Pergamon PII: SOO94-5765@7)00022-2
SATELLITE G. COLOMBO’,
Acra Asmnautica Vol. 40, No. I, pp. 4149, 1997 0 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0094-5765/97 S 17.00 + 0.00
POWER SYSTEM SIMULATION-f
U. GRASSELLI’,
A. DE LUCA’, A. SPIZZICHINO*
and S. FALZINIS* ‘Electrical Engineering Department, University of Rome “La Sapienza” Via Eudossiana, 18-00184, Rome, Italy and ‘Space Engineering S.p.A., Via dei Betio 91, 00155, Rome, Italy (Received 7 June 1996; Revised 8 November 1996)
Abstract-In order to furnish a useful tool for the power system preliminary sizing, a satellite power system simulator was developed. The simulator has a modular structure where each module implements the mathematical model of the system components (solar array, battery, voltage regulators etc.). The software allows both the verification of the rating co-ordination of all those parts composing the power system itself, once the mission is assigned, and the analysis of the time behavior of the electronic regulators during transients. Therefore, by using this simulator, any power system architecture can be easily analyzed. In this paper only the electrical preliminary sizing of the components is treated without considering power system mass and battery thermal calculations. As example of the capabilities of the tool the results of two simulations are reported; in the first, the transient behavior of a sequential switching shunt regulator (SR) is analyzed. In the second simulation the power system of a LEO satellite is simulated in order to verify the rating co-ordination in case of unregulated bus voltage. The tool was developed within MATLAB/SIMULINK environment. Copyright 10 1997 Elsevier Science Ltd
The power system behavior can be simulated in two ways; the energy balance simulation and the voltage quality simulation. The energy balance simulation is used to monitor the main parameters of a power system such as the solar array output voltage and current, the bus voltage and current, the battery output voltage, current and state of charge; and to verify the power supplied by the solar generators and the batteries with respect to the required power. These kind of simulations are characterized by a simulation time interval of the order of the orbit period (for LEO 100 min typically), therefore the typical time step is higher than 10 s. The voltage quality simulation is used for analyzing the transient behavior of the electronic devices adopted for power regulation and conditioning; for this reason the simulation time interval is of the order of 1 s with a step of the order 10m6s. In the following sections after preliminary considerations about satellite mission, the mathematical models of the power system components will be illustrated. The paper reports a simulation example for both cases.
1. INTRODUCTION
A satellite power system consists of a primary power source (solar arrays, RTG etc.), a secondary rechargeable power source (Ni-Cd or Ni-H2 batteries, which are the most widely used) and a power conditioning and control system (PCCS). Both power sources must he well sized in order to supply the necessary power to the payload during daylight and eclipse period; the PCCS design is conditioned by voltage requirements for the payload. In order to help the designer during the choice and sizing of components, in recent years various simulation programs have been carried out, including Bauer’s work in 1969 [1], the EBLOS computer program in 1982 [2] and the computer program presented by Lee et al. in 1987 [3]. What persuaded us to develop a new tool was on the one hand the availability of new off-the-shelf software environments (such as MATLAB/SIMULINK [12]) and on the other the development of a new model taking into account the new technological products in the power subsystem. The simulator allows the analysis of various power system architectures; in particular, it is possible to choose the number and orientation of the solar arrays, the satellite attitude, the bus voltage regulation (unregulated, semiregulated, regulated), the number of battery cells and the number of batteries.
2. THE SATELLITE MISSION
The tool includes a flight dynamics block that allows the propagation of any orbit (LEO, GEO, HE0 and Sun-synchronous orbit) and choice of a specific satellite attitude: Sun pointing or Earth pointing.
