Download Homework 13B

ECE 252 Introduction to Electrical Engineering
Lesson 13B. Three-Phase Power Homework
Version S17
Homework partner name: _______________________Homework partner name: ________________________
1. Quickies
a) A motor in a balanced three-phase system consumes 90 kW at 75% power factor lagging. Assuming no losses
in the power lines, the power provided by the generator is _______________ kW.
b) A motor in a balanced three-phase system consumes 70 kW at 85% power factor lagging. Write an expression
for the power consumed in the motor as a function of time.
c) In a “star” configuration, the center point of a Y-connected generator is ______________________.
d) A Y-connected motor in a balanced three-phase system consumes 30 kW at 67% power factor lagging. The
power consumed in one phase of the load is _______________ kW.
e) The ________________ in an unbalanced three-phase system is usually measured using the two-wattmeter
method.
f) Three-phase power transmission is (more efficient than, less efficient than, the same efficiency as) singlephase power transmission.
g) In a (an) _______________ three-phase system, the currents in all three phases are the same magnitude.
Signatures: ________________________________________________________________________
2. Each of the Vs voltages in the figure below is 277 V (rms). Each voltage is 120° out of phase with each other
Vs voltage. R = 50 Ω, ZL = j130 Ω. (a) Find the rms magnitude of the current in any line. (b) Find the total power
consumed by the load. Note: Do not do a phasor analysis of this circuit. Use the magnitude of the net impedance
to find the phase current.
(a)
(b)
Signatures: ________________________________________________________________________
3. A three-phase load is Y-connected. The load has a phase voltage of 220 V and a phase current of 20 A. Each
phase of the load consumes 4 kW of power. (a) Sketch and label the load. Find (b) the line voltage, (c) the line
current, and (d) the total power consumed in the load. (e) What is the power factor of the load?
(a)
(b)
(c)
(d)
(e)
Signatures: ________________________________________________________________________
4. A three-phase generator is Y-connected. It has phase voltages of 346.4 V. A delta-connected load is attached to
the lines coming from the generator. Each phase of the load has an impedance of 11/53° Ω. (a) Sketch and label
the circuit. Find (b) the magnitude of the phase current in the load, (c) the line current, and (d) the total power
consumed by the load.
(a)
(b)
(c)
(d)
Signatures: ________________________________________________________________________
5. A balanced three-phase motor is delta-connected. It is connected to three-phase lines with line voltage of 220
V. The power is provided by a Y-connected three-phase generator. The motor uses 25 kW of power at 79% power
factor lagging. (a) Sketch and label the circuit. (b) What is the line current? (c) What is the phase voltage of the
generator?
(a)
(b)
(c)
Signatures: ________________________________________________________________________
BONUS (no partial credit): In Problem 4, solve if each wire in the transmission line has a resistance of 1 Ω. (Hint:
Use delta-Y transformation.)
(a)
(b)
(c)
(d)
Signatures: ________________________________________________________________________