Increasing Power Density of Single-phase Power
Converter by Reduced Passive Components Volume
for Short-time Operation
Kodai Nishikawa
Dept. of Science of Technology
Innovation
Nagaoka University of Technology
Nagaoka, Japanknishikawa@stn.nagaokaut.ac.jp

Keisuke Kusaka
Dept. of Electrical, Electronics, andInformation Engineering
Nagaoka University of Technology
Nagaoka, Japan
kusaka@vos.nagaokaut.ac.jp

Abstract— This paper proposes a design concept of shorttime rated ripple current for electrolytic capacitors and theconcept method of inductors that accepts a magnetic saturationin order to reduce the volume of passive components. The shorttime rated ripple current for DC-link capacitors is determinedby the operation time of power converters and the transient
temperature rise characteristic of the electrolytic capacitorswith the ripple current exceeding the rated current. The relation
between the operation time of the power converters and thecurrent value of the electrolytic capacitors is derived by thethermal characteristics of the electrolytic capacitors. The
thermal characteristics are obtained by the experiment for thetemperature measurement of the element of the electrolytic
capacitors. Besides, this paper provides the design concept of thegrid-connected inductor from the magnetization characteristicof magnetic materials in order to reduce the size. The effect of
the reducing inductor volume by 15% is demonstrated by thecalculation with the experimental results.
Keywords— Short-time operation, Passive component,
Electrolytic capacitor, magnetic saturation, InterconnectedinductorI.

INTRODUCTION

Optimization methods of the passive components are
crucial for increasing the power density [1–3]. Mainly thepower density limit results from the DC-link capacitors insingle-phase inverters because the electrolytic capacitors areused as the DC-link capacitors in large-capacity power
converters[4]. Some approaches have been proposed in [1–2,
5-7] in order to reduce the DC-link capacitor volume. The
volume is reduced by adapting additional circuit in [1-2], andimproving control methods in [5]. In [6–7], the optimization
methods are proposed by selecting the DC-link capacitors
using the capacitors losses or temperature. However, the DClink capacitors is designed to satisfy the rated ripple current of
the capacitors in the conventional methods. Thus, the rated
ripple current is the constraint to the volume reduction of theDC-link capacitors especially for the electrolytic capacitors.
Besides, the grid-connected inductors is also significant
problem in terms of the volume reduction of the power
converter. Generally, increasing switching frequency orallowing large output current ripples help to reduce the gridconnected inductor volume. The optimization methods of thegrid-connected inductors have been proposed from theperspective of EMC[8-11]. However, a minimization of theinductor volume is limited because the grid-connectedinductors are generally designed in the linear region of themagnetization characteristics in order to avoid the saturationof the magnetic cores.

XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE

Jun-ichi Itoh
Dept. of Science of Technology
Innovation
Nagaoka University of Technology
Nagaoka, Japan
itoh@vos.nagaokaut.ac.jp

This paper proposes two design methods in order to reduce
the passive component volume for the specific power
converters, which operate only at the rated power for a shorttime, such as uninterruptible power supplies (UPS) and home
appliances compressors. The first method is to adapt thedesign concept of short-time rated ripple current to theelectrolytic capacitors. The electrolytic capacitors allow ripple
currents exceeding the rated value based on the transient
capacitor temperature. The second method is adapting thedesign concept of the inductor that allows the magnetic
saturation. Allowing magnetic saturation leads to increased
losses due to the expanded operating range of the magnetic
flux density; however, the increase of losses can be accepted
due to the short-time operation. The example of the inductor
design using the proposed design method is shown to confirm
reducing inductor volume. In addition, the operation of thepower converter with the inductors that allow a magnetic
saturation is experimentally demonstrated. The originality ofthis paper is providing a design procedure for the power
converters operated for a short-time for downsizing.
II.

