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systems analysis design
Questions and Answers of
Systems Analysis Design
Reconsider Problem 4.28 with still another alternate phase placement shown below.Find the inductive reactance of the line in \(\Omega / \mathrm{mi} /\) phase.Problem 4.28For the case of
Figure 4.37 shows the conductor configuration of a three-phase transmission line and a telephone line supported on the same towers. The power line carries a balanced current of \(250 \mathrm{~A} /\)
Calculate the capacitance-to-neutral in \(\mathrm{F} / \mathrm{m}\) and the admittance-to-neutral in S/km for the single-phase line in Problem 4.8. Neglect the effect of the earth plane.Problem 4.8A
Rework Problem 4.32 if the diameter of each conductor is (a) increased by \(20 \%\) to \(1.8 \mathrm{~cm}\) or (b) decreased by \(20 \%\) to \(1.2 \mathrm{~cm}\). Compare the results with those of
Calculate the capacitance-to-neutral in \(\mathrm{F} / \mathrm{m}\) and the admittance-to-neutral in S/km for the three-phase line in Problem 4.10. Neglect the effect of the earth plane.Problem 4.10A
Rework Problem 4.34 if the phase spacing is (a) increased by \(20 \%\) to \(4.8 \mathrm{ft}\) or (b) decreased by \(20 \%\) to \(3.2 \mathrm{ft}\). Compare the results with those of Problem
The line of Problem 4.23 as shown in Figure 4.32 is operating at \(60 \mathrm{~Hz}\). Determine(a) the line-to-neutral capacitance in \(\mathrm{nF} / \mathrm{km}\) per phase and in \(\mathrm{nF} /
(a) In practice, one deals with the capacitive reactance of the line in ohms ⋅⋅ mi to neutral. Show that Eq. (4.9.15) of the text can be rewritten asXC=k′logDr ohms ⋅ mi to
The capacitance per phase of a balanced three-phase overhead line is given by\[\mathrm{C}=\frac{0.0389}{\log (\mathrm{GMD} / r)} \mu \mathrm{f} / \mathrm{mi} / \text { phase }\]For the line of
Calculate the capacitance-to-neutral in \(\mathrm{F} / \mathrm{m}\) and the admittance-to-neutral in \(\mathrm{S} / \mathrm{km}\) for the three-phase line in Problem 4.18. Also calculate the
Rework Problem 4.39 if the phase spacing between adjacent conductors is (a) increased by \(10 \%\) to \(7.7 \mathrm{~m}\) or (b) decreased by \(10 \%\) to \(6.3 \mathrm{~m}\). Compare the results
Calculate the capacitance-to-neutral in \(\mathrm{F} / \mathrm{m}\) and the admittance-to-neutral in \(\mathrm{S} / \mathrm{km}\) for the line in Problem 4.20. Also calculate the total reactive power
Rework Problem 4.41 if the bundled line has (a) three ACSR, 1351-kcmil conductors per phase or (b) three ACSR, \(900 \mathrm{kcmil}\) conductors per phase without changing the bundle spacing or the
Three ACSR Drake conductors are used for a three-phase overhead transmission line operating at \(60 \mathrm{~Hz}\). The conductor configuration is in the form of an isosceles triangle with sides of
Consider the line of Problem 4.25. Calculate the capacitive reactance per phase in \(\Omega \cdot \mathrm{mi}\).Problem 4.25For the overhead line of configuration shown in Figure 4.33 operating at
For an average line height of \(10 \mathrm{~m}\), determine the effect of the earth on capacitance for the single-phase line in Problem 4.32. Assume a perfectly conducting earth plane.Problem
A three-phase \(60-\mathrm{Hz}, 125-\mathrm{km}\) overhead transmission line has flat horizontal spacing with three identical conductors. The conductors have an outside diameter of \(3.28
For the single-phase line of Problem 4.14(b), if the height of the conductor above ground is \(80 \mathrm{ft}\)., determine the line-to-line capacitance in \(\mathrm{F} / \mathrm{m}\). Neglecting
The capacitance of a single-circuit, three-phase transposed line with the configuration shown in Figure 4.38, including ground effect, and with conductors not equilaterally spaced is given by(a) Now
The capacitance-to-neutral, neglecting the ground effect, for the threephase, single-circuit, bundle-conductor line is given by\[\begin{gathered}\mathrm{C}_{a \eta}=\frac{2 \pi \varepsilon_{0}}{\ell
Calculate the conductor surface electric field strength in \(\mathrm{kVrms} / \mathrm{cm}\) for the single-phase line in Problem 4.32 when the line is operating at \(20 \mathrm{kV}\). Also calculate
Rework Problem 4.50 if the diameter of each conductor is(a) increased by \(25 \%\) to \(1.875 \mathrm{~cm}\) (b) decreased by \(25 \%\) to \(1.125 \mathrm{~cm}\) without changing the phase spacings.
