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systems analysis design

Questions and Answers of Systems Analysis Design

Repeat Problem 11.10, except assume there is a three-phase-to-ground bolted short circuit at bus five.Problem 11.10For the five bus system from Example 6.9, assume the transmission lines and
The generator in Figure 11.4 is initially operating in the steady-state condition given in Example 11.3 when circuit breaker B12 inadvertently opens. Use the equal-area criterion to calculate the
The generator in Figure 11.4 is initially operating in the steady-state condition given in Example 11.3 when a temporary three-phase-to-ground short circuit occurs at point F. Three cycles later,
If breakers B13 and B22 in Problem 11.13 open later than 3 cycles after the fault commences, determine the critical clearing time.Problem 11.13The generator in Figure 11.4 is initially operating in
Building upon Problem 11.11, assume a \(60 \mathrm{~Hz}\) nominal system frequency, that the bus fault actually occurs on the line between buses five and two but at the bus two end, and that the
Analytically determine whether there is a critical clearing time for Problem 11.15.Problem 11.15Building upon Problem 11.11, assume a \(60 \mathrm{~Hz}\) nominal system frequency, that the bus fault
Consider the first order differential equation, \(\frac{d x_{1}}{d t}=-x_{2}\), with an initial value \(x(0)=10\). With an integration step size of 0.1 seconds, determine the value of \(x(0.5)\)
The following set of differential equations can be used to represent that behavior of a simple spring-mass system, with \(x_{1}(t)\) the mass's position and \(x_{2}(t)\) its velocity:\(\frac{d
A \(60 \mathrm{~Hz}\) generator is supplying \(400 \mathrm{MW}\) (and 0 Mvar) to an infinite bus (with 1.0 per unit voltage) through two parallel transmission lines. Each transmission line has a per
Open PowerWorld Simulator case Problem 11_20. This case models the Example 11.4 system with damping at the bus 1 generator, and with a line fault midway between buses 1 and 2 . The fault is cleared
Open PowerWorld Simulator case Problem 11_21. This case models the Example 11.4 system with damping at the bus 1 generator, and with a line fault midway between buses 2 and 3. The fault is cleared by
Consider the six-bus power system shown in Figure 11.29, where all data are given in per-unit on a common system base. All resistances as well as transmission-line capacitances are neglected. (a)
Modify the matrices Y11,Y12Y11,Y12, and Y22Y22 determined in Problem 11.22 for(a) the case when circuit breakers B32 and B51 open to remove line 3-5; and(b) the case when the load PL3+jQL3PL3+jQL3 is
Open PowerWorld Simulator case Problem 11_24, which models the Example 6.9 with transient stability data added for the generators. Determine the critical clearing time (to the nearest 0.01 second)
With PowerWorld Simulator using the Example 11_9 case determine the critical clearing time (to the closest 0.01 second) for a transmission line fault on the transmission line between bus 44 (PEACH69)
PowerWorld Simulator case Problem 11_26 duplicates Example 11.10, except with the synchronous generator initially supplying \(75 \mathrm{MW}\) at unity power factor to the infinite bus.(a) Derive the
PowerWorld Simulator case Problem 11_27 duplicates the system from Problem 11.24, except the generators are modeled using a two-axis model, with the same \(\mathrm{X}_{d}^{\prime}\) and
PowerWorld Simulator case Problem 11_28 duplicates Example 11.11 except the wind turbine generator is set so it is initially supplying \(100 \mathrm{MW}\) to the infinite bus at unity power
Redo Example 11.12 with the assumption the generator is supplying \(100+j 10\) MVA to the infinite bus.Example 11.12For the system from Example 11.3, assume the synchronous generator is replaced with
The block-diagram representation of a closed-loop automatic regulating system, in which generator voltage control is accomplished by controlling the exciter voltage, is shown in Figure 12.14.
