Augmenting load flow software for reliable steady‐state voltage stability studies

Abstract

Summary For decades, researchers and practitioners have developed improvements for Newton‐Raphson (N‐R) load flow to overcome some of its limitations. In this paper, we present a novel method to solve those inherent iterative algorithm limitations. It is based on N‐R combined with a supplementary algorithm that uses the discrete Fourier transform (DFT) and robust Padé approximants (PAs) and it is suitable for planning and simulation studies. This novel method analyses bus behaviour from the loading perspective where plain N‐R may not converge to the correct results. Thus, avoiding possible performance deficiencies when bus loading approaches the stability limit or when starting point is not close enough to the actual operating value. The proposed method samples voltages in the complex domain to attain superior convergence properties, guaranteeing high accuracy within the bus‐voltage stability limits (VSLs). Additionally, as a by‐product of the proposed method, load buses can be classified according to their criticality. The presented method will suit existing N‐R‐based systems with minor modifications, allowing practitioners to preserve their investment in load flow software. Results and performance comparisons with the conventional N‐R, holomorphic embedding load flow method (HELM), and continuation power flow (CPF) are presented to demonstrate the robustness of the proposed method.

Solving realistic large‐scale ill‐conditioned power flow cases based on combination of numerical solvers

“…As seen, angles obtained with BEM usually take extreme values, which is symptomatic of unstable voltage regions. 45 On the other hand, HOLM did not actually calculate the low voltage solution of the System 5, but results obtained differed by $5% in some cases with respect to the correct solution, which has been considered unacceptable in this paper. These evidences are in concordance with the conclusions drawn in other research, 23,38 where it was evidenced the problems of Levenberg-based methods for achieving physical solutions.…”

“…To illustrate it, Figure 2 compares the voltage angles calculated by BEM from a flat start with the correct solution of the system 5 (only 100 buses are plotted for simplicity). As seen, angles obtained with BEM usually take extreme values, which is symptomatic of unstable voltage regions 45 . On the other hand, HOLM did not actually calculate the low voltage solution of the System 5, but results obtained differed by ~5% in some cases with respect to the correct solution, which has been considered unacceptable in this paper.…”

“…To this end, a predictor‐corrector scheme is used. In this paradigm, the predicted value should be sufficient robust 45 ; thereby, it should be calculated by a robust solver. The new proposal uses the Forward‐Euler method to this end, as follows: where .…”

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

“…Moreover, a technique is developed to include control limits and to increase the precision of the solution, specially in highly loaded systems by using a Padé‐Weierstrass continuation technique . A similar method is proposed in Sarnari et al to estimate voltage stability loading limits considering discrete Fourier transform and Robust Padé approximants in NR method, providing performance comparisons with respect to the HELM and other approaches. However, to the best knowledge of the authors, distributed slack bus (DSB) models still have not been implemented in the HELM to date.…”