Electrical Power Subsystem

The electrical power subsystem (EPS) provides, stores, distributes and control spacecraft electrical power. In order to size each component of this subsystem we must identify the electrical power loads for mission operations at the beginning-of-life, BOL, and end-of-life, EOL. For many missions, the end-of-life power demands must be reduced to compensate for solar array performance degradation. The average electrical power needed at EOL determines the size of the power source so a detailed power budget, at different stages of the mission, must be done. In Table 10 a sample power budget that may be used to begin the sizing process is shown but for further stages a more accurate analyses will be necessary.

Table 10 Typical power consumption by subsystem for small satellites ( less than 100 W).
Subsystem Consumption
Payload 20-50 W
Propulsion 0 W
Attitude Control 0 W
Communications 15 W
Data Handling 5 W
Thermal 0 W
Power 10-30 W
Structure 0 W

In addition to the values shown in the previous table, an extra margin (from 5 % to 25 %) of power might be added based on design maturity. We usually multiply average power by 2 or 3 to obtain peak power requirements for attitude control, payload, thermal, and EPS (when charging the batteries).

Once the power budget is done, we need to size the different elements of the EPS. Below, the basic steps to size these components are explained. Although these steps represent a simple process, it is enough to cover a preliminary design of the electrical power subsystem.

Power source

The power source generates electrical power within the spacecraft. Photovoltaic solar cells are the most common power source in most missions so we will focus on the design of this element. They convert incident solar radiation directly to electrical energy and are famous for being well-known and reliable.

The starting point of the photovoltaic solar cells design is defining the mission life and the average power requirement. The first one is often known before starting the preliminary design of any subsystem and the second one must be determined from the power budget, given in Table 10. We size a photovoltaic system to meet power requirements at EOL, with the resulting solar array often oversized for power requirements at BOL. This excess power at BOL requires coordinated systems engineering to avoid thermal problems. The longer the mission life, the larger the difference between power requirements at EOL and BOL.

Once these two key parameters have been established, the total power that the solar array must provide during daylight (\(P_{sa}\)) can be determined using

\[P_{sa} = \frac{\frac{P_e T_e}{X_e} + \frac{P_d T_d}{X_d}}{T_d}\]

where \(P_{e}\) and \(P_{d}\) are the spacecraft’s power requirements (excluding regulation and battery charging losses) during eclipse and daylight, respectively, and \(T_{e}\) and \(T_{d}\) are the lengths of these periods per orbit. \(X_{e}\) and \(X_{d}\) the efficiency of the paths from the battery to the individual loads and the path directly from the arrays to the loads, respectively. The previous formula shows the total power that must be provided for one orbit to fulfill the spacecraft power requirements. However, nothing has been said until now about how to determine the total power that the solar arrays really provide.

There are three many types of cells (Sillicon, Gallium Arsenide, Multijuction, etc.) and each one of them has an efficiency (\(\eta\)) and degradation coefficients. Gallium arsenide has the advantage of higher efficiencies, whereas indium phosphide reduces the degrading effects of radiation. Silicon solar cell technology is mature and has the advantage of lower cost per watt for most applications. Gallium arsenide and indium phosphide cost about 3 times more than silicon. In Table 11 the performance of several solar cells are shown. For a more detailed analysis, please refer to the datasheet of each particular case.

Table 11 Performance comparison for photovoltaic solar cells.
Cell type Silicone Gallium Arsenide Indium Phosphide Multijunction
Theoretical efficiency 20.8 % 23.5 % 22.8 % 25.8 %
Achieved (production) 14.8 % 18.5 % 18 % 22 %

Next, we must determine the resultant power production capability of the manufactured solar array. An assembled solar array is less efficient than single cells due to design inefficiencies, shadowing and temperature variations, collectively referred as inherent degradation, \(I_{d}\). A typical value for this coefficient is 0.77 although it might vary from 0.49 to 0.88.

Once these two parameters (efficiency and inherent degradation) have been defined, we can compute the solar array power at the beginning of life, per unit of area,

\[P_{BOL} = P_{SUN} \eta I_d \cos(\theta),\]

where \(P_{SUN}\) is the solar illumination intensity (1367 W/m²), which depends on the distance Sun-satellite, and \(\cos(\theta)\) is referred as the cosine loss. We measure the Sun incidence angle \(\theta\) between the vector normal to the surface of the array and the Sun line. So if the Sun rays are perpendicular to the solar array surface, we get maximum power. Obviously, the geometry between the array and the Sun changes throughout the mission and different solar array panels will have different geometry. The worst-case Sun incidence angle is used for our calculations.

