Power Flow Solvers for Direct Current Networks

TL;DR

This paper introduces three complementary power flow solution methods for DC networks, analyzing their convergence, existence, and uniqueness, with validation on various system configurations to improve efficiency and reliability.

Contribution

It presents novel algorithms for DC power flow solutions, including a monotone mapping, a Z-bus method, and an energy function approach, with theoretical guarantees and practical validation.

Findings

Monotone mapping converges to high-voltage solution without constant-power loads.

Z-bus method guarantees convergence with constant-power generation.

Conditions for solution existence and uniqueness are efficiently checkable.

Abstract

With increasing smart grid direct current (DC) deployments in distribution feeders, microgrids, buildings, and high-voltage transmission, there is a need for better understanding the landscape of power flow (PF) solutions as well as for efficient PF solvers with performance guarantees. This work puts forth three approaches with complementary strengths towards coping with the PF task in DC power systems. We consider a possibly meshed network hosting ZIP loads and constant-voltage/power generators. The first approach relies on a monotone mapping. In the absence of constant-power generation, the related iterates converge to the high-voltage solution, if one exists. To handle generators operating in constant-power mode at any time, an alternative Z-bus method is studied. For bounded constant-power generation and demand, the analysis establishes the existence and uniqueness of a PF solution within a predefined ball. Moreover, the Z-bus updates converge to this solution. Third, an energy function approach shows that under limited constant-power demand, all PF solutions are local minima of a function. The derived conditions can be checked without knowing the system state. The applicability of the conditions and the performance of the algorithms are numerically validated on a radial distribution feeder and two meshed transmission systems under varying loading conditions.