Basic design considerations for a three-stage dc-to-dc converter for the NEPTUNE
power system. A trade-off study comparing low-frequency, three-stage and highfrequency, fifty-stage designs
Vatché Vorpérian
February 20, 2002
I. Introduction
The original proposed design of the dc-to-dc node converter for the NEPTUNE power
system consists of fifty high-frequency dc-to-dc converters connected in series on the
primary and in series-parallel combination on the secondary to meet the requirements of a
10kW, 10kV DC input and 400V DC output converter. It is desired that the ripple current
injected on the line be less than 1mA at the switching frequency because the line consists
of a 3000 mile cable on the bottom of the ocean. It is deemed that fifty converters may
raise reliability issues from a parts count standpoint. Hence, it has been recommended
consideration be given to a design using three converters only. Among the key benefits
provided by the design using fifty converters are the low-volume and the very high
reliability of low-voltage stress and small size of high-frequency (50kHz) PWM
converters. In what follows, some key design consideration are given for a three-stage
converter in terms of part selection and frequency of operation.
II. Design of a three-stage converter.
The three stage input converter is supposed to be designed with the assumption that if one
of the stages fails short, then the remaining two will continue to operate. Assuming that
this can be done, each input stage will have to be designed to withstand half the input
voltage of 5kV. At such elevated voltages the use of high frequency parts at 50kHz is
essentially precluded. Hence, the frequency must be dropped to at least 5kHz in order to
find appropriate parts with proper de-rating. The first section of a switching converter
stage is the input filter. The LC product of these filters is essentially inversely
proportional to the square of the switching frequency while maintaining the same input
and output voltage and current ripple requirements. Hence, dropping the frequency by a
factor of ten implies an increase in the value of LC by a factor of 100. Additionally, the
voltage rating of the capacitors will have to increase by a factor of 50/2. With these facts
in mind, let us begin by considering the design of the input filter.
2.1 Design of the input filter
The input filter of each stage consists of two LC stages with their respective damping
branches as shown in Fig.1a. The average input current to the filter is 1A when
delivering 10kW. Hence, the switching power supply can be represented in a very
simplistic manner by a pulsating square wave current with 50% duty cycle and 2A
amplitude as shown in Fig.1b (its average being 1A as seen on the input side of the filter).
To show the effectiveness of the filter and its damping characteristics, the transient input
current and the steady state input ripple current are shown in Figs. 2 and 3 respectively.
The parts for the components in this filter are determined next.
L1
50mH
1
L2
50mH
2
1
R1
250
2
R2
250
C1
1uF
C4
6uF
C2
1uF
C3
6uF
0
(a)
(b)
Figure 1
Figure 2
Figure 3
I1
TD = 0
TR = 1usec
TF = 1use c
PW = 98usec
PER = 200use c
I1 = 0
I2 = 2
1. Capacitors C1, C2, C3 and C4:
These are available from Hivolt Capacotors Limited in their PMR range of capacitors.
The particular part numbers and characteristics are listed in Table 1 below. The physical
dimensions shown do not include the extra dimensions of the connectors and fastening
flanges which add another four to six centimeters.
Table 1
component
Part No.
Capacitance DC WKG Height Length Width
1F
C1,C2
PMR 100-105
10kV
16cm 8.5cm 6.7cm
6 F
C3,C4
PMR 100-605
10kV
35cm 13cm 10cm
The weight of these capacitors are as follows:
C1, C2
C3, C4
1.32kg
6.60kg
The maximum switching frequency rating is 10kHz as can be seen in Fig. 4
Figure 4
The life expectancy at 65C and 50% DC WKG (5kV) is 120000hrs or 13.7 years. A
graph of the life expectance of this part is shown in Fig. 5
Figure 5
The physical diagram of this capacitor is shown in Fig. 6.
Figure 6
2.0 Inductors L1 and L2
These are wound on a gapped core with a specified saturation flux density of 1 Tesla. In
order to keep the resistance of the winding low using reasonable gauge wire, we assume
that 25 turns will be used. Keeping the maximum flux density at 0.75T, we determine the
gap length to be:
 NI (4 10 7 )( 25)(1)
lg  o

