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Electric Power Systems Research 77 (2007) 1425–1431

Harmonics reduction of three-phase boost rectifierby modulating duty ratio

Ali M. EltamalyElectrical Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia

Received 11 February 2006; received in revised form 16 July 2006; accepted 23 October 2006Available online 28 November 2006

bstract

Line currents of three-phase diode bridge rectifier suffer from high THD. This THD is higher than IEEE standards. Injection of six harmonicomponents from the DC bus back to the duty ratio of the boost converter connected to the three-phase diode bridge rectifier reduces the THD ofhe utility line current. In this study a sine wave and a triangle wave with six times the fundamental frequency is presented. The analysis has beenarried out to reduce THD of the utility line current of three-phase boost rectifier. The THD of the utility line currents depends on the amplitude

nd phase-shift of the six-order component injected to the duty ratio of the boost converter. A complete mathematical and simulation analysis ofhe injection technique has been carried out. The mathematical analysis and simulation results of 6 kW prototype system show the superiority ofhe proposed injection technique.

2006 Elsevier B.V. All rights reserved.

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eywords: Diode bridge rectifier; Harmonics; Boost converter

. Introduction

Three-phase diode bridge single switch boost rectifier shownn Fig. 1 has many applications in adjustable speed drivesASD), wind energy systems (WES) and other applications.hree-phase diode bridge rectifier draws non-sinusoidal cur-

ent from the source. This distorts the voltage at the point ofommon coupling which greatly deteriorates the power qual-ty of distribution network and reduces the power factor ofhe load. Early works have been made to reduce THD ofhe input currents by increasing number of poles [1–4]. Thisechnique has many disadvantages like the system is large inize, heavy in weight, expensive and needs special transformer.assive filters have been used, but this technique eliminatesnly specific harmonics as well as it is not suitable for inputariable frequency applications as in WES. Moreover, pas-ive filters are bulky, expensive and cause resonance problems5].

Several efforts have been made to reduce the THD of thenput currents by injecting high harmonic components to the lineurrents. In [6], the third harmonic current has been injected from

E-mail address: eltamaly@yahoo.com.

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378-7796/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.epsr.2006.10.012

he DC link back to the utility line current. But, this techniqueeeds extra component in the re-injection path and a zigzag ordelta-way transformer to provide neutral point.

In [7], the switching is tuned on, immediately, when the DCide currents fall to zero. The main problem with this systems that at light loads the switching frequency increases whichncreases the switching losses and increases the stress on theoost inductor too.

In [8], the current harmonics are improved by reducing theix order ripple at the output. This accomplished by a feedbackontrol loop which passes the six order ripple. This techniques suitable for resistive loads only where in the real load of theectifier is capacitive which will cause phase delay for the sixrder ripple which makes the delay is load dependant. Moreover,wide control bandwidth makes the control loop unstable at light

oads. Besides, the variable switching frequency complicates theoost inductor design.

In [9,10], fixed frequency switching technique is used toeduce just fifth harmonics from the utility line currents byodulating the duty ratio of the boost converter with six order

armonics. The main disadvantage of this technique is that iteduces only fifth harmonic while it increases the seventh har-onics. Moreover, the load used in this technique is a resistive

oad.

1426 A.M. Eltamaly / Electric Power Systems Research 77 (2007) 1425–1431

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Fig. 1. Three-phase diode bridge single switch boost rectifier.

In this paper, the duty ratio of the boost converter has beenodulated by six order sine wave and triangular wave with

ix times the fundamental frequency. This technique is suitableor all kind of loads. The mathematical analysis and simu-ation results show the superiority of the proposed injectionechnique.

. Proposed system

The THD of the utility line current of three-phase dioderidge rectifier depends on the rectifier voltage gain, M, whichs defined as

= Vdc

Vllp(1)

here Vdc is the boost converter output voltage and Vllp is thenput line–line peak voltage. The higher the M is the lower theHD becomes. A higher M means a high output voltage, yieldinghigh voltage stress on the devices. In our analysis we used twoalues of M which are 3.4 and 5.

Fig. 2 shows the line current and its FFT components com-ared to IEEE-519-1992 standard limits [11] at M = 3.4 withoutny THD reduction technique. Fig. 3 shows the line currentnd its FFT component with respect to IEEE-519-1992 stan-ard limits [11] at M = 5 without any THD reduction. Table 1hows IEEE-519 current limits [11].

