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    Robust Convergence of Power Flow using Tx Stepping Method with Equivalent Circuit Formulation

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    Robust solving of critical large power flow cases (with 50k or greater buses) forms the backbone of planning and operation of any large connected power grid. At present, reliable convergence with applications of existing power flow tools to large power systems is contingent upon a good initial guess for the system state. To enable robust convergence for large scale systems starting with an arbitrary initial guess, we extend our equivalent circuit formulation for power flow analysis to include a novel continuation method based on transmission line (Tx) stepping. While various continuation methods have been proposed for use with the traditional PQV power flow formulation, these methods have either failed to completely solve the problem or have resulted in convergence to a low voltage solution. The proposed Tx Stepping method in this paper demonstrates robust convergence to the high voltage solution from an arbitrary initial guess. Example systems, including 75k+ bus test cases representing different loading and operating conditions for Eastern Interconnection of the U.S. power grid, are solved from arbitrary initial guesses.Interconnection of the U.S. power grid, are solved from arbitrary initial guesses

    Recent Advances in Computational Methods for the Power Flow Equations

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    The power flow equations are at the core of most of the computations for designing and operating electric power systems. The power flow equations are a system of multivariate nonlinear equations which relate the power injections and voltages in a power system. A plethora of methods have been devised to solve these equations, starting from Newton-based methods to homotopy continuation and other optimization-based methods. While many of these methods often efficiently find a high-voltage, stable solution due to its large basin of attraction, most of the methods struggle to find low-voltage solutions which play significant role in certain stability-related computations. While we do not claim to have exhausted the existing literature on all related methods, this tutorial paper introduces some of the recent advances in methods for solving power flow equations to the wider power systems community as well as bringing attention from the computational mathematics and optimization communities to the power systems problems. After briefly reviewing some of the traditional computational methods used to solve the power flow equations, we focus on three emerging methods: the numerical polynomial homotopy continuation method, Groebner basis techniques, and moment/sum-of-squares relaxations using semidefinite programming. In passing, we also emphasize the importance of an upper bound on the number of solutions of the power flow equations and review the current status of research in this direction.Comment: 13 pages, 2 figures. Submitted to the Tutorial Session at IEEE 2016 American Control Conferenc

    State of the art for voltage collapse point approximation using continuation power flow

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    In this study we investigate the relative ability of comprehensive income and net income to summarize firm performance as reflected in stock returns. We also examine which comprehensive income adjustments improve the ability of income to summarize firm performance. We also investigate this claim that income measured on a comprehensive basis is a better measure of firm performance than other summary income measures. The results do not show that comprehensive income is superior to net income for evaluating firm performance on the basis of stock return and price. Except for investment industrial group, In Tehran Stock Exchange, we found no evidence that comprehensive income for firm performance evaluation on the basis of cash flows prediction is superior to net income. While, we found the better results for the state companies (only in other companies group), i.e., firm performance evaluation on the basis of cash flows prediction using comprehensive income is superior to net income. Collectively, our results provide some weak evidence that show comprehensive income adjustments improve ability of income for reflecting firm performance. Continuation power flow is one method to determine the proximity to voltage collapse point and can be described as a power flow solution, which is used to analyze the stability of power system under normal and disturbance conditions. The main purpose of Continuation Power Flow is to find a continuity of power flow solution for a given load change. Conventional power flow algorithms are subjected to the convergence problems at operating condition near the stability limit. Therefore researchers proposed to use the Continuation Power Flow to solve this problem by reformulating the power flow equations and ensuring the system remains in well-conditioned at all possible loading condition. This Continuation Power Flow uses an iterative process involving predictor and corrector step. However the continuation step, parameter variation and the reliability of the system are still in question. This paper discusses several issues including the needs, demands and expectations of continuation power flow. Several solutions have been proposed by the previous researchers is been discussed