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computer science
systems analysis and design
Questions and Answers of
Systems Analysis And Design
(a) The bus impedance matrix for a three-bus power system is\[\boldsymbol{Z}_{\text {bus }}=j\left[\begin{array}{ccc}0.12&0.08&0.04\\0.08&0.12&0.06\\0.04&0.06& 0.08\end{array}\right] \text { per unit
Repeat Problem 7.24, except place the fault at bus 1.Data From Problem 7.24:-PowerWorld Simulator case Problem 7.24 models the system shown in Figure 7.14 with all data on a 1000-MVA base. Using
Repeat Problem 7.24, except place the fault midway between buses 2 and 4. Determining the values for line faults requires that the line be split, with a fictitious bus added at the point of the
One technique for limiting fault current is to place reactance in series with the generators. Such reactance can be modeled in Simulator by increasing the value of the generator's positive sequence
Using PowerWorld Simulator case Example 6.13, determine the per-unit current and actual current in amps supplied by each of the generators for a fault at the PETE69 bus. During the fault, what
Repeat Problem 7.28, except place the fault at the BOB69 bus.Data From Problem 7.28:-Using PowerWorld Simulator case Example 6.13, determine the per-unit current and actual current in amps supplied
Redo Example 7.5, except first open the generator at bus 3.Data From Example 7.5:-Data From Figure 6.2:- PowerWorld Simulator case Example 7_5 models the 5-bus power system whose one-line diagram is
A three-phase circuit breaker has a \(15.5-\mathrm{kV}\) rated maximum voltage, \(9.0-\mathrm{kA}\) rated short-circuit current, and a 2.67-rated voltage range factor. (a) Determine the symmetrical
A \(69-\mathrm{kV}\) circuit breaker has a voltage range factor \(\mathrm{K}=1.21\), a continuous current rating of \(1200 \mathrm{~A}\), and a rated short-circuit current of \(19,000 \mathrm{~A}\)
Short circuits can cause severe damage when not interrupted promptly. In some cases, high-impedance fault currents may be insufficient to operate protective relays or blow fuses. Standard overcurrent
For a balanced-Y impedance load with per-phase impedance of \(Z_{Y}\) and a neutral impedance \(Z_{n}\), the zero-sequence voltage \(V_{0}=Z_{0} I_{0}\), where \(Z_{0}=\) Fill in the Blank.
Determine the symmetrical components of the following line currents: (a) \(I_{a}=5 / 90^{\circ}\), \(I_{b}=5 / 320^{\circ}, I_{c}=5 / 220^{\circ} \mathrm{A}\); (b) \(I_{a}=j 50, I_{b}=50, I_{c}=0
Find the phase voltages \(V_{a n}, V_{b n}\), and \(V_{c n}\) whose sequence components are: \(V_{0}=50 / 80^{\circ}, V_{1}=100 / 0^{\circ}, V_{2}=50 / 90^{\circ} \mathrm{V}\).
For the unbalanced three-phase system described by\[I_{a}=12 \angle 0^{\circ} \mathrm{A}, \quad I_{b}=6 \angle-90^{\circ} \mathrm{A}, \quad I_{C}=8 \angle 150^{\circ} \mathrm{A}\]compute the
One line of a three-phase generator is open circuited, while the other two are short-circuited to ground. The line currents are \(I_{a}=0, I_{b}=1000 / 150^{\circ}\), and \(I_{c}=\) \(1000
The currents in a \(\Delta\) load are \(I_{a b}=10 \angle 0^{\circ}, I_{b c}=15 \angle-90^{\circ}\), and \(I_{c a}=20 / 90^{\circ}\) A. Calculate (a) the sequence components of the \(\Delta\)-load
Repeat Problem 8.14 with the load neutral open.Data From Problem 8.14:-The voltages given in Problem 8.10 are applied to a balanced-Y load consisting of \((12+j 16)\) ohms per phase. The load neutral
Repeat Problem 8.14 for a balanced- \(\Delta\) load consisting of \((12+j 16)\) ohms per phase.Data From Problem 8.14:-The voltages given in Problem 8.10 are applied to a balanced-Y load consisting
Repeat Problem 8.14 for the load shown in Example 8.4 (Figure 8.6).Data From Problem 8.14:-The voltages given in Problem 8.10 are applied to a balanced-Y load consisting of \((12+j 16)\) ohms per
Draw the zero-sequence reactance diagram for the power system shown in Figure 3.33. The zero-sequence reactance of each generator and of the synchronous motor is 0.05 per unit based on equipment
