Ebook Electric circuit analysis: Part 2

Part 2 book "Electric circuit analysis" includes content: Sinusoidal steady state in three phase circuits, dynamic circuits with periodic inputs – analysis by fourier series, first order RL circuits; first order RC circuits; series and parallel RLC circuits, analysis of dynamic circuits by laplace transforms, magnetically coupled circuits.
Nội dung trích xuất từ tài liệu:
Ebook Electric circuit analysis: Part 2   8.1 Chapter 8SinusoidalSteady-StateinThree-PhaseCircuitsCHAPTEROBJECTIVES • Todefineandexplainbalancedandunbalancedthree-phasesystemsandtoextendthe conceptsofactivepower,reactivepowerandcomplexpowertosuchsystems. • TodevelopandemployrelationsbetweenlineandphasequantitiesinY-connectedand D-connectedthree-phasecircuits. • Toemphasizeconstraintsonlinequantitiesinthree-phasethree-wireandfour-wiresystems. • Todevelopasystematicproceduretoanalysesinusoidalsteady-stateinthree-phasebalanced circuitsusingY-equivalentandsingle-phaseequivalentcircuits. • Toshowhowtousephasors,phasorequivalentcircuitsandphasordiagramsforsolving three-phasecircuitsundersinusoidalsteady-statecondition. • Tointroduceandillustratetheproblemofneutral-shiftvoltageinfour-wiresystems. • Toillustratecircuitanalysisproceduresforunbalancedthree-phasecircuitanalysisthrough solvedexamples. • Tointroduceandexplainsymmetricalcomponentsindetailanduseitinanalysisof unbalancedcircuits. • Todeveloppowerrelationsusingsequencecomponents.IntroductIonElectrical power generation, transmission and distribution employ a particular system of threesinusoidal voltages/currents with certain symmetry in voltage/current magnitude and relative phase.This system of three sinusoidal voltage/current waveforms is called a three-phase voltage/current and8.2  SinusoidalSteady-StateinThree-PhaseCircuitsa circuit employing a three-phase voltage/current system is called a three-phase circuit. A three-phasecircuit, like any other circuit, will have to go through a transient period subsequent to the applicationof source functions before it can settle down to a sinusoidal steady-state condition. We focus onanalysis of three-phase circuits under sinusoidal steady-state condition in this chapter. No new concepts are required for analysis of three-phase circuits under sinusoidal steady-stateconditions. It requires only the application of all the concepts we developed in the last two chapters.But before we take up the analysis of three-phase circuits, let us see why electrical engineers thoughtup three-phase system in the first place.8.1  three-Phase system Versus sIngle-Phase systemIndustrial heaters are used in various material processing industries for a variety of heatingapplications. Typically, heater boxes that contain heating elements powered by AC supply, transfer theheat developed to a gaseous (usually air) or liquid medium which conducts the heat to the material thatis to be heated up. Resistor elements made of some specially constructed wire are laid out uniformlyinside the heater box to develop uniform heating of the contact surface. Many such heating elementsare finally connected in parallel to form the heater resistive load. Consider such a heater which, afterall parallel connection of sub-elements, is finally represented by three equal resistors of R each. Thesethree resistors may be connected in parallel and supplied from a single-phase AC source or they maybe supplied individually from different AC sources – for instance, for redundancy and reliability. 3r + I VP Є0º R – 3r 3I – 3r – + r 3r R R R + VP Є0º I R R VP Є0º + 3r – r VP Є0º I 3r 3I (a) (b)Fig. 8.1-1 a) Three equal resistors powered from a single-phase supply (b) Three equal ( resistorssuppliedfromthreeidenticalsources The circuit in Fig. 8.1-1(a) shows the three heater elements tied in parallel and supplied from asingle-phase AC supply. The rms value of source is specified as VP. Let r be the resistance of theconnecting cable and 3I be the phasor current ...