Modeling of solar array and analyze the current transient

Journal of Advanced Computing and Communication Technologies (ISSN: 2347 - 2804)
Volume No.3 Issue No. 2, April 2015
33
Abstract— Spacecraft bus voltage is regulated by power
conditioning unit using switching shunt voltage regulator having
solar array cells as the primary source of power. This source
switches between the bus loads and the shunt switch for fine
control of spacecraft bus voltage. The effect of solar array cell
capacitance [5][6] along with inductance and resistance of the
interface wires between solar cells and power conditioning
unit[1], generates damped sinusoidal currents superimposed on
the short circuit current of solar cell when shunted through
switch. The peak current stress on the shunt switch is to be
considered in the selection of shunt switch in power conditioning
unit. The analysis of current transients of shunt switch in PCU
considering actual spacecraft interface wire length by
illumination of solar panel (combination of series and parallel
solar cells) is difficult with hardware simulation. Software
simulation by modeling solar cell is carried out for a single string
(one parallel) in Pspice [6]. Since in spacecrafts number of
parallels and interface cable length are variable parameters the
analysis of current transients of shunt switch is carried out by
modeling solar array with the help of solar cell model[6] for the
actual spacecraft condition.
Index Terms— Shunt regulator, Shunt switch, Current transients,
power conditioning unit
I. INTRODUCTION
In space application, solar energy is the main sources of power apart
from nuclear alternatives used for inter planetary missions. With
increase in power demand the solar array size is increased with more
number of series and parallel cells. In spacecraft bus voltage
regulation, several strings of different ratings and shunt switch
combination as shown in the input of Fig-1 are paralleled to meet the
required load power. At any point of time only one string is switching
and others are either ON or OFF depending on the load power
requirement in sequential shunt switching regulator [1]. The solar cell
capacitance and resistance along with the interface cable line
inductance, plays major role in causing current stress on the shunt
switch. This current transient study is important in the selection of
shunt switch. The effect of solar cell capacitacne and cable
inductance on the performance of power conditioning unit should be
considered in the design. The effect of solar array cell capacitance
has been considered in [ 2]–[4] for the design of shunt power
regulators. The stress on the shunt switch due to cell capacitance and
cable inductance effect has not been addressed. The solar array
strings and shunt interface is through cables of different length for
each circuits. Considering the wiring on the panel, the current
transients are not same for all circuits.
Hardware simulation for all combinations (various string rating
and cable length) wired in the spacecraft is a complex approach. This
is achieved with software simulation through solar cell modeling by
deriving internal cell capacitance and resistance. The equivalent
Fig 1. Schematic of shunt switch regulator
circuit of solar cell is as shown in Fig-2. Measurement of solar cell
capacitance[5] based on the extra output voltage ripple due to cell
capacitance is not an accurate method since cable line inductance has
not been considered in the rise time of shunt switch. The first step for
cell capacitance derivation is the hardware simulation with a single
string and known cable length in the switching path. Many
parameters are available in the current transients of shunt switch to
create a cell model for software simulation, when compared with the
output voltage extra ripple due to rise time of shunt switch.
Fig 2. Solar cell equivalent circuit
II. HARDWARE SIMULATION AND ANALYSIS
A solar string with a minimum generation of 0.5A at 42V (23 cells
Modeling of Solar array and Analyze the Current Transient
Response of Shunt Switch Voltage Regulator in Spacecraft
Power Conditioning Unit
By
1
Thriveni Eshappa, 2
Rajeev Ranjan, 3
Nitin D Ghatpande
1,2,3
Power System Group, ISRO SATELLITE CENTRE, Bangalore-560047
1
thriveni@isac.gov.in, 2
rranjan@isac.gov.in, 3
gpande@isac.gov.in

34
in series) is interfaced with the shunt circuit with definite cable
length. The schematic shown in Fig 1 is for the 42V spacecraft bus
voltage. Instead of closed loop operation a fixed 42V supply is used
as bus voltage. Shunt switch is driven by function generator to
observe the current transients at different switching frequency. String
isolation diode is connected between the solar array and the load.
Solar cells are illuminated by large area pulsed solar simulator
providing sun intensity of 2ms duration. The current and voltage
transients are as shown in Fig 3 and Fig 4 for 15 KHz switching.
