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Comparative Evaluation of Three Single-Phase NPC
Inverters
João A. F. Neto(1)
, René P. T. Bascopé(1)
, C. M. Cruz(1)
(1)
Energy Processing and Control Group – GPEC
Electrical Engineering Department - DEE
Federal University of Ceará - UFC
Fortaleza-CE, Brazil
[email protected], {rene, cicero}@dee.ufc.br
Ronny G. A. Cacau(1)
, Grover V. T. Bascopé(2)
(2)
GTB Power Electronics R&T AB
Dept. of Research and Development
Sibeliusgangen 44, 4TR, 164 72
Kista, Sweden
[email protected], [email protected]
Abstract— In this paper is presented a comparative evaluation
in steady-state of three single-phase NPC multilevel inverters.
The first is a five-level neutral point clamped (NPC) inverter
based on multi-stage switching cell (MSSC); the second is also a
five-level neutral point clamped (NPC) inverter based on
interleaved cell (IC); and the third is a three-level neutral point
clamped (NPC) inverter based on paralleled cell (PC). For this
comparative purpose, the switching frequency is constant and
the evaluated parameters are the volume of the heatsinks and
the passive components, the total harmonic distortion (THD) of
the output voltage, the power density and efficiency of each
topology. Theoretical analyses, as well as simulation and
experimental results obtained from 5kW prototype are
presented.
I. INTRODUCTION
Lately the multilevel converters have been widely explored in the world of power electronics, with numerous applications in industry and power systems [1-3]. The three-level neutral-point-clamped voltage-source converter (NPC VSC) has been the center of research and development effort for medium voltage applications [4]. Recent investigations have shown that the NPC VSC is also a promising alternative for low voltage applications, though for different reasons [5]. The main reason for the good performance of these converters is due to its ability to share the voltage across the semiconductors (switches, diodes), resulting in less expensive components with reduced breakdown voltages and, consequently, reduced conduction losses.
For high-current applications, several techniques have been introduced in the literature to increase the current capacity of the converters, including the technique of interleaving and the use of magnetically coupled cells. The interleaved converters with magnetic coupling, are found in the technical literature in two forms: interleaved converters with coupled inductors [6-8] and interleaved converters using magnetically coupled cells via an autotransformer (“Intercell Transformer” – ICT) [9,10]. The analysis of the NPC-MSSC topology using an autotransformer was performed [11].
However, such topologies require an adequate performance evaluation regarding the number of switches and diodes, volume of the heatsinks and the magnetic components, THD of the output voltage, power density and efficiency of each inverter. Therefore, this paper presents a comparative evaluation of three multilevel NPC inverters. In the first topology, the commutation cells are connected using an autotransformer (5L-NPC-MSSC). In the second topology, the commutation cells are connected using uncoupled inductors (5L-NPC-IC). Finally, in the third topology, only the commutation cells are connected in parallel (3L-NPC-PC). The three topologies under analysis are shown in Figs. 1, 2, and 3, respectively.
Lo
S1
N1
N2O A
Vo
S2
S3
S4
S5
S6
S7
S8
Dc3
Dc4
Autotransformer
Co
L
O
A
D
Filter
Capacitor
Dc1
Dc2
Filter
Inductor
2
Vin
2
Vin
1
2
Figure 1. 5L-NPC-MSSC inverter.
S1
L1
O
1 Vo
S2
S3
S4
S5
S6
S7
S8
Dc3
Dc4
Uncoupled
Inductors
Co
L
O
A
D
Filter
Capacitor
Dc1
Dc2
2
Vin
2
Vin
2L2
Figure 2. 5L-NPC-IC inverter.
L3
S1
O A
Vo
S2
S3
S4
S5
S6
S7
S8
Dc3
Dc4
C3
L
O
A
D
Filter
Capacitor
Dc1
Dc2
Filter
Inductor2
Vin
2
Vin
Figure 3. 3L-NPC-PC inverter.
