A novel harmonic reduction technique for controlled converter by third harmonic current injection

Electric Power Systems Research 91 (2012) 104–112

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A novel harmonic reduction technique for controlled converter by third harmonic current injection Ali M. Eltamaly ∗ Electrical Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia

a r t i c l e

i n f o

Article history: Received 19 December 2011 Received in revised form 17 May 2012 Accepted 18 May 2012 Available online 19 June 2012 Keywords: Controlled converter Harmonic distortion Third harmonic injection Power quality

a b s t r a c t Three-phase controlled converter has many applications in interfacing renewable energy sources and adjustable speed drives as a rectifier or inverter. The utility line currents of this converter have high harmonic distortion more than the harmonic standards. This research introduces a new technique of circulating third harmonic currents from dc-link to the line currents to reduce its harmonic contents. The new proposed system uses single-phase controlled converter to control the angle of injection current for each firing angle of the three-phase converter. A detailed analysis is introduced to achieve a relation between the firing angles of three and single-phase controlled converters. Also a detailed design for other injection path components is introduced. A simulation and experimental work is introduced to prove the mathematical derivations. Analysis, simulation and experimental results prove the superiority of the proposed technique. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Three-phase controlled converter has many applications such as ac and dc adjustable speed drives (ASD) [1–5], induction heating, HVDC power systems, power supply and utility interfacing of renewable energy (RE) systems with electric utility [6–10]. These applications use controlled converters as a rectifier or as an inverter. Line currents of the controlled converters have high harmonic contents with respect to PWM converters that used IGBT. However, apart from higher switching losses associated with PWM converters, the power handling capability and reliability of these devices are quite low in comparison to SCR [10]. Moreover, some applications especially in high ratings prefer line commutated converters than PWM due to the high EMI associated with PWM. Many techniques were introduced to reduce this harmonic such as a reduction by using increased pulse numbers, IPN [11], active and passive filters, APF [12–14], modulating the controlled signal of dc–dc converter connected with this converter by third harmonic components, MCC [15], or by third harmonic injection from dc-link to the line currents, 3rd INJ [16–19]. The third harmonic injection technique has been used in uncontrolled converters in Refs. [20–23]. A review of three-phase improved power quality of uncontrolled converter by different techniques is shown in Ref. [24]. Third harmonic injection technique in the controlled converters was first introduced in 1969 [25]. This technique uses the third harmonic voltage

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in the dc-link to inject a current to the line currents. Refs. [26,27] used three LC branches tuned around the triple of utility frequency to inject the third harmonic current to the line currents. This technique has many disadvantages due to its high cost, bulky, and need precise values for L and C to share third harmonic currents equally. Refs. [28,29] used interfacing delta-star transformer to circulate the injection current to the neutral of star. This technique increases the cost due to the interfacing transformer. Other Refs. [18,19] used star-delta transformer in the reinjection path with unloaded delta to circulate the injection current through the neutral of star to the line currents. Some other Refs. [16,20,30,31] used partial rating (20%) zigzag transformer to circulate third harmonic injection current to line currents to replace the need for full load /Y transformer. The injection of third harmonic has been controlled by using single-phase boost rectifier to circulate the power in third harmonic path back to dc-link to increase the converter efficiency [31]. This technique is suitable for uncontrolled rectifier because it is easy to control the third harmonic current in injection path but it cannot control the angle of the injection current that should be changed with changing the firing angle of three-phase controlled converter [31,32]. The new proposed technique introduced in this paper avoided this limitation by controlling the angle of injection current by controlling the firing angle of single-phase controlled converter in the injection path and the amplitude of injection current by boost converter as shown in Fig. 1 and Fig. 2 for ASD and RE respectively. So, the main contribution of the proposed technique in this paper is the decoupling between the amplitude and angle of injection current which has not been introduced before. Ref. [30] used a bidirectional switch in the third harmonic injection path to