Representing a transmission line by the two-port network, in terms of \(A B C D\) parameters,(a) express \(V_{S}\), which is the sending-end voltage, in terms of \(V_{R}\), which is the receiving-end
As applied to linear, passive, bilateral two-port networks, the \(A B C D\) parameters satisfy \(A D-B C=1\).(a) True(b) False
Express the no-load receiving-end voltage \(V_{\mathrm{RNL}}\) in terms of the sendingend voltage, \(V_{S}\), and the \(A B C D\) parameters.
The \(A B C D\) parameters, which are in general complex numbers, have units of ________, ________, ________, and ________, respectively.
The loadability of short transmission lines (less than \(25 \mathrm{~km}\), represented by including only series resistance and reactance) is determined by ________; that of medium lines (less than
Can the voltage regulation, which is proportional to \(\left(V_{\mathrm{RNL}}-V_{\mathrm{RFL}}\right)\) , be negative?(a) Yes(b) No
The propagation constant, which is a complex quantity in general, has units of ________, and the characteristic impedance has units of ________.
Express hyperbolic functions \(\cosh \sqrt{x}\) and \(\sinh \sqrt{x}\) in terms of exponential functions.
\(e^{\gamma}\), where \(\gamma=\alpha+j \beta\), can be expressed as \(e^{\alpha l} / \beta l\), in which \(\alpha l\) is dimensionless and \(\beta l\) is in radians (also dimensionless).(a) True(b)
The equivalent \(\pi\) circuit is identical in structure to the nominal \(\pi\) circuit.(a) True(b) False
The correction factors \(F_{1}=\sinh (\gamma l) \gamma l\) and \(F_{2}=\tanh (\gamma l / 2) /(\gamma l / 2)\), which are complex numbers, have the units of ________.
For a lossless line, the surge impedance is purely resistive and the propagation constant is pure imaginary.(a) True(b) False
For equivalent \(\pi\) circuits of lossless lines, the \(A\) and \(D\) parameters are pure ________, whereas \(B\) and \(C\) parameters are pure ________.
In equivalent \(\pi\) circuits of lossless lines, \(Z^{\prime}\) is pure ________, and \(Y^{\prime}\) is pure ________.
Typical power-line lengths are only a small fraction of the \(60-\mathrm{Hz}\) wavelength.(a) True(b) False
The velocity of propagation of voltage and current waves along a lossless overhead line is the same as speed of light.(a) True(b) False
Surge Impedance Loading (SIL) is the power delivered by a lossless line to a load resistance equal to ________.
For a lossless line, at SIL, the voltage profile is ________, and the real power delivered, in terms of rated line voltage \(\mathrm{V}\) and surge impedance \(\mathrm{Z}_{c}\), is given by ________.
The maximum power that a lossless line can deliver, in terms of the voltage magnitudes \(V_{S}\) and \(V_{R}\) (in volts) at the ends of the line held constant, and the series reactance
The maximum power flow for a lossy line is somewhat less than that for a lossless line.(a) True(b) False
For short lines less than \(25 \mathrm{~km}\) long, loadability is limited by the thermal rating of the conductors or by terminal equipment ratings, not by voltage drop or stability
Increasing the transmission line voltage reduces the required number of lines for the same power transfer.(a) True(b) False
Intermediate substations are often economical from the viewpoint of the number of lines required for power transfer if their costs do not outweigh the reduction in line costs.(a) True(b) False
Shunt reactive compensation improves transmission-line ________, whereas series capacitive compensation increases transmission-line ________.
