IEEE Electrification - December 2020 - 17

RP =

t ini + Torbit

t ini

Pload (t) dt

peak
load

Torbit

, (10)

where Torbit is the orbit duration.

Orbit and Eclipse Durations
Both the orbit and eclipse durations are of paramount
importance when sizing the solar array and battery. To
calculate the duration of the eclipse in circular LEO, the
third law of Kepler for planetary motion can be applied,
which provides the period of the eclipse as a function of
the orbit duration:

a R oR- h k

Torbit cos
T
Teclipse = orbit
r
2
4r 2 R o3
Torbit = G M
,
Earth
Earth
-1

; where

(11)

such that R o is the radius of the orbit, h is the altitude of the orbit, G Earth is a gravitational parameter
(G Earth = 6.67 # 10 -11 Nm 2 /kg 2 ), and M Earth is Earth's mass
(M Earth = 5.94 # 10 24 kg).

Path2
ηSun/PV

The generation, storage, distribution, and conditioning of
the electrical energy are performed at some expense,
among which are power losses. To estimate the power
losses dissipated in the EPS during the mission, the
power flow throughout the EPS needs to be identified
during both the sunlight and eclipse durations. Moreover,
the efficiency of each individual generation, storage, distribution, and conditioning subsystem need to be accurately defined.
For performing the aforementioned study, the system
in Figure 2 can be redrawn in terms of power paths and
efficiency, as explained in Figure 12. As shown in Figure 12, there are three power paths, Path 1, Path 2, and
Path 3, which take their names from the PV array to the
payload, from the PV array to the battery, and from the
battery to the payloads, respectively. These paths represent the case of injecting power directly from the PV
array to the payloads during sunlight, the case of injecting the excess of power from the PV arrays to the battery during sunlight, and the power backup from the
battery to the payloads during eclipse. Regarding their

Eclipse

ηBT-CH/DCH

Eclipse

ηBus/BT

ηPV/Bus

Path3
ηBus/Load

Path1

In the case of CubeSats in LEO, the
duration of the eclipse varies according to the sunlight incident angle
with respect to the orbit plane, which
takes different values upon the
present season as well as the orbit's
altitude and inclination. Accordingly, in LEO, the eclipse duration
may double compared to its minimum duration. Moreover, the ratio
between the duration of the eclipse
and the total orbit play an important role, as it influences the PV
array, battery, and other EPS element requirements.

Power Losses Estimation

ηBus/BT
Payloads

ηSun/PV

The ratio between the
duration of the eclipse
and the total orbit
plays an important
role, as it influences
the PV array, battery,
and other EPS
element requirements.

ηBT-CH/DCH

Separate load demand profiles for
both sunlight and eclipse and sunlight periods are key factors for the
estimation of energy generation
and storage sizing. Furthermore,
the energy losses corresponding to
the EPS's different power flows are
other factors with an important
impact in this matter. Peak and
average load demands for each subsystem also need to be defined.
Alternatively, the ratio (R p) between
average and peak power over a period of time is typically used to characterize the load demand

(a)

ηPV/Bus

Path3
ηBus/Load

Payloads

(b)

Figure 12. The power paths and energy efficiency of the power generation, storage, distribution, and conditioning subsystems during (a) sunlight
and (b) eclipse durations.

IEEE Elec trific ation Magazine / D EC EM BE R 2 0 2 0

IEEE Electrification - December 2020

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