A.M. Eltamaly / Electric Power Systems Research 91 (2012) 104–112

Nomenclature If

third harmonic injection current the voltage and current of phase a ˛ the firing angle of three-phase converter the angle of Von,3 referred to va in 180 Hz domain  on  the angle between Von,3 , and If in 180 Hz domain  opt the angle between Von,3 , and If for minimum THD in line currents in 180 Hz domain ˚ the angle between Va and If in 180 Hz domain ˚opt the angle between Va , and If for minimum THD in line currents in 180 Hz domain Vm the peak value of phase voltage ω the angular velocity of the fundamental frequency the rms value of line to line supply voltage VLL Vdn the rms value of the voltage between points d and n Vfn the rms value of the voltage between points f and n the rms value of (3k) harmonic of the voltage Von,3k between points o and n =1, 2, 3, 4,.. . .. . .. k a0 , ah , bh Fourier coefficients Ldc , Cdc inductor and capacitor in dc-link Cinj tuning capacitor in the injection path the duty ratio of boost converter D a the turns ratio of single-phase transformer Vbi the output dc voltage of single-phase controlled converter controlled or uncontrolled converters CUC ROI rectifier or inverter ACC amplitude of third harmonic current control 3rd AC third harmonic angle control interface transformer ITC CC control complexity inductance of boost converter Lboost

va , ia

control the injection current for each firing angle of the controlled converter. But, this technique has a limitation in which to control the injection current angle its amplitude will be affected too and vice versa. This limitation has been avoided in the new proposed technique in this paper by the decoupling between the amplitude and angle of injection current. The firing angle of single-phase controlled converter, is used to control the angle of the third harmonic injection current, . The duty ratio, D of boost converter is used to control the amplitude of third harmonic current, If . A generalized analysis for the three-phase controlled converter with the new proposed injection technique is proposed to be used in case of rectifier or inverter. A new mathematical derivation to get a relation between the firing angle of the three-phase controlled converter, ˛ and the corresponding optimum value of the firing angle of single-phase controlled converter, opt is introduced which is the main contribution of this paper. Also, a design details for the boost converter and single-phase transformer in third harmonic injection path is introduced in details. Excellent results in harmonic reductions of utility line currents of three-phase controlled converter have been introduced. A detailed comparison between the conventional harmonic reduction techniques and the new proposed technique is shown in Table 1. Fig. 3(a) shows supply current of phase a without injection of third harmonic along with va (ωt) at ˛ = 20◦ . Fig. 3(b) shows the injection current along with va (ωt). Fig. 3(c) shows the voltage, current of phase a and optimum third harmonic injection current. The waveforms of voltages at dc-link, Vdn , Vfn , Von are shown in Fig. 3(d). These voltages are the voltages that have been used to circulate the third harmonic current in the injection path. By using complex

105

Fourier analysis for these voltages the relation between the voltage Von,3k and angle ˛ can be obtained from the following equations. The value of Von,3k for odd values of k, can be obtained from the following equations: Von,3k =

3VLL (9k2 − 1)



1 + (9K 2 − 1) sin2 ˛

(1)

And angle of Von,3k for odd values of k is,

 on,3k = tan

−1

kn sin(kp ˛) − kp sin(kn ˛) kp cos(kn ˛) − kn cos(kp ˛)

 (2)

Von,3k = 0 for even values of k

(3)

where kn = 3k − 1, and kp = 3k + 1 Fig. 4 shows the FFT components of Von,3k at ˛ = 40◦ . It is clear from Fig. 4 that the third harmonic voltage Von,3 is the most dominant component in Von,3k . So, tuning the harmonic injection path around triple of utility frequency will circulate the third harmonic current freely. So, the following analysis will focus on the third harmonic component. By substituting k = 1 in Eqs. (1) and (2), the voltage Von,3 and its angle can be obtained as shown in Eqs. (4) and (5) respectively [31,32]. Von,3 =

3VLL 8

on,3 tan−1



1 + 8 sin2 ˛

(4)

 sin(4˛) − 2 sin(2˛) 

(5)

2 cos(2˛) − cos(4˛)

The optimum angle between the third harmonic component of injection current, If3 and supply current of phase a with respect to 180 Hz, Ia3 is 180◦ with respect to triple utility frequency, 180 Hz [20,31,32]. Depending on this logic, the injection current, If3 can be drawn with respect to Ia3 at optimum injection angle. As shown in Fig. 3, the voltage va has been taken as a reference, so the phase angle of fundamental current of phase a current is −˛ and −3˛ with respect to utility and triple of utility frequencies respectively. Then, the optimum angle opt between va and If3 is shown in Eq. (6). (opt ) = 180 − 3˛ Also, the optimum angle between Von,3 , If3 , is obtained from the following equation. opt

