where,

Vdc: DClink voltage,

Vref: reference voltage.
2.1.3 Computing total conduction losses
The conduction loss of devices,
p_{on}
, is computed from the saturation voltage and the conducting current during the ontime duration, which is expressed as
[5]
where,

von: saturation voltage,

Vo: threshold voltage,

Ron: on resistance of device,

φ: PF angle,

Ic: peak value of conducting current.
The average conduction loss of each device in the Mlevel inverter is calculated as
where ‘
D
’ means the duty ratio of conducting devices, and ‘
a
’ and ‘
b
’ denote the beginning and ending points of each conduction interval, respectively.
 2.2 Switching losses
In the multilevel inverter, the switching loss varies since the device for switching is changed according to the modulation depth. In addition, it is proportional to the switching frequency. For example, in the case of levelshifted PWM, the switching frequency of the device is not the same as the carrier frequency, which is calculated by
The switching loss in a leg of the Mlevel inverter for the positive and negative current directions is calculated as (7) and (8) respectively:
where,

ET: IGBT turnon andoff energy,

ED: diode turnoff energy,

fsw: device switching frequency,

Psw1: switching loss for the positive current direction,

Psw2: switching loss for the negative current direction,

Van(i): reference voltage.
In a leg of the inverter, the switching loss is given by
and for the three legs of the inverter,
The IGBTs and diodes which change the operating conditions in the Mlevel NPC inverters are listed in
Table 2
.
Switching state of Mlevel inverter according to current direction.
Switching state of Mlevel inverter according to current direction.
3. Power loss of Three and Fivelevel NPC Inverters
 3.1 Threelevel NPC inverters
3.1.1 Conduction losses
•
Finding the current paths and the conducting devices
Figs. 4(a)
and
(b)
show the current paths in the threelevel NPC inverter for positive and negative current directions, respectively. The conducting devices for each switching state are listed in
Table 3
. Also, the conducting devices in a legA of the threelevel NPC inverter depending on the current and voltage polarities is shown in
Fig. 5
.
Current paths of threelevel NPC inverters according to switching states: (a) Positive current; (b) Negative current.
Conducting switches in three and fivelevel NPC inverters.
Conducting switches in three and fivelevel NPC inverters.
Conducting devices in a legA of threelevel NPC inverters.
•
Finding the ontime duration
The ontime duration can be determined by setting M=3 in (3), in which the reference voltage is compared with two carrier waveforms (shown in
Fig. 6
). The onstate duration of the conducting devices in the threelevel inverter is calculated as
PWM in the threelevel inverter.
The ontime duration are calculated, which are listed in
Table 4
.
Ontime duration of conducting devices in threelevel NPC inverters.
Ontime duration of conducting devices in threelevel NPC inverters.
•
Computing the total conduction loss
The average conduction loss is calculated by integrating the power loss of each device in every time duration illustrated in
Fig. 5
. It is calculated by (13) to (16) for the threelevel inverters:
3.1.2 Switching losses
The switching loss can be calculated by setting N=3 in (7)(9) for the positive current direction in the threelevel NPC inverter as follows:
and for negative current direction
the total power loss in one leg of the threelevel NPC inverter is calculated as
The IGBTs and diodes which change the operating conditions are listed in
Table 5
.
Switching states of threelevel inverter according to current direction.
Switching states of threelevel inverter according to current direction.
 3.2 Fivelevel NPC inverter
3.2.1 Conduction losses
•
Finding the current paths and the conducting devices
Figs. 7 (a)
and
(b)
show the current paths in the fivelevel NPC inverters in positive and negative current directions. The conducting devices for each switching state are listed in
Table 3
. For 0.5 <
MI
≤ 1 , there are two cases in which the change between carrier waveforms occurs for the levelshifted PWM before the change of current polarity as shown in
Fig. 8(a)
or the current polarity is changed before the change of the carrier waveforms as shown in
Fig. 8(b)
. For 0 ≤
MI
≤ 0.5, there is no change of the MI as shown in
Fig. 8(c)
.
Current paths of fivelevel NPC inverter according to switching states: (a) Positive current; (b) Negative current.
Conducting devices in a legA of fivelevel NPC inverters.
•
Finding the ontime duration
In the case of fivelevel inverters, the reference voltage is compared with the four carrier waveforms. Ontime duration of each switch in the fivelevel NPC inverters is listed in
Table 6
in different regions of operation.
Ontime duration of conducting devices in fivelevel NPC inverters.
Ontime duration of conducting devices in fivelevel NPC inverters.
•
Computing the total conduction loss
The average conduction loss of each device in the fivelevel inverter is calculated in the same way as the threelevel one.
3.2.2 Switching Losses
The devices which change the operating condition in the fivelevel inverter are listed in
Table 7
. The total switching l loss can be calculated in the same way for the threelevel inverters.
Switching states of fivelevel inverter according to current direction.
Switching states of fivelevel inverter according to current direction.
4. Results of Power Loss Evaluation
For a power loss analysis, a 33kW system for the three and fivelevel NPC inverters is adopted. The DClink voltage is 600 V. An RL load is connected to the inverter. The semiconductor device used is SKM 75GAL063D (Semikron product), of which rated current is 100 A. Conduction and switching losses are calculated from the parameters in
Table 8
[11]
.
Figs. 9
and
10
show the conduction loss of each device in the threeand five level NPC inverters, respectively. In
Fig. 9
, it is obvious that the conduction loss for antiparallel diode is very low compared with IGBT switches whereas the clamping diodes have slightly higher conduction loss than antiparallel diodes. The conduction losses of IGBTs and diodes in the fivelevel NPC inverter are illustrated in