 42m
(1)
Bmax
0.75
Next we compute the cross sectional area according to:
Ac 
Ll g
N o
2

(50mH)(45 m)
 26.7cm 2
2
7
(25) (4 10 )
(2)
This cross sectional area corresponds to a 5.2cm  5.2cm square which, in a closed
magnetic circuit, results in a torroid, or C-core, with an outer diameter of about 16cm and
an inner diameter of 5cm. A cross-sectional view of this core is shown in Fig. 7.
Figure 7
3.0 The damping resistors R1 and R2
These resistors hardly dissipate any power in steady state, but during turn on transients
they draw large currents and they should be chosen according to their peak current usage.
Additionally, the input filter will cause a dip in the bus voltage. We shall determine and
compare the peak current in the resistors and the dip in the bus voltage for the lowfrequency, three-stage design and the high-frequency, fifty-stage design.
For the purposes of this analysis, it is more than adequate to model the cable with
only four LC sections as shown in Fig. 8. Also shown in this figure, is the equivalent
circuit of the three input filters in Fig. 1a in cascade. This equivalent circuit is simply an
impedance with three times the value of the original filter. Hence, each inductor and each
resistor in Fig. 8 is three times the values of the inductor and resistor in Fig. 1a and each
capacitor is one-third the value. The simulation result of the resistor current is shown in
Fig. 9. The peak current and the energy dissipated in each resistor are computed from Fig.
9:
I pR1  8.2A Energy in R1  29.3J
I pR2  10.2A Energy in R2  35J
The dip in the voltage at the input of the PCU is shown in Fig. 10 and is found to
be:
V  1.92kV
The same results are derived from the simulations shown in Figs. 11, 12 and 13
for the fifty-stage high frequency design whence we see:
I pR1  5.05A Energy in R1  0.117J
I pR2  6.26A Energy in R2  0.147J
V  487V
1
L1
25mH
2
R1
25
1
V _cable
10kV
L2
25mH
R2
25
2
C1
5uF
1
L3
25mH
2
R3
25
1
L4
25mH
2
R4
25
C3
5uF
C2
5uF
C6
5uF
0
S
-
+
-
+
Sw itch
L2_eq
150mH
L1_eq
150mH
1
2
1
2
V ON = 1.0V
V OFF = 0.0V
R1_eq
750
R5
C1_eq
0.33uF
100k
0
V _sw itch
TD = 24msec
V1 = 0
TR = 1usec
V 2 = 1.1
R2_eq
750
C2_eq
0.33uF
C3_eq
2.0uF
C4_eq
2.0uF
0
Figure 8
Figure 9
Figure 10
1
L1
25mH
2
R1
25
1
L2
25mH
R2
25
2
1
L3
25mH
2
R3
25
1
L4
25mH
2
R4
25
V
V _cable
10kV
C1
5uF
C3
5uF
C2
5uF
C6
5uF
0
S
-
+
-
+
Sw itch
L2_eq
32.5mH
L1_eq
32.5mH
1
2
1
2
V ON = 1.0V
V OFF = 0.0V
R1_eq
1250
R5
C1_eq
0.02uF
100k
0
V _sw itch
TD = 24msec
V1 = 0
TR = 1usec
V 2 = 1.1
C4_eq
0.12uF
R2_eq
1250
C2_eq
0.02uF
C3_eq
0.12uF
0
Figure 11
Figure 12
Figure 13
The undershoot in the input voltage in the three-stage design is so severe that it
will limit the range of input voltage for normal operation and may result in unpredictable
chatter in the distant nodes because the dip in the input voltage will exceed any
reasonable hysterisis (about 500V) in the turn-on/off power switch for the converter.
Also, it can be seen that the energy rating for the resistors is about three hundred times
greater in the three-stage design.
2.2Design of the output filter
For a three stage design, the output consists of three single stage LC filters in parallel.
Each LC filter stage is shown in Fig. 14 and should be capable of delivering 5000Watts in
the event that one of the stages fails.
1
L3
11.2mH
2
R1
32
C5
100uF
V _secondar y
0
(a)
(b)
Figure 14a and b
1. The output filter inductor L3
The isolation transformer will have 2:1 turns ratio. The inductor is designed so
that at maximum input voltage it can handle the peak input current. The secondary
voltage is shown in Fig. 14b and has an amplitude of 2500V which is determined
according to the fact that if one of the stages fails and the bus is at 10kV, then each input
stage will see 5000V and the secondary will be half that number. The duty cycle is
computed to be:
D
Ton Vout
400


