  From the perspective of the network theory, the present work illustrates how
the parametric intrinsic geometric description exhibits an exact set of pair
correction functions and global correlation volume with and without the
inclusion of the imaginary power flow. The Gaussian fluctuations about the
equilibrium basis accomplish a well-defined, non-degenerate, curved regular
intrinsic Riemannian surfaces for the purely real and the purely imaginary
power flows and their linear combinations. An explicit computation demonstrates
that the underlying real and imaginary power correlations involve ordinary
summations of the power factors, with and without their joint effects. Novel
aspect of the intrinsic geometry constitutes a stable design for the power
systems.
