(2) Power flow equation

$$\begin{cases} \quad P\_i = \mathcal{U}\_i \sum\_{j \in i} \mathcal{U}\_j (\mathcal{G}\_{ij} \cos \theta\_{ij} + \mathcal{B}\_{ij} \sin \theta\_{ij}) \\ \quad Q\_i = \mathcal{U}\_i \sum\_{j \in i} \mathcal{U}\_j (\mathcal{G}\_{ij} \cos \theta\_{ij} - \mathcal{B}\_{ij} \sin \theta\_{ij}) \end{cases} \tag{19}$$

where *P<sup>i</sup>* and *Q<sup>i</sup>* are the active power and reactive power injected into node *i,* respectively; *U<sup>i</sup>* is the voltage amplitude of node *i*, *j* ∈ *i* represents all nodes connected to node *i*; *Gij* and *Bij* are respectively the admittance matrix real part and virtual part of the system; and *θij* is the phase angle difference between node *i* and node *j*.
