Mathematical Programming Based Approach to Modular Electric Power System Design

Satellite power systems can be understood as islanded dc microgrids supplied by specialized and coordinated solar cell arrays augmented by electrochemical battery systems to handle high-power loads and periods of eclipse. The periodic availability of power, the limited capacity of batteries, and the dependence of almost all mission service on power consumption create a unique situation in which temporal power and energy scarcity exist. Any satellite power system must be properly designed so the power generation and energy storage portions of the system have enough generation potential and storage capacity to reliably meet the load requirements of a given satellite mission. A multi-period model of an orbital satellite power system's performance over a mission's duration can be constructed. A modular power system architecture is used to characterize the system's constraints. The periodic and generally predictable nature of a satellite's mission environment provides a useful opportunity for these techniques. Using mathematical programming, an optimization problem can be posed such that the optimal power and energy ratings for the power system are determined for any load schedule imposed by a given mission's requirements. The optimal energy trajectory of the electrical power system over a mission's duration is also determined when the mathematical programming problem is solved. A generic set of mission requirements is identified to test this approach, but the objective function of the resulting optimization problem can be modified in order to return different results, and these differing results can provide a clear illustration of the trade-offs that designers of such power systems consider in the design process. For this paper specifically, this means that the same mission is evaluated in two ways for comparison: first by selecting the optimally-minimum mass, and then the optimally-minimum volume, of the system's generation and battery elements. The design approach is demonstrated for a typical mission involving a CubeSat platform that periodically records image data and transfers this data once per-orbit.