For Problem 8.14, calculate the real and reactive power delivered to the three-phase load.Data From Problem 8.14:-The voltages given in Problem 8.10 are applied to a balanced-Y load consisting of
Using Gauss elimination and back substitution, solve\[\left[\begin{array}{ccc}6 & 2 & 1 \\4 & 10 & 2 \\3 & 4 & 14\end{array}\right]\left[\begin{array}{l}x_{1} \\x_{2}
Rework Problem 6.2 with the value of \(\mathrm{A}_{11}\) changed to 4 .Data From Problem 6.2:-Using Gauss elimination and back substitution, solve\[\left[\begin{array}{ccc}6 & 2 & 1 \\4 & 10 & 2 \\3
What is the difficulty in applying Gauss elimination to the following linear algebraic equations?\[\begin{aligned}-10 x_{1}+10 x_{2} & =10 \\5 x_{1}-5 x_{2} & =-10\end{aligned}\]
Use Newton-Raphson to find a solution to the polynomial equation \(f(x)=y\) where \(y=0\) and \(f(x)=x^{3}+8 x^{2}+2 x-50\). Start with \(x(0)=1\) and continue until (6.2.2) is satisfied with
Repeat Problem 6.20 with an initial guess of \(x(1)=4\).Data From Problem 6.20:-Use Newton-Raphson to find one solution to the polynomial equation \(f(x)=y\), where \(y=7\) and \(f(x)=x^{4}+3
Solve the following equations by the Newton-Raphson method:\[\begin{array}{r}2 x_{1}^{2}+x_{2}^{2}-10=0 \\x_{1}^{2}-x_{2}^{2}+x_{1} x_{2}-4=0\end{array}\]Start with an initial guess of \(x_{1}=1\)
Determine the bus admittance matrix ( \(\boldsymbol{Y}_{\text {bus }}\) ) for the following power three phase system (note that some of the values have already been determined for you). Assume a
Assume a \(0.8+j 0.4\) per unit load at bus 2 is being supplied by a generator at bus 1 through a transmission line with series impedance of \(0.05+j 0.1\) per unit. Assuming bus 1 is the swing bus
Repeat the above problem with the swing bus voltage changed to \(1.0 / 30^{\circ}\) per unit.Data From Above Problem:-Assume a \(0.8+j 0.4\) per unit load at bus 2 is being supplied by a generator at
A generator bus (with a 1.0 per unit voltage) supplies a \(150 \mathrm{MW}, 50\) Mvar load through a lossless transmission line with per unit (100 MVA base) impedance of \(j 0.1\) and no line
Repeat Problem 6.37 except use an initial voltage guess of \(1.0 / 30^{\circ}\).Data From Problem 6.37:-The bus admittance matrix of a three-bus power system is given by\[Y_{\text {bus
Repeat Problem 6.37 except use an initial voltage guess of \(0.25 / 0^{\circ}\).Data From Problem 6.37:-The bus admittance matrix of a three-bus power system is given by\[Y_{\text {bus
Determine the initial Jacobian matrix for the power system described in Problem 6.33.Data From Problem 6.33:-Repeat the above problem with the swing bus voltage changed to \(1.0 / 30^{\circ}\) per
Repeat Problem 6.42 except with the bus 2 real power load changed to 1.0 per unit.Data From Problem 6.42:-Use the Newton-Raphson power flow to solve the power system described in Problem 6.34. For
Repeat Problem 6.53, except first remove the \(138-69 \mathrm{kV}\) transformer between BLT138 and BLT69.Data From Problem 6.53:-Open PowerWorld Simulator case Problem 6.53. Plot the variation in the
Using the PowerWorld Simulator case from Problem 6.59, if the rating on the line between buses 1 and 3 is \(65 \mathrm{MW}\), the current flow is \(59 \mathrm{MW}\) (from one to three), and the
Repeat Problem 5.45 for the $500-\mathrm{kV}$ line given in Problem 5.10.Data From Problem 5.45:-For the line in Problems 5.14 and 5.38, determine: (a) the practical line loadability in
Rework Problem 4.20 if the bundled line has: (a) three ACSR, 1351-kcmil conductors per phase, (b) three ACSR, 900-kcmil conductors per phase, without changing the bundle spacing or the phase spacings
If the per-phase line loss in a $60-\mathrm{km}$-long transmission line is not to exceed $60 \mathrm{~kW}$ while it is delivering 100 A per phase, compute the required conductor diameter, if the
Find the inductive reactance per mile of a single-phase overhead transmission line operating at 60 Hz, given the conductors to be Partridge and the spacing between centers to be 20 ft.