REDUCTION METHOD OF DC-LINK CAPACITOR
VOLUME

A. Short-time rated current of electrolytic capacitors
Figure 1 shows the relationship between the ripple current
and the temperature rise of the electrolytic capacitors. The
temperature rise occurs due to dielectric loss and joule loss on
the resistance of terminals or lead wires when a ripple current
flows through the electrolytic capacitors. The excessive
temperature rise causes failures such as a vent operation due
to increasing internal pressure, increasing tan , andcapacitance reduction. The rated ripple current of theelectrolytic capacitor is determined by the allowabletemperature rise from a maximum category temperature of theelectrolytic capacitors. However, the temperature rise does notexceed the allowable temperature rise when the operation time
is sufficiently shorter than several times the thermal time
constant. Thus, the electrolytic capacitors allow an excess of
the ripple current for the short-time operation (the short-time
ripple current). The short-time rated ripple current isdetermined by considering a transient temperature risecharacteristic of the electrolytic capacitors. Here, theequivalent series resistance (ESR), thermal resistance, andthermal time constant are assumed as constant values with thetemperature change. The heating value of the electrolytic
capacitors is the product of the ESR value and the square of
XIrated, where X is the ratio of the flowing ripple current to therated ripple current. The temperature rises from the ambient
temperature to the steady temperature is the product of theheating value and the thermal resistance. Thus, the steady
temperature Tsteady is given by

where Treted is the steady temperature rise when the rated
ripple current flows, RESR is the ESR value at twice thedominant frequency, Rth is a thermal resistance from anelement of the capacitors to an ambient.
From (1), the temperature rise to the steady-state is X2
times Treted when a ripple current that is X times the rated
value flows. Therefore, the amount of the transient
temperature rise Trise is given by



2



 t   Trise = X Trated 1 − exp  −From (2), the allowable ripple current ratio X, which is theratio of the short-time rated ripple current to the rated ripple
current, is given by−1 t   Trise1 − exp  −      Trated


Table 1 shows the experimental conditions. The pulsation
voltage of the DC-link capacitor of single-phase power
converters is replicated by applying a voltage of 100 Hz AC
and DC bias. The ambient temperature is kept constant at
60°C using a constant temperature chamber, assuming that theelectrolytic capacitors are used inside a power converter
housing. The operable temperature rise is set to Trise = 29°C
based on 60°C due to the maximum allowable electrolytic
capacitor temperature.
Figure 3 shows the temperature rise characteristics when
the ripple current is twice the rated value. The temperature of
the minus tab is the highest in the measurement points. The
allowable temperature of the minus tab is sufficiently higher
than that of the element using an electrolytic solution. The
maximum temperature of the minus tab is required to bearound 110°C in order to ignore the effect of the heatdissipation from the minus tab on the life of the electrolytic
capacitors. Focusing on the temperature rise of the element ofcapacitors, the temperature at the center of the element ishigher than the temperature at the side of the element. This isbecause that heat dissipation at the center of the element isharder than at the side of the element in spite of the heatgenerated by the element of the capacitors is uniform. Thus, it
is sufficient to consider the temperature rise characteristic of
the center of the element, which is the hottest in the elementof the capacitors, when considering the short-time rated

Trated

IC = 1.5

IC = 1.0
Operating temperature

Ambient temperature

Time

Operable time t

Fig. 1. Relationship between the ripple current and the temperaturerise of the electrolytic capacitors.

+

Minus tab-Side of theelement

Center of theelementC
B A+

The elementof capacitors(a) Temperature measurement point (b) Circuit configuration
Fig 2. Experimental configuration to measure capacitor temperature(3).

B. Thermal measurement of electrolytic capacitors
Figure 2 shows the experimental configuration to measure
the transient temperature characteristics of the electrolytic
capacitors. There are three temperature measurement points
for the electrolytic capacitor: the center of the element, theside of the element, and the minus tab. T-type thermocouples
are used for temperature measurement. A DC regenerative
power supply connected in series with the electrolytic
capacitor is used as the power supply as a variable voltage
source.

IC = 2.0

IC = 1.0
Maximum category temperature(2),

where  is a thermal time constant, and t is an operation timeof power converters.

X =Temperature rise

(1),

Table 1. Experimental parameters.
DC bias voltage

V dc

30 V

Applied voltage

V sine8.1, 16.4, 20.3 V

Applied frequency

f sine100 HzApplied current

I sine42.7, 85.4, 106.8 Arms

Capacitor: ECSH401LGN123MFH0N
NIPPON CHEMI-CON
Capacitor rated voltage

C

12 mF

V rated

400 V

Maximum category temperature

T rated

85°C

Rated ripple current (85°C, ΔT :10°C)

I rated42.7 Arms

Equivalent Series Resistance(ESR)(60 °C, 100 Hz)

R ESR

2.9 ~ 3.3 m

Temperature[°C]2

C: Minus tab

120
110
100

A: Center of the element9080

B: Side of the element

70
60
50

0

1000

2000

3000

4000

5000

6000

Time[s]Fig. 3. Capacitor temperature rise characteristics.
130

Temperature[°C]Tsteady = X 2 Trated = RESR ( XI rated ) Rth

IC = 1.0p.u. : Rated ripple current
Dangerous temperature

IC = 1.0p.u. : Rated current

Calculated result

120
110

IC = 2.5100

Rated temperature90

IC = 2.080

IC = 1.0

70
60

50
0

2000

4000

6000

Time[s]Fig. 4. Temperature comparison between calculated value andmeasured value.