For the 5L-NPC-MSSC and 5L-NPC-IC inverters, the PWM drive signals of the switches corresponding to each leg are delayed by 180º. For the 3L-NPC-PC inverter, these PWM drive signals are in phase.
For this comparison, the semiconductors losses are calculated and the required heatsink volumes are evaluated for the same Cooling System Performance Index CSPI [12]. This thermal model considers a fixed heatsink temperature of 80
oC
and assumes a certain thermal conductance per heatsink volume.
II. EQUIVALENT OUTPUT CIRCUITS
The equivalent output circuits for the 5L-NPC-MSSC and 3L-NPC-PC inverters are shown in Fig. 4.a and in Fig. 4.b, respectively.
+
-
i (t)L L
O
+ v (t ) -L
+
-
v (t)o
5 Level
2.Fs
i (t)o
V (t)AOV (t)1 +V (t)2
2=
3 Level
+
-
Fs
V (t)AO
i (t)L
L3
+ v (t ) -L
+
-
v (t)o
i (t)o
(a) (b)
Figure 4. Equivalent output circuits: (a) 5L-NPC-MSSC and (b) 3L-NPC-PC.
The equivalent output circuit for the 5L-NPC-IC inverter is obtained by applying the Norton and Thévenin theorems in the individual output circuits on each leg of the converter, according to Fig. 5.
3 LevelL =1 L2
L1 L2
oi (t)
+
-
vo )(tV (t)1
w.L1
V (t)2
w.L2
+
-
3 Level
Fs
V (t)1 V +
-(t)2
i (t)1
i (t)2
Fs
L1
L2
L =1 L2 oi (t)
+
-
vo )(t
5 Level
+V (t)1 V (t)2
w.L1
L1
2+
-
vo )(t
)oi (t
5 Level
2.Fs
+
-
+V (t)1 V (t)2
2
L1
2+
-
vo )(t
oi (t)
Figure 5. Obtained the equivalent output circuit for the 5L-NPC-IC inverter.
The theoretical waveforms of the drive signals of the switches S1, S4, S5, and S8, the output voltage on each leg, V1(t) and V2(t), and the equivalent output voltage for the 5L-NPC-IC inverter are shown in Fig. 6.
0
1
Drive Signal for S1
Drive Signal for S5
Drive Signal for S4
Drive Signal for S8
0
1
0
1
0
1
p 2p
p 2p
p 2p
p 2p
0
0
+Vin/2
-Vin/2
+Vin/2
-Vin/2
p 2p
p 2p
0
+Vin/2
-Vin/2
+Vin/4
-Vin/4
p 2p
w t
Voltage V (t)1
Voltage V (t)2
Equivalent Output Voltage
(V (t) + V (t))/2 21
Figure 6. Theoretical waveforms for the 5L-NPC-IC inverter.
By observing the Fig. 6, it is verified that the waveform of the equivalent output voltage for the 5L-NPC-IC inverter using uncoupled inductors is identical to the waveform of the output voltage VAO for the 5L-NPC-MSSC inverter [11]. By comparing the equivalent output circuits for the two converters, it is concluded that (1) must be satisfied.
o21 L2LL . (1)
In equation (1), L1 e L2 represent the inductance values of the uncoupled inductors for the 5L-NPC-IC inverter, and Lo represents the inductance value of the inductor for the 5L-NPC-MSSC inverter.
III. CURRENT RIPPLE
A. Output Current Ripple
With (1) satisfied the total output current ripple for the 5L-NPC-IC inverter is exactly equal to the current ripple in the filter inductor for the 5L-NPC-MSSC inverter. The normalized equation of this current ripple, defined by (2) is represented by (3) for a half cycle of the output voltage of the inverter.
in
sooo
V
F.L.II
(2)
pwpww
pwww
www
t1,4
tsen.M.tsen.M21
1t1,4
1tsen.M2.tsen.M1
1t0,4
tsen.M.tsen.M21
Io
(3)
Where: Fs - Switching frequency. Vin - Input voltage. M - Modulation index. θ1 - Transition angle defined by (4).
