IEEE - Aerospace and Electronic Systems - January 2022 - 52

Power System Design and Performance for Low Earth Orbit Spacecraft
Knowing the MPP of the solar arrays (VAR) at a specific
temperature, and temperature coefficients, by means
of thermistors, it is possible to predict the MPP voltage
over the operating temperature range. The calculations
below can easily be implemented using a simple computer
program or spreadsheet.
First, from the simplified scheme of Figure 10, the
resistors R1 and R2 are chosen to produce a voltage of
between 2.5 V and 3 V at VA. The temperature coefficient
ofVA for changes in VAR is then calculated using
dVA
dT
dV
dTR2
¼
R1 þR2
(1)
where dVA/dT is the change in VA perC and dV/dT is the
change in VAR perC.
Resistors R3 and R5 must now be selected such that the
voltage VB is equal to VA over the full, specified temperature
range. The equation for VB is
VB ¼
Vref R4 þR5ðÞ
R3 þ R4 þR5ðÞ
:
(2)
From the thermistors datasheet (PT2000), R4 is known
over the full range of temperatures. Using (1), the desired
value ofVB (i.e., VA) is also known, leaving two unknown
(R3 and R5). The values of R3 and R5 are calculated using
Gaussian Elimination, first having created two versions of
(2) (i.e., substituting the values ofVB and R4 at two different
temperatures).
When the solar array is cold VAR is maximum and RPT
is minimum, as shown in Figure 10. Conversely, when
VAR is minimum, RPT is maximum. The objective is to
match the voltage change across R110 from solar array hot
to cold with the voltage change across RPT
Vmpp ¼ VmppEoLð25CÞ
T25C Top
0

dVmpp
dT
NS
Figure 10.
Simplified scheme of the compensation temperature method.
The string diode voltage expressed by Vstring diode and the
uncertainty voltage expressed by Vuncert
VAR ¼ Vmpp þ
1000
0
NSmax Tmaxgrad
dVmpp
dT
VString DiodeVUncert:
(6)
The expected array voltage VARExp is given by (7),
where RPT is the internal resistance of the thermistor
PT2000 on the solar array and Vrefis the voltage reference
VARExp ¼ Vmpp þ Vref Ibias RPT
þVref:


ðÞ RSOT2
R36
(7)
Ibias is the bias current across the resistor RSOT1 and it is
given by the following equation:
Ibias ¼
1000
(3)
where VmppEoLð25CÞ is the end of life MPP voltage at
25C, it is calculated by (4) below. Top is the operating
temperature and NS is the string length
Vmpp EoLð25CÞ ¼
Vmpp EoL deg NS
1000
(4)
where Vmpp EoL deg is the end of life Vmpp degradation and
can be calculated by the following equation:
Vmpp EoLdeg ¼ 0:995 Vmpp cell:
(5)
Ploss ¼
The required array voltage VAR is the voltage estimated
by taking into account various parameters including
MPP voltage margins. The most significant margins
parameters having an impact on the required value are
resumed in, the maximum temperature gradient Tmax-grad,
52
Vref
10
RSOT1
by the following equation:
Ibias Cal ¼
RPT þ100C

VAR100C


Vref VAR100C


VrefRPT100C
VAR þ100C


VAR þ100C


Vref
:
(9)
The power loss estimated is calculated by the following
equation:
VmppVAExp
1:7
1:5:
(10)
The second control loop is used to determine the battery
EoC; a battery sense is used to monitor and control the
EoC battery. The EoC battery sensing is used to improve
IEEE A&E SYSTEMS MAGAZINE
JANUARY 2022
:
(8)
The theoretical calculation of the bias current is given
IEEE - Aerospace and Electronic Systems - January 2022

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