IEEE Electrification - December 2020 - 18

The first step in
sizing the battery
is identifying its
voltage level,
especially in the
case of unregulated
bus voltage.

efficiencies, h sun/PV represents the
effectiveness of the PV array when
transferring the sunlight into electrical energy, while h PV /BUS represents
the efficiency from the solar cell to
the main bus, which includes the
solar cell series and shunt resistor
losses, antiparallel diode loss, and
boost converter losses. h BUS/BT represents the efficiency of the path from
the bus to the battery, which includes
the bidirectional converter power
losses (in the case of regulated bus),
battery diodes, and battery-protection switches, while h BT-CH/DCH represents the efficacy of the
battery itself due to electrochemical reactions and lost
stored energy. h BUS/Load summarizes the power lost in the
power conditioning modules, payload switches, and latchup protection devices. Other power losses due to the supply of the voltage, current, and temperature sensors as
well as of the integrated circuits may be included in an
efficiency evaluation for higher accuracy.
By coordinating between the aforementioned paths
and efficiencies, the following can be concluded. During
eclipse, the direct path, Path 1 for directly feeding the payloads from the PV array and Path 2 for charging the battery,
and both Path 2 and Path 3 for storing and recovering
power for high-power pulsed loads, are where the power
flows. Accordingly, the power loss during this time interval
can be expressed as

	

Sun
E Sun
loss = E load a E lossPath1 +

E lossPath2 E lossPath3 k
+ E ecliplse
E lossPath2, (12)
load
h BT-CH/DCH

where E lossPath1, E lossPath2, and E lossPath3 summarize the energy
lost in the paths, which can be expressed as function of
the efficiencies as
1 - h PV/Bus h Bus/Load
1 - h PV/Bus h Bus/BT
h PV/Bus h Bus/Load ; E lossPath2 = h PV/Bus h Bus/BT ;
	

1 - h Bus/BT h Bus/Load
(13)
E lossPath3 = h Bus/BT h Bus/Load .
E lossPath1 =

While during the eclipse, the power losses can be estimated as
	

E lossPath3
= E ecliplse
E ecliplse
loss
load
h BT-CH/DCH .(14)

Sizing of the Battery
The first step in sizing the battery is identifying its voltage level, especially in the case of unregulated bus voltage. This might be adjusted by identifying the battery
technology and number of cells that can be installed in
the string N S = vBusNom /vcellNom . Regarding the battery capacity, it is identified based on the battery's energy and can
be adjusted by considering the string voltage CBT ( Ah) =
EBT( Wh)/vBusNom and number of strings N P = CBT /(C cell N S).

18

I E E E E l e c t r i f i cati o n M agaz ine / DECEMBER 2020

Another important parameter in the
battery selection, especially from its
reliability point of view, is the maximum allowed level of the DOD, which
relates the battery energy to the energy
that supplies the payloads during the
eclipse time interval DOD = E eclipse
load / E BT .
Because the high discharging current
may affect the lifetime of the battery,
this latter has to be designed considering the cases of high-power pulsed
loads, where a possible solution could
be adding more strings.

Sizing of the Solar Array
Solar energy must always meet the balance expressed by
(1) with an additional margin, even at the EOL. This energy is calculated by integrating the PV-harvested power
during the sunlight, which itself is dependent on the
solar-array-equivalent area (A eq
PV), and average solar irradiance in the space (G AM0, W/m 2 ), as well as the solar cell's
efficiency (h Sun/PV), where the former denotes the solar
cell's area perpendicular to the Sun's radiation during the
whole orbit. In these parameters, the PV solar array efficiency and solar irradiance can be considered to be constrained, while the solar-array-equivalent area is flexible
and can be estimated as
	

A eq
PV =

#

E PV
E PV
.(15)
=
PPV (t) dt G AM0 h Sun / PV

t ini + t eclipse

t ini

The PV solar array as function of the equivalent one can
be expressed as
	

A eq
PV =

#

t ini + t eclipse

t ini

A PV (t) dt.(16)

In the case of a CubeSat, where the solar cells are installed
on all the facets, an approximation of the solar-arrayequivalent area could be made by using the projected
areas of the cube. In space, the CubeSat may be oriented
with respect to the Sun in three different positionings,
based on which the facets subjected to the Sun vary in
amounts and angles. In the case of only one facet being
subjected to the Sun, then the solar array area would be
A Facet, which is increased to 2 A Facet if two adjacent facets
are facing the sunlight, while for the case of the vertex
facing the sunlight it would be increased to 3 A Facet . By
averaging those PV solar arrays areas, the equivalent one
is deduced as A eq
PV = 1.38 A Facet .

Conclusion
This article provided an overview of the technical architectures and different parts of the EPS for CubeSats,
among which were its energy generation and storage as
well as protection system. It has been shown that triplejunction solar cells GaInP/GaAs/Ge are being employed
IEEE Electrification - December 2020

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