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Academy of Engineering Sciences Communication and Computer Programme Semester : IV/ Academic year : 2015 – 2016 ELX 227 FUNDAMENTALS OF ELECTRICAL ENGINEERING –III Lecture 3 Polyphase systems OVER VIEW : POLYPHASE SYSTEMS Circuits or systems, in which the ac sources operate at the same frequency but at different phases called Polyphase. Two and Three-phase system A two-phase system produced by generator consisting of two coils placed perpendicular to each other so that the voltage generated by one lags the other by 90◦. A three-phase system produced by generator consisting of three sources having the same amplitude and frequency but out of phase with each other by 120◦. Three-phase systems are important for the following reasons: 1- Nearly all-electric power is generated and distributed in three-phase, at the operating frequency of 50 Hz in Sudan or 60 Hz as in the United States. 2- The instantaneous power in a three-phase system can be constant (not pulsating) This results in uniform power transmission and less vibration of three-phase machines 3- The three-phase system is more economical than the single-phase as it needs less wires than single-phase system. BALANCEDTHREE-PHASEVOLTAGES Three-phase voltages often produced with a three-phase ac generator(or alternator) whose cross-sectional view shown in the below Fig: The generator consists of a rotating magnet (called the rotor) surrounded by a stationary winding (called the stator). Three separate windings or coils with terminals a–a', b–b' and c-c' are physically placed 120◦apart around the stator. Terminals a and a' for example, stand for one of the ends of coils going into and the other end coming out of the page. As the rotor rotates, its magnetic field cuts the flux from the three coils and induces voltages in the coils. Because the coils are placed 120◦apart,the induced voltages in the coils are equal in magnitude but out of phase by 120◦ Since each coil can be regard as a singlephase generator by itself, the three-phase generator can supply power to both singlephase and three-phase loads. The phase sequence: It is the time order in which the voltages pass through their respective maximum values. Since the three-phase voltages are 120◦out of phase with each other, there are two possible combinations:The sequence is [abc or bca or cab] if the phasors rotate in the countra clockwise direction with frequency ω and the sequence is [acb or bac or cba] if the phasors rotate in the clockwise direction with frequency ω The phase sequence is important in three-phase power distribution. For example, it determines the direction of the rotation of a motor connected to the power source. Example 1: Determine the phase sequence of the set of voltages Van==200 cos(ωt+10◦) Vbn==200 cos(ωt-230◦) Vcn==200 cos(ωt-110◦) Solution: The voltages can be expressed in phasor form as Van==200 10◦ Vbn==200 -230◦ Vcn==200 -110◦ We notice that Van leads Vcn by 120◦ and Vcn in turn leads Vbn by 120◦. Hence, we have an acb sequence. Example 2: Given that Vbn=110 30◦, find Van and Vcn , assuming a positive (abc) sequence. Solution: As Van leads Vbn by 120◦ and Vbn in turn leads Vcn by 120◦. Van=110 120+30◦ Vcn=110 -120+30◦ Van=110 150◦ Vcn=110 -90◦ Generators connections The voltage sources can be either wye-connected or delta-connected as in the following Fig. Loads connections Three-phase load can be either wye-connected or delta-connected, depending on the end application A wye- or delta-connected load said to be unbalanced if the phase impedances are not equal in magnitude or phase while in a balanced load the phase impedances are equal in magnitude and in phase. For a balanced wye-connected load: Z1=Z2=Z3=ZY where ZY is the load impedance per phase For a balanced delta-connected load: Za=Zb=Zc=ZΔ where ZΔ is the load impedance per phase ZΔ=3ZY or ZY =1/3 ZΔ APPLICATIONS Both wye and delta source connections have important practical applications. The wye source connection is used for long distance transmissionof electric power, where resistive losses (I 2R) should be minimal. Thisis due to the fact that the wye connection gives a line voltage that is√3greater than the delta connection; hence, for the same power, the linecurrent is√3 smaller. The delta source connection is used when threesingle-phase circuits are desired from a three-phase source. This conversion from three-phase to single-phase is required in residential wiring, because household lighting and appliances use single-phase power. Threephase power is used in industrial wiring where a large power is required. In some applications, it makes no difference whether the load is wye- or delta-connected. For example, both connections are satisfactory with inductionmotors. In fact, some manufacturers connect a motor in delta for 220 Vand in wye for 440 V so that one line of motors can be readily adapted totwo different voltages.