FORMATION OF BUS INCIDENCE AND LOOP

INCIDENCE MATRIX

Aim

To write a suitable program to form a bus incidence and loop incidence matrix for a given power system.

Algorithm

Step 1:

Start the program.

Step 2:

Using the switch cases ask either bus incidence or loop incidence matrix to be found.If loop incidence matrix is to be formed go to step6.

Step 3:

Ask number of system.

Step 4:

To form bus incidence matrix,rules are

1. +1= If current is leaving the node

2. -1= If current is entering the node.

3. 0= if branch is not incident to the node.

Step 5:

Using this rule, form bus incidence matrix.

Step 6:

To form loop incidence matrix, form loop of a graph drawn, size of the matrix and element node.

Step 7:

The direction of the loop is direction of link, the matrix is corresponding element

1.+1=If the element direction is same as that of its corresponding loop.

2.-1=If the element is opposite direction.

3.0=If the element direction does not correspond to that loop.

Step 8:

Using the above rules, form the loop incidence matrix and display it.

Step 9:

Stop the program.

Flow Chart

PROBLEM STATEMENT

Find the bus incidence matrix [A] and loop incidence matrix [L] for the four bus system shown in figure. Take ground as reference.

THEORY

Every power system can be represented by a graph. The theory useful to find the graph is called Graph theory.

In the graph theory the every element of network is represented by a line segment. Also every junction point or busbar is represented by a node.

It every element in the graph marked with direction of current then the graph is called as oriented or directed graph.

A tree is a subgraph of network which consists of all the nodes as in the graph but no closed paths.

The element which makes the closed path is called links. It is represented by dotted lines.The remaining elements are called as branches.

The node starting from the reference node is taken as row & the element are taken as in column of the bus incidence matrix.

The number of links = the number of loops . The direction of loop is as that of direction of links.

The loop number is taken as row and the elements are in column wise.

Solution

Bus incidence Matrix

Loop Incidence matrix

Result