Power system security assessment plays a critical role in ensuring the safety and stability of the electric grid, evaluated by the operating state’s proximity to the loadability limits. However, with the increasing integration of intermittent renewable energy sources and rising electricity demands, there is a growing need for fast and reliable algorithms to perform power system security assessments effectively. This work reviews state-of-the-art approaches for steady-state security assessment and demonstrates the advantages of the recently proposed Transversality Enforced Newton Raphson (TENR) algorithm. The algorithm provides better computational tractability, scalability, and the capability to incorporate various technological constraints like limits on voltage setpoints, transmission line thermal limits, generator power outputs, etc. This work presents a generalization of the TENR algorithm, proof of convergence, and an adaptive step-size strategy with improved computational performance. The proposed algorithm was used to study maximum loadability, maximum boundness of the nodal power injections, and total transfer capability on a realistic case study of the Russian Far-East power system model, which expects substantial development in the nearest future.