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controlled rectifiers and proposed an accurate Statistical

method to calculate their input current harmonic components,

and calculate THD and harmonic currents with accurate

simulation in various firing angles, then investigate influence

of load variations in terms of firing angle variations on

harmonic currents. Finally a harmonic current database of

rectiûers is obtained in terms of firing angle and load

variations.

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- 1. ACEEE Int. J. on Electrical and Power Engineering, Vol. 03, No. 02, May 2012 Three Phase Controlled Rectifier Study in Terms of firing angle variations Ali Akbar Motie Birjandi1, Zahra Ameli2, 1 Electrical Department Shahid Rajayee Teacher Training University, Tehran, Iran Email: motiebirjandi @ srttu.edu 2 Electrical Department Shahid Rajayee Teacher Training University Email: z_ameli@yahoo.comAbstract—This paper introduce topology of three phase variations in terms of firing angle variations on harmoniccontrolled rectifiers and proposed an accurate Statistical currents. Finally a harmonic current database of rectiûers ismethod to calculate their input current harmonic components, obtained in terms of firing angle and load variations.and calculate THD and harmonic currents with accuratesimulation in various firing angles, then investigate influence II. FOURIER SERIES AND POWER SYSTEM HARMONICSof load variations in terms of firing angle variations onharmonic currents. Finally a harmonic current database of Fourier Series: The primary scope of harmonics modelingrectiûers is obtained in terms of firing angle and load and simulation is in the study of periodic, steady-statevariations. distortion.[3](c1.pdf) A three phase controlled rectifier is shown in Fig. 1.Index Terms—Harmonic, Three phase controlled rectifier,Firing angle I. INTRODUCTION Harmonic is component of a sine wave with a periodicamount which the frequency of this is integer Multiple of theFundamental wave. Harmonic In a power system Cause lossesand depreciation in the transmission and distributionequipment and power consumers, so study and their controlis essential. Appearance of semiconductor and nonlinear Figure 1. Three phase controlled rectifierelements such as diode, Thyristor and so on and great use of The RMS value of the nth harmonic of input currentthem in the power system make new factor for development corresponding with the following relation:harmonic [1]. Already, use of nonlinear loads connected to distribution 2 2 Ia nnetwork, including multiple rectifiers is growing. Increase their In 1 2 a 2 n bn2 1/ 2 n sin 3 (1)number create a lot of problem in Electricity network. Some ofthis problems are Transformers and motors heating, Increasing The total RMS value of current is:current of parallel capacitors, Increasing current of Neutral I rms ( I12( rms ) I 2( rms ) I 32( rms ) ... I n2( rms ) )1 / 2 2 (2)wire in Four-wire three phase systems, destroy voltage shapeand etc[2]. Input current in the system is: Three-phase six-pulse thyristor converters are the basicelement in transmission system of Electrical energy. These 1 sin(t 1 ) sin 5(t 1 ) converter because of their nonlinear Properties generate 2 3 5 ia Idharmonic currents, which most of these currents cause series 1 1 (3)problems in system. The main features of multiple rectifier is sin 7(t 1 ) sin11 t 1 ) ... (the it’s ability to Reduce distortion of Line current harmonics. 7 11 This problem may be with set a phase shifting transformer. Which φ1 is phase angle between source voltage and meanBecause lose some of the low- order harmonic currents that current.produce with them. In general, at Higher number of pulses, Total harmonic distortion is defined as the ratio of theline current distortion is lower [3]. rectifier Because of Growing rms value of all harmonic components to the rms value of theuse of this nonlinear converters and their harmonic problems. fundamental frequency: This paper introduce topology of three phase controlledrectifiers and proposed an accurate Statistical method to ( I12(rms) I 22( rms) I 32( rms) ... I n(rms) )1 / 2 2 THD (4)calculate their input current harmonic components, and I1(rms)calculate THD and harmonic currents with accurate simulation For a p-pulse ideal rectifier, the harmonics being generatedin various firing angles, then investigate Effect of load are of orders 5, 7, 11, 13, 17, 19 ..., i.e. those of orders 6k ± 1,© 2012 ACEEE 25DOI: 01.IJEPE.03.02.5