To determine the best order of harmonics required to benjected to the duty ratio, we have to compare between the actual

lectric utility line current and the proposed sine-wave currents shown in Fig. 4. It is clear that when modulating the dutyatio with six order harmonics with angle 270◦ with respect tohase a voltage, the duty ratio increases when the line current is

able 1EEE-519 current limits [11]

CR = IS/IL H < 11 11–16 17–22 23–24 35 < h THD

<20 4.0 2.0 1.5 0.6 0.3 5.020–50 7.0 3.5 2.5 1.0 0.5 8.050–100 10.0 4.5 4 1.5 0.7 12

100–1000 12.0 5.5 5.0 2.0 1.0 15.01000 15.0 7.0 6.0 2.5 1.4 20.0

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ig. 2. Line current of three-phase diode bridge without any THD reductionechnique and its FFT components compared to IEEE-519 standards at M = 3.4.

ess than the proposed sine-wave current and reduces when theine current is higher than the proposed sine-wave current. Thisill happen with the other two phases. In this paper the duty

atio is modulated by two different waveforms. The first one issine-wave sixth order harmonic; the second is a sixth order

riangular waveform.

. Modulating duty ratio with sixth order sine wave

The dominant harmonics in the utility line currents are fifthnd seventh harmonics. The others have small amplitude and cane neglected. So, the line current of phase a can be expressed asollows:

a ∼= I1 sin ωt − I5 sin(5ωt) − I7 sin(7ωt) (2)

t is clear from Fig. 4 that the phase angle of the waveformsed to modulate the duty ratio, D is 270◦. So the instantaneousodulation index can be expressed as

(t) = D[1 + q sin(6ωt + 270)] (3)

here q is the amplitude of the sixth order component that used to

odulate the duty ratio, and d(t) is the instantaneous modulation

ndex.The value of I1, I5 and I7 are linearly proportional to the

quare of the duty ratio [12]. So, by substituting (3) into (2) the

A.M. Eltamaly / Electric Power Systems

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csystem in PSIM is shown in Fig. 5. The control system comparesthe DC output voltage with reference value, Vref. The error signalgoes to PI-controller and limiter to obtain the average value of

ig. 3. Line current of three-phase diode bridge without any THD reductionechnique and its FFT components compared to IEEE-519 standards at M = 5.

odified utility line current can be obtained as shown in (4):

aq = (d(t))2 × [I1 sin ωt − I5 sin(5ωt) − I7 sin(7ωt)] (4)

y neglecting any terms contains q2 and neglecting any har-onics greater than the seventh harmonics, modified utility line

urrent can be obtained as:

aq = [I1 − 2q(I5 − I7)]sin(ωt) + (qI1 − I5)sin(5ωt)

−[qI1 + I7]sin(7ωt) (5)

ig. 4. Duty ratio modulation concept with respect to the current of phase a.

d

Research 77 (2007) 1425–1431 1427

rom (5), the THD of the utility line current can be obtained ashown in (6):

HD =√

(qI1 − I5)2 + (qI1 + I7)2

(I1 − 2q(I5 − I7))2 (6)

he optimum value of q can be obtained by equating the firsterivative of THD with respect to q by zero as shown in (7):

d(THD)

dq= 0 (7)

y substituting (6) into (7) the optimum value of the amplitudef the sixth order component that used to modulate the duty ratios shown in (8):

= 1

2

(I5 − I7

I1

)= 1

2

(I5

I1− I7

I1

)(8)

he waveform of supply current is almost square wave. So,he relation between I5, I7 and I1 is shown in (9) and (10),espectively

I5

I1

∼= 1

5(9)

I7

I1

∼= 1

7(10)

y substituting (9) and (10) into (8) the optimum value of themplitude of the sixth order component that used to modulatehe duty ratio can be obtained as shown in (11):

∼= 1

2

(I5

I1− I7

I1

)∼= 1

2

(1

5− 1

7

)∼= 0.028571 (11)

. Simulation results

The simulation of the proposed system was done using PSIMomputer simulation package. The schematic of the proposed

uty ratio, D. The result of multiplying D by q is added to the

Fig. 5. PSIM simulation of the proposed system.

1428 A.M. Eltamaly / Electric Power Systems Research 77 (2007) 1425–1431

Fo

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0giuIaatIwbautility line current and its FFT components with triangle-waveinjected at q = 0.028.

ig. 6. The waveform of supply current, instantaneous duty ratio, PI-controllerutput, and DC link current.

alue of D to obtain the instantaneous value of the duty ratio,(t) as shown in Fig. 5.

The simulation was carried out for two different injectionaveforms, a sine wave and a triangle wave for different ampli-

udes of injection waveform. The following values are used inhe simulation program:

VLL = 110 V, 0.1 mH source inductance, 1 mF DC-link capac-itor, 30 �, and 5 mH load inductance, and 50 kHz switchingfrequency.

The simulation has been carried out for two different valuesf rectifier voltage gain, M at M = 3.4 and 5, respectively. From1) the corresponding values of reference DC voltage are 530nd 780 V, respectively.

