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All Textbook Solutions for Power System Analysis and Design (MindTap Course List)

The rms value of v(t)=Vmaxcos(t+) is given by a. Vmax b. Vmax/2 c. 2Vmax d. 2Vmax If the rms phasor of a voltage is given by V=12060 volts, then the corresponding v(t) is given by (a) 1202cos(t+60) (b) 120cos(t+60) (c) 1202sin(t+60)If a phasor representation of a current is given by I=70.745A, it is equivalent to a. 100e/45 b. 100+j100 c. 50+j50 2.4MCQ 2.5MCQ 2.6MCQ 2.7MCQ 2.8MCQ 2.9MCQ The average value of a double-frequency sinusoid, sin2(t+), is given by (a) 1 (b) (c) Zero The power factor for an inductive circuit (R-L load), in which the current lags the voltage, is said to be (a) Lagging (b) Leading (c) Zero The power factor for a capacitive circuit (R-C load), in which the current leads the voltage, is said to be (a) Lagging (b) Leading (c) One 2.13MCQ The instantaneous power absorbed by the load in a single-phase ac circuit, for a general R LC load under sinusoidal-steady-state excitation. is (a) Nonzero constant (b) Zero (c) Containing double-frequency components 2.15MCQ With generator conyention, where the current leaves the positive terminal of the circuit element, if P is positive then positive real power is delivered. (a) False (b) True Consider the load convention that is used for the RLC elements shown in Figure 2.2 of the text. A. If one says that an inductor absorbs zero real power and positive reactive power. is it (a) True (b) False B. If one says that a capacitor absorbs zero real power and negative reactive power (or delivers positive reactive power), is it (a) False (b) True C. If one says that a (positive-valued) resistor absorbs (positive) real power and zero reactive power, is it (a) True (b) False 2.18MCQ The admittance of the impedance j12 is given by (a) j2S (b) j2S2 (c) j4S Consider Figure 2.9 of the text, Let the nodal equations in matrix form be given by Eq. (2.4. 1) of the text. A. The element Y11 is given by (a) 0 (b) j/l3 (c)j7 B. The element Y31 is given by (a) 0 (b) j5 (c) jl C. The admittance matrix is always symmetric square. (a) False (b) True The three-phase source line-to-neutral voltages are given by Ean=100,Ebh=10+240, and Ecn=10240volts. Is the source balanced? (a) Yes (b) No In a balanced three-phase Y-connected system with a positive-sequence source, the line-to-line voltages are 3 times the line-to-neutral voltages and lend by 30. (a) True (b) False In a balanced system, the phasor sum of the line-to-line voltages and the phasor sum of the line-to-neutral voltages are always equal to zero. (a) False (b) True Consider a three-phase Y-connected source feeding a balanced- load. The phasor sum of the line currents as well as the neutral current are always zero. (a) True (b) False For a balanced- load supplied by a balanced positive-sequence source. the line currents into the load are 3 times the -Ioad currents and lag by 30. (a) True (b) False A balanced -load can be converted to an equivalent balanced-Y load by dividing the -load impedance by (a) 3 (b) 3 (c) 1/3 When working with balanced three-phase circuits, per-phase analysis is commonly done after converting loads to Y loads, thereby solving only one phase of the circuit. (a)True (b)False The total instantaneous power delivered by a three-phase generator under balanced operating conditions is (a) A function of time (b) A constant The total instantaneous power absorbed by a three-phase motor (under balanced steady-state conditions) as well as a balanced three-phase impedance load is (a) A constant (b) A function of time Under balanced operating conditions, consider the three-phase complex power delivered by the three-phase source to the three-phase load. Match the following expressions, those on the left to those on the right. (i) Realpower, P3 (a) (3VLLIL)VA (ii) Reactive power, Q3 (b) (3VLLILsin)var (iii) Total apparent power, S3 (c) (3VLLILcos)W (iv) Complex power, S3 (d) P3+jQ3 Note that VLL is the rms line-to-line voltage, IL is the rms line current, and is the power-factor angle.One advantage of balanced three-phase systems over separate singlephase systems is reduced capital and operating costs of transmission and distribution. (a) True (b) False While the instantaneous electric power delivered by a single-phase generator under balanced steady-state conditions is a function of time havi ng two components of a constant and a double-frequency sinusoid, the total instantaneous electric power delivered by a three-phase generator under balanced steady-state conditions is a constant. (a) True (b) False Given the complex numbers A1=630 and A2=4+j5, (a) convert A1 to rectangular form: (b) convert A2 to polar and exponential form: (c) calculate A3=(A1+A2), giving your answer in polar form: (d) calculate A4=A1A2, giving your answer in rectangular form: (e) calculate A5=A1/(A2*) giving your answer in exponential form.Convert the following instantaneous currents to phasors, using cos(t) as the reference. Give your answers in both rectangular and polar form. (a) i(t)=5002cos(t30) (b) i(t)=4sin(t+30) (c) i(t)=5cos(t15)+42sin(t+30)The instantaneous voltage across a circuit element is v(t)=400sin(t+30)volts, and the instantaneous current entering the positive terminal of the circuit element is i(t)=100cos(t+10)A. For both the current and voltage, determine (a) the maximum value, (b) the rms value, and (C) the phasor expression, using cos(t) as the reference.For the single-phase circuit shown in Figure 122,I=100A. (a) Compute the phasors I1,I2, (b) Draw a phasor diagram showing I,I1,I2, and V A 60Hz, single-phase source with V=27730 volts is applied to a circuit element. (a) Determine the instantaneous source voltage. Also determine the phasor and instantaneous currents entering the positive terminal if the circuit element is (b) a 20 resistor. (C) a 10mH inductor, and (d) a capacitor with 25 reactance.(a) Transform v(t)=75cos(377t15) to phasor form. Comment on whether =377 appears in your answer. (b) Transform V=5010 to instantaneous form. Assume that =377. (c) Add the two sinusoidal functions a(t) and b(t) of the same frequency given as follows: a(t)=A2cos(t+) and b(t)=B2cos(t+). Use phasor methods and obtain the resultant c(t). Does the resultant have the same frequency?Let a 100V sinusoidal source be connected to a series combination of a 3 resistor, an 8 inductor, and a 4 capacitor. (a) Draw the circuit diagram. (b) Compute the series impedance. (C) Determine the current I delivered by the source. Is the current lagging or leading the source voltage? What is the power factor of this circuit?Consider the circuit shown in Figure 2.23 in time domain. Convert the entire circuit into phasor domain.For the circuit shown in Figure 2.24, compute the voltage across the load terminals.For the circuit element of Problem 2.3, calculate (a) the instantaneous power absorbed, (b) the real power (state whether it is delivered or absorbed). (c) the reactive power (state whether delivered or absorbed). (d) the power factor (state whether lagging or leading). [Note: By convention the power factor cos() is positive. If | | is greater than 90, then the reference direction for current may be reversed, resulting