Fig 3. Current transient response
The current through the switch when shunted is a damped sinusoidal
with a settling time of 18 µs as shown in Fig 3. Whereas the voltage
rise across the switch when open is ringing and not a smooth
exponential as shown in Fig 4. However these dynamics are not the
actual transients present in the spacecraft since the solar string rating
and harness length are different in the setup. Modeling of solar cell is
essential to carry out software simulation incorporating solar array
circuit connected to shunt switch with required cable length
inductance. A single string is considered in the hardware setup for
derivation of cell capacitance and resistance to model solar cell.
Voltage rise
Fig 4. Voltage transient response
A method for finding solar array capacitance is discussed in [5]
considering the voltage rise across the switch where cable inductance
which also contributes for the voltage rise as shown in Fig 5 is
ignored. This method will not give exact cell capacitance value.
Hence extra ripple is due to cell capacitance as well as cable
inductance in the switching path. Current transient through shunt
switch is taken as input for modeling of solar cell since many
parameters are available compared to voltage rise in the voltage
transient response.
Fig 5. Inductance effect on Voltage rise across switch
The most efficient way of deriving solar cell capacitance, resistance
and interface cable inductance is using current transient parameters
like first peak current, second peak current and damped frequency. At
switching frequency <15 KHz the variation of current parameters are
very minimal as shown below for 10 KHz. Hence the above
mentioned values for 15Khz is considered for derivation.
Fig 6. Current response for 10Khz
III. DERIVATION OF R, L, C USING MATHEMATICAL MODEL
When the shunt switch is open, solar cell capacitor starts charging
and discharges through the switch when closed. The mathematical
model and circuit for this action, including resistance and inductance
in the path is as shown in Fig 7.
Fig 7. Circuit diagram for model
Equation for the given circuit, when switch is shunted
C
dVc
dt
+ Io* u(t) = I(t) (KCL)
sCVc(s) +
Io
s
+ CVo = I(s) (1)
Vc(t) = I(t) R + L
dI(t)
dt
(KVL)
Vc(s) = I(s) (R+Ls) (2)
From (1) and (2)
sC I(s) (R+Ls) +
Io
s
+ CVo = I(s)
I(s) =
IoWn 2
s(s2+2∗zi∗Wn ∗s+1)
+
kWn 2
(s2+2∗zi∗Wn ∗s+1)
Where, Wn =
1
LC
---- natural frequency,

35
Wd = Wn 1 − zi2 =
1
LC
−
R
2L
2
-- damping frequency
Zi =
R
2
C
L
---- damping factor
In time domain I(t) = Io (1 -
𝑒−𝑧𝑖∗𝑊𝑛 ∗𝑡
1−𝑧𝑖2
sin [Wd* t + atan
(
1−𝑧𝑖2
𝑧𝑖
)t ] +
𝑉𝑜
𝑊𝑑𝐿
𝑒−𝑧𝑖∗𝑊𝑛∗𝑡
*sin (Wd*t) (3)
To derive R, L and C, the steady state current Io is considered as zero
for simplicity.
Equation (3) reduces to
I (t) =
𝑉𝑜
𝑊𝑑𝐿
𝑒−𝑧𝑖∗𝑊𝑛∗𝑡
*sin (Wd*t) ---- (4)
Substituting 1st
positive peak, 2nd
positive peak and damping
frequency in eq (4) for different time, the values of R, L and C
obtained are----
Total cell capacitance C= 0.032µF, Total series resistance R = 4.05Ω
and Total Inductance L= 7µh. ------ (5)
A. INDUCTANCE:
One meter wire will have an inductance of 1.1H (straight or
looped). With varying diameter of 500mil (0.49 inches) to 5mil
(0.0049 inches) the change in inductance is from 1H to 1.8H only.
In the hardware setup two wires (spacecraft cable requirement) of 8
meters length was used between cell positive and negative. Mutual
inductance for this setup is given by M=k (𝐿1𝐿2) --- (6)
Where k is the coupling coefficient with 0 ≤ k ≤ 1, L1 is the
inductance of the first wire and L2 is the inductance of the second
wire. The measured effective inductance of two parallel wires of 1 mt
length when closely placed is 0.9µh. Where Leff =
(L1*L2/(L1+L2))*(1+ k) --- (7). Hence k= 0.636. For 8 mts cable
length effective L is given by 4.4*(1+0.636) = 7.19H which is
closely matching with the value in (5).
