Nodal Admittance Matrix - Design

Design

Starting from the single line diagram of a power system, there are four main steps in creating the Y Matrix. First, the single line diagram is converted to an impedance diagram. Next, all voltage sources are converted to their equivalent current source representations. From here, the impedance diagram is then converted to an admittance diagram. Finally, the Y Matrix itself is created.

Y_{ij} = \begin{cases} y_{ii} + \sum_{i \neq j} {y_{ij}}, & \mbox{if } i = j \\ -y_{ij}, & \mbox{if } i \neq j \end{cases}

Here, is the summed admittance of all power lines going directly from bus i to j (zero if no such). The parameter is often neglected, but could have a non-zero value representing the admitance-to-ground at bus i. The Y Matrix diagonal elements are called the self-admittances at the nodes, and each equals the sum of all the admittances terminating on the node identified by the repeated subscripts. The other admittances are the mutual admittances of the nodes, and each equals the negative of the sum of all admittances connected directly between the nodes identified by the double subscripts. As indicated by the provided construction, the Y Matrix is typically a symmetric matrix. However, extensions such as transformer modeling may make it asymmetrical. off diagonal always positive while diagonals are always negative.

For small transmission systems of about less than 10 nodes or buses, the Y matrix can be calculated manually. But for a realistic system with relatively large number of nodes or buses, say 1000 nodes, a computer program for computing Y is more practical to use.

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