This study was conducted to develop a design method of power density and efficiency maximization for three-phase pulse-width modulated (PWM) inverters that include AC filter. A tradeoff relationship exists between power density and efficiency. In general, increasing the switching frequency is known to increase the switching device loss and decrease the volume of the passive components. A three-phase PWM inverters design should consider the balance between conversion efficiency and inverter volume. However, best of our knowledge, no practical study has focused on the optimal design of a three-phase PWM inverter that includes an AC filter. This is because the iron loss of the AC filter inductor changes in complicated ways depending on the DC-bias excitation, amplitude of switching ripple current, etc. Therefore, the present authors clarified this iron loss mechanism and realized a highly accurate iron loss calculation method in previous studies. In this paper, the relationship between efficiency and volume for the switching frequency was analyzed when the AC filter inductor was designed for minimal loss by adjusting the core diameter, height, and number of winding turns. The efficiency and volume optimization achieved by designing a proper inductor was verified via comparison with a base design.

A power electronics converter requires both high power density (expressed in watts per unit volume) and high efficiency.1–5 However, a tradeoff relationship exists between power density and efficiency. By means of increasing the switching frequency, the volume of passive components (i.e., transformers and inductors) can be reduced. However, this approach increases the switching device loss and heatsink size. Therefore, the power electronics converter design method is important for determining the optimum point in the tradeoff relationship.4–6 However, to the best of the authors’ knowledge, no studies have yet been reported on design methods for a pulse width modulation (PWM) inverter that includes an AC filter inductor.6 The reason for this lack of research progress is that the iron loss of the inductor changes in complicated ways depending on the switching ripple current, DC-bias excitation, and other factors.7–12 Therefore, the present authors clarified this iron loss mechanism and realized a highly accurate iron loss calculation method in previous studies.7,9,12 Hence, in this study, a three-phase PWM inverter with an AC filter was designed. The relationship between efficiency and volume for the switching frequency was analyzed when the AC filter inductor was designed for minimal loss by adjusting the core diameter, height, and number of winding turns. The efficiency and volume optimization achieved by designing a proper inductor was verified via comparison with a base design. Furthermore, the design method was validated via a comparison of the simulation and experimental results.

In this study, an 835 W output three-phase PWM inverter with an AC filter, as shown in Fig. 1, was used as the design target. Herein, the inverter board (KIT8020-CRD-88FF1217P-1, Cree) was used as the main circuit board. SiC-MOSFET (SCT2280KE, ROHM) and SiC-SBD (SCS220KE2, ROHM) were used in the power device. A film capacitor (HBP series, Shizuki) was used as a filter capacitor.

FIG. 1.

Three-phase PWM inverter with AC filter.

FIG. 1.

Three-phase PWM inverter with AC filter.

Close modal

As the design requirement of the AC filter inductor, the inductor current ripple was set to 40% of the maximum amplitude of the fundamental output. At an output of 835 W, the maximum amplitude of the fundamental output was 4 A. The required inductance calculation method has been reported in Ref. 13. In accordance with Ref. 13, the inductance values of the AC filter were 1.26 mH at 20 kHz, 0.63 mH at 40 kHz, and so on. The magnetic material of the inductor incorporated an iron powder provided by Toho Zinc. Corp.; the core list is shown in Table I.

TABLE I.

Available core list.

No.Core nameVolume [cm3]
SK-14M 8.8 
SK-16M 7.4 
SK-20M 13.2 
SK-24AM 25.0 
SK-28M 28.0 
SK-36M 48.0 
No.Core nameVolume [cm3]
SK-14M 8.8 
SK-16M 7.4 
SK-20M 13.2 
SK-24AM 25.0 
SK-28M 28.0 
SK-36M 48.0 

In this study, two inductor designs were considered. The inductance value is defined as

L=μSeleN2,
(1)

where N is the number of winding turns, μ is the permeability, Se is the core surface area, and le is the effective core length.

The first method (base design) incorporated the SK-24AM inductor shown in Table I, and the design was achieved by adjusting the core height as shown in Fig. 2(a). Adjusting the core height while maintaining the core length reduced the core surface area Se; thus, the inductance value could be adjusted without changing the number of winding turns or wire diameter. In the second method (proposed design), the inductor core was selected from Table I, and the inductor was designed for minimal loss by adjusting the core diameter, height, number of winding turns, and wire diameter, as shown in Fig. 2(b). In this case, the wire diameter was selected in relation to the core size and number of winding turns, with magnetic saturation being avoided. With reference to the efficiency and volume miniaturization of the base design, the improvement in these parameters achieved upon designing a proper inductor was then analyzed.

