Adjoint Power Flow Analysis for Evaluating Feasibility

Recently it has been demonstrated that the equivalent circuit formulation for modeling and simulation of the AC Power Flow (AC-PF) problem can be used to improve the convergence properties and to facilitate scaling to large system sizes (80k+ buses). The nonlinear nature of the power flow formulation, however, still maintains the problem of identifying infeasibility system configurations with no solution. In this paper we introduce the Adjoint Power Flow formulation to evaluate the power flow feasibility. Infeasibility current source models are added to the system model to capture KCL (Kirchhoffs Current Law) violations within the power flow circuit problem as non-zero voltages in the adjoint (dual) circuit. We show that the solution of the Adjoint Power Flow circuit corresponds to the optimal currents needed to achieve feasibility for an infeasible system case.

[1]  William J. McCalla.  Fundamentals of Computer-Aided Circuit Simulation , 1987 .

[2]  Daniel K. Molzahn,et al.  Sufficient conditions for power flow insolvability considering reactive power limited generators with applications to voltage stability margins , 2013, 2013 IREP Symposium Bulk Power System Dynamics and Control - IX Optimization, Security and Control of the Emerging Power Grid.

[3]  Dhagash Mehta,et al.  On the Network Topology Dependent Solution Count of the Algebraic Load Flow Equations , 2015, IEEE Transactions on Power Systems.

[4]  R. Rohrer,et al.  Automated Network Design-The Frequency-Domain Case , 1969 .

[5]  Amritanshu Pandey,et al.  Robust and Efficient Power Flow Convergence with G-min Stepping Homotopy Method , 2019, 2019 IEEE International Conference on Environment and Electrical Engineering and 2019 IEEE Industrial and Commercial Power Systems Europe (EEEIC / I&CPS Europe).

[6]  I. Hiskens,et al.  Exploring the Power Flow Solution Space Boundary , 2001, IEEE Power Engineering Review.

[7]  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.

[8]  P. Kundur,et al.  Power system stability and control , 1994 .

[9]  Gabriela Hug,et al.  Improving robustness and modeling generality for power flow analysis , 2016, 2016 IEEE/PES Transmission and Distribution Conference and Exposition (T&D).

[10]  Marko Jereminov,et al.  Equivalent Circuit Formulation for Solving AC Optimal Power Flow , 2019, IEEE Transactions on Power Systems.

[11]  L. Nagel,et al.  Computer analysis of nonlinear circuits, excluding radiation (CANCER) , 1971 .

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

[13]  L.C.P. da Silva,et al.  Analysis of ill-conditioned power-flow problems using voltage stability methodology , 2001 .

[14]  Gabriela Hug,et al.  Unified power system analyses and models using equivalent circuit formulation , 2016, 2016 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT).

[15]  Chen-Sung Chang,et al.  Toward a CPFLOW-based algorithm to compute all the type-1 load-flow solutions in electric power systems , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  T. Overbye.  A power flow measure for unsolvable cases , 1994 .

[17]  R. Rohrer.  The Generalized Adjoint Network and Network Sensitivities , 1969 .

[18]  Gabriela Hug,et al.  Improving power flow robustness via circuit simulation methods , 2017, 2017 IEEE Power & Energy Society General Meeting.

[19]  Gabriela Hug,et al.  Robust Convergence of Power Flow Using TX Stepping Method with Equivalent Circuit Formulation , 2018, 2018 Power Systems Computation Conference (PSCC).

[20]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[21]  Gabriela Hug,et al.  An equivalent circuit formulation for three-phase power flow analysis of distribution systems , 2016, 2016 IEEE/PES Transmission and Distribution Conference and Exposition (T&D).