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computer science
systems analysis design

Questions and Answers of Systems Analysis Design

The fuel-cost curves for a two-generator power system are given as follows:\[\begin{aligned}& \mathrm{C}_{1}\left(\mathrm{P}_{1}ight)=600+15 \cdot \mathrm{P}_{1}+0.05
Expand the summations in (6.12.14) for \(N=2\), and verify the formula for \(\partial \mathrm{P}_{\mathrm{L}} / \partial \mathrm{P}_{i}\) given by (6.12.15). Assume \(\mathrm{B}_{i j}=\mathrm{B}_{j
Given two generating units with their respective variable operating costs as\[\begin{array}{ll}\mathrm{C}_{1}=0.01 \mathrm{P}_{\mathrm{G} 1}^{2}+2 \mathrm{P}_{\mathrm{G} 1}+100 \$ / \mathrm{hr} &
Resolve Example 6.20, except with the generation at bus 2 set to a fixed value (i.e., modeled as off of Automatic Generation Control). Plot the variation in the total hourly cost as the generation at
Using PowerWorld case Example 6_22 with the Load Scalar equal to 1.0, determine the generation dispatch that minimizes system losses. Manually vary the generation at buses 2 and 4 until their loss
Repeat Problem 6.69, except with the Load Scalar equal to 1.4.Problem 6.69Using PowerWorld case Example 6_22 with the Load Scalar equal to 1.0, determine the generation dispatch that minimizes system
Using LP OPF with PowerWorld Simulator case Example 6_23, plot the variation in the bus 5 marginal price as the Load Scalar is increased from 1.0 in steps of 0.02. What is the maximum possible load
Load PowerWorld Simulator case Problem 6_72. This case models a slightly modified, lossless version of the 37-bus case from Example 6.13 with generator cost information, but also with the transformer
The asymmetrical short-circuit current in series \(\mathrm{R}-\mathrm{L}\) circuit for a simulated solid or "bolted fault" can be considered as a combination of symmetrical (ac) component that is a
Even though the fault current is not symmetrical and not strictly periodic, the rms asymmetrical fault current is computed as the rms ac fault current times an "asymmetry factor," which is a function
The amplitude of the sinusoidal symmetrical ac component of the three-phase short-circuit current of an unloaded synchronous machine decreases from a high initial value to a lower steady-state value,
The duration of subtransient fault current is dictated by time ____________ constant and that of transient fault current is dictated by time ____________ constant.
The reactance that plays a role under steady-state operation of a synchronous machine is called ____________.
The dc-offset component of the three-phase short-circuit current of an unloaded synchronous machine is different in the three phases and its exponential decay is dictated by ____________.
Generally, in power-system short-circuit studies, for calculating subtransient fault currents, transformers are represented by their ____________ transmission lines by their equivalent ____________
In power-system fault studies, all nonrotating impedance loads are usually neglected.(a) True(b) False
Can superposition be applied in power-system short-circuit studies for calculating fault currents?(a) Yes(b) No
Before proceeding with per-unit fault current calculations, based on the single-line diagram of the power system, a positive-sequence equivalent circuit is set up on a chosen base system.(a) True(b)
The inverse of the bus-admittance matrix is called a ____________ matrix.
For a power system, modeled by its positive-sequence network, both busadmittance matrix and bus-impedance matrix are symmetric.(a) True(b) False
The bus-impedance equivalent circuit can be represented in the form of a "rake" with the diagonal elements, which are ____________ and the non-diagonal (off-diagonal) elements, which are ____________.
A circuit breaker is designed to extinguish the arc by ____________.
Power-circuit breakers are intended for service in the ac circuit above ____________ V.
In circuit breakers, besides air or vacuum, what gaseous medium, in which the arc is elongated, is used?
Oil can be used as a medium to extinguish the arc in circuit breakers.(a) True(b) False
Besides a blast of air/gas, the arc in a circuit breaker can be elongated by ____________.
For distribution systems, standard reclosers are equipped for two or more reclosures, whereas multiple-shot reclosing in EHV systems is not a standard practice.(a) True(b) False
Breakers of the \(115 \mathrm{kV}\) class and higher have a voltage range factor \(\mathrm{K}=\) ____________, such that their symmetrical interrupting current capability remains constant.
A typical fusible link metal in fuses is ____________, and a typical filler material is
The melting and clearing time of a current-limiting fuse is usually specified by a ____________ curve.
