined by the instanta-neous value of the dc voltage measured by a voltage sensor. Usinga small bipolar capacitor, instead of a large electrolytic capacitoron the dc-link, increases the lifetime of the converter and reducesits size. The input current quality of this converter has been shownto be superior to that of the conventional ac–dc–ac converter withfront-end diode rectifier. The perfectly sinusoidal local average

output voltage can still be achieved under unbalanced inputvoltage condition by implementing a time-varying modulationindex. The rule for determining the dc capacitance has also beenstudied in this paper. The simulation results obtained from PSIMsimulation software and experimental results obtained from thelab prototype are used to verify the theoretical expectations.

Index Terms—AC–DC–AC converter, front-end diode rectifier,reduced dc capacitor, space vector modulation, unbalanced inputvoltage.

I. INTRODUCTION

IN RECENT years, the trend in the design of ac–dc–ac con-verters for motor drive applications has been in the direction

of reducing the size, integrating the converter with the motor,

improving the efficiency and lifetime, and reducing the cost. As

a result, eliminating or reducing the size of the dc-link capacitor

has received a lot of attention [1], [2]. Replacing large dc-link

electrolytic capacitors with small nonelectrolytic capacitors of-

fers the advantages of compact size and longer lifetime.

Many researchers have investigated the performance of

ac–dc–ac converters with front-end controlled rectifier and

without dc-link capacitors or ac–ac converters such as indirect

matrix converters in motor drive applications [3], [4]. Nearly

sinusoidal output voltage and input current waveforms, without

low-order harmonics, as well as unity or regulated input powerfactor can be achieved in these converters. Because of the

capability of power regeneration and high quality of waveforms

on both input and output sides, these converters are widely

Manuscript received February 8, 2005; revised July 29, 2005. Recommendedby Associate Editor B. Wu.

X. Chen is with the Department of Electrical and Electronics Engineering,Dalian University of Technology, Dalian 116023, China (e-mail: [email protected]).

M. Kazerani is with the Department of Electrical and Computer Engi-neering, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail:[email protected]).

Digital Object Identifier 10.1109/TPEL.2006.880236

used in medium or high power industrial applications or when

frequent start/stop operations are required.

On the other hand, there are many low-power industrial appli-

cations such as fan and pump drive systems, where it is not fea-

sible to regenerate energy from the load to the source. In these

applications, the front-end diode rectifier ac–dc–ac converters

are still being used because of their lower cost and higher reli-

ability. In the dc–ac stage of such converters, sinusoidal pulse

width modulation (SPWM) or space vector pulse width mod-ulation (SVPWM) are often used in order to obtain sinusoidal

output voltage waveforms. The operation of SPWM inverters

are based on the comparison between the output voltage refer-

ence and a triangular carrier signal to generate the switch con-

trol signals or duty cycles. In these inverters, the dc-link voltage

should be kept constant and a large electrolytic capacitor should

be used in the dc-link. In SVPWM inverters, six fixed active

voltage vectors and two zero vectors are used to synthesize the

rotating desired output voltage vector [5]. The switch duty cy-

cles are calculated according to the position of the desired output

voltage vector with respect to the two adjacent active fixed vec-

tors. In this case, too, a constant dc-link voltage should be main-

tained.In this paper, a novel SVPWM strategy based on time-varying

dc-link voltage is investigated for front-end diode rectifier

ac–dc–ac converter with a small nonelectrolytic dc-link capac-

itor which provides snubbing. The lifetime of the converter can

be increased and its size reduced by adopting this strategy. A

comparative evaluation with respect to the ac–dc–ac converter

with dc-link electrolytic capacitor has been carried out based

on constant motor drive strategy. Simulations using PSIM

software package and experiments on a lab prototype have been

performed to verify the validity of the method proposed in this

paper.

II. FUNDAMENTALS OF SPACE VECTOR MODULATED INVERTER

BASED ON CONSTANT DC-LINK VOLTAGE

The ideal local average values of the output three-phase

line-to-line voltages with amplitude , angular frequency ,

and initial phase angle , can be expressed as

(1)

These voltages can be represented in a three-axis frame, with the

axes , , and phase shifted by 2 3 radians with

0885-8993/$20.00 © 2006 IEEE



CHEN AND KAZERANI: SPACE VECTOR MODULATION CONTROL 1471

Fig. 1. Three-axis frame, rotating space vector, and three-phase output volt-

ages.

respect to one another, as shown in Fig. 1. The instantaneous

values , , and are equal to the projections of a ro-

tating voltage vector along the axes of , , and , re-

spectively. This rotating vector is called the voltage space vector

and is determined as follows:

(2)

For the three-phase balanced voltages expressed in (1), the

voltage space vector (2) can be simplified as

(3)

where represents the initial position

(at 0) of .

