EE $462$

POWER SYSTEM ANALYSIS

HOMEWORK #$5($Due Jan. $02,2025,23$:$59)$

Consider the $3-$bus power system given below. The branch and bus data, as well as analyze the network using Gauss$-$Seidel method.

a$)$ Perform at most $2$ iterations. Take the convergence criteria in power mismatches as $lon=0\mathrm{.}05$ p$.$u$.$ Check the convergence after each iteration. For initial guesses, use $0$ for angles and $|V_3|=1\mathrm{.}00$ p$.$u$.$ Neglect reactive power minimum and maximum limits for generators. Give your results after $2$ iterations.

b$)$ Assume that the exact solution obtained after convergence is $V_2=\frac{1\mathrm{.}02}{H}\frac{?}{46\mathrm{.}4}$ and $V_3=1\mathrm{.}0043-0\mathrm{.}959.$ Compute slack bus active and reactive power generation. What is the total losses in MW$?$

$=\left[\begin{array}{ccc}15-35j& -10+20j& -5+15j\\ -10+20j& 30-60j& -20+40j\\ -5+15j& -20+40j& 25-55j\end{array}\right]$

$\backslash$table$[[$Bus$,$Voltage $($p$.$u$.),$Power,Line,Impedance $($p$.$u$.)],[1,1\mathrm{.}02,($stack$),1-2,0\mathrm{.}02+0\mathrm{.}04j$