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systems analysis design

Questions and Answers of Systems Analysis Design

Three single-phase, two-winding transformers, each rated 450 MVA, \(20 \mathrm{kV} / 288.7 \mathrm{kV}\), with leakage reactance \(\mathrm{X}_{\mathrm{eq}}=0.10\) per unit, are connected to form a
Consider a bank of three single-phase two-winding transformers whose high-voltage terminals are connected to a three-phase, \(13.8-\mathrm{kV}\) feeder. The low-voltage terminals are connected to a
Three single-phase two-winding transformers, each rated 25 MVA, \(34.5 / 13.8 \mathrm{kV}\), are connected to form a three-phase \(\Delta-\Delta\) bank. Balanced positive-sequence voltages are
Three single-phase two-winding transformers, each rated 25 MVA, 54.2/5.42kV54.2/5.42kV, are connected to form a three-phase Y−ΔY−Δ bank with a balanced Y-connected resistive load of 0.6Ω0.6Ω
Consider a three-phase generator rated \(300 \mathrm{MVA}, 23 \mathrm{kV}\), supplying a system load of \(240 \mathrm{MVA}\) and 0.9 power factor lagging at \(230 \mathrm{kV}\) through a 330 MVA,
The leakage reactance of a three-phase, \(300-\mathrm{MVA}, 230 \mathrm{Y} / 23 \Delta-\mathrm{kV}\) transformer is 0.06 per unit based on its own ratings. The \(\mathrm{Y}\) winding has a solidly
Choosing system bases to be \(240 / 24 \mathrm{kV}\) and 100 MVA, redraw the perunit equivalent circuit for Problem 3.39.Problem 3.39The leakage reactance of a three-phase, \(300-\mathrm{MVA}, 230
Consider the single-line diagram of the power system shown in Figure 3.38. Equipment ratings areNeglecting resistance, transformer phase shift, and magnetizing reactance, draw the equivalent
For the power system in Problem 3.41, the synchronous motor absorbs \(1500 \mathrm{MW}\) at 0.8 power factor leading with the bus 3 voltage at \(18 \mathrm{kV}\). Determine the bus 1 and bus 2
Three single-phase transformers, each rated \(10 \mathrm{MVA}, 66.4 / 12.5 \mathrm{kV}, 60 \mathrm{~Hz}\), with an equivalent series reactance of 0.1 per unit divided equally between primary and
A 130-MVA, 13.2-kV three-phase generator, which has a positivesequence reactance of 1.5 per unit on the generator base, is connected to a 135-MVA, \(13.2 \Delta / 115 \mathrm{Y}-\mathrm{kV}\) step-up
Figure 3.39 shows a oneline diagram of a system in which the three-phase generator is rated \(300 \mathrm{MVA}, 20 \mathrm{kV}\) with a subtransient reactance of 0.2 per unit and with its neutral
The motors \(M_{1}\) and \(M_{2}\) of Problem 3.45 have inputs of 120 and \(60 \mathrm{MW}\), respectively, at \(13.2 \mathrm{kV}\), and both operate at unity power factor. Determine the generator
Consider the oneline diagram shown in Figure 3.40. The three-phase transformer bank is made up of three identical single-phase transformers, each specified by \(X_{1}=0.24 \Omega\) (on the
With the same transformer banks as in Problem 3.47, Figure 3.41 shows the oneline diagram of a generator, a step-up transformer bank, a transmission line, a step-down transformer bank, and an
Consider the single-line diagram of a power system shown in Figure 3.42 with equipment ratings given:Choose a base of 100 MVA for the system and \(132-\mathrm{kV}\) base in the transmission-line
A single-phase three-winding transformer has the following parameters: \(Z_{1}=Z_{2}=Z_{3}=0+j 0.05, \mathrm{G}_{C}=0\), and \(\mathrm{B}_{M}=0.2\) per unit. Three identical transformers, as
The ratings of a three-phase three-winding transformer are Primary (1): Y connected, \(66 \mathrm{kV}, 15\) MVASecondary (2): Y connected, \(13.2 \mathrm{kV}, 10\) MVATertiary (3): A connected,
Draw the per-unit equivalent circuit for the transformers shown in Figure 3.34. Include ideal phase-shifting transformers showing phase shifts determined in Problem 3.32. Assume that all windings
The ratings of a three-phase, three-winding transformer are Primary: Y connected, 66kV,15MVA66kV,15MVASecondary: Y connected, 13.2 kV, 10 MVATertiary: ΔΔ connected, 2.3kV,5MVA2.3kV,5MVANeglecting
An infinite bus, which is a constant voltage source, is connected to the primary of the three-winding transformer of Problem 3.53. A 7.5-MVA, 13.2-kV synchronous motor with a subtransient reactance
A single-phase \(10-\mathrm{kVA}, 2300 / 230-\) volt, \(60-\mathrm{Hz}\) two-winding distribution transformer is connected as an autotransformer to step up the voltage from 2300 to 2530 volts. (a)
Three single-phase two-winding transformers, each rated \(3 \mathrm{kVA}, 220 / 110\) volts, \(60 \mathrm{~Hz}\), with a 0.10 per-unit leakage reactance, are connected as a three-phase extended
A two-winding single-phase transformer rated 60kVA,240/1200 V,60 Hz60kVA,240/1200 V,60 Hz60kVA,240/1200 V,60 Hz, has an efficiency of 0.96 when operated at rated load,
A single-phase two-winding transformer rated \(90 \mathrm{MVA}, 80 / 120 \mathrm{kV}\) is to be connected as an autotransformer rated \(80 / 200 \mathrm{kV}\). Assume that the transformer is ideal.
