Ybus matrix

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In power engineering, Y Matrix is one of the data requirements needed to formulate a power flow study program. It represents the line admittance between the buses in a power system.

Ybus matrix form: $\begin{bmatrix} Y_{11} & Y_{12} & \cdots & Y_{1n} \\ Y_{21} & Y_{22} & \cdots & Y_{2n} \\ \cdots & \cdots & \cdots & \cdots \\ Y_{n1} & Y_{n2} & \cdots & Y_{nn} \end{bmatrix}$

[edit] Context

Electric power transmission needs optimization. Only Computer simulation allows the complex handling required. The Ybus matrix is a tool in that domain.

[edit] Design

The Y Matrix is designated by Ybus and called the bus admittance matrix. Y matrix is a symmetric and square matrix that completely describes the configuration of power transmission lines. In realistic systems which are quite large containing thousands of buses, the Y matrix is quite sparse. Each bus in a real power system is usually connected to only a few other buses through the transmission lines.

The admittances Y11, Y22,.. Ynn 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.

For small transmission systems of about less than 10 nodes or buses, 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 Ybus is more practical to use. The Y matrix for transmission system with n number of nodes has a size of n x n'’.