?A list of acronyms will be found in Appendix A at the end of the paper. SE-mail:
[email protected] 41
G. Colombo et al.
42
First of all, a group of reference frames was set: heliocentric-ecliptic frame; geocentric-equatorial frame tial); 0 perifocal frame; l body axes frame; 0 solar panel frame. l
l
(considered
iner-
These reference systems are useful to describe the satellite’s position with respect to the Earth and the solar array’s orientation with respect to the Sun; in fact the solar array output power depends on the incidence of the Sun’s rays on the solar panel, and it may change continuously during the orbit propagation. Frame changes are made by suitable rotation matrices: in particular, the transition matrix from the body axes reference system (roll, pitch, yaw) to the solar panel one (x,, y,, z,) is:
for a rotation CIaround the roll axis,
($_i:;
x
---;)@(;?JJ
(2)
for a rotation /I around the pitch axis,
The second important specification is the required average power profile for the whole operative life and for each orbit. Therefore, we need to establish the average sunlight power, the average eclipse power and peak power values, with their respective orbital and eclipse periods and the peak power durations. On the basis of these specific requirements we can then estimate the available output power for BOL conditions. If P, and Pd are the required powers during eclipse and sunlight periods T and x respectively, the available solar array power (payload + battery charge) in EOL conditions will be:
where X, and X, are the efficiencies of the paths from the solar arrays through the batteries to the loads and the path directly from the arrays to the loads respectively. These efficiencies are about X, = 0.8 and X, = 0.9. The EOL available power PEoLmust be calculated at the maximum foreseen solar array temperature: when the solar cell efficiency is the lowest. The BOL power is calculated considering the foreseen operative life and the solar array correspondent degradation due to the cosmic radiation. It is convenient to introduce a degradation coefficient L, defined as Ld = (1 - degradation
($=
(I$
r?
;jf
;
#
per yr)Pfe”“e‘Ire< I
(9
W m - ‘)
(6)
then P BoL= PdL
(3)
for a rotation y around the yaw axis. In this way it becomes possible to install the solar panels in any position and orientation with respect to the body-axes reference frame. A BAPTA simulation is not foreseen; therefore by choosing a Sun pointing attitude it is possible to simulate a solar array self-oriented towards the Sun, while in the case of an Earth-pointing attitude, the solar array may be considered fixed at the satellite structure. The satellite’s orbit is considered a Keplerian orbit perturbed by the Earth’s non spherical mass distribution and the Sun’s third body interaction. It is defined by the six classical Keplerian orbital elements which give the initial satellite position and speed in the inertial frame; the computer program provides for the integration of the equation of motion and the propagation of the orbit [4]. In addition, a subroutine provides for the calculation of the Sun position in the inertial frame for each step of simulation if it becomes necessary [S]. Once the reciprocal position of Earth, Sun and satellite are known, it becomes possible to verify the sunlight or eclipse condition [6].
The battery sizing is done using the formula:
where: Ns = NB =
C, = PE = hs = DOD,,,
=
number of series battery cells number of batteries battery amp&e-hour capacity average eclipse power requirement discharge path efficiency maximum depth of discharge.
The DOD% is determined in function of the number of foreseen cycles, hence it depends on the satellite operative life and orbit. 3. SOLAR
ARRAYS
A solar array is composed of a large number of photovoltaic cells. A silicon solar cell has an efficiency h of about 0.15 at 25°C AM0 condition. The efficiency varies with the temperature, hence it is necessary to develop an electrical and a thermal model of the solar array in order to determine the output power at each simulation step. The electrical model is suggested in Tada and Carter [7]
43
Satellite power system simulation
maximum power point values calculated in EOL conditions at the maximum foreseen temperature: ZEOL I
I
I
J
I
Fig. I. Photovoltaic cell equivalent circuit.