In the circuit of Figure 7.1, \(\mathrm{V}=277\) volts, \(\mathrm{L}=2 \mathrm{mH}, \mathrm{R}=0.4 \Omega\), and \(\omega=2 \pi 60 \mathrm{rad} / \mathrm{s}\). Determine (a) the rms symmetrical
Repeat Example 7.1 with \(\mathrm{V}=4 \mathrm{kV}, \mathrm{X}=2 \Omega\), and \(\mathrm{R}=1 \Omega\)Example 7.1A bolted short circuit occurs in the series R–L circuit of Figure 7.1 with V = 20
In the circuit of Figure 7.1, let \(\mathrm{R}=0.125 \Omega ., \mathrm{L}=10 \mathrm{mH}\), and the source voltage is \(e(\mathrm{t})=151 \sin (377 \mathrm{t}+\alpha) \mathrm{V}\). Determine the
Consider the expression for \(i(t)\) given by\[i(t)=\sqrt{2} \mathrm{I}_{\mathrm{rms}}\left[\sin \left(\omega t-\theta_{z}ight)+\sin \theta_{z} \cdot e^{-(\omega R / X) t}ight]\]where
If the source impedance at a \(13.2-\mathrm{kV}\) distribution substation bus is \((0.5+\) j1.5) \(\Omega\) per phase, compute the rms and maximum peak instantaneous value of the fault current for a
A 1000-MVA, \(20-\mathrm{kV}, 60-\mathrm{Hz}\), three-phase generator is connected through a \(1000-\mathrm{MVA}, 20-\mathrm{kV}, \Delta / 345-\mathrm{kV}\), Y transformer to a \(345-\mathrm{kV}\)
For Problem 7.6, determine(a) the instantaneous symmetrical fault current in kA in phase \(a\) of the generator as a function of time, assuming maximum dc offset occurs in this generator phase,
A 300-MVA, 13.8-kV, three-phase, \(60-\mathrm{Hz}\), Y-connected synchronous generator is adjusted to produce rated voltage on open circuit. A balanced three-phase fault is applied to the terminals
Two identical synchronous machines, each rated \(60 \mathrm{MVA}\) and \(15 \mathrm{kV}\) with a subtransient reactance of 0.1 p.u., are connected through a line of reactance 0.1 p.u. on the base of
Recalculate the subtransient current through the breaker in Problem 7.6 if the generator is initially delivering rated MVA at 0.80 p.f. lagging and at rated terminal voltage.Problem 7.6A 1000-MVA,
Solve Example 7.3 parts (a) and (c) without using the superposition principle. First calculate the internal machine voltages \(E_{g}^{\prime \prime}\) and \(E_{m}^{\prime \prime}\) using the prefault
Equipment ratings for the four-bus power system shown in Figure 7.14 are as follows: A three-phase short circuit occurs at bus 1, where the prefault voltage is \(525 \mathrm{kV}\). Prefault load
For the power system given in Problem 7.12, a three-phase short circuit occurs at bus 2, where the prefault voltage is \(525 \mathrm{kV}\). Prefault load current is neglected. Determine the(a)
Equipment ratings for the five-bus power system shown in Figure 7.15 are as follows:A three-phase short circuit occurs at bus 5, where the prefault voltage is 15kV15kV. Prefault load current is
For the power system given in Problem 7.14, a three-phase short circuit occurs at bus 4 , where the prefault voltage is \(138 \mathrm{kV}\). Prefault load current is neglected. Determine(a) the
In the system shown in Figure 7.16, a three-phase short circuit occurs at point F. Assume that prefault currents are zero and that the generators are operating at rated voltage. Determine the fault
A three-phase short circuit occurs at the generator bus (bus 1) for the system shown in Figure 7.17. Neglecting prefault currents and assuming that the generator is operating at its rated voltage,
(a) The bus impedance matrix for a three-bus power system iswhere subtransient reactances were used to compute \(\boldsymbol{Z}_{\text {bus }}\). Prefault voltage is 1.0 per unit and prefault current
Determine \(\boldsymbol{Y}_{\text {bus }}\) in per unit for the circuit in Problem 7.12. Then invert \(\boldsymbol{Y}_{\text {bus }}\) to obtain \(\boldsymbol{Z}_{\text {bus }}\).Problem
Determine \(\boldsymbol{Y}_{\text {bus }}\) in per unit for the circuit in Problem 7.14. Then invert \(\boldsymbol{Y}_{\text {bus }}\) to obtain \(\boldsymbol{Z}_{\text {bus }}\).Problem
Figure 7.18 shows a system reactance diagram. (a) Draw the admittance diagram for the system by using source transformations. (b) Find the bus admittance matrix \(\boldsymbol{Y}_{\text {bus }}\) (c)
For the network shown in Figure 7.19, impedances labeled 1 through 6 are in per unit. (a) Determine \(\boldsymbol{Y}_{\text {bus }}\), preserving all buses. (b) Using MATLAB or a similar computer
