Linear approximations to AC power flow in rectangular coordinates

This paper explores solutions to linearized power-flow equations with bus-voltage phasors represented in rectangular coordinates. The key idea is to solve for complex-valued perturbations around a nominal voltage profile from a set of linear equations that are obtained by neglecting quadratic terms in the original nonlinear power-flow equations. We prove that for lossless networks, the voltage profile where the real part of the perturbation is suppressed satisfies active-power balance in the original nonlinear system of equations. This result motivates the development of approximate solutions that improve over conventional DC power-flow approximations, since the model includes ZIP loads. For distribution networks that only contain ZIP loads in addition to a slack bus, we recover a linear relationship between the approximate voltage profile and the constant-current component of the loads and the nodal active-and reactive-power injections.

[1]  Brian B. Johnson,et al.  Optimal Dispatch of Residential Photovoltaic Inverters Under Forecasting Uncertainties , 2014, IEEE Journal of Photovoltaics.

[2]  S. Zampieri,et al.  On the Existence and Linear Approximation of the Power Flow Solution in Power Distribution Networks , 2014, IEEE Transactions on Power Systems.

[3]  Christoforos N. Hadjicostis,et al.  A Two-Stage Distributed Architecture for Voltage Control in Power Distribution Systems , 2013, IEEE Transactions on Power Systems.

[4]  C. W. Taylor,et al.  Load representation for dynamic performance analysis , 1993 .

[5]  N. Martins,et al.  Developments in the Newton Raphson power flow formulation based on current injections , 1999 .

[6]  Dick Duffey,et al.  Power Generation , 1932, Transactions of the American Institute of Electrical Engineers.

[7]  Allen J. Wood,et al.  Power Generation, Operation, and Control , 1984 .

[8]  Qing-Chang Zhong,et al.  Robust Droop Controller for Accurate Proportional Load Sharing Among Inverters Operated in Parallel , 2013, IEEE Transactions on Industrial Electronics.

[9]  Germano Lambert-Torres,et al.  OPTIMAL POWER FLOW IN RECTANGULAR FORM VIA AN INTERIOR POINT METHOD , 1996 .

[10]  F. Bullo,et al.  Novel insights into lossless AC and DC power flow , 2013, 2013 IEEE Power & Energy Society General Meeting.

[11]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[12]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

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

[14]  Thomas J. Overbye,et al.  Effective calculation of power system low-voltage solutions , 1996 .

[15]  Florian Dörfler,et al.  Fast power system analysis via implicit linearization of the power flow manifold , 2015, 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[16]  A. Abur,et al.  Comparative study of polar and Cartesian co-ordinate algorithms for power-system state-estimation problems , 1985 .

[17]  M. E. El-Hawary.  Optimal Power Flow , 2006 .

[18]  L. Roy,et al.  A Cartesian Coordinate Algorithm for Power System State Estimation , 1983, IEEE Transactions on Power Apparatus and Systems.

[19]  O. Alsaç,et al.  DC Power Flow Revisited , 2009, IEEE Transactions on Power Systems.

[20]  David Tse,et al.  Geometry of injection regions of power networks , 2011, IEEE Transactions on Power Systems.

[21]  D. Hill,et al.  Computation of Bifurcation Boundaries for Power Systems: a New , 2000 .

[22]  S. G. Petoussis,et al.  Nonlinear interior-point optimal power flow method based on a current mismatch formulation , 2005 .