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systems analysis design

Questions and Answers of Systems Analysis Design

A circuit consists of two impedances, \(Z_{1}=20 / 30^{\circ} \Omega\) and \(Z_{2}=25 / 60^{\circ} \Omega\), in parallel, supplied by a source voltage \(V=100 / 60^{\circ}\) volts. Determine the
An industrial plant consisting primarily of induction motor loads absorbs \(500 \mathrm{~kW}\) at 0.6 power factor lagging. (a) Compute the required \(\mathrm{kVA}\) rating of a shunt capacitor to
The real power delivered by a source to two impedances, \(Z_{1}=4+j 5 \Omega\) and \(Z_{2}=10 \Omega\), connected in parallel, is \(1000 \mathrm{~W}\). Determine (a) the real power absorbed by each
A single-phase source has a terminal voltage \(V=120 / 0^{\circ}\) volts and a current \(I=15 / 30^{\circ}\) A, which leaves the positive terminal of the source. Determine the real and reactive
A source supplies power to the following three loads connected in parallel: (1) a lighting load drawing \(10 \mathrm{~kW}\), (2) an induction motor drawing \(10 \mathrm{kVA}\) at 0.90 power factor
Consider the series RLC circuit of Problem 2.7 and calculate the complex power absorbed by each of the \(\mathrm{R}, \mathrm{L}\), and \(\mathrm{C}\) elements, as well as the complex power absorbed
A small manufacturing plant is located \(2 \mathrm{~km}\) down a transmission line, which has a series reactance of \(0.5 \Omega / \mathrm{km}\). The line resistance is negligible. The line voltage
An industrial load consisting of a bank of induction motors consumes \(50 \mathrm{~kW}\) at a power factor of 0.8 lagging from a \(220-\mathrm{V}, 60-\mathrm{Hz}\), single-phase source. By placing a
Three loads are connected in parallel across a single-phase source voltage of \(240 \mathrm{~V}\) (RMS).Load 1 absorbs \(15 \mathrm{~kW}\) and \(6.667 \mathrm{kvar}\);Load 2 absorbs \(3
Modeling the transmission lines as inductors, with \(S_{i j}=S_{j i}^{*}\), Compute \(\mathrm{S}_{13}\), \(S_{31}, S_{23}, S_{32}\), and \(S_{G 3}\) in Figure 2.25. complex power balance holds good
Figure 2.26 shows three loads connected in parallel across a \(1000-\mathrm{V}\) (RMS), 60-Hz single-phase source.Load 1: Inductive load, \(125 \mathrm{kVA}, 0.28 \mathrm{PF}\) lagging.Load 2:
Consider two interconnected voltage sources connected by a line of impedance \(Z=j \mathrm{X} \Omega\), as shown in Figure 2.27.(a) Obtain expressions for \(\mathrm{P}_{12}\) and
In PowerWorld Simulator case Problem 2_32 (see Figure 2.28) a 8 MW and 4 Mvar load is supplied at \(13.8 \mathrm{kV}\) through a feeder with an impedance of \(1+j 2 \Omega\). The load is compensated
For the system from Problem 2.32, plot the real and reactive line losses as Ωcap Ωcap is varied between 0 and 10.0 Mvars.Problem 2.32In PowerWorld Simulator case Problem 2_32 (see Figure 2.28) a
For the system from Problem 2.32, assume that half the time the load is 10MW and 5 Mvar, and for the other half it is 20MW and 10 Mvar. What single value of Qcap would minimize the average losses?
