# FORMATION OF Z BUS MATRIX

**FORMATION OF Z BUS MATRIX**

To know about Z bus formation first of all we have to know about Z bus matrix.

**Z BUS MATRIX: **

Z bus matrix contains the driving point impedance of each and every node with respect to a reference bus.And the driving point impedance of a node is equivalent impedance between it and the reference.The off diagnol are known as the transfer impedence between each bus of the network and with every other bus with respect to the reference bus.The Z bus are also known as bus impedence matrix which is built from the branch consisting data of the positive sequence,negative sequence and zero sequence impedence.During practical purposes,the positive and negative sequence are treated equally.

** FORMATION OF Z BUS MATRIX**:

The whole system is assembled by starting with a single element connected to the reference bus,and if one element is added at a time ,we have to modify the matrix for that added element.Each of the element added should be connected to the system by a single node or two nodes.There are some types which are described below

TYPE 1: A branch from reference bus

Suppose current of 1.0pu is injected into a new bus Q ,connected to the reference but it will produce no voltage on other buses.And also injection of current into any bus of PN will produce no voltage on the new bus Q.

Z_{i,q}=Z_{q,i}=0 where i is not equal to q

Z_{q,q}=Z_{p,q}

Hence from above equation the driving point impedence of new bus is impedence of new element added.

TYPE2:A Branch not from reference bus

Suppose a current of 1.0pu is injected into busQ which is same as injecting the current on bus P.

A new axis is been added to the Z bus matrix corresponding to new bus Q.And the off diagnol elements of new row –coloum is same as the element of bus P.The diagnol element is Zq where q is Zp,P plus a series line impedence .

Z_{i,q}=Z_{i,p}

Z_{q,i}=Z_{p,i}

Z_{qq}=Z_{pp}+Z_{p,q}

IMPORTANT QUESTIONS:

1-What is Z bus matrix?

Ans- Z bus matrix contains the driving point impedance of each and every node with respect to a reference bus.And the driving point impedance of a node is equivalent impedance between it and the reference.The off diagnol are known as the transfer impedence between each bus of the network and with every other bus with respect to the reference bus.The Z bus are also known as bus impedence matrix which is built from the branch consisting data of the positive sequence,negative sequence and zero sequence impedence.During practical purposes,the positive and negative sequence are treated equally.

2-Write down briefly about formation of Z bus matrix?

Ans-The whole system is assembled by starting with a single element connected to the reference bus,and if one element is added at a time ,we have to modify the matrix for that added element.Each of the element added should be connected to the system by a single node or two nodes

3-Write down for the type of Z bus formation for a branch from reference bus?

Ans- Suppose current of 1.0pu is injected into a new bus Q ,connected to the reference but it will produce no voltage on other buses.And also injection of current into any bus of PN will produce no voltage on the new bus Q.

Z_{i,q}=Z_{q,i}=0 where i is not equal to q

Z_{q,q}=Z_{p,q}

Hence from above equation the driving point impedence of new bus is impedence of new element added.

4-Write down for formation of Z bus where a branch is not from the reference bus?

Ans- Suppose a current of 1.0pu is injected into busQ which is same as injecting the current on bus P.

A new axis is been added to the Z bus matrix corresponding to new bus Q.And the off diagnol elements of new row –coloum is same as the element of bus P.The diagnol element is Zq where q is Zp,P plus a series line impedence .

Z_{i,q}=Z_{i,p}

Z_{q,i}=Z_{p,i}

Z_{qq}=Z_{pp}+Z_{p,q}

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