MODULE 9 THREE PHASE AC SYSTEM FUNDAMENTALS: BALANCED LOAD 9.1 INTRODUCTION A polyphase system consists of an arrangement of two or more similar single-phase systems in which the maximum values of the independent phase voltages do not occur at the same time. Advantages of Polyphase over Single-Phase Systems: a) Sizes of conductors are smaller for the same power transmitted b) Polyphase transmission lines deliver more power for the same weight and cost as in single phase c) Higher power transmission efficiency (lower voltage drop) d) Voltage regulation of a polyphase line is inherently better e) Three-phase motor are self-starting while single phase motors are not f) Electrical machines are smaller in size for the same power a single phase machine g) Using star system makes available lower phase voltage for domestic use and higher line voltages for industrial use without extra cost. Generation, transmission and distribution of electricity via the National Grid system is accomplished by three-phase alternating currents. The voltage induced by a single coil when rotated in a uniform magnetic field is known as a single-phase voltage. Most consumers are fed by means of a single-phase a.c. supply. Two wires are used, The majority of single-phase supplies are obtained by connection to a three-phase supply. A three-phase supply is generated when three coils are placed 120° apart and the whole rotated in a uniform magnetic field as shown in the left figure. The result is three independent supplies of equal voltages which are each displaced by 120° from each other as shown in the right figure. If the three-phase windings shown in the figure are kept independent then six wires are needed to connect a supply source (such as a generator) to a load (such as motor). To reduce the number of wires it is usual to interconnect the three phases. There are two ways in which this can be done, these being: (a) a star connection, and (b) a delta, or mesh, connection. Sources of three-phase supplies, i.e. alternators, are usually connected in star, whereas three-phase transformer windings, motors and other loads may be connected either in star or delta. A star-connected load is shown in the figure where the three line conductors are each connected to a load and the outlets from the loads are joined together at N to form what is termed the neutral point or the star point. VΦ are called the phase voltages IΦ are called the phase currents VL are called the line voltages IL are called the line currents In star or wye system IN in 3 phase 4-wire: IN = - (IA + IB + IC) In balanced 3 phase wye system the line voltages and phase voltages are displaced 30°, while all phase voltages are 120° displaced each other also all the line voltages are 120° displaced to each other. The star connection of the three phases of a supply, together with a neutral conductor, allows the use of two voltages—the phase voltage and the line voltage. A 4-wire system is also used when the load is not balanced. The standard electricity supply to consumers in Great Britain is 415/240 V, 50 Hz, 3-phase, 4wire alternating current, and a diagram of connections is shown in the Figure A delta (or mesh) connected load is shown in the figure below where the end of one load is connected to the start of the next load. Self-Assessment Problems 1) A three-phase three wire, 110 volt, ABC system supplies a delta connection of three equal impedances of 5∟45° ohms. Determine the line currents IA, IB, and IC 2) A three-phase, four wire, CBA system with an effective line voltage of 120 V, has three impedances of 20∟-30° Ω in a Y-connection. Determine line currents 3) A three-phase, three wire ABC system, with an effective line voltage of 106.1 V, has a balanced connected load with impedances of Z = 15∟30° Ω. Obtain the line and phase currents by the single line equivalent method. 4) A star-connected load consists of three identical coils each of resistance 30 and inductance 127.3 mH. If the line current is 5.08 A, calculate the line voltage if the supply frequency is 50 Hz. 5) Three identical capacitors are connected in delta to a 415 V, 50 Hz, 3-phase supply. If the line current is 15 A, determine the capacitance of each of the capacitors. 6) A balanced ∆-connected load, with Z∆ = 30∟30°Ω, is connected to a three-phase, three-wire system conductors having impedances ZC = 0.4 + j 0.3Ω. obtain the line to line voltage at the load.
