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computer science
systems analysis design

Questions and Answers of Systems Analysis Design

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
Repeat Problem 5.53, but now assume any two line segments may be out of service.Problem 5.53Open PowerWorld Simulator case Example 5_8. If the load bus voltage is greater than or equal to 730kV730kV
Recalculate the percent voltage regulation in Problem 5.15 when identical shunt reactors are installed at both ends of the line during light loads, providing \(65 \%\) total shunt compensation. The
Rework Problem 5.17 when identical shunt reactors are installed at both ends of the line, providing \(50 \%\) total shunt compensation. The reactors are removed at full load.Problem 5.17At full load,
Identical series capacitors are installed at both ends of the line in Problem 5.14, providing \(40 \%\) total series compensation. Determine the equivalent \(A B C D\) parameters of this compensated
Identical series capacitors are installed at both ends of the line in Problem 5.16, providing 30\% total series compensation.(a) Determine the equivalent \(A B C D\) parameters for this compensated
Determine the theoretical maximum real power that the seriescompensated line in Problem 5.57 can deliver when \(V_{S}=V_{R}=1.0\) per unit. Problem 5.57Identical series capacitors are installed at
What is the minimum amount of series capacitive compensation \(N_{\mathrm{C}}\) in percent of the positive-sequence line reactance needed to reduce the number of \(765-\mathrm{kV}\) lines in Example
Determine the equivalent \(A B C D\) parameters for the line in Problem 5.14 if it has \(70 \%\) shunt reactive (inductors) compensation and \(40 \%\) series capacitive compensation. Half of this
Consider the transmission line of Problem 5.18. (a) Find the \(A B C D\) parameters of the line when uncompensated. (b) For a series capacitive compensation of \(70 \%(35 \%\) at the sending end and
Given the uncompensated line of Problem 5.18, let a three-phase shunt reactor (inductor) that compensates for \(70 \%\) of the total shunt admittance of the line be connected at the receiving end of
Let the three-phase lossless transmission line of Problem 5.31 supply a load of 1000 MVA at 0.8 power factor lagging and at \(500 \mathrm{kV}\).(a) Determine the capacitance/phase and total
Open PowerWorld Simulator case Example 5_10 with the series capacitive compensation at both ends of the line in service. Graph the load bus voltage as a function of load real power (assuming unity
Open PowerWorld Simulator case Example 5_10 with the series capacitive compensation at both ends of the line in service. With the reactive power load fixed at 400 Mvar, graph the load bus voltage as
Transform the following sinusoids into phasor form and draw a phasor diagram. Use the additive property of phasors to find \(v_{1}(t)+v_{2}(t)\).(a) \(v_{1}(t)=240 \cos (\omega t+43) \mathrm{V}\)(b)
Transform the following sinusoids into phasor form and draw a phasor diagram. Use the additive property of phasors to find \(i_{1}(t)+i_{2}(t)\).(a) \(i_{1}(t)=-10 \sin (\omega t) \mathrm{mA}\)(b)
Transform the following sinusoids into phasor form and draw a phasor diagram. Use the additive property of phasors to find \(v_{1}(t)+v_{2}(t)+v_{3}(t)\).(a) \(v_{1}(t)=480 \cos \left(\omega
Figure P8-4 shows two phasor diagrams.(a) Add the voltage phasors into a new phasor \(\mathbf{V}_{3}\). Draw the sum of this new phasor on a phasor diagram.(b) Add the current phasors into a new
Convert the following phasors into sinusoidal waveforms.(a) \(\mathbf{V}_{1}=220 e^{-j 45^{\circ}} \mathrm{V}, \omega=314.2 \mathrm{rad} / \mathrm{s}\)(b) \(\mathbf{V}_{2}=440 e^{-j 225^{\circ}}