Next, we must consider the factors that degrade the solar array’s performance during the mission. Life degradation, \(L_d\) occurs because of thermal cycling in and out of eclipses, micrometeoroid strikes, plume impingement from thrusters, and material outgassing for the duration of the mission. In general, for a silicon solar array in LEO, the degradation is about 3.75 % per year. For gallium-arsenide cells in LEO, power production can decrease by as much as 2.75 % per year. The actual lifetime degradation can be estimated using

\[L_{d} = (1 - c)^{t_f},\]

where \(c\) is the degradation per year and \(t_f\) is the satellite lifetime. The array performance per unit of area at the end of life is

\[P_{EOL} = P_{BOL} L_d.\]

Finally, the solar array area, \(A_{sa}\) required to support the spacecraft power requirements is given by

\[A_{sa} = \frac{P_{sa}}{P_{EOL}}\]

Solar-array sizing is more difficult than it appears from the above discussion. Typically, we must consider several arrays with varying geometry. Also, the angle of incidence on the array surface is constantly changing. We must predict that angle continuously or at least determine the worst-case angle to develop an estimate of \(P_{EOL}\).

Energy Storage

Any spacecraft that uses photovoltaics or solar thermal dynamics as a power source requires a system to store energy for peak-power demands and eclipse periods. Energy storage typically occurs in a battery, although systems such as flywheels and fuel cells have been considered in some particular cases.

A battery consists of individual cells connected in series. The number of cells required is determined by the bus-voltage. The amount of energy stored within the battery is the ampere-hour capacity or watt-hour (ampere-hour times operating voltage) capacity. The design capacity of the battery derives from the energy storage requirements. Batteries can be connected in series to increase the voltage or in parallel to increase the current.

One of the most important parameters which characterize a discharge period is known as the Depth of Discharge (\(DoD\)). It is simply the percentage of total battery capacity consumed during a discharge period. Once we know the average depth of discharge, determining the different currents that each load needs, we can determine the total capacity of the batteries (\(C_r\)) by using the following expression

\[C_{r} = \frac{P_{e} \cdot T_e}{DoD \cdot N \cdot X_e},\]

where \(N\) is the number of non-redundant batteries. To obtain the battery capacity in ampere-hour, the previous result must be divided by the bus voltage (usually 28 V).

Once the total capacity has been determined, finding a suitable battery or batteries is the task of the electrical power engineer.

Power distribution

A spacecraft power distribution system consists of cabling, fault protection, and switching gear to turn power on and off to the spacecraft loads. Power distribution designs for various power systems depend on source characteristics, load requirements and subsystem functions. In selecting a type of power distribution, we focus on keeping power losses and mass at a minimum while attending to survivability, cost, reliability, and power quality.

In this section no detailed analysis will be described. We only insist on the fact that we must account for the cable and harness mass when designing the EPS. Operating low current (less than 30 A) devices helps to keep this mass low. In Fig. 11 , an estimation of the mass of wire per meter with respect to the current is shown.

../../_images/MassWire.PNG

Fig. 11 Cable mass per meter over current. Retrieved from [WL99] (Section 11.4.3).

The harness or cabling that interconnects the spacecraft subsystems is a large part (10-25 %) of the electrical power system mass. We must keep harness as short as possible to reduce voltage drops and to keep the total spacecraft mass low.

[DRDF12]Anton H De Ruiter, Christopher Damaren, and James R Forbes. Spacecraft dynamics and control: an introduction. John Wiley & Sons, 2012.
[Uni07]California Polytechnic State University. Poly Picosatellite Orbital Deployer Mk. III Rev. E User Guide. The CubeSat Program, Cal Poly SLO, 2007.
[WL99]James R Wertz and Wiley J Larson. Space Mission Analysis and Design, Space Technology Library. Microcosm Press and Kluwer Academic Publishers, El Segundo, CA, USA, 1999.
[Wer78]James R. Wertz, editor. Spacecraft Attitude Determination and Control. Springer Netherlands, 1978. URL: https://doi.org/10.1007/978-94-009-9907-7, doi:10.1007/978-94-009-9907-7.