  This paper introduces a new model for highly accurate distribution voltage
solutions, coined as a parameterized linear power flow model. The proffered
model is grounded on a physical model of linear power flow equations, and uses
learning-aided parameterization to increase the fidelity of voltage solutions
over a wide range of operating points. To this end, the closed-form analytic
solution of the parameterization approach is obtained via a Gaussian Process
using a deliberately small input sample and without the need for recomputation.
The resulting "self-adjusting" parameter is system-specific and controls how
accurate the proposed power flow equations are according to loading conditions.
Under a certain value of the resulting parameter, the proposed model can fully
recover the linearized formulation of a specialized branch flow model for
radial distribution systems, the so-called simplified DistFlow model. Numerical
examples are provided to illustrate the effectiveness of the proposed model as
well as the improvement in solution accuracy for voltage magnitudes over the
simplified DistFlow model and several other linear power flow models, at
multiple loading levels. Simulations were carried out on six small- and
medium-sized test systems.