In Fig. 1 the electrical equivalent diagram of a photovoltaic cell is illustrated; the resistances R, and R, represent the series and leakage resistances; i,. is the illumination current; i,, and is are the inverse currents of the diodes D, and D, simulating the diffusion process and the carrier generation recombination effects. The model equations are
i,=i,-i,[exp($)-l]
-i.[exp($j)-
I]-
~EOL/VB”S
=
(12)
NP = ZEOL/&,
(13)
Ns = Km/K,
(14)
The solar array may be composed of some sections shunt connected. If NsEZ is the section number per solar array, each section will be composed of (NP/NsEZ)shunt connected and Ns series connected solar cells. The operating temperature of the solar cell is strongly affected by the structure of the panel, the orbit and the satellite’s attitude. The solar array heat exchange goes on only by radiation. Both solar panel’s sides exchange heat with the earth which is considered at the black body temperature of 250 K, and with deep space (3 K, cosmic radiation temperature). The thermal model can be represented by the differential equation
3
Cz =a,(1 V, = VD- R,i,
q)Z,,,+ a,(1 + AIF,,)Z,
(8) + ae,F,(T: - T4) + a&,F,(T: - T”)
R, and R, are considered constant with respect to temperature. i, is the illumination current:
+ O(E, + E,)T“
(15)
where where K(T) is a coefficient which is a function of temperature; r~(T) is the solar cell efficiency; I,,, is the total incident radiation; and i. and iR are related to the temperature via i. = CDT’!’ exp
iR = CR exp
(10)
a, = a, = e, = e, = C= fj = Al = F, = F, = F,, = u= r = I, =
where E, is the forbidden band energy, and
front side absorption rear side absorption front side emissivity rear side emissivity thermal capacitance solar cell efficiency albedo factor front side view factor rear side view factor rear side albedo view factor Stephan-Boltzmann constant Earth black body temperature solar radiation intensity
Radiation (W/cm’)
Incidence (deg)
CD = i,(TJTf’* exp
cR = iR(T) exp
(11) 3oo Temperature (K)
iL(?J), iD(ZJ and iR(ZJ are determined by applying the less square method to eqn (9) referred to the experimental characteristics at T = 25°C as determined by its three fundamental points M,, M2 and M, which are respectively the short-circuit current (I,, 0), the maximum power point (ZM,Vh()and the opencircuit voltage (0, VW). The number of solar cells connected in series and parallel is determined
on the basis of the Paor and the
zrd
,m
I
Y
law 0 Time (mln)
I
I
O.ll---c-k 0
I
Time (min)
Fig. 2. Rotation r¶ around pitch axis: 0”. .Earth ..-. . ._ pointing attttude. Thermal exchange on both sides.
G. Colombo et al.
44
Main load array
Incidence (deg)
Charge
array
Bus
150
Efficence 0.25
Fig. 5. Unregulated bus topology.
02
The diodes D, and D, simulate the charge transfer effect according to the equation
0.15 0.1LZI 0
100
50
1, = ~~{exp(~~K) - exp(-&VI
Time (min)
Time (min)
Fig. 3. Rotation p around pitch axis: 0”. Sun pointing attitude. Thermal exchange on both sides. It can be seen that in the equation there are five main terms: a”(1 - rl)l,,, aAl - 1&t
heat absorbed by the front side heat absorbed by the rear side
oe,F,(T: - T4) heat exchanged with the Earth by the front side heat exchanged with the Earth by the aAl - rl)L rear side K = K.c.llU% heat exchanged with deep space
If the solar panel is fixed at the satellite’s body, it can be hypothesized that only one side exchanges heat, while the other is thermally insulated from the rest of the satellite. In Figs 2 and 3 the temperature profiles resulting from the simulation are shown (LEO mission). 4. BATTERIES
The mathematical model of batteries has been developed on the basis of what was proposed by Zimmermann and Peterson [8] as showed in Fig. 4. The two capacitances are Gaussian voltage dependent: C= A exp[-B(V-
V,)l+
D
where A = is the maximum capacitance value, = is the minimum capacitance value V, = is the mean voltage level B = is the distribution constant.
(16)
(17)
the coefficients K, and K2 are determined from the experimental data. The diode D, represents the self-discharge of the battery cell. The battery model yields from the series connecting of the single battery cells, then the output battery voltage is obtained by multiplying the output voltage of a single cell by the number of cells. If two or more batteries are shunt connected, then the total output current of the battery package is obtained by multiplying the single battery current by the number of batteries. 5. BUS VOLTAGE
REGULATION
Regarding bus voltage regulation, various solutions can be adopted according to the payload’s input-voltage requirements. Hence the bus voltage my be unregulated, sunlight regulated or fully regulated. 5.1. Unregulated bus (Fig. 5)
This approach is based on the idea of simplifying the power system when the users can accept the variable characteristics of the power sources. The solar generator feeds directly the platform equipment and the payload The operating
by way of a distribution block. point N (Fig. 6) is defined by the
intersection of the current-voltage characteristics of the generator and that representing operations at constant power P.
D
0
VB vo VFl
---Drru Fig. 4. Electrochemical cell equivalent circuit.
Voltagefp.u.1 -mar-
Fig. 6. Operating points with the various types of voltage regulators buses.
Satellite power system simulation
Fig. 7. Sun regulated bus power supply.
