Robust Matrix Free Power Flow Algorithm for Solving T&D Systems

A new approach to system computations, Graph Trace Analysis (GTA), is applied to the power flow problem. A matrix free GTA power flow algorithm that solves unbalanced, three-phase transmission, substations, and multi-phase distribution, all in the same model, is presented. GTA traces are used to combine both Gauss-Seidel (GS) and continuation methods into a GTA algorithm. Testing circuits are used to demonstrate the capability of the new GTA power flow, and solutions are compared and/or verified against Newton-Raphson and forward/backward sweep based power flow algorithms. The comparisons include convergence characteristics for steady-state voltage stability analysis. It is shown that the computational complexity of GS-GTA grows linearly with the size of the model.

[1]  Ivar Jacobson,et al.  The unified modeling language reference manual , 2010 .

[2]  Y. Tamura,et al.  A Load Flow Calculation Method for Ill-Conditioned Power Systems , 1981, IEEE Transactions on Power Apparatus and Systems.

[3]  B. Stott,et al.  Review of load-flow calculation methods , 1974 .

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

[5]  R. G. Carpenter,et al.  Principles and procedures of statistics, with special reference to the biological sciences , 1960 .

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

[7]  K. R. Padiyar,et al.  ENERGY FUNCTION ANALYSIS FOR POWER SYSTEM STABILITY , 1990 .

[8]  Yasuo Tamura,et al.  A Load Flow Calculation Method for Ill-Conditioned Power Systems , 1981, IEEE Transactions on Power Apparatus and Systems.

[9]  S.M. Halpin,et al.  Sparse Matrix Techniques in Power Systems , 2007, 2007 Thirty-Ninth Southeastern Symposium on System Theory.

[10]  Ahmad Tbaileh,et al.  Graph Trace Analysis: An object-oriented power flow, verifications and comparisons , 2017 .

[11]  Fangxing Li,et al.  Distributed algorithms with theoretic scalability analysis of radial and looped load flows for power distribution systems , 2003 .

[12]  Robert J. Thomas,et al.  A posturing strategy against voltage instabilities in electric power systems , 1988 .

[13]  O. Malik,et al.  Load-Flow Solutions for Ill-Conditioned Power Systems by a Newton-Like Method , 1982, IEEE Transactions on Power Apparatus and Systems.

[14]  Francisco de Leon,et al.  A Robust Multiphase Power Flow for General Distribution Networks , 2010, IEEE Transactions on Power Systems.