PROPERTIES OF A ZBUS MATRIX

(i) Z_BUS can be obtained as inverse of Y_BUS given by

(ii) In Z_BUS matrix, the diagonal elements are short circuit driving point impedance and the off-diagonal elements are short circuit transfer impedances.
(iii) Z_BUS is generally used for short circuit studies.
(iv) Z_BUS is a full matrix i.e. zero elements in Y_BUS become non-zero elements in the corresponding Z_BUS.
(v) The size of Z_BUS matrix is equal to number of buses other than the reference bus.
(vi) Z_BUS matrix is difficult to form and difficult to modify (Z_BUS matrix is formed by algorithum method).
(vii) Z_Bus is very useful in fault study. Hence, Z_Bus matrix will be preferred over Y_Bus matrix in fault study of the system.

Note: 

• In a pure imaginary Y_BUS matrix, the off-diagonal elements are positive imaginary and the diagonal elements are negative imaginary.
• When a shunt element is connected to the existing system then, only diagonal elements of Y_BUS will be affected.
• If a series element is connected to the existing system then, diagonal as well as off diagonal elements will be affected in the Y_BUS matrix.
• The condition for convergence of a load flow problem is that all the diagonal elements of the Y_BUS must dominate the off-diagonal elements.
• When a shunt capacitor is connected in the existing system then, the chances of divergence of the load flow problem is increased while if a shunt reactor is connected then, the changes of convergence of the load flow study is increased.