Mathematical Modelling and Lyapunov Stability Analysis of Solar-Powered Recirculating-Water Gravity Energy Storage Systems Under False Data Injection Attacks

Solar-powered recirculating-water gravity energy storage (SRWGES) is a electromechanical storage technology that holds energy as gravitational potential energy of water, yet its digital sensing and control layer is exposed to false data injection (FDI) attacks. Existing gravity storage research addresses sizing, economics and dispatch, while cybersecurity studies of storage concentrate on batteries and on detectors that ignore plant dynamics. No earlier study provides a physics-based stability analysis of a gravity-storage plant under adversarial sensing. This paper closes that gap with a four-state nonlinear model whose turbine generator dynamics are derived from a torque balance. Established Lyapunov and input-to-state stability tools are used as such. The original contributions are three. First, a proportional-only flow governor is shown to produce an exact, parameter-independent cancellation that leaves the speed and flow subsystem marginally stable, and a speed droop term is shown to remove it. Second, a closed-form attack tolerance threshold of 20.16 m3 for a 20 m3 safety margin is derived in physical parameters and agrees with nonlinear simulation within 0.6%; it shows that tighter proportional regulation does not improve resilience. Third, a physics-based observer limits the volume deviation to 1.31 m3 under single and coordinated attacks, whereas, without measurement noise, a raw threshold detector never alarms against a constructed masking attack. Stability results are local, the region of attraction is an estimate and not a certificate, and global stability is not claimed.