The Gauss-Seidel method is an iterative technique used in power system analysis to solve the non-linear equations that arise in load flow studies. It's a refinement of the Jacobi method, offering faster convergence by incorporating updated values as soon as they are calculated.

Load flow analysis aims to determine the steady-state operating conditions of a power system. This involves calculating the voltage magnitude and phase angle at each bus, as well as the real and reactive power flow through each transmission line. The core of this problem lies in solving a set of non-linear algebraic equations derived from Kirchhoff's current law at each bus.

1. Initialization: Assign initial voltage values to all buses. Typically, slack bus voltage is known, and for other buses, $V=1.0 \angle 0^{\circ}$ is used.
2. Calculate Bus Powers: Determine the complex power injected at each bus based on the current voltage estimates.
3. Update Bus Voltages: For each bus (except the slack bus), calculate its new voltage using the Gauss-Seidel iterative formula. This involves using the most recently updated voltages for buses with indices less than the current bus.
4. Check for Convergence: Compare the newly calculated voltages with the voltages from the previous iteration. If the difference (or error) is within a predefined tolerance for all buses, the solution has converged. Otherwise, repeat from step 2.
5. Final Results: Once converged, the calculated voltages represent the steady-state operating conditions.

For GATE Electrical Engineering, understanding the iterative process, the update formula, and the convergence criteria is crucial. You should be able to:

• Identify the bus types (Slack, PV, PQ).
• Formulate the Y-bus matrix.
• Apply the Gauss-Seidel iterative formula for a few iterations.
• Understand the conditions for convergence and potential issues like divergence.