Download A 20 kHz hybrid resonant power source for the space

I. INTRODUCTION
A 20 KHz Hybrid Resonant
Power Source for the Space
Station
E JAIN
M. TANJU
Canadian Astronautics Ltd.
A concept of hybrid resonant inverter topology is given
and steady state behavior analyzed A method to optimize the
design of the resonant network is described. The performance
characteristics such as the total harmonic distortion of output
voltage, rms output voltage, and efficiency of the inverter are
presented. Finally, it is illustrated that the hybrid resonant
inverter system maintains an excellent efficiency over varying
output load demand.
In the proposed International Space Station, power
conversion from dc input voltage to 20 kHz, a single
phase sine wave ac output voltage is contemplated.
Some of the requirements for this conversion are:
high conversion efficiency (> 95 percent), tight
output voltage regulation (< 2 percent) from full
load to no load, low total harmonic distortion of the
output voltage (< 2.5 percent) and a constant output
frequency (20 k H z f 400 Hz).
The mobile servicing system (MSS), the Canadian
contribution to the International Space Station, may be
required to supply electrical power of this quality to
its operating equipment and attached payloads while
in motion and/or otherwise disconnected from the
main space station power bus. In this space station
application the MSS power source may operate at
reduced load over a considerable portion of the
operating period. One of the main objectives in
designing the power source is to minimize both the
no-load and full-load conversion losses. A number
of different topologies have been reported in the
literature, but they [l,21 appear to fail to satisfy all
the requirements simultaneously or require [3, 41
complicated power and control circuitry. Presented
here is an inverter topology concept with the objective
of satisfying these requirements simultaneously.
The system description and operating principle
of the inverter is described. A steady state analysis
is presented to obtain the behavior of the inverter.
A method to select the optimal components of
the resonant network is given. The performance
characteristics such as the total harmonic distortion
of output voltage, rms output voltage, the peak switch
current at the instant of turn-off and efficiency of the
inverter are presented.
II.
Manuscript received August 5, 1988.
IEEE Log No. 28659.
Presented at the IEE Third International Conference on Power
Electronics and Variable-Speed Drives, London, England, July 1988.
(IEE Conference Publication 291).
Authors’ address: Space Systems Group, Canadian Astronautics,
Ltd., 1050 Morrison Dr., Ottawa, Ontario, Canada, K2H 8K7.
0018-9251/89/0700-0491$1.00 @ 1989 IEEE
SYSTEM DESCRIPTION AND OPERATING
PRINCIPLE
Fig. 1 shows a circuit diagram of a hybrid resonant
inverter system. This circuit consists of a dc voltage
source, a high frequency inverter, an output resonant
network, a matching and/or isolating transformer
and a control circuit. The output resonant network
is comprised of a series circuit (Ls and Cs) and
a parallel circuit ( L p and C p ) .The basic working
principle associated with the power and control
circuitry of the inverter is explained in the following
paragraph.
A voltage-controlled oscillator (VCO), with center
frequency equal to the operating frequency Cfo) and
proportional to a control voltage (Vc),generates
two output signals: 1) a full voltage command (Son),
and 2) a pulsewidth ramp (Sr). A threshold voltage
V, is derived from the output voltage feedback.
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491
appears at the input of output resonant network. Both
the series and parallel branches of the output network
are tuned at the inverter operating frequency. The
resonating action of this network, on the application of
voltage V,,filters the harmonics to an acceptable level
and provides a sinusoidal stiff voltage source at the
output. Waveforms illustrating the operating principle
of the inverter are shown in Fig. 2.
Ill.
I
Control Circuit
Fig. 1. Circuit diagram of 20 KHz hybrid resonant inverter
system.
REALIZATION OF AN IDEAL VOLTAGE SOURCE
In an ideal voltage source the output voltage is
constant and current drawn from the source decreases
from rated value to zero as the output load varies
from full load to no load. The fundamental circuit of
the inverter of Fig. 1 and Thevenin’s equivalent of
Fig. 1 are shown in Fig. 3. From Fig. 3 the following
expressions are obtained
- t f us
Fig. 2. Waveforms illustrating working principle of hybrid resonant
inverter.
vth,
rs,
VOare the source, Thevenin’s,
In
output voltages, respectively, Zth, Z,, Z, are the
Thevenin’s, series, and parallel impedances and, ISN
is the no-lead source current. From (1)-(4), Vo = V, at
any load and ISN = 0 if and only if
2, = O
8-
ZP
Fig. 3. Fundamental inverter circuit and Thevenin’s equivalent.
