Problem with unbalanced,Star connected loads

Thread Starter


Joined May 22, 2007
I have a problem solving the folloing assignment question.

I am familiar with the condition in balanced star-connected load but do not no how to star solving unbalanced loads.The convertion to delta is will be straight forward once Q1.1 is solved.I do not know where to start as I have not seen a Example like this in any of our studie books.

The question reads.

An unbalanced,Star connected load is connected to a 380-V,Thee-Phase,Four-wire supply.Take Vnc as the reference Phasor with a positive phase sequence.

The impedances are as follows.

Z an = 7,8 /_35,6 Ohm
Z bn = unknown ?
Z cn = 10,5 /_63.8 Ohm

I n = 24,6 /_ -76 A

1.1 Calculate the value of the impedance in phase b
1.2 Convert the system to an equivalent Delta-connected system.

Can anyone help?


Joined Apr 2, 2007
the analysis of three phase unbalanced system requires the method of symmetrical components, try reading abt it ,you will need a book which thoroughly deals with the concept of electrical distribution.
you can have a try at it this way (which wud have been the way i wud have done it without the knowledge of symmetrical components)
since u already know the impedance of other phases apply ohm's law
in each phase with voltage taken as v(line)/sqrt(3) --because its a star connection each phase voltage lags/leads preceding one by 120 degree.
now apply kirchoff's current law at neutral pt
i;e summation of all current entering including the unknown one shud equal
to neutral current (all calculation shud be done in polar form or rectangular form since angles are of importance here)
this way current in the unknown impedance phase can be found out.
apply ohm's law to get the value of impedance.

conversion of star to delta is very simple u can get it in any book touching the 3 phase topic. in case u cant i will try to explain it.


Joined Mar 31, 2012
It's been a while since I did this stuff, but it appears that you have a four-wire star-connected load (so three phase wires and one neutral wire) and that the neutral wire is playing a role, since it is carrying current. So what does it mean to find an equivalent delta-connected load since that is a three-wire connection with no neutral? The whole concept of an equivalent load is that you can swap out the original load for its equivalent and the rest of the system can't tell the difference, but you will be going from one load that has a non-zero current in the neutral connection to another than has no neutral connection at all.


Joined Mar 6, 2009
I agree with your 'proposal' that the two cases are incompatible. There is no means of handling the neutral connection in the Y- Delta transformation. The Delta equivalent must have line currents which add to zero - as would be the case with the neutral open in the Y connected equivalent.