Spacecraft Battery Sizing

Spacecraft Battery Sizing (space-systems/subsystems/spacecraft-battery-sizing)

Use when sizing the energy storage battery of an Earth-orbiting spacecraft power subsystem. The battery covers the spacecraft load during the orbit eclipse, when the solar array produces no power; this leaf sizes that battery: the energy it must deliver in the eclipse, the required nameplate capacity from the depth of discharge (DOD) limit and the discharge efficiency, the capacity in ampere hours at the regulated bus voltage, the series and parallel Li-ion cell layout, the discharge C-rate check against the cell limit, and the pack mass from the pack specific energy. It implements the standard ECSS-style sizing chain in pure Python, stdlib only, deterministic and offline. It pairs with space-systems/subsystems/solar-array-sizing (the charge source this battery complements), space-systems/subsystems/power-thermal-budget (the orbit average power balance the battery covers), space-systems/orbit-mechanics/ eclipse-time (the eclipse duration input) and space-systems/subsystems/ thermal-design (battery temperature control). The array sizing, the thermal loop, the eclipse geometry and electric aircraft traction packs are outside this leaf.

Domain quick reference

• Eclipse energy: E = P_eclipse * t_eclipse / 3600, with the eclipse load P_eclipse in W and the eclipse duration t_eclipse in s giving Wh.
• Required nameplate capacity: C = E / (DOD * eta_discharge), where DOD is the depth of discharge limit in (0, 1] and eta_discharge is the discharge efficiency, module constant EFF_DISCHARGE = 0.95. The nameplate capacity must exceed the eclipse energy because only the DOD fraction of it is usable and the discharge leg loses the efficiency fraction.
• Capacity at the bus voltage: Ah = C / V_bus.
• Series cells: n_series = ceil(V_bus / V_cell); the pack nominal voltage n_series * V_cell must reach at least the regulated bus voltage.
• Parallel strings: n_parallel = ceil(Ah / Ah_cell); the installed capacity n_parallel * Ah_cell must reach at least the required ampere hours.
• Discharge C-rate: I = P_orbit / V_bus and C-rate = I / Ah_installed, checked against the cell maximum C-rate (within limit when c_rate <= cell_max_c_rate).
• Pack mass: m = C / e_spec, with the pack specific energy module constant SPEC_ENERGY_WH_KG = 150.0 Wh/kg.
• Module constants: CELL_VOLTAGE = 3.7 V and CELL_AMPHOUR = 50.0 Ah are the nominal Li-ion cell defaults. Units are SI throughout: W, s, Wh, Ah, V, A, kg.
• ECSS frames the spacecraft power context; the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the eclipse duty point: the eclipse load P_eclipse (W) and the eclipse duration t_eclipse (s, from space-systems/orbit-mechanics/ eclipse-time), then run eclipse_energy_wh.
2. Apply the depth of discharge limit and the discharge efficiency with required_capacity_wh to get the required nameplate capacity; the efficiency argument defaults to EFF_DISCHARGE.
3. Convert the capacity to the bus with capacity_ah at the regulated bus voltage.
4. Lay out the cells with cell_layout at the bus voltage, the cell nominal voltage and the cell ampere hours; read n_series, n_parallel, total_cells, pack_nominal_voltage and installed_capacity_ah.
5. Check the discharge rate with discharge_rate_check against the orbit load, the installed capacity and the cell maximum C-rate, and read the within_limit verdict.
6. Estimate the pack mass with battery_mass_kg from the required capacity and the pack specific energy (default SPEC_ENERGY_WH_KG).
7. For the full summary, run size_battery once and read the dict (eclipse_energy_wh, required_capacity_wh, capacity_ah, n_series, n_parallel, total_cells, mass_kg, discharge_verdict).
8. Confirm the deterministic checks with the contract test scripts/test_spacecraft_battery_sizing.py.

Worked example

A LEO spacecraft with a 1200 W eclipse load and a 35 min (2100 s) eclipse, DOD limit 0.40, 95 percent discharge efficiency, 28 V bus and 3.7 V / 50 Ah Li-ion cells with a 1.0 cell maximum C-rate.

• Eclipse energy: eclipse_energy_wh(1200, 2100) = 1200 * 2100 / 3600 = 700.0 Wh.
• Required capacity: required_capacity_wh(700, 0.40, 0.95) = 700 / (0.40 * 0.95) = 1842.1 Wh.
• Capacity at the bus: capacity_ah(1842.1, 28) = 65.8 Ah.
• Cell layout: cell_layout(1842.1, 28, 3.7, 50) gives n_series = ceil(28 / 3.7) = ceil(7.57) = 8, n_parallel = ceil(65.8 / 50) = ceil(1.32) = 2, total_cells = 16, pack_nominal_voltage = 29.6 V and installed_capacity_ah = 100 Ah.
• Discharge rate: discharge_rate_check(1200, 28, 100, 1.0) gives current_A = 42.86 A, c_rate = 0.429, within_limit True.
• Mass: battery_mass_kg(1842.1, 150) = 12.28 kg.
• size_battery(1200, 2100, 0.40, 28) returns the summary with discharge_verdict "within-cell-limit".
• Second case, a 90 min LEO with a 35 min eclipse at 800 W: eclipse energy 466.7 Wh and required capacity 1228.1 Wh.

