Basic Engineering Circuit Analysis
11th Edition
ISBN: 9781118539293
Author: J. David Irwin, R. Mark Nelms
Publisher: WILEY
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Two balanced loads are connected to a 240-kV rms 50-Hz line. Load 1 draws 30 kW at a power factor of 0.6 lagging, while load 2 draws 45 kVAr at a power factor of 0.8 lagging. Assuming the RYB sequence, determine: (a) the complex, real, and reactive powers absorbed by the combined load, (b) the line currents, and (c) the kVAr rating of the three capacitors ∆-connected in parallel with the load that will raise the power factor to 0.9 lagging and the capacitance of each capacitor.
Verify the results by creating a MATLAB Simulink model and program. Obtain the plots for the currents and voltages
A 3-phase Y-connected load draws power from a 3-phase Y-connected source. The source voltage, ?=440∠0º?_rms and the load impedance, Z_y=(30+j15) Ω. The line impedance, Z_line= (1+j1)Ω and the system operates at 60 Hz.
a) Draw the single-phase equivalent circuit and label all given quantities numerically.
b) Calculatethe rms line (phase) current phasor in each phase.
c) Calculate the total active or real power supplied by the source.
d) Calculate the total active or real power consumed by the load.
e) Calculate the total line loss i.e. the total activepower lost due to line.
f) Determine the power efficiency of the system.
Under balanced operating conditions, consider the 3-phase complex power delivered by the 3-phase source to the 3-phase load. Match the following expressions, those on the left to those on the right. 0) Real power, Py (ii) Reactive power, Qu (ii) Total apparent power Sy (iv) Complex power, Sy (a) (V3 VLL. IL)VA (b) (V3 Vu sng) var (e) (V3 VLL. IL cos ø) W (d) Py +Qy Note that VLL is the rms line-to-line voltage, IL is the ms line current, and o is the power-factor angle.
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- 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.arrow_forwardA 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.arrow_forwardUnder 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.arrow_forward
- 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.arrow_forwardA three-phase line has an impedance of 1 + j3 Ω per phase. The line feeds a balanced delta-connected load, which absorbs a total complex power of 12 + j5 kVA. The line voltage at the load end has a magnitude of 250 V. Find the source power factor. The source power factor pf = Please answer in typing format pleasearrow_forwardA balanced three phase wye-delta system, the source has abc sequence and Van = 124 40 V rms. If the line impedance is 0,5 +j0.4 G and load impedance is 24 +18 G. Calculate the delta load currents and the real (P) and reactive (Q) powers at each phase of the load. ..arrow_forward
- A balanced delta connected load of "14+j19" 2- per phase is connected at the end of a three-phase line. The line impedance is "6+18j" 2- per phase. The line is supplied from a three-phase source with a line-to-line voltage of 207.85 Vrms. Taking phase "a" voltage Va as reference, determine the following: (a) Current in phase a. (b) Total complex power supplied from the source. (c) Magnitude of the line-to-line voltage at the load terminal.arrow_forwardIn a balanced Y-Delta connection the magnitude of the line voltages VL = 1500 V (rms), the load impedance per phase Z= 75 + j33 Ω, and the phase angle of Van = 00. Find the phase voltages, line voltages, phase currents, and line currents. Find also the complex power, apparent power, average power, reactive power, and power factor of the load.arrow_forwardGiven: 1. 2 wye-connected loads per phase to a 3 phase power source 2. first load consists of a 55ohm resistance and a 0.05H inductance per phase 3. second load consumes 1kW and power factor of 0.7 lagging per phase 4. RMS of voltage across the loads are 220V, frequency 120Hz per phase 5. single phase equivalent is shown in the figure: Question: What are the RMS line current at load 1 and 2 respectively?arrow_forward
- Three balanced three-phase loads are connected in parallel. Load 1 is Y-connected with an impedance of 400+j300 Ω/ϕ; load 2 is Δconnected with an impedance of 2400+j1800 Ω/ϕ; and load 3 is 172.8+j2203.2 kVA. The loads are fed from a distribution line with an impedance of 2+j16 Ω/ϕ. The magnitude of the line-to-neutral voltage at the load end of the line is 243 kV. 1. a) Calculate the total complex power at the sending end of the line. 2. b) What percentage of the average power at the sending end of the line is delivered to the loads?arrow_forwardThree symmetrical three-phase loads are connected in parallel. Load 1 is connected in Y with an impedance of 400 + j300Ω / φ, load 2 is connected in with with an impedance of 2400 - j1800Ω / φ and load 3 is evaluated at 172.8 + j2203.2 kVA. Loads are supplied from a distribution line with an impedance of 2 + j16Ω / φ. Size of the voltage between the line and the neutral conductor at the end of the charge the line is 24√3 kV. The operating frequency is 50 Hz.(a) Calculate the line currents and the phase currents of the loads.(b) Calculate the total complex power at the receiving end of the system.(c) Calculate the total complex power at the transmitting end of the line.(d) Calculate the values of the compensation capacitors which are connected from the line to the neuron at the load end of the system so that the power factor at the load end reaches pf ≥ 0.98.(e) What if the capacitors are connected from one line to another? What would be the best choice for compensation, the…arrow_forwardA three-phase Δ-connected generator has an internal impedance of 9+j90 m Ω/ϕ. When the load is removed from the generator, the magnitude of the terminal voltage is 13,800 V. The generator feeds a Δconnected load through a transmission line with an impedance of 20+j180 m Ω/ϕ. The per-phase impedance of the load is 7.056+j3.417 Ω. Calculate the magnitude of the line current.arrow_forward
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