The two parallel lines in Example 3.13 supply a balanced load with a load current of 1.0∠−30∘1.0∠−30∘ per unit. Determine the real and reactive power supplied to the load bus from each
PowerWorld Simulator case Problem 3_60 duplicates Example 3.13 except that a resistance term of 0.06 per unit has been added to the transformer and 0.05 per unit to the transmission line. Since the
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?Problem 3.60PowerWorld
Rework Example 3.12 for a \(+10 \%\) tap, providing a \(10 \%\) increase for the high-voltage winding.Example 3.12A three-phase generator step-up transformer is rated \(1000 \mathrm{MVA}, 13.8
A \(23 / 230-\mathrm{kV}\) step-up transformer feeds a three-phase transmission line, which in turn supplies a 150-MVA, 0.8 lagging power factor load through a step-down \(230 / 23-\mathrm{kV}\)
The per-unit equivalent circuit of two transformers \(T_{a}\) and \(T_{b}\) connected in parallel, with the same nominal voltage ratio and the same reactance of 0.1 per unit on the same base, is
Reconsider Problem 3.64 with the change that now \(T_{b}\) includes both a transformer of the same turns ratio as \(T_{a}\) and a regulating transformer with a \(4^{\circ}\) phase shift. On the base
ACSR stands for(a) Aluminum-clad steel conductor(b) Aluminum conductor steel supported(c) Aluminum conductor steel reinforced
Overhead transmission-line conductors are bare with no insulating cover.(a) True(b) False
Alumoweld is an aluminum-clad steel conductor.(a) True(b) False
EHV lines often have more than one conductor per phase; these conductors are called a
Shield wires located above the phase conductors protect the phase conductors against lightning.(a) True(b) False
Conductor spacings, types, and sizes do have an impact on the series impedance and shunt admittance.(a) True(b) False
A circle with diameter \(D\) in. \(=1000 D\) mil \(=d\) mil has an area of \(c\) mil.
An ac resistance is higher than a dc resistance.(a) True(b) False
Match the following for the current distribution throughout the conductor cross section:(i) For dc(a) uniform(ii) For ac(b) nonuniform
Transmission line conductance is usually neglected in power system studies.(a) True(b) False
The internal inductance \(L_{\text {int }}\) per unit-length of a solid cylindrical conductor is a constant, given by \(\frac{1}{2} \times 10^{-7} \mathrm{H} / \mathrm{m}\) in SI system of units.(a)
The total inductance \(L_{\mathrm{P}}\) of a solid cylindrical conductor (of radius \(r\) ) due to both internal and external flux linkages out of distance \(\mathrm{D}\) is given by (in \(\mathrm{H}
For a single-phase, two-wire line consisting of two solid cylindrical conductors of same radius, \(r\), the total circuit inductance, also called loop inductance, is given by (in \(\mathrm{H} /
For a three-phase three-wire line consisting of three solid cylindrical conductors, each with radius \(r\) and with equal phase spacing \(\mathrm{D}\) between any two conductors, the inductance in
For a balanced three-phase positive-sequence currents \(I_{a}, I_{b}, I_{c}\), does the equation \(I_{a}+I_{b}+I_{c}=0\) hold good?
