optimal capacitor placement, considering power system loss reduction, voltage profile improvement, line reactive power decrease and power factor correction, is of particular importance in power system planning and control. the distribution system operator calculates the optimal place, number and capacity of capacitors based on two major purposes: active power loss reduction and return on invest...

Let J be a unitary almost complex structure on a Riemannian manifold (M, g). If x is a unit tangent vector, let π := Span{x, Jx} be the associated complex line in the tangent bundle of M . The complex Jacobi operator and the complex curvature operators are defined, respectively, by J (π) := J (x) + J (Jx) and R(π) := R(x, Jx). We show that if (M, g) is Hermitian or if (M,g) is nearly Kähler, th...

Optimal capacitor placement, considering power system loss reduction, voltage profile improvement, line reactive power decrease and power factor correction, is of particular importance in power system planning and control. The distribution system operator calculates the optimal place, number and capacity of capacitors based on two major purposes: active power loss reduction and return on invest...

. (1.2) In the manipulations above we have used the linearity of the superoperator M in the first line. In the second line we have used Lemma 0.4 with γ = I ⊗ σ , noting that |X|= s. The third line follows from the concavity of the square root. We will now use a helpful identity for the trace of an operator squared: TrZ =Tr(Z ⊗ Z)F , where F is defined as follows. Definition 1.1. The swap opera...