Question

Sparse-matrix techniques are used in Newton-Raphson power flow programs in order to reduce computer ___________ and ___________ requirements.

Short answer

Sparse-matrix techniques are used in Newton-Raphson power flow programs in order to reduce computer storage and time requirements.

Step-by-step solution

Definition of Newton-Raphson method.

Newton-Raphson method is used for finding a real root of a given differential polynomial function. It is defined as:

$\mathbf{y}\mathbf{=}\mathbf{f}\left(\mathbf{x}\right)$ …… (1)

Here, $\mathbf{y}$ is $\mathbf{N}$ vector and $\mathbf{f}\left(\mathbf{x}\right)$ is a $\mathbf{N}$vector of functions.

Substitute $\left[\begin{array}{c}{\mathbf{f}}_1\left(\mathbf{x}\right)\\ {\mathbf{f}}_2\left(\mathbf{x}\right)\\ \begin{array}{l}⋮\\ {\mathbf{f}}_N\end{array}\end{array}\right]$ for $\mathbf{f}\left(\mathbf{x}\right)$.

$\mathbf{y}=\left[\begin{array}{c}{\mathbf{f}}_1\left(\mathbf{x}\right)\\ {\mathbf{f}}_2\left(\mathbf{x}\right)\\ \begin{array}{l}⋮\\ {\mathbf{f}}_N\end{array}\end{array}\right]$

Prove the Sparse-matrix techniques are used in Newton-Raphson power flow method.

The sparse matrix is composed of techniques that includes compact $Y_{\text{bus}}$ and $J\left(i\right)$ storage, as well as bus reordering that further avoid the elements $\mathrm{J}\left(\mathrm{i}\right)$ that is filled-in during Gauss elimination steps.

Here, $Y_{\text{bus}}$ is the admittance matrix of bus -$Y$, and $J\left(i\right)$is the Jacobian matrix of element $i$.

Therefore, Sparse-matrix techniques are used in Newton-Raphson power flow programs in order to reduce computer storage and time requirements.