In power engineering, nodal admittance matrix (or just admittance matrix) or Y Matrix or Ybus is an n x n matrix describing a power system with n buses. It represents the nodal admittance of the buses in a power system. In realistic systems which contain 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 Y Matrix is also one of the data requirements needed to formulate a power flow study.
The nodal admittance matrix form: 
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