Figs. 10(a)
and
(b)
, respectively.
Parameters of SKM 100GB063D module[16]. (VCES= 600[V], T = 25° )
Parameters of SKM 100GB063D module [16]. (V_{CES} = 600[V], T = 25° )
Conduction loss of each device in threelevel NPC inverters versus MI.
Conduction loss of upper devices in oneleg of fivelevel NPC inverters versus MI: (a) IGBT switches; (b) Clamping and antiparallel diodes.
In
Fig. 11
the conduction power loss of inverters are investigated as a function of MI and
φ
respectively. The conduction loss of the threelevel inverter at MI=1 and MI=0.5 are 237W and 85W, respectively, which are 495W and 218W, respectively in the fivelevel inverter (
Fig. 11(a)
). The conduction loss as a function of angle
φ
is illustrated in
Fig. 11(b)
, where the conduction loss of three and five level inverters in the case of
φ
=
π
/2 are 210W and 450W, respectively at which condition the MI=1.
Conduction loss of threephase NPC inverters versus MI in. (a) φ = 0°. (b) MI=1.
In
Fig. 12
the total power loss of inverters are investigated as a function of MI and
f_{sw}
respectively. In
Fig. 12(a)
, the power losses of inverters are investigated in different MI in which the switching frequency is
f_{sw}
= 5[kHz] . The loss of the threeand fivelevel inverters at MI=1 are 295W and 619W, respectively, which are 151W and 305W in the case of MI=0.5. The power loss of threeand fivelevel inverters as a function of switching frequency are illustrated in
Fig. 12(b)
, where the MI=1 and
φ
= 0°.
Total power loss of threephase NPC inverters versus (a) MI at φ = 0°, f_{sw} = 5[kHz]. (b) Switching frequency at ϕ = 0°, MI = 1 .
The switching loss as a function of the switching frequency is illustrated in
Fig. 13(a)
. In the threelevel inverter, the switching loss is 58W at 5kHz switching frequency, which is 87W in the fivelevel inverter. The switching loss as a function of switching frequency is shown in
Fig. 13(b)
.
Switching loss of threephase NPC inverters versus (a) MI at φ = 0°, f_{sw} = 5[kHz]. (b) Switching frequency at φ = 0°, MI = 1 .
Fig. 14
illustrates the 3D plots of power loss in threephase inverters. The total power loss as a function of MI and PF angle is illustrated in
Fig. 14(a)
, in which the power loss varies abruptly at MI=0.5 in the fivelevel NPC inverter. The 3D plots of switching versus MI and
φ
are shown in
Fig. 14(b)
, where the switching frequency is
f_{sw}
= 5[kHz] . It is shown that, in the case of fivelevel inverter, the switching loss is affected by MI and power factor angle, however the switching loss of threelevel inverter is not changed in different MI and have a slight changes in various power factor angles which is not distinguishable in the figure. The 3D plot for the conduction losses of inverters are presented in
Fig. 14(c)
.
The 3D plot of the power losses in NPC inverters in 5[kHz] switching frequency: (a) Total power losses; (b) Switching losses; (c) Conduction losses.
5. Verification through Simulation
The power loss analysis is verified by simulation. The inverter operates at the same conditions as analysis aforementioned. The DClink voltage is 600 V and the load current is 50 A. For simulation, the forward voltage, onresistance and the turnon and off times of IGBT and diodes are required, which are set from the datasheet parameters. The simulation is carried out for the threeand fivelevel NPC inverters. The total power loss of the inverter is obtained from the difference between the measured input and output powers.
Figs. 15
and
Fig. 16
show the total power loss in the three and fivelevel NPC inverters, where the operating condition is changed three times during running simulation In the zone (a), the MI=0.55 and PF=1, in the zone (b) the MI=1 and the PF=1, and in the zone (c) the MI=0.4 and PF=0.86. After a transient period due to the changing of simulation conditions, the average power loss of the inverter conditions, the average power loss of the inverter is obtained. For a comparison between the simulation and analysis results, the total power losses are listed in
Table 9
. The simulation and analysis results are very close each other, so the loss analysis developed can be validated.
Measured power loss of threelevel NPC inverters.
Measured power loss of fivelevel NPC inverters.
Simulation and analysis results of power loss in threeand fivelevel NPC inverters.
Simulation and analysis results of power loss in threeand fivelevel NPC inverters.
6. Verification through Experiment
The power loss analysis of threelevel NPC inverter is verified by experiment. The inverter is implemented by using the Semikron IGBT module SKM 75GB128D. The parameters of selected IGBT module are listed in
Table. 10
.
Parameters of SKM 75GB128D module[16]. (VCES= 1200[V], T = 25° )
Parameters of SKM 75GB128D module [16]. (V_{CES} = 1200[V], T = 25° )
Analysis results:
The power loss is analyzed by using the selected module (SKM 75GB128D). The DClink voltage is 310 V and the load current is 14 A. The results of analysis are illustrated in
Fig. 17
.
In
Fig. 17(a)
the total power loss, conduction and switching loss of inverter versus MI is shown, where the switching loss is constant in different MI, which is changed as a function of switching frequency in
Fig. 17(b)
. The conduction power loss and total power loss of inverter are shown in
Figs. 17(a)
,
(b)
as a function of MI and switching frequency respectively.
Power loss analysis results for threelevel inverter using SKM 75GB128D module versus: (a) MI; (b). f_{sw}
Experimental results:
The experiment is performed in the same condition as analysis. The total power loss of the inverter is obtained from the difference between the measured input and output powers. The output power is measured by two FLUKE 39 watt meters, which used the line voltage and phase current to measure the power. The threephase power is calculated as a sum of two watt meters. The inverter input power is obtained by sensing the DClink capacitor current and voltage. Since the DClink current is the pulse type, the low pass filter is included to find the capacitor current. The results of loss measurement according to various phase difference, MI and switching frequencies are listed in
Tables 11