In the dc–ac inverter shown in Fig. 2, there are 8 possible

switch states. Each of these states refers to a certain set of output

voltages ( , and ) and therefore a specific voltage

space vector. The six nonzero active vectors with the same am-

plitude of 2 3 , and the two zero vectors, resulting from

the eight switch states, are shown in Fig. 3 and Table I. For ex-

ample, in the switch state ( ), where the top switch in leg

A and bottom switches in legs B and C of inverter are ON

and

and

(4)

For the switch state ( ), the equivalent circuit of Fig. 4 can

be obtained. From Fig. 4,

(5)

At any moment of time, one can get any of active and zerovectors by selecting the corresponding switch states shown in

Fig. 2. Inverter with constant dc-side voltage.

Fig. 3. Active voltage space vectors.

TABLE ISWITCH STATES, VOLTAGE SPACE VECTORS AND

PHASE-A V OLTAGE( j V j = ( 2 =

p

3 ) V )

Fig. 4. Equivalent circuit for switch state (p ; n ; n

).

Table I. These vectors can be used to synthesize approximately

the rotating output voltage space vector . From the desiredposition of , two adjacent active vectors and , and a




Fig. 5. Synthesis of output voltage space vector.

zero vector are selected to construct , as formulated in (6)

and shown in Fig. 5

(6)

where , and are the duty ratios of the switch states

corresponding to the active vectors , , and , respectively.Defining the modulation index as

(7)

the following duty cycles can be obtained from the “Law of

Sines”:

(8)

where 1 , is t he s witching f requency, a nd , , a nd

are the time intervals in a switching period, corresponding to

, , and , respectively.

III. PROPOSED SPACE VECTOR MODULATION STRATEGY

WITH TIME-VARYING DC VOLTAGE

Fig. 6 shows the front-end diode rectifier ac–dc–ac converter

with reduced dc capacitor, which is only used to suppress the

high-frequency voltage ripple caused by the negative dc-link

high-frequency current, instead of smoothing dc-link voltage.

The voltage sensor measures and provides the dc voltage value

to the low-pass filter (LPF), which is used to remove the ripplecontents of the dc voltage signal. The LPF can be realized by an

RC network. The output signal of LPF is fed to the SVPWM

controller to calculate the instantaneous value of modulation

index.

Due to time-varying nature of dc-bus voltage , the am-

plitudes of the space vectors will change with time.

For the front-end diode rectifier ac–dc–ac converter with re-

duced dc capacitor, this paper presents a novel SVPWM strategy

with time-varying modulation index , given by (9), for si-

nusoidal output voltages

(9)

Fig. 6. Front-end diode rectifier ac–dc–ac converter with reduced dc-link ca-

pacitor.

In simulation and practical realization, is obtained from

a voltage sensor on the dc-link, and is calculated in each

switching period, according to (9).

From (6), (8), and (9), the following output voltage space

vector can be obtained.

(10)

Equation (10) shows that the desired sinusoidal output voltage

local average can be obtained by implementing the time-varying

modulation index.In order to get a perfectly sinusoidal local average for the

output voltage, the desired output voltage should meet the fol-

lowing criterion at any given moment of time:

(11)

Therefore, the maximum voltage gain will be

(12)

According to (12), the voltage gain is lower than that of the

ac–dc–ac converter with large dc-link electrolytic capacitor,

which is nearly 1. As a result, there will not be enough output

voltage to run the motor at full utility voltage. This can limit

the applications where this technology could be used.

IV. DC-LINK CAPACITOR DESIGN

Due to the inductive nature of the load, the dc-link current

may contain high-frequency reverse pulses that tend to increase

the dc-link capacitor voltage. In order to limit the ripple contents

of the dc-link voltage, the dc-link capacitor should be properly

designed.

From the simulation waveforms shown in Fig. 7(a),12 and 3 can be found. During the time period ,




Fig. 7. Voltage and current waveforms of VSI for T > T = 12 ( R = 2 , L =

10 mH, f = 50 Hz). (a) v and its local average. (b) DC-link current andline current

i

.

2/3 and the switch state ( ) given by Table I

exists. In this switch state, the dc-link current will equal to .

Therefore, if it is desired to keep the dc-link current always pos-

itive, with no capacitor installed in dc-link, the time period

should meet the constraint given by

(13)

In other words, the displacement angle of the load should satisfy

(14)

In order to suppress high-frequency voltage ripples generated

when displacement angle of load is greater than 6, one should

select an appropriately-sized dc-link capacitor. This can be done

by following the two steps described as follows.

