In this work a new and fast network-wide framework is addressed for modeling and tracking the dynamic behavior of transmission lines in Power Networks (PN). A sparse-based mathematical formulation for Transmission Line Dynamic Behavior Tracking (TLDBT) is formed by incorporating a PN Port-Hamiltonian model. Among the TLDBT a new set of intermediate parameters called the line dynamic index coefficients (LDIC) are defined based on the wave propagation analysis of current waves in transmission lines. It is shown how these coefficients can reflect the dynamic behavior of the transmission lines. The online monitoring of variations in these index coefficients is interpreted as an alternative approach for TLDBT in power grids. Finally, exploiting the inherent sparsity in the PN structure this TLDBT problem is reformulated as a Structured Sparse Recovery Problem (SSRP) and the TLDBT-SSRP is solved for LDICs. The simulation results indicate that the proposed framework can be considered as an alternative approach to address the new challenges in the future generation of smart power grids modeling, monitoring and congestion-management strategies.