M2
1sen 1
1 (4)
Equation (3) is illustrated graphically in Fig. 7 for some values of the modulation index M, during half cycle of the output voltage for the 5L-NPC-MSSC inverter.
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
w tpp/2
M = 0.7
M = 0.75
M = 0.8
M = 0.85
(w t
,M)
oI
1
p – 1
Figure 7. Current ripple in the filter inductor for the 5L-NPC-MSSC inverter.
By observing the graphic in Fig. 7, it is noted that the current ripple in the filter inductor for the 5L-NPC-MSSC inverter is zero for ωt = θ1 e ωt = π – θ1.
B. Current Ripple in the Magnetic Elements
For the 5L-NPC-MSSC inverter using an autotransformer, assuming zero magnetizing current and the same number of turns of each winding, the currents of the legs are identical and equivalent to the half output current. This way, the current ripple of each winding is half of the output current ripple and the ripple frequency of total current is twice the switching frequency [13].
For the 5L-NPC-IC inverter, the current ripple through the inductors presents the same switching frequency of the switches. The sum of the currents through both inductors has twice the switching frequency of the switches. The normalized equation of the current ripple in the inductor L1, defined by (5) is represented by (6) for a half cycle of the output voltage.
in
so11
V
F.L.II
(5)
pw
ww
t0,
4
tsen.M.tsen.M1I1
(6)
Equation (6) is illustrated graphically in Fig. 8 for some values of the modulation index for a half cycle of the output voltage.
p/2 p0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
w t
M = 0.7
0.75
0.8
0.85
0.9
I
(w t
,M)
1
Figure 8. Current ripple in the inductor L1 for the 5L-NPC-IC inverter.
Current ripples in the winding N1 for the 5L-NPC-MSSC inverter, and in the inductor L1 for the 5L-NPC-IC inverter using uncoupled inductors, are shown in Fig. 9 for a value of M equal to 0.9.
p/2 p0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
M = 0.9
p w t
1 1
I (w t)1
oI (w t)/2
Figure 9. Current ripples in the winding N1 (5L-NPC-MSSC) and in the
inductor L1 (5L-NPC-IC) for M equal to 0.9.
It is noted that for a same waveform of the total output current, the current ripple in the windings of the autotransformer for the 5L-NPC-MSSC inverter is smaller relative to the current ripple in the uncoupled inductors for the 5L-NPC-IC inverter. Thus, the RMS current through the semiconductors of the first topology is smaller compared to the RMS current through the semiconductors of the second topology. Therefore, the conduction losses in the 5L-NPC-MSSC inverter are somewhat smaller compared to that in the 5L-NPC-IC inverter.
IV. TOTAL HARMONIC DISTORTION
The total RMS value of the output voltage VAO for the 5L-NPC-MSSC inverter is given by (7). The waveform of this voltage is identical to that of the equivalent output voltage for the 5L-NPC-IC inverter.
2
1
1
2
inef_AO
2
1
M.2
1sin.
11M.4M.
2
VV
ppp(7)
The RMS value of the fundamental output voltage VAO can be obtained from (8).
2
M.
2
VV in
ef_1AO (8)
The THD of the output voltage VAO, before the filter, can be calculated by (9). Fig. 10 represents the THD of this voltage as a function of the modulation index.
1V
VTHD
2
ef_1AO
ef_AO
(9)
0.5 0.6 0.7 0.8 0.925
30
35
40
45
50
55
TH
D (
%)
M1.0
Figure 10. THD variation of the output voltage VAO for the 5L-NPC-MSSC
inverter as a function of M.
V. THEORETICAL APPROACH
All topologies use the same set of switches (8 IGBT’s IRGP50B60PD1 from International Rectifier) and diodes (30EPH06 from International Rectifier), and the design parameters: Vin = 500 V, Vo = 127 Vrms, Po = 5 kW and Fs = 20 kHz. The passive components were calculated according to the equivalent output circuit of each configuration.
