Masking of measurements in a photovoltaic system using an incommensurate fractional-order chaotic system based on string dynamics around the Bardeen-AdS black hole

Abstract

Considering environmental factors and global warming, the use and installation of photovoltaic (PV) systems have become widespread. However, the integration of these PV systems into smart grids raises concerns regarding cybersecurity. Since PV systems rely on communication networks, remote monitoring, and grid-connected inverters, they exhibit a cyber–physical structure and are therefore vulnerable to cyber-attacks. Cyber threats targeting PV infrastructure can lead to system failures, energy theft, grid instability, and financial losses. While many studies focus on cyber-attack detection for PV system cybersecurity, this paper aims to design a cybersecure PV system by employing a novel chaos-based encryption method. Due to their unpredictable and highly sensitive nature, chaotic algorithms are utilized to ensure secure communication within PV systems. The encryption algorithm is derived from the incommensurate fractional analysis of the ‘‘strings around the Bardeen-AdS black hole surrounded by quintessence dark energy’’, a cosmological system. Simulation results performed in MATLAB/Simulink confirm the effectiveness of the proposed encryption framework. The underlying pseudo-random number generator (PRNG) successfully passed all 15 standard NIST SP800-22 statistical tests, validating its strong statistical randomness and unpredictability. Furthermore, the encrypted signals consistently exhibit high information entropy (e.g., 𝑉𝑃 𝑉 encrypted entropy = 5.3213 compared to actual entropy = 4.0931), indicating strong randomization and obscurity of original patterns. The decrypted outputs precisely recover the original measurements, with entropy values perfectly matching the actual signals (e.g., decrypted 𝑉𝑃 𝑉 entropy = 4.0931), thereby validating the reliability, reversibility, and cyber resilience of the approach.