The pulsewidth ramp is compared with the threshold
voltage. Any time the ramp voltage becomes greater
than the threshold voltage, a zero voltage command
signal (S,ff)is generated. Using the signals So,and
Soffthe pulsewidth angle (6) is obtained. Both the
operating frequency (to) and pulsewidth (6) can be
controlled by controlling the voltages V, and V,,
respectively.
In steady state, the gating pulses generated by the
control circuit are applied to the gates of the high
frequency inverter system. A quasi-square voltage (V,)
492
and
Z, = 00.
(7)
_I
From (5) and (6), the constraints of (7) will be
satisfied if
XLS = XCS
and
X L P = Xcp.
(8)
Equation (8) reveals that the series branch and
parallel branch of the inverter of Fig. 1 should be
tuned at the operating frequency of the inverter in
order to achieve an ideal voltage source. Since both
the series and parallel branches of the output resonant
network of the inverter are tuned at the inverter
operating frequency, this inverter system, therefore,
can be named as a “double-tuned resonant inverter
system.” The following sections present the steady
state analysis of the inverter system.
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0i,
with n as the order of harmonic, 6 as the pulsewidth
angle, and W O is the operating frequency.
Voltage Across Series Capacitor. The voltage across
the series capacitor is given by
Fig. 5. Per unit nth harmonic equivalent circuit.
IV.
(19)
= tan-'(bi,/q,)
STEADY STATE ANALYSIS OF INVERTER
O0
The following simplifying assumptions are made in
analyzing the steady state behavior of the inverter.
1) The power semiconductor switches are ideal.
2) The output load is resistive.
3) The resistances of capacitors and inductors are
negligible as compared with the capacative and
inductive reactances.
iep(t) =
Under these assumptions the simplified inverter
circuit is shown in Fig. 4.Since the output voltage is
defined, the Fourier series method is used to obtain
the steady state expressions for the voltages and
currents. The inverter input voltage (V), the load
resistance (R)and the operating frequency ( W O ) of the
inverter are chosen as the base quantities. The per unit
equivalent circuit of the inverter for the nth harmonic
is shown in Fig. 5.
Output Voltage of Inverter. The output voltage of
the inverter can be expressed in the form of Fourier
series as follows:
c
O0
Wt)=
4
nb
na
sin 2 sin 2 sinnwot per unit.
4X,
nb
na
sin -sin -cos(nwot - $in),
n=1,3n2r1Zinl 2
2
per unit.
(20)
Current Through Parallel Capacitor. The current
through the parallel capacitor is given by
vcs(t) =
(9)
n=1.3
Output Current of Inverter. The output current of
the inverter is given by
Voltage Across Load. The voltage across the load
is given by
4
nii
na
sin -sin -cos(ntW0t - $,,),
2
2
7r[AnlXp
per unit.
(21)
na
2
per unit.
(22)
Current Through Parallel Inductor.
ilp(1)
V.
=
n6
4
sin -sin
-En2alAnlXp
2
-cos(nwOt - # n ) ,
COMPONENT SELECTION OF OUTPUT
RESONANT NETWORK
The load imposes the following two basic
requirements on the design of the invert-.?'.
1) The output voltage of the inverter should be
constant under all load conditions.
2) The total harmonic distortion (THD) of the output
voltage should be within an acceptable level under
all load conditions.
As illustrated in Section 111, the requirement
1) is met by tuning both the series branch and
parallel branch at the inverter operating frequency.
However, the selected values of the series and parallel
impedances should be such that the worst case
harmonic voltage, given by the following equation, is
less than or equal to an acceptable level. The worst
harmonic voltages are given by
0.9sin( n6/2)
VI, = n [ l - q(n - l/n)2]
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493
'
5I
i::;:p
,\:
6 2.5
'\\\
.-.--.-.
...
where
q = xs/xp.
(24)
The ratio q as a function of the worst third
harmonic content of the output voltage (Vo3) is shown
in Fig. 6. For a given harmonic content the ratio of
X s / X p can be obtained from Fig. 6. However, another
relationship is also required in order to obtain the
values of each X , and X,. The required relationship is
established by optimizing the total volt-ampere rating
of the resonating components with respect to the
circulating current losses (P,,)of the parallel branch.
