Differences between Newton Raphson & Gauss Seidel Methods ?

[Serena_hm]

Differences between Newton Raphson & Gauss Seidel Methods !?

hello everyone ...

can anyone please summarize me the differences between Newton Raphson & Gauss Seidel Methods in load flow study !?


I'll be really thankful

 

[rbj]

i'm an EE and i have no idea what a "load flow study" is.

the Newton-Raphson and Gauss-Seidel are two different things.

as best as i can tell Gauss-Seidel is sort of equivalent to what we usually call Gaussian elimination, but i may be wrong. both are for solving a set of N linear equations with N unknowns. i don't imagine there are too many problems (like multiple, equally-valid solutions) if the N equations are all linearly independent.

Newton-Raphson is for solving for the roots of N non-linear equations. it's an iterative method that converges on a result. there are possibilities of the thing not converging on a solution, or sometimes converging on a valid solution, but it isn't the set of roots that you want. a set of N non-linear equations might have more than one result set of the N unknowns.

 

[Serena_hm]

thanks for your explanation , I meant with load flow study , power flow study in power system

 

[rbj]

okay, whatever the application is, the Gauss Seidel is for a system of linear equations and Newton-Raphson is for a single non-linear equation or a system of non-linear equations.

 

[alphysicist]

!

The Newton Raphson method and the Gauss Seidel method are both numerical methods used in load flow studies to solve power system equations. However, there are some key differences between the two methods.

1. Algorithm: The Newton Raphson method uses an iterative approach that involves solving a linearized version of the power system equations, while the Gauss Seidel method uses a sequential approach where the equations are solved one at a time.

2. Convergence: The Newton Raphson method is guaranteed to converge to the correct solution as long as the initial guess is close enough, while the Gauss Seidel method may not always converge or may converge to a wrong solution.

3. Speed: The Newton Raphson method typically converges faster than the Gauss Seidel method, especially for larger and more complex systems.

4. Memory requirements: The Newton Raphson method requires more memory as it needs to store the Jacobian matrix, while the Gauss Seidel method only needs to store the system variables.

5. Accuracy: The Newton Raphson method is more accurate as it uses second-order derivatives in its calculations, while the Gauss Seidel method only uses first-order derivatives.

6. Parallelization: The Gauss Seidel method can easily be parallelized, meaning it can be divided into smaller tasks and solved simultaneously on multiple processors, while the Newton Raphson method is more difficult to parallelize.

In summary, the Newton Raphson method is faster and more accurate, but may require more memory and can be harder to parallelize. The Gauss Seidel method, on the other hand, is simpler and can be easily parallelized, but may not always converge and may be slower for larger systems. Ultimately, the choice between the two methods depends on the specific needs and constraints of the load flow study being performed.