A single-phase overhead transmission line consists of two solid aluminum conductors having a radius of 2.5 cm2.5 cm, with a spacing 3.6 m3.6 m between centers. (a) Determine the
Rework Problem 4.18 if the phase spacing between adjacent conductors is: (a) increased by 10%10% to 8.8 m8.8 m, (b) decreased by 10%10% to 7.2 m7.2 m. Compare the results with
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 balancedFIGURE 4.37:- a 4.6 m 1 b -1.2 m.
Calculate the capacitance-to-neutral in F/mF/m and the admittance-to-neutral in S/kmS/km for the line in Problem 4.20. Also calculate the total reactive power in Mvar /km/km supplied by the line
Rework Problem 4.50 if the diameter of each conductor is: (a) increased by 25%25% to 1.875 cm1.875 cm, (b) decreased by 25%25% to 1.125 cm1.125 cm, without changing the phase
Two transmission articles are presented here. The first article covers transmission conductor technologies including conventional conductors, high-temperature conductors, and emerging conductor
Representing a transmission line by the two-port network, in terms of ABCDABCD parameters, (a) express VSVS, the sending-end voltage, in terms of VRVR, the receiving-end voltage, and IRIR, the
The loadability of short transmission lines (less than 80 km, represented by including only series resistance and reactance) is determined by___________; that of medium lines (less than 250 km,
For short lines less than 80 km long, loadability is limited by the thermal rating of the conductors or by terminal equipment ratings, not by voltage drop or stability considerations. (a)
A 25-km, 34.5-kV, 60-Hz three-phase line has a positive-sequence series impedance z = ¼ 0:19 þ j0:34 W/km. The load at the receiving end absorbs 10 VA at 33 kV. Assuming a short line, calculate:
Rework Problem 5.2 in per-unit using 100-MVA (three-phase) and 230-kV (line-toline) base values. Calculate: (a) the per-unit $A B C D$ parameters, (b) the per-unit sending-end voltage and current,
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 $900 \mathrm{~kW}$ at 0.8 p.f. lagging. If the
A 400−km,500−kV,60−Hz400−km,500−kV,60−Hz uncompensated three-phase line has a positive-sequence series impedance z=0.03+j0.35Ω/kmz=0.03+j0.35Ω/km and a positive-sequence shunt
At full load the line in Problem 5.14 delivers 1000MW1000MW at unity power factor and at 475kV475kV. Calculate: (a) the sending-end voltage, (b) the sending-end current, (c) the sending-end power
At full load, the line in Problem 5.16 delivers 1500 MVA at 480 kV to the receivingend load. Calculate the sending-end voltage and percent voltage regulation when the receiving-end power factor is
Starting with (5.1.1) of the text, 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 }
A 300−km,500−kV,60−Hz300−km,500−kV,60−Hz three-phase uncompensated line has a positive-sequence series reactance x=0.34Ω/kmx=0.34Ω/km and a positive-sequence shunt admittance
Repeat Problem 5.43, but now vary the load reactive power, assuming the load real power is fixed at $1000 \mathrm{MW}$.Data From Problem 5.43:-Open PowerWorld Simulator case Example 5.4 and graph the
High Voltage Direct Current (HVDC) applications embedded within ac power system grids have many benefits. A bipolar HVDC transmission line has only two insulated sets of conductors versus three for
A single-phase 100-kVA, 2400/240-volt, $60-\mathrm{Hz}$ distribution transformer is used as a step-down transformer. The load, which is connected to the 240 -volt secondary winding, absorbs $80
For a conceptual single-phase, phase-shifting transformer, the primary voltage leads the secondary voltage by 30∘30∘. A load connected to the secondary winding absorbs 100kVA100kVA at 0.9 power
A single-phase step-down transformer is rated $15 \mathrm{MVA}, 66 \mathrm{kV} / 11.5 \mathrm{kV}$. With the $11.5 \mathrm{kV}$ winding short-circuited, rated current flows when the voltage applied
A three-phase transformer is rated 500MVA,220Y/22ΔkV500MVA,220Y/22ΔkV. The wye-equivalent short-circuit impedance, considered equal to the leakage reactance, measured on the low-voltage side is
