Free Expert Guides on Power Systems, Circuit Design & Electrical Troubleshooting

Atree of electric networkis set of branches which is a set of branches which contains all the nodes of the network but does not form any closed path. It is similar to what anetwork topologyis to a communications network.Let us explain the tree of electric network as defined above.The above figure-1, shows an electric network with five nodes 1,2,3,4 and 5.Now, if we remove the branches 1-2, 2-3, 3-4 and 4-1 from the circuit, we will get, the graph as shown below in figure-2.The above graph as sho

When we talk of cut set matrix in graph theory, we generally talk of fundamental cut-set matrix. A cut-set is a minimum set of branches of a connected graph such that when removed these branches from the graph, then the graph gets separated into 2 distinct parts called sub-graphs and the cut set matrix is the matrix which is obtained by row-wise taking one cut-set at a time. The cutset matrix is denoted by symbol [Qf].Example of Cutsets Matrix of a CircuitTwo sub-graphs are obtained from a graph

Incidence matrix is that matrix which represents the graph such that with the help of that matrix we can draw a graph. This matrix can be denoted as [AC] As in every matrix, there are also rows and columns in incidence matrix [AC].The rows of the matrix [AC] represent the number of nodes and the column of the matrix [AC] represent the number of branches in the given graph. If there are ‘n’ number of rows in a given incidence matrix, that means in a graph there are ‘n’ number of nodes. Similarly,