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The Balanced Three-Phase Delta-Connected Load

Author: E.E. Kimberly

If a group of three identical resistances R12, R23 and R31 or three identical impedances Z12, Z23, and Z31 are connected in delta, as in Fig. 9-3 (a) or Fig. 9-3 (b), and are then connected to a source of three-phase voltages, three equal currents will flow in the three phase or branch impedances. If the three line-to-line voltages have the phase sequence V31, V23, and V12, they will produce currents I31, I23, and I12, respectively, in the three impedances. If the impedances are purely resistive, the currents are in phase with the voltage drops across the respective impedances, as in (c). The angle θ in (d) between any current and the voltage which produces it will be the characteristic angle of the impedance through which the current flows.

Fig. 9-3. Voltage and Current Relationships in Δ-Connected Systems

At a corner of the voltage delta, such as 3, I23 is positive to the corner and I31 is negative to the corner. The corner 3 of the voltage delta corresponds to line 3 on the associated circuit diagram. The line current at terminal 3 is made up of the currents of the two phase branches connected to it. Therefore, I3 = I23 + (- I31) or I23-I31. Inasmuch as the phases have been assumed to be of identical impedances, the angle between I23 and -I31 is 60°. Therefore,

I3 = 1.732*I23


I3 = *I23 [9-3]

Last Update: 2010-10-06