A Mathematical Model for Managing Renewable Energy Fluctuations and Automated Battery Activation

This paper presents a mathematical model for managing renewable energy fluctuations through automated battery activation by monitoring the time derivatives of the system's state. The model employs an exponential formula to measure consistency between wave acceleration and velocity, yielding a stable reference value of (1/e) at quadrant angles during simple harmonic motion. This index enables the instantaneous detection of disturbances and shifts in wave acceleration, ensuring an immediate grid response. To enhance reliability, the model incorporates noise damping and techniques to prevent the accumulation of numerical errors in the denominator.