5.2. Sun regulated bus (Fig. 7)
In order to limit voltage variations for most of the time, voltage regulation outside periods of eclipse can be considered. The solar generator feeds the equipment at constant voltage by means of a voltage regulator. Outside eclipses the bus voltage is kept constant (equal to VR)within a range of a few percent depending on the performance of the regulator. Two operating points are now defined in Fig. 6; these are that of the solar generator, point R, and that of the load, point R’. The segment RR’ represents the current shunted through the regulator. A charge regulator connected to the bus provides recharging and maintains constant battery current outside the eclipses. When the satellite is in eclipse, the battery is directly connected to the bus, the bus voltage is imposed by the battery voltage V,.
Fig. 9. The sequential switching shunt regulator
The inputs are: solar array section number; 0 solar array section current; l load current.
l
5.3. Regulated bus (Fig. 8) Day and night voltage regulation is obtained by decoupling the battery from the bus by means of a discharge regulator. Out of eclipse, a regulating circuit fixes the potential of the solar generator and the supply bus. During the eclipse, the battery provides the power to the load by way of a discharge regulator which keeps the bus terminal voltage constant and equal to VR. Various types of voltage regulators are used. In this paper we present only the model of the sequential switching shunt regulator, widely used on European satellites. For this regulator (Fig. 9) two different models were developed. The first, very simple, can be used for the simulation of the entire orbit, where the simulation time step is about 10 s. In Appendix B the MATLAB simulation function is reported.
+A ALRelay
1
Ralay2'
A?Ralay 3
+Rday
4
StepInput
E El
I-Loac
Fig. 8. Regulated bus power supply.
Fig. 10. SIMULINK
block diagram of the S’R.
46
G. Colombo et al. Load current (A)
~,
.
But current (A)
Time (see) x lo-5
Fig. 11. S3R simulation results: load current.
Fig. 13. S’R simulation results: output bus current.
The outputs are: l l l
The BCR and BDR are respectively represented by their steady state continuous conduction mode equations [lo]:
bus voltage; bus current; shunted solar array section number.
D = v,,,lKn
The second model should be used for the simulation of the transients when the load current suddenly changes; in this case the simulation time step is about 10e6 s. In Fig. 10 the SIMULINK block diagram of the S’R is reported with the regulation of four solar army sections (see Fig. 9). In Figs 11-13 the S3R transient simulation results are shown; we can see that when the load current, for instance, suddenly rises from 2 to 13 A, the bus voltage restarts to ripple around a lower voltage value less than 50 V, which is the chosen reference bus voltage. The power dump operates only in switching mode due to the hysteresis nature of ripple control end results in on-off dumping of a single solar array section. Only one section is in switching mode, the others are in a digital status. For more details we suggest the article of O’Sullivan and Weinberg [9].
BCR duty ratio
1 sV K” =- 1-D BDR duty ratio I,,, = (1 - D)I,,
(19)
These models are adequate for our purposes when the time simulation step is about 10 s. Because the interface with the thermal subsystem has not yet been developed, the battery charge is controlled by the comparison of the actual battery state of charge with the battery’s nominal capacity, instead of using the battery temperature as control variable. 6. POWER SYSTEM SIMULATION
Bus voltage (V) 50.02 8.0,
50.01
I
1 / ; i ; f ..
.
. .
i..
_i
.
i..
The satellite power system simulation reported here is only an example of the capabilities of the computer program [ 111. We wanted to simulate the energy balance of a satellite power system in low earth orbit, with an average load power of 360 W and two peak power Main load array
,9.985
Charge array
Bus
.
Time (set) x IO-~
Fig. 12. S’R simulation results: output bus voltage.
Fig. 14. Unregulated bus clamped solar array concept.
41
Satellite power system simulation 320,
.
. Cell ympe.raturF(K)
.
,~,
.
260.
* Required Ijower.(W)
01
0
240.
.
,
I llxm2ooo3mO4omsooo6oco7wOeooo
Solar array power (W) 1500
1
220. 200. 180.
led
0
1000
2000
3000
4000
so00
6000
0
7000
Time (set)
‘:: 0
Time (set)
Fig. 15. Solar cell temperature.
