The main objective of a modern electrical power system is to provide quality and reliable electric power to consumers of electricity; the quality is determined by the voltage magnitude and the frequency at which it is delivered. Load flow analysis is essential for power system planning, operation, and expansion. The Nigerian 330kV transmission network faces persistent challenges including voltage instability, high technical losses, and inadequate power supply despite the country's significant energy resources. This work presents a comprehensive investigation of load flow solution methods — Gauss-Seidel (GS), Newton-Raphson (NR) and Fast Decoupled (FDLF comparing their performance, convergence characteristics, and computational efficiency. Model of power system generates non-linear algebraic equations and to solve these equations three solution algorithms based on power equations for the three methods was adopted. The result reveals the well-known properties of these algorithms: speed, rate of convergence and the convergence characteristics. The findings indicate that Newton-Raphson offers superior convergence, speed and accuracy for ill-conditioned systems, Fast Decoupled provides adequate accuracy with reduced computational requirements, and Gauss-Seidel remains useful for small-scale implementations despite slower convergence. Recommendations for practical implementation in the Nigerian context are provided. Findings provide practical guidance for grid operators and planners in selecting appropriate load flow methods for specific applications within the Nigerian power system.