Solution: In a balanced three-phase system, the source has

Sketch a phasor representation of an abc-sequence balanced three-phase Y-connected source, including Van, Vbn, and Vcn if Van = 120 15 V rms.

A positive-sequence three-phase balanced wye voltage source has a line voltage of Vbc = 200 30 V. Determine the phase voltages of the source.

For a balanced three-phase wyewye connection with ZY = 50 20 , determine the phase voltages, line voltages, line currents, and phase currents if Van = 120 0 V. Assume a positive phase sequence

A positive-sequence three-phase balanced wye voltage source has a phase voltage of Van = 240 90 V rms. Determine the line voltages of the source.

Sketch a phasor representation of a balanced three-phase system containing both phase voltages and line voltages if Vab = 208 60 V rms. Label all phasors and assume an abc-phase sequence.

Find the equivalent Z of the network in Fig. P11.6. 1 2 1 1 1 2 j2 j2 j1 j1 j1 Z Figure P11.6

Find the equivalent Z of the network in Fig. P11.7. 2 Z a d c b 1 1 1 2 2 j1 j1 j1 j1 Figure P11.7

A positive-sequence balanced three-phase wye-connected source with a phase voltage of 120 V rms supplies power to a balanced wye-connected load. The per-phase load impedance is 40 + j10 . Determine the line currents in the circuit if Van = 0.

Find the equivalent impedances Zab, Zbc, and Zca in the network in Fig. P11.9. 1 a c b 1 1 j1 j1 j1 Figure P11.9

Find the equivalent Z of the network in Fig. P11.10. 2 12 1 j1 j1 j2 j2 j2 j1 1 j1 Z Figure P11.10

A positive-sequence balanced three-phase wye-connected source supplies power to a balanced wye-connected load. The line voltage is 100 V. The line impedance is 2 per phase, and the load impedance is 50 + j30 per phase. Determine the load voltages if Van = 0.

A positive-sequence balanced three-phase wye-connected source supplies power to a balanced wye-connected load. The magnitude of the line voltages is 208 V rms. If the load impedance per phase is 36 + j12 , determine the line currents if Van = 0.

In a three-phase balanced wyewye system, the source is an abc-sequence set of voltages with Van = 120 60 rms. The per-phase impedance of the load is 12 + j16 . If the line impedance per phase is 0.8 + j1.4 , find the line currents and the load voltages.

In a balanced three-phase system, the abc-phase-sequence source is delta-connected and Vab = 120 30 V rms. The load consists of two balanced wyes with phase impedances of 10 + j1 and 20 + j5 . If the line impedance is zero, find the line currents and the load phase voltage

An abc-phase-sequence three-phase balanced wye-connected 60-Hz source supplies a balanced delta-connected load. The phase impedance in the load consists of a 20- resistor in series with a 50-mH inductor, and the phase voltage at the source is Van = 120 20 V rms. If the line impedance is zero, find the line currents in the system.

An abc-phase-sequence three-phase balanced wye-connected source supplies power to a balanced wye-connected load. The impedance per phase in the load is 14 + j12 . If the source voltage for the a phase is Van = 120 80 V rms, and the line impedance is zero, find the phase currents in the wye-connected source.

An abc-sequence balanced three-phase wye-connected source supplies power to a balanced wye-connected load. The line impedance per phase is 1 + j5 , and the load impedance per phase is 25 + j25 . If the source line voltage Vab = 208 0 V rms, find the line currents.

An abc-sequence set of voltages feeds a balanced threephase wyewye system. If the line current in the a phase is 16.78 20.98 A rms, the line impedance is 1.2 + j1.8 , and the input voltage Vab = 440 70 V rms, find the load impedance.

An abc-sequence set of voltages feeds a balanced threephase wyewye system. The line and load impedances are 1 + j1 and 10 + j10 , respectively. If the load voltage on the a phase is VAN = 110 30 V rms, determine the line voltages of the input.