FIG. 2.

AC filter inductor design: (a) Base design, (b) Proposed method.

FIG. 2.

AC filter inductor design: (a) Base design, (b) Proposed method.

Close modal

The efficiency η of a three-phase PWM inverter can be calculated using

η=PoutPin=PinPInductorPDevicePin,
(2)

where Pin is the input power of the inverter, Pout is the output power of the inverter, PInductor is the AC filter inductor loss, and PDevice is the power device loss.14 

The semiconductor device loss PDevice in the three-phase inverter using the PWM inverter has been previously reported in Ref. 15. Furthermore, if the switching device loss is known, the heatsink can be selected from the heatsink catalog to operate at temperatures under 100°C.6 

The AC filter inductor loss PInductor is the sum of the total value of copper loss PCu and iron loss PFe, as shown in Eq. (3). The iron loss PFe of the AC filter inductor used in the three-phase PWM inverter was divided into two losses expressed by the total value of the low- and high-frequency iron losses (PLF and PHF, respectively), as reported in Ref. 7:

PInductor=PCu+PFe=PCu+PLF+PHF.
(3)

The iron loss PFe was calculated using the Steinmetz equation16 and loss map method.7 The copper loss PCu was calculated using Eq. (4). In this calculation, the skin effect was considered because the high-frequency switching ripple current flows to the outer part of the copper wire. Swire was varied according to skin depth δf=1πfμσ.

PCu=3f=0RwirefiLf2=3f=0ρNlturnSwire(f)iL(f)2,
(4)

where ρ is the resistivity of the winding, lturn is the average turn length, Rwire(f) is the resistance of the winding for each frequency component, iL(f) is the effective value of the output current for each frequency component, Swiref=πr2π(rδ(f))2 is the cross-sectional area of the winding for each frequency component, and r is the radius of the cross-sectional area of the winding.

FIG. 3.

Inductor losses: (a) Inductor loss, (b) Copper loss, and (c) Iron loss.

FIG. 3.

Inductor losses: (a) Inductor loss, (b) Copper loss, and (c) Iron loss.

Close modal
FIG. 4.

Pareto front curve.

FIG. 4.

Pareto front curve.

Close modal

Estimated inductor losses for the proposed method are shown in Fig. 3(a), and the breakdown of inductor losses is shown in Fig. 3(b) and Fig. 3(c). The number in each figure is the rerated core name listed in Table I. As per the heuristic knowledge of a power electronics designer, the iron loss is proportional to core size, and the copper loss is inversely proportional to core size. However, the iron loss of an AC filter inductor does not always follow such a heuristic trend. This characteristic arises from the high-frequency iron loss, because this loss manifests in complicated ways depending on the switching ripple current, DC-bias excitation, and other factors.7–12 In the proposed method, the inductor core for switching frequency is selected in minimal loss points. For example, core No. 5 is selected for a switching frequency of 40 kHz.

To evaluate not only the AC filter inductor design but also total PWM inverter performance, a Pareto front curve was created. The Pareto front curve indicates the tradeoff relationship between the power density and efficiency for various switching frequencies.3Fig. 4 shows the Pareto front curve when the switching frequency is changed from 20 kHz to 80 kHz. As observed, for the base design, the optimum point was 60 kHz. On the other hand, for the proposed design, the optimum point was 40 kHz. The volume breakdown for the proposed method is shown in Fig. 5. After the optimum point of 40 kHz, the rate of increase in the volume of the heatsink exceeded the rate of decrease in the volume of the filter inductor after the optimum points. The efficiency in the experiment was measured using a power meter (YOKOGAWA: WT3000). The simulation and experimental efficiencies differed by less than 0.4%. The PWM inverter with an AC filter was well designed using the proposed method. Furthermore, for a proper AC filter inductor design, the inverter efficiency and volume miniaturization were improved by 0.2% and 0.25 W/cm3, respectively.

FIG. 5.

Volume breakdown of proposed method.

FIG. 5.

Volume breakdown of proposed method.