A stranded conductor is an example of a composite conductor.(a) True(b) False
\(\Sigma \ln A_{k}=\ln \Pi A_{k}\)(a) True(b) False
Is Geometric Mean Distance (GMD) the same as Geometric Mean Radius (GMR)?(a) Yes(b) No
Expand \(6 \sqrt{\Pi_{k=1}^{3} \Pi_{m=1^{\prime}}^{2^{\prime}} \mathrm{D}_{k m}}\).
If the distance between conductors are large compared to the distances between subconductors of each conductor, then the GMD between conductors is approximately equal to the distance between
For a single-phase two-conductor line with composite conductors \(x\) and \(y\), express the inductance of conductor \(x\) in terms of GMD and its GMR.
In a three-phase line, in order to avoid unequal phase inductances due to unbalanced flux linkages, what technique is used?
For a completely transposed three-phase line identical conductors, each with GMR denoted \(\mathrm{D}_{\mathrm{S}}\) with conductor distance \(\mathrm{D}_{12}, \mathrm{D}_{23}\), and
For EHV lines, a common practice of conductor bundling is used. Why?
Does bundling reduce the series reactance of the line?(a) Yes(b) No
Does \(r^{\prime}=e^{-\frac{1}{4}} r=0.788 r\), which comes in calculation of inductance, play a role in capacitance computations?(a) Yes(b) No
In terms of line-to-line capacitance, the line-to-neutral capacitance of a single-phase transmission line is(a) Same(b) Twice(c) One-half
For either single-phase two-wire line or balanced three-phase three-wire line with equal phase spacing \(D\) and with conductor radius \(r\), the capacitance (line-to-neutral) in \(\mathrm{F} /
In deriving expressions for capacitance for a balanced three-phase threewire line with equal phase spacing, the following relationships may have been used.(i) Sum of positive-sequence charges,
When calculating line capacitance, it is normal practice to replace a stranded conductor by a perfectly conducting solid cylindrical conductor whose radius equals the out side radius of the stranded
For bundled-conductor configurations, the expressions for calculating \(\mathrm{D}_{\mathrm{SL}}\) in inductance calculations and \(\mathrm{D}_{\mathrm{SC}}\) in capacitance calculations are
The current supplied to the transmission-line capacitance is called
For a completely transposed three-phase line that has balanced positivesequence voltages, the total reactive power supplied by the three-phase line, in var, is given by \(\mathrm{Q}_{\mathrm{C} 3}=\)
Considering lines with neutral conductors and earth return, the effect of earth plane is accounted for by the method of conducting earth plane. with a perfectly
The affect of the earth plane is to slightly increase the capacitance, and as the line height increases, the effect of earth becomes negligible.(a) True(b) False
When the electric field strength at a conductor surface exceeds the breakdown strength of air, current discharges occur. This phenomenon is called
To control corona, transmission lines are usually designed to maintain the calculated conductor surface electric field strength below \(\mathrm{kV}_{\mathrm{rms}} / \mathrm{cm}\).
Along with limiting corona and its effects, particularly for EHV lines, the maximum ground-level electric field strength needs to be controlled to avoid the shock hazard.(a) True(b) False
Considering two parallel three-phase circuits that are close together, when calculating the equivalent series-impedance and shunt-admittance matrices, mutual inductive and capacitive couplings
The Aluminum Electrical Conductor Handbook lists a dc resistance of \(0.01558 \mathrm{ohm}\) per \(1000 \mathrm{ft}\) at \(20^{\circ} \mathrm{C}\) and a \(60-\mathrm{Hz}\) resistance of \(0.0956
The temperature dependence of resistance is also quantified by the relation \(\mathrm{R}_{2}=\mathrm{R}_{1}\left[1+\alpha\left(\mathrm{T}_{2}-\mathrm{T}_{1}ight)ight]\) where \(\mathrm{R}_{1}\) and
A transmission-line cable with a length of \(2 \mathrm{~km}\) consists of 19 strands of identical copper conductors, each \(1.5 \mathrm{~mm}\) in diameter. Because of the twist of the strands, the
One thousand circular mils or \(1 \mathrm{kcmil}\) is sometimes designated by the abbreviation MCM. Data for commercial bare-aluminum electrical conductors lists a \(60 \mathrm{~Hz}\) resistance of
A \(60-\mathrm{Hz}, 765-\mathrm{kV}\), three-phase overhead transmission line has four ACSR \(900 \mathrm{kcmil} 54 / 3\) conductors per phase. Determine the \(60 \mathrm{~Hz}\) resistance of this
A three-phase overhead transmission line is designed to deliver 190.5 MVA at \(220 \mathrm{kV}\) over a distance of \(63 \mathrm{~km}\), such that the total transmission line loss is not to exceed
If the per-phase line loss in a 70-km-long transmission line is not to exceed \(65 \mathrm{~kW}\) while it is delivering 100 A per phase, compute the required conductor diameter if the resistivity of
A 60-Hz, single-phase two-wire overhead line has solid cylindrical copper conductors with a \(1.5 \mathrm{~cm}\) diameter. The conductors are arranged in a horizontal configuration with \(0.5
Rework Problem 4.8 if the diameter of each conductor is(a) increased by \(20 \%\) to \(1.8 \mathrm{~cm}\) or(b) decreased by \(20 \%\) to \(1.2 \mathrm{~cm}\) without changing the phase spacing.