in a positive value of cos() ].2.11P The voltage v(t)=359.3cos(t)volts is applied to a load consisting of a 10 resistor in parallel with a capacitive reactance XC=25. Calculate (a) the instantaneous power absorbed by the resistor, (b) the instantaneous power absorbed by the capacitor. (c) the real power absorbed by the resistor, (d) the reactive power delivered by the capacitor, and (e) the load power factor.2.13P A single-phase source is applied to a two-terminal, passive circuit with equivalent impedance Z=3.045, measured from the terminals. The source current is i(t)=22cos(t)kA. Determine the (a) instantaneous power, (b) real power, (c) reactive power delivered by the source, and (d) source power factor.Let a voltage source v(t)=4cos(t+60) be connected to an impedance Z=230. (a) Given the operating frequency to be 60 Hz, determine the expressions for the current and instantaneous power delivered by the source as functions of time. (b) Plot these functions along with v(t) on a single graph for comparison. (c) Find the frequency and average value of the instantaneous power.A single-phase, 120V(rms),60Hz source supplies power to a series R-L circuit consisting of R=10 and L=40mH. (a) Determine the power factor of the circuit and state whether it is lagging or leading. (b) Determine the real and reactive power absorbed by the load. (c) Calculate the peak magnetic energy Wint stored in the inductor by using the expression Wint=L(Irms)2 and check whether the reactive power Q=Wint is satisfied. (Note: The instantaneous magnetic energy storage fluctuates between zero and the peak energy. This energy must be sent twice each cycle to the load from the source by means of reactive power flows.)Consider a load impedance of Z=jwL connected to a voltage and V let the current drawn be I. (a) Develop an expression for the reactive power Q in terms of ,L, and I, from complex power considerations. (b) Let the instantaneous current be i(t)=2Icos(t+). Obtain an expression for the instantaneous power p(t) into L, and then express it in terms of Q. (c) Comment on the average real power P supplied to the inductor and the instantaneous power supplied.Let a series RLC network be connected to a source voltage V, drawing a current I. (a) In terms of the load impedance Z=ZZ, find expressions for P and Q, from complex power considerations. (b) Express p(t) in terms of P and Q, by choosing i(t)=2Icost. (c) For the case of Z=R+jL+1/jC, interpret the result of part (b) in terms of P,QL, and Qc. In particular, if 2LC=1, when the inductive and capacitive reactances cancel, comment on what happens.Consider a single-phase load with an applied voltage v(t)=150cos(t+10)volts and load current i(t)=5cos(t+50)A. (a) Determine the power triangle. (b) Find the power factor and specify whether it is lagging or leading. (c) Calculate the reactive power supplied by capacitors in parallel with the load that correct the power factor to 0.9 lagging.A circuit consists of two impedances, Z1=2030 and Z2=2560, in parallel, supplied by a source voltage V=10060volts. Determine the power triangle for each of the impedances and for the source.An industrial plant consisting primarily of induction motor loads absorbs 500 kW at 0.6 power factor lagging. (a) Compute the required kVA rating of a shunt capacitor to improve the power factor to 0.9 lagging. (b) Calculate the resulting power factor if a synchronous motor rated at 500 hp with 90 efficiency operating at rated load and at unity power factor is added to the plant instead of the capacitor. Assume constant voltage (1hp=0.746kW).The real power delivered by a source to two impedances, Z1=4+j5 and Z2=10 connected in parallel, is 1000 W. Determine (a) the real power absorbed by each of the impedances and (b) the source current.A single-phase source has a terminal voltage V=1200volts and a currentI=1530, which leaves the positive terminal of the source. Determine the real and reactive power and state whether the source is delivering or absorbing each.A source supplies power to the following three loads connected in parallel: (1) a lighting load drawing 10kW. (2) an induction motor drawing 10kVA at 0.90 power factor lagging, and (3) a synchronous motor operating at 10hp,85 effIciency and 0.95 power factor leading (1hp=0.746kW). Determine the real, reactive, and apparent power delivered by the source. Also, draw the source power triangle.Consider the series RLC circuit of Problem 2.7 and calculate the complex power absorbed by each of the R, L, and C elements, as well as the complex power absorbed by the total load. Draw the resultant power tna ngle. Check whether the complex power delivered by the source equals the total complex power absorbed by the load.A small manufacturing plant is located 2 km down a transmission line, which has a series reactance of 0.5/km. The line resistance is negligible. The line voltage at the plant is 4800V(rms). and the plant consumes 120kW at 0.85 power factor lagging. Determine the voltage and power factor at the sending end of the transmission line by using (a) a complex power approach and (b) a circuit analysis approach.An industrial load consisting of a bank of induction motors consumes 50 kW at a power factor of 0.8 lagging from a 220-V,60-Hz, single-phase source. By placing a bank of capacitors in parallel with the load, the resultant power factor is to be raised to 0.95 lagging. Find the net capacitance of the capacitor bank in F that is required.Three loads are connected in parallel across a single-phase source voltage of 240V(RMS). Load 1 absorbs 15 kW and 6.667 kvar; Load 2 absorbs 3 kVA at O.96PF leading; Load 3 absorbs 15 kW at unity power factor. Calculate the equivalent impedance, Z, for the three parallel loads, for two cases: (i) Series combination of R and X, and (ii) parallel combination of R and X.2.29P Figure 2.26 shows three loads connected in parallel across a 1000-V(RMS),60Hz single-phase source. Load 1: Inductive load, 125kVA,0.28PF lagging. Load 2: Capacitive load, 10kW,40kvar. Load 3: Resistive load, 15kW. (a) Determine the total kW, kvar, kva, and supply power factor. (b) In order to improve the power factor to 0.8 lagging. a capacitor of negligible resistance is connected in parallel with the above loads. Find the kvar rating of that capacitor and the capacitance in F. Comment on the magnitude of the supply current after adding the capacitor.Consider two interconnected voltage sources connected by a line of impedance Z=jX, as shown in Figure 2.27. (a) Obtain expressions for P12 and Q12. (b) Determine the maximum power transfer and the condition for it to 2.35P 2.36P 2.37P 2.38P 2.39P A balanced three-phase 240-V source supplies a balanced three-phase Load. If the line current IA is measured to be 15 A and is in phase with the line-to-line voltage, VBC, find the per-phase load impedance if the load is (a) Y-connected, (b) -conneeted.2.41P A balanced -connected impedance load with (12+j9) per phase is supplied by a balanced three-phase 60-Hz,208-V source, (a) Calculate the line current, the total real and reactive power absorbed by the load, the load power factor, and the apparent load power, (b) Sketch a phasor diagram showing the line currents, the line-to-line