The Automatic Voltage Regulator (AVR) system of a generator is represented by the simplified block diagram shown in Figure 12.15, in which the sensor is modeled by a simple first-order transfer
Open PowerWorld Simulator case Problem 12_3. This case models the system from Example 12.1 except with the rate feedback gain constant, \(\mathrm{K}_{\mathrm{f}}\), has been set to zero and the
An area of an interconnected \(60-\mathrm{Hz}\) power system has three turbinegenerator units rated 200,300, and 500 MVA. The regulation constants of the units are \(0.03,0.04\), and 0.05 per unit,
Each unit in Problem 12.5 is initially operating at one-half its own rating when the load suddenly increases by 100 MW. Determine(a) the steadystate decrease in area frequency, and(b) the MW increase
Each unit in Problem 12.5 is initially operating at one-half its own rating when the frequency increases by 0.005 per unit. Determine the MW decrease of each unit. The reference power setting of each
Repeat Problem 12.7 if the frequency decreases by 0.005 per unit. Determine the MW increase of each unit.Problem 12.7Each unit in Problem 12.5 is initially operating at one-half its own rating when
An interconnected \(60-\mathrm{Hz}\) power system consisting of one area has two turbine-generator units, rated 500 and \(750 \mathrm{MVA}\), with regulation constants of 0.04 and 0.06 per unit,
Open PowerWorld Simulator case Problem 12_10. The case models the system from Example 12.4 except 1) the load increases is a \(50 \%\) rise at bus 6 for a total increase of \(250 \mathrm{MW}\) (from
Open PowerWorld Simulator case Problem 12_11, which includes a transient stability representation of the system. Each generator is modeled using a two-axis machine model, an IEEE Type 1 exciter and a
Repeat Problem 12.11 except first double the \(\mathrm{H}\) value for each of the machines. This can be most easily accomplished by selecting Stability Case Info, Transient Stability Case Summary to
For a large, \(60 \mathrm{~Hz}\), interconnected electrical system assume that following the loss of two \(1400 \mathrm{MW}\) generators (for a total generation loss of \(2800 \mathrm{MW}\) ) the
A \(60-\mathrm{Hz}\) power system consists of two interconnected areas. Area 1 has \(1200 \mathrm{MW}\) of generation and an area frequency response characteristic \(\beta_{1}=400 \mathrm{MW} /
Repeat Problem 12.14 if \(\mathrm{LFC}\) is employed in area 2 alone. The area 2 frequency bias coefficient is set at \(\mathrm{B}_{f 2}=\beta_{2}=600 \mathrm{MW} / \mathrm{Hz}\). Assume that LFC in
Repeat Problem 12.14 if \(\mathrm{LFC}\) is employed in both areas. The frequency bias coefficients are \(\mathrm{B}_{f 1}=\beta_{1}=400 \mathrm{MW} / \mathrm{Hz}\) and \(\mathrm{B}_{f
Rework Problems 12.15 through 12.16 when the load in area 2 suddenly decreases by \(300 \mathrm{MW}\). The load in area 1 does not change.Problem 12.15Repeat Problem 12.14 if \(\mathrm{LFC}\) is
On a 1000-MVA common base, a two-area system interconnected by a tie line has the following parameters:The two areas are operating in parallel at the nominal frequency of \(60 \mathrm{~Hz}\). The
From the results of Example 13.2, plot the voltage and current profiles along the line at times \(\tau / 2, \tau\), and \(2 \tau\). That is, plot \(v(x, \tau / 2)\) and \(i(x, \tau / 2)\) versus
Rework Example 13.2 if the source voltage at the sending end is a ramp, \(e_{\mathrm{G}}(t)=\mathrm{E} u_{-2} \mathrm{M}=\mathrm{E} t u_{-1}(t)\), with \(\mathrm{Z}_{\mathrm{G}}=2
Referring to the single-phase two-wire lossless line shown in Figure 13.3, the receiving end is terminated by an inductor with \(2 \mathrm{~L}_{\mathrm{R}}\) henries. The source voltage at the
