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:

\[Y_{br} = \begin{bmatrix} \frac{1}{{\tau^2}} \cdot (y_{ser} + 0.5 \cdot y_{shunt}) & -y_{ser} \cdot \frac{1}{{\tau e^{-j\phi}}} \\ -y_{ser} \cdot \frac{1}{{\tau e^{j\phi}}} & (y_{ser} + 0.5 \cdot y_{shunt}) \end{bmatrix}\]

where:

• $y_ser$ is the series admittance,
• $y_shunt$ is the shunt admittance,
• $R$ is the resistance component, and
• $X$ is the reactance component,
• $G$ is the conductance component, and
• $B$ is the susceptance component,
• $N$ is the complex transformation factor (eg 1 for power lines)

\[N = \tau \cdot e^{j\phi}\]

\[y_{ser} = \frac{1}{R + jX}\]

\[y_{shunt} = G + j \cdot B\]

Circuit diagram

                    y_ser
      x--┓┏---------###----------x
         ||   |             |
         ||   # y_shunt     # y_shunt
         ||   |             |
      x--┛┗----------------------x 
         N = tau * e^(j*phi)