Output Filter for the High-Voltage DC/DC Converter

Doctoral school of energy- and geo-technology
January 15–20, 2007. Kuressaare, Estonia
Output Filter for the High-Voltage DC/DC Converter
Margus Müür, Dmitri Vinnikov
Tallinn University of Technology
margus.muur@ttu.ee
Abstract
This paper presents the output filter analysis and
design for the high-voltage isolated DC/DC
converter. The topology of the filter is the second
order low-pass LC but in row with the relative
simplicity it demonstrates excellent performance.
Filter steady state analysis as well as simulation
results are discussed.
Keywords
Second order LC-filter, simulation, voltage ripple
Introduction
All DC/DC converter topologies have an output
filter to supply the load with an almost constant
voltage waveform. The output filter has a strong
influence on the performance of the converter and an
important impact in its size. One of the most
common output filter configuration is the LC
network. The values of the inductor and capacitor
are determined by the output voltage requirements
and by the topology of the converter.
Nowadays the Department of Electrical Drives and
Power Electronics of Tallinn University of
Technology is developing a prototype of a brandnew
isolated 3 kV DC/DC converter for the
supplying internal 350 V DC-bus of a commuter
train. The implementation of new 6.5 kV IGBTs
enable further simplification of power circuits
(Fig. 1) with no changes in the blocking voltage
capability of the inverter leg. The DC/DC converter
parameters are submitted in Table 1.
+U in
L 0 I out
+U out
T 1 D 1 C 1 D 3 D 4
I L
U 3 C 0
TX
T 2 C 2 D 5 D 6
D 2
Fig. 1. High-voltage DC/DC converter circuit
The converter output is connected to an intermediate
DC-bus of a train. The function of the intermediate
DC-bus is to interconnect secondary converters
(output modules). Despite the very wide primary
voltage fluctuations the output voltage must remain
stable. The desired output voltage regulation
overshoot is only 2.5 % (i.e. 8.75 V), which makes
the design of control system and output filter very
challenging.
Table 1. High-voltage DC/DC converter parameters
Parameters
Values
Input voltage range (V) 2200...4000
Output voltage (V) 350 ± 2.5%
Peak output current (A), 143
(during 1 min)
Switching frequency (Hz) 1000
In the discussed half-bridge topology the maximum
duty cycle D (D=t on /T) of each switch is 80% from
the half-period at rated load. In practice it means that
isolation transformer must be specified to provide
maximal current just with the minimal input voltage
(i.e., 2200 V). The respective voltage before the
output filter (U 3 ) and the output filter inductor
current (I L ) are shown in Fig. 2.
Apparently, the most demanding operation
conditions to the output filter are at the maximum
input voltage (i.e., 4000 V) and rated load, when the
duty cycle D becomes 44% of the half-period
(Fig. 3). [1]
I, U
U 3
T
Fig. 2. Diode rectifier output voltage U 3 and
inductor current I L during the minimum input
voltage conditions (maximal switch duty cycle)
I, U
I nout
U 3
T
Fig. 3. Diode rectifier output voltage U 3 and
inductor current I L during the maximum input
voltage conditions (minimal switch duty cycle)
I L
dI
t
t
I L
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1 Output filter design relations
The output LC-filter is used primarily in power
supplies where voltage regulation is important and
where the output current is relatively high and
subject to varying load conditions. This filter is
mainly used in the high power applications.
Low-pass LC-filter consists of an input inductor (L 0 )
and an output filter capacitor (C 0 ) (for the details see
Fig. 1). Inductor L 0 is placed at the input of the filter
and is in series with the output of the rectifier circuit.
Since the action of an inductor is to oppose any
change in current flow, the inductor tends to keep a
constant current flowing to the load throughout the
complete cycle of the applied voltage. As a result,
the output voltage never reaches the peak value of
the outgoing transformer voltage. The reactance of
the inductor (X Lo ) reduces the amplitude of ripple
voltage without reducing the DC output voltage by
an appreciable amount (the DC resistance of the
inductor is just a few ohms). [2]
The shunt capacitor (C 0 ) charges and discharges at
the ripple frequency rate, but the amplitude of the
ripple voltage is relatively small because the
inductor (L 0 ) tends to keep a constant current
flowing from the rectifier circuit to the load. In
addition, the reactance of the shunt capacitor (X Co )
presents low impedance to the ripple component
existing at the output of the filter, and thus shunts
the ripple component around the load. The capacitor
attempts to hold the output voltage relatively
constant at the average value of the voltage.
