Free preview · Power course v2.1

Spacecraft power systems

How spacecraft make, store and deliver electrical power, from the physics of a solar cell to a complete CubeSat and a GEO comsat. Short sections, worked examples and graded practice, with every number checked by a script.

Free preview: chapter 1 of 17, complete. The full course: 17 chapters · 35 worked examples · 51 practice problems · 2089 script checks.

How to use this pack

1Read 'The idea in one minute' and the 'You will be able to' list.
2Work through the short sections and the worked examples with a pencil.
3Try each practice problem before opening the hint; open the full solution only to check.
4Do the three-question check and the spaced recap before moving on.

What is in the full course

1The power subsystem and the power budgetFree preview30 min
2Sunlight, orbits and eclipse30 min
3How a solar cell works35 min
4Cell types, efficiency and temperature30 min
5Array geometry: pointing, cosine losses and layout35 min
6Sizing the array: beginning and end of life40 min
7Batteries: how Li-ion cells behave35 min
8Sizing the battery: eclipse, cycle life and recharge40 min
9Regulating power: DET, MPPT and the bus40 min
10Distribution, harness and protection35 min
11Margins, worst cases and end of life30 min
12Power modes, energy balance and contingency35 min
13CubeSat power systems30 min
14RTGs, fuel cells and other sources25 min
15Testing and verifying the power system30 min
16Mission case: a 6U CubeSat in Sun-synchronous orbit50 min
17Contrast case: a GEO communications satellite40 min

This preview is chapter 1, complete. Your ticks are saved in this browser only. Original work, and a study aid, not assignment answers.

Chapter 1

The power subsystem and the power budget

30 minutes

The idea in one minute

A spacecraft's electrical power subsystem has four jobs: generate power (usually solar cells), store it (a battery for eclipse and peaks), regulate it (keep the bus voltage in range), and distribute it (switch and protect every load). Everything starts from the power budget: a list of every load, how much it draws when on, and how often it is on. The orbit average sizes the solar array; the peak and the eclipse load size the battery and the electronics.

Loads switch on and off, so the power drawn jumps around. The dashed line is the orbit average: the number the solar array must supply. The tall spikes are what the battery and converters must handle.

You will be able to

Name the four jobs of an electrical power subsystem (EPS)
Build a load list with duty cycles and find orbit-average and peak power
Split the budget into daylight and eclipse loads

What the EPS is made of

A solar array converts sunlight to electricity. A battery stores energy for eclipse and for peaks the array cannot cover. A power control unit regulates the bus, charges and discharges the battery, and a distribution unit switches and protects each load. Many designs put the last two in one box, the PCDU (power control and distribution unit).^[R1]

The load list

List every unit with its power when on and its duty cycle D, the fraction of time it is on. The orbit-average load is P̄ = Σ P_i D_i. The peak is what can be on at the same time. Write it per operating mode (Chapter 12), because a safe mode and a downlink pass are very different.

Average, peak, daylight and eclipse

Energy, not power, is what must balance over an orbit. The array only works in sunlight, so it must cover the daylight loads and refill the battery that carried the eclipse loads. That is why you need P_e (eclipse) and P_d (daylight) separately, not just P̄.

Key equations

Orbit-average power

P̄ = Σ P_i D_i

where

P̄orbit-average power, W

P_ipower drawn by load i when it is on, W

D_iduty cycle of load i: fraction of the time it is on, dimensionless

Energy per orbit

E = P̄ T_orb

where

Eenergy, Wh

T_orborbit period, s

Divide seconds by 3600 to get Wh.

Orbit average from the two phases

P̄ = (P_e T_e + P_d T_d)/(T_e + T_d)

where

P_eload power during eclipse, W

T_etime in eclipse per orbit, s

P_dload power during daylight, W

T_dtime in sunlight (daylight) per orbit, s

Worked examples

Worked example 1.1

Orbit-average and peak power from a load list

Given

A 3U Earth-observation CubeSat has the loads below (power when on, and the fraction of the orbit each is on). On-board computer 1.5 W × 1.00; EPS housekeeping 0.4 W × 1.00; Attitude control 2.8 W × 1.00; UHF receiver 0.5 W × 1.00; S-band transmitter 9.0 W × 0.06; Imager payload 6.0 W × 0.18; Battery heater 1.5 W × 0.30; GPS receiver 0.8 W × 0.40. Find the orbit-average load, the peak load and the energy used per orbit at 550 km.