B. RESISTANCE:
The total series resistance includes, cell internal impedance, wire
resistance and shunt switch ON resistance. The split up of total
resistance is as given below
 The On resistance of 2N7391 is 0.2 Ω.
 Wire resistance: Any wire carrying alternating current will have
higher resistance than wires carrying dc current due to skin effect
which is given by
10−6 𝑓
𝐷
in Ω/ft. Where D = diameter of wire in
inch, f= frequency of alternating current in hertz. Since transient
response is alternating current, the AC resistance for 22 gauge wire
with D=0.025 inch and f= 333 KHz (frequency is taken from the
practical result from fig3) is Rac= 0.0231 Ω/ft or 0.0757 Ω/mt. For 8
meters length Rac=0.606Ω. Hence for 2 wires effective AC resistance
Rac> 0.3 Ω and ≤ 0.6 Ω because of proximity effect for closely
running wires. Here maximum of 0.6 Ω is considered which
introduces very small percentage variation in the cell resistance
calculations. Hence for 8mtr wire Rac=0.606Ω. Whereas the DC
resistance of the wires (22 gauge) for 1mt length= 50m Ω. And for
8mts parallel wire Rdc= 0.2Ω.
 Cell internal resistance: The internal resistance for 23 cells in
series= (4.05 - 0.606-0.2) = 3.244 Ω. Hence the cell internal
impedance= 141mΩ.
C. CELL CAPACITANCE:
The capacitance of each cell is derived from total capacitance. Hence
individual cell capacitance is given by (0 .032*23) = 0.736F.
This value closely matches with the cell data.
IV. CELL MODEL
From the value derived above, cell model is created as shown in
Fig 8. The four diodes in parallel with the current source gives the
open circuit voltage of 2.64 which is equal to actual open circuit
voltage of onboard cells for 42V application. Manufacturer’s data
sheet describes the internal impedance of the cell to vary from 0.1 to
Fig 8. Solar cell model
0.5 Ω. And the cell impedance will tend towards the lower side of
this range. Accordingly impedance of 141mΩ to 153mΩ (considering
the small percentage error due to proximity effect) is obtained in the
calculation.
V. CELL VALIDATION
The solar cell model is validated by connecting 23 equivalent circuits
in series to get one parallel of 0.52A @ 42V and interface with the
shunt switch circuit as shown in Fig 10. When the switch is closed
the current dynamics through it as shown in Fig 9 is same as the
result obtained from the hardware experiment shown in Fig 3.
Fig 9. Simulation Result
 Initial Current Io= 0.52A
 + ve Peak current = 2.838A
 -ve Peak current= -878mA
 Period= 3.04s
 tr = 750ns,
 Settling time = 20s

36
Since all parameters are matching with respect to hardware results,
the cell model created is validated. Using this cell model, solar string
of any rating connected to shunt regulator with any harness length
can be modeled in the software to analyze shunt switch current stress.
In any spacecraft each string is combination of series and parallel
cells to achieve required string current at required voltage.
Fig 10. Circuit model
VI. ANALYSIS
When the switch is shunted, capacitor is fully charged. Current flow
through the switch is due to generation current of the cell and the
capacitor discharge current. This closed circuit becomes second order
under damped system with damping factor zeta (ξ) <1 given by
R/2 (C/L) . The response of under damped system is always
oscillatory with frequency of damped oscillation Wd= Wn*sqrt (1-ξ2
),
Wn=Natural frequency= 1/ (L C) . The peak current is given by e-
πξ/sqrt (1-ξ^2)
. The contribution of capacitor voltage for peak current is
higher than the solar cell current. The damping occurs due to the
presence of resistance in the switching path where the energy gets
dissipated. Hence the amplitude of current peaks damps
exponentially and settles at 4 * T, (T=
1
Wn ∗ ξ
).
A bypass diode is connected across each cell on the panel to bypass
the cell failed in open mode. The negative peak is limited at 880mA
due to the conduction of this bypass diode when reverse voltage is
greater than total cut in voltage for 23 diodes.
VII. EFFECT OF SERIES DIODE
For higher string rating, single parallel (minimum current) strings are
diode ORed to achieve total string current thereby preventing one
string failure under short circuit of any single parallel. The current
transient through switch with the series diode is as shown below.
