Exercise set

Spacecraft Power and Battery Energy Budget Exercises

Solved spacecraft power exercises for eclipse energy, battery DoD, solar-array EOL, recharge margin, bus current, safe-mode endurance and release gates.

Branch: Aerospace Engineering
Content: Exercise set
Updated: Jul 03, 2026
Revision: v1.1.0 · reviewed

These exercises focus on spacecraft electrical power and battery energy budgets. They cover eclipse energy, depth of discharge, converter efficiency, solar-array end-of-life power, recharge margin, state of charge, battery derating, bus current, payload duty cycle, safe-mode endurance and release evidence.

Use the calculations as screening checks. Flight release still needs solar-array degradation data, battery qualification, cell temperature limits, converter maps, harness losses, load shedding rules, telemetry thresholds and operations constraints tied to the same mission mode.

How to use these exercises

Work through the set as a mode-by-mode power review. Exercises 1 to 4 translate eclipse loads into battery-side energy and depth-of-discharge demand. Exercises 5 to 9 compare that demand with end-of-life solar-array generation, recharge time and battery capacity derating. Exercises 10 to 17 then check current, duty-cycle loads, safe-mode endurance, incidence loss and guarded margin. Exercise 18 converts the arithmetic into a release decision.

Before each calculation, name the mission mode, orbit case, thermal state, battery temperature, attitude constraint and load table being used. A nominal sunlit science mode, a worst eclipse survival mode and a safe-mode recovery pass are different budgets even if they share hardware. The engineering comment below each exercise identifies the evidence that must be present before the result can support flight release.

Release Evidence Notes

Power release evidence should state the mode power table, eclipse duration, battery boundary, depth-of-discharge rule, solar incidence, end-of-life degradation, converter efficiency, bus-current limit, heater allocation, safe-mode load shedding and recharge plan. A positive energy margin in one mode does not prove survival in another.

The evidence package should keep bus-side, converter-side and battery-side values separate. It should also identify whether the value comes from measured hardware, a qualified component model, a thermal vacuum test, a radiation degradation estimate, operations analysis or a conservative placeholder. Flight release is weakest where those sources are mixed without a common mode definition.

Worst-case evidence must include time. A battery can pass an eclipse energy check but fail if recharge does not complete before the next eclipse, if communications windows force transmitter duty during recovery, or if heaters dominate a cold safe-mode case. The release basis therefore needs an energy timeline, not only a static power table.

Engineering Boundary Notes

The exercises use first-order energy and power balances. They do not replace battery cell modeling, solar-array IV curves, radiation degradation analysis, converter thermal derating, harness voltage drop, load transient testing or flight-software power-mode validation. Treat each pass result as a screen for the next analysis level, not as proof that the flight electrical power subsystem is complete.

The main boundary is consistency of mode definition. Loads, array incidence, eclipse duration, heater allocation, communication duty, battery temperature and autonomy rules must all describe the same case. Another boundary is aging: beginning-of-life array power and fresh battery capacity are useful for early tests, but end-of-life release must include degradation, capacity fade and uncertainty.

Common Release Mistakes

using beginning-of-life solar power for end-of-life release;
sizing battery energy without depth-of-discharge and converter losses;
ignoring peak bus current while average energy closes;
treating safe-mode power as a static load without communication windows;
assuming recharge time from ideal sunlight while attitude and eclipse reduce generation;
omitting uncertainty and telemetry thresholds from the release record.

Another common mistake is closing energy at the payload interface while ignoring power conversion and distribution. Battery energy, bus current, regulator losses, harness voltage drop and converter thermal limits can all control the same mode. A spreadsheet that balances watts but omits those boundaries is not a release package.

Do not treat safe mode as a low-power version of normal mode. Safe mode has its own recovery communications, heater priorities, attitude constraints, fault management rules and command opportunities. If the safe-mode endurance test is missing, a nominal power margin elsewhere cannot prove spacecraft survival.

Scenario Map

The exercises move from eclipse load energy to battery capacity, solar generation, recharge, SOC, current, load shedding and guarded release.

Exercise 1: Eclipse Load Energy

A spacecraft consumes $210\ \text{W}$ during a $35\ \text{min}$ eclipse. Compute required bus energy.

Solution

E=Pt=210\left(\dfrac{35}{60}\right)=122.5\ \text{Wh}

Engineering Comment

This is bus-side load energy. Battery-side energy must include converter losses and allowed depth of discharge.

