Question 1

A $500-\mathrm{km}, 500-\mathrm{kV}, 60-\mathrm{Hz}$ uncompensated three-phase line has a positive-sequence series impedance $z=0.03+j 0.35 \Omega / \mathrm{km}$ and a positive-sequence shunt admittance $y=j 4.4 \times 10^{-6} \mathrm{~S} / \mathrm{km}$. Calculate: (a) $Z_{c}$, (b) $(\gamma l)$, and (c) the exact $A B C D$ parameters for this line.

Accepted Answer

The answer of A $500-\mathrm{km}, 500-\mathrm{kV}, 60-\mathrm{Hz}$ uncompensated three-phase line...

Question 2

A $320-\mathrm{km} 500-\mathrm{kV}, 60-\mathrm{Hz}$ three-phase uncompensated line has a positive-sequence series reactance $x=0.34 \Omega / \mathrm{km}$ and a positive-sequence shunt admittance $y=j 4.5 \times$ $10^{-6} \mathrm{~S} / \mathrm{km}$. Neglecting losses, calculate: (a) $\mathrm{Z}_{c}$, (b) $(\gamma l)$, (c) the $A B C D$ parameters, (d) the wavelength $\lambda$ of the line, in kilometers, and (e) the surge impedance loading in MW.

Accepted Answer

(a) $\bar{Ƶ}_{C}=\sqrt{\frac{\bar{z}}{\bar{y}}}=\sqrt{\frac{j 0.34}{j 4.5 \times 10^{-6}}}=274.9 \Omega$
(b) $\bar{\gamma} l=\sqrt{\bar{z} \bar{y}} l=\sqrt{(j 0.34)\left(j 4.5 \times 10^{-6}\right)}(320)=j 0.3958 \mathrm{pu}$
(c) $\bar{\gamma} l=j \beta l ; \quad \beta l=0.3958 \mathrm{pu}$
$\bar{A}=\bar{D}=\cos \beta l=\cos (0.3958$ radians $)=0.9227 \angle 0^{\circ} \mathrm{pu}$
$\bar{B}=j \bar{Ƶ}_{C} \sin \beta l=j(274.9) \sin (0.3958$ radians $)$
$=j 108.81 \Omega$
$\bar{C}=j\left(\frac{1}{Ƶ_{C}}\right) \sin \beta l=j \frac{1}{274.9} \sin (0.3958$ radians $)$
$=j 1.44 \times 10^{-3} \mathrm{~S}$
(d) $\beta=\beta l / l=0.3958 / 300=1.319 \times 10^{-3}$ radians $/ \mathrm{km}$
$\lambda=2 \pi / \beta=4766 \mathrm{~km}$
(e) $\mathrm{SIL}=\frac{V_{\text {rated } L-L}^{2}}{Ƶ_{C}}=\frac{(500)^{2}}{274.9}=909.4 \mathrm{MW}(3 \phi)$

Question 3

Repeat Test Bank Problems 5.5 and 5.11 if the line length is (a) $200 \mathrm{~km}$ and (b) $550 \mathrm{~km}$.

Accepted Answer

The thermal limit of $3.33 \mathrm{kA} /$ phase corresponds to $\sqrt{3}(500)(3.33)=2884 \mathrm{MW}$ at 500 $\mathrm{kV}$ and unity power factor.

Question 4

Rated line voltage is appliedto the sending end of the line in Test Bank Problem 5.8.Calculate the receiving-end voltage when thereceiving end is terminated by (a) an open circuit, (b) the surge impedance of the line,and (c) one-half of thesurge impedance. (d)Also calculate the theoretical maximum realpower that the line can deliver when rated voltage is applied toboth ends of the line.

Accepted Answer

The answer of Rated line voltage is appliedto the sending...