Rework Problem 13.3 if \(Z_{\mathrm{R}}=Z_{c}\) at the receiving end and the source voltage at the sending end is \(e_{\mathrm{G}}(t)=\mathrm{E} u_{-1}(t)\), with an inductive source impedance
Rework Example 13.4 with \(\mathrm{Z}_{\mathrm{R}}=5 \mathrm{Z}_{c}\) and \(\mathrm{Z}_{\mathrm{G}}=\mathrm{Z}_{c} / 3\).Example 13.4At the receiving end, \(\mathrm{Z}_{\mathrm{R}}=\mathrm{Z}_{c} /
The single-phase, two-wire lossless line in Figure 13.3 has a series inductance \(\mathrm{L}=(1 / 3) \times 10^{-6} \mathrm{H} / \mathrm{m}\), a shunt capacitance \(\mathrm{C}=(1 / 3) \times 10^{-10}
The single-phase, two-wire lossless line in Figure 13.3 has a series inductance \(\mathrm{L}=2 \times 10^{-6} \mathrm{H} / \mathrm{m}\), a shunt capacitance \(\mathrm{C}=1.25 \times 10^{-11}
The single-phase, two-wire lossless line in Figure 13.3 has a series inductance \(\mathrm{L}=0.999 \times 10^{-6} \mathrm{H} / \mathrm{m}\), a shunt capacitance \(\mathrm{C}=1.112 \times 10^{-11}
Draw the Bewley lattice diagram for Problem 13.5.Problem 13.5Rework Example 13.4 with \(\mathrm{Z}_{\mathrm{R}}=5 \mathrm{Z}_{c}\) and \(\mathrm{Z}_{\mathrm{G}}=\mathrm{Z}_{c} / 3\).Example 13.4At
Rework Problem 13.9 if the source voltage is a pulse of magnitude \(\mathrm{E}\) and duration \(\tau / 10\); that is, \(e_{\mathrm{G}}(t)=\mathrm{E}\left[u_{-1}(t)-u_{-1}(t-\tau / 10)ight]\).
As shown in Figure 13.32, a single-phase two-wire lossless line with \(Z_{c}=\) \(400 \Omega, v=3 \times 10^{8} \mathrm{~m} / \mathrm{s}\), and \(1=100 \mathrm{~km}\) has a \(400-\Omega\) resistor,
The junction of four single-phase two-wire lossless lines, denoted A, B, \(\mathrm{C}\), and \(\mathrm{D}\), is shown in Figure 13.13. Consider a voltage wave \(v_{\mathrm{A}}^{+}\)arriving at the
Referring to Figure 13.3, the source voltage at the sending end is a step \(e_{\mathrm{G}}(t)=\mathrm{Eu}_{-1}(t)\) with an inductive source impedance \(\mathrm{Z}_{\mathrm{G}}(s)=s
As shown in Figure 13.33, two identical, single-phase, two-wire, lossless lines are connected in parallel at both the sending and receiving ends. Each line has a \(400-\Omega\) characteristic
As shown in Figure 13.34, an ideal current source consisting of a 10-kA pulse with \(50-\mu\) s duration is applied to the junction of a single-phase, lossless cable and a single-phase, lossless
For the circuit given in Problem 13.3, replace the circuit elements by their discrete-time equivalent circuits and write nodal equations in a form suitable for computer solution of the sending-end
Repeat Problem 13.18 for the circuit given in Problem 13.13. Assume \(\Delta t=0.03333 \mathrm{~ms}\).Problem 13.18For the circuit given in Problem 13.3, replace the circuit elements by their
For the circuit given in Problem 13.7, replace the circuit elements by their discrete-time equivalent circuits. Use \(\Delta t=100 \mu \mathrm{s}=1 \times 10^{-4} \mathrm{~s}\). Determine and show
For the circuit given in Problem 13.8, replace the circuit elements by their discrete-time equivalent circuits. Use \(\Delta t=50 \mu \mathrm{s}=5 \times 10^{-5} \mathrm{~s}\) and \(\mathrm{E}=\)
Rework Problem 13.18 for a lossy line with a constant series resistance \(\mathrm{R}=0.3 \Omega / \mathrm{km}\). Lump half of the total resistance at each end of the line.Problem 13.18For the circuit
Repeat Example 13.8 for a \(500-\mathrm{kV}\) system with a 1.08 per-unit maximum \(60-\mathrm{Hz}\) voltage under normal operating conditions and with a \(2000-\mathrm{kV}\) BIL.Example 13.8Consider
Select a station-class metal-oxide surge arrester from Table 13.2 for the high-voltage side of a three-phase 400 MVA, \(345-\mathrm{kV}\) Y/13.8-kV \(\Delta\) transformer. The maximum
Are laterals on primary radial systems typically protected from short circuits? If so, how (by fuses, circuit breakers, or reclosers)?
