The Holomorphic Embedding Load Flow method

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.

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

[2]  Antonio Montes.  Algebraic solution of the load-flow problem for a 4-nodes electrical network , 1998 .

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

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

[5]  L. Ahlfors.  Complex analysis : an introduction to the theory of analytic functions of one complex variable / Lars V. Ahlfors , 1984 .

[6]  F. Wu,et al.  Theoretical study of the convergence of the fast decoupled load flow , 1977, IEEE Transactions on Power Apparatus and Systems.

[7]  I. Dobson.  Observations on the geometry of saddle node bifurcation and voltage collapse in electrical power systems , 1992 .

[8]  John G. Vlachogiannis.  Control adjustments in fast decoupled load flow , 1994 .

[9]  Georgios Leonidopoulos.  Approximate linear decoupled solution as the initial value of power system load flow , 1995 .

[10]  S.-K. Chang,et al.  Solving the adjustment interactions in fast decoupled load flow , 1991 .

[11]  Herbert Stahl,et al.  Extremal domains associated with an analytic function I , 1985 .

[12]  Thomas J. Overbye,et al.  Techniques for improving power flow convergence , 2000, 2000 Power Engineering Society Summer Meeting (Cat. No.00CH37134).

[13]  Brian Stott,et al.  Decoupled Newton Load Flow , 1972 .

[14]  O.A.S. Carpinteiro,et al.  Non-iterative load-flow method as a tool for voltage stability studies , 2007 .

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

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

[17]  Robert Rumely,et al.  Capacity theory on algebraic curves , 1989 .

[18]  Claudio A. Caiiizares.  ON BIFURCATIONS, VOLTAGE COLLAPSE AND LOAD MODELING , 1995 .

[19]  Herbert Stahl,et al.  The convergence of Padé approximants to functions with branch points , 1997 .

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

[21]  Wenzhong Gao,et al.  The application of the Groebner Basis technique in power flow study , 2009, 41st North American Power Symposium.

[22]  H. Wilf,et al.  Direct Solutions of Sparse Network Equations by Optimally Ordered Triangular Factorization , 1967 .

[23]  J. C. Salmon,et al.  Series load flow : A novel non-iterative load flow method , 1998 .

[24]  L. Ahlfors.  Complex Analysis , 1979 .

[25]  Slobodan T. Despotovic,et al.  A Rapid and Reliable Method for Solving Load Flow Problems , 1971 .

[26]  J. Hubbard,et al.  How to find all roots of complex polynomials by Newton’s method , 2001 .

[27]  Herbert Stahl,et al.  The structure of extremal domains associated with an analytic function , 1985 .

[28]  P. Sauer,et al.  Explicit Load Flow Series and Functions , 1981, IEEE Transactions on Power Apparatus and Systems.

[29]  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).

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

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

[32]  B. Sturmfels.  SOLVING SYSTEMS OF POLYNOMIAL EQUATIONS , 2002 .

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

[34]  J. B. Ward,et al.  Digital Computer Solution of Power-Flow Problems [includes discussion] , 1956, Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems.

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

[36]  Lars V. Ahlfors.  An introduction to the theory of analytic functions of one complex variable , 1978 .