SYS.CURRICULUM // MODULE 03 OF 12·6 MIN READ

Solar Power Generation & Li-Ion Battery Ageing

Body-mounted GaAs solar cells, MPPT conversion losses, eclipse Depth-of-Discharge (DoD), and why derating charge voltage to 4.10 V doubles mission life.

Core Engineering Principles & Equations

  • A body-mounted 1P cube generates ~0.75–0.85 W in sunlight, yielding ~0.50–0.55 W orbit-average power after eclipse and MPPT efficiency.
  • Keeping eclipse Depth-of-Discharge (DoD) at 15–20% with a 4.10 V charge cut-off (20 °C) yields ~7,700–12,100 LEO cycles (~1.4–2.2 years to 80% capacity in our illustrative empirical model), and limiting DoD ≤ 12% extends life past 15,000 cycles (>2.7 years).
  • Li-ion cells must never be charged below 0 °C to prevent metallic lithium plating on the anode.

1. Body-Mounted III-V Solar Cells, Tumbling Geometry & Deployable Wings

At 1 au, unattenuated solar irradiance is S₀ = 1,361 W/m². Space-grade triple-junction III-V (GaInP/GaAs/Ge) solar cells convert ~30% of incident sunlight into electricity (reaching 34% in premium cells, versus ~20% for silicon). Accounting for backplate keep-outs, separation switches, and inter-cell gaps on a 50 mm cube, the repository power solver uses a conservative beginning-of-life efficiency η = 0.28 and active cell packing factor p = 0.60.

For an unstabilized 1P cube (A_tot = 150 cm², Cauchy mean projected area Ā_proj = 37.5 cm²), mean sunlit generation is P̄_sun = 0.86 W (0.71–0.86 W across five to six populated faces), yielding P̄ ≈ 0.54–0.55 W orbit-average in a 525 km Sun-synchronous orbit (f_e = 0.36–0.375). Counter-intuitively, pointing one 25.0 cm² cube face directly at the Sun lowers sunlit power from 0.86 W to 0.57 W because five faces go dark; even optimal body-diagonal pointing (√3·a² = 43.3 cm²) adds only 15% over free tumbling.

Breaking past body-mounted limits (~1.5–2.4 W orbit-average on a tumbling 1U CubeSat carrying two 30.18 cm² cells per face, or 4.3–5.2 W on a body-mounted 3U) requires Sun-pointed deployable wings. Hinged panels lift a 3P PocketQube above 10 W, while 3U dual-wing arrays generate 26–34 W peak BOL (16.5–21.8 W orbit-average) and 6U quad-wing arrays reach 58–68 W peak BOL (37.0–43.5 W orbit-average) to sustain reaction wheels and X-band transmitters.

Tumbling body-mounted vs. Sun-pointed solar generation
P̄_tumbling = S₀ · η · p · (A_tot / 4) · (1 − f_e),   P_pointed(θ) = S₀ · η · N_cell · A_cell · I_d · cos θ

From lib/physics/power.ts: at S₀ = 1361 W/m², η = 0.28, p = 0.60, f_e = 0.36, a 150 cm² 1P produces 0.86 W in sunlight and 0.55 W orbit-average.

2. MPPT Conversion, Orbital Energy Balance & Duty-Cycle Fragility

More than 90% of small satellites pair solar arrays with rechargeable Li-ion storage through a Maximum Power Point Tracking (MPPT) converter stage, battery charge regulator, regulated 3.3 V / 5.0 V point-of-load rails (derived from a 1S 3.6–3.7 V bus on 1P spacecraft or a 2S 8.2 V / 14.8 V bus on CubeSats), and current-limited load switches. Mechanical separation switches and a remove-before-flight (RBF) pin isolate all loads inside the deployer, while per-rail current limiters contain radiation-induced single-event latch-ups (SEL).

Closing the per-orbit energy balance requires sunlit array output to supply both daylight load consumption P_load·t_sun and eclipse battery draw P_load·t_ecl divided by battery round-trip efficiency η_bat ≈ 0.90. In the reference 1P load budget—OBC (15 mW), continuous UHF receiver (30 mW), magnetometer/IMU (10 mW), EPS housekeeping (8 mW), magnetorquers (60 mW at 15% duty), spectrum payload (120 mW at 10% duty), and a 0.5 W RF / 40%-efficient UHF transmitter (1,250 mW DC at 4% duty)—mean load is 134 mW, drawing just ~4% Depth-of-Discharge from a 1.85 Wh LiPo cell.

That headline margin erodes rapidly if unscaled peak loads creep upward: increasing UHF transmitter duty cycle from 4% to 10% adds 75 mW (+56% total bus load), while solar cell heating and radiation degradation trim end-of-life array output. In flight, Grizu-263A coordinated 0.75 W sunlit generation (~0.46–0.55 W orbit-average) against 1.5 W active load, demonstrating why picosatellites maintain ≥15–20% preliminary design energy reserve and strictly duty-cycle transmissions.