For the circuit shown in Figure 2.29, convert the voltage sources to equivalent current sources and write nodal equations in matrix format using bus 0 as the reference bus. Do not solve the
For the circuit shown in Figure 2.29,(a) determine the \(2 \times 2\) bus admittance matrix \(\boldsymbol{Y}_{\text {bus }}\),(b) convert the voltage sources to current sources and determine the
Determine the \(4 \times 4\) bus admittance matrix \(\boldsymbol{Y}_{\text {bus }}\) and write nodal equations in matrix format for the circuit shown in Figure 2.30. Do not solve the equations. 1 =
Given the impedance diagram of a simple system as shown in Figure 2.31, draw the admittance diagram for the system and develop the \(4 \times 4\) bus admittance matrix \(\boldsymbol{Y}_{\text {bus
(a) Given the circuit diagram in Figure 2.32 showing admittances and current sources at nodes 3 and 4 , set up the nodal equations in matrix format.(b) If the parameters are given by: \(Y_{a}=-j 0.8
A balanced three-phase \(240-\mathrm{V}\) source supplies a balanced three-phase load. If the line current \(I_{\mathrm{A}}\) is measured to be \(15 \mathrm{~A}\) and is in phase with the
A three-phase \(25-\mathrm{kVA}, 480-\mathrm{V}, 60-\mathrm{Hz}\) alternator, operating under balanced steady-state conditions, supplies a line current of \(20 \mathrm{~A}\) per phase at a 0.8
A balanced \(\Delta\)-connected impedance load with \((12+j 9) \Omega\) per phase is supplied by a balanced three-phase \(60-\mathrm{Hz}, 208-\mathrm{V}\) source, (a) Calculate the line current, the
A three-phase line, which has an impedance of \((2+j 4) \Omega\) per phase, feeds two balanced three-phase loads that are connected in parallel. One of the loads is Y-connected with an impedance of
Two balanced three-phase loads that are connected in parallel are fed by a three-phase line having a series impedance of \((0.4+j 2.7) \Omega\) per phase. One of the loads absorbs \(560
Two balanced Y-connected loads, one drawing \(10 \mathrm{~kW}\) at 0.8 power factor lagging and the other \(15 \mathrm{~kW}\) at 0.9 power factor leading, are connected in parallel and supplied by a
Three identical impedances \(Z_{\Delta}=30 / 30^{\circ} \Omega\) are connected in \(\Delta\) to a balanced three-phase \(208-\mathrm{V}\) source by three identical line conductors with impedance
Two three-phase generators supply a three-phase load through separate three-phase lines. The load absorbs \(30 \mathrm{~kW}\) at 0.8 power factor lagging. The line impedance is \((1.4+j 1.6) \Omega\)
Two balanced Y-connected loads in parallel, one drawing \(15 \mathrm{~kW}\) at 0.6 power factor lagging and the other drawing \(10 \mathrm{kVA}\) at 0.8 power factor leading, are supplied by a
Figure 2.33 gives the general \(\Delta-Y\) transformation.(a) Show that the general transformation reduces to that given in Figure 2.16 for a balanced three-phase load.(b) Determine the impedances of
Consider the balanced three-phase system shown in Figure 2.34. Determine \(v_{1}(t)\) and \(i_{2}(t)\). Assume positive phase sequence. C A N j0.192 Va = 100/0 V wimm (0.1 + j001) 2 B A' j1.0g N' B'
A three-phase line with an impedance of \((0.2+j 1.0) \Omega /\) phase feeds three balanced three-phase loads connected in parallel.Load 1: Absorbs a total of \(150 \mathrm{~kW}\) and \(120
A balanced three-phase load is connected to a \(4.16-\mathrm{kV}\), three-phase, fourwire, grounded-wye dedicated distribution feeder. The load can be modeled by an impedance of
The "Ohm's law" for the magnetic circuit states that the net magnetomotive force ( \(\mathrm{mmf}\) ) equals the product of the core reluctance and the core flux.(a) True(b) False
For an ideal transformer, the efficiency is(a) \(0 \%\)(b) \(100 \%\)(c) \(50 \%\)
For an ideal 2-winding transformer, the ampere-turns of the primary winding, \(N_{1} I_{1}\), is equal to the ampere-turns of the secondary winding, \(\mathrm{N}_{2} \mathrm{I}_{2}\)(a) True(b) False