Close modal

This paper proposes a design method for three-phase PWM inverters that include an AC filter. The inverter efficiency and volume-miniaturization are improved when designing an inductor are based on numerical analysis values rather than on heuristics. A simulation of the proposed design method showed that the inverter efficiency and volume miniaturization can be improved compared to those of the base design by up to 0.5 % and 0.25 W/cm3, respectively. In addition, the validity of the proposed method was established in the experiment because the efficiency difference is less than 0.4 %. Since no practical research has been published regarding the optimization of AC filter design in PWM inverter, this paper represents a breakthrough in this area.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
M.
Nakahara
,
Y.
Kawaguchi
,
K.
Furukawa
,
M.
Kadota
,
Y.
Mabuchi
, and
A.
Kanoda
, “
Development of a control method for LLC converter utilized for input-parallel-output-series inverter system with solid-state transformers
,”
IEEJ J. Industry Applications
8
(
4
),
652
659
(
2019
).
2.
G.
Engelmann
,
A.
Sewergin
,
M.
Neubert
, and
R. W. D.
Doncker
, “
Design challenges of SiC devices for low- and medium-voltage DC-DC converters
,”
IEEJ J. Industry Applications
8
(
3
),
505
511
(
2019
).
3.
J. W.
Kolar
 et al, “
Exploring the Pareto front of multi–objective single-phase PFC rectifier design optimization −99.2% efficiency vs. 7 kW/dm3 power density
,” in
IPEMC 2009
,
China
,
2009
.
4.
R.
Pilawa-Podgurski
, “
The future of power electronics circuits: New technologies and managed complexity will drive the future
,”
IEEE Power Electron. Mag.
7
(
2
),
41
43
(
2020
).
5.
A. J.
Marques Cardoso
, “
Power electronics design methods and automation in the digital era: Evolution of design automation tools
,”
IEEE Power Electron. Mag.
7
(
2
),
36
40
(
2020
).
6.
M.
Mirjafari
and
R. S.
Balog
, “
Survey of modeling techniques used in optimization of power electronics components
,”
IET Power Electron.
7
,
1192
1203
(
2014
).
7.
H.
Matsumori
,
T.
Shimizu
,
K.
Takano
, and
H.
Ishii
, “
Evaluation of iron loss of AC filter inductor used in three-phase PWM inverters based on an iron loss analyzer (ILA)
,”
IEEE Trans. on Power Electronics
31
,
3080
3095
(
2016
).
8.
Y.
Miwa
,
T.
Shimizu
,
K.
Takano
, and
H.
Ishii
, “
Calculating the iron losses in gapped inductors using the loss-map method
,”
IEEJ Journal of Industry Applications
8
(
1
),
57
65
(
2019
).
9.
H.
Matsumori
,
T.
Shimizu
,
X.
Wang
, and
F.
Blaabjerg
, “
A practical iron loss model for filter inductors of switched power converters
,”
IEEE Journal of Emerging and Selected Topics in Power Electronics
6
,
29
39
(
2018
).
10.
J.
Mühlethaler
,
J.
Biela
,
J. W.
Kolar
, and
A.
Ecklebe
, “
Core losses under the DC bias condition based on Steinmetz parameters
,”
IEEE Trans. Power Electron.
27
,
953
963
(
2012
).
11.
C. R.
Sullivan
,
J. H.
Harris
, and
E.
Herbert
, “
Core loss predictions for general PWM waveforms from a simplified set of measured data
,” in
Proceedings of the Applied Power Electronics Conference and Exposition
,
2010
, pp.
1048
1055
.
12.
H.
Matsumori
,
T.
Kosaka
, and
N.
Matsui
, “
Core loss calculation for power electronics converter excitation from a sinusoidal excited core loss data
,”
AIP Advances
10
(
4
),
045001
(
2020
).
13.
G.
Grandi
and
J.
Loncarski
, “
Evaluation of current ripple amplitude in three-phase PWM voltage source inverters
,” in
2013 International Conference-Workshop Compatibility and Power Electronics
,
Ljubljana
,
2013
, pp.
156
161
.
14.
K.
Berringer
,
H.
Marvin
, and
P.
Perruchoud
, “
Semiconductor power losses in AC inverters
,” in
IEEE IAS Annual Meeting
,
1995
, pp.
341
345
.
15.
D.
Mizutani
,
H.
Matsumori
,
T.
Kosaka
,
N.
Matsui
,
T.
Miyazaki
, and
Y.
Okawauchi
, “
Design study on AC filter inductor for three-phase PWM inverter
,” IEEJ Japan, SPC-20-147,
2020
(in Japanese).
16.
C. P.
Steinmetz
, “
On the law of hysteresis
,”
Proc. IEEE
72
(
2
),
197
221
(
1984
).