Fig. 17. Required power profile and solar array output power.
of 1100 W of 5 min each. The simulation is made in EOL conditions with a satellite life of 1 year. The satellite attitude is Sun-pointing, so that the incident sunlight remains constant. There are two independent solar arrays; the first provides for the requested load power, the second is exclusively used for battery recharging. The power control unit controls whether the system is in peak power or eclipse conditions comparing the solar array current with the load current, the difference between them is the battery discharge current. The battery control unit provides control of the battery charge and discharge; if the system is not in eclipse or in peak power, the battery is recharged by the second solar array until the state of charge reaches the nominal capacity. The bus voltage is unregulated, there are no regulators at all, but two concepts were analyzed. The first concept, the unclamped solar array, offers the simplest approach for the centralized functions of the power subsystem. In sunlight the bus voltage level
is dictated by the product of the total array current and the bus load impedance. The array current is a parameter that can vary with the array temperature. We can notice that at the eclipse exit the solar array will be very cold, then the conversion efficiency will be high and so will the output voltage. During eclipse or peak power the bus voltage will be the same as that of the battery and, in the last case, the solar array will operate at the battery level. The second concept, the clamped solar array (Fig. 14) limits the upper excursion of the solar array voltage at eclipse exit by clamping the whole array to the battery level. With this approach the battery is directly connected to the main bus just prior to eclipse entry and consequently the bus voltage performance is dictated solely by the battery characteristics. Upon exiting from eclipse all the array sections remain connected to the battery and causing the bus voltage to be clamped at battery potential. After the solar array temperature has increased to an acceptable level, the battery is disconnected from the main bus and the bus voltage shifts to its normal sunlight operating level.
periods
Batten,
Solar array current (A)
30
Battery current (A) I
:/-I o0
mO0
2mO
voltage (VI
20,
1
i-- I :B~_J--LI 3OOa
4OOO
E400
6000
mO0
nOOa
-201 0
I
1ooo200030004omYmmo7mO~
Time (set)
Time (set)
Fig. 16. Solar array output voltage and current.
Fig. 18. Battery voltage and current
48
G. Colombo et al. Battery
Bus voltage (V)
charge (Ah)
Battery DOD%
Bus current (A)
A’
liEL_Y 0
lcm
2000
ma
4000
5Ooo
$Lll__-_1 6000
7000
01 0
aooo
Time (SW)
1OOa
2000
3000
4000
5000
6000
7000
I 3000
Time (set)
Fig. 19. Battery state of charge and DOD%.
Fig. 21. Bus voltage and current for clamped solar array.
In the following figures the simulation results are reported, in Appendix B the mission requirements list are given. In Fig. 15 the solar cell temperature is shown; we can see the very low temperature at the eclipse exit, and hence the photovoltaic efficiency will be high. In Fig. 16 the solar array output voltage and current are shown; we can observe the high output voltage at the eclipse exit, when the solar array is cold. In addition, during the peak power periods (before the eclipse), the solar array voltage level is equal to the battery voltage (lock-up phenomenon). Finally, the output voltage is higher than the chosen bus reference voltage because the solar array works below the maximum foreseen temperature (305 K). We emphasize once more that there are no voltage regulators. In Fig. 17 the required power profile and the solar array output power are shown. The output power is higher than the required level because the solar array is oversized in order to compensate for the losses distributed over the whole power system (harness, etc.) (see eqn (4)). In Fig. 18 the battery voltage and current are shown: we can observe the difference between
the voltage values during charge and discharge. The negative values of the battery current are referred to the discharge mode. In Fig. 19 the battery’s state of charge and the depth of discharge are shown; the satellite mission was fixed at 1 yr, so the battery should undergo 5000 cycles and the foreseen depth of discharge for a Ni-Cd battery may be 40%; the simulation results show that the DOD, in this case, reaches 30%. In Figs 20 and 21 the bus voltage and current diagrams for both solutions (unclamped and clamped solar array) are reported. It is clear that in the second case the voltage excursions are considerably less than in the first case. Disconnection of the battery, after the eclipse, is made when the solar array temperature is greater than 290 K.
Bus voltage (V) so
I
7. CONCLUSIONS This paper presents a new method for satellite power system simulation. In particular, it allows any
power system architecture to be analyzed by means of modular software tools organized on built-in blocks developed within MATLAB/SIMULINK environment. We report the models of the main blocks and two simulation cases. The simulation cases demonstrate the capabilities of the method in terms of modularity, flexibility and accuracy. In order to improve this tool the next goals will be: l
40
30
0
I’ . . I Bus current (A)
40.