Plausibility Check

Hundreds of watts for about half an hour should be about one hundred watt-hours.

Exercise 2: Battery Capacity with DoD Limit

Use $E=122.5\ \text{Wh}$ . Maximum allowed depth of discharge is 35 percent. Estimate required nominal battery capacity.

Solution

C=\dfrac{122.5}{0.35}=350\ \text{Wh}

Engineering Comment

The nominal capacity must still be available at end of life and at the relevant battery temperature.

Plausibility Check

The required capacity is larger than the eclipse energy because only part of the battery may be used.

Exercise 3: Converter Input Power

The eclipse bus load is $210\ \text{W}$ and converter efficiency is 88 percent. Compute battery input power.

Solution

P_\mathrm{bat}=\dfrac{210}{0.88}=238.6\ \text{W}

Engineering Comment

The difference becomes heat in the power system and also increases battery energy draw.

Plausibility Check

Input power must be greater than output power when efficiency is below one.

Exercise 4: Battery-Side Eclipse Energy

Battery input power is $238.6\ \text{W}$ for $35\ \text{min}$ . Compute battery energy removed.

Solution

E_\mathrm{bat}=238.6\left(\dfrac{35}{60}\right)=139.2\ \text{Wh}

Engineering Comment

Battery-side energy is the correct value for state-of-charge and depth-of-discharge accounting.

Plausibility Check

This is larger than the 122.5 Wh bus load because conversion is not ideal.

Exercise 5: Solar Array End-of-Life Power

A solar array produces $620\ \text{W}$ beginning of life. The degradation factor is 0.78. Compute end-of-life power.

Solution

P_{EOL}=620(0.78)=483.6\ \text{W}

Engineering Comment

End-of-life power is the release basis for long missions, not beginning-of-life qualification data.

Plausibility Check

The EOL value is a little less than 80 percent of beginning-of-life power.

Exercise 6: Sunlit Recharge Margin

End-of-life solar power is $484\ \text{W}$ and sunlit load is $300\ \text{W}$ . How much power is available for recharge?

Solution

P_\mathrm{recharge}=484-300=184\ \text{W}

Engineering Comment

Recharge margin should be checked against charger limits, attitude, eclipses and thermal constraints.

Plausibility Check

Solar power exceeds load by less than 200 W, so recharge is positive but finite.

Exercise 7: Recharge Time

Battery-side eclipse energy removed is $139\ \text{Wh}$ and recharge power is $184\ \text{W}$ . Estimate ideal recharge time.

Solution

t=\dfrac{139}{184}=0.756\ \text{h}=45.4\ \text{min}

Engineering Comment

Ideal recharge time ignores charge acceptance, taper, attitude changes and load transients.

Plausibility Check

About 140 Wh at about 180 W takes less than one hour.

Exercise 8: State-of-Charge Drop

A battery has usable capacity $410\ \text{Wh}$ at current temperature. Eclipse removes $139\ \text{Wh}$ . Estimate SOC drop.

Solution

\Delta SOC=\dfrac{139}{410}=0.339

The drop is 33.9 percent.

Engineering Comment

SOC estimates should be validated with telemetry and battery model uncertainty.

Plausibility Check

Removing about one-third of usable capacity gives about one-third SOC drop.

Exercise 9: End-of-Life Capacity Derating

Beginning-of-life battery capacity is $520\ \text{Wh}$ . End-of-life capacity factor is 0.76. Estimate EOL capacity.

Solution

C_{EOL}=520(0.76)=395.2\ \text{Wh}

Engineering Comment

EOL capacity must be compared with worst eclipse, safe-mode and heater loads.

Plausibility Check

The result is slightly below 400 Wh, consistent with 76 percent derating.

Exercise 10: Regulator Current

A $28\ \text{V}$ bus feeds a $150\ \text{W}$ regulated load with 92 percent efficiency. Estimate bus current.

Solution

I=\dfrac{P}{\eta V}=\dfrac{150}{0.92(28)}=5.82\ \text{A}

Engineering Comment

Harness, connector and regulator current limits should be checked at peak and thermal worst case.

Plausibility Check

At 28 V, 150 W would be about 5.4 A before efficiency loss.

Exercise 11: Peak Bus Current Margin

Peak bus current is $9.4\ \text{A}$ and allowable current is $12.0\ \text{A}$ . Compute margin.

