Optimizing Power Line Inspection: A Novel Bézier Curve-Based Technique for Sag Detection and Monitoring

Power line sag monitoring is critical for ensuring transmission system reliability and optimizing grid capacity utilization. Traditional sag detection methods rely on hyperbolic cosine models that assume ideal catenary behavior under uniform loading conditions. However, these models impose restrictive assumptions about weight distribution and suspension conditions that limit accuracy under real-world scenarios involving wind loading, ice accumulation, and non-uniform environmental forces. This study introduces a novel Bézier curve-based mathematical framework for transmission line sag detection and monitoring. Unlike traditional hyperbolic cosine approaches, the proposed methodology eliminates idealized assumptions and provides enhanced flexibility for modeling actual conductor behavior under variable environmental conditions. The Bézier curve approach offers enhanced precision and computational efficiency through intuitive control point manipulation, making it well suited for Dynamic Line Rating (DLR) applications. Experimental validation was performed using a controlled laboratory setup with a 1:100 scaled transmission line model. Results demonstrate improvement in sag measurement accuracy, achieving an average error of 1.1% compared to 6.15% with traditional hyperbolic cosine methods—representing an 82% improvement in measurement precision. Statistical analysis over 30 independent experiments confirms measurement consistency with a 95% confidence interval of [0.93%, 1.27%]. The framework also demonstrates a 1.5 to 2 times increase in computational efficiency improvement over conventional template matching approaches. This mathematical framework establishes a robust foundation for advanced transmission line monitoring systems, with demonstrated advantages for power grid applications where traditional catenary models fail due to non-ideal environmental conditions. The enhanced accuracy and efficiency support improved Dynamic Line Rating implementations and grid modernization efforts.