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systems analysis design

Questions and Answers of Systems Analysis Design

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},
Reconsider Problem 8.8 and choosing \(V_{b c}\) as the reference, show that\[V_{b c, 0}=0 ; \quad V_{b c, 1}=-j \sqrt{3} V_{a, 1} ; \quad V_{b c, 2}=j \sqrt{3} V_{a, 2}\]Problem 8.8Let an unbalanced,
Given the line-to-ground voltages \(V_{a g}=280 \angle 0^{\circ}, V_{b g}=250 \angle-110^{\circ}\), and \(V_{c g}=290 \angle 130^{\circ}\) volts, calculate (a) the sequence components of the
A balanced \(\Delta\)-connected load is fed by a three-phase supply for which phase \(\mathrm{C}\) is open and phase \(\mathrm{A}\) is carrying a current of \(10 \angle 0^{\circ} \mathrm{A}\). Find
A Y-connected load bank with a three-phase rating of \(500 \mathrm{kVA}\) and \(2300 \mathrm{~V}\) consists of three identical resistors of \(10.58 \Omega\). The load bank has the following applied
The currents in a \(\Delta\) load are \(I_{a b}=10 \angle 0^{\circ}, I_{b c}=12 \angle-90^{\circ}\), and \(I_{c a}=15 \angle 90^{\circ} \mathrm{A}\). Calculate (a) the sequence components of the
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 is solidly grounded. Draw the sequence networks and calculate \(I_{0},
Repeat Problem 8.14 with the load neutral open.Problem 8.14Given the line-to-ground voltages \(V_{a g}=280 \angle 0^{\circ}, V_{b g}=250 \angle-110^{\circ}\), and \(V_{c g}=290 \angle 130^{\circ}\)
Repeat Problem 8.14 for a balanced- \(\Delta\) load consisting of \((12+j 16)\) ohms per phase.Problem 8.14Given the line-to-ground voltages \(V_{a g}=280 \angle 0^{\circ}, V_{b g}=250
Repeat Problem 8.14 for the load shown in Example 8.4.Problem 8.14Given the line-to-ground voltages \(V_{a g}=280 \angle 0^{\circ}, V_{b g}=250 \angle-110^{\circ}\), and \(V_{c g}=290 \angle
Perform the indicated matrix multiplications in (8.2.21) and verify the sequence impedances given by (8.2.22) through (8.2.27).Eq. (8.2.21)Eq. (8.2.22)Eq. (8.2.27) Zo Zab Zac 1 1 a Zbb Zbc 1 3 Z Z
The following unbalanced line-to-ground voltages are applied to the balanced-Y load shown in Figure 3.3: \(V_{a g}=100 \angle 0^{\circ}, V_{b g}=75 \angle 180^{\circ}\), and \(V_{c g}=50 \angle
(a) Consider three equal impedances of (j27) \(\Omega\) connected in \(\Delta\). Obtain the sequence networks.(b) Now, with a mutual impedance of (j6) \(\Omega\) between each pair of adjacent
The three-phase impedance load shown in Figure 8.7 has the following phase impedance matrix:Determine the sequence impedance matrix \(Z_{\mathrm{S}}\) for this load. Is the load symmetrical?Figure
The three-phase impedance load shown in Figure 8.7 has the following sequence impedance matrix:Determine the phase impedance matrix \(Z_{\mathrm{P}}\) for this load. Is the load symmetrical?Figure
Consider a three-phase balanced Y-connected load with self and mutual impedances as shown in Figure 8.23. Let the load neutral be grounded through an impedance \(Z_{n}\). Using Kirchhoff's laws,
A three-phase balanced voltage source is applied to a balanced Y-connected load with ungrounded neutral. The Y-connected load consists of three mutually coupled reactances, where the reactance of
A three-phase balanced Y-connected load with series impedances of \((6+j 24) \Omega\) per phase and mutual impedance between any two phases of \(j 3 \Omega\) is supplied by a three-phase unbalanced
Repeat Problem 8.14 but include balanced three-phase line impedances of \((3+j 4)\) ohms per phase between the source and load.Problem 8.14The voltages given in Problem 8.10 are applied to a
Consider the flow of unbalanced currents in the symmetrical three-phase line section with neutral conductor as shown in Figure 8.24. (a) Express the voltage drops across the line conductors given by
Let the terminal voltages at the two ends of the line section shown in Figure 8.24 be given byThe line impedances are given by:\[Z_{\mathrm{aa}}=j 60 \Omega \quad Z_{\mathrm{ab}}=j 20 \Omega \quad
A completely transposed three-phase transmission line of \(200 \mathrm{~km}\) in length has the following symmetrical sequence impedances and sequence admittances:\[\begin{aligned}& Z_{1}=Z_{2}=j 0.5
As shown in Figure 8.25, a balanced three-phase, positive-sequence source with \(V_{\mathrm{AB}}=480 \angle 0^{\circ}\) volts is applied to an unbalanced \(\Delta\) load. Note that one leg of the