Consider a bank of three single-phase two-winding transformers whose high-voltage terminals are connected to a three-phase, 13.8−kV13.8−kV feeder. The low-voltage terminals are connected to a
Three single-phase two-winding transformers, each rated 25MVA,38.1/3.81kV25MVA,38.1/3.81kV, are connected to form a three-phase Y−ΔY−Δ bank with a balanced Y-connected resistive load of
Choosing system bases to be $240 / 24 \mathrm{kV}$ and $100 \mathrm{MVA}$, redraw the per-unit equivalent circuit for Problem 3.39.Data From Problem 3.39:-The leakage reactance of a three-phase,
Consider the single-line diagram of a power system shown in Figure 3.42 with equipment ratings given below:\[ \begin{array}{ll} \text { Generator } G_{1}: & 50 \mathrm{MVA},13.2\mathrm{kV}, x=0.15 ho
Repeat Problem 3.60, except keep the phase-shift angle fixed at 3.0 degrees, while varying the LTC tap between 0.9 and 1.1. What tap value minimizes the real power losses?Data From Problem
Rework Example 3.12 for a $+10 %$ tap, providing a $10 %$ increase for the high-voltage winding.Data From Example 3.12:- A three-phase generator step-up transformer is rated 1000 MVA, 13.8 kV A/345
The following article describes how transmission transformers are managed in the Pennsylvania–New Jersey (PJM) Interconnection. PJM is a regional transmission organization (RTO) that operates
Throughout most of the \(20^{\text {th }}\)-century, electric utility companies built increasingly larger generation plants, primarily hydro or thermal (using coal, gas, oil, or nuclear fuel). At the
Convert the following instantaneous currents to phasors, using \(\cos (\omega t)\) as the reference. Give your answers in both rectangular and polar form.(a) \(i(t)=400 \sqrt{2} \cos \left(\omega
The instantaneous voltage across a circuit element is \(v(t)=359.3 \sin \left(\omega t+15^{\circ}\right)\) volts, and the instantaneous current entering the positive terminal of the circuit element
(a) Transform \(v(t)=100 \cos \left(377 t-30^{\circ}\right)\) to phasor form. Comment on whether \(\omega=\) 377 appears in your answer. (b) Transform \(V=100 / 20^{\circ}\) to instantaneous form.
For the circuit element of Problem 2.3, calculate (a) the instantaneous power absorbed, (b) the real power (state whether it is delivered or absorbed), (c) the reactive power (state whether delivered
Repeat Problem 2.12 if the resistor and capacitor are connected in series.Data From Problem 2.12:-The voltage \(v(t)=359.3 \cos (\omega t)\) volts is applied to a load consisting of a \(10-\Omega\)
A single-phase source is applied to a two-terminal, passive circuit with equivalent impedance \(Z=2.0 /-45^{\circ} \Omega\) measured from the terminals. The source current is \(i(t)=4 \sqrt{2} \cos
Let a series R-L-C network be connected to a source voltage \(V\), drawing a current \(I\).(a) In terms of the load impedance \(Z=Z
The real power delivered by a source to two impedances, \(Z_{1}=3+j 4 \Omega\) and \(Z_{2}=10 \Omega\), connected in parallel, is \(1100 \mathrm{~W}\). Determine (a) the real power absorbed by each
A single-phase source has a terminal voltage \(V=120 \angle 0^{\circ}\) volts and a current \(I=\) \(10 \angle 30^{\circ} \mathrm{A}\), which leaves the positive terminal of the source. Determine the
Consider the series R-L-C circuit of Problem 2.7 and calculate the complex power absorbed by each of the elements R, L, and C, as well as the complex power absorbed by the total load. Draw the
Three loads are connected in parallel across a single-phase source voltage of \(240 \mathrm{~V}\) (RMS).Load 1 absorbs \(12 \mathrm{~kW}\) and \(6.667 \mathrm{kVAR}\);Load 2 absorbs \(4
A balanced three-phase 208-V source supplies a balanced three-phase load. If the line current \(I_{A}\) is measured to be \(10 \mathrm{~A}\) and is in phase with the line-to-line voltage
Compute the following quantity using MATLAB in the Command Window:\[\frac{17 \sqrt{5}-1}{15^{2}-13^{2}}+\frac{5^{7} \log _{10}\left(e^{3}\right)}{\pi \sqrt{121}}+\ln \left(e^{4}\right)+\sqrt{11}\]
Compute the following quantity using MATLAB in the Command Window:\[B=\frac{\tan x+\sin 2 x}{\cos x}+\log \left|x^{5}-x^{2}\right|+\cosh x-2 \tanh x\]for $x=5 \pi / 6$.
