Lines
\[\begin{aligned}
S &= VI^*
\end{aligned} \]
\[\begin{aligned}
p_i &= g v_i^2 - g v_i v_j \cos(\theta_i - \theta_j) - b v_i v_j \sin(\theta_i - \theta_j)\\
q_i &= -b v_i^2 + b v_i v_j \cos(\theta_i - \theta_j) - g v_i v_j \sin(\theta_i - \theta_j)
\end{aligned} \]