# A Lunar-Orbiting Satellite Constellation for Wireless Energy Supply
## 6 EPS Pre-Design  
To simulate multiple charge and discharge cycles of a battery pack, while considering the laser's operating conditions and the satellite orbit, the Simscape Tool from Matlab and Simulink (R2022b) was employed. The sizing scenario investigated pertains to a 600 km circular orbit. In this case, the battery pack was designed by arranging batteries in series and parallel configurations within modules. Subsequently, the battery parameters were determined and remain fixed as follows:  
* Cell capacity: 20 Ah.
* Thermal Mass: 400 J/K.
* Cell level coolant thermal path resistance: 1.0 K/W.
* Cell level ambient thermal path resistance: 20 K/W.
* Open-circuit voltage: [3.49-4.19] V.
* Initial State of Charge: 0.3.  
In the Simulink model, a constant current and voltage algorithm was implemented to control the charging and discharging of the battery. The battery's discharge, charge, and rest phases are regulated by a function that calculates the satellite's position relative to the transmission cone, whether it is in the light or shadow of the Sun, based on the orbital information.  
The electrical power system (EPS) was studied through preliminary sizing, focusing on the battery pack connected for power generation from solar panels and transmission through lasers. The concept involves charging the batteries during the orbital phase outside the receiver's transmission cone and discharging them during laser operation. The charge-discharge cycle was planned to ensure the battery's state of charge remains within the limits of 10% and 90% to preserve its lifespan.  
Figure 10 illustrates the behavior of the battery during charging, operating at a constant current of 15 A, and discharging at 50 A. The selected laser has a power output of 30 kW and operates at 600 V. The battery pack consists of two parallel configurations, each comprising two pouches in parallel, with a series connection of 40 modules. Furthermore, two of these assemblies are connected in series, resulting in a total of 320 individual cells.  
The battery pack has a weight of 64 kg and occupies a volume of 0.04 m\({}^{3}\). The significant weight, considering additional electronic components such as boost converters and switches, is in line with expectations for a satellite where the majority of mass is distributed among lasers and the EPS system.  
Figure 9: Scenario 3: a ten-satellite constellation in Earth–Moon distant retrograde orbit.  
Figure 11 illustrates the optimized state of charge (SoC) of the battery, specifically tailored for the laser system. The battery operation is designed to cease energy storage when the SoC reaches 90% to preserve its operational lifespan. The figure demonstrates the system's capability to recharge during orbital periods that do not involve power transfer. In this study, the system was initially set with a disadvantageous SoC level of 30%, yet it successfully achieves a duty-cycle condition where reliable power transfers can be sustained. The verification process involved combining orbital propagation algorithms while considering shadow periods caused by both the Moon and occasional Earth eclipses. This analysis ensures that the system is capable of consistently performing power transfers despite intermittent shadowing events.  
The estimation of the satellite solar array area takes into account various factors. These include an initial efficiency of 0.34, an inherent degradation factor of 0.77 and an annual  
Figure 11: SoC of the battery pack vs. the time of three orbital periods.  
Figure 10: Current of the battery pack and voltage of the single cell vs. the time of three orbital periods.  
degradation factor of 2.7%. The projected lifetime is 10 years with an efficiency of 0.65 for the paths from the solar panels through the batteries to the individual loads, and an efficiency of 0.85 for the path directly from the arrays to the loads [59]. Based on these considerations, the total computed solar array area is determined to be 22 m\({}^{2}\).