Question 9: Steady-state stability (Everyone must do this question) (25 points)
Transmission Line
A synchronous generator is operating in steady state, connected to an electrical load through an assumed-lossless 1AWG ACSR transmission line. The generator parameters, nominal load bus voltage, and transmission line parameters (and ABCD matrix) are given below. Assume 60Hz electrical frequency.
$P_{rat}^{per-phase} = 20MW$
Generator rated output active power:
Load bus nominal voltage: $V_{Load \ Bus}^{nominal} = 15kV_{RMS}$
Transmission line parameters:
$L = 0.9296 \frac{\mu H}{m}$
$Z_0 = 265.5 \Omega$
$\tilde{C} = 13.186 \frac{pF}{m}$
$y = j1.3199 \cdot 10^{-6} \frac{rad}{m}$
$l = 10km$
$\begin{bmatrix} A & B \\ C & D \end{bmatrix}_{T-line} = \begin{bmatrix} 1 & j0.35045 \frac{V}{A} \\ j4.971 \cdot 10^{-6} \frac{A}{V} & 1 \end{bmatrix}$
a. (8 pts) For a load impedance of $Z_L = 6\Omega + j2\Omega$, compute the load impedance on the generator phase terminals, which is equal to the input impedance of the loaded transmission line $Z_{in}^{gen} = R_{in} + jX_{in}$. Express in real/imaginary form. Does the load look inductive or capacitive?
b. (5 pts) You analyze the input impedance of another cascade of transmission line and parallel load, and determine it to be $Z_{in}^{gen} = R_{in} + jX_{in} = 8\Omega + j10\Omega$. If a shunt reactive component were placed in parallel with the generator terminals, what value reactance is required to compensate the load (transmission line and parallel load) reactance? Is the shunt component inductive or capacitive?
c. (12 pts) If the power factor of the load is 0.8 lagging, compute the full-load load impedance magnitude ($|Z_{L}^{Full \ Load}| = |R_{in} + jX_{in}|$) and the voltage regulation percentage. Assume in your analysis that the full-load load voltage is the nominal bus voltage given above.
