Virtual Sensing Model for Power Prediction of Satellite Solar array: J₂ Perturbation Dynamics Resolution via Dual-Coordinate Transformation and Adaptive Runge-Kutta

This model resolves <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${J} _{{2}}$ </tex-math></inline-formula> perturbation orbital dynamics equations via dual-coordinate transformation, utilizing the Earth-centered inertial (ECI) coordinate system for orbital dynamics and the geocentric solar ecliptic (GSE) system for solar vector alignment. Adaptive Runge–Kutta integral solution for ordinary differential equations (ODEs) converts initial orbital parameters into continuous power profiles to achieve high-precision and long-term forecasting for satellite solar arrays with replacing physical measurements. To mitigate the error accumulation issue inherent in conventional methods that overlook orbital perturbations, the proposed model integrates <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${J} _{{2}}$ </tex-math></inline-formula> perturbation effects to refine orbital parameters and utilizes an adaptive Runge–Kutta algorithm to effectively resolve satellite attitude dynamics. The use of dual-coordinate transformation and decoupled dynamics analysis substantially reduces computational complexity. Additionally, an equivalent power model for solar array under illumination and eclipse conditions is developed based on a cylindrical projection method, enabling rapid calculations in complex lighting environments. The experimental results indicate that the proposed method achieves long-term power forecasting using only initial orbital parameters, obviating the need for professional tools or frequent data updates. Compared to traditional two-body models, this approach demonstrates significant advantages in computational efficiency (requiring only one-third of STK’s runtime) and prediction accuracy (achieving a 60% reduction in mean squared error), thereby providing reliable theoretical support for dynamic power management and mission planning in satellite energy systems.