Use the phasors below and the additive property to find the sinusoidal waveforms \(v_{3}(t)=v_{1}(t)-v_{2}(t)\) and \(i_{3}(t)=2 i\) \({ }_{1}(t)+3 i_{2}(t)\).\[\begin{aligned}& \mathbf{V}_{1}=15
Convert the following phasors into sinusoidal waveforms.(a) \(\mathbf{V}_{1}=5+j 5 \mathrm{~V}, \omega=10 \mathrm{krad} / \mathrm{s}\)(b) \(\mathbf{V}_{2}=2 j(5+j 5) \mathrm{V}, \omega=200
Thinking about the derivative property of phasors as multiplication of the phasor by \(j \omega\), the integral property of phasors should be the inverse operation. Verify that the integration
Given the sinusoids \(i_{1}(t)=250 \cos \left(\omega t-60^{\circ}ight)\) \(\mathrm{mA}\) and \(i_{2}(t)=750 \sin (\omega t) \mathrm{mA}\) use the additive property of phasors to find \(i_{3}(t)\)
Given a sinusoid \(v_{1}(t)\) whose phasor is \(\mathbf{V}_{\mathbf{1}}=4-j 3 \mathrm{~V}\) and its frequency is \(10 \mathrm{rad} / \mathrm{s}\), use phasor methods to find a voltage \(v_{2}(t)\)
A design engineer needs to know what value of \(R, L\), or \(C\) to use in circuits to achieve a certain impedance.(a) At what radian frequency will a \(0.015-\mu \mathrm{F}\) capacitor's impedance
For the circuit of Figure P8-13}(a) Find the equivalent impedance \(Z\) when \(\omega=2000 \mathrm{rad} / \mathrm{s}\). Express the result in both polar and rectangular forms.(b) Select standard
A certain \(R L C\) series load has a load impedance of \(Z=1000-j 998 \Omega\) when excited by a \(1-\mathrm{krad} / \mathrm{s}\) source and a \(Z=1000-j 80 \Omega\) when driven by a
The circuit in Figure P8-17 is operating in the sinusoidal steady state with \(\omega=10 \mathrm{krad} / \mathrm{s}\).(a) What is the equivalent impedance of the circuit?(b) If one wanted to cancel
The circuit in Figure P8-18 is operating in the sinusoidal steady state with \(\omega=100 \mathrm{krad} / \mathrm{s}\).(a) Find the equivalent impedance \(Z\).(b) What circuit element can be added in
The circuit of Figure P8-19 is operating at \(50 \mathrm{~Hz}\). Find the equivalent impedance \(Z\).
A capacitor \(C\) is connected in parallel with a resistor \(R\). Select values of \(R\) and \(C\) so that the equivalent impedance of the parallel combination is \(600-j 800 \Omega\) at \(\omega=1\)
Two impedances \(Z_{1}=100-j 50 \Omega\) and \(Z_{2}=500+j 100\) \(\Omega\) are connected in parallel. Find the equivalent impedance of the pair.
A voltage source \(\mathrm{V}_{\mathrm{S}}=100 \angle 90^{\circ} \mathrm{V}\) is connected in series to a resistor of \(10 \Omega\) and an inductor of \(j 10 \Omega\). Find the phasor current
(a) Convert the circuit in Figure P8-25 into the phasor domain.(b) Find the phasor current flowing through the circuit and the phasor voltages across the capacitor and the resistor.(c) Plot all three
A complex load is driven by a current source \(i(t)\) \(=10 \cos (2 \mathrm{k} t) \mathrm{mA}\). The voltage measured across the load is \(v(t\) )\(=100 \cos \left(2 \mathrm{k} t-85^{\circ}ight)
A current source delivering \(i(t)=120 \cos (500 t) \mathrm{mA}\) is connected across a parallel combination of a \(10-k \Omega\) resistor and a \(0.2-\mu \mathrm{F}\) capacitor. Find the
A practical voltage source can be modeled using an ideal voltage source \(v_{\mathrm{S}}(t)=120 \cos (2000 t) \mathrm{V}\) in series with a5o- \(\Omega\) resistor. Convert the source into the phasor
A circuit consisting of a resistor, capacitor, and inductor is driven by a sinusoidal voltage source \(\mathbf{V}_{S}\) with a 1 \(\mathrm{krad} / \mathrm{s}\) frequency. A phasor diagram of the
Use the unit-output method to find \(\mathbf{V}_{\mathrm{X}}\) and \(\mathbf{I}_{\mathrm{X}}\) in the circuit of Figure P8-34.