.1. Simulation results at M = 3.4

In this case the reference voltage is adjusted to be 530 V.ig. 6 shows the waveform of supply current, the instantaneousuty ratio, the waveform out from PI-controller, and the DCink current. It is clear that the control system work effectivelyn controlling the DC output voltage. The waveform out fromhe PI-controller, Vpiout is increasing when the DC voltage isess than the reference value and visa versa. The peak to peakariation of DC voltage is about 0.04% as shown in Fig. 6 whichroves the stability of the DC voltage. The same response arebtained also in case of M = 5 for a sine wave and a triangularave used to modulate the duty ratio.Fig. 7 shows the relation between the percentage of THD and

he amplitude of injected waveform for a sine wave and a triangle

ave. As shown in Fig. 7 the minimum THD occurs with sineave at about 18.5% when the amplitude of the injected wave-

orm is 0.022 V. Also the minimum THD occurs with triangleave at 17% when the amplitude of the injected waveform is

Ft

ig. 7. The variation of THD% with amplitude of injected wave for sine &riangle-waves at M = 3.4.

.027 V at M = 3.4. It is clear that the THD associated with trian-ular wave is better than the one associated with sine wave thats because the all harmonics become smaller than the other val-es associated with sine wave. Fig. 8 shows the relation between5/I1 and the amplitude of injected waveform for a sine wave andtriangle wave at M = 3.4. Fig. 9 shows the relation between I7/I1nd the amplitude of the injected waveform for sine wave andriangle wave at M = 3.4. Fig. 10 shows the relation between11/I1 and the amplitude of the injected waveform for a sineave and a triangle wave at M = 3.4. Fig. 11 shows the relationetween I13/I1 and the amplitude of the injected waveform forsine wave and a triangle wave at M = 3.4. Fig. 12 shows the

ig. 8. The variation of I5 / I1 with amplitude of injected wave for sine &riangle-waves at M = 3.4.

A.M. Eltamaly / Electric Power Systems Research 77 (2007) 1425–1431 1429

Fig. 9. The variation of I7 / I1 with amplitude of injected wave for sine &triangle-wave at M = 3.4.

Fig. 10. The variation of I11 / I1 with the amplitude of injected waveform forsine-wave and triangle-wave at M = 3.4.

Fig. 11. The variation of I13 / I1 with the amplitude of injected aveform forsine-wave and triangle-wave at M = 3.4.

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ig. 12. The variation of utility line current and its FFT components withriangle-wave injection at q = 0.027 and M = 3.4.

.2. Simulation results at M = 5

Fig. 13 shows the relation between THD and the amplitudef injected waveform for a sine wave and a triangle wave. As

hown in Fig. 13, the minimum THD with a sine wave is 17%t amplitude of injected waveform is 0.009 V and the minimumHD with triangle wave is 16.5% at amplitude of the injected

ig. 13. The variation of THD% with amplitude of injected waveform for sine-ave and triangle-wave.

1430 A.M. Eltamaly / Electric Power Systems Research 77 (2007) 1425–1431

Fig. 14. The variation of I5 / I1 with amplitude of injected wave for sine andtriangle-waves at M = 5.

Fig. 15. The variation of I7 / I1 with amplitude of injected wave for sine andtriangle-waves at M = 5.

Fig. 16. The variation of I11 / I1 with amplitude of injected wave for sine andtriangle-waves at M = 5.

Fig. 17. The variation of I13 / I1 with amplitude of injected wave for sine andtriangle-waves at M = 5.

Fig. 18. The utility line current and its FFT components with triangle-waveinjection at q = 0.015 and M = 5.

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1998, pp.430–436.[12] P. Barbosa, F. Canales, J.-C. Crebier, F.C. Lee, Interleaved three-phase

boost rectifiers operated in the discontinuous conduction mode: analysis,

A.M. Eltamaly / Electric Power Sy

aveform is 0.015 V at M = 5. Fig. 14 shows the relation between5/I1 and the amplitude of the injected waveform for a sine wavend a triangle wave at M = 5. Fig. 15 shows the relation between7/I1 and the amplitude of the injected waveform for a sine wavend a triangle wave at M = 5. Fig. 16 shows the relation between11/I1 and the amplitude of the injected waveform for a sine wavend a triangle wave at M = 5. Fig. 17 shows the relation between13/I1 and the amplitude of the injected waveform for a sine wavend a triangle wave at M = 5. Fig. 18 shows the line current andts FFT components with a triangle-wave injection at q = 0.015.

Figs. 7 and 13 demonstrate the following:

The triangle waveform gives better THD than the sine wave-form for same value of M.The amplitude of modulation waveform depends on the rec-tifier voltage gain for the best THD.The higher the rectifier voltage gain the lower the amplitudeof the required modulating waveform.

. Conclusions

In this paper a complete analysis of THD in the utility lineurrent of three-phase boost rectifier with modulating duty ratios carried out for sine and triangle waveforms. From the simu-ation results, it is recommended to use triangle waveform withix times the fundamental frequency in modulation of duty ratiof boost converter. The phase angle of modulating waveformhould be 270◦. The amplitude of the modulating waveformepends on the rectifier voltage gain for the best THD. Theigher the rectifier voltage gain the lower the amplitude of theequired modulating waveform. The modulation of duty ratioith sine or triangle waves with proper amplitude reduces theHD of line current to meet IEEE-519 standard limits.

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