A. Total Losses in Semiconductors
From the values of the currents through the semiconductors, calculated based on the equations presented in [11], the conduction and switching losses for a single switch are calculated in accordance with (10) and (11), respectively.
)on(CEavg_SS_cond V.IP (10)
frsinPK
Ssw ttFV4
IP ..._
p (11)
Where:
IS_avg - Average value of the current in the switch. VCE(on) - Collector-to-Emitter saturation voltage. IPK - Peak value of the current in the semiconductors. tr - Rise time. tf - Fall time.
The switching losses in S2, S3, S6 and S7 are nearly zero due to the low switching frequency of the switches. The total losses for a single switch are calculated by adding the respective conduction and switching losses. This way, the total losses for the eight switches of each converter are calculated by (12).
2Stot1StotS8tot P4P4P ___ .. (12)
Where:
Ptot_S1 - Total losses for S1. Ptot_S2 - Total losses for S2.
The conduction and switching losses for a single clamping diode are calculated by (13) and (14), respectively.
FavgDcDccond VIP .__ (13)
srrRRMinDcsw FtIV
4
1P ...._ (14)
Where:
IDc_avg - Average value of the current in the diode. VF - Forward voltage. IRRM - Peak recovery current. trr - Reverse recovery time.
The total losses for a single diode (Ptot_Dc) are calculated by adding the respective conduction and switching losses. Thus, the total losses in semiconductors for each converter are calculated by (15).
DctotS8tottot P4PP __ . (15)
B. Heatsink Volume
With the total losses calculated, the required thermal resistance of the heatsink can be obtained by (16).
tot
ambHSHS_th
P
TTR
(16)
Where:
THS = 80oC - Heatsink temperature.
Tamb = 40oC - Ambient temperature.
This way, the heatsink volume required for the semiconductors of each converter can be calculated by (17).
1
HS_thHS R.CSPIVol
(17)
Where:
CSPI = 17.88 mW/K.cm3 - Cooling System Performance
Index for a typical aluminium heatsink.
C. Magnetic Components
The parameters of each magnetic component designed are presented in Table I. All designs use the same current density (J = 380 A/cm
2) and the same core (NEE-65/33/52 IP12-
Thorton). The inductor L3 is implemented with two inductors Lo connected in series. The copper, core, and total losses of each magnetic component are presented in Table II.
TABLE I. MAGNETIC PARAMETERS – NEE-65/33/52, J = 380 A/cm2
Component Volume of
Copper (cm3) Turns Wire
Autotransformer 34.14 N1 = N2 = 12 40 x 26AWG
Inductor Lo 42.67 15 80 x 26AWG
Inductor L1 36.98 26 40 x 26AWG
Inductor L2 36.98 26 40 x 26AWG
TABLE II. LOSSES IN MAGNETIC COMPONENTS
Component Copper losses
(W)
Core losses
(W) Total losses (W)
Autotransformer 8.08 5.66 13.74
Inductor Lo 10.10 0.21 10.31
Inductor L1 8.76 0.87 9.63
Inductor L2 8.76 0.87 9.63
Inductor L3 20.20 0.42 20.62
It is noted that the core losses in the inductor Lo for the 5L-NPC-MSSC inverter are negligible compared to losses in the windings. This is due the fact of the high frequency current ripple in the inductor has a maximum value reduced compared to the peak value.
D. Comparison of Topologies
Table III presents some values used and obtained theoretically for each topology. By observing these values, it can be seen that even using the filter inductor Lo in the 5L-NPC-MSSC inverter, the efficiency is nearly equal to those of similar topologies (5L-NPC-IC and 3L-NPC-PC inverters). The power density of the 5L-NPC-MSSC inverter using an autotransformer is also approximately equal to that of the 5L-NPC-IC inverter using uncoupled inductors and slightly above to that of the 3L-NPC-PC inverter using a single inductor.