 0.16
Ts Vsec 2500
(3)
The inductor is designed for a peak-to-peak ripple current of 6A so that we have:
L3 
VoutToff
I

400V (1  0.16)200 sec
 11.2mH
6A
(4)
The peak current for which the inductor has to be designed is given by:
I p  I dc 
I 5000W 6A


 15.5A
2
400V
2
(5)
This inductor, just like the input filter inductor, is wound on a gapped core with a
specified saturation flux density of 1 Tesla. In order to keep the resistance of the winding
low using reasonable gauge wire, we assume that 25 turns will be used. Keeping the
maximum flux density at 0.75T, we determine the gap length to be:
lg 
 o NI
Bmax

(4 10 7 )( 25)(15.5)
 650m
0.75
(6)
Next we compute the cross sectional area according to:
Ac 
Ll g
N o
2

(11.2mH)(650 m)
 92.7cm 2
2
7
(25) (4 10 )
(7)
This cross sectional area corresponds to a 9.63cm  9.63cm square which, in a closed
magnetic circuit, results in a torroid, or C-core, with an outer diameter of about 27cm and
an inner diameter of 5cm. A cross-sectional view of this core is shown in Fig.15
Figure 15
2. The output filter capacitor C5
The output filter capacitor is chosen to be 100F because that is a standard value which
yields an output peak-to-peak ripple voltage of 1.5V which is comparable to the 1.27V of
the fifty-stage design. The output ripple voltage is shown in Fig. 16.
This capacitor may be selected in one of two different ways. The first way is to
configure sixteen 200V, 100F in four series and four parallel combination. Such a
configuration will result in 100F capacitor with 100% voltage de-rating as in the case of
the high-frequency, fifty-stage design. The type of capacitor for this configuration is the
same one used in the high frequency design made by American Capacitor Corporation:
Component
Part No
C5
VW2G107J
Capacitance DCWKG Length Width Thickness
100F
200V
2.17
1.88
1.65
With a total of 48 capacitors for this three-stage design, the volume of the output
capacitance is the same as that of the fifty-stage design which requires 50 capacitors.
Figure 16
The second choice of capacitor is the one manufactured by Hivolt Capacotors Limited,
Part No. PMR-08-107. This is a single 800V part.
2.3 Design of the isolation transformer
The magnetizing inductance of the isolation transformer referred to the primary is
designed so that magnetizing current is about 1A for a volt-second product of 5000V.Ton.
This yields:
L prim  5000V
0.16(200 sec)
 160mH
1A
(8)
The cross-sectional area of each isolation transformer has to be such that it will be able to
withstand a volt-seconds product of 5000V.Ton :
NBmax Ac  5000 V  0.16  200  sec  0.21V. sec
(9)
Using a core material with a saturation flux density of 1T and operating it at 0.75T, we
obtain for a 40-turn (on the primary) design:
Ac 
5000V(.16  200 sec) 4
10  53cm 2
40(0.75T)
(10)
Next, we compute the gap according to:
N 2  o Ac (40) 2 (4 10 7 )(53  10 4 m 2 ) 6
lg 