These losses are chosen as they contribute a major
portion of the no-load losses of the inverter system.
Assuming that the circulating current in the parallel
branch is 1/Kth times the rated current through the
series branch in order to reduce the no-load losses of
the inverter, the following relationship is obtained
0.9
0.9
_ - - --
0.97
2) Corresponding to the value q, obtained in step l),
determine the value of K from Fig. 7 such that the
optimal reactive rating of the resonant network
with reasonably small circulating current losses is
achieved.
3) Obtain the value of each of the components
of the resonant network by using the following
relationships.
KRB
Lp = WO
C, = l / K R ~ w o .
VI.
(F)
(31)
PERFORMANCE OF INVERTER
or X, = Kq.
(25)
K
xs
K is an arbitrary constant and its value is chosen
such that it results in the optimum total reactive rating
of the resonant network with respect to the circulating
This section illustrates the performance of the
inverter with respect to 1) the THD of the output
3) the Peak switch
voltage, 2) the rms Output
CUrrt3nt at the instant Of turn-off, and 4) efficiency.
current losses.
The total reactive rating of the resonant network is
given by
ST = 1.62(Kq + l / K ) .
(26)
A.
x,
THD of Output Voltage
The worst harmonic distortion of the output voltage
of the inverter is given by
The total circulating losses are given by
0.81
K2
Pd = -r
(27)
where r p is the total resistance of the circulating path.
Fig. 7 shows the total reactive rating (ST)of the
resonating network and circulating current losses
(PCl/rp)as a function of K for various values of q.
This figure clearly demonstrates that the value of K
is approximately equal to 1.5 in order to obtain the
optimal rating of the resonant network and reasonably
small circulating current losses.
Following is a step-by-step procedure to select the
components of the resonant network.
1) For a given harmonic content of the output voltage,
read the value of r,~from Fig. 6.
494
Since THD of the output voltage is small, the
contribution of harmonic voltages in the output rms
voltage is negligible. The rms output voltage of the
inverter is, therefore, given by
VOR = 0.9~in6/2.
(33)
Fig. 8 shows the output rms voltage and THD as a
function of pulsewidth angle (6) for various values of
q. This figure reveals that the inverter system should
be operated for a pulsewidth close to 120' for two
reasons. First, it will provide a control of output
voltage against a possible f 1 0 percent variation in
nominal input dc voltage and second, it will lower the
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~
Fig. 10. Loss factors of inverter as function of load.
Fig. 8. THD and per unit rms output voltage (VOR)as function
of pulsewidth angle (8) for various q.
b) nrn-off losses of the switches. The turn-off
losses of the switches are given by
PtOE= Kz(1.281~sin6fo)tf
(W)
c) Losses in the series branch. The losses in the
series branch are given by
Pseries= K3(3.241jsin26/2)rs
0
= K3 F3 r,
-
120
60
'6
(W)
180
Fig. 9. Peak switch current (Is) at time of turn-off versus
pulsewidth (6) for various 9.
THD in the output voltage under nominal operating
conditions.
(37)
where K1, K2, K3 are the loss factors, Ron is the on
state resistance of the switch, tf is the fall time of
the switch, r, is the equivalent resistance of the series
branch, and IB is the base current of the inverter. The
total variable losses are given by
In equation (38), loss factors K1, K2, K3 are load
dependant and are given by Fig. 10. For given
application factors, Fl, F2, F3 are constant. Therefore,
The peak switch current at the instant of turn-off
the variable losses are dependent on the on-resistance
(Is) determines the requirements of the gating circuit
(Ron),fall time ( t f )of the switch, and the equivalent
and used in calculating the turn-on losses. The switch
resistance (r,) of the series branch. These losses can
current at the instant uf turn-off is given by
be reduced significantly by using a switch (such as
Hexfets) with low on resistance and fall time.
n r n6
1*273sinn6/2sinnr/2sin - - - - Oh).
2) Constant Losses. These losses consist of the
2
2
following components.
a) Snubber losses. The snubber losses are given by
(34)
B.
Peak Switch Current at Instant of Turn-off (I,)
'"'CW
(
Fig. 9 shows the switch current (Is)as a function of
pulsewidth angle (6) for various values of q.
C.
Efficiency of Inverter
The several losses associated with the inverter can
be grouped together in the following two categories.