TABLE III. COMPARISON OF TOPOLOGIES - Vin = 500 V, VO = 127 Vrms, PO = 5 kW and Fs = 20 kHz
Topology 5L-NPC-MSSC 5L-NPC-IC 3L-NPC-PC
Output Filter Inductance Lo = 180 µH L1 = L2 = 360 µH L3 = 360 µH
Output Filter Capacitance Co = 10 µF Co = 10 µF C3 = 20 µF
Maximum Current Ripple in each Leg 2.1 A 8.44 A 4.22 A
Total Losses in the Semiconductors (W) 145.44 152.4 148.54
Heatsink Volume (cm3) 203.36 213.09 207.69
Magnetic Components Volume (cm3) 389.61 386.76 398.14
Capacitor Volume (cm3) 43.82 43.82 59.65
Total Losses in the Autotransformer (W) 13.74 - -
Total Losses in Inductors (W) 10.31 19.26 20.62
Total Volume (cm3) 636.79 643.67 665.48
Power Density (kW/dm3) 7.85 7.77 7.51
Efficiency (%) 96.72 96.68 96.73
THD (Output voltage before the filter) 41.27 % 41.27 % 87.66 %
VI. SIMULATION RESULTS
In order to verify the theoretical analysis and some values presented in the previous sessions, the designed inverters were simulated. Fig. 11 shows the waveforms of the output voltages VAO and Vo for the 5L-NPC-MSSC inverter.
Time50ms 60ms 70ms 80ms 90ms 100ms
-400V
-200V
0V
200V
400V
Output Voltage VAO
Output Voltage Vo
Figure 11. Waveforms of the output voltages for the 5L-NPC-MSSC inverter.
The waveforms of the currents through the inductor Lo and through the windings of the autotransformer for the 5L-NPC-MSSC inverter are shown in Fig. 12. The waveforms of the total output current and the currents through the uncoupled inductors for the 5L-NPC-IC inverter are shown in Fig. 13.
50ms 60ms 70ms 80ms 90ms 100ms
-50A
0A
50ACurrent
through N1
Current
through N2
Current through Lo
Time
Figure 12. Current waveforms for the 5L-NPC-MSSC inverter.
Time50ms 60ms 70ms 80ms 90ms 100ms
Total Output Current
-80A
-40A
0A
40A
80A
Current through L1
Current through L2
Figure 13. Current waveforms for the 5L-NPC-IC inverter.
A detailed view of the currents through the inductor Lo and through the windings of the autotransformer for the 5L-NPC-MSSC inverter is illustrated in Fig. 14, which shows that the current ripple in each winding is half of the current ripple in the inductor Lo. The detailed view of the total output current and the currents through the uncoupled inductors for the 5L-NPC-IC inverter is shown in Fig. 15.
52A
60A
i o
i = 4.2A o
26A
30A
i N1
i = 2.1A N1
Time54.10ms 54.12ms 54.14ms 54.16ms 54.18ms 54.20ms
30A
26A54.22ms
i N2
i = 2.1A N2
40 kHz
40 kHz
40 kHz
Figure 14. Detailed view of the currents for the 5L-NPC-MSSC inverter (θ =
π/2).
40 kHz
52.5A
55A
57.5A
60A
i = 4.24Ao
io
Time54.10ms 54.12ms 54.14ms 54.16ms 54.18ms 54.20ms 54.22ms
20 kHz
22.5A
25A
27.5A
30A
32.5Ai = 6.36AL
iL
Figure 15. Detailed view of the currents for the 5L-NPC-IC inverter (θ = π/2).
By observing the results obtained by simulation, it is verified that they are in agreement with the theoretical analysis performed.
VII. EXPERIMENTAL RESULTS
The waveforms obtained experimentally of the output voltages VAO and Vo for the 5L-NPC-MSSC inverter are shown in Fig. 16. The waveforms of the output voltage Vo and the total output current for the 5L-NPC-MSSC and 5L-NPC-IC inverters are shown in Figs. 17 and 18, respectively.