new symbols

P_ipower drawn by load i when it is on, W

D_iduty cycle of load i: fraction of the time it is on, dimensionless

P̄orbit-average power, W

P_peakpeak power: every load that can be on at once, W

Working

On-board computer: 1.5 × 1.001.500 W
EPS housekeeping: 0.4 × 1.000.400 W
Attitude control: 2.8 × 1.002.800 W
UHF receiver: 0.5 × 1.000.500 W
S-band transmitter: 9.0 × 0.060.540 W
Imager payload: 6.0 × 0.181.080 W
Battery heater: 1.5 × 0.300.450 W
GPS receiver: 0.8 × 0.400.320 W
Orbit-average P̄ = Σ P_i D_i7.59 W
Peak P_peak = Σ P_i22.5 W(every load on at once)
Orbit period at 550 km: T_orb = 2π√(r³/μ) = 5739 s95.6 min
Energy per orbit E = P̄ T_orb = 7.59 × 5739 / 360012.10 Wh

Answer. P̄ = 7.59 W, P_peak = 22.5 W, E = 12.1 Wh per orbit.

Sanity check. The peak is 3.0 times the average: the array is sized on the average, the battery and the regulators on the peak.

Pythonedit a value, then Run

# Worked example 1.1: Orbit-average and peak power from a load list
import math
# (name, power when on in W, duty cycle)
loads = [("On-board computer", 1.5, 1.00), ("EPS housekeeping", 0.4, 1.00),
         ("Attitude control", 2.8, 1.00), ("UHF receiver", 0.5, 1.00),
         ("S-band transmitter", 9.0, 0.06), ("Imager payload", 6.0, 0.18),
         ("Battery heater", 1.5, 0.30), ("GPS receiver", 0.8, 0.40)]
h = 550.0            # km, altitude
RE = 6378.137        # km, Earth radius
MU = 398600.4418     # km3/s2

for name, P, D in loads:
    print(f"{name}: {P} x {D:.2f} = {P * D:.3f} W")
P_avg = sum(P * D for _, P, D in loads)        # orbit average, sum of P_i D_i
P_peak = sum(P for _, P, _ in loads)           # every load on at once
T_orb = 2 * math.pi * math.sqrt((RE + h)**3 / MU)   # s
E = P_avg * T_orb / 3600                       # Wh per orbit
print(f"P_avg = {P_avg:.2f} W, P_peak = {P_peak:.1f} W")
print(f"T_orb = {T_orb:.0f} s = {T_orb / 60:.1f} min, E = {E:.2f} Wh per orbit")

# Worked example 1.1: Orbit-average and peak power from a load list
import math
# (name, power when on in W, duty cycle)
loads = [("On-board computer", 1.5, 1.00), ("EPS housekeeping", 0.4, 1.00),
         ("Attitude control", 2.8, 1.00), ("UHF receiver", 0.5, 1.00),
         ("S-band transmitter", 9.0, 0.06), ("Imager payload", 6.0, 0.18),
         ("Battery heater", 1.5, 0.30), ("GPS receiver", 0.8, 0.40)]
h = 550.0            # km, altitude
RE = 6378.137        # km, Earth radius
MU = 398600.4418     # km3/s2

for name, P, D in loads:
    print(f"{name}: {P} x {D:.2f} = {P * D:.3f} W")
P_avg = sum(P * D for _, P, D in loads)        # orbit average, sum of P_i D_i
P_peak = sum(P for _, P, _ in loads)           # every load on at once
T_orb = 2 * math.pi * math.sqrt((RE + h)**3 / MU)   # s
E = P_avg * T_orb / 3600                       # Wh per orbit
print(f"P_avg = {P_avg:.2f} W, P_peak = {P_peak:.1f} W")
print(f"T_orb = {T_orb:.0f} s = {T_orb / 60:.1f} min, E = {E:.2f} Wh per orbit")

On-board computer: 1.5 x 1.00 = 1.500 W
EPS housekeeping: 0.4 x 1.00 = 0.400 W
Attitude control: 2.8 x 1.00 = 2.800 W
UHF receiver: 0.5 x 1.00 = 0.500 W
S-band transmitter: 9.0 x 0.06 = 0.540 W
Imager payload: 6.0 x 0.18 = 1.080 W
Battery heater: 1.5 x 0.30 = 0.450 W
GPS receiver: 0.8 x 0.40 = 0.320 W
P_avg = 7.59 W, P_peak = 22.5 W
T_orb = 5739 s = 95.6 min, E = 12.10 Wh per orbit