current and the operable time of short-time operation power
converters.
Figure 4 shows measurement results and calculation
results of temperature rise characteristics with one time, twotimes, and 2.5 times the rated current. The thermal time
constant in calculation results is set to 4150 seconds calculated
from the initial temperature to the 63.2% of steady
temperature based on the heat generation test result under thecondition of 68 Arms (IC = 1.6p.u.), 40°C and 120 Hz. The
thermal resistance from the center of the capacitor to ambient
has been obtained from the slope of the approximate curve byplotting the relationship between the heat generation, which isthe product of ESR and a ripple current squared, and thesteady temperature. The heat capacity has been calculated
from the relation between the thermal time constant andthermal resistance.
According to the temperature rise characteristics, theoperable time is 2508 seconds in the measurement result and2587 seconds in the calculation result, which is about 3%
longer than the measurement result with 2.5 times the rated
current. Therefore, the derived relationship between the shorttime rated current and the operable time is confirmed from theexperiment. Error factors in calculation results are that the loss
caused by the anodic oxide films of the electrolytic capacitors
has temperature dependence.
C. Calculation method of the short-time rated current
The short-time rated current can be obtained by the steady
temperature, thermal resistance, and thermal time constantusing the heat generation test results for a certain period oftime. Thus, doing the heat generation test is not necessary until
the time that the temperature rise is saturated. Assuming that
ESR, thermal resistance Rth, and thermal time constant  areconstant at the time of temperature change, the temperature Ttafter t seconds derived by the steady temperature Tsteady andthe ambient temperature Tambient, is given by t 
Tt = Tsteady − Tambient 1 − exp  −  + Tambient

(

)



The following equationtransformation of (4)(4).

  
isobtained t
Tsteady − Tt = (Tsteady − Tambient ) exp  − byformula
(5).

 

(

)

t

(6).



The temperature is measured at regular time intervals, t = t1,
t2, t3, ..., tn, in the heat generation test. The following equation
is obtained from substituting the two adjacent measurement
points t1 and t2 into (6) to obtain the differenceln (Tsteady − Tt1 ) − ln (Tsteady − Tt 2 ) =1Tsteady − Tt 3

 t −t = exp  3 2 
 

(9).



Because the right sides of (8) and (9) are equal, Tsteady isgiven byTsteady =Tt 1Tt 3 − Tt 2 2(10).

Tt1 + Tt 3 − 2Tt 2

The steady temperature can be obtained from the heatgeneration test results in a short time by applying (10) tomultiple measurement points and finding the average of thecalculated Tsteady. The thermal resistance and thermal time
constant can be estimated using the obtained steady
temperature average Tsteady_avg. The thermal resistance Rthderived ESR and applied current Iripple is given byRth =Tsteady(11).

RESR  I ripple 2

The thermal time constant derived by Tsteady_avg, Tambient andthe measured temperature Ttn is given by Tsteady _ avg − Tambient t= ln  T
 steady _ avg − Ttn (12).
From (12), it can be obtained by substituting themeasurement results and calculating the slope by the leastsquares approximation since the thermal time constant  is thereciprocal of the slope.
The instance of the calculation the short-time rated current
for an operating time of 10 minutes is shown using themeasurement results at 2.5 times the rated ripple current. The
steady temperature Tsteady, thermal resistance Rth, the thermal
time constant  are 123.1°C, 1.79 K/W and 3383 seconds
using (10), (11) and (12), respectively. The ESR is 3.1 m
from table 1. The temperature rise value at the steady
temperature with the rated ripple current is Trated = 10.1°C
substituting the obtained thermal resistance into (1).
Assuming that the allowed temperature rise value is 29°C, theshort-time rated current is the current at which Trise = 29°C
at t = 600 seconds, 10 minutes. The ratio of the short-time
rated current to the rated ripple current X derived from (3) isgiven by−1

Finding the equation of a natural logarithm on both sides of(5) produces
ln Tsteady − Tt = ln (Tsteady − Tambient ) −Tsteady − Tt 2(t − t )
2

1

(7).