Orbital energy balance & daylight array power requirement
E_need = P_load · t_sun + (P_load · t_ecl) / η_bat,   P_sa = (P_e·T_e / X_e + P_d·T_d / X_d) / T_d

Evaluated in lib/physics/power.ts (η_bat = 0.90): a 134 mW mean 1P load over a 35.7 min eclipse at 525 km draws 0.080 Wh per shadow (~4.3% DoD on 1.85 Wh).

3. 5,500 Annual Eclipses, Depth-of-Discharge & 4.10 V Charge Derating

At 525 km altitude (95.1 min period, ~15.14–15.15 orbits/day), a spacecraft enters Earth's shadow ~5,530 times per year. Commercial cylindrical 18650 Li-ion cells (150–270 Wh/kg, 3.6 V nominal) and laminated LiPo pouch cells (150–200 Wh/kg, 3.7 V nominal) survive only 300–800 deep cycles at 80–100% Depth-of-Discharge (DoD), whereas LiFePO₄ cells (~60–90 Wh/kg, 3.2 V) trade specific energy for high thermal stability.

Multi-year LEO longevity therefore hinges on shallow eclipse cycling: for a 0.45 W eclipse load over 35.7 min (0.268 Wh drawn), a single 2,500 mAh (9.25 Wh) 18650 cell runs at just 2.9% DoD and a 600 mAh (2.22 Wh) LiPo pouch runs at 12.1% DoD. Simultaneously, derating the charge termination ceiling from 4.20 V to 4.10 V sacrifices ~10% of initial capacity but nearly doubles cycle life before solid-electrolyte interphase (SEI) growth lowers State of Health (SoH) to 80%.

In the illustrative empirical ageing model of lib/physics/battery.ts at 20 °C and a 4.10 V charge cut-off, holding eclipse DoD at 15–20% yields ~7,700–12,100 LEO cycles (~1.4–2.2 years to 80% capacity), and restricting DoD ≤ 12% pushes life past 15,000 cycles (>2.7 years)—compared with just ~3,840 cycles (~0.7 years) if charged aggressively to 4.20 V at 20% DoD.

Eclipse Depth-of-Discharge & illustrative Li-ion cycle-life relation
DoD = (P_ecl · t_ecl) / E_nom,   N_80 = 6200 · (0.2 / DoD)¹·⁵⁸ · exp(−2600·(T_ref⁻¹ − T⁻¹)) · 0.62 · 2^((4.2 − V_chg)/0.1)

From lib/physics/battery.ts (illustrative trade-study curve, T_ref = 293.15 K): derating V_chg from 4.20 V to 4.10 V doubles N_80 at any given DoD.

4. Sub-Zero Lithium Plating, Vacuum Containment & Flight Screening

Commercial graphite-anode Li-ion cells discharge across −20 to +60 °C, but charging is strictly restricted to 0 to +45 °C. Below 0 °C, slow lithium-ion intercalation into the graphite lattice causes irreversible metallic lithium dendrite plating on the anode surface, permanent capacity loss, and internal short-circuit risk. Because a 250 g 1P (τ_th ≈ 56 min) cools to ≈ −11 °C in a 550 km single-node eclipse model—and SMOG-1 thermal modeling showed sub-zero eclipse batteries that curtailed charging to half the sunlit pass—flight EPS designs pair a thermistor hardware inhibit with a 0.3–0.5 W Kapton heater to hold cells above +2 °C before charging.

Cell packaging inside a 42 × 42 mm 1P board footprint introduces further mechanical and magnetic trade-offs. A cylindrical 18650 cell (Ø 18 × 65 mm, 45–48 g) cannot lie flat inside a 1P cube—fitting axially only in 1.5P–3P stacks—and its nickel-plated steel can acquires remanent magnetic dipoles during spot welding that disturb passive magnetic attitude control. Flat LiPo pouch cells (2.0–5.5 Wh) fit 1P stacks cleanly with minimal magnetic remanence, but must be clamped between rigid FR-4 or aluminium plates with a preload pad to prevent vacuum swelling and delamination at 0 atm.

Across 32 verified CubeSat and PocketQube hardware anomalies audited in monograph SQ-R-004, electrochemical battery assemblies initiated 33.3% (7 of 21) of all materials-related mission failures, second only to deployment mechanisms (47.6%). Cell-level thermal-vacuum cycling, vacuum dwell inspection, and hardware over-charge/under-temperature cut-off verification are therefore non-negotiable before flight integration.

Thermistor-gated sub-zero charge inhibit & heater logic
T_cell < +2 °C ⇒ I_chg = 0 ∧ P_heat = 0.3–0.5 W;   +2 °C ≤ T_cell ≤ +45 °C ⇒ I_chg = I_MPPT

Blocks metallic lithium anode plating at eclipse exit when sunlit arrays deliver peak current into a cold-soaked picosatellite battery.

Specifications, Interactive Calculators & Topic Hubs

MODULE STATUS

Engineering Verification Check

Why do small-satellite EPS designs inhibit Li-ion battery charging when cell temperature drops below 0 °C?