(6) opt

= on,3 + 3˛ − 180

which can be

(7)

From Eqs. (6) and (7) the phase angle between each vectors for various firing angles; ˛ = 20◦ and 40◦ (as an example for rectifier mode) and ˛ = 130◦ and 150◦ (as an example for inverter mode) are shown in Fig. 5. From Eq. (4) the relation between Von,3 /VLL and the firing angle ˛ is shown in Fig. 6. In the same way, from Eqs. (6) and (7), the variation of  on,3 , opt , and opt along with the firing angle of three-phase converter, ˛ is shown in Fig. 6. 2. The optimum amplitude of injection current The amplitude of optimum injection current for minimum THD, is a function of dc-link current, Io . So, the amplitude of injected current can be assumed to be qIo where q is a proportional constant. Then, the equation of injected current, if3 can be obtained from the following equation: q if 3 = − Io sin(3(ωt − ˛)) 3

(8)

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Fig. 1. The proposed approach as a rectifier in ASD.

Fig. 2. The proposed approach as an inverter in renewable energy applications.

In case of phase a voltage, va is a reference voltage, then, the current of phase a can be determined from the following equation.

⎧ if ⎪ ⎪ ⎪ Io + 6 ⎪ ⎨

ia (ωt) =

⎪ ⎪ ⎪ ⎪ ⎩

= Io −

−Io −

q Io sin(3(ωt − ˛)) 6

q Io sin(3(ωt − ˛)) 6

if q − = Io sin(3(ωt − ˛)) 3 3

5  < ωt − ˛ < 6 6 7 11 < ωt − ˛ < 6 6

Ia,rms =

6

for elsewhere

q2 + 24

The THD of supply current can be determined from Eq. (12).

(9)



THD =

The rms value of the supply current, Ia,rms can be obtained as shown in Eq. (10). Io 

transform to Eq. (9) and the result is shown in the following equation. √ 6(q + 15)Io (11) Ia1,rms = 16

(12)

2 Ia1,rms

Substituting Eqs. (10) and (11) into (12) the following equation can be obtained.



(10)

Also the rms value of the fundamental component of supply current, Ia1,rms can be obtained with the help of applying Fourier

2 2 Ia,rms − Ia1,rms

THD =

322 27



q2 + 24 (q + 16)2

−1

(13)

Table 1 A comparison between the conventional harmonic reduction and the proposed techniques. Technique

CUCa

ROIa

ACCa

3rd ACa

ITCa

CCa

Costa

IPN [12] APF [12–14] MCC [15] LC branches [26,27] 3rd INJ [18,19] 3rd INJ [28,29] 3rd INJ [16,20,30] 3rd INJ [31] Proposed IGBT

Diode only Both Diode only Both Both Both Both Both Both NA

Rec. only Both Rec. only Both Rec. only Rec. only Rec. only Both Both Both

Yes Yes Yes Yes Yes Yes Yes Yes Yes NA

NA NA NA Yes No No No No Yes NA

Complex No need No need No need Y/unloaded  /Y Zig-zag Zig-zag Zig-zag No need

Complex Complex Complex Simple Complex Simple Complex Simple Simple Complex

Expensive Expensive Cheap Cheap but not effective Expensive Expensive Expensive Cheap Cheap Cheap

a

Cost is referenced to the proposed technique.

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Fig. 4. FFT components of Von at ˛ = 40◦ .

Substituting Eq. (13) into (14) the optimum value of q is; qopt = 1.5

(15)

The value of qopt is exactly the same as the value obtained for diode rectifier [16,33]. The theoretical minimum THD associated with this technique can be obtained from substituting Eq. (15) into (13). Then, the minimum THD that can be obtained from third harmonic injection technique is 5.12%. The optimum value of reinjection current can be obtained from Eqs. (6) and (15) and shown in Eq. (16). 3 If 3 = − Io sin (3ωt − 3˛) 2

(16)

In case of q = 1.5 and variable reinjection current angle, Eq. (9) can be modified to be as shown in Eq. (17).