Question 5

A $150-\mathrm{km}, 230-\mathrm{kV}, 60-\mathrm{Hz}$ three-phase line has a positive-sequence series impedance $z=0.08+j 0.48 \Omega / \mathrm{km}$ and a positive-sequence shunt admittance $y=j 3.33 \times 10^{-6} \mathrm{~S} /$ $\mathrm{km}$. At full load, the line delivers $250 \mathrm{MW}$ at 0.99 p.f. lagging and at $220 \mathrm{kV}$. Using the nominal $\pi$ circuit, calculate: (a) the $A B C D$ parameters, (b) the sending-end voltage and current, and (c) the percent voltage regulation.

Accepted Answer

The answer of A $150-\mathrm{km}, 230-\mathrm{kV}, 60-\mathrm{Hz}$ three-phase line has...

Question 6

Rework Test Bank Problem 5.2 in per-unit using 100-MVA (three-phase) and 230-kV(line-to-line) base values. Calculate (a) the per-unitABCDparameters, (b) the per-unitsending-end voltage and current, and (c) the percent voltage regulation.

Accepted Answer

The answer of Rework Test Bank Problem 5.2 in per-unit...

Question 7

Evaluate $\cosh (\gamma l)$ and $\tanh (\gamma l / 2)$ for $\gamma l=0.45 \angle 87^{\circ}$ per unit.

Accepted Answer

The answer of Evaluate $\cosh (\gamma l)$ and \(\tanh (\gamma...

Question 8

Determine the equivalent  circuit for the line in Test Bank Problem 5.8.

Accepted Answer

The answer of Determine the equivalent  circuit for the...

Question 9

Determine the practical line loadability in MWand in per unit of SIL for the line in Test Bank Problem 5.5 if the length is(a) 200 km and (b) 600 km. Assume V_S = 1.0 per unit, V_R =0.95 per unit , and 0.99 leading power factor at the receiving end.

Accepted Answer

The answer of Determine the practical line loadability in MWand...

Question 10

The line in Test Bank Problem 5.5 has three ACSR 1113-kcmil conductors per chase.Calculate the theoretical maximum real power that this line can deliver and compare withthe thermal limit of the line. Assume V_S-V_R=1.0 per unit and unity power factor at thereceiving end.

Accepted Answer

The answer of The line in Test Bank Problem 5.5...

Question 11

A $30-\mathrm{km}, 34.5-\mathrm{kV}, 60-\mathrm{Hz}$ three-phase line has a positive-sequence series impedance $z=0.19+j 0.34 \Omega / \mathrm{km}$. The load at the receiving end absorbs 10 MVA at $33 \mathrm{kV}$. Assuming a short line, calculate: (a) the $A B C D$ parameters, (b) the sending-end voltage for a load power factor of 0.9 lagging, (c) the sending-end voltage for a load power factor of 0.9 leading.

Accepted Answer

The answer of A $30-\mathrm{km}, 34.5-\mathrm{kV}, 60-\mathrm{Hz}$ three-phase line has...

Question 12

For the line in Test Bank Problems 5.5 and 5.11 , determine (a) the practical line loadability in MW, assuming $V_{S}=1.0$ per unit, $V_{R} \approx 0.95$ per unit, and $\delta_{\max }=35^{\circ}$; (b) the full-load current at 0.99 leading power factor, based on the above practical line loadability; (c) the exact receiving-end voltage for the full-load current in (b) above; and (d) the percent voltage regulation. For this line, is loadability determined by the thermal limit, the drop limit, or stead-state stability?

Accepted Answer

The answer of For the line in Test Bank Problems...

Question 13

etermine the equivalent  circuit for the line in TestBank Problem 5.5 and compare it with the nominal  circuit.

Accepted Answer

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Question 14

At full load the line in Test Bank Problem 5.5 delivers 1000 MW at unity power factor and at 480 kV. Calculate (a) thesending-end voltage, (b) the sending-end current, (c) the sending-end power factor, (d) the full-loadline losses, and (e) the percent voltage regulation.

Accepted Answer

The answer of At full load the line in Test...

Exam 4: Transmission Lines: Steady-State Operation

Repeat Test Bank Problems 5.5 and 5.11 if the line length is (a) $200 \mathrm{~km}$ and (b) $550 \mathrm{~km}$ .

