Load Flow Analysis (LFA) is the computational backbone of power-system operations: solving the network’s nonlinear AC equations to determine bus voltage magnitudes/angles and the real/reactive power flowing through generators, loads, and branches. Built on top of that, optimal power flow (OPF) is a constrained optimization problem targeted to minimize an operational criterion (e.g., operating cost or losses), while respecting nonlinear limits such as voltage bounds, generator capabilities, and line ratings.
In this notebook, I demonstrate a small Newton–Raphson solver with a simple optimization engine built from scratch. It runs power-flow optimization experiments on the IEEE 9-bus benchmark network, a standard compact case widely used for validation purposes. This example program is still far from production-grade grid analytics: in particular, it lacks better component models (tap changers, phase shifters, shunts, limits and saturation behavior), a solver improvements (better initialization, convergence diagnostics, analytical Jacobians for faster convergence), and specialized optimization techniques.
Large utilities and software vendors embed these algorithms in comprehensive suites used for transmission planning, contingency studies, and economic dispatch in grids with thousands of buses; examples include tools such as ETAP and grid planning offerings from GE Vernova. Emerging services combine classic models with predictive analytics and optimization engines to support the integration of renewable energy, storage devices, and demand-response resources.