Finding the equation of an exponential function on both sidesof (7) produces
Tsteady − Tt1
 t −t (8).
= exp  2 1 
Tsteady − Tt 2
  
Furthermore, substituting t2 and t3 into (6) to obtain the
difference producesX = 600   29
 4.48
1 − exp  − 3884   10.1


(13).

It can be estimated that the current of 4.48 times the rated
ripple current can be accepted as the short-time rated current
during a 10-minutes operation.
D. Expected lifetime during the short-time operation
In order to estimate the expected lifetime of the electrolytic
capacitors with a short-time operation, it is necessary toestimate the expected lifetimes when the converter isoperating and when it is not operating. In [12], an expected
lifetime LX (hours) of a screw terminal type electrolytic
capacitor derived by an endurance time Le, maximum categorytemperature Tmax, ambient temperature Tambient, temperaturerise value with the rated ripple current Trated, acceleration
factor of temperature rise value due to the ripple current A,
correction factor of an ambient temperature acceleration factor
Kt and derating voltage factor KV is givenKt (Tmax −Tambient )Trated −T

2

10

(14).

 KV

A

From (14), the expected lifetimes that the converter isoperating LX1 and not operating LX2 (shelf lifetime) can be
estimated. The combined expected lifetime LXcombined of the
combined LX1 and LX2 derived the ratio of an operation time
R1, the ratio of a non-operation time R2, LX1 and LX2 is givenbyLXcombined =

1

(15).

R 
 R1
+ 2 

L
L
 X1
X2 
Table 2 shows the example of the condition for theestimation to the combined expected lifetime of theelectrolytic capacitors using (14). Substituting the conditions
into (14), the expected lifetimes during operation LX1 and nonoperation LX2 are 26,677 hours and 219,230 hours,
respectively. Assuming that the operating time is 10 minutes
per day, R1 and R2 are 0.69% and 99.31%, respectively. The
combined expected lifetime LXcombined is about 23.8 years whencalculated by substituting into (15).

III.

REDUCTION METHOD OF INTERCONNECTEDINDUCTOR VOLUME

A. Design concept of inductors that allow a magnetic
saturation
Figure 5 shows the circuit diagram of the grid-tied inverter.
The inductance L as the grid-tied inductor is designed under
the condition that the allowable ripple current rI is satisfied at
the point where the maximum value of an inverter output
current.
Figure 6 shows the magnetization characteristic of themagnetic material used in a design. In this case, the boundary
between the linear region and the non-linear region of themagnetization characteristic is approximately 0.9 T. Nonlinearity due to a magnetic saturation is expressed by thefunction H(B), which is a polynomial approximation of themagnetic field H with the magnetic flux density B. The
derivative of H(B) is the reciprocal of the magnetic
permeability of an iron core C. The effect of air gaps on
magnetic permeability is expressed by C and the relationshipbetween an iron core magnetic path lC and an air gap length lg.
When lC >> lg, the equivalent magnetic permeability eq,
which combines the magnetic permeability of the core and the
air gap, is given by
−1

−1

lg 
lg 
 1
 dH ( B )eq = ++ =lC  0  C lC 0  dB
where 0 is a magnetic permeability in a vacuum.

(16),

The integral of the reciprocal of eq is the equivalentmagnetization characteristic Heq(B). Thus, Heq(B) is given by
H eq ( B ) = H ( B ) +

lg
lC 0

(17).

B

Figure 7 shows the shape of the inductor to be designed. It is
assumed that the cross-section and the magnetic path of theiron core are square. When lC >> lg, the volume VolL covered
rectangular is approximated by(

VolL  2 AW + 2 AC)( A + 2 A )( 2 A + A ) (18),
W

C

W

C

Table 2. Condition of estimation to the life time with the short-time
operation.
The conditions when
SymbolThe conditionsof characteristicsof the capacitor

The converter isoperation

The converter is
not operation

Le

2000

2000

T max

85

85

 T rated

10

10

T ambient

45

45

T

16.2

0

Kt

1.09

1.09

KV

1

2.67

A

10

10

The conditions
depending usage
environment

Prated : 50 kVA

Iout : 250 Arms

Iripple : rIIout rI : 0.2
fSW : 10 kHz

VDC : 350 V

L: 76.8 H%Z: 3.01%

VGrid : 200 Vrms
fGrid : 50 Hz

Magnetic flux density [T]

