Concept explainers
A certain store contains three balanced three-phase loads. The three loads are:
Load 1: 16kVA at 0.85 pf lagging
Load 2: 12 kVA at 0.6 pf lagging
Load 3: 8 kW at unity pf
The line voltage at the load is 208 V rms at 60 Hz, and the line impedance is
Find the line currents and the complex power delivered to the loads.
Answer to Problem 69P
The line currents
The complex power delivered to the loads is
Explanation of Solution
Given data:
The given three balanced three-phase loads are,
The reactive power of the Load 1 is
The reactive power of the Load 2 is 12 kVA and the power factor is 0.6 (lagging).
The real power of the Load 3 is
The line voltage at the load is
The line impedance is
Formula used:
Write the expression to find the complex power
Here,
Write the expression to find the average power
Here,
Write the expression to find the reactive power
Write the expression to find the complex power of the Load 2.
Here,
Write the expression to find the real power of the Load 2.
Here,
Write the expression to find the reactive power of the Load 2.
Write the expression to find the complex power of the Load 3.
Here,
Write the expression to find the real power of the Load 3.
Here,
Write the expression to find the reactive power of the Load 3.
Write the expression to find the total complex power.
Here,
Write the expression to find the phase voltage.
Here,
Write the expression to find the line to neutral voltage
Here,
Write the expression to find the complex power
Here,
Write the expression to find the line current
Here,
Write the expression to find the line current
Calculation:
The given lagging power factor of the Load 1 is,
Rewrite the above equation to find the angle
Substitute
Substitute
Substitute
The given lagging power factor of the Load 2 is,
Rearrange the above equation to find the angle
Substitute
Substitute
Substitute
The given unity power factor of the Load 3 is,
Rewrite the above equation to find the angle
Substitute
Rewrite the above equation to find
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Re-write the above equation to find the current
The complex current
The line current
Substitute
Substitute
Conclusion:
Thus,
The line currents
The complex power delivered to the loads is
Want to see more full solutions like this?
Chapter 12 Solutions
EBK FUNDAMENTALS OF ELECTRIC CIRCUITS
- 2. For the following system shown in the figure, calculate: a. The current through each phase of the load. b. The total real and reactive power of the three-phase load. c. The power factor at the load side. A 220 V 20° 220VL-120° U8 vol 152 I 220 VI20° 9. M.arrow_forwardThe output of the balanced positive-sequence three-phase source in the figure is 64 kVA at a lagging factor of 0.8. The line voltage at the source is 256/3 V. power (Figure 1) Find the magnitude of the line voltage at the load. Express your answer in volts to three significant figures. Figure Balanced three-phase source 0.04 2 w 10,2 2 m 0.04 0.2 0 0.04 w 10,2 2 Balanced three-phase load 1 of 1 |VAB= Submit Request Answer Part B V Find the total complex power at the terminals of the load. Express your answer in volt-amperes to three significant figures. Enter your answer in rectangular form. S= Submit Request Answer VAarrow_forwardTwo parallel connected loads A and B are supplied by a 440 V line to line, 3-phase, 60 Hz generator. Load A draws an apparent power of 100 kVA at 0.80 pf lagging and load B draws an apparent power of 70 kVA at unity pf. Determine the line current supplied by the source.arrow_forward
- Consider the following three phase balanced circuit. 21020° Vrms j0.5 N rell 24- j21 N 210Z-120° Vrms j0.5 N 24- j21 2 12 rell 24- j21 2 210/120° Vrms j0.5 N rell Find average power dissipated by the delta connected load. (a) 8587.18 W (b) -8587.18 W (c) 7514.41 W (d) -7514.41 warrow_forwardDraw Wye- Delta three phase transformers connection ( no-load and full-load) in Lt-spicearrow_forwardIn the circuit in the figure; L1 load draws 15 kVA with lagging power factor 0.6. The L2 load draws 6 kVA with a leading power factor of 0.8. According to this; What is the value of the complex power for the L2 load?arrow_forward
- A Y-connected balanced three-phase source is connected to a three-phase balanced load through a four-wire three-phase cable. The generator has an impedance of 0.1+j0.3 Q/phase. Each phase of the cable has an impedance of 2+2j 2 The phase "B" load voltage is 102-140° kV. The impedance of each phase of the Y-connected load is 3-j5 Q/phase. For a negative sequence: 1- tto pointe) Calculate "terminal" phase voltage of phases "a" and "c" of generator. 2- E points] Calculate Vab and Vca across the load. 5 points Calculate three phase power supplied by the source. 4- 10 point] Calculate three phase power losses.arrow_forwardThere is an installation with two equal three-phase loads of 150 kW each and a power factor of 0.9 in lagging. By connecting a pure reactive element in parallel, the reactive power at the input of the installation is 160 kVARS, with a lagging power factor. It can be said that:A)Capacitors were connected and the fp improved. B) Capacitors were connected and the fp improved. C) Reactors were connected and the fp improved. D)Reactors were connected and fp improved. E) None of the abovearrow_forwardThe following loads are served by a balanced three-phase source: Load 1: 18 kVA at 0.8 pf lagging Load 2: 8 kVA at 0.8 pf leading Load 3: 12 kVA at 0.75 pf lagging. Give the complex power expression for Load 3. Select one: O a. 29.80 +j13.94 O b. O c. 9.00+ j7.94 kVA 6.40 -j4.80 KVA O d. 32.90225.07° KVA O e. 14.40 +j10.80 kVAarrow_forward
- 2. Three-Phase SystemThree loads are connected in parallel to a 12.47 kV, 60 Hz three-phase supply.Load 1: Inductive load, 60 kW and 660 KVARLoad 2: Capacitive load, 240 kW at 0.8 . power factorLoad 3: Resistive load 60 kWDefine:a. Active power, reactive power and total apparent power?b. Total power factor ?c. What is the total supply current?A Y-connected capacitor bank, connected in parallel withload, to improve the overall power factor to 0.95 lagging.Define:d. Total capacitor capacity (KVAR)?e. Capacitance of a phased capacitor (UF)?f. How big is the line current after the capacitor bank is installed?arrow_forwardTwo balanced three phase loads are connected in parallel, the loads are L1= 20 kW at 0.7 pf lead, and L2= 12 kVA at 0.9 pf lag. The loads are fed from a distribution line with an impedance of 0.05+j0.2 Q/P. The line to neutral voltage at the load end is 203 V and zero phase shift, the capacitance of A-connected capacitor bank that connected parallel to the loads to improve the power factor to unity in uF is; (f=60 Hz) O A. None B. 325.49 O C. 976.48 O D. 108.50 O E. 36.17arrow_forwardIn a three-phase balanced Y-Y system, the source phase currents have a magnitude of 9 A. The magnitude of the current on each load is Select one: O a. 9A O b. 12 A O c. None of these O d. 27 A In a three phase Y connected generator, the phase voltages are 2 kV. The magnitudes of the line voltages are Select one: O a. 3464.1 V O b. 6000 V Oc. 2000 V O d. 1154.7 Varrow_forward
- Power System Analysis and Design (MindTap Course ...Electrical EngineeringISBN:9781305632134Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. SarmaPublisher:Cengage Learning