In a balanced three-phase wyewye system, the source is an abc-sequence set of voltages. The load voltage on the a phase is VAN = 108.58 79.81 V rms, Zline = 1 + j1.4 , and Zload = 10 + j13 . Determine the input sequence of voltages.

An abc-sequence balanced three-phase wye-connected source supplies power to a balanced wye-connected load. The line impedance per phase is 1 + j0 , and the load impedance per phase is 20 + j20 . If the source line voltage Vab is 100 0 V rms, find the line currents.

In a balanced three-phase wyewye system, the source is an abc-sequence set of voltages. The load voltage on the a phase is VAN = 120 60 V rms, Zline = 2 + j1.4 , and Zload = 10 + j10 . Determine the input voltages.

In a balanced three-phase wyewye system, the source is an abc-sequence set of voltages. Zline = 1 + j1 , Zload = 14 + j12 , and the load voltage on the a phase is VAN = 440 30 V rms. Find the line voltage Vab.

In a balanced three-phase wyewye system, the source is an abc-sequence set of voltages. The load voltage on the a phase is VAN = 110 80 V rms, Zline = 1 + j1.4 , and Zload = 10 + j13 . Determine the input sequence of the line-toneutral voltages.

A balanced abc-sequence of voltages feeds a balanced threephase wyewye system. The line and load impedances are 0.6 + j0 and 8 + j12 , respectively. The load voltage on the a phase is VAN = 116.63 10 V rms. Find the line voltage Vab.

In a balanced three-phase wyewye system, the source is an abc-sequence set of voltages. Zline = 1 + j1.8 , Zload = 14 + j12 , and the load voltage on the a phase is VAN = 398.1 17.99 V rms. Find the line voltage Vab.

In a balanced three-phase wyedelta system, the source has an abc phase sequence and Van = 120 40 V rms. The line and load impedances are 0.5 + j0.4 and 24 + j18 , respectively. Find the delta currents in the load

In a balanced three-phase wyewye system, the load impedance is 8 + j4 . The source has phase sequence abc and Van = 120 0 V rms. If the load voltage is VAN = 111.62 1.33 V rms, determine the line impedance.

In a balanced three-phase wyewye system, the total power loss in the lines is 400 W. VAN = 105.28 31.56 V rms and the power factor of the load is 0.77 lagging. If the line impedance is 2 + j1 , determine the load impedance.

In a balanced three-phase wyewye system, the load impedance is 10 + j1 . The source has phase sequence abc and the line voltage Vab = 22030 V rms. If the load voltage VAN = 120 0 V rms, determine the line impedance.

In a balanced three-phase wyewye system, the load impedance is 20 + j12 . The source has an abc-phase sequence and Van = 120 0 V rms. If the load voltage is VAN = 111.49 0.2 V rms, determine the magnitude of the line current if the load is suddenly short-circuited.

In a balanced three-phase wyewye system, the source is an abc-sequence set of voltages and Van = 120 40 V rms. If the a-phase line current and line impedance are known to be 7.10 10.28 A rms and 0.8 + j1 , respectively, find the load impedance.

In a balanced three-phase wyewye system, the source is an abc-sequence set of voltages and Van = 153.53 30.13 V rms. The load voltage on the a phase is 110.65 29.03 V rms and the load impedance is 16 + j20 . Find the line impedance

A balanced three-phase system has a balanced wye load in parallel with a balanced delta load. If the source is a balanced wye connection with a positive phase sequence and the phase voltage Van = 20030 V, determine the line currents when the load impedances, Z = 50 + j70 and ZY = 15 + j30 , are converted to an equivalent delta.

Repeat Problem 11.34 if the loads are converted to an equivalent wye. Compare the results of both problems.

A balanced wyedelta system with a positive phase sequence has a load current of IAB = 25 60 A. Determine all the line currents

In a balanced wyedelta system with a positive phase sequence, the load per phase is 20 + j10 . If the voltage Vab = 208 30 V, determine the line currents in the system.

