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

or

I3 = *I23

[9-3]