An ideal transformer has no real or reactive power loss.(a) True(b) False
For an ideal 2-winding transformer, an impedance \(Z_{2}\) connected across winding 2 (secondary) is referred to winding 1 (primary) by multiplying \(Z_{2}\) by(a) The turns ratio \(\left(N_{1} /
Consider Figure 3.4. For an ideal phase-shifting transformer, the impedance is unchanged when it is referred from one side to the other.(a) True(b) FalseFigure 3.4 S, - E + 3 || 1 E2 S2 + 2 = 8 E
Consider Figure 3.5. Match the following, those on the left to those on the right.(i) ImIm(a) Exciting current(ii) IcIc(b) Magnetizing current(iii) IeIe(c) Core loss currentFigure 3.5 V R jX wwwm Ge
The units of admittance, conductance, and susceptance are siemens.(a) True(b) False
Match the following:(i) Hysteresis loss(ii) Eddy current loss(a) Can be reduced by constructing the core with laminated sheets of alloy steel(b) Can be reduced by the use of special high grades of
For large power transformers rated more than \(500 \mathrm{kVA}\), the winding resistances, which are small compared with the leakage reactances, can often be neglected.(a) True(b) False
For a short-circuit test on a 2-winding transformer, with one winding shorted, can you apply the rated voltage on the other winding?(a) Yes(b) No
The per-unit quantity is always dimensionless.(a) True(b) False
Consider the adopted per-unit system for the transformers. Specify true or false for each of the following statements:(a) For the entire power system of concern, the value of \(S_{\text {base }}\) is
The ideal transformer windings are eliminated from the per-unit equivalent circuit of a transformer.(a) True(b) False
To convert a per-unit impedance from "old" to "new" base values, the equation to be used is(a) \(Z_{\text {p.u.new }}=Z_{\text {p.u.old }}\left(\frac{\mathrm{V}_{\text {baseold }}}{\mathrm{V}_{\text
In developing per-unit circuits of systems such as the one shown in Figure 3.10, when moving across a transformer, the voltage base is changed in proportion to the transformer voltage ratings.(a)
Consider Figure 3.10 of the text. The per-unit leakage reactance of transformer \(T_{1}\), given as 0.1 p.u., is based on the name plate ratings of transformer \(T_{1}\).(a) True(b) FalseFigure 3.10
For balanced three-phase systems, \(\mathrm{Z}_{\text {base }}\) is given by(a) True(b) False Zbase baseLL Sbase3
With the American Standard notation, in either a \(\mathrm{Y}-\Delta\) or \(\Delta-\mathrm{Y}\) transformer, positive- sequence quantities on the high-voltage side shall lead their corresponding
In either a \(\mathrm{Y}-\Delta\) or \(\Delta-\mathrm{Y}\) transformer, as per the American Standard notation, the negative-sequence phase shift is the reverse of the positivesequence phase shift.(a)
In order to avoid difficulties with third-harmonic exciting current, which three-phase transformer connection is seldom used for step-up transformers between a generator and a transmission line in
Does an open- \(\Delta\) connection permit balanced three-phase operation?(a) Yes(b) No
Does an open- \(\Delta\) operation, the kVA rating compared to that of the original three-phase bank is(a) \(2 / 3\)(b) \(58 \%\)(c) 1
It is stated that(i) balanced three-phase circuits can be solved in per unit on a per-phase basis after converting \(\Delta\)-load impedances to equivalent \(Y\) impedances.(ii) Base values can be
In developing per-unit equivalent circuits for three-phase transformers, under balanced three-phase operation.(i) A common \(\mathrm{S}_{\text {base }}\) is selected for both the \(\mathrm{H}\) and
In per-unit equivalent circuits of practical three-phase transformers, under balanced three-phase operation, in which of the following connections would a phase-shifting transformer come up?(a)
A low value of transformer leakage reactance is desired to minimize the voltage drop, but a high value is desired to limit the fault current, thereby leading to a compromise in the design