Worked example 1.2

Splitting the budget into daylight and eclipse

Given

On the same CubeSat the imager and the transmitter run only in sunlight; everything else runs all the time at its duty. The orbit has a 35.6 min eclipse (Chapter 2 shows how to find it). Find the eclipse load P_e and the daylight load P_d.

new symbols

T_etime in eclipse per orbit, s

T_dtime in sunlight (daylight) per orbit, s

P_eload power during eclipse, W

P_dload power during daylight, W

Working

T_e = 2137 s, T_d = T_orb − T_e3602 s
Eclipse load = all loads except imager and transmitter: P_e5.97 W
Energy of the day-only loads per orbit = (9.0 × 0.06 + 6.0 × 0.18) × 5739 = 9297 J, squeezed into T_d
P_d = P_e + 9297 / 36028.55 W
Check: (P_e T_e + P_d T_d)/T_orb = 7.59 W = P̄

Answer. P_e = 5.97 W, P_d = 8.55 W.

Sanity check. Moving loads into daylight raises P_d but lowers P_e, which shrinks the battery. Array sizing (Chapter 6) needs both numbers, not just the average.

Pythonedit a value, then Run

# Worked example 1.2: Splitting the budget into daylight and eclipse
import math
loads = [("On-board computer", 1.5, 1.00), ("EPS housekeeping", 0.4, 1.00),
         ("Attitude control", 2.8, 1.00), ("UHF receiver", 0.5, 1.00),
         ("S-band transmitter", 9.0, 0.06), ("Imager payload", 6.0, 0.18),
         ("Battery heater", 1.5, 0.30), ("GPS receiver", 0.8, 0.40)]
day_only = ["Imager payload", "S-band transmitter"]   # run only in sunlight
h = 550.0            # km, altitude (beta = 0)

RE = 6378.137        # km, Earth equatorial radius
MU = 398600.4418     # km3/s2, Earth gravitational parameter

r = RE + h
T_orb = 2 * math.pi * math.sqrt(r**3 / MU)                          # s
f_e = math.acos(math.sqrt(h**2 + 2 * RE * h) / r) / math.pi         # eclipse fraction at beta = 0
T_e = f_e * T_orb; T_d = T_orb - T_e
P_e = sum(P * D for name, P, D in loads if name not in day_only)   # W, eclipse load
E_day = sum(P * D for name, P, D in loads if name in day_only) * T_orb   # J of day-only loads per orbit
P_d = P_e + E_day / T_d                                             # squeezed into daylight
print(f"T_e = {T_e:.0f} s ({T_e / 60:.1f} min), T_d = {T_d:.0f} s")
print(f"P_e = {P_e:.2f} W, P_d = {P_d:.2f} W")
print(f"check: orbit average = {(P_e * T_e + P_d * T_d) / T_orb:.2f} W")

# Worked example 1.2: Splitting the budget into daylight and eclipse
import math
loads = [("On-board computer", 1.5, 1.00), ("EPS housekeeping", 0.4, 1.00),
         ("Attitude control", 2.8, 1.00), ("UHF receiver", 0.5, 1.00),
         ("S-band transmitter", 9.0, 0.06), ("Imager payload", 6.0, 0.18),
         ("Battery heater", 1.5, 0.30), ("GPS receiver", 0.8, 0.40)]
day_only = ["Imager payload", "S-band transmitter"]   # run only in sunlight
h = 550.0            # km, altitude (beta = 0)

RE = 6378.137        # km, Earth equatorial radius
MU = 398600.4418     # km3/s2, Earth gravitational parameter

r = RE + h
T_orb = 2 * math.pi * math.sqrt(r**3 / MU)                          # s
f_e = math.acos(math.sqrt(h**2 + 2 * RE * h) / r) / math.pi         # eclipse fraction at beta = 0
T_e = f_e * T_orb; T_d = T_orb - T_e
P_e = sum(P * D for name, P, D in loads if name not in day_only)   # W, eclipse load
E_day = sum(P * D for name, P, D in loads if name in day_only) * T_orb   # J of day-only loads per orbit
P_d = P_e + E_day / T_d                                             # squeezed into daylight
print(f"T_e = {T_e:.0f} s ({T_e / 60:.1f} min), T_d = {T_d:.0f} s")
print(f"P_e = {P_e:.2f} W, P_d = {P_d:.2f} W")
print(f"check: orbit average = {(P_e * T_e + P_d * T_d) / T_orb:.2f} W")