source voltages, and the -load currents. Use Vab as the reference.A three-phase line, which has an impedance of (2+j4) per phase, feeds two balanced three-phase loads that are connected in parallel. One of the loads is Y-connected with an impedance of (30+j40) per phase, and the other is -connected with an impedance of (60j45) per phase. The line is energized at the sending end from a 60-Hz, three-phase, balanced voltage source of 1203V (rms. line-to-line). Determine (a) the current, real power. and reactive power delivered by the sending-end source: (b) the line-to-line voltage at the load: (C) the current per phase in each load: and (d) the total three-phase real and reactive powers absorbed by each load and by the line. Check that the total three- phase complex power delivered by the source equals the total three-phase power absorbed by the line and loads.Two balanced three-phase loads that are connected in parallel are fed by a three-phase line having a series impedance of (0.4j2.7) per phase. One of the loads absorbs 560 kVA at 0.707 power factor lagging, and the other 132 kW at unity power factor. The line-to-line voltage at the load end of the line is 2203V. Compute (a) the line-to-line voltage at the source end of the line. (b) the total real and reactive power losses in the three-phase line, and (c) the total three-phase real and reactive power supplied at the sending end of the line. Check that the total three-phase complex power delivered by the source equals the total three-phase comp lex power absorbed by the line and loads.Two balanced Y-connected loads, one drawing 10 kW at 0.8 power factor lagging and the other IS kW at 0.9 power factor leading, are connected in parallel and supplied by a balanced three-phase Y-connected, 480-V source. (a) Determine the source current. (b) If the load neutrals are connected to the source neutral by a zero-ohm neutral wire through an ammeter, what will the ammeter read?Three identical impedances Z=3030 are connected in to a balanced three-phase 208-V source by three identical line conductors with impedance ZL=(0.8+j0.6) per line. (a) Calculate the line-to-line voltage at the load terminals. (b) Repeat part (a) when a s-connected capacitor bank with reactance (j60) per phase is connected in parallel with the load.Two three-phase generators supply a three-phase load through separate three-phase lines. The load absorbs 30 kW at 0.8 power factor lagging. The line impedance is (1.4+j1.6) per phase between generator G1 and the load, and (0.8+j1) per phase between generator G2 and the load. If generator G1 supplies 15 kW at 0.8 poir factor lagging, with a terminal voltage of 460 V line-to-line, determine (a) the voltage at the load terminals. (b) the voltage at the terminals of generator G2, and (c) the real and reactive power supplied by generator G2. Assume balanced operation.2.48P Figure 2.33 gives the general -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 the equivalent Y for the following impedances: ZAB=j10,ZBC=j20, and ZCA=j25. ZAB=ZAZB+ZBAC+ZCZAZCZA=ZABZCAZAB+ZBC+ZCAZBC=ZAZB+ZBAC+ZCZAZAZB=ZABZBCZAB+ZBC+ZCAZCA=ZAZB+ZBAC+ZCZAZBZA=ZCAZBCZAB+ZBC+ZCA Consider the balanced three-phase system shown in Figure 2.34. Deter mine v1(t) and i2(t). Assume positive phase sequence.A three-phase line with an impedance of (0.2+j1.0)/ phase feeds three balanced three-phase loads connected in parallel. Load 1: Absorbs a total of 150 kW and 120 kvar. Load 2: Delta connected with an impedance of (150j48)/phase. Load 3: 120 kVA at 0.6 PF leading. If the line-to-neutral voltage at the load end of the line is 2000 v (rms), determine the magnitude of the line-to-line voltage at the source end of the line.A balanced three-phase load is connected to a 4.16-kV, three-phase, fourwire, grounded-wye dedicated distribution feeder. The load can be mode led by an impedance of ZL=(4.7+j9)/phase, wye-connected. The impedance of the phase conductors is (0.3+j1). Determine the following by using the phase A to neutral voltage as a reference and assume positive phase sequence: (a) Line currents for phases A, B, and C. (b) Line-to-neutral voltages for all three phases at the load. (c) Apparent. active, and reactive power dissipated per phase, and for all three phases in the load. (d) Active power losses per phase and for all three phases in the phase conductors.What is a microgrid?What are the benefits of microgrids?CCSQ DCSQ The Ohms law for the magnetic circuit states that the net magnetomotive force (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, N1I1 is equal to the ampere-turns of the secondary winding, N2I2 (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 Z2 connected across winding 2 (secondary) is referred to winding 1 (primary) by multiplying Z2 by (a) The turns ratio (N1/N2) (b) The square of the turns ratio (N1/N2)2 (c) The cubed turns ratio (N1/N2)3 Consider Figure 3.4. For an ideal phase-shifting transformer, the imda nce is unchanged when it is referred from one side to the other. (a) True (b) False Consider Figure 3.5. Match the following, those on the left to those on the right. (i) Im (a) Exciting current (ii) Ic (b) Magnetizing Current (iii) Ie (c) core loss current The units of admittance, conductance, and susceptance are siemens. (a) True (b) False Match the following: (i) Hysteresis loss (a) Can be redud by constructing the core with laminated sheets of alloy steel (ii) Eddy current loss (b) Can be reduced by the use of special high grades of alloy stl as core material.For large power transformers rated more than 500 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 Sbase is not the same. (b) The ratio of the voltage bases on either side of a transformer is selected to be the same as the ratio of the transformer voltage ratings. (c) Per-unit impedance remains unchanged when referred from one side of a transformer to the other.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 Zp.u.new=Zp.u.old(VbaseoldVbasenew)2(SbasenewSbaseold)Zp.u.new=Zp.u.old(VbaseoldVbasenew)2(SbasenewSbaseold)Zp.u.new=Zp.u.old(VbaseoldVbasenew)2(SbasenewSbaseold)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) True (b) False 3.17MCQ 3.18MCQ With the American Standard notation, in either a Y-or-Y transformer, positive- sequen quantities on the high-voltage side shall lead their corresponding quantities on the low-voltage side by 30. (a) True (b) False 3.20MCQ 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 power systems. (a) Y- (b) -Y (c) Y-Y Does an open connection permit balanced three-phase operation? - (a) Yes (b) No Does an open- operation, the kVA rating compared to that of the original thr-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 - load impedances to equivalent Y impedances. (ii) Base values can be selected either on a per-phase basis or on a three-phase basis. (a) Both statements are true. (b) Neither is true. (c) Only one of the above is true.In developing per-unit equivalent circuits for three-phase transformers. under balanced three-phase operation. (i) A common Sbase is selected for both the H and X terminals. (ii) The ratio of the voltage bases Vbase/VbaseX is selected to be equal to the ratio of the rated line-to-line voltages