Delta Winding - Common Mode Removal

A set of three-phase AC (alternating current) transformer windings is connected in a delta configuration, as shown above. Other windings are not shown. Winding currents $$(\vec{I_A},\vec{I_B}, \vec{I_C})$$ and line currents $$(\vec{I_{AL}},\vec{I_{BL}}, \vec{I_{CL}})$$ are also pictured.

The following relationship holds for these currents (to a close numerical approximation):

$\large{\vec{I_{AL}} = \vec{\alpha} (\vec{I_A} - \vec{\beta}) \\ \vec{I_{BL}} = \vec{\alpha} (\vec{I_B} - \vec{\beta}) \\ \vec{I_{CL}} = \vec{\alpha} (\vec{I_C} - \vec{\beta})}$

To one decimal place, what is the magnitude (absolute value) of $$(\vec{\alpha} + \vec{\beta})$$?

Notes:

• $$\vec{\alpha}$$ and $$\vec{\beta}$$ are complex numbers.

• In general, $$A \angle \theta$$ denotes a complex number with a magnitude of $$A$$ and an angle $$\theta$$ with respect to the positive real axis

• Angles are given in degrees

• Vector multiplication here is NOT the dot product. For example: $$(A + jB)(C + jD) = AC - BD + j(AD + BC)$$.

• Feel free to use a calculator to do the complex arithmetic.

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