Which statement best describes why Newton-Raphson is more robust than Gauss-Seidel for power-flow solution?

Which statement best describes why Newton-Raphson is more robust than Gauss-Seidel for power-flow solution?

• A. Gauss-Seidel uses a Jacobian and has quadratic convergence.
• B. NR uses a Jacobian and has quadratic convergence, typically converging faster and more reliably for large, ill-conditioned systems.
• C. NR is a linear method with slow convergence.
• D. GS is always faster and more reliable.

Answer: (B)

The main idea being tested is how the solver handles nonlinear power-flow equations. Newton-Raphson is more robust because it uses the full Jacobian to linearize those nonlinear equations at each step and then solves for a correction vector. This gives quadratic convergence: as you get closer to the solution, the error shrinks very quickly, so you reach a solution from a wider range of starting points, even in large or ill-conditioned systems. Gauss-Seidel, on the other hand, updates voltages one bus at a time without solving the complete linearized system, so its convergence is typically linear and more sensitive to the system’s conditioning and the starting point. In stressed or highly coupled networks, this makes Gauss-Seidel less reliable and slower, whereas Newton-Raphson tends to converge faster and more reliably.

The main idea being tested is how the solver handles nonlinear power-flow equations. Newton-Raphson is more robust because it uses the full Jacobian to linearize those nonlinear equations at each step and then solves for a correction vector. This gives quadratic convergence: as you get closer to the solution, the error shrinks very quickly, so you reach a solution from a wider range of starting points, even in large or ill-conditioned systems. Gauss-Seidel, on the other hand, updates voltages one bus at a time without solving the complete linearized system, so its convergence is typically linear and more sensitive to the system’s conditioning and the starting point. In stressed or highly coupled networks, this makes Gauss-Seidel less reliable and slower, whereas Newton-Raphson tends to converge faster and more reliably.