Seq. Imp. of balanced Y-load: Vag = ZYIa + Zn In

= ZYIa+ Zn(Ia + Ib + Ic)

Vag =(Zy+Zn)Ia + ZnIb +ZnIc Similarly, Vbg =ZnIa + (Zy+Zn)Ib +ZnIc Vcg =ZnIa + ZnIb +(Zy+Zn)Ic

In matrix form, Vph = Zph Iph

In terms of sym components,

c

b

a

nYnn

nnYn

nnnY

cg

bg

ag

I

I

I

ZZZZ

ZZZZ

ZZZZ

V

V

V

2

1

0

2

1

0

a

a

a

nYnn

nnYn

nnnY

ag

ag

ag

I

I

I

A

ZZZZ

ZZZZ

ZZZZ

V

V

V

A

Vph = Zph Iph

A Vs = Zph A Is

Vs = A-1 Zph A Is

Vs = Zs Is

where Zs = A-1 Zph A

Simplifying; A-1 Zph A

or where

Z0 = ZY+3Zn Z1

= ZY

Z2 = ZY

2

1

0

2

1

0

2

1

0

00

00

00

a

a

a

ag

ag

ag

I

I

I

Z

Z

Z

V

V

V

2

1

0

2

1

0

00

00

003

a

a

a

Y

Y

nY

ag

ag

ag

I

I

I

Z

Z

ZZ

V

V

V

If neutral is grounded through Zn

Z0 = ZY + 3 Zn

If neutral is solidly grounded, i.e., Zn = 0 Z0 = ZY

If neutral is not grounded, i.e., Zn = ∞Z0 = ZY + ∞ = ∞ i.e., open circuit

Thus zero-sequence currents cannot flow if neutral to ground connection is absent

Sequence Impedance of balanced Δ-load

Convert Δto Y:ZY = ZΔ/3The delta connected load is converted into non grounded Y connected loadTherefore, Zn = ∞Z0 = ZΔ/3+3Zn Z0 = ∞Z1 = ZY = ZΔ/3

Z2 = ZY = ZΔ/3