VratedHLL/VratedXLL. (a) Only one of the above is true. (b) Neither is true. (C) Both statements are true.In per-unit equivalent circuits of practical three-phase transformers, under balanced thr-phase operation, in which of the following connect ions would a phase-shifting transformer come up? (a) Y-Y (b) Y- (c) -3.27MCQ 3.28MCQ For developing per-unit equivalent circuits of single-phase three-winding transformer, a common Sbase is selected for all three windings and voltage bases are selected in proportion to the rated voltage of the windings (a) True (b) False 3.30MCQ 3.31MCQ 3.32MCQ The direct electrical connection of the windings allows transient over voltages to pass through the auto transfonner more easily, and that is an important disadvantage of the autotransformer. (a) True (b) False 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 some computer programs. (a) True (b) False (ii) In the - circuit representation for real c in part (d), the admittance parameters Y11 and Y12 would be unequal. (a) True (b) False (iii) For complex c, can the admittance parameters be synthesized with a passive RLC circuit? (a) Yes (b) No (a) An ideal single-phase two-winding transformer with turns ratio at=N1/N2 is connected with a series impedance Z2 across winding 2. If one wants to replace Z2, with a series impedance Z1 across winding 1 and keep the terminal behavior of the two circuits to be identical, find Z1 in terms of Z2. (b) Would the above result be true if instead of a series impedance there is a shunt impedance? (c) Can one refer a ladder network on the secondary (2) side to the primary (1) side simply by multiplying every impedance byat2 ?An ideal transformer with N1=1000andN2=250 is connected with an impedance Z22 across winding 2. If V1=10000VandI1=530 A, determine V2,I2,Z2, and the impedance Z2, which is the value of Z2 referred to the primary side of the transformer.Consider an ideal transformer with N1=3000andN2=1000 turns. Let winding 1 be connected to a source whose voltage is e1(t)=100(1| t |)volts for 1t1ande1(t)=0 for | t |1 second. A2- farad capacitor is connected across winding 2. Sketch e1(t),e2(t),i1(t),andi2(t) versus time t.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 kVA at 0.8 power factor lagging and is at 230 volts. Assuming an ideal transformer, calculate the following: (a) primary voltage, (b) load impedance, (c) load impedance referred to the primary, and (d) the real and reactive power supplied to the primary winding.3.5P 3.6P Consider a source of voltage v(t)=102sin(2t)V, with an internal resistance of 1800. A transformer that can be considered as ideal is used to couple a 50 resistive load to the source. (a) Determine the transformer primary-to-secondary turns ratio required to ensure maxi mum power transfer by matching the load and source resistances. (b) Find the average power delivered to the load, assenting maximum power transfer.3.8P 3.9P A single-phase step-down transformer is rated 13MVA,66kV/11.5kV. With the 11.5 kV winding short-circuited, rated current flows when the voltage applied to the primary is 5.5 kV. The power input is read as 100 kW. Determine Req1andXeq1 in ohms referred to the high-voltage winding.For the transformer in Problem 3.10. The open-circuit test with 11.5 kV applied results in a power input of 65 kW and a current of 30 A. Compute the values for GcandBm in siemens referred to the high-voltage winding. Compute the efficiency of the transformer for a load of 10 MW at 0.8 p.f. lagging at rated voltage.3.12P A single-phase 50-kVA,2400/240-volt,60-Hz distribution transformer has a 1-ohm equivalent leakage reactance and a 5000-ohm magnetizing reactance referred to the high-voltage side. If rated voltage is applied to the high-voltage winding, calculate the open-circuit secondary voltage. Neglect I2RandGc2V losses. Assume equal series leakage reactances for the primary and the referred secondary.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+j2.0) ohm. The equivalent series impedance of the transformer is (1.0+j2.5) ohms referred to the high-voltage (primary) side. The transformer is delivering rated load at a 0.8 power factor lagging and at a rated secondary voltage. Neglecting the transformer exciting current, determine (a) the voltage at the transformer primary terminals, (b) the voltage at the sending end of the feeder, and (c) the real and reactive power delivered to the sending end of the feeder.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 3.14. -A single-phase, 50-kVA,2400/240-V,60-Hz distribution transformer has the following parameters: Resistance of the 2400-V winding: R1=0.75 Resistance of the 240-V winding: R2=0.0075 Leakage reactance of the 2400-V winding: X1=1.0 Leakage reactance of the 240-V winding: X2=0.01 Exciting admittance on the 240-V side =0.003j0.02S (a) Draw the equivalent circuit referred to the high-voltage side of the transformer. (b) Draw the equivalent circuit referred to the low-voltage side of the transformer. Show the numerical values of impedances on the equivalent circuits.The transformer of Problem 3.16 is supplying a rated load of 50 kVA at a rated secondary voltage of 240 V and at 0.8 posr factor lagging. Neglect the transformer exciting current. (a) Determine the input terminal voltage of the transformer on the high-voltage side. (b) Sketch the corresponding phasor diagram. (c) If the transformer is used as a step-down transformer at the load end of a feeder whose impedance is 0.5+j2.0, find the voltage VS and the power factor at the sending end of the feeder.Using the transformer ratings as base quantities, work Problem 3.13 in per-unit.Using the transformer ratings as base quantities. work Problem 3.14 in per-unit.Using base values of 20 kVA and 115 volts in zone 3, rework Example 3.4.3.21P A balanced Y-connected voltage source with Eag=2770volts is applied to a balanced-Y load in parallel with a balanced- load where ZY=20+j10andZ=30j15ohms. The Y load is solidly grounded. Using base values of Sbase1,=10kVAandVbaseLN=277volts, calculate the source current Ia in per-unit and in amperes Figure 3.32 shows the oneline diagram of a three-phase power system. By selecting a common base of 100 MVA and 22 kV on the generator side, draw an impedance diagram showing all impedances including the load impedance in per-unit. The data are given a follows: G:90MVA22kVx=0.18perunitT1:50MVA22/220kVx=0.10perunitT2:40MVA220/11kVx=0.06perunitT3:40MVA22/110kVx=0.064perunitT4:40MVA110/11kVx=0.08perunitM:66.5MVA10.45kVx=0.185perunit Lines I and 2 have series reactances of 48.4 and 65.43, respectively. At bus 4, the three-phase load absorbs 57 MVA at 10.45 kV and 0.6 power factor lagging.For Problem 3.18, the motor operates at full load, at 0.8 power factor leading, and at a terminal voltage of 10.45 kV. Determine (a) the voltage at bus 1, which is the generator bus, and (b) the generator and motor internal EMFs.Consider a single-phase electric system shown in Figure 3.33. Transformers are rated as follows: XY15MVA,13.8/138kV, leakage reactance 10 YZ15MVA,138/69kV, leakage reactance 8 With the base in circuit Y chosen as 15MVA,138kV determine the per-unit impedance of the 500 resistive load in circuit Z, referred to circuits