电子电工技术英文课件 (62).pdf

6.4 Three-Phase Circuits 6.4.1 Balanced Three-Phase Voltages Have you ever wondered a question:where does the power of lamp,TV,air conditioner in your home come from?The answer is that most of the electricity in modern society comes from three-phase generators.A three-phase generator can be equivalent to a three-phase voltage source.ABCNANvBNvCNv Figure 1:Three-Phase voltage source.The three phase voltages of the three-phase voltage source are ()()()ooocoscos120cos240cos120CBNmmmANmNVtVttvVvvVt=+(1)Fig.2 shows the waveforms of the three phase voltages.tANvBNvCNv Figure 2:Waveforms of three-phase voltages.The rms phasor form of the three phase voltages can be written as oooooo00212012021201202mpmpmBNCANNpVVVVVV=+=+VVV(2)The phasor diagram of the phase voltages is shown in Fig.3.ANVBNVCNVo120o120o120 Figure 3:Phasor diagram of three-phase voltages.From Fig.3,we can conclude that the phasor sum of the three phase voltages is zero.That is,0BNANCN+=VVV(3)Therefore,the three phase voltages are balanced.6.4.2 Single-Phase Equivalent Circuits of Balanced Three-Phase Circuits Through transmission lines,the three-phase voltage source supplies power to the load such as lamp,television,and air conditioner.Thus a three-phase circuit comes into being,as shown in Fig.4.ABCNANVBNVCNVacbaZbZcZn Figure 4:Three-Phase circuit with the three-phase voltage source and three-phase load.If abc=ZZZZ,the three-phase circuit is balanced,as shown in Fig.5.ABCNANVBNVCNVacbZZZnAIBICI Figure 5:Balanced three-phase circuit.According to KCL,0ACBIII+=(4)We set the node N in Fig.5 as the reference node,that is,0N=V.Thus,BNCNANACnnnBIII=VZVVVZVVZ(5)Substitute(5)and(3)into(4),0nnANNnNCB+=VVVVZVZVZ(6)According to(6)and(3),0n=V(7)(7)means that the potential of the node n is equal to the potential of the node N.Therefore,we can use a wire to connect the n and N,as shown in Fig.6.ABCNANVBNVCNVacbZZZnAIBICI Figure 6:The voltage between the node n and node N is zero in the balanced three-phase circuit.From Fig.6.,the single-phase equivalent circuits are shown in Fig.7.ANANVaZnAI BNBNVbZnBI CNCNVcZnCI Figure 7:Single-Phase equivalent circuit of balanced three-phase circuit.From Fig.7.,the three phase currents are AANNBNCCBIII=VZVZVZ(8)6.4.3 Source-Load Connections There are four possible source-load connections:wye-wye(Y-Y)connection shown in Fig.8(a),wye-delta(-Y)connection shown in Fig.8(b),delta-wye (Y-)connection shown in Fig.8(c),and delta-delta(-)connection shown in Fig.8(d).ABCNANVBNVCNVacbaZbZcZn(a)ABCNANVBNVCNVacbabZcaZbcZ(b)ABCacbaZbZcZnABVBCVCAV(c)ABCABVBCVCAVacbabZcaZbcZ(d)Figure 8:Three-Phase source-load connections:(a)Y-Y;(b)Y-;(c)-Y;(d)-From Fig.8(a)and Fig.3,the line-to-line voltages(line voltages)of Y-Y connection are related to the phase voltages,as shown in Fig.9.ANVBNVCNVo120o120o120ABVBCVCAV Figure 9:Phasor diagram showing the relation between the line voltages and the phase voltages for Y-Y connection.From Fig.9,ooo3090150CBNBNABpBCpCANpNCANANVVV=VVVVVVVVV(9)From Fig.8(d),the line-to-line voltages(line voltages)of-connection are equal to the phase voltages.That is,6.4.4 Unbalanced Three-Phase Circuits Unbalance of three-phase circuits may results from two situations:unbalanced source voltages and load impedances are not equal.Here,we only discuss the unbalanced three-phase circuits with unequal load impedances.If the load impedances in Fig.4 are not equal,that is，abcZZZ(10)We can conclude that the voltage of the node n is generally not equal to zero,that is,0nV(11)In order to keep the voltage of the node n be zero,the fourth wire is placed between n and N,as shown in Fig.10.The circuit in Fig.10 is a three-phase four-wire Y-Y system.ABCNANVBNVCNVacbaZbZcZn Figure 10:Three-Phase four-wire circuit.6.4.5 Power in Balanced Three-Phase Circuits In the balanced three-phase circuit shown in Fig.5,the active powers of three phases are equal.That is 2ABCpPPPI R=(12)where ppVI=Z and Re()R=Z.The total active power of the balanced three-phase circuit in Fig.5 is 2T3ABCpPPPPI R=+=(13)Similarly,the total reactive power of the balanced three-phase circuit in Fig.5 is 23ABCpQQQQI X=+=T(14)where Re()X=Z.An interesting and important result for the balanced three-phase circuit is that the total instantaneous power is equal to the total active power.That is,2TT()()()()3ABCpp tp tp tptPI R=+=(15)