The value of the filter capacitor (C 0 ) must be
relatively large to present a low opposition (X Co ) to
the pulsating current and to store a substantial
charge. The rate of the charge for the capacitor is
limited by the low impedance of the AC source (the
transformer), by the small resistance of the diode,
and by the counter electromotive force (CEMF)
developed by the coil. Therefore, the RC-charge
time constant is short compared to its discharge
time. Consequently, when the pulsating voltage is
first applied to the LC-filter, the inductor (L 0 )
produces a CEMF which opposes the constantly
increasing input voltage. The net result is to
effectively prevent the rapid charging of the filter
capacitor (C 0 ). Thus, instead of reaching the peak
value of the input voltage, C 0 only charges to the
average value of the input voltage. After the input
voltage reaches its peak and decreases sufficiently,
the capacitor (C 0 ) attempts to discharge through the
load resistance (R Load ), what is connected to filter
output. C 0 will only partially discharge because of its
relatively long discharge time constant. The larger is
the value of the filter capacitor, the better the
filtering action. However, because of physical size,
there is a practical limitation to the maximum value
of the capacitor.
The first step is to choose an output filter inductor.
In the filter inductance calculation is assumed that
the inductor current is not discontinuous. It is
discontinuous only when the front end of the
inductor current ramp has dropped to zero and that
this occurs when the output DC current (minimum)
has fallen to half of the filter inductor ripple current
amplitude dI. Then: [2]
ton
ton
dI = 2⋅
Ioutm
= U
L
⋅ = ( U3
−U
out
) ⋅ , (1)
L
L
0
where I outm – minimal output current (half the ramp
amplitude dI), U L – voltage drop on filter inductor,
U 3 –rectifier output voltage, U out – converter output
voltage (filtered), t on –switch on-state time, L 0 –filter
inductance to be calculated.
Output voltage defining equation [2]
U
out
= U
2⋅t
⋅
T
on
3
, (2)
thus, the t on calculation equation is [2]
t
on
Uout
⋅T
2 ⋅U 3
= . (3)
As it was stated before, for the values of the output
filter components L 0 and C 0 , the worst operating
point is at the maximum input voltage level and at
the rated load conditions (i.e., minimum duty cycle
operation). At this point, the operating duty cycle of
the inverter switches becomes 44% from the halfperiod.
Thus, t on is
t
on
U
out
2⋅U3
⋅T
0.44⋅T
=
2
= . (4)
The voltage U 3 can be derived from Eq. 4
U
U ⋅T
= = 2. 27 ⋅U
0.44⋅T
out
3 out
. (5)
If Eqs. 4 and 5 are placed in Eq. 1, then
0.44 ⋅T
/ 2
dI = 2
L
( 2.27 ⋅U
) ( ) out
−U
out
⋅
= ⋅ Ioutm
The filter inductance equation derived from Eq. 6 is
L
U
= 0. 14 ⋅
⋅T
0
0
(6)
out
. (7)
0
Ioutm
Then if the minimum current I outm is specified as 5%
(7.15 A) of the nominal output current I nout the
inductance equation is
L
= 2. 8⋅
U
⋅T
out
. (8)
0
Inout
Based on equation 8, the chosen filter inductor
inductance has to be at least 6.86 mH.
The next step is to choose output filter capacitor. It
is assumed that the output capacitor size will be
determined by the ripple current and ripple voltage
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specifications only. Assume that the ripple voltage at
the terminals of C 0 can be 17.5 V (5% of the output
voltage). The current change in L 0 during the “on”
period will mainly flow into C 0 , and hence the
capacitance value required to give a voltage change
of 17.5 V can be calculated as follows (the following
equation assumes a perfect capacitor with zero ESR)
[3]
C
dI ⋅t
=
U
r
on
0
. (9)
Thus, the output filter capacitor capacitance
minimum value is 180 µF, if the peak-to-peak ripple
voltage is 5% of the output voltage and the allowed
filter inductor current ramp amplitude is 10% of the
nominal output current.
With the minor modifications the same equations
(1-9) can be applied to the maximum duty cycle
operation (minimal amplitude value of U 3 ). Table 2
shows the duty cycle variation when input voltage
changes. Furthermore, it is shown the values of L 0
and C 0 to obtain required inductor current ripple
(10%) and output voltage ripple (5%).
Table 2. Calculated filter parameters for the
different operation points
Amplitude value of U 3 440 V 795 V
Switch duty cycle D 0.8(T/2) 0.44(T/2)
Value of L 0 2.45 mH 6.86 mH
Value of C 0 327 µF 180 µF
2.1 Simulation with the minimal input voltage
The output voltage pulse amplitude of an isolation
transformer is minimal and the pulse width is
longest (on-state time of each IGBT transistor is
0.4 T).
Fig. 5 demonstrates simulated inductor current (I L )
and output current (I out ) waveforms. The peak-topeak
inductor current ripple is not exceeding 5%,
which is in the good agreement with the
requirements. Output current ripple is less than 1%.
150A
145A
140A
135A
130A
12.0ms 12.4ms 12.8ms 13.2ms 13.6ms 14.0ms 14.4ms 14.8ms 15.2ms 15.6ms 16.0ms
I L
I out
Fig. 5. Inductor current (I L ) and output current (I out )
waveforms with the maximum switch duty cycle
Fig. 6 demonstrates rectifier output voltage (U 3 ) and
converter output voltage (U out ) waveforms. The
peak-to-peak output voltage ripple is less than 1%.