Figure 16. Output voltages VAO (CH2) and Vo (CH1) for the 5L-NPC-MSSC
inverter.
Figure 17. Output voltage Vo (CH1) and current through Lo (CH3) for the 5L-
NPC-MSSC inverter.
Figure 18. Output voltage Vo (CH1) and total output current (CH4) for the 5L-
NPC-IC inverter.
The waveforms of the currents through the inductor Lo and through the winding N1 of the autotransformer for the 5L-NPC-MSSC inverter are presented in Fig. 19 and the waveforms of the total output current and the current through the inductor L1 for the 5L-NPC-IC inverter are presented in Fig. 20.
Figure 19. Currents through the inductor Lo (CH3) and through the winding N1
of the autotransformer (CH4) for the 5L-NPC-MSSC inverter.
Figure 20. Total output current (CH4) and current through the inductor L1
(CH3) for the 5L-NPC-IC inverter.
A detailed view of the currents through the inductor Lo and through the winding N1 of the autotransformer for the 5L-NPC-MSSC inverter is shown in Fig. 21, in which may be checked that the current ripple in each winding is half of the current ripple in the inductor Lo. The detailed view of the currents through the windings of the autotransformer, for θ = π/2, is represented in Fig. 22.
Figure 21. Detailed view of the currents through the inductor Lo (CH3) and
through the winding N1 (CH4) for the 5L-NPC-MSSC inverter (θ = π/2).
Figure 22. Detailed view of the currents through the windings of the
autotransformer for the 5L-NPC-MSSC inverter (θ = π/2).
A detailed view of the total output current and the current through the inductor L1 for the 5L-NPC-IC inverter is shown in Fig. 23, for θ = π/2. The detailed view of the currents through the uncoupled inductors is shown in Fig. 24, in which can be observed that they are delayed by 180
o.
Figure 23. Detailed view of the total output current (CH4) and the current
through the inductor L1 (CH3) for the 5L-NPC-IC inverter.
Figure 24. Detailed view of the currents through the uncoupled inductors for
the 5L-NPC-IC inverter (θ = π/2).
The efficiency curves, obtained experimentally, for the 5L-NPC-MSSC and 5L-NPC-IC inverters as function of the
output power are presented in Fig. 25. Note that even using the filter inductor Lo, the efficiency of the 5L-NPC-MSSC inverter is nearly equal to that of the 5L-NPC-IC inverter using uncoupled inductors and greater than 96.2% at full load.
0 1 2 3 4 595
96
97
98
99
100
Output Power (kW)
5L-NPC-MSSC
5L-NPC-IC
Eff
icie
ncy
(%
)
Figure 25. Efficiency versus output power curves for the 5L-NPC-MSSC and
5L-NPC-IC inverters.
The THD variation of the output voltage VAO in function of the modulation index for the 5L-NPC-MSSC inverter is shown in Fig. 26.
0.5 0.6 0.7 0.8 0.920
30
40
50
60
M1.0
TH
D (
%)
Theoretical
Experimental
Figure 26. THD of the output voltage VAO versus M.
VIII. CONCLUSION
This paper presented a steady-state comparative evaluation
of three multilevel inverters, named as 5L-NPC-MSSC, 5L-
NPC-IC, and 3L-NPC-PC. For this evaluation, the current
ripple before of the output filter capacitor and the switching
frequency of the switches were considered equals. Comparing
the volume and weight it was observed that the 5L-NPC-
MSSC and 5L-NPC-IC inverters have approximately the
same value. Moreover, the 3L-NPC-PC inverter has a greater
weight and volume compared to the indicated inverters
because the output filter is subjected only to the switching
frequency. For this comparison the semiconductors losses are
calculated and the required heatsink volumes are evaluated for the same Cooling System Performance Index CSPI. The passive components were calculated according to the equivalent output circuit of each configuration.
Simulation and experimental results demonstrate the similar efficiency of the three inverters. In terms of involved RMS currents, the 5L-NPC-IC inverter has higher currents in semiconductors and magnetic elements.
