Distributed slack bus model formulation for the holomorphic embedding load flow method

Abstract

Summary Distributed slack bus (DSB) models for the resolution of power flow problems are a more realistic approach than the classical single slack bus concept. DSB models have been widely implemented in iterative approaches such as in Newton‐Raphson power flow methods. However, iterative algorithms may lead to incorrect solutions or may fail to reach convergence under inappropriate initial estimations. The holomorphic embedding load‐flow method (HELM) deals with the solution of the nonlinear power flow equations by means of complex analysis techniques, resulting in a deterministic and noniterative method, which is independent of initial estimations. As such, this paper proposes, from two different methodologies, a novel formulation and implementation of the DSB model for the HELM, which overcomes in that way the disadvantages of iterative methods and also incorporates the inherent advantages of DSB models. Moreover, this paper performs convergence and speed capability tests of the two proposed methodologies using two real‐size benchmark systems.

A Fast Holomorphic Embedding Power Flow Approach for Meshed Distribution Networks

“…􏽥 Y − 1 is an N × N matrix implicitly indicating the bus 20) can be solved for 􏽥 V either iteratively or recursively. To solve the equation recursively, equations ( 16) and ( 20) are embedded with parameter, α as shown in (21) and (22). is embedding implies that α is a parameter for constant power injections.…”

“…e authors in [19,20] showed the benefits from utilizing the HELM approach for three-phase unbalanced optimal power flow and for probabilistic power flow for small distribution test networks; however, the long time needed to solve the power flow equations impeded extending the application to larger distribution test networks. In [21,22], the authors notably used static approximate Newton-Raphson-Sidel (ANRS) and the developed down-hill (DDH) algorithm methods to derive a reliable and efficient holomorphic approach to evaluate dynamic available transfer capability and proposed distributed slack bus model formulation for the holomorphic embedding load flow method, respectively; however, Padé Approximation is still used.…”

HELMpy, Open Source Package of Power Flow Solvers, Including the Holomorphic Embedding Load Flow Method (HELM), Developed on Python 3

“…A DSB model based on the participation factors proposed in [3] is developed in HELMpy to be used along with the HELM and NR method. In the case of the NR algorithm, the DSB model is formulated according to [18] and adapted to balanced systems, while in the case of the HELM, the formulations devised in [14] are used.…”

“…Convergence is achieved when all of these mismatch errors are less or equal than a predefined tolerance. Similarly, the convergence criteria for the HELM consists in checking whether the difference between magnitudes and phase angles of two consecutive voltages (obtained through analytic continuation of power series) at each bus is less or equal than a predefined tolerance [14].…”

“…This software is available as a repository on GitHub [11] and stored on Zenodo [12] under the GNU Affero General Public License v3.0 or later [13] (AGPL-3.0or-later). HELMpy was developed to implement and validate the DSB model formulation devised in the research paper [14].…”