Power Flow Solvers for Direct Current Networks

Abstract

With increasing direct current (DC) deployments in distribution feeders, microgrids, smart buildings, and highvoltage transmission, there is a need for better understanding the landscape of power flow (PF) solutions and 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 PF solution, if one exists. To handle distributed renewable generators typically operating in constantpower mode, 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 minimization approach shows that under limited constant-power demand, all PF solutions are locally stable. The derived conditions can be readily checked without knowing the system state. The applicability of the conditions and the performance of the iterative schemes are numerically validated on a radial distribution feeder and two meshed transmission systems under varying loading conditions.

Advanced Hierarchical Control and Stability Analysis of DC Microgrids

“…In DC networks there are several types of loads one can encounter. The presence of ZIP model loads in DC microgrids, for instance, has become more and more predominant recently (see [82][83][84][85][86][87][88]). Consider the electronic circuit in Figure 2.6, consisting of a constant current source i L , a DC capacitor C, and a generic load.…”

Solvability of the Power Flow Problem in DC Overhead Wire Circuit

“…Although there exists a rich literature on the alternating current (AC) power flow problem [14], papers on the DC PF problem were limited in the past. In the majority of cases, they dealt with the DC PF problem only from application point of view [12,1,5,10] and without mentioning the solvability of the problem or uniqueness of the solution.…”

Solvability of the power flow problem in DC overhead wire circuit modeling

“…In this manuscript, we consider the well-known DC power flow (PF) problem, where electric traction substations are modelled as constant voltage sources with voltages V • ; the resistance of overhead wires is replaced by ideal resistor elements with the resistances R • linearly dependent on the distances between nodes; trolleybuses are substituted by an electric current sources with power loads P • proportional to source currents I • ; and the corresponding connection nodes are associated with electric potentials ϕ • (see a sample DC network in Figure 1). Although there exists a rich literature on the alternating current (AC) power flow problem [16], papers on the DC PF problem were limited in the past. In the majority of cases, they dealt with the DC PF problem only from application point of view [14], [11], [18], [10] and without mentioning the solvability of the problem or uniqueness of the solution.…”

“…Further, Taylor's series expansion was used to linearize the DC PF problem in [13]. Taheri and Kekatos [16] proposed three various approaches to solve the DC PF problem assuming bounded power demands, and suggested a decision tree to select the proper method with guaranteed convergence. The DC PF problem was also reformulated as an optimization task [17], [7] and its solvability was discussed.…”