Fig. 3. Various voltages and currents of the proposed approach at ˛ = 20◦ [31].

For minimum THD, the derivative of the THD should be equal to zero, d THD = 0 dq

(14)

⎧ if Io + ⎪ ⎪ 6 ⎪ ⎨

ia (ωt) =

⎪ ⎪ ⎪ ⎩

= Io +

−Io + −

if 3

1 Io sin (3ωt + ) 4

1 Io sin (3ωt + ) 4

1 = − Io sin (3ωt + ) 2

 5 < ωt − ˛ < 6 6 7 11 < ωt − ˛ < 6 6

(17)

for elsewhere

The rms value of the supply current, Ia,rms can be obtained from Eqs. (17) and rms of the fundamental component of line current, Ia,rms can be obtained by Fourier transform of the current shown in Eq. (17). Substituting the new values of Ia,rms in Eq. (13) and equating the derivative of THD by zero, the optimum relation between ˛,

Fig. 5. Phase difference between components for, ˛ = 20◦ , 40◦ , 130◦ and 150◦ respectively.

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Fig. 8. Tuning the third harmonic injection path around the third harmonic frequency.

Fig. 6. The variation of Von3 /VLL ,  on,3 ,  opt,3 ,

opt,3

along with ˛.

and opt can is obtained, which same as obtained before in Eq. (6). The variation on the THD with the firing angle ˛ at q = 1.5 is shown in Fig. 7. 3. Design example A prototype model has been used to demonstrate the above analysis. The model is designed to feed 2 kV A loads with supply line voltage of 220 V. The model is used in simulation and experimental work. The dc-link parameters XL,dc and XC,dc are chosen to be 0.5 and 0.1 pu respectively. From the nominal values of the components in the model the base value of supply current is 5.25 A, and base impedance is Zbase = 24.2 . Then, XL,dc = 2.42 , XC,dc = 12.1 , Ldc = 6.42 mH, and Cdc = 220 ␮F. These values of Ldc and Cdc is equally divided in the dc-link as shown in Figs. 1 and 2. To tune the third harmonic injection path around the 180 Hz frequency to represent a short circuit with respect to this frequency, a 545 ␮F capacitor is used in series with the injection path, Cinj as shown in Fig. 8 (i.e. 3ω × Ldc /2 = (3ω)−1 × [(2Cdc )−1 + Cinj −1 ]). So, most of the value of Von,3 will be across single-phase transformer, in case of neglecting the series impedance of zigzag transformer. The values of each components of the model are shown in Table 2. 3.1. Design of single-phase transformer Single-phase transformer is needed to step-up the third harmonic voltage, Von,3 to become suitable to circulate third harmonic current [31]. The values of Von,3 /VLL varies between Von,3 /VLL (˛ = 0) = 0.1194 pu to Von,3 /VLL (˛ = 90◦ ) = 0.358 pu. If the operating range of the firing angle ˛ of controlled converter is

assumed to be between 0◦ and 60◦ for rectifier and between 120◦ and 170◦ for inverter mode of operations, then the values of Von,3 varies between Von,3 /VLL (˛ = 0) = 0.1194 pu to Von,3 /VLL (˛ = 60◦ ) = 0.3158 pu. For the suggested maximum possible dc current, Io = 3 A = 0.57 pu, then from (16), the third harmonic injected current is If = 3.182 A = 0.606 pu. Then the highest possible VA of single-phase transformer occurs √ at highest possible values of Von,3 and If3 which is, 0.316 × 0.606/ 3 = 0.11 pu. Then, the rating of single-phase transformer is about 11% of the rated VA of the controlled converter. 3.2. Design of single-phase boost converters The output ac voltage from single-phase transformer should be converted to dc using single-phase controlled converter to become suitable input for boost converter. Single-phase controlled rectifier replaced the single-phase uncontrolled converter in Ref. [31] to control the angle of injection current. Third harmonic injection current can be controlled by varying the duty ratio of the boost converter. Current sensor is used to measure the actual dc-link current and the third harmonic injection current. The error signal between these two currents is used to control the duty ratio of the boost converter. 10 kHz switching frequency of the boost converter is used in simulation and in the practical prototype. The schematic of the control circuit of the boost converter is shown in Fig. 9. The output dc voltage of single-phase controlled converter Vbi can be obtained from Eq. (18). The relation between output voltage from single-phase controlled converter and dc-link output voltage can be obtained by the boost converter duty ratio as shown in Eq. (19). From Eqs. (18) and (19) and solving the resultant equation for turns ratio of single-phase transformer, a, Eq. (20) can be obtained. From Eq. (20), the relation between optimum turns ratio of single-phase transformer and firing angle, ˛, for different duty ratio of boost converter can be drawn as shown in Fig. 10. It is clear from Fig. 10 that Table 2 The values of each components of the proposed model. Component

