3.3.1. Equality Constraints

The power flow equations are taken as the equality constraints for the RPP. Using the output power of wind farms and also considering the probabilistic nature of the problem, Equations (25) and (26) can be rewritten as follows:

$$P\_{i,s} = P\_{Gi,s} + P\_{Wi,s} - (1 + \Gamma(s))P\_{Di,s} - \text{Re}\{V\_{i,s} \sum\_{j=1}^{N\_B} \left(V\_{j,s} Y\_{i,j,s}\right)^\*\}, \qquad \forall s \in \Omega\_s \tag{29}$$

$$Q\_{i,s} = Q\_{\overline{\alpha},s} + Q\_{\overline{\alpha}i,s} - (1 + \Gamma(s))Q\_{\overline{\alpha},s} - \operatorname{Im} \langle V\_{i,s} \sum\_{j=1}^{N\_{\overline{\alpha}}} \left( V\_{j,s} \boldsymbol{Y}\_{i,j,s} \right)^{\*} \rangle\_{\prime} \qquad \forall s \in \Omega\_{s} \tag{30}$$

where *PWi*,*<sup>s</sup>* and *QWi*,*<sup>s</sup>* show the output active and reactive power of the *ith* wind farm for the *sth* scenario, respectively. It should be noted that the output reactive power of the wind farms is neglected in this paper.
