S.A. Naqavi

Bio: S.A. Naqavi is an academic researcher from Cornell University. The author has contributed to research in topics: Fractal. The author has an hindex of 1, co-authored 1 publications receiving 36 citations.

Load-flow fractals draw clues to erratic behaviour

Abstract: Fractal images have been discovered in many areas of science and engineering in the past two decades, so it is not surprising that they have also appeared in power system literature. This article provides a brief introduction to fractals and presents some fractal patterns produced by Newton-Raphson load-flow calculations for a small power system. If we imagine performing load-flow calculations from a dense grid of initial conditions, the region of initial conditions that converge to a particular equilibrium point using the Newton-Raphson method is seen to have a fractal boundary.

[IEEE 37th Annual Hawaii International Conference on System Sciences, 2004. Proceedings of the - Big Island, HI, USA (2004.01.8-2004.01.8)] 37th Annual Hawaii International Conference on System Sciences, 2004. Proceedings of the - A comparison of the AC and DC power flow models for LMP calculations

Abstract: The paper examines the tradeoffs between using a full ac model versus the less exact, but much faster, dc power flow model for LMP-based market calculations. The paper first provides a general discussion of the approximations associated with using a dc model, with an emphasis on the impact these approximations will have on security constrained OPF (SCOPF) results and LMP values. Then, since the impact of the approximations can be quite system specific, the paper provides case studies using both a small 37 bus system and a somewhat larger 12,965 bus model of the Midwest U.S. transmission grid. Results are provided comparing both the accuracy and the computational requirements of the two models. The general conclusion is that while there is some loss of accuracy using the dc approximation, the results actually match fairly closely with the full ac solution.

A comparison of the AC and DC power flow models for LMP calculations

Abstract: The paper examines the tradeoffs between using a full ac model versus the less exact, but much faster, dc power flow model for LMP-based market calculations. The paper first provides a general discussion of the approximations associated with using a dc model, with an emphasis on the impact these approximations will have on security constrained OPF (SCOPF) results and LMP values. Then, since the impact of the approximations can be quite system specific, the paper provides case studies using both a small 37 bus system and a somewhat larger 12,965 bus model of the Midwest U.S. transmission grid. Results are provided comparing both the accuracy and the computational requirements of the two models. The general conclusion is that while there is some loss of accuracy using the dc approximation, the results actually match fairly closely with the full ac solution.

The Holomorphic Embedding Load Flow method

Abstract: The Holomorphic Embedding Load Flow is a novel general-purpose method for solving the steady state equations of power systems. Based on the techniques of Complex Analysis, it has been granted two US Patents. Experience has proven it is performant and competitive with respect established iterative methods, but its main practical features are that it is non-iterative and deterministic, yielding the correct solution when it exists and, conversely, unequivocally signaling voltage collapse when it does not. This paper reviews the embedded load flow method and highlights the technological breakthroughs that it enables: reliable real-time applications based on unsupervised exploratory load flows, such as Contingency Analysis, OPF, Limit-Violations solvers, and Restoration plan builders. We also report on the experience with the method in the implementation of several real-time EMS products now operating at large utilities.

The Holomorphic Embedding Method Applied to the Power-Flow Problem

Abstract: The Holomorphic Embedding Load-Flow Method (HELM) solves the power-flow problem to obtain the bus voltages as rational approximants, that is, a ratio of complex-valued polynomials of the embedding parameter. The proof of its claims (namely that: 1) it is guaranteed to find a solution if it exists; 2) it is guaranteed to find only a high-voltage (operable) solution; and 3) that it unequivocally signals if no solution exists) are rooted in complex analysis and the theory developed by Antonio Trias and Herbert Stahl. HELM is one variant of the holomorphic embedding method (HEM) for solving nonlinear equations, the details of which may differ from those available in its published patents. In this paper we show that the HEM represents a distinct class of nonlinear equation solvers that are recursive, rather than iterative. As such, for any given problem, there are an infinite number of HEM formulations, each with different numerical properties and precision demands. The objective of this paper is to provide an intuitive understanding of HEM and apply one variant to the power-flow problem. We introduce one possible PV bus model compatible with the HEM and examine some features of different holomorphic embeddings, giving step-by-step details of model building, germ calculation, and the recursive algorithm.

A comparison of the optimal multiplier in polar and rectangular coordinates

Abstract: Studies of the optimal multiplier (or optimal step size) modification to the standard Newton-Raphson (NR) load flow have mainly focused on highly stressed and unsolvable systems. This paper extends these previous studies by comparing performance of the NR load flow with and without optimal multipliers for a variety of unstressed, stressed, and unsolvable systems. Also, the impact of coordinate system choice in representing the voltage phasor at each bus is considered. In total, four solution methods are compared: the NR algorithm with and without optimal multipliers using polar and rectangular coordinates. This comparison is carried out by combining analysis of the optimal multiplier technique with empirical results for two-bus, 118-bus, and 10 274-bus test cases. These results indicate that the polar NR load flow with optimal multipliers is the best method of solution for both solvable and unsolvable cases.