10  66m
L
0.160H
(11)
The approximate dimensions of such a core are shown in Fig. 17 which is seen to have an
outer diameter of 22cm and height of 7.3cm.
Figure 17
III. Comparison of three-stage and fifty stage designs
In this section we will mainly compare the volume requirements of the two designs and
comment on some other performance issues.
3.1 volume comparison
The volume of the input filter capacitors for the three stage design is computed
using the results derived in the previous section. Hence we have:
Total Volume of C1 and C2  6  (16  8.5  6.7)  5467cm3
(12)
Total Volume of C3 and C4  6  (35  13  10)  27300cm3
(13)
Total Volume of C1, C2, C3 and C4  32767cm3
(14)
Note that C3 and C4 do not fit inside the prescribed diameter of 12 inches. The volume
of the output filter capacitors are the same so that no comparison is given to those.
The volume of the input filter inductors (including the hole in the middle of the
core but not the winding) is determined next for the three-stage design. Hence, we have:
Total Volume of L1 and L2  6   (8) 2 5.2  6273cm3
(15)
Total Volume of L3  3   (13.5) 2 9.6  16489cm3
(16)
Note that L3 barely fits inside the 12inch diameter requirement.
The volume of the isolation transformer (including the hole in the middle of the
core but not the winding) is determined next. Hence, we have:
Total Volume of isolation xfmr  3   (11) 2 7.3  8325cm3
(17)
The total volume for the magnetic components is computed to be:
Total magnetic volume  31087cm3
(18)
Next we determine the volume of the reactive elements of the fifty-stage, high
frequency design.
The volume of the input filter capacitors for the fifty-stage design is computed
next. The input filter capacitors are made by the American Capacitor Corporation and
have the following part number and physical dimensions:
component
Part No.
Capacitance DC WKG Height Length Width
1F
C1,C2
VW2G105J
400V
2.97cm 1.52cm .86cm
10F
C3,C4
VW2G106J
400V
5.5cm 2.77cm 2.11cm
Total Volume of C1 and C2  100  (2.97  1.524  .864)  391cm3
(19)
Total Volume of C3 and C4  100  (5.51  2.77  2.11)  3220cm3
(20)
Total Volume of C1, C2, C3 and C4  3611cm3
(21)
The total volume of the inductors is computed next. The cores and their
dimensions are listed in the table below.
Component
L1, L2
Part No.
OD
MPP 58929-A2 26.9mm
ID
Height
14.7
11.2mm
L3
MPP 58547-A2
33mm
20mm 10.7mm
Transformer
F42915-TC
29mm
19mm 15.2mm
The total volume for the magnetic elements is computed next.
Total Volume of L1 and L2  100   (1.345) 21.12  568cm3
(22)
Total Volume of L3  50   (1.65) 21.07  458cm3
(23)
Total transform er volume  50   (1.45) 21.52  502cm3
(24)
Total magnetics volume  1528cm3
(25)
We now have the following volume comparison for the two designs:
Design
Total input filter capacitance volume Total magnetics volume
3-stage
32767cm3
31087cm3
50-stage
3611cm3
1528cm3
Volume
Ratio
9
20
(The reason the ratio for the magnetics is higher is that the output filter inductor in the
three-stage designed is much more heavily penalized when one of the filter stages fails
because the current rating of the inductor must be 3/2 times its normal rating. This is not
the case for the input inductor where the input current remains the same regardless
whether there are two or three operating stages. Hence, when comparing Eqs. (15) and
(22) we see that the ratio is about 11, close to that of the capacitors. However, when we
compare Eqs. (16) and (23), we see that the ratio is about 36).
Other problems related to volume are that some of the parts for the three-stage
design do not fit or barely fit inside the 12-inch diameter case.
3.2 Performance comparison
One of the major problems with the three-stage design is that it creates a 1.9KV voltage
dip on the input voltage when turned on regardless of load conditions, which will cause
serious chatter problems for distant nodes where the input voltage can be as low as 7KV
for which a 2KV switching hysteresis cannot be designed. The switching hysterisis is
about 400V which can clear the way for a turn on at 5.8KV and a drop out at 5.4KV.
Other problems are related to parts reliability when operated simultaneously at
high voltage and high current. Switching high voltages at high frequencies, even at
5kHz, need special corona prevention layout and construction techniques. All such
problems are non-existent in the fifty-stage design.
IV. Conclusion
The trade-off study in this report shows that from a volumetric as well as a performance
point of view, the fifty-stage, high-frequency, low voltage stress design is a much better
design choice then the three-stage, high-voltage, low-frequency design.