Simulation parameters are as follows:
SVPWM parameters:
Modulation index m = 0.8
dc supply voltage = 300 V
No. of switching intervals n = 48
Sampling frequency = 2400 Hz
Sampling time Ts = 4.166 e−4 seconds
Three-phase induction motor:
3 HP, 220 V, 50 Hz, 4 poles, 1500 rpm
Rs = 0.55 Ω; Rr = 0.78 Ω
Ls = 93.38 mH; Lr = 93.36 mH
Lm = 90.5 mH
J = 0.019 kg-m2
Fr = 0.000051 N-m/rad/s
TL = 10.32 N-m
Simulation parameters are as follows:
SVPWM parameters:
Modulation index m = 0.8
dc-link voltage = 400 V
No. of switching intervals n = 72
Sampling frequency = 3600 Hz
Sampling time Ts = 2.7778 e−4 seconds
Three-phase induction motor:
3 HP, 400 V, 50 Hz, 4 poles, 1500 rpm
Rs = 1.405 Ω; Rr = 1.395 Ω
Ls = 5.839 mH; Lr = 5.839 mH
Lm = 172.2 mH
J = 0.0131 kg-m2
Fr = 0.002985 N-m/rad/s
TL = 10.00 N-m
Simulation parameters are as follows:
SVPWM parameters:
Modulation index m = 0.8
dc-link voltage = 400 V
No. of switching intervals n = 192
Sampling frequency = 9600 Hz
Sampling time Ts = 1.0417 e−4 seconds
Three-phase induction motor:
2 HP, 400 V, 1500 W, 50 Hz, 4 poles, 1430 rpm
Rs = 1.405 Ω; Rr = 1.395 Ω; Ls = 5.839 mH; Lr = 5.839 mH; Lm = 143 mH
J = 0.0131 kg-m2; Fr = 0.002985 N-m/rad/s; TL = 10.00 N-m
1.The conditions for identifying reference vector location in multilevel inverters and corrections required to duty cycles are given in Tabs. A6.1, A6.2, and A6.3.
Tab. A6.1: Location of the reference vector and corrected duty cycles of the three-level inverter.
| Region | Condition for location of the reference vector | Corrected m1, m2, and m3 for the switching states |
| 2 | m1 > 0.5 | m1 = m1 − 0.5 |
| m2 = m2 | ||
| m3 = 1 − m1 − m2; | ||
| 3 | m1 < 0.5,m2 < 0.5 and m1 + m2 > 0.5 | m1 = 0.5 − m1 |
| m2 = 0.5 − m2 | ||
| m3 = m1 + m2 − 0.5; | ||
| 4 | m2 > 0.5 | m1 = m1 |
| m2 = m2 − 0.5 | ||
| m3 = 1 − m1 − m2; |
Tab. A6.2: Location of the reference vector and corrected duty cycles of the four-level inverter.
Tab. A6.3: Location of the reference vector and corrected duty cycles of five-level inverter.
| Region | Condition for location of the reference vector | Corrected m1, m2, and m3 for the switching states |
| 10 | 0.75 < m1 < 1 and m2 < 0.25 and m1 + m2 < 1 | m 1 = m 1 − 0.75; m2 = m2; m3 = 1 − m1 − m2 |
| 11 | 0.5 < m1 < 0.75 and m2 < 0.25 and m1 + m2 > 0.75 | m1 = 0.75 − m1; m2 = 0.25 − m2; m3 = m1 + m2 − 0.75 |
| 12 | 0.5 < m1 < 0.75 and 0.25 < m2 < 0.5 and m1 + m2 < 1 | m1 = m1 − 0.5; m2 = m2 − 0.25; m3 = 1 − m1 − m2 |
| 13 | 0.25 < m1 < 0.5 and 0.25 < m2 < 0.5 and m1 + m2 > 0.75 | m1 = 0.5 − m1; m2 = 0.5 − m2; m3 = m1 + m2 − 0.75 |
| 14 | 0.25 < m1 < 0.5 and 0.5 < m2 < 0.75 and m1 + m2 < 1 | m 1 = m1 − 0.25; m2 = m2 − 0.5; m3 = 1 − m1 − m2 |
| 15 | m1 < 0.25 and 0.5 < m2 < 0.75 and m1 + m2 > 0.75 | m1 = 0.25 − m1; m2 = 0.75 − m2; m3 = m1 + m2 − 0.75 |
| 16 | m1 < 0.25 and 0.75 < m2 < 1 and m1 + m2 < 1 | m1 = m1; m2 = m2 − 0.75; m3 = 1 − m1 − m2 |
2.The look-up tables for multilevel inverters
Tab. A6.4: Switching sequence of the two-level inverter.
Tab. A6.5: Switching sequence of the three-level inverter.
Tab. A6.6: Switching sequence of the four-level inverter.
Tab. A6.7: Switching sequence of the five-level inverter.
The simulation parameters are as follows:
SVPWM parameters:
Modulation index m = 0.8
dc-link voltage = 400 V
No. of switching intervals n = 72
Sampling frequency = 3600 Hz
Sampling time Ts = 2.7778 e−4 seconds
Three-phase induction motor:
5.4 HP, 400 V, 50 Hz, 4 poles, 1430 rpm
Rs = 1.405 Ω; Rr = 1.395 Ω
Ls = 5.839 mH; Lr = 5.839 mH
Lm = 172.2 mH
J = 0.0131 kg-m2
Fr = 0.002985 N-m/rad/s
TL = 10.00 N-m
The simulation parameters are as follows:
SVPWM parameters:
Modulation index m = 0.8
dc-link voltage = 400 V/500 V (eleven-level inverter)
No. of switching intervals n = 66
Sampling frequency = 3300 Hz
Sampling time Ts = 3.0303 e−4 seconds
2 HP, 400 V, 1500 W, 50 Hz, 4 poles, 1500 rpm
Rs = 1.405 Ω; Rr = 1.395 Ω
Ls = 5.839 mH; Lr = 5.839 mH
Lm = 172.2 mH
J = 0.0131 kg-m2
Fr = 0.002985 N-m/rad/s
TL = 10.00 N-m