Value

kV A rating of the model Line voltage Ldc , Cdc , and Cinj

2 kV A 220 V 6.42 mH, 220 ␮F and 545 ␮F respectively 5 mH 3 A and 3.182 respectively 0.11 × 2000 = 220 V A 0.2 0.202 × 2000 = 404 V A PIV = 380 V, average current = 0.7 A 380 V, 1 A

Inductance of boost converter, Lboost Io and If VA rating of single-phase transformer Turns ratio of single-phase transformer, a VA rating of zig-zag transformer Thyristors of single phase converter Fig. 7. The variation of THD with the angle  at q = 1.5 for different firing angles ˛.

IGBT of boost converter

A.M. Eltamaly / Electric Power Systems Research 91 (2012) 104–112

109

30 Equation (33) Experimental

25

THD %

20 15 10 5

Optimum Turns Ratio of single-phase Transformer

Fig. 9. The schematic of the control circuit of the boost converter.

0

0.45

D=0.8

D=1−

D=0.8

0.3 D=0.4

D=0.2

D=0.6

D=0.0

D=0.2

D=0.4

D=0.6

140

160

0.25 D=0.0

0.2 0.15 0.1 0.05 0

20

40

60

80

100

120

180

Firing Angle

Fig. 10. The relation between optimum turns-ratio of single-phase transformer and ˛, for different duty ratio.

the optimum value of the turns-ratio of the transformer is the one in the middle of the diagram for flexible operation around this value. Then, a = 0.2 was chosen for turns ratio of single-phase transformer which means the duty ratio will be around 0.6. In the same way as (20) an equation can be obtained for the optimum duty ratio of boost converter in terms of a as shown in Eq. (21). Fig. 11 shows the relation between optimum duty ratio of boost converter and firing angle, ˛, for different turns-ratio of single-phase transformer. √ Von,3 2× 2 (18) × × cos ( opt ) Vbi =  a Vdc 1 = Vbi 1−D

(19)



1 + 8 sin2 ˛ × cos ( 4(1 − D) cos ˛

opt )

(20)

0.9 0.8

Optimum Duty Ratio

1.5

q

2

2.5

3

1 + 8 sin2 ˛ × cos ( 4a cos ˛

opt )

(21)

The angle of injection current,  can be controlled by controlling the firing angle of single-phase controlled converter, . The relation between the optimum values of , and the firing angle, ˛ of three-phase converter can be obtained from Eqs. (5)–(7) and as shown in Fig. 6. In case of operating range of firing angle, ˛ between 0◦ and 60◦ in a rectifier mode and from 120◦ to 170◦ in inverter mode, the corresponding optimum values of firing angle of single, opt is between 0◦ and 180◦ for rectifier and inverter modes of operations. In case of the turns ratio of single-phase transformer, a = 0.2, then the maximum reverse voltage for each thyristor is 0.3158/0.2 = 1.579 pu = 347.4 V and the maximum current is the maximum current of injected current times the turns ratio of singlephase transformer = 0.606 × 0.2 = 0.1212 pu = 0.6363 A. 4. Design of zigzag transformer Third harmonic injection can be transferred to line current using zig-zag transformer [16,20,22,23,30–32] or three-phase transformer with open delta [18,19]. The required √ kV A rating of three-phase transformer with open delta is 3 times the kV A required for zig-zag transformer [23]. For this reason zig-zag transformer has been used in this research. The rms values of the winding voltages are VLL /3 [23]. VA rating of zigzag transformer can be obtained from Eq. (22), and as discussed before that If3 = 0.606 pu. The VA rating of zigzag transformer is Szig-zag = 0.606/3 = 0.202 pu, which means that, the VA rating of zigzag transformer is about 20.2% of the VA rating of the controlled converter. Szig-zag = Vph-zig-zag × If