Z, Y, and X. Neglecting magnetizing currents, transformer resistances, and line impedances, draw the impedance diagram in per unit.A bank of three single-phase transformers, each rated 30MVA,38.1/3.81kV, are connected in Y- with a balanced load of three 1, Y-connected resistors. Choosing a base of 90MVA,66kV for the high-voltage side of the three-phase transformer. spify the base for the low-voltage side. Compute the per-unit resistance of the load on the base for the low-voltage side. Also, determine the load resistance in ohms referred to the high-voltage side and the per-unit value on the chosen base.A three-phase transformer is rated 1000MVA,220Y/22kV. The Y-equivalent short-circuit impedance, considered equal to the leakage reactance, measured on the low-voltage side is 0.1. Compute the per-unit reactance of the transformer. In a system in which the base on the high-voltage side of the transformer is 100MVA,230kV what value of the per-unit reactance should be used to represent this transformer?For the system shown in Figure 3.34. draw an impedance diagram in per unit by choosing 100 kVA to be the base kVA and 2400 V as the base voltage for the generators.Consider three ideal single-phase transformers (with a voltage gain of ) put together as three-phase bank as shown in Figure 3.35. Assuming positive-sequence voltages for Va,Vb, and Vc find Va,Vb, and VC. in terms of Va,Vb, and Vc, respectively. (a) Would such relationships hold for the line voltages as well? (b) Looking into the current relationships, express IaIb and Ic in terms of IaIb and Ic respectively. (C) Let S and S be the per-phase complex power output and input. respectively. Find S in terms of S.Reconsider Problem 3.29. If Va,VbandVc are a negative-sequence set, how would the voltage and current relationships change? (a) If C1 is the complex positive-sequence voltage gain in Problem 3.29 and (b) if C2 is the negative sequence complex voltage gain, express the relationship between C1andC2 3.31P Determine the positive- and negative-sequence phase shifts for the three- phase transformers shown in Figure 3.36.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 , place the polarity marks, and label the terminals a, b, and c in accordance with the American standard. (b) Relabel the terminals a, b, and c such that VAN is 90 out of phase with Va for positive sequence.Three single-phase, two-winding transformers, each rated 450MVA,20kV/288.7kV, with leakage reactance Xeq=0.10perunit, are connected to form a three-phase bank. The high-voltage windings are connected in Y with a solidly grounded neutral. Draw the per-unit equivalent circuit if the low-voltage windings are connected (a) in with American standard phase shift or (b) in Y with an open neutral. Use the transformer ratings as base quantities. Winding resistances and exciting current are neglected.Consider a bank of this single-phase two-winding transformers whose high-voltage terminals are connected to a three-phase, 13.8-kV feeder. The low-voltage terminals are connected to a three-phase substation load rated 2.0 MVA and 2.5 kV. Determine the required voltage, current, and MVA ratings of both windings of each transformer, when the high-voltage/low- voltage windings are connected (a) Y-, (b) -Y, (c) Y-Y, and (d) -.Three single-phase two-winding transformers, each rated 25MVA,34.5/13.8kV, are connected to form a three-phase bank. Balanced positive-suence voltages are applied to the high-voltage terminals, and a balanced, resistive Y load connected to the low-voltage terminals absorbs 75 MW at 13.8 kV. If one of the single-phase transformers is removed (resulting in an open connection) and the balanced load is simultaneously reduced to 43.3 MW (57.7 of the original value), determine (a) the load voltages Va,Vb, and Vc; (b) load currents Ia,Ib, and Ic; and (c) the MVA supplied by each of the remaining two transformers. Are balanced voltages still applied to the load? Is the open transformer overloaded?Three single-phase two-winding transformers, each rated 25MVA,54.2/5.42kV, are connected to form a three-phase Y- bank with a balanced Y-connected resistive load of 0.6 per phase on the low-voltage side. By choosing a base of 75 MVA (three phase) and 94 kV (line-to-line) for the high-voltage side of the transformer bank, specify the base quantities for the low-voltage side. Determine the per-unit resistance of the load on the base for the low-voltage side. Then determine the load resistance RL in ohms referred to the high-voltage side and the per-unit value of this load resistance on the chosen base.Consider a three-phase generator rated 300MVA,23kV, supplying a system load of 240 MA and 0.9 power factor lagging at 230 kV through a 330MVA,23/230Y-kV step-up transformer with a leakage reactance of 0.11 per unit. (a) Neglecting the exciting current and choosing base values at the load of 100 MVL and 230 kV. Find the phasor currents IA,IB, and IC supplied to the load in per unit. (b) By choosing the load terminal voltage IA as reference, specify the proper base for the generator circuit and determine the generator voltage V as well as the phasor currents IA,IB, and IC, from the generator. (Note: Take into account the phase shift of the transformer.) (C) Find the generator terminal voltage in kV and the real power supplied by the generator in MW. (d) By omitting the transformer phase shift altogether, check to see whether you get the same magnitude of generator terminal voltage and real power delivered by the generator.The leakage reactance of a three-phase, 300-MVA,230Y/23-kV transformer is 0.06 per unit based on its own ratings. The Y winding has a solidly grounded neutral. Draw the per-unit equivalent circuit. Neglect the exciting admittance and assume the American Standard phase shift.3.40P Consider the single-line diagram of the power system shown in Figure 3.38. Equipment ratings are Generator 1: 1000MVA,18kV,X=0.2perunit Generator 2: 1000MVA,18kV,X=0.2p.u. Synchronous motor 3: 1500MVA,20kV,X=0.2p.u. Three-phase -Y transformers T1,T2,T3,T4,: 1000MVA,500kV,Y/20kV,X=0.1p.u. Three-phase YY transformer T5: 1500MVA,500kV,Y/20kVY,X=0.1p.u. Neglecting resistance, transformer phase shift, and magnetizing reactance, draw the equivalent reactance diagram. Use a base of 100 MA and 500 kV for the 50-ohm line. Determine the per-unit reactances.For the power system in Problem 3.41, the synchronous motor absorbs 1500 MW at 0.8 power factor leading with the bus 3 voltage at 18 kV. Determine the bus I and bus 2 voltages in kV Assume that generators I and 2 deliver equal real powers and equal reactive powers. Also assume a balanced three-phase system with positive-sequence sources.Three single-phase transformers, each rated 10MVA,66.4/12.5kV,60Hz, with an equivalent series reactance of 0.1 per unit divided equally between primary and secondary, are connected in a three-phase bank. The high-voltage windings are V-connected and their terminals are directly connected to a 115-kV three-phase bus. The secondary terminals are all shorted together. Find the currents entering the high-voltage terminals and leaving the low-voltage terminals if the low-voltage windings are (a) Y-connected and (b) - connected.A 130-MVA,13.2-kV