Derive an equation for the total instantaneous power absorbed by a balanced three-phase load. Be sure to clearly list any assumptions you make in your derivation.
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- Consider a load impedance of Z=jwL connected to a voltage and V let the current drawn be I. (a) Develop an expression for the reactive power Q in terms of ,L, and I, from complex power considerations. (b) Let the instantaneous current be i(t)=2Icos(t+). Obtain an expression for the instantaneous power p(t) into L, and then express it in terms of Q. (c) Comment on the average real power P supplied to the inductor and the instantaneous power supplied.A balanced -connected impedance load with (12+j9) per phase is supplied by a balanced three-phase 60-Hz,208-V source, (a) Calculate the line current, the total real and reactive power absorbed by the load, the load power factor, and the apparent load power, (b) Sketch a phasor diagram showing the line currents, the line-to-line source voltages, and the -load currents. Use Vab as the reference.Under 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.
- For the circuit element of Problem 2.3, calculate (a) the instantaneous power absorbed, (b) the real power (state whether it is delivered or absorbed). (c) the reactive power (state whether delivered or absorbed). (d) the power factor (state whether lagging or leading). [Note: By convention the power factor cos() is positive. If | | is greater than 90, then the reference direction for current may be reversed, resulting in a positive value of cos() ].A single-phase source is applied to a two-terminal, passive circuit with equivalent impedance Z=3.045, measured from the terminals. The source current is i(t)=22cos(t)kA. Determine the (a) instantaneous power, (b) real power, (c) reactive power delivered by the source, and (d) source power factor.Let a series RLC network be connected to a source voltage V, drawing a current I. (a) In terms of the load impedance Z=ZZ, find expressions for P and Q, from complex power considerations. (b) Express p(t) in terms of P and Q, by choosing i(t)=2Icost. (c) For the case of Z=R+jL+1/jC, interpret the result of part (b) in terms of P,QL, and Qc. In particular, if 2LC=1, when the inductive and capacitive reactances cancel, comment on what happens.
- Consider a single-phase load with an applied voltage v(t)=150cos(t+10)volts and load current i(t)=5cos(t+50)A. (a) Determine the power triangle. (b) Find the power factor and specify whether it is lagging or leading. (c) Calculate the reactive power supplied by capacitors in parallel with the load that correct the power factor to 0.9 lagging.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.While the instantaneous electric power delivered by a single-phase generator under balanced steady-state conditions is a function of time havi ng two components of a constant and a double-frequency sinusoid, the total instantaneous electric power delivered by a three-phase generator under balanced steady-state conditions is a constant. (a) True (b) False
- The three-phase source line-to-neutral voltages are given by Ean=100,Ebh=10+240, and Ecn=10240volts. Is the source balanced? (a) Yes (b) NoA single-phase, 120V(rms),60Hz source supplies power to a series R-L circuit consisting of R=10 and L=40mH. (a) Determine the power factor of the circuit and state whether it is lagging or leading. (b) Determine the real and reactive power absorbed by the load. (c) Calculate the peak magnetic energy Wint stored in the inductor by using the expression Wint=L(Irms)2 and check whether the reactive power Q=Wint is satisfied. (Note: The instantaneous magnetic energy storage fluctuates between zero and the peak energy. This energy must be sent twice each cycle to the load from the source by means of reactive power flows.)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.