- 2. ACEEE Int. J. on Electrical and Power Engineering, Vol. 03, No. 02, May 2012where k is an integer. In fig. 2 is shown input voltage and current, output voltageand tyristor voltage waveforms of three phase controlledrectifier when fire angle is 30. Figure 2. Various waveforms of three phase rectifier(α=30) III. METHODS OF HARMONIC ANALYSIS Many research have been carried out to provide anaccurate and easy method to obtain harmonic currents in Figure 4. a) Input current waveform and b) spectra harmonicrectifier. Harmonic interactions in thyristor bridges may be The THD and Harmonic currents variations in terms ofcalculated either in the frequency domain or in the time domain firing angle variations is shown in table I.or with statistical method. Any of them have advantage and TABLE I: THD AND HARMONIC CURRENTS VARIATIONS IN TERMS OF FIRING ANGLEdisadvantage [cp14.pdf]. VARIATIONS For example, The time domain method is easy to use andallow control of system operation under any number ofdifferent operating states. However they do not provide ananalytical vision required for optimal design; besidesfrequency dependence cannot be accurately modeled. analternative method for calculating the harmonic currents of apower converter uses the Fourier series and the switchingfunctions. With a frequency domain model, the closed loopfrequency responses can be established, which will facilitatethe analysis of system stability and design optimization(paper4.pdf) Compare between multiple and other current harmonics in This paper proposed an accurate Statistical method to Fig. 5.calculate the current harmonic components of controlledrectifiers. IV. SIMULATION OF THREE PHASE CONTROLLED RECTIFIER At the first, as shown in fig. 3, a three phase controlledrectifiers with inductive load is simulated with MATLABsoftware and then, input current waveforms and harmonicspectra is simulated for some of firing angle(α=30) Fig 4. Figure 3. Simulation of three phase controlled rectifier with MAT LAB© 2012 ACEEE 26DOI: 01.IJEPE.03.02.5
- 3. ACEEE Int. J. on Electrical and Power Engineering, Vol. 03, No. 02, May 2012 V. THE INFLUENCE OF LOAD VARIATIONS ON THD AND HARMONIC CURRENTS In this section impact load variations on THD and harmonic current is shown. Load is resistive and inductive. It is clearly that increasing in resistive load increase THD and harmonic current. So inductor of load is changed. In fig. 7 is shown input current waveforms and harmonic spectra is simulated for some of firing angle(α=30) Figure 5. compare between a) multiple and b) other current ha rmonicsThis rectifier is tested at laboratory. The obtained waveformsfor input current with harmonic spectra for two fire angle isshown at fig.6. Figure 7. a) Input current waveform b) harmonic spectra(α=30) In table II, The THD and Harmonic currents variations in terms of inductor variations is shown for some firing angle TABLE II: THD AND HARMONIC CURRENTS VARIATIONS IN TERMS OF INDUCTOR VARIATIONS Figure 6. Obtained waveforms for input current at laboratoryAccording to obtained figures, can be observed that THDand harmonic currents is increased with increasing firingangles. The reason is that because thyristors are switchedon with delay, so input current waveform Is out of Sinusoidalmode.© 2012 ACEEE 27DOI: 01.IJEPE.03.02.5
- 4. ACEEE Int. J. on Electrical and Power Engineering, Vol. 03, No. 02, May 2012The variation of THD in terms of inductance variations is Also a harmonic current database of rectiûers is obtainedshown in fig. 8 from table II. this database allows all harmonic currents of any three-phase rectiûer by inductive load to be easily calculated with interpolation and without numerical simulation tools. CONCLUSIONS This paper proposed an accurate Statistical method to calculate input current harmonic components of three phase controlled rectifier, and calculate THD and harmonic currents with accurate simulation in various firing angles, then study influence of load variations in terms of firing angle variations on harmonic currents. Finally a harmonic current database of rectiûers is obtained in terms of firing angle variations. According to obtained results, the THD and harmonic currents because of caused delay in firing tyristors is Figure 8. Variations of THD in terms of L increased with increasing of firing angle while they decreasesAlso, according to tables variation of 5th harmonic current in by rising load inductance. Because more inductor valueterms of inductance variations is shown in fig. causes output current waveform be smoother, therefore reduce harmonic currents. REFERENCES [1] K. L. Lian, Brian K. Perkins, and P. W. Lehn, Harmonic analysis of a Three-Phase Diode Bridge Rectiûer Based on Sampled- Data Model, IEEE Transactions on power delivery, VOL. 23, NO. 2, APRIL 2008 [2] V.Grigore, Topological issues insigne phase power factor correction. Institute of Intelligent Power Electronics Publications, pp.1718,2001 [3] Taylor & Francis Group. Harmonic and power system. CRC Press. 2006 [4] Technical guide No. 6 Guide to harmonics with AC drives, ABB. All rights reserved. 2011 [5] Arrillaga, J, Bradley, D and Bodger.. Power System Harmonics. J Wiley & Sons,London. Second edition. 2003 Figure 9. Variation of 5 th harmonic current in terms of inductance [6] Luis Sainz, , Juan Jose Mesas, Albert Ferrer. Three-phase variation full-wave rectifier study with experimental measurements.According to obtained results with the increasing induction Electric Power Systems Research. 2009load vitality, THD and current harmonic is increased. Because [7] L. Sainz, J. Pedra, J.J. Mesas. Single-phase full-wave rectifierof decreases by rising load inductance. Because more study with experimental measurements, Electric Power Syst.inductor value causes output current waveform be smoother, 2007therefore reduce harmonic currents.© 2012 ACEEE 28DOI: 01.IJEPE.03.02.5

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