three-phase generator, which has a positive-sequence reactance of 1.5 per unit on the generator base, is connected to a 135-MVA,13.2/115Y-kV step-up transformer with a series impedance of (0.005+10.1) per unit on its own base. (a) Calculate the per-unit generator reactance on the transformer base. (b) The load at the transformer terminals is 15 MW at unity power factor and at 115 kV Choosing the transformer high-side voltage as the reference phasor, draw a phasor diagram for this condition. (C) For the condition of part (b), find the transformer low-side voltage and the generator internal voltage behind its reactance. Also compute the generator output power and power factor.Figure 3.39 shows a oneline diagram of a system in which the three-phase generator is rated 300 MVA, 20 kV with a subtransient reactance of 0.2 per unit and with its neutral grounded through a 0.4- reactor. The transmission line is 64km long with a cries reactance of 0.5-/km. The three-phase transformer T1 is rated 350MVA.230/20kV with a leakage reactance of 0.1 per unit. Transformer T2 is composed of three single-phase transformers, each rated 100 MVA, 127/13.2kV with a leakage reactance of 0.1 per unit. Two 13.2kV motors M1 and M2 with a subtransient reactance of 0.2 per unit for each motor represent the load. M1 has a rated input of 200 MVA with its neutral grounded through a 0.4- current-limiting reactor, M2 has a rated input of 100 MVA with its neutral not connected to ground. Neglect phase shifts associated with the transformers. Choose the generator rating as base in the generator circuit and draw the positive-sequence reactance diagram showing all reactances in per unit.The motors M1andM2 of Problem 3.45 have inputs of 120 and 60 MW, respectively, at 13.2 kV, and both operate at unity power factor. Determine the generator terminal voltage and voltage regulation of the line. Neglect transformer phase shifts.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 X1=0.24 (on the low-voltage side), negligible resistance and magnetizing current, and turns ratio =N2/N1=10. The transformer bank is delivering 100 MW at 0.8 p.f. lagging to a substation bus whose voltage is 230 kV. (a) Determine the primary current magnitude, primary voltage (line-to-line) magnitude, and the three-phase complex power supplied by the generator. Choose the line-to-neutral voltage at the bus, Va as the reference Account for the phase shift, and assume positive-sequence operation. (b) Find the phase shift between the primary and secondary voltages.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 stepown transformer bank, and an impedan load. The generator terminal voltage is 15 kV (line-to-line). (a) Draw the per-phase equivalent circuit, aounting for phase shifts for positive-sequence operation. (b) By choosing the line-to-neutral generator terminal voltage as the reference, determine the magnitudes of the generator current, transmiss ion-line current, load current, and line-to-line load voltage. Also, find the three-phase complex power delivered to the load.Consider the single-Line diagram of a power system shown in Figure 3.42 with equipment ratings given: Generator G1: 50MVA,13.2kV,x=0.15p.u. Generator G2: 20MVA,13.8kV,x=0.15p.u. Three-phase -Y transformer T1: 80MVA,13.2/165YkV,X=0.1p.u. Three-phase Y- transformer T2: 40MVA,165Y/13.8kV,X=0.1p.u. Load: 40MVA,0.8PFlagging,operatingat150kV Choose a base of 100 MVA for the system and 132-kV base in the transmission-line circuit. Let the load be modeled as a parallel combination of resistance and inductance. Neglect transformer phase shifts. Draw a per-phase equivalent circuit of the system showing all impedances in per unit.A single-phase three-winding transformer has the following parameters: Z1=Z2=Z3=0+j0.05,Gc=0, and BM=0.2 per unit. Three idenucal transformers, as described, are connected with their primaries in Y (solidly grounded neutral) and with their secondaries and tertiaries in . Draw the per-unit sequence networks of this transformer bank.The ratings of a three-phase three-winding transformer are Primary(1): Y connected 66kV,15MVA Secondary (2): Y connected, 13.2kV,10MVA Tertiary (3): A connected, 2.3kV,5MVA Neglecting winding resistances and exciting current, the per-unit leakage reactances are X12=0.08 on a 15-MVA,66-kV base X13=0.10 on a 15-MVA,66-kV base X23=0.09 on a 10-MVA,13.2-kV base (a) Determine the per-unit reactances X1,X2,X3 of the equivalent circuit on a 15-MVA,66-kV base at the primary terminals. (b) Purely resistive loads of 7.5 MW at 13.2 kV and 5 MW at 2.3kV are connected to the secondary and tertiary sides of the transformer, respectively. Draw the per- unit impedance diagram, showing the per-unit impedances on a 15-MVA,66-kV base at the primary terminals.3.52P The ratings of a three-phase, three-winding transformer are Primary: Y connected, 66kV,15MVA Secondary: Y connected, 13.2kV,10MVA Tertiary: connected, 2.3kV,5MVA Neglecting resistances and exciting current, the leakage reactances are: XPS=0.09 per unit on a 15-MVA,66-kV base XPT=0.08 per unit on a 15-MVA,66-kV base XST=0.05 per unit on a 10-MVA,13.2-kV base Determine the per-unit reactances of the per-phase equivalent circuit using a base of 15 MVA and 66 kV for the primary.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 sub transient reactance of 0.2 per unit is connected to the transformer secondary. A5-MW,2.3-kV three-phase resistive load is connected to the tertiary Choosing a base of 66 kV and 15 MVA in the primary, draw the impedance diagram of the system showing per-unit impedances. Neglect transformer exciting current, phase shifts, and all resistances except the resistive load.A single-phase l0-kVA,2300/230-volt,60-Hz two-winding distribution transformer is connected as an autotransformer to step up the voltage from 2300 to 2530 volts (a) Draw a schematic diagram of this arrangement, showing all voltages and currents when delivering full load at rated voltage. (b) Find the permissible kVA rating of the autotransformer if the winding currents and voltages are not to exceed the rated values as a two-winding transformer. How much of this kVA rating is transformed by magnetic induction? (C) The following data are obtained from tests carried out on the transformer when it is connected as a two-winding transformer: Open-circuit test with the low-voltage terminals excited: Applied voltage =230V, input current =0.45A, input power =70W. Short-circuit test with the high-voltage terminals excited: Applied voltage =120, input current =4.5A, input power =240W. Based on the data, compute the efficiency of the autotransformer corresponding to full load, rated voltage, and 0.8 power factor lagging. Comment on why the efficiency is higher as an autotransformer than as a two-winding transformer.Three single-phase two-winding transformers, each rated 3kVA,220/110volts,60Hz, with a 0.10 per-unit leakage reactance, are connected as a three-phase extended autotransformer bank, as shown in Figure 3.36(c). The low-voltage winding has a 110 volt rating. (a) Draw the positive-sequence phasor diagram and show that the high-voltage winding has a 479.5 volt rating. (b) A three-phase load connected to the low-voltage terminals absorbs 