A. Step 1

Determine the maximum value of the charge flowing in the

reverse direction towards dc-link capacitor in each switching

period.

From Fig. 8, which is a zoom-in view of the phase voltage,

line current, and dc current, the charge flowing in reverse direc-

tion in each switching period can be found as

(15)

where is the pulse width of the negative dc current, which

is also equal to . If the origin of time is chosen as shown in

Fig. 8, can be represented as

(16)

Fig. 8. Zoom-in of Fig. 7.

For a constant inductive load with constant resistance and in-

ductance, the dc-link negative current can be expressed as

(17)

Substituting (16) and (17) in (15), the charge flowing in re-

verse direction can be determined as a function of both and

(18)

In order to determine the maximum value of , the

derivative of with respect to time and should be

set to zero

(19)

(20)

From (19) and (20)

(21)

From (21)

(22)




Substituting (22) in (18), the maximum value of charge for a

constant inductive load can be found as

(23)

For inductive loads corresponding to 6 18,from (19)

(24)

Substituting (24) into (18)

(25)

For a motor, it is more effective to calculate the charge using

rated power , rated voltage and load displacementpower factor (DPF). The line current magnitude and displace-

ment angle are

and the negative dc-link current is

(26)

From (15), (16), and (26), at 1, the charge for motor load

can be obtained as

(27)

It can be proven that if

(28)

has the maximum value of

(29)

B. Step 2

Determine the capacitance based on and permitted

peak-to-peak dc-link voltage ripple .

As mentioned earlier in the paper, the job of the dc-link ca-pacitor is to absorb the energy released by the load in the form of

negative dc-link current pulses and the capacitor should be de-

signed based on the permitted peak-to-peak ripple on the dc-link

voltage. The capacitance of the dc-link capacitor can be related

to the maximum charge and the permitted peak-to-peak

dc-link voltage ripple , through the following expres-

sion:

(30)

For inductive load with constant resistance and inductance,

from (23), (24), and (30), the reduced capacitance needed in the

dc-link can be determined as

(31)

(32)

where .

For motor load, from (29) and (30), the reduced capacitance

needed in the dc-link can be determined as

(33)

Equation (33) implies that the reduced dc-link capacitor can be

used in cases where the motor displacement power factor does

not vary in a wide range and does not assume very low values,

such as near-zero values which happen at low- and no-load con-

ditions. The smaller the power factor that is allowed, the larger

the capacitance that has to be used.

V. SIMULATION RESULTS

In this section, the simulation results obtained from PSIMsimulation software for the proposed method are presented. The

following parameters have been used in the simulation of the

system shown in Fig. 6.

Source: three-phase, 60 Hz, 200 V (line-to-line, RMS).

DC-link capacitor: 30 F.

Low-pass filter: 796 Hz.

SVPWM controller: 6.2, 40 Hz, 0,

8 kHz.

The induction motor and mechanical load parameters are listedin Table II.




TABLE II

INDUCTION MOTOR AND MECHANICAL LOAD PARAMETERS

USED IN SIMULATIONS

Fig. 9. Simulation results atsteady-state: (a)dc-link voltage V (V)and outputvoltage

v

(V) and (b) modulation index.

TABLE III

COMPARISON OF OUTPUT VOLTAGE THD OF CONVENTIONAL

AND PROPOSED AC–DC–AC CONVERTERS

A. Output Voltage Simulation Results

Fig. 9 shows the simulation results for dc-link voltage ,

output voltage , and modulation index . From Fig. 9(a),

one can clearly see that the envelope of is defined by the dc

voltage .

In order to investigate the effect of the dc capacitance reduc-

tion on the quality of the output voltage, the total harmonic dis-

tortion (THD) values of the output voltage for the cases of a reduced dc capacitance with variable modulation index and a

large dc capacitance with fixed modulation index were obtained

through simulation. The results are summarized in Table III. As

seen, the improvement in the THD of the inverter output voltage

due to a large dc capacitance is on the order of 0.1%, which is

not considered an advantage, considering the size, weight and

cost of the 2000- F capacitor that has to be used.

B. Comparison Between Input Current Qualities of Proposed

and Conventional AC–DC–AC Converters

Duo to the nature of front-end diode rectifier, both low- and

high-order harmonics will be present in the input current. Thephase-a input current waveforms and their respective frequency

Fig. 10. Phase-a input current of ac–dc–ac converter with 2500- F dc elec-trolytic capacitor: (a) input current waveform and (b) input current spectrum.

