Chapter 3: Network Admittance and Impedance Matrices

Node Elimination by Kron Reduction

Consider an equation of the form

(3.18)

 

where A is an ( n X n ) real or complex valued matrix, x and b are vectors in either Rn or Cn . assume that the b vector has a zero element in the n th row such that (3.18) is given as

(3.19)

 

 

 

 

We can then eliminate the kth row and kth column to obtain a reduced ( n - 1) number of equations of the form

(3.20)

 

 

 

 

The elimination is performed using the following elementary operations

(3.21)

 

 

 

Do an example