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Markov-Constrained Isolation Forest for Early Detection of Battery Anomalies in Solar-Grid Applications
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DOI：10.3390/math14071192.png)
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Abstract
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Lithium-ion batteries in hybrid solar-grid systems experience complex electro-thermal dynamics and stochastic mode switching that threshold-based battery management systems fail to capture. This paper proposes a hybrid deviation detection framework that treats anomaly detection as a trajectory-consistency problem over a power-feasible Markov jump nonlinear system. A disturbance-robust invariant operating region is first established under explicit current bounds. A reachable-set equivalence is then derived, linking residual consistency to disturbance-augmented trajectory membership. Building on this structure, Isolation Forest empirically estimates the support of admissible electro-thermal trajectories, capturing nonlinear and mode-dependent behaviors not fully described by the analytical disturbance model. A unified sequential detection rule integrates structural constraint violations, model-based residual deviations, and empirical support inconsistencies into a coherent real-time monitor. The framework is validated on a hybrid solar-grid platform with a 6 W photovoltaic panel, a 3.7 V 1820 mAh lithium-ion battery, and a Raspberry Pi, collecting 3976 samples over four days. Results demonstrate early detection of depletion events and mode-transition anomalies before hard threshold violations, with zero false alarms during steady operation and an overall deviation rate of 4.8%, aligning with the configured contamination level. Early warning was observed at 20% state of charge, providing a 10% margin before the hardware threshold of 10%, while 88% of detected anomalies occurred in sequences, validating the persistence rule. Real-time inference required 47 ms per cycle with a 156 MB memory footprint, confirming edge deployment feasibility.
Keywords:
lithium-ion batteries
hybrid solar-grid systems
anomaly detection
reachability analysis
Isolation Forest
electro-thermal modeling
machine learning
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