Network Branch Model

Each branch is treated with the same four-terminal network model. It is a four-terminal network with an ideal transformer connected upstream. For power lines, the transmission ratio (N) is set to 1. For transformers, the transformation ratio (N) is given as a complex value. The admittance matrix (Y) looks like this:

\[Y_{br} = \begin{bmatrix} \frac{1}{{\tau^2}} \cdot (y_s + j\frac{b_c}{2}) & -y_s \cdot \frac{1}{{\tau e^{-j\phi}}} \\ -y_s \cdot \frac{1}{{\tau e^{j\phi}}} & (y_s + j\frac{b_c}{2}) \end{bmatrix}\]

where:

• $y_s = \frac{1}{R + jX}$ is the series admittance,
• $R$ is the resistance component, and
• $X$ is the reactance component,
• $b_c$ is the transverse admittance,
• $N = \tau \cdot e^{j\phi}$ is a complex transformation factor (eg 1 for power lines)

Circuit diagram

                    ys
      x--┓┏---------###----------x
         ||   |             |
         ||   # jbc/2       # jbc/2
         ||   |             |
      x--┛┗----------------------x 
         N (complex number)