Rework Test Bank Problem 5.2 in per-unit using 100-MVA (three-phase) and 230-kV(line-to-line) base values. Calculate (a) the per-unitABCDparameters, (b) the per-unitsending-end voltage and current, and (c) the percent voltage regulation.

Evaluate $\cosh (\gamma l)$ and $\tanh (\gamma l / 2)$ for $\gamma l=0.45 \angle 87^{\circ}$ per unit.

Determine the equivalent circuit for the line in Test Bank Problem 5.8.

Determine the practical line loadability in MWand in per unit of SIL for the line in Test Bank Problem 5.5 if the length is(a) 200 km and (b) 600 km. Assume V_S = 1.0 per unit, V_R =0.95 per unit , and 0.99 leading power factor at the receiving end.

The line in Test Bank Problem 5.5 has three ACSR 1113-kcmil conductors per chase.Calculate the theoretical maximum real power that this line can deliver and compare withthe thermal limit of the line. Assume V_S-V_R=1.0 per unit and unity power factor at thereceiving end.

etermine the equivalent circuit for the line in TestBank Problem 5.5 and compare it with the nominal circuit.

At full load the line in Test Bank Problem 5.5 delivers 1000 MW at unity power factor and at 480 kV. Calculate (a) thesending-end voltage, (b) the sending-end current, (c) the sending-end power factor, (d) the full-loadline losses, and (e) the percent voltage regulation.

Exam 4: Transmission Lines: Steady-State Operation

Repeat Test Bank Problems 5.5 and 5.11 if the line length is (a) 200 km200 \mathrm{~km}200 km and (b) 550 km550 \mathrm{~km}550 km .

Rework Test Bank Problem 5.2 in per-unit using 100-MVA (three-phase) and 230-kV(line-to-line) base values. Calculate (a) the per-unitABCDparameters, (b) the per-unitsending-end voltage and current, and (c) the percent voltage regulation.

Evaluate cosh⁡(γl)\cosh (\gamma l)cosh(γl) and tanh⁡(γl/2)\tanh (\gamma l / 2)tanh(γl/2) for γl=0.45∠87∘\gamma l=0.45 \angle 87^{\circ}γl=0.45∠87∘ per unit.

Determine the equivalent circuit for the line in Test Bank Problem 5.8.

Determine the practical line loadability in MWand in per unit of SIL for the line in Test Bank Problem 5.5 if the length is(a) 200 km and (b) 600 km. Assume VS = 1.0 per unit, VR =0.95 per unit , and 0.99 leading power factor at the receiving end.

The line in Test Bank Problem 5.5 has three ACSR 1113-kcmil conductors per chase.Calculate the theoretical maximum real power that this line can deliver and compare withthe thermal limit of the line. Assume VS-VR=1.0 per unit and unity power factor at thereceiving end.

etermine the equivalent circuit for the line in TestBank Problem 5.5 and compare it with the nominal circuit.

At full load the line in Test Bank Problem 5.5 delivers 1000 MW at unity power factor and at 480 kV. Calculate (a) thesending-end voltage, (b) the sending-end current, (c) the sending-end power factor, (d) the full-loadline losses, and (e) the percent voltage regulation.

Repeat Test Bank Problems 5.5 and 5.11 if the line length is (a) $200 \mathrm{~km}$ and (b) $550 \mathrm{~km}$ .

Evaluate $\cosh (\gamma l)$ and $\tanh (\gamma l / 2)$ for $\gamma l=0.45 \angle 87^{\circ}$ per unit.

Determine the practical line loadability in MWand in per unit of SIL for the line in Test Bank Problem 5.5 if the length is(a) 200 km and (b) 600 km. Assume V_S = 1.0 per unit, V_R =0.95 per unit , and 0.99 leading power factor at the receiving end.

The line in Test Bank Problem 5.5 has three ACSR 1113-kcmil conductors per chase.Calculate the theoretical maximum real power that this line can deliver and compare withthe thermal limit of the line. Assume V_S-V_R=1.0 per unit and unity power factor at thereceiving end.