Introduction:
The Newton-Raphson (Polar) load flow and the fast decoupled load flow are both numerical methods used in power system analysis to solve the load flow problem. The load flow problem involves calculating the steady-state voltages and currents in a power system network.

Explanation:
The Newton-Raphson (Polar) load flow and the fast decoupled load flow differ in their approach to solving the load flow problem. The Newton-Raphson (Polar) method uses polar coordinates to represent the complex voltages and currents in the system, while the fast decoupled method uses rectangular coordinates.

The main difference between the two methods lies in the number of iterations required to obtain a solution. The Newton-Raphson (Polar) method typically requires a larger number of iterations compared to the fast decoupled method. This is because the Newton-Raphson (Polar) method requires solving a set of non-linear equations iteratively, which can be computationally expensive.

Reasons for the answer:
There are several reasons why the fast decoupled load flow method takes a lesser number of iterations compared to the Newton-Raphson (Polar) method:

1. Decoupling: The fast decoupled method makes an approximation by neglecting certain terms in the power system equations, which allows the equations to be decoupled into sets of linear equations. This approximation reduces the complexity of the equations and speeds up the convergence of the solution.

2. Simplified calculations: The fast decoupled method uses simplified calculations for the Jacobian matrix and the power mismatches, which reduces the computational burden compared to the Newton-Raphson (Polar) method.

3. Reduced computational load: The fast decoupled method requires fewer calculations per iteration compared to the Newton-Raphson (Polar) method. This reduces the overall computational load and allows for faster convergence.

4. Improved convergence: The fast decoupled method has been shown to have better convergence properties compared to the Newton-Raphson (Polar) method, especially for ill-conditioned systems or systems with high R/X ratios.

Conclusion:
In conclusion, the fast decoupled load flow method takes a lesser number of iterations compared to the Newton-Raphson (Polar) load flow method. This is due to the decoupling approximation, simplified calculations, reduced computational load, and improved convergence properties of the fast decoupled method.