What is the most common type of grounding on primary distribution systems?
What is the most common primary distribution voltage class in the United States?
Why are reclosers used on overhead primary radial systems and overhead primary loop systems? Why are they not typically used on underground primary radial systems and underground primary loop systems?
What are the typical secondary distribution voltages in the United States?
What are the advantages of secondary networks? Name two disadvantages.
Using the Internet, name three cities in the Western Interconnection of the United States that have secondary network systems.
A three-phase \(138 \mathrm{kV} \Delta / 13.8 \mathrm{kV} \mathrm{Y}\) distribution substation transformer rated \(40 \mathrm{MVA}\) OA/50 MVA FA/65MVA FOA has an 9\% impedance. (a) Determine the
As shown in Figure 14.24, an urban distribution substation has one 30-MVA (FOA) and three 33.3 MVA (FOA), \(138 \mathrm{kV} \Delta / 12.5 \mathrm{kV}\) Y transformers denoted TR1-TR4, which feed
For the distribution substation given in Problem 14.9, assume that each of the four circuit breakers on the \(12.5-\mathrm{kV}\) side of the distribution substation transformers has a maximum
(a) How many Mvars of shunt capacitors are required to increase the power factor on a 10 MVA load from 0.85 to 0.9 lagging? (b) How many Mvars of shunt capacitors are required to increase the power
Rework Example 14.3 with RLoad =40Ω/RLoad =40Ω/ phase, XLoad =60Ω/XLoad =60Ω/ phase, and XC=60Ω/XC=60Ω/ phase.Example 14.3Figure 14.21 shows a single-line diagram of a 13.8−kV13.8−kV
Table 14.10 gives 2010 annual outage data (sustained interruptions) from a utility's CIS database for feeder 8050 . This feeder serves 4500 customers with a total load of \(9 \mathrm{MW}\). Table
Assume that a utility's system consists of two feeders: feeder 7075 serving 2000 customers and feeder 8050 serving 4000 customers. Annual outage data during 2010 is given in Table 14.6 and 14.10 for
Open PowerWorld Simulator case Problem 14_15, which represents a lower load scenario for the Figure 14.22 case. Determine the optimal status of the six switched shunts to minimize the system
Open PowerWorld Simulator case Problem 14_16, which represents a lower load scenario for the Figure 14.22 case and has the LTC transformer taps each changed to 1.025 . Determine the optimal status of
Open PowerWorld Simulator case Problem 14_17 and note the case losses. Then close the bus tie breaker between buses 2 and 3. How do the losses change? How can the case be modified to reduce the
Usually in power flow studies the load is treated as being independent of the bus voltage. That is, a constant power model is used. However, in reality the load usually has some voltage dependence,
Repeat Problem 14.18, except using PowerWorld Simulator case Problem 14_19 which has a different load level from the Problem 14.18 case.Problem 14.18Usually in power flow studies the load is treated
Select one of the smart grid characteristics from the list given in this section. Write a one page (or other instructor-selected length) summary and analysis paper on a current news story that
(a) Design a passive \(R C\) first-order low-pass circuit with a passband gain of \(\mathrm{odB}\) and a cutoff frequency of \(5 \mathrm{krad} / \mathrm{s}\).(b) Cascade two identical circuits of
The transfer function of a first-order circuit is\[T(s)=\frac{100 s}{s+5000}\](a) Identify the type of gain response. Find the cutoff frequency and the passband gain.(b) Use MATLAB to plot the
A circuit has the following transfer function:\[T(s)=\frac{5000 s}{s^{2}+100 s+10^{6}}\]Use MATLAB to plot the Bode diagram of the transfer function. From the plot, determine the following:(a) The
Design a circuit with the transfer function in Problem 12-23. Validate your design using Multisim.
