Problem Formulation
Reduction real power loss is the key goal and written as follows:
\(F=P_{L}=\sum_{k\in\text{Nbr}}\text{\ \ g}_{k}\left(V_{i}^{2}+V_{j}^{2}-2V_{i}V_{j}{\cos\theta}_{\text{ij}}\right)\)(1)
\(F=P_{L}+\omega_{v}(weight\ factor)\times\text{Voltage\ Deviation}\)(2)
\(\ Voltage\ Deviation\ \ \ \ \ \ \ \ =\sum_{i=1}^{\text{Npq}}\left|V_{i}-1\right|\)(3)
Constraint (Equality)
\(\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P}_{G}(Power\ generation)=P_{D}(power\ demand)+P_{L}(power\ losses)\)(4)
Constraints (Inequality)
\(\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P}_{\text{gslack}}^{\min}\leq P_{\text{gslack}}\leq P_{\text{gslack}}^{\max}\)(5)
\(\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Q}_{\text{gi}}^{\min}\leq Q_{\text{gi}}\leq Q_{\text{gi}}^{\max}\ ,\ i\in N_{g}\)(6)
\(\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ V}_{i}^{\min}\leq V_{i}\leq V_{i}^{\max}\ ,\ i\in N_{B}\)(7)
\(\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T}_{i}^{\min}\leq T_{i}\leq T_{i}^{\max}\ ,i\in N_{T}\)(8)
\(\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Q}_{c}^{\min}\leq Q_{c}\leq Q_{C}^{\max}\ ,i\in N_{C}\)(9)