T_e = 2137 s (35.6 min), T_d = 3602 s
P_e = 5.97 W, P_d = 8.55 W
check: orbit average = 7.59 W

Practice

Practice P1.1 · warm-up

A transmitter's duty cycle

Given

A ground station sees the satellite 4 times a day for 9 minutes each pass. The transmitter draws 8 W only during passes. What is its duty cycle and its daily-average power?

Mark as done

Hint

Duty cycle = time on / total time. A day has 1440 minutes.

Answer. D = 2.50 %, average 0.20 W.

Working

Time on per day = 4 × 936 min
D = 36 / 14400.0250(2.50 %)
Average = P D = 8 × 0.02500.200 W

Answer. D = 2.50 %, average 0.20 W.

Sanity check. An 8 W transmitter costs only about 0.2 W on average, but the battery must still supply 8 W for nine minutes at a time.

Pythonedit a value, then Run

# Practice P1.1: A transmitter's duty cycle
passes = 4           # passes per day
t_pass = 9.0         # min per pass
P_tx = 8.0           # W, transmitter power when on

t_on = passes * t_pass            # min per day
minutes_per_day = 24 * 60
D = t_on / minutes_per_day
P_avg = P_tx * D
print(f"D = {D:.4f} = {D * 100:.2f} %")
print(f"daily-average power = {P_avg:.2f} W")

D = 0.0250 = 2.50 %
daily-average power = 0.20 W

Practice P1.2 · standard

A daily energy budget with margin

Given

A 6U satellite has: bus avionics 3.2 W at duty 1.00; payload 14.0 W at duty 0.35; radio 6.0 W at duty 0.10; heaters 4.0 W at duty 0.25. Add a 20 % margin to the average. What average power must the power system support, and how much energy is that per day?

Mark as done

Hint

Average first (Σ P_i D_i), then apply the margin, then multiply by 24 h.

Answer. 11.6 W average, 279 Wh per day.

Working

P̄ = 3.2×1.00 + 14.0×0.35 + 6.0×0.10 + 4.0×0.259.70 W
With margin: 9.70 × 1.2011.64 W
Daily energy = 11.64 × 24279 Wh

Answer. 11.6 W average, 279 Wh per day.

Sanity check. The payload dominates: halving its duty would save more than switching every avionics box off.

Pythonedit a value, then Run

# Practice P1.2: A daily energy budget with margin
loads = [("bus avionics", 3.2, 1.00), ("payload", 14.0, 0.35),
         ("radio", 6.0, 0.10), ("heaters", 4.0, 0.25)]   # (name, W, duty)
margin = 0.20        # 20 % margin on the average

P_avg = sum(P * D for _, P, D in loads)
P_req = P_avg * (1 + margin)
E_day = P_req * 24                 # Wh per day
print(f"P_avg = {P_avg:.2f} W, with margin {P_req:.2f} W")
print(f"daily energy = {E_day:.0f} Wh")

P_avg = 9.70 W, with margin 11.64 W
daily energy = 279 Wh

Practice P1.3 · challenge

How long can the payload run?

Given

Averaged over an orbit the array delivers 14.0 W to the loads (after all conversion losses). The rest of the satellite draws 5.8 W all the time. The payload draws 18 W when on. What is the largest payload duty cycle that keeps the energy budget balanced, and how many minutes per 95.6-min orbit is that?

Mark as done

Hint

Energy balance per orbit: generation = base + payload × duty.

Answer. D_max = 45.6 %, about 44 min per orbit.

Working

Balance: 14.0 = 5.8 + 18 D_max
D_max = (14.0 − 5.8) / 180.4556
Minutes per orbit = 0.4556 × 95.643.6 min

Answer. D_max = 45.6 %, about 44 min per orbit.

Sanity check. This is the operations view of the power budget: the payload's 'on time' is what the power system sells to the mission. Any margin you hold reduces it.