A three-phase balanced system has a load consisting of a delta in parallel with a wye. The impedance per phase for the delta is 12 + j9 and for the wye is 6 + j3 . The source is a balanced wye with a positive phase sequence. If Van = 120 30 V, determine the line currents

Determine the line currents in Problem 11.38 if Vab = 100 60 V.

In a three-phase balanced deltadelta system, the source has an abc-phase sequence. The line and load impedances are 0.5 + j0.1 and 10 + j5 , respectively. If VAB = 115 30 V rms, find the phase voltage of the sources

In a balanced three-phase system, the source has an abcphase sequence and is connected in delta. There are two loads connected in parallel. Load 1 is connected in wye and has a phase impedance of 6 + j2 . Load 2 is connected in delta and has a phase impedance of 9 + j3 . The line impedance is 0.6 + j0.2 . Determine the phase voltages of the source if the current in the a phase of load 1 is I AN1 = 10 30 A rms.

An abc-phase-sequence three-phase balanced wye-connected 60-Hz source supplies a balanced delta-connected load. The phase impedance in the load consists of a 20- resistor series with a 20-mH inductor, and the phase voltage at the source is Van = 120 30 V rms. If the line impedance is zero, find the line currents in the system

In a balanced three-phase wyewye system, the source is an abc-sequence set of voltages and Van = 120 50 V rms. The load voltage on the a phase is 110 50 V rms, and the load impedance is 16 + j20 . Find the line impedance.

In a balanced three-phase deltawye system, the source has an abc-phase sequence. The line and load impedances are 0.6 + j0.3 and 12 + j7 , respectively. If the line current IaA = 9.6 20 A rms, determine the phase voltages of the source

In a three-phase balanced system, a delta-connected source supplies power to a wye-connected load. If the line impedance is 0.2 + j0.4 , the load impedance 6 + j4 , and the source phase voltage Vab = 210 40 V rms, find the magnitude of the line voltage at the load.

An abc-sequence set of voltages feeds a balanced threephase wyewye system. If Van = 440 30 V rms, VAN = 413.28 29.78 V rms, and Zline = 2 + j1.5 , find the load impedance.

An abc-phase-sequence three-phase balanced wye-connected source supplies a balanced delta-connected load. The impedance per phase of the delta load is 20 + j4 . If VAB = 115 35 V rms, find the line current.

In a three-phase balanced system, a delta-connected source supplies power to a wye-connected load. If the line impedance is 0.2 + j0.4 , the load impedance is 3 + j2 , and the source phase voltage Vab = 208 10 V rms, find the magnitude of the line voltage at the load.

In a balanced three-phase wyewye system, the source is an abc-sequence set of voltages and Van = 120 40 V rms. If the a-phase line current and line impedance are known to be 6 15 A rms and 1 + j1 , respectively, find the load impedance

An abc-phase-sequence three-phase balanced wye-connected source supplies a balanced delta-connected load. The impedance per phase in the delta load is 12 + j6 . The line voltage at the source is Vab = 120 3 40 V rms. If the line impedance is zero, find the line currents in the balanced wyedelta system.

An abc-phase-sequence three-phase balanced wye-connected source supplies power to a balanced delta-connected load. The impedance per phase in the load is 14 + j7 . If the source voltage for the a phase is Van = 120 80 V rms and the line impedance is zero, find the phase currents in the wye-connected source.

In a three-phase balanced deltadelta system, the source has an abc-phase sequence. The line and load impedances are 0.3 + j0.2 and 9 + j6 , respectively. If the load current in the delta is IAB = 15 40 A rms, find the phase voltages of the source

An abc-phase-sequence three-phase balanced wyeconnected source supplies a balanced delta-connected load. The impedance per phase of the delta load is 10 + j8 . If the line impedance is zero and the line current in the a phase is known to be IaA = 28.1028.66 A rms, find the load voltage VAB.

In a balanced three-phase wyedelta system, the source has an abc-phase sequence and Van = 1200 V rms. If the line impedance is zero and the line current IaA = 5 20 A rms, find the load impedance per phase in the delta.