Fig. 11. Phase-a input current of ac–dc–ac converter with reduced (30- F)dc-link capacitor: (a) input current waveform, (b) input current spectrum.

TABLE IVCOMPARISON OF INPUT CURRENT QUALITY INDICES OF CONVENTIONAL

AND PROPOSED AC–DC–AC CONVERTERS

spectrums for the conventional and proposed ac–dc–ac con-

verters are shown in Figs. 10 and 11, respectively.

In order to show in more detail the qualities of the input

currents, the THD, root-mean-square (RMS), maximum value,

crest factor (CF) and displacement power factor (DPF) have

been calculated for both conventional and proposed ac–dc–ac

converters. The CF is defined as

CFPeak value of input current

RMS value of input current(34)

Table IV lists the results obtained from PSIM software package.




Fig. 12. Steady-state simulation results for unbalanced input voltage: (a)dc-link voltage, (b) modulation index, and (c) output voltage

v

and its local

average.

From Table IV, one can conclude that the quality of the input

current of an ac–dc–ac converter with reduced capacitor is supe-

rior to that with a large electrolytic capacitor. Lower THD im-

plies reduced filtering requirements. Lower input current RMS

and peak values mean that diodes of lower current rating and

thus lower cost are required. Finally, CF of 1.27 implies that the

input current waveform is closer to a perfect sinusoid.

C. Simulations for Unbalanced Input Voltage

Since the modulation index is calculated based on the mea-

sured instantaneous value of the dc-link voltage, the output

voltage sinusoidal local average waveform, without low-order

harmonics, can still be obtained under unbalanced input voltage

conditions. Fig. 12 shows the waveforms of dc-link voltage,

modulation index, and output voltage for the unbalanced inputvoltage

(35)

Other parameters of simulation have been kept the same as in

parts A and B.

Comparing Fig. 12(a) and (b), one can find out that the mod-

ulation index responds to variations in the instantaneous value

of the dc-link voltage to shape the local average of the output

voltage to be a sinusoid of desired amplitude, phase angle andfrequency. It is worth noting that an imbalance in the input

voltage can distort the dc-link voltage and reduce its minimum

value that determines the maximum possible output voltage that

can be obtained. It can also distort the output voltage waveform.

The variable modulation index approach adopted in this paper

can compensate for this effect and guarantee a sinusoidal local

average for the output voltage waveform.

VI. EXPERIMENTAL RESULTS

A prototype based on the intelligent power module

(PM30CSJ060) and a DSP controller was constructed inthe lab to test the performance of the SVPWM strategy pro-

TABLE V

ENVIRONMENT OF EXPERIMENT

posed in this paper. Table V lists the basic environment of the

experiment.

A. Input Currents and Power Factor

Fig. 13(a) and (b) show the input currents of the ac–dc–ac

converter and their spectrums with 11- F reduced capacitor and

2000- F normal electrolytic capacitor, respectively. The currentshown in Fig. 13(a) contains less low-frequency harmonics and

has lower crest factor than that shown in Fig. 13(b). As a re-

sult, the quality of the input current has been improved consid-

erately. Fig. 14 shows that the displacement power factor of the

converter in the case of reduced capacitor is near unity.

B. DC Currents With Different Inductive Loads

Fig. 15 shows the dc currents of the inductive load with

28 mHand different resistances at outputfrequency 50Hz.

Curve 1 ) 5 60.37 30 , negative pulses caused by

the heavily inductive load are present in the dc current.

Curve 2 ) 15 , 30.38 30 , negative pulses are notpresent in the dc current.

Curve 3 ) 27 , 18.04 30 , negative pulses are not

present in the dc current.

C. Output Voltage and Current

An inductive load with 10 and 28 mH was

used in this experiment. The load impedance angle at the output

frequency 50 Hz was 0.7212

6. According to (32), the dc capacitor was calculated as

A bipolar capacitor of a bit larger capacitance, i.e., 11 F, was

used on the dc-link in the prototype.

Fig. 16 shows the dc voltage (curve 1) and the output line-to-

line voltage (curve 2). The dc-link voltage dose not contain

high-frequency ripple after the proper capacitor is connected to

the dc-link, but it is not constant due to the fact that the capac-

itor has been reduced greatly compared with the conventional

converter. The envelope of the output voltage is determined by

the dc voltage.

In order to compare with the conventional ac–dc–ac con-

verter based on SVPWM, Fig. 17 shows the load currents corre-sponding to the SVPWM method proposed in this paper (curve




Fig. 13. Input current (1 A/100 mV) and its spectrum: (a) with 11-

F reduced dc bipolar capacitor and (b) with 2000-

F dc electrolytic capacitor.