Pythonedit a value, then Run

# Practice P1.3: How long can the payload run?
P_array = 14.0       # W, orbit-average power delivered to the loads
P_rest = 5.8         # W, rest of the satellite, always on
P_payload = 18.0     # W, payload when on
T_orb = 95.6         # min, orbit period

D_max = (P_array - P_rest) / P_payload   # balance: P_array = P_rest + P_payload D
minutes = D_max * T_orb
print(f"D_max = {D_max:.4f} = {D_max * 100:.1f} %")
print(f"payload time = {minutes:.1f} min per orbit")

D_max = 0.4556 = 45.6 %
payload time = 43.6 min per orbit

Common mistakes

Summing the 'on' powers and calling it the average. That is the peak.
Mixing units: W × h = Wh, W × s = J. Keep one system per calculation.
Forgetting always-on loads (receiver, OBC, EPS housekeeping). They dominate small satellites.
Using one average for the whole orbit when the payload only runs in daylight or only in eclipse.

Sources for this chapter

R1NASA Ames Research Center, Small Spacecraft Systems Virtual Institute, Small Spacecraft Technology State of the Art, 2024 edition (PDF dated Feb 2025). Chapter 3, Power.

Where in each source, and links: References.

I have finished chapter 1

Full course

16 more chapters in the full course

The full Spacecraft power systems course continues with 16 more chapters (560 minutes of study and 48 more graded problems), the formula sheet, the glossary, every assumption with its source, and a printable PDF. It comes with the founding membership.

Founding membership

Founding membership opens soon. Join the free weekly email to hear first.

Reference

Answers

Problem	Answer
P1.1	D = 2.50 %, average 0.20 W.
P1.2	11.6 W average, 279 Wh per day.
P1.3	D_max = 45.6 %, about 44 min per orbit.

Reference

References

Every reference the pack cites. "Where" names the section, table or page that holds the cited value; an entry says so when the source was not read in full or is not openly available.

Id	Reference
R1	NASA Ames Research Center, Small Spacecraft Systems Virtual Institute, Small Spacecraft Technology State of the Art, 2024 edition (PDF dated Feb 2025). Chapter 3, Power.Where: §3.2.1 and Table 3-1 solar cells (report p. 33-34); §3.2.2 specific power ~30 W/kg, range 1-200 W/kg (p. 40); §3.4 energy storage, Li-ion 3.6 V average, 18650 cells, Table 3-3 battery packs 75-178 Wh/kg, Table 3-4 18650 cells (LG ICR18650 B3 191 Wh/kg), Table 3-6 Li-ion vs supercapacitor (p. 43-50); §3.5.3 Li-ion -20 to 60 °C (p. 51); §3.6 CubeSat EPS 8.2 V battery bus, 5.0 and 3.3 V rails, Table 3-9 PMAD efficiencies 75-99 % (p. 52-54)https://www.nasa.gov/wp-content/uploads/2025/02/soa-2024.pdfCited in: Chapter 1

Reference

NASA Ames Research Center, Small Spacecraft Systems Virtual Institute, Small Spacecraft Technology State of the Art, 2024 edition (PDF dated Feb 2025). Chapter 3, Power.Where: §3.2.1 and Table 3-1 solar cells (report p. 33-34); §3.2.2 specific power ~30 W/kg, range 1-200 W/kg (p. 40); §3.4 energy storage, Li-ion 3.6 V average, 18650 cells, Table 3-3 battery packs 75-178 Wh/kg, Table 3-4 18650 cells (LG ICR18650 B3 191 Wh/kg), Table 3-6 Li-ion vs supercapacitor (p. 43-50); §3.5.3 Li-ion -20 to 60 °C (p. 51); §3.6 CubeSat EPS 8.2 V battery bus, 5.0 and 3.3 V rails, Table 3-9 PMAD efficiencies 75-99 % (p. 52-54)https://www.nasa.gov/wp-content/uploads/2025/02/soa-2024.pdfCited in: Chapter 1

The references cited by this preview. The full course lists every source it uses.

Spacecraft power systems

How to use this pack

What is in the full course

You will be able to

What the EPS is made of

The load list

Average, peak, daylight and eclipse

Key equations

Worked examples

Orbit-average and peak power from a load list

Splitting the budget into daylight and eclipse

Practice

A transmitter's duty cycle

A daily energy budget with margin

How long can the payload run?

Common mistakes

Check yourself

Sources for this chapter

16 more chapters in the full course

Answers

References