Positive , Negative and Zero sequence impedance - A discussion

The sequence components are used to analysis a 3 phase unbalanced system by splitting the unbalance current ( or Voltage ) to some balanced components .
Suppose the unabalanced currents are IA, IB and IC
then IA can be made up of 3 componenents ie positive , negative and zero sequence ( say IA1, IA2, IA0 respectively
similarly IB ( IB1 , IB2, IB0) and IC ( IC1,IC2,IC0)

Now the positive sequence components in each phases are ( IA1 , IB1, IC1 ) and they are balanced and have the same phase sequence as that of original unbalanced IA , IB. IC (120deg apart )
Similary Negative sequence componenets in each phases are ( IA2, IB2, IC2) and they are balanced and have the opposit phase sequence as that of the original unblaned IA, IB and IC ( 120 deg apart )
and the zero sequence components are IA0, IB0 , IC0 they are in phase .( zero phase displacement )

Now one must try to find out the path at which the sequence components flow . As the positive sequence components ( IA1 , IB1 and IC1) are balanced - meaning they add up to zero at any instant , they can not flow in the neutral to earth !

Similarly negative sequence components ( IA2, IB2, IC2 ) are balanced , they add up to zero at any moment and hence it can not flow from neutral to earth !

But the zero sequence component ( IA0, IB0, IC0 ) are in phase - meaning they do not add to zero at any instant , they add up at the neutral and can flow to the earth !!!

Similary in a delta winding , the positive and negative sequence current can not circulate as they add up to zero hence they come out in lines and the zero sequence componenets will circulate in delta winding as its magnitud are same !!

The conclusion is positive and negetive sequence current can not flow to earth but the zero sequence can .
It is very clear that the sequence components take different paths in the network because of its nature . In transmission network the positive and negative sequence take the same path which does not include the earth where as the zero sequence current takes different path including earth .

Now the impedance offered by the network against positive sequence current is called postive sequence impedance and that to negative is called negative sequence impedance and the impedence offered by the network to zero sequence current is called the zero sequence impedance .

Now to determine the positive sequence impedance of transmission line

Apply balanced 3 phase voltage to 3 phases of the transmission line at one end keeping the other end of the line short circuited with out any earth at the shorted end and the ratio of phase voltage to current gives the positive sequence and negative sequence impedance

Zero sequence impedance
Remember the zero sequence currents are in phase in all phases and naturally apply the in phase voltage to the three phases !!

procedure

Short all the phases of the transmission line at one end apply single phase voltage keeping the other end shorted and earthed !!! measure the ratio of voltage to current and multiply by 3 will give the zero sequence impedance

Remember . The sequence component can not exists in one phase only . if it exists it exists in all the phases ! even in case of a single phase to earth fa