Consider a single-phase three-winding transformer with the primary excited winding of N1N1 turns carrying a current I1I1 and two secondary windings of N2N2 and N3N3 turns, delivering currents of I2I2
For developing per-unit equivalent circuits of single-phase three-winding transformer, a common \(\mathrm{S}_{\text {base }}\) is selected for all three windings, and voltage bases are selected in
Consider the equivalent circuit of Figure 3.20 (c) in the text. After neglecting the winding resistances and exciting current, could \(X_{1}, X_{2}\), or \(X_{3}\) become negative, even though the
Consider an ideal single-phase 2-winding transformer of turns ratio \(N_{1} / N_{2}=a\). If it is converted to an autotransformer arrangement with a transformation ratio of \(V_{H} / V_{X}=1+a\),
For the same output, the autotransformer (with not too large a turns ratio) is smaller in size than a two-winding transformer and has high efficiency as well as superior voltage regulation.(a)
The direct electrical connection of the windings allows transient over voltages to pass through the autotransformer more easily, and that is an important disadvantage of the autotransformer.(a)
Consider Figure 3.25 of the text for a transformer with off-nominal turns ratio.(i) The per-unit equivalent circuit shown in part (c) contains an ideal transformer which cannot be accommodated by
(a) An ideal single-phase two-winding transformer with turns ratio \(a_{t}=\) \(N_{1} / N_{2}\) is connected with a series impedance \(Z_{2}\) across winding 2 . If one wants to replace \(Z_{2}\),
An ideal transformer with \(N_{1}=1000\) and \(N_{2}=250\) is connected with an impedance \(Z_{22}\) across winding 2. If \(V_{1}=1000 \angle 0^{\circ} \mathrm{V}\) and \(I_{1}=5 \angle-30^{\circ}\)
Consider an ideal transformer with \(N_{1}=3000\) and \(N_{2}=1000\) turns. Let winding 1 be connected to a source whose voltage is \(e_{1}(t)=100(1-|t|)\) volts for \(-1 \leq t \leq 1\) and
A single-phase 100-kVA, 2400/240-volt, 60-Hz distribution transformer is used as a step-down transformer. The load, which is connected to the 240 -volt secondary winding, absorbs \(60 \mathrm{kVA}\)
Rework Problem 3.4 if the load connected to the \(240-\mathrm{V}\) secondary winding absorbs \(110 \mathrm{kVA}\) under short-term overload conditions at an 0.8 power factor leading and at 230
For a conceptual single-phase phase-shifting transformer, the primary voltage leads the secondary voltage by \(30^{\circ}\). A load connected to the secondary winding absorbs \(110 \mathrm{kVA}\) at
Consider a source of voltage \(v(t)=10 \sqrt{2} \sin (2 t) \mathrm{V}\), with an internal resistance of \(1800 \Omega\). A transformer that can be considered as ideal is used to couple a
For the circuit shown in Figure 3.31, determine \(v_{\text {out }}(t)\) Vin 18 sin 10t V + 18 36 www 2:1 Ideal transformer w 1:2 Ideal transformer 8 + Vout(t)
A single-phase transformer has 2000 turns on the primary winding and 500 turns on the secondary. Winding resistances are \(R_{1}=2 \Omega\), and \(R_{2}=\) \(0.125 \Omega\); leakage reactances are
A single-phase step-down transformer is rated \(13 \mathrm{MVA}, 66 \mathrm{kV} / 11.5 \mathrm{kV}\). With the \(11.5 \mathrm{kV}\) winding short-circuited, rated current flows when the voltage
For the transformer in Problem 3.10, the open-circuit test with \(11.5 \mathrm{kV}\) applied results in a power input of \(65 \mathrm{~kW}\) and a current of \(30 \mathrm{~A}\). Compute the values
The following data are obtained when open-circuit and short-circuit tests are performed on a single-phase, \(50-\mathrm{kVA}, 2400 / 240\)-volt, \(60-\mathrm{Hz}\) distribution transformer.(a)
A single-phase 50-kVA, 2400/240-volt, \(60-\mathrm{Hz}\) distribution transformer has a 1 -ohm equivalent leakage reactance and a 5000 -ohm magnetizing reactance referred to the high-voltage side. If
