# An Integrated Thermal-Electrical Model for Simulations of Battery Behavior in CubeSats
## 1 Introduction  
As a result of electronic miniaturization, compact and light platforms were projected for space applications, including the CubeSat standard proposed in 1999 [1]. In parallel to that, the introduction of CubeSat standard and COTS components reduced the price to put a small satellite in orbit by sharing the costs of a launch with multiple CubeSats as piggyback payloads, enabling universities and private companies worldwide to undertake technology demonstration missions in outer space at affordable prices and sustainable businesses models dedicated to CubeSats. Ten CubeSats were launched in 2000 and 297 in 2017; 458 launches are expected in 2020, and 2500 new CubeSats expected by 2025. The projections are that around 49% of them will be from private initiatives, 32% from universities, 5% from space agencies, and 4% from militaries [2]. A CubeSat is usually covered by photovoltaic panels (PV) on its surface to recharge the batteries and power the subsystems. However, due to the solar panels' small size and volume, the energy harvesting capability heavily depends on its attitude concerning the Sun [3]. Additionally, as a consequence of the attitude, other parameters of great concern in CubeSats are PV and battery temperatures. While extreme cold and hot scenarios damagethese parts and other electronic components, the optimum PV and battery performance only exists in a narrow range of temperature [4; 5]. Therefore, the energy efficiency and harvested energy distribution are critical for the CubeSat missions, especially when the CubeSat cannot efficiently maintain its attitude towards the solar rays [6]. In this sense, a fundamental challenge in CubeSat missions is to cope with the shortage of available energy to power its subsystems throughout the satellite's lifetime through simulations. A battery's life cycle is a function of diverse factors, mainly: the state of charge (SoC), the temperature, the charge/discharge current, and the end of charge voltage (EOCV). As a rule of thumb, a lower SoC means a worse life cycle, and the lower the temperature field, the charge/discharge current, and the EOCV, the better the cycle life [7; 8]. Additionally, the batteries' internal resistance shows a strong temperature dependence, increasing for low temperatures and impacting the CubeSat voltage drops and the mission's power budget. Usually, the operational temperature recommended for batteries in CubeSat applications is between 253 and 333 K [9]. However, as experimentally demonstrated in [5], typical COTS batteries for CubeSat missions are Li-ion cells, whose energy storage capacity may be around 20% of its maximum (at 293 K) when exposed to 253 K. The \"Mars Cube One\" (MarCO) CubeSat is a good example where temperature control is a major challenge. The two MarCO CubeSats had Li-ion batteries kept within 273 to 303 K during all mission phases. Heaters attached to the battery were used to sustain the temperature, and passive materials were employed to allow heat exchanging with other satellite parts [10; 11]. Similarly to the battery, the PV degradation in orbit is a function of the conditions in space, such as irradiance temperature field [3; 4; 12]. Only a fraction of the solar spectrum is useful for energy generation. The larger wavelengths of radiation are harmful for its operation because they heat the cells and reduce the photovoltaic effect's efficiency, which is hardly ever above 30% [13]. Therefore, for efficient operation, a PV panel must avoid high levels of temperature and low irradiance. However, the desire for high radiation levels to generate more energy in solar cells contradicts the inherent rise in PV panels' temperature by this effect itself. The authors in [14] tested solar cells, and they measured a drop of 3% in the efficiency for temperatures ranging from 280 to 320 K--the hottest temperature and the worst performance. The work of [15] measured a coefficient of loss of around 0.5% per degree.