“…Nomenclature: nd, total number of nodes; nbr, total number of branches; V i , bus voltage at node i; P slack , active power supplied by the slack bus; Q slack , reactive power supplied by the slack bus; P di , active power demand respectively at node i; Q di , reactive power demand respectively at node i; V max i ; V min i , maximum and minimum limit of bus voltage at ith node; δ max i ; δ min i , maximum and minimum limit of voltage angle at ith node; tap max i ; tap min i , maximum and minimum limit of tap position; S max ij , maximum complex power flow limit in branch ij; S ij , complex power flow in a branch ij; G ij , conductance of the branch ij; B ij , susceptance of the branch ij; pf up i ; pf lo i , upper and lower limit of average power factor of system; Q DST max , maximum limit of reactive power compensation; Q DST min , minimum limit of reactive power compensation; Q DST , reactive power compensation; NDST max , maximum number of D-STATCOMs; K e , cost of energy loss; C p , purchase cost; DG ins , installation cost of DG; DG o&m , operation and maintenance cost of DG; DST ins , installation cost of D-STATCOM; DST o&m , operation and maintenance cost of D-STATCOM; P loss , real power loss; Q loss , reactive power loss; TP loss , total real power loss without compensation; OLTC, on-load tap changer circuit; TP after loss , total real power loss after compensation; CEL , cost of energy loss; P o , nominal real power load; Q o , nominal reactive power load; α, composition of residential load; β, composition of commercial load; γ, composition of industrial load; n pr , n qr , exponential coefficients for residential load; n pc , n qc , exponential coefficients for commercial load; n pi , n qi , exponential coefficients for industrial load minimize line losses. Voltage management in distribution systems was addressed 16 in two levels by controlling reactive power of renewable-based DGs. Distribution network was divided into different areas and equipped with DGs.…”