13
. The total power losses of inverter have a slight difference with analysis results in various PF (
Fig. 18
).
The loss measurement according to different phase difference.
The loss measurement according to different phase difference.
The loss measurement according to various switching frequency.
The loss measurement according to various switching frequency.
The loss measurement according to various MI.
The loss measurement according to various MI.
Fig. 18. Measured loss of threelevel inverter versus PF (MI = 1, f_{sw} = 5[kHz] ).
In
Figs. 19
,
20
the measured power loss is compared with analysis results as a function of MI and switching frequency. The differences are very small, which are mainly due to the measurement device accuracy and the performed experiment condition.
Measured loss of threelevel inverter versus MI ( φ = 0° , f_{sw} = 5[kHz] ).
Measured loss of threelevel inverter versus switching frequency (ϕ = 0°, MI = 1).
7. Conclusion
In this paper, a generalized evaluation algorithm for the semiconductor losses in the multilevel NPC inverter has been proposed. From the loss analysis results, several conclusions can be made as follows:

The conduction and switching losses of the higherlevel inverter than the threelevel depend on the MI, whereas the switching loss is constant in different MI in the threelevel inverter.

In the fivelevel inverter, the jumps of the conduction and switching power losses occur at MI=0.5 where the modulation depth changes.

The proposed algorithm can be applied to the power loss evaluation for any higher level of inverters.

The validity of the power loss analysis has been verified by simulation results and experimental results.
Acknowledgements
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2012R1A1A4A01015362).
BIO
Payam Alemi was born in Tabriz, Iran in 1982. He received the B.Sc. degree from the University of Tabriz, Tabriz, Iran in 2005 and the M.S. degree from the science and research branch, Tehran Azad University in 2008. He is currently working toward his Ph.D. degree. His research interests include the control of multilevel power converters, power loss analysis for converters, LCL filter and machine drives.
DongChoon Lee received his B.S., M.S., and Ph.D. in Electrical Engineering from Seoul National University, Seoul, Korea, in 1985, 1987, and 1993, respectively. He was a Research Engineer with Daewoo Heavy Industry, Korea, from 1987 to 1988. Since 1994, he has been a faculty member in the Department of Electrical Engineering, Yeungnam University, Gyeongbuk, Korea. As a Visiting Scholar, he joined the Power Quality Laboratory, Texas A&M University, College Station, TX, USA, in 1998, the Electrical Drive Center, University of Nottingham, Nottingham, U.K., in 2001, the Wisconsin Electric Machines & Power Electronic Consortium, University of Wisconsin, Madison, Wisconsin, USA, in 2004, and the FREEDM Systems Center, North Carolina State University, Raleigh, North Carolina, USA, from September 2011 to August 2012. His current research interests include ac machine drives, control of power converters, wind power generation, and power quality. Prof. Lee is currently a Publication Editor of the Journal of Power Electronics of the Korean Institute of Power Electronics.
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