Two three-phase generators are supplying the same load bus, as shown in Figure P

2 Three-Phase Circuits

2.28 Two three-phase generators are supplying the same load bus, as shown in Figure P

Both generators produce balanced voltages of abc phase sequence. Use Va = 120∠0° V and Va′=115∠ °0 V as the reference voltages for the left and right generators in the figure, FIGURE P2.28 Circuit of Problem 2.28.

respectively. If a balanced three-phase load is connected in the middle of the bus, as shown in the figure, determine the following:

(a) The phasor currents Ia, Ia′, and Ia″ (Hint: First convert the delta-connected load into its equivalent wye-connected load and then apply the nodal analysis method using the line-to-neutral approach since both the generators and the load are balanced.)

(b) The total complex power supplied to the load (c) The line-to-line voltage at the terminals of the load

(d) The complex power supplied by the left generator to the bus (e) The complex power supplied by the right generator to the bus

2.29 Solve Example 2.5, but use the following data. Let Zab = 6 − j6 Ω, Zbc = 0 + j6 Ω, Zca = 6 + j6 Ω, and use a line impedance ZL = 3 + j3 Ω per phase. Use Va b′ ′=120 0∠ °V, Vb c′ ′=120 240∠ °V and Vc a′ ′=120 120∠ °V as the balanced source voltages.

2.30 Consider Figure P2.30 and assume that the balanced delta-connected load is made up of three impedances of Z_ϕ = 27.71∠−40° Ω per phase and that source voltages Va, Vb, and Vc

are 277.1∠0°, 277.1∠− 120°, and 277.1∠120° V, respectively. Determine the following:

(a) The load voltages V1, V2, and V3

(b) The load (phase) currents I1, I2, and I3

2.31 Solve Example 2.7, but use the following data. Assume that Vab = 480∠0° V, and that the load impedances Zab, Zbc, and Zca are given as 20∠30°, 10∠ − 60°, and 15∠45° Ω, respectively.

2.32 A balanced and delta-connected, three-phase voltage source is supplying power to a balanced and delta-connected, three-phase load, as shown in Figure P2.32. The source voltages Vab, Vbc, Vca are 208∠30°, 208∠270°, and 208∠150° V, respectively. The load impedances are

FIGURE P2.30 Circuit of Problem 2.30.

I_a a

FIGURE P2.32 Circuit of Problem 2.32.

2.33 An unbalanced, phase, wire, wye-connected load is connected to a balanced, three-phase, wye-connected source, and only two wattmeters are used and connected, as shown in Figure P2.8. The line-to-neutral source voltages Va, Vb, and Vc are 220∠30°, 220∠270°, and 220∠150° V, respectively, and the line currents Ia, Ib, and Ic are 71.62∠ − 11°, 61.28∠16.2°, and 13.26∠133.6° A, respectively. Determine the following:

(a) The power recorded on each wattmeter (b) The total power absorbed by the load

2.34 Consider Figure P2.32 and assume that a delta-connected source is supplying power to a delta-connected balanced load. If the generator has Vab = 480∠30° V, Vbc = 480∠270° V, Vca = 480∠150° V, and load impedances of Zab = Zbc = Zca = 5 + j5 Ω, determine the following:

(a) The load (phase) currents Iab, Ibc, and Ica. (b) The line currents Ia, Ib, and Ic.

(d) The total complex power supplied to the load.

(e) Draw the current and voltage diagrams.

2.35 Consider Figure P2.32 and assume that a delta-connected source is supplying power to a delta-connected balanced load. If the generator has Vab = 380∠30° V, Vbc = 380∠270° V, Vca = 380∠150° V and load impedances of Zab = Zbc = Zca = 2 + j3 Ω, determine the following:

(a) The load (phase) currents Iab, Ibc, and Ica. (b) The line currents Ia, Ib, and Ic.

(d) The total complex power supplied to the load.

(e) Draw the current and voltage diagrams.

2.36 Assume that a three-phase, 480 V power line is supplying a delta-connected load and that Vab = 480∠30° V, Vbc = 480∠270° V, Vca = 480∠150° V. Also assume that the current in each phase of the delta-connected load is 10 A at a 0.85 lagging power factor. If Van is used as a reference phasor and the phase sequence is abc, determine the following:

(a) Draw the circuit, as given.

(b) The line-to-line voltages of Vab, Vbc, and Vca. (c) The line-to-neutral voltages of Van, Vbn, and Vcn. (d) All phase and line currents.

(e) Draw the phasor diagram for the phase and line voltages.

(f) Draw the phasor diagram for the phase and line currents.

2.37 Assume that a three-phase, 380 V power line is supplying a delta-connected load and that Vab = 380∠30° V, Vbc = 380∠270° V, and Vca = 380∠150° V. Also assume that the current in each phase of the delta-connected load is 5 A at a 0.75 lagging power factor. If Van is used as a reference phasor and the phase sequence is abc, determine the following:

(a) Draw the circuit, as given.

(b) The line-to-line voltages of Vab, Vbc, and Vca. (c) The line-to-neutral voltages of Van, Vbn, and Vcn. (d) All phase and line currents.

(e) Draw the phasor diagram for the phase and line voltages.

(f) Draw the phasor diagram for the phase and line currents.

2.38 A 2.4 kV, single-phase circuit supplies a load of 250 kW at a lagging power factor, and the load current is 160 A. If it is necessary to improve the power factor, determine the following:

(a) The uncorrected power factor and reactive load

(b) The new corrected power factor after installing a shunt capacitor unit with a rating of 250 kvar

2.39 A three-phase, 50 hp, 60 Hz, 480 V, wye-connected induction motor has a full-load efficiency of 0.85%, and a lagging power factor of 0.75. If it is required to correct the power factor of the load to a lagging power factor of 0.95 by connecting three capacitors, find the following:

(a) The rating of such a capacitor bank, in kVA

(b) The capacitance of each single-phase unit, if the capacitors are connected in delta, in μF (c) The capacitance of each single-phase unit, if the capacitors are connected in wye, in μF 2.40 Redo Example 2.4 (except part c) by using MATLAB^®. Use the other given values and

deter-mine the following:

(a) Write the MATLAB program script.

(b) Give the MATLAB program output.

2.41 Redo Example 2.6 by using MATLAB. Use the other given values and determine the following:

(a) Write the MATLAB program script.

(b) Give the MATLAB program output.

In document TURAN GONEN-Electrical Machines With MATLAB Second Edition (Page 71-75)