A single-line diagram of a four-bus system is shown in Figure 7.20, for which \(\boldsymbol{Z}_{\text {bus }}\) is given below:Let a three-phase fault occur at bus 2 of the network.(a) Calculate the
PowerWorld Simulator case Problem 7_24 models the system shown in Figure 7.14 with all data on a 1000 MVA base. Using PowerWorld Simulator, determine the current supplied by each generator and the
Repeat Problem 7.24, except place the fault at bus 4.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 PowerWorld
Repeat Problem 7.24, except place the fault midway between buses 2 and 3 . 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 PowerWorld Simulator by increasing the value of the generator's positive
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 POPLAR69 bus. During the fault, what
Repeat Problem 7.28, except place the fault at the REDBUD69 bus.Problem 7.28Using PowerWorld Simulator case Example 6_13, determine the per-unit current and actual current in amps supplied by each of
Using PowerWorld Simulator case Example 7_5, open the line connecting buses 4 and 5 . Then, determine the per unit current supplied by the generator at bus 3 due a fault at bus 2.Example
A three-phase circuit breaker has a \(15.5-\mathrm{kV}\) rated maximum voltage, \(9.0-\mathrm{kA}\) rated short-circuit current, and a 2.50-rated voltage range factor. (a) Determine the symmetrical
A \(345-\mathrm{kV}\), three-phase transmission line has a 2.2-kA continuous current rating and a \(2.5-\mathrm{kA}\) maximum short-time overload rating with a \(356-\mathrm{kV}\) maximum operating
A \(69-\mathrm{kV}\) circuit breaker has a voltage range factor \(\mathrm{K}=1.25\), a continuous current rating of \(1200 \mathrm{~A}\), and a rated short-circuit current of 19,000 A at the maximum
As shown in Figure 7.21, a 25-MVA, 13.8-kV, 60-Hz, synchronous generator with \(\mathrm{X}_{d}{ }^{\prime \prime}=0.15\) per unit is connected through a transformer to a bus that supplies four
Positive-sequence components consist of three phasors with _________ magnitudes and _________ phase displacement in positive sequence; negativesequence components consist of three phasors with
In symmetrical-component theory, express the complex-number operator \(a=1 \angle 120^{\circ}\) in exponential and rectangular forms.
In terms of sequence components of phase \(a\) given by \(V_{a 0}=V_{0}, V_{a 1}=V_{1}\), and \(V_{a 2}=V_{2}\), give expressions for the phase voltages \(V_{a}, V_{b}\), and \(V_{c}\).
The sequence components \(V_{0}, V_{1}\), and \(V_{2}\) can be expressed in terms of phase components \(V_{a}, V_{b}\), and \(V_{c}\).\(V_{0}=\) _______________; \(V_{1}=\)_______________ \(;
In a balanced three-phase system, what is the zero-sequence voltage? \(V_{0}=\)_______________.
In an unbalanced three-phase system, line-to-neutral voltage _____________ have a zero-sequence component, whereas line-to-line voltages ____________ have a zero-sequence component.
Can the symmetrical component transformation be applied to currents, just as it is applied to voltages?(a) Yes(b) No
In a three-phase Y-connected system with a neutral, express the neutral current in terms of phase currents and sequence-component terms.\(I_{n}=\)____________ \(=\)____________.
In a balanced Y-connected system, what is the zero-sequence component of the line currents?
In a \(\Delta\)-connected three-phase system, line currents have no zero-sequence component.(a) True(b) False
Balanced three-phase systems with positive sequence do not have zerosequence and negative-sequence components.(a) True(b) False
Unbalanced three-phase systems may have nonzero values for all sequence components.(a) True(b) False
For a balanced- \(Y\) impedance load with per-phase impedance of \(Z_{Y}\) and a neutral impedance \(Z_{n}\) connected between the load neutral and the close space ground, the \(3 \times 3\)
Express the sequence impedance matrix \(Z_{\mathrm{S}}\) in terms of the phaseimpedance matrix \(\boldsymbol{Z}_{\mathrm{P}}\), and the transformation matrix \(\boldsymbol{A}\) which relates
The sequence impedance matrix \(Z_{S}\) for a balanced- \(Y\) load is a diagonal matrix and the sequence networks are uncoupled.(a) True(b) False
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 \(Z_{0}=\)____________.
