The Holomorphic Embedding Loadflow Method for DC Power Systems and Nonlinear DC Circuits

The Holomorphic Embedding Loadflow Method is extended here from AC to DC-based systems. Through an appropriate embedding technique, the method is shown to extend naturally to DC power transmission systems, preserving all the constructive and deterministic properties that allow it to obtain the white branch solution in an unequivocal way. Its applications extend to nascent meshed HVDC networks and also to power distribution systems in more-electric vehicles, ships, aircraft, and spacecraft. In these latter areas, it is shown how the method can cleanly accommodate the higher-order nonlinearities that characterize the I-V curves of many devices. The case of a photovoltaic array feeding a constant-power load is given as an example. The extension to the general problem of finding DC operating points in electronics is also discussed, and exemplified on the diode model.

[1]  William F. Tinney,et al.  Power Flow Solution by Newton's Method , 1967 .

[2]  Ernst Joachim Weniger,et al.  Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series , 1989 .

[3]  Herbert Stahl,et al.  Spurious poles in Pade´ approximation , 1998 .

[4]  D. C. Hamill,et al.  Nonlinear phenomena in a model spacecraft power system , 1998, COM.P.EL.98. Record 6th Workshop on Computer in Power Electronics (Cat. No.98TH8358).

[5]  J. Nuttall,et al.  THE CONVERGENCE OF PADÉ APPROXIMANTS TO FUNCTIONS WITH BRANCH POINTS , 1977 .

[6]  W. Gragg,et al.  The Padé Table and Its Relation to Certain Algorithms of Numerical Analysis , 1972 .

[7]  Fred C. Lee,et al.  Large-signal stability analysis of spacecraft power processing systems , 1990 .

[8]  David Y. Y. Yun,et al.  Fast Solution of Toeplitz Systems of Equations and Computation of Padé Approximants , 1980, J. Algorithms.

[9]  Thomas J. Overbye,et al.  Low voltage power flow solutions and their role in exit time based security measures for voltage collapse , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[10]  Ljiljana Trajkovic.  Homotopy Methods for Computing Dc Operating Points , 1999 .

[11]  Avram Sidi,et al.  Practical Extrapolation Methods - Theory and Applications , 2003, Cambridge monographs on applied and computational mathematics.

[12]  Antonio J. Conejo,et al.  Electric Energy Systems : Analysis and Operation , 2008 .

[13]  Henry C. Thacher,et al.  Applied and Computational Complex Analysis. , 1988 .

[14]  Y. Tamura,et al.  Relationship Between Voltage Instability and Multiple Load FLow Solutions in Electric Power Systems , 1983, IEEE Transactions on Power Apparatus and Systems.

[15]  H. Mori,et al.  Chaotic behavior of the Newton-Raphson method with the optimal multiplier for ill-conditioned power systems , 2000, 2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353).

[16]  B. Buchberger,et al.  Gröbner bases and applications , 1998 .

[17]  Timothy A. Davis,et al.  Direct methods for sparse linear systems , 2006, Fundamentals of algorithms.

[18]  Herbert Stahl,et al.  On the convergence of generalized Padé approximants , 1989 .

[19]  Lloyd N. Trefethen,et al.  Robust Padé Approximation via SVD , 2013, SIAM Rev..

[20]  Jaijeet S. Roychowdhury,et al.  Delivering global DC convergence for large mixed-signal circuits via homotopy/continuation methods , 2006, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[21]  L. Wehenkel,et al.  Contingency Ranking With Respect to Overloads in Very Large Power Systems Taking Into Account Uncertainty, Preventive, and Corrective Actions , 2013, IEEE Transactions on Power Systems.

[22]  Ian M. Mitchell,et al.  DC Operating Point Analysis – A Formal Approach , 2009 .

[23]  Mark Zwolinski,et al.  Globally convergent algorithms for DC operating point analysis of nonlinear circuits , 2003, IEEE Trans. Evol. Comput..

[24]  Antonio Trias,et al.  Fundamentals of the Holomorphic Embedding Load-Flow Method , 2015, ArXiv.

[25]  Alan N. Willson,et al.  Nonlinear networks : theory and analysis , 1975 .

[26]  S. A. Naqavi,et al.  Load flow fractals , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[27]  Seth R. Sanders,et al.  Multi-parameter homotopy methods for finding DC operating points of nonlinear circuits , 1993, ISCAS.

[28]  W. Press,et al.  Numerical Recipes: The Art of Scientific Computing , 1987 .

[29]  Dirk Van Hertem,et al.  Feasibility of DC transmission networks , 2011, 2011 2nd IEEE PES International Conference and Exhibition on Innovative Smart Grid Technologies.

[30]  R.A.M. VanAmerongen.  A general-purpose version of the fast decoupled loadflow , 1989 .

[31]  O. Alsac,et al.  Fast Decoupled Load Flow , 1974 .

[32]  Leon O. Chua,et al.  Linear and nonlinear circuits , 1987 .

[33]  Konstantin S. Turitsyn,et al.  Appearance of multiple stable load flow solutions under power flow reversal conditions , 2014, 2014 IEEE PES General Meeting | Conference & Exposition.

[34]  E. Allgower,et al.  Introduction to Numerical Continuation Methods , 1987 .

[35]  Venkataramana Ajjarapu,et al.  The continuation power flow: a tool for steady state voltage stability analysis , 1991 .

[36]  Ivan Niven.  Formal Power Series , 1969 .

[37]  Ljiljana Trajkovic,et al.  Artificial parameter homotopy methods for the DC operating point problem , 1993, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[38]  S. Cabay,et al.  A weakly stable algorithm for Pade´ approximants and the inversion of Hankel matrices , 1993 .

[39]  R D Zimmerman,et al.  MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education , 2011, IEEE Transactions on Power Systems.

[40]  Kenneth J. Metcalf.  Power Management and Distribution (PMAD) Model Development: Final Report , 2011 .

[41]  James S. Thorp,et al.  Load-flow fractals draw clues to erratic behaviour , 1997 .

[42]  A. Trias,et al.  The Holomorphic Embedding Load Flow method , 2012, 2012 IEEE Power and Energy Society General Meeting.

[43]  George Labahn,et al.  Effective Computation of Rational Approximants and Interpolants , 2000, Reliab. Comput..

[44]  Thomas J. Overbye,et al.  A new method for finding low-voltage power flow solutions , 2000, 2000 Power Engineering Society Summer Meeting (Cat. No.00CH37134).

[45]  Robert A. W. van Amerongan.  A general-purpose version of the fast decoupled load flow , 1989 .

[46]  Ljiljana Trajkovic,et al.  DC operating points of transistor circuits , 2012 .