The power budget of a 1P PocketQube

The problem#

A 1P PocketQube has 150 cm² of outer surface, and part of it goes to the antenna, the separation switches and the backplate. The literature puts the orbit-average power of body-mounted 1P designs at a few hundred milliwatts[1][2]. In this note we derive that number from first principles, close the energy balance with a reference load list and quantify the effects that upset it.

Generation#

In sunlight a cell generates power in proportion to the solar constant, its efficiency and its area projected on the Sun direction. We use $S=1361$ W/m²[3]. Multi-junction III-V cells have nominal efficiencies around 30%, up to 34% for the best products[4]; following the PocketQube review we take $\eta =0.28$ as a conservative beginning-of-life value and a packing factor $p=0.6$ for the fraction of the surface that carries active cell area[1].

If attitude is not controlled, every orientation is equally likely. For a convex body, the mean projected area over all orientations is a quarter of its total surface (Cauchy’s theorem), so the mean power in sunlight and the orbit average are

where $f_{\mathrm{e}}$ is the eclipse fraction. For a 1P, $A_{\mathrm{tot}}=150$ cm² and the mean projected area is 37.5 cm²:

The 1P collects 857 mW on average in sunlight. Note what the model does not contain: there is no "cell face" bookkeeping. The packing factor stands for everything that is not active cell area, including the face behind the backplate and the gaps between cells.

Eclipse#

In a circular orbit the fraction of each revolution spent in the Earth’s cylindrical shadow depends on altitude and on the beta angle between the Sun vector and the orbit plane:

At 525 km and $\beta =0°$ the eclipse lasts 35.7 minutes of a 95.1-minute orbit, $f_{\mathrm{e}}=0.375$; the review rounds the longest eclipse of a 525 km SSO to $f_{\mathrm{e}}=0.36$ for its comparisons. Above a beta angle of about 67.5° the shadow disappears, and a dawn–dusk orbit sees the Sun all year.

The load list#

A load list gives each consumer’s power when on and its duty cycle. The transmitter dominates: radiating 0.5 W of RF through a 40%-efficient amplifier draws 1.25 W of DC, but only while beacons and passes are being served, about 4% of the time.11The duty cycle follows from the beacon interval, the packet length and the number of passes per day. A 1 s beacon every 60 s alone is 1.7%.

Balancing the energy per orbit makes explicit that what the battery delivers in eclipse must be put back in sunlight, with charging losses. The energy needed per orbit is the direct consumption in sunlight plus the eclipse energy divided by the round-trip efficiency of the battery[5]:

In this example the cells deliver 850 mWh per orbit against the 221 mWh needed, a margin of 284%, and the eclipse draws only 4.3% of a 1.85 Wh battery.

Depth of discharge and battery life#

A spacecraft at 525 km goes through about 5500 charge and discharge cycles a year. Li-ion cycle life depends strongly on depth of discharge, and multi-year missions usually keep it below 20–30%[5]. At 1P scale the eclipse energy is small, so the design question is not the size of the battery but its temperature: it must not be charged when cold, and the system must not brown out when it leaves eclipse at low voltage.

What upsets the balance#

The comfortable margin rests on assumptions that are optimistic in places. A real design must quantify each of these effects separately:

• End-of-life degradation. Radiation and thermal cycling lower cell efficiency by a few per cent over a short 1P mission, more above 600 km.
• Temperature. The efficiency of GaAs cells falls as they heat up, and a 1P with little heat capacity heats quickly in sunlight.
• Transmitter duty cycle. Raising it from 4% to 10% adds 75 mW to the mean load, more than half of the reference consumption.
• Peaks. Even with a balanced average, short peaks from the transmitter, magnetorquers or payload must stay within the battery’s internal resistance and the converters’ current limits.
• Attitude control. Pointing a face at the Sun does not help a cube, as the next section shows.

Tumbling beats pointing#

The intuition that controlled pointing raises power fails for a cube with body-mounted cells. One 25 cm² face held normal to the Sun presents 25 cm², whereas the tumbling average is 37.5 cm²: the sunlit power drops from 0.86 W to 0.57 W. Even the best orientation, along a body diagonal, presents only $\sqrt{3}{a}^2=43.3$ cm², 15% more than tumbling. Pointing pays only with deployable panels, which a 3P can use to exceed 10 W[2].

A flown example#

Grizu-263A filed an average generation of 0.75 W and an average active consumption of 1.5 W for its frequency coordination. The generation figure matches the sunlit mean of the model for five to six populated faces, 0.71–0.86 W; the corresponding orbit average is 0.46–0.55 W. With twice as much demand as supply in its active mode, the satellite necessarily duty-cycled that mode and let the battery bridge eclipses and transmissions[1].

Architecture#

flowchart LR
  SA["Body-mounted cells"] --> MPPT["MPPT converter"]
  MPPT --> BCR["Charge control"]
  BCR --> BAT["LiPo, 1.85 Wh"]
  BCR --> BUS["Battery bus"]
  BUS --> REG["3.3 V regulator"]
  REG --> LS["Current-limited load switches"]
  LS --> OBC["OBC"]
  LS --> COM["UHF transceiver"]
  LS --> ADCS["Magnetorquers"]
  LS --> PL["Payload"]

Current-limited load switches keep a single-event latch-up in one subsystem from shutting the whole spacecraft down, and let the EPS restart subsystems one at a time.

Conclusion#

A 1P with body-mounted cells can carry a continuous budget of a few hundred milliwatts, provided the transmitter duty cycle is planned carefully. The limit is not total energy but the timing of transmitter and payload peaks and the temperature of the battery. Missions that need more power should move to 2P or 3P, which scales power with surface, or to deployable panels with pointing.