where D2=Y,Y,+Y.+ Y,Y Equation(9.1)can also be written in the for 2.+2+2 Za z+z +Z1+Z The T is a wye-connected network and the nl is a delta-connected network, as we discuss in the next section 9.2 Three-Phase Connections By far the most important polyphase voltage source is the bal- anced three-phase source. This source, as illustrated by Fig 9.2, has the following properties. The phase voltages, that is, the voltage from each line a, b, and c to the neutral n, are given by V=V,∠-120° =V.∠+120° FIGURE 9.2 Balanced three-phase voltage source An important property of the balanced voltage set is that Van+Vl+Ⅴa=0 From the standpoint of the user who connects a load to the balanced three-phase voltage source, it is not important how the voltages are generated. It is important to note, however, that if the load currents generated by connecting a load to the power source shown in Fig. 9.2 are also balanced, there are two possible equivalent configurations for the load. The equivalent load can be considered as being connected in either a wye(yor a delta(A)configuration. The balanced wye configuration is shown in Fig. 9.3. The delta configuration is shown in Fig. 9.4. Note that in the case of the delta connection, there is no neutral line. The actual function of the FIGURE 9.3 Wye( y-connected lo FIGURE9.4 Delta(A)-connected loads e 2000 by CRC Press LLC© 2000 by CRC Press LLC where D2 = YaYb + YbYc + YaYc . Equation (9.1) can also be written in the form The T is a wye-connected network and the P is a delta-connected network, as we discuss in the next section. 9.2 Three-Phase Connections By far the most important polyphase voltage source is the bal￾anced three-phase source. This source, as illustrated by Fig. 9.2, has the following properties. The phase voltages, that is, the voltage from each line a, b, and cto the neutral n, are given by Van = Vp –0° Vbn = Vp ––120° (9.2) Vcn = Vp –+120° An important property of the balanced voltage set is that Van + Vbn + Vcn = 0 (9.3) From the standpoint of the user who connects a load to the balanced three-phase voltage source, it is not important how the voltages are generated. It is important to note, however, that if the load currents generated by connecting a load to the power source shown in Fig. 9.2 are also balanced, there are two possible equivalent configurations for the load. The equivalent load can be considered as being connected in either a wye (Y) or a delta (D) configuration. The balanced wye configuration is shown in Fig. 9.3. The delta configuration is shown in Fig. 9.4. Note that in the case of the delta connection, there is no neutral line. The actual function of the FIGURE 9.3 Wye (Y)-connected loads. FIGURE 9.4 Delta (D)-connected loads. Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z 1 2 3 = + + = + + = + + a b a b c b c a b c a c a b c FIGURE 9.2 Balanced three-phase voltage source. Van + – Balanced three-phase power source Vbn Vcn a b c n phase a phase b phase c + + a b c n ZY ZY ZY a b c ZD ZD ZD