A three-phase load impedance consists of a balanced wye in parallel with a balanced delta. What is the equivalent wye load and what is the equivalent delta load if the phase impedances of the wye and delta are 6 + j3 and 15 + j10 , respectively?

In a balanced three-phase system, the source is a balanced wye with an abc-phase sequence and Vab = 215 50 V rms. The load is a balanced wye in parallel with a balanced delta. The phase impedance of the wye is 5 + j3 , and the phase impedance of the delta is 18 + j12 . If the line impedance is 1 + j0.8 , find the line currents and the phase currents in the loads.

In a balanced three-phase system, the source has an abc-phase sequence and is connected in delta. There are two loads connected in parallel. The line connecting the source to the loads has an impedance of 0.2 + j0.1 . Load 1 is connected in wye, and the phase impedance is 4 + j2 . Load 2 is connected in delta, and the phase impedance is 12 + j9 . The current IAB in the delta load is 16 45 A rms. Find the phase voltage of the source.

A balanced three-phase delta-connected source supplies power to a load consisting of a balanced delta in parallel with a balanced wye. The phase impedance of the delta is 24 + j12 , and the phase impedance of the wye is 12 + j8 . The abc-phase-sequence source voltages are Vab = 440 60 V rms, Vbc = 440 60 V rms, and Vca = 440 180 V rms, and the line impedance per phase is1 + j0.08 . Find the line currents and the power absorbed by the wye-connected load.

Calculate the instantaneous power for a balanced threephase load in which the load current is 2 40 A rms and the load voltage is 240 0 V rms.

A three-phase positive sequence wye-connected source supplying 1.20 kVA with a power factor of 0.60 lagging has a line voltage Vab = 120 45 V rms and is connected to two balanced wye loads. If the first wye-connected load is purely inductive and uses 800 var, find the phase impedance of the second load.

Determine the magnitude of the current flowing through each of the loads in the network described in Problem 11.60.

A delta-connected three-phase source with a positive phase sequence is connected through a transmission line with an impedance of 0.05 + j0.1 per phase to a wye-connected load with a per-phase impedance of 20 + j8 . The source voltages are Vab = 208 40 V rms, Vbc = 208 80 V rms, and Vca = 208 200 V rms. Determine the line currents, the magnitude of the line voltage at the load, and the real power loss in the lines

A balanced three-phase wyewye system has two parallel loads. Load 1 is rated at 4000 VA, 0.9 pf lagging, and load 2 is rated at 3600 VA, 0.85 pf lagging. If the line voltage is 208 V rms, determine the magnitude of the line current.

In a balanced three-phase system, the abc-phase-sequence source is wye-connected and Van = 120 20 V rms. The load consists of two balanced wyes with phase impedances of 8 + j2 and 12 + j3 . If the line impedance is zero, find the line currents and the phase current in each load.

In a balanced three-phase deltadelta system, the source has an abc-phase sequence. The phase angle for the source voltage is Vab = 40 and Iab = 4 15 A rms. If the total power absorbed by the load is 1400 W, find the load impedance.

In a balanced three-phase system, the source is a balanced wye with an abc-phase sequence and Vab = 208 60 V rms. The load consists of a balanced wye with a phase impedance of 8 + j5 in parallel with a balanced delta with a phase impedance of 21 + j12 . If the line impedance is 1.2 + j1 , find the phase currents in the balanced wye load.

In a balanced three-phase system, the source has an abcphase sequence and is connected in delta. There are two parallel wye-connected loads. The phase impedance of load 1 and load 2 is 4 + j4 and 10 + j4 , respectively. The line impedance connecting the source to the loads is 0.3 + j0.2 . If the current in the a phase of load 1 is I AN1 = 10 20 A rms, find the delta currents in the source

An abc-phase-sequence balanced three-phase source feeds a balanced load. The system is connected wyewye and Van = 0. The line impedance is 0.5 + j0.2 , the load impedance is 16 + j10 , and the total power absorbed by the load is 2000 W. Determine the magnitude of the source voltage Van.