Fig. 14. Input current and input phase voltage.

Fig. 15. DC currents withL =

28 mH and 1)R =

5

, 2)R =

15

, and 3)R =

27

atf =

50 Hz.

Fig. 16. DC voltage and output voltage.

1) and the conventional method (curve 2). The perfectly sinu-

soidal local average output voltage can still be achieved by the

SVPWM strategy proposed in this paper.

VII. CONCLUSION

The front-end diode rectifierac–dc–ac converter with reduceddc-link capacitor investigated in this paper offers longer life-

time, smaller size, and higher-quality input current waveforms

compared with the conventional ac–dc–ac converter with large

electrolytic dc-link capacitor. The SVPWM strategy proposed

in this paper enables successful operation in steady-state under

balanced and unbalanced input voltage conditions as well as

during sudden input voltage variations. This has been made pos-

sible by implementing a variable modulation index strategy. The

modulation index varies inversely proportional to the dc-link

voltage to realize the desired output voltage sinusoidal local av-

erage from the dc-link voltage which is time-varying due to the

small size of the dc-link capacitor. Two rules for the design of

the reduced dc capacitor are analytically derived for the cases of constant inductive load and motor load. For a reasonably small




Fig. 17. Output currents: 1) with reduced dc capacitor (11- F) and 2) with2000- F dc electrolytic capacitor.

dc-link capacitor, the load power factor should be high. This im-plies that when the ac–dc–ac converter is used as a motor drive,

the motor should be always loaded so that the load displacement

angle is smaller. The drawbacks of the proposed scheme are the

need for a fast microprocessor, voltage gain being lower than

the conventional ac–dc–ac converter, and lack of regenerative

braking capability.

REFERENCES

[1] J.S. Kim and S.K.Sul, “New control scheme for AC-DC-ACconverter

without dc link electrolyticcapacitor,” in Proc. 24thAnnu. IEEEPower Electron. Spec. Conf. (PESC ’93), 1993, pp. 300–306.

[2] M. Muroya, K. Shinohara, K. Iimori, and H. Sako, “Four-step commu-

tation strategy of PWM rectifier of converter without dc link compo-nents for induction motor drive,” in Proc. Elect. Machines Drives Conf.(EMDC ’01), 2001, pp. 770–772.

[3] L. Wei and T. A. Lipo, “A novel matrix converter topology with simplecommutation,” in Proc. 36th Annu. IEEE Ind. Appl. Soc. Meeting(IAS ’01), 2001, vol. 3, pp. 1749–1754.

[4] M. Jussila, M. Salo, and H. Tuusa, “Realization of a three-phase indi-rect matrix converter with an indirect vector modulation method,” inProc. 34th Annu. IEEE Power Electron. Spec. Conf. (PESC ’03), 2003,vol. 2, pp. 689–694.

[5] L. Huber and D. Borojevic, “Space vector modulated three-phase to

three-phase matrix converter with input power factor correction,” IEEE Trans. Ind. Appl., vol. 31, no. 6, pp. 1234–1246, Nov./Dec. 1995.

Xiyou Chen received the B.Sc., M.Sc., and Ph.D.degrees from the Harbin Institute of Technology,Harbin, China, in 1982, 1985, and 2000, respectively.

Currently, he is a Professor in the Departmentof Electrical and Electronics Engineering, DalianUniversity of Technology, Dalian, China. From April2004 to March 2005, he was with the Departmentof Electrical and Computer Engineering, Universityof Waterloo, Waterloo, ON, Canada, as a Visiting

Scholar. His research interests are in applicationsof power electronics in power systems, matrix

converters, motor drives, and chaos control in electrical engineering.

Mehrdad Kazerani (S’88–M’96–SM’02) receivedthe B.Sc. degree from Shiraz University, Shiraz,Iran, in 1980, the M.Eng. degree from ConcordiaUniversity, Montreal, QC, Canada, in 1990, and thePh.D. degree from McGill University, Montreal, QC,Canada, in 1995.

From 1982 to 1987, he was with the Energy Min-istry, Iran. He is presently an Associate Professorwith the Department of Electrical and ComputerEngineering, University of Waterloo, Waterloo,

ON, Canada. His research interests are in the areasof power electronic circuits and systems design, active power filters, matrixconverters, pulsed power, distributed power generation, hybrid vehicles, and

FACTS.Dr. Kazerani is a member of the Society of Automotive Engineers (SAE). He

is a Professional Engineer in the province of Ontario, Canada.

Documents

Space Vector Modulation Control of an AC–DC–AC061