Solution

\mathrm{margin}=\dfrac{12.0-9.4}{9.4}=0.277

The margin is 27.7 percent.

Engineering Comment

Peak current should include startup, transmitter turn-on, heater cycling and fault recovery cases.

Plausibility Check

The peak is below the limit by 2.6 A, a moderate margin.

Exercise 12: Payload Duty-Cycle Energy

A payload draws $80\ \text{W}$ for 18 min each orbit. Compute energy per orbit.

Solution

E=80\left(\dfrac{18}{60}\right)=24\ \text{Wh}

Engineering Comment

Duty-cycle energy should be added to mode energy and recorder/downlink planning.

Plausibility Check

Eighty watts for 0.3 h gives 24 Wh.

Exercise 13: Load-Shedding Savings

Safe mode disables a $45\ \text{W}$ payload and a $20\ \text{W}$ transmitter. How much energy is saved over 2.5 h?

Solution

E=(45+20)(2.5)=162.5\ \text{Wh}

Engineering Comment

Load shedding is useful only if the disabled functions are not required for recovery.

Plausibility Check

About 65 W for a few hours gives roughly 160 Wh.

Exercise 14: Safe-Mode Endurance

Battery usable energy is $260\ \text{Wh}$ and safe-mode load is $38\ \text{W}$ . Estimate endurance.

Solution

t=\dfrac{260}{38}=6.84\ \text{h}

Engineering Comment

Endurance must include beacon duty, heaters, battery temperature and autonomy rules.

Plausibility Check

A few hundred Wh at tens of watts gives several hours.

Exercise 15: Solar Incidence Loss

A solar array produces $484\ \text{W}$ normal to the Sun. The incidence angle is $35^\circ$ . Estimate cosine-reduced power.

Solution

P=484\cos(35^\circ)=396\ \text{W}

Engineering Comment

Attitude mode can make a power budget fail even when the array is large enough normal to the Sun.

Plausibility Check

Cosine 35 degrees is about 0.82, so the result should be near 400 W.

Exercise 16: Battery Reserve Guard

Mission rule requires 20 percent battery reserve. Current predicted minimum SOC is 27 percent and SOC uncertainty is 4 percent. Compute guarded reserve margin.

Solution

M=27-4-20=3\ \text{percent}

Engineering Comment

Three percent guarded margin is thin; operations may need load shedding or a stricter mode rule.

Plausibility Check

The uncertainty nearly consumes the difference between predicted SOC and reserve.

Exercise 17: Power Margin with Uncertainty

Available power is $396\ \text{W}$ , load is $360\ \text{W}$ and power uncertainty is $18\ \text{W}$ . Compute guarded margin.

Solution

M=396-360-18=18\ \text{W}

Engineering Comment

Guarded power margin should remain positive in the same attitude and thermal state used for release.

Plausibility Check

The unguarded margin is 36 W; subtracting 18 W leaves 18 W.

Exercise 18: Power and Battery Release Gate

A power release package has 16 required evidence items. Fourteen are complete, but EOL solar-array degradation and safe-mode endurance test are missing. Should release pass?

Solution

\mathrm{completion}=\dfrac{14}{16}=0.875

The package is 87.5 percent complete, but release should fail because both missing items affect survival and recharge.

Engineering Comment

Power release depends on worst-case energy continuity, not on nominal mode closure alone.

Plausibility Check

Two missing power-survival items are enough to block the mode.

Validation Package Checklist

Before accepting a spacecraft power or battery mode, collect:

mode power table, duty cycle, peak current and bus boundary;
eclipse duration, battery capacity, DoD rule and SOC uncertainty;
EOL solar-array power, incidence angle and recharge plan;
converter efficiency, harness loss and current-limit evidence;
safe-mode load shedding, beacon/heater allocation and endurance case;
battery temperature, degradation, charge acceptance and cell-balance assumptions;
load transient, startup, transmitter, heater cycling and fault-recovery cases;
telemetry thresholds for SOC, current, voltage, temperature and mode transition;
guarded release margin tied to flight telemetry thresholds.

A complete validation package should make the mode decision reproducible from flight data. The reviewer should be able to identify which loads can be shed, which loads are mandatory for recovery, how the battery reserve is protected and which telemetry condition would force a mode change before the energy margin is consumed.

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