Static-var-compensators can absorb reactive power during light loads and deliver reactive power during heavy loads.(a) True(b) False
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
A \(200-\mathrm{km}, 230-\mathrm{kV}, 60-\mathrm{Hz}\), 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
Rework Problem 5.2 in per unit using 1000-MVA (three-phase) and \(230-\mathrm{kV}\) (line-to-line) base values. Calculate:(a) the per-unit \(A B C D\) parameters,(b) the per-unit sending-end voltage
Derive the \(A B C D\) parameters for the two networks in series, as shown in Figure 5.4.Figure 5.4 +0+ +0 Vs + Is Vs Vs Is +0 Series impedance Is Circuit Z Z Y Shunt admittance la Z T circuit Z TT
Derive the \(A B C D\) parameters for the T circuit shown in Figure 5.4.Figure 5.4 +0+ +0 Vs + Is Vs Vs Is +0 Series impedance Is Circuit Z Z Y Shunt admittance la Z T circuit Z TT circuit V Series
(a) Consider a medium-length transmission line represented by a nominal \(\pi\) circuit shown in Figure 5.3 of the text. Draw a phasor diagram for lagging power-factor condition at the load
The per-phase impedance of a short three-phase transmission line is \(0.5 / 53.15^{\circ} \Omega\). The three-phase load at the receiving end is \(1200 \mathrm{~kW}\) at 0.8 p.f. lagging. If the
Reconsider Problem 5.7 and find the following:(a) sending-end power factor,(b) sending-end three-phase power, (c) the three-phase line loss.Problem 5.7The per-phase impedance of a short three-phase
The 100−km,230−kV,60−Hz100−km,230−kV,60−Hz, three-phase line in Problems 4.18 and 4.39 delivers 300MVA300MVA at 218kV218kV to the receiving end at full load. Using the nominal ππ
The 500-kV, 60-Hz, three-phase line in Problems 4.20 and 4.41 has a \(180-\mathrm{km}\) length and delivers \(1600 \mathrm{MW}\) at \(475 \mathrm{kV}\) and at 0.95 power factor leading to the
A \(40-\mathrm{km}, 220-\mathrm{kV}, 60-\mathrm{Hz}\), three-phase overhead transmission line has a per-phase resistance of \(0.15 \Omega / \mathrm{km}\), a per-phase inductance of \(1.3263
A \(60-\mathrm{Hz}, 100-\) mile, three-phase overhead transmission line, constructed of ACSR conductors, has a series impedance of \((0.1826+j 0.784) \Omega / \mathrm{mi}\) per phase and a shunt
Evaluate \(\cosh (\gamma l)\) and \(\tanh (\gamma l / 2)\) for \(\gamma l=0.40 ot 85^{\circ}\) per unit.
