THREE-LEVEL MULTI-PULSE INVERTER MODEL
2.3 The 6-Pulse Three-Level Inverter
2.3.3 The Frequency-Domain Characteristics Of The 6-Pulse Three-Level Inverter
The three-phase load is connected to a neutral that is not connected to the midpoint of the inverter dc voltages i.e. the neutral is not connected to ground. If the neutral were grounded, each inverter output phase voltage (VAO, VBO and VCO) would have three voltage levels and would be similar in appearance to the voltages shown in Fig. 2.4. Since the neutral is left floating, the zero sequence components of each pole current have no return paths to the midpoint of the dc sources, so they are zero. The zero sequence components of each pole voltage,VNO
=
(VAO+VBO+VCO)I 3, appear between the neutral point and the midpoint of the inverter's dc sources. Therefore the load voltage per phase is in effect thedifference between the phase to ground voltage and the zero sequence voltage component, i.e. VAN=VAO - VNO, VBN=VBO - VNO, andVCN=VCO - VNO [27], giving rise to the seven voltage levels that appear in the phase to neutral voltages in Fig. 2.8.By comparing Fig. 2.7 (y= 3.75°) and Fig. 2.8(a) (y= 20°), it can be seen that at the higher y value, the "on" time spent in both the maximum and minimum of the seven voltage levels has decreased. When yis increased further to 40°, as shown in Fig. 2.8(b), the number of voltage levels is still seven but instead of the waveform looking "convex", as it peaks, it is now "concave".
When yis further increased to 60° the output voltage spends time in only four of the available seven voltage levels and the maximum and minimum values of the output voltage have also decreased in magnitude when compared to y= 20°. Therefore, the RMS value of the output voltage decreases from 39.3kV to 32.8kV to 21.6kV, as y increases from 20° to 40° to 60°
respecti vel y.
voltage can be varied by changing the input dc voltage or the angle y, whereas the ac output voltage of a two-level inverter is strictly a function of the input dc voltage.
A plot showing the nonnalized amplitudes of the fundamental and individual hannonic components as a function of y for a 6-pulse inverter (calculated using Equation (2.1)) is shown in Fig. 2.9. The same nonnalization method described in section 2.2.5 is applied here. The fundamental output voltage amplitude is 1.0 pu at y = 0°, and decreases with increasing dead angle, decreasing to zero at y = 90°; whereas the nonnalized hannonic voltages rise and fall throughout the same range ofy.
Fig 2.9 shows that at y = 0°, the fundamental as well as all the hannonic components have the highest possible amplitudesl. At this angle, a three-level pole acts as a two-level pole that switches from +vdc/2 to -Vdc12 and offers the maximum possible DC to AC utilization. For angles y> 0°, the three-level pole is switched between the above-mentioned two states and zero, and thus produces improved output wavefonn quality but at the expense of reduction in the fundamental voltage.
Fig. 2.9 illustrates that the per unit amplitude of each of the hannonic components initially decreases as y is increased from zero. Each hannonic component's per unit amplitude decreases to zero at a particular value of y then successively increases from zero and decreases back to zero as y is increased towards 90°. Thus, each particular harmonic component has zero amplitude at a few specific values of dead angle, as given by the equation
where11is the hannonic number [36].
2y= (180° I 11) (2.4)
For example, the seventh harmonic is zero when y= 12.85°,38.55°, and again at 51.5°. After its first zero, the nth hannonic amplitude rises again, reaching a peak amplitude at a value of y given by
2y = 2 x (180° I 11) (2.5)
1: Note on normalization method - at first glance the amplitudes of the harmonics might appear to be highest at r= 90° in Fig. 2.9. However the harmonic amplitudes are expressed here as per unit of the fundamental magnitude, and the fundamental magnitude decreases with increasing y. Thus as rincreases the absolute amplitude of the harmonics decreases but their amplitude relative to that of the fundamental alternately increases and decreases.
l"~
§ !~ 0.6~
"0 I
~ I
~ I
C I
Ql ,
~ot
=' I
u.
I
10 20 30
5
40 50
Angley(degrees)
60 70 80 90
Fig 2.9: Fundamental and harmonic voltages for a 6-pulse three-level inverter based on theory [27].
Because of the zero amplitude of all harmonic voltages at different specific dead angles, there are certain angles where the inverter may be operated to have the same response as a higher pulse-number inverter. For example, in Fig. 2.9, for y between 13° and 18°, both 5th and 7th harmonics have very small amplitudes, and the inverter almost behaves like a 12-pulse inverter [36]. However, for operation at 18°, the fundamental voltage drops to 0.95 pu which means 5%
loss of capacity. Hence there is effectively a compromise between a desired reduction in some specific harmonics and an associated loss in useable output voltage capacity. In many applications, if allowed, a combination of higher pulse inverter, dc voltage control and use of three-level phase-legs are considered [36]. It is important to note that with the split de capacitor topology of Fig. 2.6, it is essential to ensure that the two capacitors are charged to equal voltages:
unequal voltages would result in a generation of even harmonics [36].
The final aspect to consider is the total harmonic distortion (THD) of the 6-pulse three-level inverter. A measure of the harmonic content can be defined [27] as
(2.6)
where Vnis the amplitude of thenthharmonic voltage given by Equation (2.1), and n = 6k±1 for k = 1, 2, 3, etc.
A'measure of the total harmonic distortion of the inverter ac voltage is then defined as
(2.7)
where VI is the amplitude of the fundamental voltage given by Equation (2.2).
VNI
THDv
15.35.0.16
°J::-O----:'1;;-0---;;2!;;-0----:30:!::----:4;;;-10---.50;;---;60;:;----:;70;:;----t,;---~
AngleY(degrees) 0.2
o::I:
f- O.B
"C
c::
'"
.J
criCl>
~Cl0.6
~15
"E
Cl>
E'"
-g 0.4
u.::l
'c::>
a.CD
Fig 2.10: Amplitude offundamental voltage, harmonic content and total harmonic distortion (THDv) as a function of
r
for the 6-pulse inverter, based on theory [27J.Based on the theoretical Equations (2.1), (2.2), (2.6) and (2.7), the amplitude of the fundamental voltage, harmonic content and total harmonic distortion factor of the 6-pulse three-level inverter
as a function of 'Yare shown in Fig. 2.10. The curves show that at 'Y
=
15.35°, the fundamental amplitude decreases by 3.57% compared to that obtained from a two-level operation of the poles, i.e. when 'Y=
0°. However, at 'Y=
15.35° the harmonic content is reduced to 16% from the value of 31 %, obtained from a two-level operation of the inverter, resulting in the smallest THDv.Therefore, angle 15.35° is described as the optimum value of dead angle in the case of the 6-pulse three-level inverter [27].