(22)

5. Simulation and experimental results

1

0.7 0.6 a=0.5

a=0.5

a=0.4 a=0.3

a=0.4

a=0.3

a=0.2

0.4

a=0.2

0.3 0.2 0.1 0 0

1



0.35

0.5

0.5

Fig. 12. The relation between THD and the value of q.

0.4

a=

0

a=0.1 20

a=0.1 40

60

80

100

120

140

160

180

Firing Angle Fig. 11. The relation between optimum duty ratio and firing angle, ˛, for different turns-ratio of single-phase transformer.

A prototype model has been introduced to demonstrate the above analysis. The prototype model is designed to feed 2 kV A loads with supply line voltage of 220 V. The prototype model is used in simulation and experimental work. The simulation of the proposed technique has been performed by using PSIM computer program. Same values of the components used in simulation program have been used in the experimental prototype to compare these results. The simulation and experimental work has been performed in a rectifier and inverter modes of operations. The simulation and experimental results are identical and agree with the mathematical analysis. Fig. 12 shows the relation between THD and the value of q for mathematical analysis (22) and experimental analysis at ˛ = 20◦ . This figure reveals that the optimal value of q is 1.5 for the minimum THD as previously concluded from Eq. (15). Also, this figure shows the importance of third harmonic injection technique in reducing the harmonic contents in utility line currents. The simulation and

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A.M. Eltamaly / Electric Power Systems Research 91 (2012) 104–112

Fig. 13. The voltages vd , vf , von at ˛ = 20◦ (100 V/div., 4 ms/div.).

Fig. 14. The voltages vd , vf , von at ˛ = 140◦ (100 V/div., 5 ms/div.).

experimental waveforms for ˛ = 20◦ and 40◦ as an examples are shown in the following sections. 5.1. Experimental results at ˛ = 20◦ Fig. 13 shows the waveforms of voltages vd , vf , von at ˛ = 20◦ . Fig. 14 shows the voltages vd , vf , von at ˛ = 140◦ . Figs. 15 and 16

Fig. 15. The supply current along with va at ˛ = 20◦ without harmonic injection (5 ms/div., 100 V/div., and 1 A/div.).

Fig. 16. The supply current along with va at ˛ = 140◦ without harmonic injection (5 ms/div., 100 V/div., 1 A/div.).

Fig. 17. The FFT components of ia without harmonic injection (0.5 A/div., 100 Hz/div.).

show the supply current waveform with respect to phase a voltage without injection of 3rd harmonic current at ˛ = 20◦ as an example of rectifier and ˛ = 140◦ as an example of inverter respectively. Fig. 17 shows the FFT components of ia without harmonic injection. It is clear from this figure that the supply current has very high THD

Fig. 18. The utility line current, ia and injection current, if along with va , with optimum harmonic injection current for ˛ = 30◦ (5 ms/div., 100 V/div., and 1 A/div.).

A.M. Eltamaly / Electric Power Systems Research 91 (2012) 104–112

Fig. 19. The utility line current, ia and injection current, if along with va , with optimum harmonic injection current for ˛ = 130◦ (5 ms/div, 100 V/div., and 1 A/div.).