A circuit has the following transfer function:\[T(s)=\frac{s+10^{6}}{s^{2}+B s+10^{6}}\]\(B\) is a constant multiplier that can change the behavior of the circuit. With \(B=50\), use MATLAB to plot
There is a need to visualize the gain plot of the following transfer function:\[T(s)=\frac{5(s+100)}{s^{2}+2000 s+10^{6}}\](a) Use MATLAB to determine what type of filter it is (LP, HP, BP, or
The circuit in Figure P12-27 produces a bandpass response for a suitable choice of element values. Identify the elements that control the two cutoff frequencies. Select the element values so that the
The circuit in Figure P12-28 produces a bandpass response for a suitable choice of element values. Identify the elements that control the two cutoff frequencies. Select the element values so that the
The circuit in Figure P12-30 produces a bandstop response for a suitable choice of element values.(a) Find the circuit's transfer function.(b) Identify the elements that control the two cutoff
Design an audio amplifier that amplifies signals from \(20 \mathrm{~Hz}\) to \(20 \mathrm{kHz}\). Your approach should be to use a cascade connection of two first-order passive circuits separated by
The circuit in Figure P12-32 is a typical \(R L C\) filter circuit.(a) Find the circuit's transfer function \(T(s)\) if \(C=33 \mu \mathrm{F}, L=\) \(47 \mathrm{mH}\), and \(R=10 \Omega\).(b)
Design an \(R L C\) bandstop filter with a center frequency of \(400 \mathrm{krad} / \mathrm{s}\) and a \(Q\) of 20 . The passband gain is \(\mathrm{dB}\). Use practical values for \(R, L\), and
Design an \(R L C\) bandpass filter with a center frequency of \(1000 \mathrm{rad} / \mathrm{s}\) and a \(Q\) of 0.1 . The passband gain is \(+20 \mathrm{~dB}\). Use practical values for \(R, L\),
A series \(R L C\) bandpass circuit with \(R=2 \mathrm{k} \Omega\) is designed to have a bandwidth of \(150 \mathrm{Mrad} / \mathrm{s}\) and a center frequency of \(50 \mathrm{Mrad} / \mathrm{s}\).
A parallel \(R L C\) bandpass circuit with \(C=0.005 \mu \mathrm{F}\) and \(Q=15\) has a center frequency of \(500 \mathrm{krad} / \mathrm{s}\). Find \(R, L\), and the two cutoff frequencies. Could
(a) Design a parallel \(R L C\) circuit with \(R=150 \mathrm{k} \Omega\), a center frequency of \(50 \mathrm{krad} / \mathrm{s}\), and a \(Q\) of 15 .(b) Validate your design using Multisim.
A series \(R L C\) bandpass filter is required to have resonance at \(f_{0}=50 \mathrm{kHz}\). The circuit is driven by a sinusoidal source with a Thévenin resistance of \(60 \Omega\). The following
A series \(R L C\) bandstop circuit is to be used as a notch filter to eliminate a bothersome \(100-\mathrm{Hz}\) hum in an international audio channel application. The signal source has a Thévenin
Find the transfer function \(T_{\mathrm{V}}(s)=V_{2}(s) / V_{1}(s\) ) for the bandpass circuit in Figure P12-40. Use MATLAB to visualize the Bode characteristics if \(R=50 \Omega, L=50 \mu
Show that the transfer function \(T_{\mathrm{V}}(s)=V_{2}(\) \(s) / V_{1}(s)\) of the circuit in Figure P12-41 has a bandstop filter characteristic. Derive expressions relating the notch frequency
A professor gave the following quiz to his students:Look at Figure P12-42. Each curve represents the voltage across an individual element in a series \(R L C\) circuit. Identify which curve belongs
(a) Using MATLAB, plot the gain and phase of the transfer functions below:\[\begin{aligned}& T_{1}(s)=\frac{5000}{s+1000} \\& T_{2}(s)=\frac{10 s}{s+2000}\end{aligned}\](b) From the plots, determine

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