A single-phase 50-kVA, 2400/240-volt, 60-Hz distribution transformer is used as a step-down transformer at the load end of a 2400 -volt feeder whose series impedance is \((1.0+j 2.0)\) ohms. The
Rework Problem 3.14 if the transformer is delivering rated load at rated secondary voltage and at(a) unity power factor,(b) 0.8 power factor leading. Compare the results with those of Problem
A single-phase, \(50-\mathrm{kVA}, 2400 / 240-\mathrm{V}, 60-\mathrm{Hz}\) distribution transformer has the following parameters:Resistance of the \(2400-\mathrm{V}\) winding: \(\mathrm{R}_{1}=0.75
The transformer of Problem 3.16 is supplying a rated load of \(50 \mathrm{kVA}\) at a rated sec ondary voltage of \(240 \mathrm{~V}\) and at 0.8 power factor lagging. Neglect the transformer exciting
Using the transformer ratings as base quantities, work Problem 3.13 in per-unit.Problem 3.13A single-phase 50-kVA, 2400/240-volt, \(60-\mathrm{Hz}\) distribution transformer has a 1 -ohm equivalent
Using the transformer ratings as base quantities, work Problem 3.14 in per-unit.Problem 3.14A single-phase 50-kVA, 2400/240-volt, 60-Hz distribution transformer is used as a step-down transformer at
Using base values of \(20 \mathrm{kVA}\) and 115 volts in zone 3, rework Example 3.4.Example 3.4Three zones of a single-phase circuit are identified in Figure 3.10(a). The zones are connected by
Rework Example 3.5; using \(\mathrm{S}_{\text {base } 3 \phi}=100 \mathrm{kVA}\) and \(\mathrm{V}_{\text {baseLL }}=600\) volts.Example 3.5As in Example 2.5, a balanced-Y-connected voltage source
A balanced Y-connected voltage source with \(E_{a g}=277 / 0^{\circ}\) volts is applied to a balanced- \(Y\) load in parallel with a balanced- \(\Delta\) load where \(Z_{Y}=20+\) \(j 10\) and \(Z
Figure 3.32 shows the oneline diagram of a three-phase power system. By selecting a common base of 100 MVA and \(22 \mathrm{kV}\) on the generator side, draw an impedance diagram showing all
For Problem 3.18, the motor operates at full load, at 0.8 power factor leading, and at a terminal voltage of \(10.45 \mathrm{kV}\). Determine (a) the voltage at bus 1 , which is the generator bus,
Consider a single-phase electric system shown in Figure 3.33. Transformers are rated as follows:X-Y 15 MVA, 13.8/138 kV, leakage reactance 10\%Y-Z 15 MVA, 138/69 kV, leakage reactance 8\%With the
A bank of three single-phase transformers, each rated 30 MVA, \(38.1 / 3.81 \mathrm{kV}\), are connected in \(\mathrm{Y}-\Delta\) with a balanced load of three \(1 \Omega\), Y-connected resistors.
A three-phase transformer is rated \(1000 \mathrm{MVA}, 220 \mathrm{Y} / 22 \Delta \mathrm{kV}\). The Y-equivalent short-circuit impedance, considered equal to the leakage reactance, measured on the
For the system shown in Figure 3.34, draw an impedance diagram in per unit by choosing \(100 \mathrm{kVA}\) to be the base kVA and \(2400 \mathrm{~V}\) as the base voltage for the generators. 10 KVA
Consider three ideal single-phase transformers (with a voltage gain of \(\eta\) ) put together as a \(\Delta-\Omega\) three-phase bank as shown in Figure 3.35. Assuming positive-sequence voltages for
Reconsider Problem 3.29. If \(V_{a n}, V_{b n}\), and \(V_{c n}\) are a negative-sequence set, how would the voltage and current relationships change?(a) If \(C_{1}\) is the complex positive-sequence
If positive-sequence voltages are assumed and the Y- \(\Delta\) connection is considered, again with ideal transformers as in Problem 3.29, find the complex voltage gain \(C_{3}\).(a) What would the
Determine the positive- and negative-sequence phase shifts for the threephase transformers shown in Figure 3.36. N turns. N turns N turns. HA HB 111 MC XC MA HC MB XB (a) Y-1-1 transformer N turns N
Consider the three single-phase two-winding transformers shown in Figure 3.37. The high-voltage windings are connected in Y.(a) For the low-voltage side, connect the windings in \(\Delta\), place the

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