mostly of 5th and 7th harmonics. The THD of this current is about 54%, which is greater than all harmonic standards. Figs. 18 and 19 show the utility line current, ia and injection current, if along with va , with optimum harmonic injection current for ˛ = 30◦ and ˛ = 130◦ respectively. It is clear from Figs. 18 and 19 that the THD is 5.085% and 5.103% respectively which is acceptable by the harmonic injection standards. The results shown in Figs. 18 and 19 prove the superiority of the proposed injection technique. 6. Conclusions Utility line currents of three-phase controlled converters have THD higher than harmonic standard limits. This high THD can produce a lot of problems in the power systems. One of the most effective techniques is the circulation of third harmonic current from dc-link to the line currents. This paper introduces a singlephase controlled converter in the injection path to control the angle of injection current for each firing angle of three-phase controlled converter. The power circulated in the third harmonic injection path is recovered by using boost converter connected between the output of single-phase controlled converter and the dc-link. Boost converter can control the amplitude of injected current. In this paper, the optimum relation between the firing angles of threephase and single-phase controlled converters for minimum THD is introduced. Also the optimum amplitude of the injected current is introduced mathematically and experimentally. The THD of the utility line current from simulation and experimental results proves the mathematical results for this technique. The THD of the utility line current with optimal harmonic injection current is about 5% which is lower than limits of harmonics standards. Acknowledgment The authors acknowledge the National Plan for sciences and Technology program (Project No.: ENE226-02-08) by King Saud University for the financial support to carry out the research work reported in this paper. References [1] S.C. Bera, R. Sarkar, N. Mandal, An opto-isolator based linearization technique of a typical thyristor driven pump, ISA Transactions 51 (January (1)) (2012) 220–228 (Original Research Article). [2] S.C. Bera, N. Mandal, R. Sarkar, A novel technique of using a thyristor driven pump as the final control element and flow indicator of a flow control loop, ISA Transactions 50 (July (3)) (2011) 496–503 (Original Research Article).