6 kW at 110 volts and at 0.8 power factor lagging. Draw the per-unit impedance diagram and calculate the voltage and current at the high-voltage terminals. Assume positive-sequence operation.A two-winding single-phase transformer rated 60kVA,240/1200V,60Hz, has an efficiency of 0.96 when operated at rated load, 0.8 power factor lagging. This transformer is to be utilized as a 1440/1200-V step-down autotransformer in a power distribution system. (a) Find the permissible kVA rating of the autotransformer if the winding currents and voltages are not to exceed the ratings as a two-winding transformer. Assume an ideal transformer. (b) Determine the efficiency of the autotransformer with the kVA loading of part (a) and 0.8 power factor leading.A single-phase two-winding transformer rated 90MVA,80/120kV is to be connected as an autotransformer rated 80/200kV. Assume that the transformer is ideal. (a) Draw a schematic diagram of the ideal transformer connected as an autotransformer. showing the voltages, currents, and dot notation for polarity. (b) Determine the permissible kVA rating of the autotransformer if the winding currents and voltages are not to exceed the rated values as a two-winding transformer. How much of the kA rating is transferred by magnetic induction?3.59P PowerWorid 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 system is no longer lossless, a field showing the real power losses has also been added to the oneline. With the LTC tap fixed at 1.05, plot the real power losses as the phase shift angle is varied from 10 to +10 degrees. What value of phase shift minimizes the system losses?Rework Example 3.12 for a+10 tap, providing a 10 increase for the high-voltage winding.A 23/230-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-kV transformer. The impedance of the line and transformers at 230kVis18+j60. Determine the tap setting for each transformer to maintain the voltage at the load at 23 kV.The per-unit equivalent circuit of two transformers Ta and Tb connected in parallel, with the same nominal voltage ratio and the same reactan of 0.1 per unit on the same base, is shown in Figure 3.43. Transformer Tb has a voltage-magnitude step-up toward the load of 1.05 times that of Ta (that is, the tap on the secondary winding of Tb is set to 1.05). The load is represented by 0.8+j0.6 per unit at a voltage V2=1.0/0 per unit. Determine the complex power in per unit transmitted to the load through each transformer, comment on how the transformers share the real and reactive powers.Reconsider Problem 3.64 with the change that now Tb includes both a transformer of the same turns ratio as Ta and a regulating transformer with a 4 phase shift. On the base of Ta, the impedance of the two comp onents of Tb is jO.1 per unit. Determine the complex power in per unit transmitted to the load through each transformer. Comment on how the transformers share the real and reactive pors.What are the advantages of correctly specifying a transformer most Suita ble for its application?Why is it important to reduce the moisture within a transformer to acceptable levels during transformer installation?What should be the focus of transformer preventive maintenance efforts?ACSR stands for Aluminum-clad steel conductor Aluminum conductor steel supported 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. True 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. True False Conductor spacings, types, and sizes do have an impact on the series impedance and shunt admittance. True False A circle with diameter Din.=1000Dmil=dmil has an area of ___________ c mil.An ac resistance is higher than a dc resistance. True False 4.9MCQ Transmission line conductance is usually neglected in power system studies. True False 4.11MCQ 4.12MCQ 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 H/m) 2107ln(Dr) 4107ln(Dr) where r=e14r=0.778r For a three-phase three-wire line consisting of three solid cylindrical conductors each with radius r and with equal phase spacing D between any two conductors, the inductance in H/m per phase is given by 2107ln(Dr)4107ln(Dr)6107ln(Dr) where r=e14r=0.778r For a balanced three-phase positive-sequence currents Ia,Ib,Ic, does the equation Ia+Ib+Ic=0 hold good?A stranded conductor is an example of a composite conductor. True False lnAk=lnAk True False 4.18MCQ Expand 6k=13m=12Dkm.4.20MCQ 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 DS with conductor distance D12,D23, and D31 give expressions for GMD between phases and the average per-phase inductance.4.24MCQ Does bundling reduce the series reactance of the line? Yes No Does r=e14r=0.788r, which comes in calculation of inductance, play a role in capacitance computations? Yes No In terms of line-to-line capacitance, the line-to-neutral capacitance of a single-phase transmission line is Same Twice 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 F/m is given by Can=.4.29MCQ 4.30MCQ 4.31MCQ 4.32MCQ 4.33MCQ 4.34MCQ The affect of the earth plane is to slightly increase the capacitance, and as the line height increases, the effect of earth becomes negligible. True False When the electric field strength at a conductor surface exceeds the break-down strength of air, current discharges occur. This phenomenon is called _________.4.37MCQ 4.38MCQ 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 between the two circuits can be neglected. True False The Aluminum Electrical Conductor Handbook lists a dc resistance of 0.01558 ohm per 1000 ft at 20C and a 60-Hz resistance of 0.0956 ohm per mile at 50C for the all-aluminum Marigold conductor, which has 61 strands and whose size is 1113 kcmil. Assuming an increase in resistance of 2 for spiraling, calculate and verify the dc resistance. Then calculate the dc resistance at 50C, and determine the percentage increase due to skin effect.The temperature dependence of resistance is also quantified by the relation R2=R1[ 1+(T2T1) ] where R1 and R2 are the resistances at temperatures T1 and T2, respectively, and is known as the temperature coefficient of resistance. If a copper wire has a resistance of 55 at 20C, find the maximum permissible operating temperature of the wire if its resistance is to increase by at most 20. Take the temperature coefficient at 20C to be =0.00382.A transmission-line cable with a length of 2 km consists of 19 strands of identical copper conductors, each 1.5 mm in diameter. Because of the twist of the strands, the actual length of each conductor is increased by 5. Determine the resistance of the cable if the resistivity of copper is 1.72-cm at 20C.One thousand circular mils or 1 kcmil is sometimes designated by the abbreviation MCM75C. Data for commercial bare-aluminum electrical conductors lists a 60 Hz resistance of 0.0080 ohm per kilometer at for a 793-MCM AAC conductor. Determine the cross-sectional conducting area of this conductor in square meters. Find the 60 Hz resistance of this conductor in ohms per kilometer at 50C.A 60-Hz, 765-kV, three-phase overhead transmission line has four ACSR 900 kcmil 54/3 conductors per phase. Determine the 60 Hz resistance of this line in ohms per kilometer per phase at 50C.A three-phase overhead transmission line is designed to deliver 190.5 M VA at 