The magnitude of the complex power (apparent power) supplied by a three-phase balanced wyewye system is 3600 VA. The line voltage is 208 V rms. If the line impedance is negligible and the power factor angle of the load is 25, determine the load impedance.

An abc-sequence wye-connected source having a phase-a voltage of 120 0 V rms is attached to a wye-connected load having a per-phase impedance of 100 70 . If the line impedance is 1 20 , determine the total complex power produced by the voltage sources and the real and reactive power dissipated by the load.

A three-phase balanced wyewye system has a line voltage of 208 V rms. The line current is 6 A rms and the total real power absorbed by the load is 1800 W. Determine the load impedance per phase if the line impedance is negligible

A three-phase abc-sequence wye-connected source supplies 14 kVA with a power factor of 0.75 lagging to a delta load. If the delta load consumes 12 kVA at a power factor of 0.7 lagging and has a phase current of 10 30 A rms, determine the per-phase impedance of the load and the line

In a balanced three-phase wyewye system, the source is an abc-sequence set of voltages and Van = 120 30 V rms. The power absorbed by the load is 3435 W and the load impedance is 10 + j2 . Find the two possible line impedances if the power generated by the source is 3774 W. Which line impedance is more likely to occur in an actual power transmission system?

Two small industrial plants represent balanced three-phase loads. The plants receive their power from a balanced threephase source with a line voltage of 4.6 kV rms. Plant 1 is rated at 300 kVA, 0.8 pf lagging, and plant 2 is rated at 350 kVA, 0.8 pf lagging. Determine the power line current.

A cluster of loads is served by a balanced three-phase source with a line voltage of 4160 V rms. Load 1 is 240 kVA at 0.8 pf lagging and load 2 is 160 kVA at 0.92 pf lagging. A third load is unknown except that it has a power factor of unity. If the line current is measured and found to be 62 A rms, find the complex power of the unknown load.

A three-phase abc-sequence wye-connected source supplies 14 kVA with a power factor of 0.75 lagging to a parallel combination of a wye load and a delta load. If the wye load consumes 9 kVA at a power factor of 0.6 lagging and has an a-phase current of 10 30 A rms, determine the phase impedance of the delta load.

In a balanced three-phase system, the source has an abcphase sequence, is wye-connected, and Van = 120 20 V rms. The source feeds two parallel loads, both of which are wye-connected. The impedance of load 1 is 8 + j6 . The complex power for the a phase of load 2 is 600 36 VA. Find the line current for the a phase and the total complex power of the source.

A balanced three-phase source serves the following loads: Load 1: 60 kVA at 0.8 pf lagging Load 2: 30 kVA at 0.75 pf lagging The line voltage at the load is 208 V rms at 60 Hz. Determine the line current and the combined power factor at the load.

A balanced three-phase source serves two loads: Load 1: 36 kVA at 0.8 pf lagging Load 2: 18 kVA at 0.6 pf lagging The line voltage at the load is 208 V rms at 60 Hz. Find the line current and the combined power factor at the load.

A balanced three-phase source supplies power to three loads. The loads are Load 1: 30 kVA at 0.8 pf lagging Load 2: 24 kW at 0.6 pf leading Load 3: unknown The line voltage at the load and line current at the source are 208 V rms and 166.8 A rms, respectively. If the combined power factor at the load is unity, find the unknown load

A balanced three-phase source serves the following loads: Load 1: 18 kVA at 0.8 pf lagging Load 2: 10 kVA at 0.7 pf leading Load 3: 10 kW at unity pf Load 4: 16 kVA at 0.6 pf lagging The line voltage at the load is 208 V rms at 60 Hz, and the line impedance is 0.02 + j0.04 . Find the line voltage and power factor at the source.