Compute the following quantity using MATLAB in the Command Window:\[\begin{aligned}x=a & +\frac{a b}{c} \frac{(a+b)}{\sqrt{|a b|}}+c^{a}+\frac{\sqrt{14} b}{e^{3 c}}+\ln (2)+\frac{\log _{10} c}{\log
Use MATLAB to create(a) a row and column vectors that has the elements: $11,-3, e^{7.8}, \ln (59), \tan (\pi / 3), 5$ $\log _{10}(26)$.(b) a row vector with 20 equally spaced elements in which the
Enter the following matrix A in MATLAB and create:\[A=\begin{array}{cccccccc}1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 \\17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 \\25 & 23 &
Given the function $y=\left(x^{\sqrt{2}+0.02}+e^{x}\right)^{1.8} \ln x$. Determine the value of $y$ for the following values of $x: 2,3,8,10,-1,-3,-5,-6.2$. Solve the problem using MATLAB by first
Define $a$ and $b$ as scalars, $a=0.75$, and $b=11.3$, and $x, y$ and $z$ as the vectors, $x=2,5$, $1,9, y=0.2,1.1,1.8,2$ and $z=-3,2,5,4$. Use these variables to calculate $A$ using
Enter the following three matrices in MATLAB and show that\[A=\begin{array}{ccc}1 & 2 & 3 \\-8 & 5 & 7 \\-8 & 4 & 6\end{array} \quad B=\begin{array}{ccc}12 & -5 & 4 \\7 & 11 & 6 \\1 & 8 &
Consider the function\[H(s)=\frac{n(s)}{d(s)}\]where $n(s)=s^{4}+6 s^{3}+5 s^{2}+4 s+3$\[d(s)=s^{5}+7 s^{4}+6 s^{3}+5 s^{2}+4 s+7\](a) Find $n$ (-10), $n$ (-5), $n$ (-3), and $n$ (-1)(b) Find
Consider the polynomials\[\begin{aligned}& p_{1}(s)=s^{3}+5 s^{2}+3 s+10 \\& p_{2}(s)=s^{4}+7 s^{3}+5 s^{2}+8 s+15 \\& p_{3}(s)=s^{5}+15 s^{4}+10 s^{3}+6 s^{2}+3 s+9\end{aligned}\]Determine(a)
The following polynomials are given:\[\begin{aligned}& p_{1}(x)=x^{5}+2 x^{4}-3 x^{3}+7 x^{2}-8 x+7 \\& p_{2}(x)=x^{4}+3 x^{3}-5 x^{2}+9 x+11 \\& p_{3}(x)=x^{3}-2 x^{2}-3 x+9 \\& p_{4}(x)=x^{2}-5
Determine the roots of the following polynomials:(a) $\quad p_{1}(x)=x^{7}+8 x^{6}+5 x^{5}+4 x^{4}+3 x^{3}+2 x^{2}+x+1$(b) $p_{2}(x)=x^{6}-7 x^{6}+7 x^{5}+15 x^{4}-10 x^{3}-8 x^{2}+7 x+15$(c)
Consider the two matrices\[\boldsymbol{A}=\begin{array}{ccc}1 & 0 & 2 \\2 & 5 & 4 \\-1 & 8 & 7\end{array} \text { and } \quad \boldsymbol{B}=\begin{array}{ccc}7 & 8 & 2 \\3 & 5 & 9 \\-1 & 3 &
Use MATLAB to define the following matrices:\[\begin{array}{ll}\boldsymbol{A}=\begin{array}{cc}2 & 1 \\0 & 5 \\7 & 4\end{array} & \boldsymbol{B}=\begin{array}{cc}5 & 3 \\-2 & -4\end{array}
Consider the two matrices\[\boldsymbol{A}=\begin{array}{cr}3 & 2 \pi \\5 j & 10+\sqrt{2}\end{array} \quad j \quad \boldsymbol{B}=\begin{array}{cc}7 j & -15 j \\2 \pi & 18\end{array}\]Using MATLAB,
Consider the two matrices\[A=\begin{array}{rrr}1 & 0 & 1 \\2 & 3 & 4 \\-1 & 6 & 7\end{array} \quad \text { and } B=\begin{array}{rrr}7 & 4 & 2 \\3 & 5 & 6 \\-1 & 2 & 1\end{array}\]Using MATLAB,
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