A \(500-\mathrm{km}, 500-\mathrm{kV}, 60-\mathrm{Hz}\), uncompensated three-phase line has a positivesequence series impedance \(z=0.03+j 0.35 \Omega / \mathrm{km}\) and a positivesequence shunt
At full load, the line in Problem 5.14 delivers 900 MW at unity power factor and at \(475 \mathrm{kV}\). Calculate:(a) the sending-end voltage,(b) the sending-end current,(c) the sending-end power
The \(500-\mathrm{kV}, 60-\mathrm{Hz}\), three-phase line in Problems 4.20 and 4.41 has a 300-km length. Calculate:(a) \(Z_{c}\),(b) \((\gamma l)\), (c) the exact \(A B C D\) parameters for this
At full load, the line in Problem 5.16 delivers \(1500 \mathrm{MVA}\) at \(480 \mathrm{kV}\) to the receiving-end load. Calculate the sending-end voltage and percent voltage regulation when the
A \(60-\mathrm{Hz}, 230-\) mile, three-phase overhead transmission line has a series impedance \(z=0.8431 \angle 79.04^{\circ} \Omega / \mathrm{mi}\) and a shunt admittance \(\gamma=5.105 \times\)
Using per-unit calculations, rework Problem 5.18 to determine the sending-end voltage and current.Problem 5.18A \(60-\mathrm{Hz}, 230-\) mile, three-phase overhead transmission line has a series
(a) The series expansions of the hyperbolic functions are given by\[\begin{aligned}& \cosh \theta=1+\frac{\theta^{2}}{2}+\frac{\theta^{4}}{24}+\frac{\theta^{6}}{720}+\cdots \\& \sinh
Show that\[A=\frac{V_{\mathrm{S}} I_{\mathrm{S}}+V_{\mathrm{R}} I_{\mathrm{R}}}{V_{\mathrm{R}} I_{\mathrm{S}}+V_{\mathrm{S}} I_{\mathrm{R}}} \quad \text { and } \quad
Consider the \(A\) parameter of the long line given by \(\cosh \theta\), where \(\theta=\) \(\sqrt{Z Y}\). With \(x=e^{-\theta}=x_{1}+j \mathrm{x}_{2}\) and \(A=\mathrm{A}_{1}+j \mathrm{~A}_{2}\),
Determine the equivalent \(\pi\) circuit for the line in Problem 5.14 and compare it with the nominal \(\pi\) circuit.Problem 5.14A \(500-\mathrm{km}, 500-\mathrm{kV}, 60-\mathrm{Hz}\), uncompensated
Determine the equivalent \(\pi\) circuit for the line in Problem 5.16. Compare the equivalent \(\pi\) circuit with the nominal \(\pi\) circuit.Problem 5.16The \(500-\mathrm{kV}, 60-\mathrm{Hz}\),
Let the transmission line of Problem 5.12 be extended to cover a distance of 200 miles. Assume conditions at the load to be the same as in Problem 5.12. Determine the(a) sending-end voltage,(b)
A 350−km,500−kV,60−Hz350−km,500−kV,60−Hz, three-phase uncompensated line has a positivesequence series reactance x=0.34Ω/kmx=0.34Ω/km and a positive-sequence shunt admittance
Determine the equivalent ππ circuit for the line in Problem 5.26.Problem 5.26A 350−km,500−kV,60−Hz350−km,500−kV,60−Hz, three-phase uncompensated line has a positivesequence series
Rated line voltage is applied to the sending end of the line in Problem 5.26. Calculate the receiving-end voltage when the receiving end is terminated by(a) an open circuit,(b) the surge impedance of
Rework Problems 5.9 and 5.16, neglecting the conductor resistance. Compare the results with and without losses.Problem 5.9The \(100-\mathrm{km}, 230-\mathrm{kV}, 60-\mathrm{Hz}\), three-phase line in
From (4.6.22) and (4.10.4), the series inductance and shunt capacitance of a three-phase overhead line are\[\begin{aligned}\mathrm{L}_{a} & =2 \times 10^{-7} \ln \left(\mathrm{D}_{\mathrm{eq}} /
A \(500-\mathrm{kV}, 300-\mathrm{km}, 60-\mathrm{Hz}\), three-phase overhead transmission line, assumed to be lossless, has a series inductance of \(0.97 \mathrm{mH} / \mathrm{km}\) per phase and a
The following parameters are based on a preliminary line design: \(\mathrm{V}_{\mathrm{S}}=\) 1.0 per unit, \(\mathrm{V}_{\mathrm{R}}=0.9\) per unit, \(\lambda=5000 \mathrm{~km},
Consider a long radial line terminated in its characteristic impedance \(Z_{c}\). Determine the following:(a) \(V_{1} / I_{1}\), known as the driving point impedance.(b) \(\left|V_{2}ight| / V_{1}