An \(R C\) series circuit is excited by a sinusoidal source \(v(t)=V_{\mathrm{A}} \cos (\omega t+\phi) \mathrm{V}\). Determine the effects on the magnitudes of the current, voltages, and impedances
The OP AMP circuit of Figure P8-41 has \(\mathbf{V}_{\mathrm{S}}=2 \angle-15^{\circ} \mathrm{V}, Z_{\mathrm{S}}=50 \angle+30^{\circ} \Omega, Z_{\mathrm{F}}=100 \angle-45^{\circ} \Omega\), and a
Design an equivalent \(Z_{\mathrm{S}}=50 \angle+30 \Omega, Z_{\mathrm{F}}=100\) \(\angle-45^{\circ} \Omega\), and \(Z_{\mathrm{L}}=500 \angle-90^{\circ} \Omega\), if the circuit of Figure P8-41 is
A load of \(Z_{\mathrm{L}}=1000+j 1000 \Omega\) is to be driven by a phasor source \(\mathbf{V}_{\mathrm{S}}=150 \angle 0^{\circ} \mathrm{V}\). The voltage across the load needs to be
Design an interface voltage \(v_{\mathrm{S}}(t)=100 \cos \left(2 \times 10^{4} tight) \mathrm{V}\) delivers a steady-state output current of \(i_{\mathrm{O}}(t)=10 \cos \left(2 \times 10^{4}
Use MATLAB and mesh-current analysis to find the branch currents \(\mathbf{I}_{1}, \mathbf{I}_{2}\), and \(\mathbf{I}_{3}\) in Figure P8-52.
Use mesh-current analysis to find the phasor branch currents \(\mathbf{I}_{1}, \mathbf{I}_{2}\), and \(\mathbf{I}_{3}\) in the circuit shown in Figure P8-53. Validate your answer using Multisim.
Use MATLAB and mesh-current analysis to find the phasor currents \(\mathbf{I}_{\mathrm{A}}\) and \(\mathbf{I}_{\mathrm{B}}\) in Figure P8-55 .
The OP AMP circuit in Figure P8-56 is operating in the sinusoidal steady state.(a) Show that Image(b) Find the value of the magnitude of \(\mathbf{V}_{\mathrm{O}} / \mathbf{V}_{\mathrm{S}}\) at
The circuit in Figure P8-57 is operating in the sinusoidal steady state.(a) If \(v_{\mathrm{S}}(t)=1 \cos (2128 t) \mathrm{V}\), find the output \(v_{\mathrm{O}}(t)\).(b) At what frequency is the
For the circuit in Figure P8-5 phasor branch currents as follows:(a) Write a set of mesh-current equations. You can reduce the number of mesh equations by doing a source transformation with the
The circuit in Figure P8-60 is operating with \(\omega=20\) \(\mathrm{krad} / \mathrm{s}\).(a) Find the phasor outputs \(\mathbf{V}_{\mathrm{O}}\) and \(\mathbf{I}_{\mathrm{O}}\) in Figure P8-60 when
For the circuit of Figure P8-61 find the Thévenin equivalent circuit seen at the output.
The two competing OP AMP circuits in Figure P8-62 are operating in the sinusoidal steady state with \(\omega=100\) \(\mathrm{krad} / \mathrm{s}\). The two manufacturers both claim that their circuit
Find the phasor gain \(K=V_{\mathrm{O}} / \mathrm{V}_{\mathrm{S}}\) and input impedance Z IN of the circuit in Figure P8-64.
A load consisting of a 3.3-k \(\mathrm{k}\) resistor in series with a 3.3\(\mu \mathrm{F}\) capacitor is connected across a voltage source \(v_{\mathrm{S}}(t)=339.4\) \(\cos (314.2 t)\) V. Find the

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