For a balanced- \(\Delta\) load with per-phase impedance of \(Z_{\Delta}\), the equivalent Y-load has an open neutral; for the corresponding uncoupled sequence networks, \(Z_{0}=\)____________
For a three-phase symmetrical impedance load, the sequence impedance matrix is and hence the sequence networks are (a) coupled or (b) uncoupled.
Sequence networks for three-phase symmetrical series impedances are (a) coupled or (b) uncoupled; positive-sequence currents produce only ____________ voltage drops.
The series-sequence impedance matrix of a completely transposed three-phase line is ____________ with its nondiagonal elements equal to ____________.
A Y-connected synchronous generator grounded through a neutral impedance \(Z_{n}\) with a zero-sequence impedance \(Z_{g 0}\)____________ has zero-sequence impedance \(Z_{0}=\) in its zero-sequence
In sequence networks, a Y-connected synchronous generator is represented by its source per-unit voltage only in ____________ network, while (a) synchronous, (b) transient or (c) sub-transient
In the positive-sequence network of a synchronous motor, a source voltage is represented, whereas in that of an induction motor, the source voltage (a) does or (b) does not come into picture.
With symmetrical components, the conversion from phase to sequence components decouples the networks and the resulting KVL equations.(a) True(b) False
Consider the per-unit sequence networks of \(\mathrm{Y}-\mathrm{Y}, \mathrm{Y}-\Delta\), and \(\Delta-\Delta\) transformers with neutral impedances of \(Z_{N}\) on the high-voltage Y-side and
In per-unit sequence models of three-phase three-winding transformers, for the general zero-sequence network, the connection between terminals \(\mathrm{H}\) and \(\mathrm{H}^{\prime}\) depends on
The total complex power delivered to a three-phase network equals (a) 1, (b) 2, or (c) 3 times the total complex power delivered to the sequence networks.
Express the complex power \(S_{\mathrm{S}}\) delivered to the sequence networks in terms of sequence voltages and sequence currents, where \(S_{\mathrm{S}}=\)
Using the operator \(a=1 / 120^{\circ}\), evaluate the following in polar form:(a) \((a-1) /\left(1+a-a^{2}ight)\),(b) \(\left(a^{2}+a+jight) /\left(j a+a^{2}ight)\),(c) \((1+a)\left(1+a^{2}ight)\),
Using \(a=1 \angle 120^{\circ}\), evaluate the following in rectangular form:a. \(a^{10}\)b. \((j a)^{10}\)c. \((1-a)^{3}\)d. \(\mathrm{e}^{a}\)
Determine the symmetrical components of the following line currents: (a) \(I_{a}=6 \angle 90^{\circ}, I_{b}=6 \angle 320^{\circ}, I_{c}=6 \angle 220^{\circ} \mathrm{A}\) and (b) \(I_{a}=j 40,
Find the phase voltages \(V_{a n}, V_{b n}\), and \(V_{c n}\) whose sequence components are \(V_{0}=45 \angle 80^{\circ}, V_{1}=90 \angle 0^{\circ}, V_{2}=45 \angle 90^{\circ} \mathrm{V}\).
For the unbalanced three-phase system described by\[I_{a}=10 \angle 0^{\circ} \mathrm{A}, I_{b}=8 \angle-90^{\circ} \mathrm{A}, I_{\mathrm{c}}=6 \angle 150^{\circ} \mathrm{A}\]compute the symmetrical
(a) Given the symmetrical components to be\[V_{0}=10 \angle 0^{\circ} \mathrm{V}, V_{1}=80 \angle 30^{\circ} \mathrm{V}, V_{2}=40 \angle-30^{\circ} \mathrm{V}\]determine the unbalanced phase voltages
One line of a three-phase generator is open-circuited, while the other two are short-circuited to ground. The line currents are \(I_{a}=0, I_{b}=1200 \angle 150^{\circ}\), and \(I_{c}=1200
Let an unbalanced, three-phase, Y-connected load (with phase impedances of \(Z_{a}, Z_{b}\), and \(Z_{c}\) ) be connected to a balanced three-phase supply, resulting in phase voltages of \(V_{a},

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