A balanced three-phase source supplies power to three loads. The loads are Load 1: 24 kVA at 0.6 pf lagging Load 2: 10 kW at 0.75 pf lagging Load 3: unknown If the line voltage at the load is 208 V rms, the magnitude of the total complex power is 35.52 kVA, and the combined power factor at the load is 0.88 lagging, find the unknown load

A balanced three-phase source serves the following loads: Load 1: 20 kVA at 0.8 pf lagging Load 2: 10 kVA at 0.7 pf leading Load 3: 10 kW at unity pf Load 4: 16 kVA at 0.6 pf lagging The line voltage at the load is 208 V rms at 60 Hz, and the line impedance is 0.02 + j0.04 . Find the line voltage and power factor at the source.

A small shopping center contains three stores that represent three balanced three-phase loads. The power lines to the shopping center represent a three-phase source with a line voltage of 13.8 kV rms. The three loads are Load 1: 400 kVA at 0.9 pf lagging Load 2: 200 kVA at 0.85 pf lagging Load 3: 100 kVA at 0.90 pf lagging Find the power line current.

The following loads are served by a balanced three-phase source: Load 1: 20 kVA at 0.8 pf lagging Load 2: 4 kVA at 0.8 pf leading Load 3: 10 kVA at 0.75 pf lagging The load voltage is 208 V rms at 60 Hz. If the line impedance is negligible, find the power factor at the source.

A balanced three-phase source supplies power to three loads: Load 1: 30 kVA at 0.8 pf lagging Load 2: 24 kW at 0.6 pf leading Load 3: unknown If the line voltage and total complex power at the load are 208 V rms and 60 0 kVA, respectively, find the unknown load.

A balanced three-phase source supplies power to three loads: Load 1: 24 kW at 0.8 pf lagging Load 2: 10 kVA at 0.7 pf leading Load 3: unknown If the line voltage at the load is 208 V rms, the magnitude of the total complex power is 41.93 kVA, and the combined power factor at the load is 0.86 lagging, find the unknown load.

Find the value of C in Fig. P11.88 such that the total load has a power factor of 0.87 lagging. C Balanced C C three-phase source 60 Hz Balanced three-phase load 20 MVA 0.707 pf lagging 34.5 kV rms + Figure P11.88

Find C in the network in Fig. P11.89 so that the total load has a power factor of 0.9 leading. C C C 4.6 kV rms Balanced three-phase source 60 Hz Balanced three-phase load 6 MVA 0.8 pf lagging + Figure P11.89

A three-phase abc-sequence wye-connected source with Van = 2200 V rms supplies power to a wyeconnected load that consumes 50 kW of power in each phase at a pf of 0.8 lagging. Three capacitors are found that each have an impedance of j2.0 , and they are connected in parallel with the load in a wye configuration. Determine the power factor of the combined load as seen by the source.

If the three capacitors in the network in Problem 11.90 are connected in a delta configuration, determine the power factor of the combined load as seen by the source.

Find C in the network in Fig. P11.92 such that the total load has a power factor of 0.87 leading. C Balanced C C three-phase source 60 Hz Balanced three-phase load 20 MVA 0.707 pf lagging 34.5 kV rms + Figure P11.92

Find C in the network in Fig. P11.93 such that the total load has a power factor of 0.9 lagging. C C C 4.6 kV rms Balanced three-phase source 60 Hz Balanced three-phase load 6 MVA 0.8 pf lagging + Figure P11.93

A standard practice for utility companies is to divide customers into single-phase users and three-phase users. The utility must provide three-phase users, typically industries, with all three phases. However, single-phase users, residential and light commercial, are connected to only one phase. To reduce cable costs, all single-phase users in a neighborhood are connected together. This means that even if the three-phase users pre sent perfectly balanced loads to the power grid, the single-phase loads will never be in balance, resulting in current flow in the neutral connection. Consider the 60-Hz, abc-sequence network in Fig. P11.94. With a line voltage of 416 30 V rms, phase a supplies the single-phase users on A Street, phase b supplies B Street, and phase c supplies C Street. Furthermore, the three-phase industrial load, which is connected in delta, is balanced. Find the neutral current.