Efficient Load Flow Techniques Based on Holomorphic Embedding for Distribution Networks

Abstract

The Holomorphic Embedding Load flow Method (HELM) employs complex analysis to solve the load flow problem. It guarantees finding the correct solution when it exists, and identifying when a solution does not exist. The method, however, is usually computationally less efficient than the traditional Newton-Raphson algorithm, which is generally considered to be a slow method in distribution networks. In this paper, we present two HELM modifications that exploit the radial and weakly meshed topology of distribution networks and significantly reduce computation time relative to the original HELM implementation. We also present comparisons with several popular load flow algorithms applied to various test distribution networks.

A Fast Holomorphic Embedding Power Flow Approach for Meshed Distribution Networks

“…In the proposed approach, bus voltages are modelled as holomorphic functions in the constant power injections scaling parameter. is is different from the approaches in [9,15,16], where bus voltages are modelled as holomorphic functions in a scaling parameter chosen to reduce computational effort at the first recursion only; thus, the proposed approach is more intuitive than the previous approaches. e approach proposed in this paper allows solving the power flow equations in one recursion if constant power injections are not present while the approaches in [9,15,16] require more than one recursion; thus, the proposed approach has better computational efficiency than the previous approaches.…”

“…(2) e radius of convergence is checked at each recursion instead of applying analytic continuation methods such as PA. is is different from the approaches in [9,15,16], where analytic continuation methods are used for all recursions resulting in higher computational efforts. Checking the radius of convergence at each recursion avoids the computational efforts needed for the application of analytic continuation methods and ensures the robustness of the proposed method under various operating conditions.…”

“…Nevertheless, a comparison between NR and HELM shows that HELM main disadvantage is that it requires more computational time than NR when high precision solutions are desired [12][13][14]. is is mainly due to the application of the time intensive PA. To reduce computational time and increase the benefits from the original HELM, the authors in [15,16] astonishingly exploited the radial and weakly meshed topology of the traditional distribution systems. us, the reduction in computational time is not achievable for meshed distribution systems.…”

Holomorphic Embedding Load Flow Method in Three-Phase Distribution Networks With ZIP Loads

“…There are also works that present HELM applications, e.g., see [21] for probabilistic load flow analysis, [22], [23], [24] for voltage stability assessment, [25] for network reduction, [26] for locating multiple load flow solutions, [27] for line outage distribution factors, and [28] for dynamic simulation. Furthermore, there are a few works that extend HELM to solve the load flow problem in DC power transmission systems [29], single-phase distribution networks [30], [31], three-phase distribution networks [32], [33], and AC/DC hybrid power systems [34].…”

“…Apparently, there has been limited discussion on HELM's performance on the distribution network load flow problem. In our previous work [31], we proposed two HELM variants by exploiting the typical radial/weakly-meshed topology in single-phase distribution networks. Due to the nature of distribution network loads, modeling voltage-dependent ZIP load models, i.e., constant-impedance, constant-current, and constant-power, as well as ensuring holomorphicity for the representation of the current injections as a function of voltages, are of significant importance.…”