For the case of a lossless line, how would the results of Problem 5.33 change?In terms of ZcZc, which is a real quantity for this case, express P12P12 in terms |I1||I1| and |V1||V1|.Problem
For a lossless open-circuited line, express the sending-end voltage, \(V_{1}\), in terms of the receiving-end voltage, \(V_{2}\), for the three cases of short-line model, medium-length line model,
For a short transmission line of impedance (R+jX)(R+jX) ohms per phase, show that the maximum power that can be transmitted over the line
(a) Consider complex power transmission via the three-phase short line for which the per-phase circuit is shown in Figure 5.19. Express \(S_{12}\), the complex power sent by bus 1 (or \(V_{1}\) ),
The line in Problem 5.14 has three ACSR \(1113 \mathrm{kcmil}\) conductors per phase. Calculate the theoretical maximum real power that this line can deliver and compare with the thermal limit of the
Repeat Problems 5.14 and 5.38 if the line length is(a) \(200 \mathrm{~km}\) or(b) \(600 \mathrm{~km}\).Problem 5.14A \(500-\mathrm{km}, 500-\mathrm{kV}, 60-\mathrm{Hz}\), uncompensated three-phase
For the \(500 \mathrm{kV}\) line given in Problem 5.16,(a) calculate the theoretical maximum real power that the line can deliver to the receiving end when rated voltage is applied to both ends;(b)
A \(230-\mathrm{kV}, 100-\mathrm{km}, 60-\mathrm{Hz}\), three-phase overhead transmission line with a rated current of \(900 \mathrm{~A} /\) phase has a series impedance \(z=0.088+j 0.465\) \(\Omega
A three-phase power of \(460 \mathrm{MW}\) is transmitted to a substation located \(500 \mathrm{~km}\) from the source of power. With \(\mathrm{V}_{\mathrm{S}}=1\) per unit,
Open PowerWorld Simulator case Example 5_4 and graph the load bus voltage as a function of load real power (assuming unity power factor at the load). What is the maximum amount of real power that can
Repeat Problem 5.43, but now vary the load reactive power, assuming the load real power is fixed at \(1499 \mathrm{MW}\).Problem 5.43Open PowerWorld Simulator case Example 5_4 and graph the load bus
For the line in Problems 5.14 and 5.38, determine(a) the practical line loadability in \(\mathrm{MW}\), assuming \(\mathrm{V}_{\mathrm{S}}=1.0\) per unit, \(\mathrm{V}_{\mathrm{R}} \approx 0.95\) per
Repeat Problem 5.45 for the \(500 \mathrm{kV}\) line given in Problem 5.10.Problem 5.45For the line in Problems 5.14 and 5.38, determine(a) the practical line loadability in \(\mathrm{MW}\), assuming
Determine the practical line loadability in MW and in per-unit of SIL for the line in Problem 5.14 if the line length is(a) \(200 \mathrm{~km}\) or(b) \(600 \mathrm{~km}\). Assume
It is desired to transmit \(2000 \mathrm{MW}\) from a power plant to a load center located \(300 \mathrm{~km}\) from the plant. Determine the number of \(60 \mathrm{~Hz}\), threephase, uncompensated
Repeat Problem 5.48 if it is desired to transmit:(a) 3200 MW to a load center located \(300 \mathrm{~km}\) from the plant or(b) \(2000 \mathrm{MW}\) to a load center located \(400 \mathrm{~km}\) from
A three-phase power of \(4000 \mathrm{MW}\) is to be transmitted through four identical \(60-\mathrm{Hz}\) overhead transmission lines over a distance of \(300 \mathrm{~km}\). Based on a preliminary
The power flow at any point on a transmission line can be calculated in terms of the \(A B C D\) parameters. By letting \(A=|\mathrm{A}| \angle \alpha, B=|B|\left\langle\beta,
(a) Consider complex power transmission via the three-phase long line for which the per-phase circuit is shown in Figure 5.20. See Problem 5.37 in which the short-line case was considered. Show
Open PowerWorld Simulator case Example 5_8. If the load bus voltage is greater than or equal to \(730 \mathrm{kV}\) even with any line segment out of service, what is the maximum amount of real power
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