1 ) Variable Losses. These losses are comprised of the
following load-dependent losses.
a) Forward conduction losses of the switches. The
forward conduction losses are given by
b) Circulating current losses in the parallel branch.
These losses are given by
P ~ r=c K5(0.81Z~sin26/2rp/K2)
= KsF5
(40)
where r p is the resistance of circulating current
loop and K4, K5 are the loss factors.
Fig. 11 shows the losses and efficiency of the
hybrid resonant inverter when using Hexfets (IRF
150) switches. This figure shows that the inverter losses
decrease significantly with reduced output load and the
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495
.-I
Efficiency
--- Variable lasses
-CO"Sta"f
s
G
F
I
r
losses
\.
ACKNOWLEDGMENTS
This work was performed for Spar Aerospace,
the prime contractor for the NRCC Canadian Space
Station program by Canadian Astronautics Ltd.,
Ottawa, Canada.
90
100
25
($) -+
Fig. 11. Inverter losses (PI)
and efficiency (9) as function of load
demand. (vi = 50 V, Po = 1 KW, fo = 20 KHz.)
Load
inverter maintains an excellent efficiency over a wide
range of output load.
VII.
CONCLUSIONS
A hybrid resonant inverter system has been
presented which satisfies the steady state operating
requirements of a power source for the Space Station
MSS. The steady state behavior of the inverter has
been analyzed. A method to optimize the design of
the resonant network has been described. Finally, it
has been illustrated that the hybrid resonant inverter
system maintains an excellent efficiency over varying
output load demand.
REFERENCES
Mapham, N. (1%7)
An SCR inverter with good regulation and sine wave
output.
IEEE Transactions on Industry and General Applicatwm,
IGA-3 (Mar.-Apr. 1967), 176-187.
[2] Chen, J., and Bonert, R. (1983)
Load independent DC/AC power supply for higher
frequencies with sine wave output.
IEEE TransactiOnr on Industry Applications, IA-19, 2
(Mar.-Apr. 1983), 223-227.
[3] Savary, P., Nakoka, M., and Maruhashi, T (1985)
Resonant vector control base high frequency inverter.
In Proceedings of Power Electronics Specialist Conference,
1985, 204-213.
[4] Tsai, E, and Lee, E C. (1986)
Constant-frequency phase controlled resonant power
processor.
In IEEE U S Annual Meeting Conference Record, 1986,
617422.
[I]
Praveen K. Jain received the B.E. (Hons.) degree in electrical engineering from
the University of Allahabad, Allahabad, India, in 1980, the M.A.Sc. and Ph.D.
degrees in electrical engineering at the University of Toronto, Toronto, Canada,
in 1984 and 1987, respectively.
Currently he is with the Space Systems Group, Canadian Astronautics Ltd.,
Ottawa, Canada, where he is involved in the design and development of high
frequency ac-dc and dc-ac converter systems for the Canadian Mobile Servicing
System of the Space Station, and feasibility studies and design of the Space
Power Systems. During the period of 1980-1981, he was a Design Engineer and a
Production Engineer at Hindustan Brown Boveri Company and Crompton Greaves
Limited, India, respectively. His current research interests are high frequency
resonant invertedconverter systems, modeling of hybrid power devices, and
simulation of the space power systems.
Dr. Jain has published over 25 technical papers and reports in the area of
power electronics applications to space systems and induction heating. He is the
co-recipient of the 1988 Best Published Paper Award of Canadian Astronautics
Ltd.
M. Celal Tanju received the B.Sc. and M.Sc. degrees in electrical engineering in
1964 and 1965, respectively, and the Ph.D. degree in power electronics in 1973, all
from the Middle East Technical University, Ankara, Turkey.
Until 1980, Dr. Tanju taught (and became Associate Professor) in the electrical
engineering department of the Middle East Technical University. In 1980, he
taught and did research at the University of Waterloo, Ontario, Canada. From
1981-1983 he worked with Lumacell, Inc., Markham, Ontario, and in 1983 joined
Canadian Astronautics, Ltd., Ottawa, Ontario, where he is currently the Electrical
Power Group Leader in the Space Systems Group.
Dr. Bnju has published various papers in the field of power electronics design,
analysis, and simulation. He is the co-recipient of the 1988 Best Published Paper
Award of Canadian Astronautics Ltd.
4%
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