4. HARMONIC ANALYSIS
4.1 Multipulse Diode Rectifier Harmonics
Six-pulse diode rectifier causes high order current harmonics on the utility side. Due to the limitation of current harmonic distortion by IEEE Standard 519-1992, rectifier pulse number is increased in order to keep harmonic distortion in the limits. The DC link is connected to a resistive load for all following diode rectifier simulations and multipulse diode rectifiers are series connected. Secondary side windings are zigzag connected to have desired phase shifting for all rectifier pulse levels.
Figure 39 shows a six pulse diode rectifier which is connected to a synchronous generator through a delta/wye connected transformer and Figure 40 shows the primary side current waveform. 3rd harmonic cancelled by the transformer thus; 5th and 7th harmonics are the dominant harmonics as shown in Figure 41. While 22% THD occurs on the primary side windings, 29% THD occurs on the secondary side windings.
Figure 39: Six pulse rectifier is connected to a generator
Two six-pulse diode rectifiers are connected to series to see the effect of the 12- pulse diode rectifier on the primary side windings of the phase shifting transformer as shown in Figure 42. Phase shifting angle 𝛿 = 60 2⁄ = 30° between the secondary side windings. Figure 43 shows the primary side current waveform. 11th and 13th are the dominant harmonics while cancelling low order harmonics with the phase displacement in the transformer as shown in Figure 44, and THD is about 12%.
Figure 43: Primary side current waveform of the twelve pulse rectifier
Figure 44: Current harmonic order of the twelve pulse rectifier
18-pulse diode rectifier is built by 3 series connected diode rectifiers as shown in Figure 45. Required phase shifting angle 𝛿 = 60 3⁄ = 20° between the zig-zag connected secondary side windings of the phase shifting transformer. Primary side current waveform is illustrated in Figure 46. 17th and 19th harmonics are the dominant harmonics for the 18- pulse diode rectifier as shown in Figure 47, and THD occurs about 7% in the primary side windings of the phase shifting transformer.
Figure 46: Primary side current waveform of the eighteen pulse rectifier
Figure 47: Current harmonic order of the eighteen pulse rectifier
4 six-pulse diode rectifiers are series connected for 24-pulse rectifier as shown in Figure 48. Required phase shifting angle 𝛿 = 60 4⁄ = 15° between the secondary side windings of the phase-shifting transformer. Figure 49 shows the primary side current waveform of the phase-shifting transformer and THD is about 5%. 23rd and 25th are the dominant harmonics for the 24-pulse rectifier as shown in Figure 50.
Figure 49: Primary side current waveform of the twenty-four pulse rectifier
Figure 50: Current harmonic order of the twenty-four pulse rectifier
30-pulse diode rectifier consists of 5 series connected six-pulse diode rectifiers as shown in Figure 51. Phase shifting angle 𝛿 = 60 5⁄ = 12° between secondary side windings of the phase-shifting transformer. The primary side current waveform is shown in Figure 52 and THD is about 3%. 29th and 31st are the dominant harmonics for the 30- pulse rectifier as shown in Figure 53.
Figure 52: Primary side current waveform of the thirty pulse rectifier
Figure 53: Current harmonic order of the thirty pulse rectifier
6 six-pulse diode rectifiers are series connected for 36-pulse rectifier as shown in Figure 54. Desired phase shifting angle 𝛿 = 60 6⁄ = 10° between the secondary side windings of the transformer. The primary side current waveform is closer to sine wave as shown in Figure 55 and THD is about 2% which is within the limits. 35th and 37th are the dominant harmonics for the 36-pulse rectifier as shown in Figure 56.
Figure 55: Primary side current waveform of the thirty-six pulse rectifier
Figure 56: Current harmonic order of the thirty-six pulse rectifier
It is possible to achieve almost sine primary side current waveform with the 48- pulse rectifier and 72-pulse rectifier as shown in Figure 57 and Figure 58 respectively. Although the rectifier pulse number can be increased more to achieve less THD, it is costly and unnecessary. The phase-shifting transformer size will also be much larger for more pulses. Figure 59 shows the reducing THD graph up to 72-pulse diode rectifier. 36-pulse rectifier provides THD in the limits of the harmonic distortion standards, thus the system
Figure 57: Primary side current waveform of the forty-eight pulse rectifier
Figure 59: THD occurring in the secondary side windings
Table 5: Total harmonic distortion for the primary side and the secondary side windings
4.2 Multilevel Inverter
In this section, output voltage harmonics of the cascaded H-bridge inverter harmonic results are simulated from 3-level to 17 level. 100 Volt DC supply is used for each H-bridge inverter cell. Each cell consists of 4 IGBTs and proposed PWM method is used for switching them. Triangular carrier frequency is 900 Hz for all simulation results. 3-level H-bridge multilevel inverter cell is supplied with a 100 V DC voltage source shown in Figure 60 and output voltage of the cell VAC as shown in Figure 61. THD of the VAC is around 76%.
Figure 60: 3-level H-bridge multilevel inverter
5-level cascaded H-bridge multilevel inverter cells are connected to 100 V DC voltage sources as shown in Figure 62. Output AC peak voltage is 200 V as shown in Figure 63 and THD is measured 38%.
Figure 62: 5-level H-bridge multilevel inverter
7-level cascaded H-bridge multilevel inverter cells are connected to the DC voltage sources as shown in Figure 64. Output AC peak voltage is 300 V as shown in Figure 65 and THD is measured 38%.
Figure 64: 7-level H-bridge multilevel inverter
9-level cascaded H-bridge multilevel inverter is connected as shown in Figure 66. Output peak voltage is 400 V as shown in Figure 67 and THD is measured 14%.
11-level cascaded H-bridge multilevel inverter is connected as shown in Figure 68. Output peak voltage is 500 V as shown in Figure 69 and THD is measured 11.1%.
Figure 68: 11-level H-bridge multilevel inverter
13-level cascaded H-bridge multilevel inverter is connected as shown in Figure 70. Output AC voltage waveform is closer to sine wave with 600 peak voltage as shown in Figure 71 and THD is reduced to 9.2% for 13-level cascaded H-bridge inverter.
Figure 71: 13-level output voltage waveform
Figure 72: 15-level output voltage waveform
Output voltages waveforms of 15-level and 17-level cascaded H-bridge inverter are almost pure sine wave as shown in Figure 72 and Figure 73 respectively. The harmonic standards limit the utility side harmonic percentage, thus cascaded H-bridge inverter level should be depended on the pulse number of the multipulse rectifier. As explained before, 36-pulse rectifier causes current THD within the limits, thus 13-level H-bridge cascaded inverter should be the best for most of the motor drive applications. Even though increasing the inverter level above 13-level is able to obtain a better output voltage waveform, it is not efficient due to cost and size. THD reduction is not big for 13-level cascaded H-bridge multilevel inverter and higher levels as shown in Figure 74.