A balanced Y-connected generator with terminal voltage \(V_{b c}=200 \angle 0^{\circ}\) volts is connected to a balanced- \(\Delta\) load whose impedance is \(10 / 40^{\circ} \mathrm{ohms}\) per
In a three-phase system, a synchronous generator supplies power to a 200 -volt synchronous motor through a line having an impedance of \(0.5 ot 80^{\circ}\) ohm per phase. The motor draws \(5
Calculate the source currents in Example 8.6 without using symmetrical components. Compare your solution method with that of Example 8.6. Which method is easier?Example 8.6A Y-connected voltage
A Y-connected synchronous generator rated \(20 \mathrm{MVA}\) at \(13.8 \mathrm{kV}\) has a positive-sequence reactance of \(j 2.38 \Omega\), negative-sequence reactance of \(j 3.33 \Omega\), and
Figure 8.26 shows a single-line diagram of a three-phase, interconnected generator-reactor system, in which the given per-unit reactances are based on the ratings of the individual pieces of
Consider Figures 8.13 and 8.14 of the text with reference to a Y-connected synchronous generator (grounded through a neutral impedance \(Z_{n}\) ) operating at no load. For a line-to-ground fault
Reconsider the synchronous generator of Problem 8.36. Obtain sequencenetwork representations for the following fault conditions.(a) A short-circuit between phases \(b\) and \(c\).(b) A double
Three single-phase, two-winding transformers, each rated 450 MVA, \(20 \mathrm{kV} / 288.7 \mathrm{kV}\), with leakage reactance \(X_{\text {eq }}=0.12\) per unit, are connected to form a three-phase
The leakage reactance of a three-phase, 500-MVA, \(345 \mathrm{Y} / 23 \Delta-\mathrm{kV}\) transformer is 0.09 per unit based on its own ratings. The \(\mathrm{Y}\) winding has a solidly grounded
Choosing system bases to be \(360 / 24 \mathrm{kV}\) and 100 MVA, redraw the sequence networks for Problem 8.39.Problem 8.39The leakage reactance of a three-phase, 500-MVA, \(345 \mathrm{Y} / 23
Draw the zero-sequence reactance diagram for the power system shown in Figure 3.38. The zero-sequence reactance of each generator and of the synchronous motor is 0.05 per unit based on equipment
Three identical Y-connected resistors of \(1.0 \angle 0^{\circ}\) per unit form a load bank that is supplied from the low-voltage Y-side of a Y- \(\Delta\) transformer. The neutral of the load is not
Draw the positive-, negative-, and zero-sequence circuits for the transformers shown in Figure 3.34. Include ideal phase-shifting transformers showing phase shifts. Assume that all windings have the
For Problem 8.14, calculate the real and reactive power delivered to the three-phase load.Problem 8.14Given the line-to-ground voltages \(V_{a g}=280 \angle 0^{\circ}, V_{b g}=250
A three-phase impedance load consists of a balanced- \(\Delta\) load in parallel with a balanced-Y load. The impedance of each leg of the \(\Delta\) load is \(Z_{\Delta}=\) \(6+j 6 \Omega\), and the
For Problem 8.12, compute the power absorbed by the load using symmetrical components. Then verify the answer by computing directly without using symmetrical components.Problem 8.12A Y-connected load
For Problem 8.25, determine the complex power delivered to the load in terms of symmetrical components. Verify the answer by adding up the complex power of each of the three phases.Problem 8.25A
Using the voltages of Problem 8.6(a) and the currents of Problem 8.5, compute the complex power dissipated based on(a) phase components and(b) symmetrical components.Problem 8.6(a)Given the
For power-system fault studies, it is assumed that the system is operating under balanced steady-state conditions prior to the fault, and sequence networks are uncoupled before the fault occurs.(a)
The first step in power-system fault calculations is to develop sequence networks based on the single-line diagram of the system, and then reduce them to their Thévenin equivalents, as viewed from
When calculating symmetrical three-phase fault currents, only _________ sequence network needs to be considered.
In order of frequency of occurrence of short-circuit faults in three-phase power systems, list those: _________, _________, _________, _________.
For a bolted three-phase-to-ground fault, sequence-fault currents _________ are zero, sequence fault voltages are _________, and line-to-ground voltages are _________.

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