PRIMITIVE NETWORK AND BUS ADMITTANCE MATRIX

 Primitive network matrices

 A diagonal element in the matrices, [z] or [y] is the self impedance zpq-pq or self admittance, ypq-pq. An off-diagonal element is the mutual impedance, zpq-rs or mutual admittance, ypq-rs, the value present as a mutual coupling between the elements p-q and r-s. The primitive network admittance matrix, [y] can be obtained also by inverting the primitive impedance matrix, [z]. Further, if there are no mutually coupled elements in the given system, then both the matrices, [z] and [y] are diagonal. In such cases, the self impedances are just equal to the reciprocal of the corresponding values of self admittances, and vice-versa.

Bus Admittance Matrix

Bus admittance matrix (YBus) for an n-bus power system is square matrix of size n × n. The diagonal elements represent the self or short circuit driving point admittances with respect to each bus. The off-diagonal elements are the short circuit transfer admittances (or) the admittances common between any two number of buses. In other words, the diagonal element yii of the YBus is the total admittance value with respect to the ith bus and yik is the value of the admittance that is present between ith and kth buses. YBus can be obtained by the following methods:

1. Direct inspection method

2. Step-by-step procedure

3. Singular transformation

4. Non-singular transformation

 

Direct inspection method

Formulation of YBus by direct inspection method is suitable for the small size networks. In this method the YBus matrix is developed simply by inspecting structure of the network without developing any kind of equations. Let us consider a 3-bus power system shown in figure below:

Since [B]T * i is zero because, algebraic sum of all the currents meeting at a node is zero. The source current matrix [j] can be partitioned into,