A \(60-\mathrm{Hz}\), three-phase three-wire overhead line has solid cylindrical conductors arranged in the form of an equilateral triangle with 4-ft conductor spacing. The conductor diameter is
Rework Problem 4.10 if the phase spacing is (a) increased by \(20 \%\) to \(4.8 \mathrm{ft}\) or (b) decreased by \(20 \%\) to \(3.2 \mathrm{ft}\). Compare the results with those of Problem
Find the inductive reactance per mile of a single-phase overhead transmission line operating at \(60 \mathrm{~Hz}\) given the conductors to be Partridge and the spacing between centers to be \(30
A single-phase overhead transmission line consists of two solid aluminum conductors having a radius of \(3 \mathrm{~cm}\) with a spacing \(3.5 \mathrm{~m}\) between centers. (a) Determine the total
(a) In practice, one deals with the inductive reactance of the line per phase per mile and use the logarithm to the base 10. Show that Eq. (4.5.9) of the text can be rewritten as\[\begin{aligned}x
Find the GMR of a stranded conductor consisting of six outer strands surrounding and touching one central strand, all strands having the same radius \(r\).
A bundle configuration for UHV lines (above \(1000 \mathrm{kV}\) ) has identical conductors equally spaced around a circle, as shown in Figure 4.29. \(N_{b}\) is the number of conductors in the
Determine the GMR of each of the unconventional stranded conductors shown in Figure 4.30. All strands have the same radius \(r\). (a) o (b) (c)
A \(230-\mathrm{kV}, 60-\mathrm{Hz}\), three-phase completely transposed overhead line has one ACSR \(954 \mathrm{kcmil}\) conductor per phase and flat horizontal phase spacing, with \(7
Rework Problem 4.18 if the phase spacing between adjacent conductors is (a) increased by \(10 \%\) to \(7.7 \mathrm{~m}\) or (b) decreased by \(10 \%\) to \(6.3 \mathrm{~m}\). Compare the results
Calculate the inductive reactance in \(\Omega / \mathrm{km}\) of a bundled \(500-\mathrm{kV}, 60-\mathrm{Hz}\), three-phase completely transposed overhead line having three ACSR \(1113
Rework Problem 4.20 if the bundled line has (a) three ACSR, \(1351 \mathrm{kcmil}\) conductors per phase or (b) three ACSR, \(900 \mathrm{kcmil}\) conductors per phase, without changing the bundle
The conductor configuration of a bundled single-phase overhead transmission line is shown in Figure 4.31. Line \(\mathrm{X}\) has its three conductors situated at the corners of an equilateral
Figure 4.32 shows the conductor configuration of a completely transposed three-phase overhead transmission line with bundled phase conductors. All conductors have a radius of \(0.74 \mathrm{~cm}\)
Consider a three-phase overhead line made up of three phase conductors: Linnet, \(336.4 \mathrm{kcmil}\), and ACSR 26/7. The line configuration is such that the horizontal separation between center
For the overhead line of configuration shown in Figure 4.33 operating at \(60 \mathrm{~Hz}\) and a conductor temperature of \(70^{\circ} \mathrm{C}\), determine the resistance per phase, inductive
Consider a symmetrical bundle with \(N\) subconductors arranged in a circle of radius A. The inductance of a single-phase symmetrical bundleconductor line is given by\(\mathrm{L}=2 \times 10^{-7} \ln
Figure 4.34 shows double-circuit conductors' relative positions in segment 1 of transposition of a completely transposed three-phase overhead transmission line. The inductance is given
For the case of double-circuit, bundle-conductor lines, the same method indicated in Problem 4.27 applies with \(r^{\prime}\) replaced by the bundle's GMR in the calculation of the overall GMR.Now
Reconsider Problem 4.28 with an alternate phase placement given below:Calculate the inductive reactance of the line in \(\Omega / \mathrm{mi} /\) phase.Problem 4.28For the case of double-circuit,

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