Power Flow and State Estimation using Newton Algorithm andWeighted Least Squares Method

Power flow and state estimation are fundamental processes in the operation and planning of power systems. This paper presents a brief review, implementation, and evaluation of these techniques on a benchmark IEEE three-generator, six-bus network. TheNewton-Raphson method is employed to solve the nonlinearAC power flow equations, with results validated against industrial software (PSSE). Additionally, weighted least squares algorithms were implemented for both DC and AC models. While the DC estimator achieved an acceptable residual of 5.57 MW in active power estimation, it still exhibited measurable accuracy loss on high-R/X or voltage-deviation branches, with line-flow mean absolute percentage errors increasing by ∼1–3% and bus angle deviations reaching up to 19° relative to AC estimator results. Ultimately, an overview of how classical estimation and analysis techniques can be practically applied and evaluated for both industrial and benchmarking purposes in power systems engineering are presented and discussed in detail.