In a three phase system the phase currents are given as follows: i1=30.cos(t+90°) A; i2=30.cos(t+210°) A; i3=30.cos(t

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In a three phase system the phase currents are given as follows:
i1=30.cos(t+90°) A;
i2=30.cos(t+210°) A;
i3=30.cos(t-30°) A;
The neutral line current i0 is monitored. Reference directions of all four currents are
given in the circuit diagram below.
What is the value of i0 for balanced operation?
In order to prove the balanced operation with data given above, please, find i0
analytically and sketch the phasors graphics scaled proportionally as good as
possible by free hand.
Please find proper tools (compass and ruler) or a graphics software and construct
the precise phasor graphics.
Hints: calculate the values by using phasor transformed quantities and applying KCL on the node “n” for
frequency domain. Based on the results, you can sketch the graphical situation schematically by
keeping approximated geometrical relations, with a scaling e.g. 5 A correspond 1 cm.
No special knowledge about three phase systems is needed. Three phase related conditions are
embedded in the example. The task is to be solved by basic knowledge about circuit analysis and
phasors.