Series diode
Fig.11
Hardware Simulation:
CH4= Switch Current, CH2= Drain Voltage
Fig.12
Software Simulation:
Fig.13
As observed in fig12/fig13, there is a ringing current of small
magnitude when the resonating negative current flows through the
diode in the switching path. Since diode blocks this negative current
the reverse voltage across the diode increases for a small duration.
The reverse voltage stress on the series diode for one parallel as
observed in the simulation is shown in fig12.
The reverse voltage across the series diode is 157V as seen above.
The reverse breakdown voltage of 1N5811 used is 160V. This series
diode is blocking negative 880mA (fig9) which causes current
ringing during the entire negative cycle of resonant current. At
negative peak of 200mA ringing current, maximum reverse voltage is
observed across the diode. This peak reverse voltage reduces with
decrease in the ringing current magnitude and becomes zero at the
end of the cycle. Lower the string rating higher is the voltage stress
on the device.

37
Fig.14
VIII. SOLAR ARRAY MODEL
The shunt switch in the spacecraft is switching to regulate the bus
voltage. The string current used onboard is a variable component.
The effect of solar cell capacitance and cable inductance for
maximum and minimum string rating is simulated and analyzed by
creating solar array model. Here minimum of 1A and maximum of
3.6A (2Parallels to 7parallels) is considered.
Solar Array model is generated using solar cell model and measured
cable length from panel to the shunt switch including wiring done on
the spacecraft solar panel. 23 cell models are connected in series to
get one parallel generating 0.52A @ 42V Vmp. The number of
parallels connected depends upon the rating of the switching string to
be connected to the shunt switch. Hence the extreme condition of
minimum and maximum strings solar array model is generated to
study the current response.
A. Maximum string current
The maximum switching current through the shunt switch
considered is 3.6A.
1. Solar String Model
Maximum string is simulated by connecting seven parallels each
0.52A @42V having 23 solar cell models in series. Each parallel
on the panel is running through a series diode to form one string.
2. Estimation of interface cable length
The length of the cable from solar string to the shunt switch includes
 Wiring on the panel from cell positive through diode to the
panel connector
 From panel connector to SADA connector
 From SADA connector to the shunt switch in PCU
Measured cable length is as given below
 Panel wiring
Each parallel to the diode anode = 1mt
Diode cathode to panel connector maximum = 3.25mts
String return to Panel connector = 1.65mts
 Panel connector to SADA connector = 3mts
 SADA to shunt switch in PCU = 3mts
 Shunt switch return from the PCU to panel connector =6mts
The total harness length from solar cell live to return is 16.9mts.
Hence L can vary from 16.9H to 8.45H since two wires are
running from series diode cathode to shunt switch drain.
The array model, circuit connection and simulation results are as
shown below.
Fig.15
S1in to S7in » 23 Solar cell equivalent circuit
Bypassdiode1 to bypassdiode7 » 39diodes connected across each
parallel
L17 to L23 »inductance of single wire from each cell positive to
series diode
L40» Inductance from series diode cathode to panel connector
L41» Inductance from panel connector to shunt switch
1) Current transient through shunt switch for L=16.9µH
(with maximum coupling between wires)
Fig.16
 +ve Peak = 8A through the switch
 -ve peak = 1A above the ground level
 Period= 12.14µs, frequency= 82Khz
 Settling time= 137µs
For 7 parallels the effective capacitance increases when compared
with single parallel (0.032µ*7). The actual spacecraft harness length
is more than the set up harness length (16.9mts>8mts) which
increases the inductance value. The damping factor reduces since L
is inversely proportional and C is directly proportional to damping
factor. This low value of damping increases the settling time. The
frequency has reduced because of low value of damping factor. The
peak current is not very high since it is dependent on damping factor
200mA
157V

38
as mentioned in page 3 analysis. Also the peak current is mainly due
to capacitor initial voltage which is still at 42V. A DC shift of 3.6A is
present instead of 0.5A (one parallel).
2) Current transient through shunt switch for L/2= 8.59µH
(with no coupling between wires)
Fig.17
 +ve Peak of 9.4A flows through the switch
 Small current ringing at –ve peak at ground level
 Period= 8.71µs, frequency= 114Khz
For lower value of inductance, peak currents (both +ve and –ve)
increases while settling time decreases. The maximum reverse
voltage across series diode during the blockage of negative swing
current is 17V for <1µs as shown below
Fig.18
The AC resistance of the harness depends directly on the frequency
of damping current and the harness length as described in page 3.