220 kV over a distance of 63 km, such that the total transmission line loss is not to exceed 2.5 of the rated line MVA. Given the resistivity of the conductor material to be 2.84108-m, determine the required conductor diameter and the conductor size in circular mils. Neglect power losses due to insulator leakage currents and corona.If the per-phase line loss in a 70-km-long transmission line is not to exceed 65 kW while it is delivering 100 A per phase, compute the required conductor diameter if the resistivity of the conductor material is 1.72108-m.A 60-Hz, single-phase two-wire overhead line has solid cylindrical copper conductors with a 1.5 cm diameter. The conductors are arranged in a horizontal configuration with 0.5 m spacing. Calculate in mH/km (a) the inductance of each conductor due to internal flux linkages only, (b) the inductance of each conductor due to both internal and external flux linkages, and (c) the total inductance of the line.4.9P A 60-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 0.5 in. Calculate the positive-sequence inductance in Wm and the positive-sequence inductive reactance in /km.4.11P Find the inductive reactance per mile of a single-phase overhead transmission line operating at 60 Hz given the conductors to be Partridge and the spacing between centers to be 30 ft.A single-phase overhead transmission line consists of two solid aluminum conductors having a radius of 3 cm with a spacing 3.5 m between centers. (a) Determine the total line inductance in mH/m. (b) Given the operating frequency to be 60 Hz, find the total inductive reactance of the line in /km and in/mi. (c) If the spacing is doubled to 7 m, how does the reactance change?4.14P 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.4.16P Determine the GMR of each of the unconventional stranded conductors shown in Figure 4.30. All strands have the same radius r.A 230-kV, 60-Hz, three-phase completely transposed overhead line has one ACSR 954 kcmil conductor per phase and flat horizontal phase spacing, with 7 m between adjacent conductors Determine the inductance in H/m and the inductive reactance in /km.4.19P Calculate the inductive reactance in /km of a bundled 500-kV, 60-Hz, three-phase completely transposed overhead line having three ACSR 1 113 kcmil conductors per bundle, with 0.5 m between conductors in the bundle. The horizontal phase spacings between bundle centers are 10, 10, and 20 m.Rework Problem 4.20 if the bundled line has (a) three ACSR, 1351 kcmil conductors per phase or (b) three ACSR, 900 kcmil conductors per phase, without changing the bundle spacing or the phase spacings between bundle centers. Compare the results with those of Problem 4.20.4.22P 4.23P 4.24P For the overhead line of configuration shown in Figure 4.33 operating at 60 Hz and a conductor temperature of 700C, determine the resistance per phase, inductive reactance in ohms/mile/phase, and the current-carrying capacity of the overhead line. Each conductor is ACSR Cardinal of Table A.4.4.26P Figure 4.34 shows double-circuit conductors' relative positions in segment I of transposition of a completely transposed three-phase overhead transmission line. The inductance is given by L=2107lnGMDGMRH/m/phase Where GMD=(DABeqDBCeqDACeq)1/3 With mean distances defined by equivalent spacings DABeq=(D12D12D12D12)1/4DBCeq=(D23D23D23D13)1/4DACeq=(D13D13D13)1/4 And GMR=[ (GMR)A(GMR)B(GMR)C ]1/3 with phase GMRs defined by (GMR)A=[ rD11 ]1/2;(GMR)B=[ rD22 ]1/2;(GMR)C=[ rD33 ]1/2 and r is the GMR of phase conductors. Now consider a 345-kV, three-phase, double-circuit line with phase-conductors GMR of 0.0588 ft and the horizontal conductor configuration shown in Figure 4.35. Determine the inductance per meter per phase in Henries (H). Calculate the inductance of just one circuit and then divide by 2 to obtain the inductance of the double circuit.For the case of double-circuit, bundle-conductor lines, the same method indicated in Problem 4.27 applies with r' replaced by the bundles GMR in the calculation of the overall GMR. Now consider a double-circuit configuration shown in Figure 4.36 that belongs to a 500-kV, three-phase line with bundle conductors of three subconductors at 21 in. spacing. The GMR of each subconductor is given to be 0.0485 ft. Determine the inductive reactance of the line in ohms per mile per phase. You may use XL=0.2794logGMDGMR/mi/phase 4.29P Figure 4.37 shows the conductor configuration of a three-phase transmission line and a telephone line supported on the same towers. The power line carries a balanced current of 250 A/phase at 60 Hz, while the telephone line is directly located below phase b Assume balanced three-phase currents in the power line. Calculate the voltage per kilometer induced in the telephone line.4.32P 4.33P 4.34P 4.35P 4.36P 4.38P Calculate the capacitance-to-neutral in F/m and the admittance-to-neutral in S/km for the three-phase line in Problem 4.18. Also calculate the line-charging current in kA/phase if the line is 110 km in length and is operated at 230 kV. Neglect the effect of the earth plane.4.40P 4.41P 4.42P Three ACSR Drake conductors are used for a three-phase overhead transmission line operating at 60 Hz. The conductor configuration is in the form of an isosceles triangle with sides of 20, 20, and 38 ft. (a) Find the capacitance-to-neutral and capacitive reactance-to-neutral for each 1-mile length of line. (b) For a line length of 175 mi and a normal operating voltage of 220 kV, determine the capacitive reactance-to-neutral for the entire line length as well as the charging current per mile and total three-phase reactive power supplied by the line capacitance.Consider the line of Problem 4.25. Calculate the capacitive reactance per phase in mi.4.45P 4.46P 4.47P The capacitance of a single-circuit, three-phase transposed line with the configuration shown in Figure 4.38, including ground effect, and with conductors not equilaterally spaced is given by C20lnDeqrlnHmH8 F/mÂ line-to-neutral where Deq=D12D23D133=GMD r= conductors outside radiusHm=(H12H23H13)1/3HS=(H1H2H3)1/3 Now consider Figure 4.39 in which the configuration of a three-phase, single circuit, 345-kV line with conductors having an outside diameter of 1.065 in. is shown. Determine the capacitance to neutral in F/m, including the ground effect. Next, neglecting the effect of ground, see how the value changes.4.49P 4.50P 4.51P Approximately how many physical transmission interconnections are there between the United States and Canada? Across which states and provinces are the interconnections located?BCSQ CCSQ DCSQ Representing a transmission line by the two-port network, in terms of ABCD parameters, (a) express VS, which is the sending-end voltage, in terms of VR, which is the receiving-end voltage, and IR, the receiving-end current, and (b) express IS, which is the sending-end current, in terms of VR and IR. (a) VS= _________ (b) IS= ________5.2MCQ 5.3MCQ 5.4MCQ 5.5MCQ 5.6MCQ 5.7MCQ 5.8MCQ 5.9MCQ 5.10MCQ 5.11MCQ 5.12MCQ 5.13MCQ 5.14MCQ 5.15MCQ 5.16MCQ 5.17MCQ 5.18MCQ 5.19MCQ The maximum power flow for a lossy line is somewhat less than that for a lossless line. True False 5.21MCQ 5.22MCQ

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