111

[3] D. Banerjee, V.T. Ranganathan, Load-commutated SCR current-source-inverterfed induction motor drive with sinusoidal motor voltage and current, IEEE Transactions on Power Electronics 24 (4) (2009) 1048–1061. [4] B. Wu, Multipulse SCR Rectifiers in High-Power Converters and ac Drives, John Wiley & Sons, Inc., Hoboken, NJ, USA, 2005, http://dx.doi.org/10.1002/9780471773719(Chapter 4). [5] A.H. Hoevenaars, I.C. Evans, B. Desai, Preventing AC drive failures due to commutation notches on a drilling rig, in: Record of Conference Petroleum and Chemical Industry Conference, 2009, pp. 1–6. [6] D. Habibinia, R. Ghandehari, Y. Najafi, M. Rahimzadeh, H. Khalilpoor, Study of inverter and rectifier substations islanding fault in HVDC system and comparison between different control-protective methods, in: International Symposium on Power Electronics Electrical Drives Automation and Motion (SPEEDAM), 2010, pp. 1622–1627. [7] B. Jun-feng, X. Jia-zhu, L. Long-fu, Characteristics of power transmission and dynamic recovery of FCC-HVDC with different SCR, International Conference on Power System Technology (POWERCON) (2010) 1–6. [8] Z. Chen, Compensation schemes for a SCR converter in variable speed wind power systems, IEEE Transactions on Power Delivery 19 (2) (2004) 813–821. [9] H. Akagi, R. Kondo, A transformerless hybrid active filter using a three-level pulse width modulation (PWM) converter for a medium-voltage motor drive, IEEE Transactions on Power Electronics 25 (June (6)) (2010) 1365–1374. [10] A. Sarwar, M.S.J. Asghar, Multilevel converter topology for solar PV based grid-tie inverters, IEEE International on Energy Conference and Exhibition (EnergyCon) (2010) 501–506. [11] S. Yang, F. Meng, W. Yang, Optimum design of interphase reactor with doubletap changer applied to multipulse diode rectifier, Transactions on Industrial Electronics, IEEE 57 (September (9)) (2010) 3022–3029. [12] A. Bhattacharya, C. Chakraborty, A shunt active power filter with enhanced performance using ANN-based predictive and adaptive controllers, Transactions on Industrial Electronics, IEEE 58 (February (2)) (2011) 421–428. [13] A. Luo, X. Xu, L. Fang, H. Fang, J. Wu, C. Wu, Feedback–feedforward PItype iterative learning control strategy for hybrid active power filter with injection circuit, IEEE Transactions on Industrial Electronics 57 (11) (2010) 3767–3779. [14] S. Rahmani, N. Mendalek, K. Al-Haddad, Experimental design of a nonlinear control technique for three-phase shunt active power filter, Transactions on Industrial Electronics, IEEE 57 (October (10)) (2010) 3364–3375. [15] Ali M. Eltamaly, Harmonics reduction of three-phase boost rectifier by modulating duty ratio, Electric Power Systems Research 77 (August) (2007) 1425–1431. [16] P. Pejovic, D. Shmilovitz, Low-harmonic thyristor rectifiers applying current injection, IEEE Transactions on Aerospace and Electronic Systems 39 (October (4)) (2003) 1365–1374. [17] Y.H. Liu, J. Arrilaga, N.R. Watson, L.B. Perera, Application of the DC-ripple reinjection concept to forced-commutated conversion, Proceedings of IEEE Power Engineering Conference (2005) 1–6. [18] B.M. Saied, H.I. Zynal, Harmonic current reduction of a six-pulse thyristor converter, Proceedings of IEEE Electrical Machines and Power Electronics Conference (September) (2007) 596–602. [19] A. Maswood, Optimal harmonic injection in thyristor rectifier for power factor correction, IEE Proceedings on Electric Power Applications 150 (September (5)) (2003) 615–622. [20] A.M. El-Tamaly, P.N. Enjeti, H.H. El-Tamaly, An improved approach to reduce harmonics in the utility interface of wind, photovoltaic and fuel cell power systems, in: Proceedings of IEEE Applied Power Electronics Conference and Exposition, APEC 2000, vol. 2, 2000, pp. 1059–1065. [21] B.M. Saied, H.I. Zynal, Minimizing current distortion of a three-phase bridge rectifier based on line injection technique, IEEE Transactions on Power Electronics 21 (6) (2006) 1754–1761. [22] P. Bozovic, P. Pejovic, Current-injection-based 12-pulse rectifier using a single three-phase diode bridge, Electric Power Applications, IET 1 (March (2)) (2007) 209–216. ´ Three-Phase Diode Rectifiers with Low Harmonics, Power Electronics [23] P. Pejovic, and Power Systems, Springer, 2007. [24] B. Singh, B.N. Singh, A. Chandra, K. Al-Haddad, A. Pandey, D.P. Kothari, A review of three-phase improved power quality AC–DC converters, IEEE Transactions on Industrial Electronics 51 (June (3)) (2004) 641–660. [25] B.M. Bird, et al., Harmonic reduction in multiplex converters by triple frequency current injection, Proc. of the Institution of Electrical Engineers 116 (October (10)) (1969). [26] B.M. Saied, R.Kh. Antar, Harmonic mitigation technique for the power quality improvement of DC motor drives, in: International Aegean Conference on Electrical Machines and Power Electronics, ACEMP’07, September 2007, pp. 592–595. [27] W. Mielczarski, W.B. Lawrance, R. Nowacki, D. Grahame Holmes, Harmonic current reduction in three-phase bridge-rectifier circuits using controlled current injection, IEEE Transactions on Industrial Electronics 44 (October (5)) (1997) 604–611. [28] M. Villablanca, J. Arrillaga, Single-bridge unit-connected HVDC generation with increased pulse number, IEEE Transactions on Power Delivery 8 (April (2)) (1993) 681–688. [29] J. Boys, B. Mitchell, Current-forced neutral injection in a three-phase rectifier/converter, Electric Power Applications, IEE Proceedings 146 (July (4)) (1999) 441–446.

112

A.M. Eltamaly / Electric Power Systems Research 91 (2012) 104–112

[30] P. Bozovic, P. Pejovic, A novel three-phase full bridge thyristor rectifier based on the controlled third harmonic current injection, in: Power Tech Conference Proceedings, IEEE Bologna, vol. 1, 2003. [31] Ali M. Eltamaly, A modified harmonics reduction technique for a three-phase controlled converter, IEEE Transactions on Industrial Electronics 55 (February (3)) (2008) 1190–1197.

[32] Ali M. Eltamaly, Harmonics reduction techniques in renewable energy interfacing converters, in: Renewable Energy, Intechweb, December 2009, ISBN 978-953-7619-52-7 (Renewable Energy). [33] P. Pejovic, Two three-phase high power factor rectifiers that apply the third harmonic current injection and passive resistance emulation, IEEE Transactions on Power Electronics 15 (6) (Nov 2000) 1228–1240.