I
:~l_L_ 1 OL 0
l
l l
the addition of the battery thermal model interfaced with the satellite thermal subsystem; the addition of a “memory effect” and the solar array degradation models for Ni-Cd batteries; the development of Ga-As solar cell model; the development of program blocks which allow mass computation. REFERENCES
I
looo2oal3ooo4woLwo~~~ Time (set)
Fig. 20. Bus voltage and current for unclamped solar array.
1. Bauer, P., Computer simulation of satellite electric power systems. IEEE Trans. Aerospace Electron. Syst., 1969,
AES-5, 6, 934-942.
49
Satellite power system simulation 2. Capel, A., Ferrante, J., Cornett, J. and Leblanc, P., Power system simulation for low orbit spacecraft: the EBLOS computer program. E&t J., 1982, 6, 319-337. 3. Lee, J. R. et al., Modeling simulation of spacecraft power systems. IEEE Trans. Aerospace Electron. Syst.,
geostationary Earth orbit high elliptical orbit low Earth orbit power conditioning control system radioisotope thermoelectric generator
GE0 HE0 LEO PCCS RTG
1988, 24, 295-303.
4. Bate, R. R., Mueller, Fundamentals
9. 10. 11.
12.
D. D. and White, J. E., Dover Publications,
APPENDIX B
of Astrodynamics,
New York, 1971. Montenbruck, 0. and Pfleger, T., Astronomy on the Personal Computer, 2nd edn., Springer, Berlin, 1994. Wertz, J. M., Spacecraft, Atttude Determination and Control, Reidel, Dordrecht, 1978. Tada, H. and Carter, J., Solar Cell Radiation Handbook, JPL Report 77-56, Caltech, Pasadena, CA, 1977. Zimmermann, H. and Peterson, R., An electrochemical cell equivalent circuit for storage battery/power system calculation by digital computer. In IECE Proc., Las Vegas, 1970. O’Sullivan, D. and Weinberg, A., The sequential switching shunt regulator S’R. ESA SP, 1977, 126, 97-102. Mohan, Undeland and Robbins, Power Electronics, 2nd edn., Wiley, New York, 1995. De Luca, A., Simulazione de1 sistema elettrico di un satellite. B.S. dissertation, “La Sapienza” University, Rome; ESA-EAD EE90682, 1996. MATLAB, The Math Works Inc., 24 Prime Park Way, Natick, MA 01760.
APPENDIX A
This appendix is limited to the satellite mission’s detailed list and the SIMULINK block diagram of the simulated power system (Fig. 22). The MATLAB program that initializes all the parameters used during the simulation, the MATLAB function that simulates the PCU for the unclamped solar array concept, and the MATLAB function that simulates the S’R for a time simulation step of 10 s can be obtained directly from the authors. The output variables are plotted by the “scope” blocks. Time simulation step ORBIT Semimajor axis a Eccentricity F Inclination i Ascending node long. R Perigee argument 0 True anomaly at epoch y0 Epoch (initial analysis date)
Mission duration
10 s LEO (equatorial) 8000 km 0.01 0.
0 0 0 1996 March 21 0 h 0 min 0 s 365.25 days
Required power (payload) List of acronyms G’R)
BAPTA BCR BDR BOL EOL
sequential switching shunt regulator bearing and power transfer assembly battery charge regulator battery discharge regulator beginning of life end of life
P mali P nl,” P d*i
Available power from solar array I (papad + platform + harness) EDL Pt0L
Fig. 22. Satellite power system simulator-SIMULINK
1100 w 360 W 400 w
715 w 743 w
block diagram unregulated bus voltage.
50
G. Colombo
Available power from solar array 2 (battery charge) P EOL PElOL
Bus reference voltage Solar array’s configuration Solar array 1 Section number Shunt cell number per section Series cell number Solar array 2
375 w 390 w 30 v
4 150 58
et al.
Section number Shunt cell number per section Series cell number
2 157 58
Orientation and attitude: along pitch axis, Sun pointing, thermal exchange on both sides Batteries Battery number 4 Cell number 25 Capacity 20 A h DOD% 40 Temperature 268 K