2 Output filter simulations
PSpice simulation circuit of the output LC-filter for
a high voltage DC/DC converter is shown in Fig. 4.
500V
400V
U 3
300V
U out
200V
100V
0V
Fig. 4. PSpice simulation circuit of the output
LC-filter
All used components are ideal, what means that the
voltage drops were not considered in simulations. To
simplify the circuit only the resistive load was used.
Two pulse voltage sources were used to simulate the
transformer output voltage. For finding transformer
output voltage amplitude Eq. 2 was used.
The output filter was proven in two different
conditions: with maximum switch duty cycle
(minimal converter input voltage U in ) and with
minimum switch duty cycle (maximal converter
input voltage U in ). Both simulations were made with
maximum load that is most demanding for the
output filter design. Values of filter elements to be
tested are L 0 =7 mH and C 0 =180 µF.
-100V
0s 2ms 4ms 6ms 8ms 10ms 12ms 14ms 16ms
V(D3:2) V(RLoad:2)
Time
Fig. 6. Rectifier output voltage (U 3 ) and converter
output voltage (U out ) with the maximum switch duty
cycle
2.2 Simulation with the maximal input voltage
The output voltage pulse amplitude of an isolation
transformer is reaching its maximum and the pulse
width is shortest (on-state time of each IGBT
transistor is 0.22 T).
Fig. 7 demonstrates simulated inductor current (I L )
and output current (I out ) waveforms. The peak-topeak
inductor current ripple is not exceeding 10%,
which is in the good agreement with the
requirements. Output current ripple is about 1.5%.
120

160A
155A
I L
160
140
IL, A
Inductor Current
150A
120
145A
100
140A
80
135A
60
130A
125A
I out
40
Output Current, Iout
1 501 18 1001 36 1501 54 2001
72 t, ms
Output Current
160
IOUT, A
120A
12.0ms 12.4ms 12.8ms 13.2ms 13.6ms 14.0ms 14.4ms 14.8ms 15.2ms 15.6ms 16.0ms
I(L2) -I(RLoad)
Time
Fig. 7. Inductor current (I L ) and output current (I out )
waveforms with the minimum switch duty cycle
Fig. 8 demonstrates rectifier output voltage (U 3 ) and
converter output voltage (U out ) waveforms. The
peak-to-peak output voltage ripple is about 1.5%.
800V
700V
U 3
140
120
100
80
60
40
Output Voltage, Uout
1 501 18 1001 36 1501 54 72
2001 t, ms
Output Voltage
410
UOUT, V
390
370
600V
350
500V
400V
U out
330
310
300V
290
200V
270
1 501 18 1001 36 1501 54 72 t, ms
2001
100V
0V
Fig. 9. Simulated waveforms of the isolated halfbridge
DC/DC converter with proposed LC-filter
-100V
0s 2ms 4ms 6ms 8ms 10ms 12ms 14ms 16ms
V(RLoad:2) V(L2:1)
Time
Fig. 8. Rectifier output voltage (U 3 ) and converter
output voltage (U out ) with the minimum switch duty
cycle
3 Converter dynamic response
Above-presented simulations are demonstrating that
filter components were selected properly.
Corresponding voltage and current ripple values are
minimal. Thus, for the prototype it was decided to
implement the laminated iron-core inductor with
inductance value of 5 mH. Two electrolytic
capacitors (EPCOS B437 560 µF, 450 V) will be
connected in series with the total capacitance value
of 280 µF.
To test the converter dynamic response with the
selected output filter components the generalized
mathematical model of the converter was developed
by help of Simplorer® simulation software.
The converter model was tested with the maximal
input voltage conditions (4000 V) and during the
random load step change (see Fig. 9), when the
output current of the converter is changing instantly
from some intermediate value (70 A) to a maximal
value (143 A).
The maximum inductor current ripple is about 10%,
while the output current ripple is less than 2%. The
voltage ripple of unregulated output is about 1.5%.
The voltage overshoot during load step change is
14%, which can be fully compensated by the
appropriated control system algorithm.
Conclusion
Output filters play a very important role in DC/DC
converters. Important aspects of converters such as
dynamic response, size and cost are closely related
to the components of the filter. Small values for the
filter components improve the performance of the
converters and increase the power density, whereas
minimum values should be provided to guarantee the
filtering objective.
References
[1] D. Vinnikov, „Research, Design and
Implementation of Auxiliary Power Supplies
for the Light Rail Vehicles”, PhD Thesis,
Tallinn, 2005.
[2] Pressman, A.I., “Switching Power Supply
Design”, Second Edition, McGraw-Hill, 1998.
[3] Billings, K.H., “Switchmode Power Supply
Handbook”, McGraw-Hill, 1989.
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