A Graph-Based Power Flow Method for Balanced Distribution Systems

Abstract

Abstract:A power flow method based on graph theory is presented for three-phase balanced distribution systems. The graph theory is used to describe the power network and facilitate the derivation of the relationship between bus Currents and the bus Voltage Bias from the feeder bus (the CVB equation). A distinctive feature of the CVB equation is its unified form for both radial and meshed networks. The method requires neither a tricky numbering and layering of nodes nor breaking meshes and loop-analysis, which are both necessary in previous works for meshed networks. The convergence of the proposed method is proven using the Banach fixed-point theorem.

Reduction of Losses and Operating Costs in Distribution Networks Using a Genetic Algorithm and Mathematical Optimization

“…where t represents the iterations indicator. The successive approximations method guarantees convergence as shown by [42], as this method is a particular case of the Banach fixed-point theorem. Is is considered that the solution has been achieved when the error between the voltages of two consecutive iterations is less than a determined tolerance, i.e., min…”

On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence

“…The main challenge in the power-flow analysis of distribution networks is the constant power loads that produce nonlinear relationships between the voltages and powers [9,10], which makes the use of numerical methods for solving the power-flow problem necessary [11]. A typical tendency in the power-flow analysis of electrical distribution networks is the use of graph-based methods to address the power-flow problem based on the radial structure of the grid [12,13]. However, these methodologies are not useful in the case of weakly or strongly meshed distribution networks [14], which can cause major issues in modern power systems where meshed structures can help with grid performance in terms of realizing lower power losses and improvement voltage profiles [15].…”

“…However, this research is motivated by the fact that the classical backward-forward power-flow method is commonly formulated via sequential steps that require that the grid is ordered in layers [21]. It has a radial structure as, all the currents are calculated in the backward stage, while all the voltages are defined in the forward stage [13]. As this operation can be efficient, these stages exclude meshed configurations, which implies that it is not applicable to weakly or strongly meshed distribution networks.…”

Optimisation of electrical network configuration: Complexity and algorithms for ring topologies

“…In such planning schedules, vulnerability of configurations can be taken into account by considering various graph theory metrics [1]. Note that in this context, balanced planning schedules can also be provided by configuring the network in balanced subnetworks [21,9,12] or by considering balanced configurations in terms of power of loads [20].…”

“…In this paper, we focus on such approaches related to Steiner tree problems [10,23] with a specific metric focusing balanced distribution of the required load on all the sources. Indeed in our context, the electric flow in a network is a direct consequence of the chosen configuration and the consumers [20]. Thus the objective is not to compute an electric flow in a graph (such as in [5]) but rather to determine the best spanning sub-DAG of the whole network optimizing the balance of proportional use of sources capacities.…”