LX = Le  2

Fig. 5. Single-phase inverter.
Conventional
Proposal design
design

1.4

B

1.2
Bm

1

Non-linear region
0.9 T

0.8

H

0.6

Iripple

0.4
0.2

Linear region

0
0

50

Hm

100

150

200

250

Magnetic field [A/m]300

Fig. 6. Magnetization characteristic of the inductor core.
Plan view

Side view
lC

AC

AW

lg

N
Space factor, Ku: 0.7

Current density, J: 4 A/mm2

Fig. 7. Configuration of the designed inductor.

where AC is a cross-sectional area and AW is a window area ofthe core. The window area AW is given byAW =I out N
Ku J

(19),

where N is a number of turns of wire, J is a current density ofwire, Ku is a space factor of an inductor, Iout is an RMS output
current value.
The cross-sectional area AC of the iron core is derived byan allowable magnetic flux density Bm and an allowable ripple
current ratio rI. Assuming that there is no leakage in themagnetic field generated by the inductor winding, the crosssection AC1 derived by Bm is given by 2 I out N
AC1 = 
 4 H ( B ) − AW 
m



2

(20).

The ripple magnetic flux density B corresponding rI is
estimated by Heq(B). The cross-section AC2 derived by B isAC 2 =(

2VGrid VDC − 2VGrid

)

(21),

N Bf SW VDC

where VDC is an input voltage of a DC-AC converter, VGrid is
a RMS voltage value of a power grid, and fSW is a switchingfrequency.
The condition for the inductor to satisfy rI is AC1 ≥ AC2.
Therefore, AC is determined by the minimum number of N thatsatisfies this condition.

Ripple current peak-peak [A]given by

VDC: 500 V, Vgird: 200 Vrms

40
35

30

VDC: 350 V, Vgird: 100 Vrms

25
20
15
VDC: 350 V, Vgird: 200 V rms

1038.2 deg.

562.1 deg.

050

Figure 8 shows the example of the ripple current value
characteristics according to an inductor current phase  withassuming that a power factor is a unity and an inductance L isconstant. From (21), AC2 is calculated on the condition that = 90 deg. that a sin wave and a magnetic flux density is
maximum. Thus, the considering of the ripple current value
characteristics is required when the decreasing of inductanceby magnetic saturation is a few henries. Assuming a power
factor equals one, a ripple current value Iripple derived by VDC
and VGrid sin(), is given byI ripple =(2VGrid sin ( ) VDC − 2VGrid sin ( )Lf SW VDC)

100

Fig. 8. Ripple current characteristics.
START
Approximate H(B) of used magnetic substance
Decide VDC, VGrid, fSW, Iout, rI, J, Ku, lCref
Set Bm to initial value
Set lg to initial value
Set N to initial value
Set lCref to initial value
Estimate Heq(B) by H(B), lCref ,lg

Calculate ΔH by Iout, rI
Calculate Hm by Bm
using Heq(B)Estimate ΔB by ΔH(22).
Increase N

Calculate AC1, AC2

Increaseordecrease lCref

2 2VGrid(23).

From (23), the phase that a ripple current value ismaximum ripple_max equals 90 deg. on the condition that VDC
is higher than 2 2 VGrid. Thus, using (21) is only required forthe calculation of AC2 on this condition. On the other hand, thecalculation of AC2ripple_max is required for the considering of aripple current value characteristic on the condition that VDC islower than 2 2 VGrid. From (21), the cross-section AC2ripple_max
is calculated by Bripple_max and 2 VGrid sin(ripple_max). The
ripple magnetic flux density Bripple_max is estimated by rI,
Heq(B) and the inductor current that the phase is ripple_max. The
additional condition for the inductor to satisfy rI is AC1 ≥AC2ripple_max.
Figure 9 shows the flowchart of the proposed design
method. Considered conditions of the method are an allowablemagnetic flux density Bm, an air-gap length lg. Variables are
the number of the turn of wire N and the magnetic path length
lCref. The magnetic mean path length lC is calculated frominductors and variables at the estimated volume. The volume
is decided when variables satisfy conditions AC1 ≥ AC2, AC1 ≥AC2ripple_max and lCref ≈ lC.
B. Design Example
The interconnection inductor is designed using the circuit
parameters shown in Figure 5.
Figure 10 shows the calculation results of the inductor
volume with changing Bm from 0.05 to 2.0 T in 0.05 T
increments and lg from zero to 30 mm in 0.5 mm increments.
The minimum inductor volume is 2.04 L at Bm = 1.2 T and lg= 8.5 mm. In contrast, the minimum inductor volume is 2.40
L when a non-liner region of magnetization characteristics (BmCalculate AC2ripple_max

Yes
AC1>AC2
AC1>AC2ripple_max

Increase lg

Yes
Estimate a inductor volume

Increase Bm
No

lCref ≒ lC

No

Yes
lg = lgmax

NoYes
Bm = Bmmax
Yes
END

Fig. 9. The flowchat of calculation for inductor volume.
6

Inductor volume [L] ripple _ max = sin

No

VDC ≥ 2 2 VGrid
No

VDC

150

Inductor current phase [deg.]

