On Linear Analysis of the Power Flow Equations for DC and AC Grids With CPLs

This express brief presents an approximation of the power flow problem for alternating-current (ac) and directcurrent (dc) distribution networks by using a linear representation of the hyperbolic constraints i = p/v ↔ II* = ℤ/V related to the power balance at each constant power load node. Taylor's or Laurent's series expansion methods are not required to obtain an equivalent linear power flow model. The proposed linear method allows us to achieve a high quality approximation of the power flow modeling without iterative procedures. Our simulation results show the accurate estimation of the voltage profile in distribution networks by the proposed linear approach in comparison to existing methods in specialized literature for ac and dc networks, including linear estimators or classical numerical methods, such as Gauss-Seidel and Newton-Raphson approaches. Numerical implementation of those approaches is carried out in the MATLAB 2017a programming environment.