150 km line by T-model, 60 MW

Given: $R = 45\ \Omega$, $X = 85\ \Omega$ per phase (totals); $C = 9$ nF/km × 150 km $= 1.35\ \mu$F; load 60 MW, 132 kV, 0.9 p.f. lagging. Frequency assumed 50 Hz.

$$\begin{aligned} Z &= 45 + j85\ \Omega, \quad \frac{Z}{2} = 22.5 + j42.5\ \Omega \\ Y &= j2\pi\times50\times1.35\times10^{-6} = j4.241\times10^{-4}\ \text{S} \\ V_R &= \frac{132}{\sqrt3} = 76.21\angle 0^\circ\ \text{kV} \\ I_R &= \frac{60\times10^6}{\sqrt3\times132\times10^3\times0.9} = 291.6\angle -25.84^\circ = 262.43 - j127.10\ \text{A} \end{aligned}$$

Nominal-T working

 IS     Z/2            Z/2     IR
 o-->--[R/2 jX/2]--+--[R/2 jX/2]-->--o
                   |
 VS              [ Y ] Ic   (VC)     VR
                   |
 o-----------------+-----------------o

$$\begin{aligned} V_C &= V_R + I_R\frac{Z}{2} = 87{,}517 + j8294 = 87.91\angle 5.41^\circ\ \text{kV} \\ I_C &= YV_C = -3.52 + j37.12 = 37.28\angle 95.41^\circ\ \text{A} \\ I_S &= I_R + I_C = 258.91 - j89.98 = 274.1\angle -19.17^\circ\ \text{A} \\ V_S &= V_C + I_S\frac{Z}{2} = 97{,}167 + j17{,}273 = 98.69\angle 10.08^\circ\ \text{kV} \\ V_{S(L)} &= \sqrt3\times98.69 = 170.94\ \text{kV} \end{aligned}$$

Sending p.f. $= \cos(10.08^\circ + 19.17^\circ) = 0.8725$ lagging.

(i) Sending-end active power

$$P_S = 3|V_S||I_S|\cos\phi_S = 3\times98.69\times10^3\times274.1\times0.8725 = 70.81\ \text{MW}$$

(iii) Line losses (series resistance, $R/2$ in each arm)

$$\begin{aligned} P_{loss} &= 3\left(|I_R|^2 + |I_S|^2\right)\frac{R}{2} = 3(291.6^2 + 274.1^2)(22.5) \\ &= 10.81\ \text{MW} \end{aligned}$$

Check: $P_S - P_R = 70.81 - 60 = 10.81$ MW.

(ii) Efficiency

$$\eta = \frac{P_R}{P_S}\times100 = \frac{60}{70.81}\times100 = 84.73\ \%$$

(iv) Voltage regulation

$A = 1 + ZY/2 = 0.982\angle 0.56^\circ$. No-load receiving voltage:

$$\begin{aligned} V_{R(NL)} &= \frac{|V_S|}{|A|} = \frac{98.69}{0.982} = 100.50\ \text{kV/phase} = 174.07\ \text{kV (line)} \\ \%\text{VR} &= \frac{174.07 - 132}{132}\times100 = 31.87\ \% \end{aligned}$$

Answer: (i) $P_S = 70.81$ MW, (ii) $\eta = 84.73\%$, (iii) line loss $= 10.81$ MW, (iv) regulation $= 31.87\%$ (with $V_S = 170.94$ kV, $I_S = 274.1$ A).

The large regulation and loss arise because $R = 45\ \Omega$ and $X = 85\ \Omega$ are high for a 132 kV line carrying 60 MW.