Since length of the harness has increased and frequency is reduced as
shown in the result below, the effective change in the Rac value is
negligible. Hence Rac=0.606Ω is considered.
B. Minimum string current
Simulation is carried out with 2 parallels connected for the same
harness length.
1) Current transient through shunt switch for L=16.9µH
(with maximum coupling between wires)
Fig.19
 The negative peak is blocked at zero level
 +ve Peak = 3.3A through the switch
 Period= 6.72µs, frequency= 149 KHz
 Reverse voltage across series diode is 70V for 1µs
2) Current transient through shunt switch for L/2= 8.59µH
(with no coupling between wires)
 The negative peak is blocked at zero level
 +ve Peak = 3.83A = through the switch
 Period= 4.75µs, frequency= 211 KHz
 Reverse voltage across series diode is 115V for 1µs
Higher the amplitude of negative current to be blocked by the diode
more is the reverse voltage across it.
IX. Conclusion
The solar cell capacitance and line inductance induces damped
oscillating current through the shunt regulator when the shunt switch
is closed. This peak current stress on the regulator must be considered
during the selection of the shunt switch. Higher the string rating and
harness length the effective capacitance and inductance increases
which reduce the damping factor zeta thereby increasing the settling
time. Hence during switching, the switch may open before the
settling time of damping current. High peak currents are mainly due
to capacitor initial voltage rather than short circuit current from solar
array. A DC shift of short circuit (Isc) current is present in the
dynamics. For higher string rating, each parallel (minimum current)
is diode ORed to achieve total string current. This series diode is
stressed for a short duration during blocking of negative peak current
of the transients. The reverse voltage stress also has to be considered
in the selection of series diode.
REFERENCES
[1] D.O'Sullivan, A. H. Weinberg "The Sequential Switching Shunt Regulator
(S3R)", in Record, ESTEC Spacecraft Power Conditioning Seminar,
1977, ESA SP-126, pp. 123-131.
[2] A.R.Patil,B.H.Cho anf F.C.Lee, “Design consideration for a solar array
switching unit,” in Proc. IECEC’90 Conf.,1990, pp. 373-379.
[3] G.J.Madden and A.Le, “Solar panel model for design and analysis of
power generation equipment,” in Proc. AIAA’94 Conf., 1994, pp. 151-
156.
[4] ----, “Design and test hardware for a solar array switching unit,” in Proc
IECEC’92 Conf., vol. 1, pp. 1.79-1.84

39
[5] R. Anil Kumar, M.S. Suresh and J.Nagaraju, “Effect of Solar Array
Capacitance on the performance of switching shunt voltage regulator,”
IEEE trans on power electronics, Vol.21, No2, March2006.
[6] T Eshappa, R Ranjan "The Effect of Solar Cell Capacitance and Interface
Cable Inductance on the Shunt Switch Current Transients in Spacecraft
Power Conditioning Unit", in ICRAIE , 2014, pp. 1-5.
Thriveni Eshappa received B.E degree in
electronics and communication from National
institute of Engineering, Mysore University, Mysore,
India in 1997. She was Lecturer in R.V. college of
Engineering, Bangalore from 1998 to 1999. She has
been with ISRO satellite Centre since 1999 in Power
System Group. She is involved in the design and
realization of satellite power systems. Her areas of
interest are solar cell capacitance, spacecraft bus
voltage regulators, Test simulators for spacecraft power system.
Rajeev Ranjan received B.Tech degree in Avionics
from Indian Institute of space science and
technology, Trivandrum, India in 2011. He has been
with ISRO Satellite Centre, Bangalore since 2011.
He is involved in the design of Dc-Dc Converter,
LDOs and satellite power systems. He has published
one conference paper related to artificial intelligence
in international conference. His areas of interest are
solar cell capacitance, S3R, Dc-Dc converters
Design, Magnetics and artificial intelligence.
Nitin D Ghatpande received his B.Tech in Electronics
in 1976 and M.E. in Electrical Engineering in 1990
from Indian Institute of Science. He is
Scientist/Engineer with ISRO since 1977 and worked
in many area related to spacecraft application like
Core Power of spacecraft, EMI/EMC compatibility of
spacecraft, development & analysis of power
conditioning and processing unit. He is currently
Group Director, Power System Group at ISRO
satellite centre. His work area includes development & miniaturization of
power processing unit for onboard usage in spacecraft.

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