From (22), the phase that a ripple current value is maximum
ripple_max is given by−1

90 deg.

0

5

4
3

Proposal
design region

Conventional
design region

21

Minimum volume
Bm: 1.2 T, lg: 8.5 mm

Minimum volume
Bm: 0.9 T, lg: 12 mm

0
0

0.5

1

1.5

Main magnetic flux density, Bm [T]2

Fig. 10. Results of inductor volume calculation.

is from 0.95 to 2.0 T) is not used. The proposed design method
reduces the inductor volume by 15%
C. Experiment with inductors that allowed magnetic
saturation
Figure 11 shows the inductance characteristics with theinductor current value iL used in the experiment. The required
inductance conditions of the used inductor are determined to
be two types of inductance to satisfy rI. The first is the required
inductance without allowing a magnetic saturation Lconst. The
second is the required inductance with allowing a magnetic
saturation on the maximum magnetic flux density Lsaturated.
Lconst is given by(

2VGrid sin ( ripple _ max ) VDC − 2VGrid sin (ripple _ max )rI I Out f SW VDC) (24).

LVolmin ( iL ) =lC _ Volmin

300

NVolmin iL
lC _ Volmin

200

(25).

CONCLUSION

This paper proposes the design concept of short-time rated
current for the electrolytic capacitors and the estimation
method of inductor volume using magnetic saturation. The
temperature measurement in the experiment clarifies thederived relationship between the operable time and the shorttime current rating. The result is an error of 3% between themeasured and calculated operable times under the condition
that the current of 2.5 times the rated current is flowing.
Besides, the design example of the inductors that allow amagnetic saturation is shown to demonstrate the effect of the
proposed design method. The proposed design achieves the
reduction of the inductor volume by 15% compared to thevolume of non-magnetic saturation design. In addition, theexperimental results shows the THD is 15.1% on the samelevel with the non-saturated inductor.
REFERENCES

[2]

[3]

rI = 0.4100
50

2 I out

00

The inductance Lsaturated is the range represented by iL =2 Iout  0.5rIIout in LVolmin(iL).
Figure 12 shows the output current waveform of theexperiment with the inductor that allowed magnetic
saturation. The ripple current ratio of the inductor current
satisfies the condition. In addition, the total harmonic
distortion (THD) of the inductor current is 15.1%. Thus, it isconfirmed that the desired ripple current ratio can be satisfied
by the appropriate inductance characteristics when the
reduction of the inductance due to a magnetic saturation isallowed.

[1]

Lsaturated

150

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May/June 2017.

10

20
30
40
Inductor current, iL [A]50

Fig. 11. Inductance characteristics of the interconnected inductor.
Table 3. Experimental parameter.

(26).

IV.

Lconst250

where eq_Volmin is derived by (16) using the magnetic path
length lC_Volmin and the air-gap length lg_Volmin. A magnetic field
derived by NVolmin and lC_Volmin, is given by
H ( iL ) =Interconnected inductor

350

The inductance Lsaturated is derived by the inductancecharacteristic LVolmin(iL) with the calculated inductor shapeconditions that the volume is minimum. The inductancecharacteristic LVolmin(iL) derived by the number of turns NVolmin,the magnetic path length lC_Volmin, the cross-section AC_Volmin
and the equivalent magnetic permeability with eq_Volmin , isgiven by2
NVolmineq _ Volmin ( H ( iL ) ) AC _ Volmin

400

Inductance, L [H]

Lconst =DC-link voltage

V DC

350 V

Power grid voltage

V Grid200 Vrms

Output current

I out

25 Arms

Switching frequency

f SW

10 kHzRipple current maximum phase ripple_max

38 deg.

Required constant inductance

L const310 HrI

0.4

Allowable ripple current ratio

0V

350 V

Input voltage, VDC [200 V/div]

THD: 15.1%
rI = 0.4

Inductor current, iL[10 A/div]
25 Arms

0A

5 ms/div

Fig. 12. Inductor current waveform with the inductor that allowedmagnetic saturation.
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