Pitfalls

• Sizing against the raw eclipse energy: the nameplate capacity must divide by both the DOD limit and the discharge efficiency (700 Wh of eclipse energy needs 1842.1 Wh of nameplate at 40% DOD and 95% efficiency), so quoting E / DOD alone under-sizes the battery.
• Forgetting the hour conversion: the eclipse energy formula divides W * s by 3600, and the 35 min eclipse enters as 2100 s, not 35; a minutes-as-hours slip changes the capacity by 60x.
• Taking the round-up for granted in both axes: n_series = ceil(V / V_cell) and n_parallel = ceil(Ah / Ah_cell) round up independently, so an exact multiple must NOT round up (the contract test pins the exact-multiple behavior) and the installed 100 Ah always over-shoots the required 65.8 Ah.
• Checking the C-rate against the wrong current: the discharge check uses the ORBIT load (1200 W), not the eclipse load, divided by the bus voltage and the INSTALLED capacity; a bank that fits the eclipse energy can still exceed the cell C-rate limit under a high draw (2000 W on 50 Ah gives 1.43 C).
• Confusing this leaf with the electric aircraft battery: the spacecraft bus battery is the eclipse-storage chain above; the traction pack sizing for aircraft and eVTOL lives in vehicle-design/sizing/battery-sizing.
• Using a pack specific energy outside the module model: the mass estimate divides the required capacity by the pack specific energy (150 Wh/kg default); a zero or negative specific energy raises ValueError and a datasheet value must be passed explicitly.

Verification

• Confirm eclipse_energy_wh(1200, 2100) returns 700.0 Wh and required_capacity_wh(700, 0.40, 0.95) returns 1842.1 Wh (tolerance 0.1).
• Confirm capacity_ah(1842.1, 28) returns 65.8 Ah and the round trip capacity_ah(C, V_bus) * V_bus recovers C.
• Confirm cell_layout(1842.1, 28, 3.7, 50) returns 8 series, 2 parallel, 16 total, 29.6 V pack and 100 Ah installed, with ceil rounding verified on both axes (a 30 V bus gives 9 series cells; a 4000 Wh requirement gives 3 parallel strings).
• Confirm discharge_rate_check(1200, 28, 100, 1.0) reports 0.429 C-rate within the 1.0 limit, that 800 W on a 50 Ah bank gives 0.57 C-rate within limit, and that 2000 W on the same bank gives 1.43 C-rate and exceeds the limit; size_battery with a 0.4 C-rate limit reports "exceeds-cell-limit".
• Confirm battery_mass_kg(1842.1, 150) returns 12.28 kg.
• Confirm every non-physical input raises ValueError: negative eclipse load, eclipse duration 0 or negative, DOD 0 or above 1, discharge efficiency outside (0, 1], bus voltage 0 or negative, cell voltage or cell capacity 0, cell max C-rate 0, negative energies and zero or negative specific energy.
• Run the contract test offline: python3 scripts/test_spacecraft_battery_sizing.py (33 tests, deterministic, under 20 s).

Related leaves

• space-systems/subsystems/solar-array-sizing: the charge source that recharges this battery in daylight.
• space-systems/subsystems/power-thermal-budget: the orbit average power balance that the eclipse storage covers.
• space-systems/subsystems/thermal-design: radiator and heater sizing for the battery temperature control.
• space-systems/orbit-mechanics/eclipse-time: the eclipse duration input from the orbit geometry.
• space-systems/subsystems/command-data-handling and space-systems/subsystems/communication-link-budget: the payload loads that set the eclipse draw.
• vehicle-design/sizing/battery-sizing: the electric aircraft and eVTOL traction pack counterpart, not a spacecraft bus battery.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_spacecraft_battery_sizing.py

The test covers the LEO worked example (700.0 Wh eclipse energy, 1842.1 Wh required capacity, 65.8 Ah, series 8 / parallel 2 / total 16 cells, 29.6 V pack, 100 Ah installed, 0.429 C-rate within limit, 12.28 kg mass), the 800 W second case (466.7 Wh, 1228.1 Wh), the discharge rate pass and exceed verdicts (0.57 and 1.43 C-rate on a 50 Ah bank), ceil rounding on both layout axes, exact-multiple no-round-up behavior, the round-trip identities and ValueError rejection of non-physical inputs.

Compliance

• Standards referenced, not reproduced: ECSS is a free ESA standards set (ecss.nl/standards); the sizing relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.