Estimating the saddle-node bifurcation point of static power systems using the holomorphic embedding method

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.

Section: Holomorphic Embedding Load Flow Methodsmentioning

confidence: 99%

Section: Dft‐padé Helm and N‐r Comparisonmentioning

confidence: 95%

“…The HELM solution for the 2‐bus system was obtained by applying () and (), while the direction‐of‐change formulation was used for the 30‐bus system …”

Section: Dft‐padé Helm and N‐r Comparisonmentioning

confidence: 99%

“…More recently, optimization algorithms and neural networks have made their contributions. Quadratic approximation and the HELM, also of late appearance, are noniterative methods.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Sarnari

Živanović

Al-Sarawi

2019

“…Further studies carried out embeddings of PV buses . Also, a polynomial ZIP load model is devised for HELM applications, and HELM‐based approaches are proposed to estimate saddle node bifurcations . Similarly, a holomorphic embedding method is conceived for computing type‐1 power flow solutions .…”

Section: Introductionmentioning

confidence: 99%

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

Ortega

Molina

Muñoz

et al. 2020

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.

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

Tostado‐Véliz

Hasanien

Turky

et al. 2021

With the increasing electricity consumption and difficulty in upgrading existing infrastructures, ill-conditioned power flow (PF) cases are becoming more frequent nowadays. In this context, classical robust solvers may be unsuitable for realistic networks, which typically encompass thousands of buses, because of their high computational burden or low convergence rate. This article tackles this issue by proposing a novel PF solver, which presents acceptable robustness and efficiency in solving large-scale ill-conditioned systems. The proposed algorithm collects the advantage of various numerical solvers, which by separate present different weaknesses, but actuating in coordination their strengths can be jointly exploited. More precisely, the robust Forward-Euler and Trapezoidal rules are combined with the efficient Darvishi cubic technique. Thereby, an original predictor-corrector algorithm is developed to effectively coordinate the different numerical algorithms involved, obtaining a robust but efficient yet solution procedure. Various large-scale illconditioned benchmark systems are studied under different stressing conditions. The results obtained with the developed technique are promising, outperforming other robust and standard PF solvers. K E Y W O R D S computational efficiency, ill-conditioned cases, large-scale systems, power flowList of Symbols and Abbreviations: t, time instant; (.) sch , scheduled value; i, denotes the ith bus of the system; k, Denotes the kth iteration of an iterative algorithm; n l , total number of PQ buses; n g , total number of PV buses; n, size of the power flow state vector (n = 2n l + n g in polar coordinates); N, number of iterative loops; ω, state vector of a dynamic system; Δt, time step; P, nodal active power injection; Q, nodal reactive power injection; V∠δ, nodal voltage; Y∠θ, element of the admittance matrix; h, step size; ε, convergence tolerance; k max , maximum number of iterations allowed; g, power flow equations; [Á] T , transpose operator; [Á] À1 , inverse operator; kÁk ∞ , infinity norm; r x , vector/matrix gradient (first derivative) with respect to x; max{a,b}, returns b if b > a and a otherwise; min{a,b}, returns b if b < a and a otherwise; x, y, z, power flow state vector; δ PV , voltage angles at PV buses; δ PQ , voltage angles at PQ buses; V PQ , voltage magnitudes at PQ buses; g x , Jacobian matrix formed by the first partial derivatives of g with respect x; I, identity matrix; BEM, Backward-Euler method; HKW, Heun-King Werner approach; HOLM, high order Levenberg-Marquardt solver; LU, lower-upper; NR, Newton-Raphson technique; OMP, optimal multiplier method in polar coordinates; PF, power flow; TR, trapezoidal rule applied to PF analysis; 3OD, darvishi's cubic method applied to PF analysis.