In the laboratory it was observed that the 5L-NPC-IC and 3L-NPC-PC inverters are more susceptible to current unbalanced through the components due to small variations in duty cycle, gate resistors and other non-idealities, especially in the layout. Therefore, when implemented many precautions should be taken.
ACKNOWLEDGMENT
The authors would like to thank to Energy Processing Control Group (GPEC) of Electrical Engineering Department (DEE-UFC) for the providing the facilities and adequate support to this work.
REFERENCES
[1] J. Rodriguez, J.-S. Lai, and F. Z. Peng, “Multilevel Inverters: A Survey of Topologies, Controls, and Applications,” IEEE Transactions on Industrial Electronics, vol. 49, no. 4, pp. 724-738, Aug. 2002.
[2] J. Dixon and L. Morán, “High-Level Multistep Inverter Optimization Using a Minimum Number of Power Transistors,” IEEE Transactions on Power Electronics, vol. 21, no. 2, pp. 330-337, Mar. 2006.
[3] J. Rodriguez, S. Bernet, B. Wu, J. O. Pontt, and S. Kouro, “Multilevel Voltage-Source-Converter Topologies for Industrial Mediun-Voltage drives,” IEEE Transactions on Industrial Electronics, vol. 54, no. 6, pp. 2930-2945, Dec. 2007.
[4] A. Nabae, I. Takahashi, H. Akagi, “A New Neutral-Point-Clamped PWM Inverter,” IEEE Trans. Ind. Appl., vol. IA-17, no. 5, pp. 518–523, September/October 1981.
[5] R. Teichmann and S. Bernet, “A Comparison of Three-Level Converters Versus Two-Level Converters for Low-Voltage Drives, Traction, and Utility Applications,” IEEE Transactions On Industry Applications, vol. 41, no. 3, pp. 855-865, May/Jun. 2005.
[6] J. Salmon, A. M. Knight, and J. Ewanchuk, “Single-Phase Multilevel PWM Inverter Topologies Using Coupled Inductors,” IEEE Transactions on Power Electronics, vol. 24, no. 5, pp. 1259-1266, May 2009.
[7] R. Hausmann, R. Silva, and I. Barbi, “Three-Phase NPC Inverter Using Three-Phase Coupled Inductor,” in Proc. Energy Convers. Congr. Expo., San Jose, CA, pp. 913–918, Sep. 2009.
[8] D. Floricau, E. Floricau, and G. Gateau, “New Multilevel Converters with Coupled Inductors: Properties and Control,” IEEE Transactions on Industrial Electronics, vol. 58, no. 12, pp. 5344-5351, Dec. 2011.
[9] M. T. Peraça and I. Barbi, “Three-Level Half-Bridge Inverter Based on the Three-State Switching Cell,” Presented at the INDUSCON, Recife, Brazil, 2006.
[10] E. Labouré, A. Cunière, T. Meynard, F. Forest, and E. Sarraute, “A Theoretical Approach to Intercell Transformers, Application to Interleaved Converters,” IEEE Transactions on Power Electronics, vol. 23, no. 23, pp. 464–474, Jan. 2008.
[11] R. P. T. Bascopé, J. A. F. Neto, and G. V. T. Bascopé, “Multi-state Commutation Cells to Increase Current Capacity of Multi-Level Inverters,” Presented at the Telecommunications Energy Conference (INTELEC), Amsterdam, Netherlands, 2011, IEEE 33rd International.
[12] U. Drofenik and J. W. Kolar, “Analyzing the theoretical limits of forced air-cooling by employing advanced composite materials with thermal conductivities > 400 W/mK,” IEEE CIPS, Naples, Italy, Jun. 2006.
[13] F. Forest, E. Labouré, T. A. Meynard, and V. Smet, “Design and Comparison of Inductors and Intercell Transformers for Filtering of PWM Inverter Output,” IEEE Transactions on Power Electronics, vol. 24, no. 3, pp. 812-821, March 2009.
