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(20 pts) 4. The following current waveform are observed. How many pulse rectifier is used in the circuit? And give your explanation. 130Hz 2208H2 2 x3 5 x79 x10 x11 12 13 x14 x15 x16 Harmonic Conterk Frequency Content Waveform Amplitude against time Figure 1: A current waveform.

Answer 1

ANALYSIS OF 12-PULSE RECTIFIER/ CONVERTER In the given question (diagram) there are only fundamental, 11th, 13th harmonics etc., and so on which are the harmonics present only in 12 pulse rectifier.The following information may help you to understand it. 1.0 INTRODUCTION TO 12-PULSE CONTROLLED RECTIFIER: A six-pulse bridge rectifier reduces the output ripple considerably as compared with that of a three- pulse rectifier. In applications such as power transmission, a further reduction in output ripple is achieved with a twelve-pulse converter lo Y-Y transformer 1A1 lp1 Vor ABC Figure 1. Twelve-pulse Connection Using two Series Connected Six-pulse Bridge A twelve-pulse converter can be obtained by connecting two six pulse bridges in series or parallel One six-pulse bridge use star-star transformer and other use star-delta transformer resulting there can get 30 degree phase shift between output voltage waves. The resultant converter output voltage is the sum of the individual converter output voltages.

J. I. Figure 2. Winding arrangement and Phasor Diagrams of Y-Y transformer The resultant output voltage is a twelve-pulse as each converter gives a six-pulse output. A typical twelve-pulse converter connected in series of two six-pulse bridges is shown in Figure 1. For the sake of simplicity in analysis, source impedance is neglected and assumed thyristors are ideal. A common solution for harmonic reduction is passive filters which are turned to trap a particular harmonic frequency However, harmonics also can be eliminated using special configurations of converters connected as shown in Figure 1. This type of rectifier is called line commutated rectifier and can be used for high power applications.

Figure 3. Winding arrangement and Phasor Diagrams of Y-A transformer According to Figure 2 and 3, line to line voltage of secondary star transformer is lead 30 degree to line to neutral voltage. Line to line voltage of secondary delta transformer is in phase with line to neutral voltage. Therefore, total output voltage waves of two transformers are shifted 60degree each other. The output voltage magnitudes of two transformers must same. Due to the series connection, the same output current will flow through the two converters. 2.0 OUTPUT AND INPUT WAVEFORMS OF CONVERTER: The total output voltage of the converter is The output current of the two converters is the same and pure DC due to large inductance of the output side.

콜, Figure 4. Current Division in Delta Secondary Figure 4 shows the winding current magnitudes of delta connected transformer secondary for the condition of line A and B are conducted. Let consider as Nsec/Nor for star-delta transformer while Nsec/Npri 1 for star-star transformer Vi Voi α-30" 14 Figure 5. Output Voltage and Input Current Waveforms for Upper Converter

-30 l7 la-l-l Figure 6. Output Voltage and Input Current Waveforms for Lower Converter Voi Vor ot

Figure 7. Total Resultant Output Voltage Waveforms at a-30 ไม่ la Figure 8. Transformer's Secondary Currents and Primary Line Current Waveforms Average output voltage is the twice of each six-pulse bridge rectifier. Therefore, Where V is the maximum line to neutral voltage From Figure 4 ( Lines A and B are both conducting Only one of line A or B is conducting (a 3.0 FOURIER SERIES OF INPUT CURRENT WAVEFORM: Fourier series of the input line current of the upper converter is

4 Fourier series of the input line current of the lower converter is Total resultant AC line current is given by the sum of equation (4) and (5) 13 23 These Fourier series only contain the odd number of harmonics in order of 12 k t1. k is the odd number (i.e. 11, 13th, 23t,25t",.) The resulting line current of the 12-pulse rectifier is closer to a sinusoidal waveform as shown in Figure 8. The instantaneous dc voltage is also smoother with this connection RMS value of line current is 0.5 42v3 Anm From equation (6), RMS value of the fundamental components of the line current is 4V3 Lag 1s Displacement factor = cos = cos α Distortion factor = 0.9886

几 Figure 10. Waveform of Input Line Current Figure 11. Harmonic Spectrums of Input Line Current The harmonics of the 12-pulse rectifier is analyzed using the FFT (Fast Fourier Transform) analysis tool of MatLab. The simulation result of line current is shown in Figure 10 and harmonic spectrums are shown in Figure 11. The result of total harmonic distortion is same as shown in equation (10). Firing angle can be controlled between 0 degree and 120 degree. Output voltage of the converter is maximum at firing angle 0 degree and minimum at firing angle 120 degree THUS, THE RESULTS SHOWN IN YOUR QUESTION ARE EXACTLY MATCHED WITH MY SIMULATION RESULTS THANK YOU
IN YOUR QUESTION FUNDAMENTAL FREQUENCY IS 138Hz