A Time-Domain Companion-Circuit Newton-Based Methodology Applied to the Harmonic Analysis of Electrical Networks With PV Systems

This contribution proposes an efficient methodology in time domain (TD) based on companion-circuit analysis (CCA) and a Newton method of extrapolation to the Limit Cycle (periodic steady state solution) based on a Numerical Differentiation (ND) process. Its formulation is amenable to the solution approach followed by standardized digital simulators widely accepted by the power industry, such as EMTP and/or EMTDC. The particular application reported in this research is oriented to the dynamic and fast periodic steady state solution of nonlinear single-phase electrical networks incorporating photovoltaic (PV) systems under harmonic distortion conditions. Fundamentally, the proposed methodology is based on the representation of linear and nonlinear elements (e.g., switching elements), using Norton equivalents. This solution method is based on the determination of discrete differential equations sets, obtained by nodal analysis. The solution process is iteratively obtained by using LU decomposition. In general terms, the application is based on the combination of the CCA and ND methods (CCA-ND), for the applying in different case studies associated with the assessment of harmonics distortion, in terms of individual and total harmonic distortion at the point of common coupling (PCC) between the PV system and the electrical system are reported. It is shown that the methodology is precise, reliable and efficient. The documented results have been successfully validated against those obtained PSCAD/EMTDC® simulator, widely accepted by the power industry.

[1]  J. Baba.  Calculation of transient voltage and current in power systems by means of a digital computer,1. , 1962 .

[2]  A. Brameller,et al.  Sparsity: Its practical application to systems analysis , 1976 .

[3]  Jos Arrillaga,et al.  Power Systems Electromagnetic Transients Simulation , 2002 .

[4]  Jim Hefferon,et al.  Linear Algebra , 2012 .

[5]  J. Segundo-Ramírez,,et al.  An Enhanced Process for the Fast Periodic Steady State Solution of Nonlinear Systems by Poincare Map and Extrapolation to the Limit Cycle , 2010 .

[7]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[8]  Hyosung Kim,et al.  PV cell modeling on single-diode equivalent circuit , 2013, IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society.

[9]  W. McMurray.  Efficient snubbers for voltage-source GTO inverters , 1985, 1985 IEEE Power Electronics Specialists Conference.

[10]  Tore Undeland,et al.  A snubber configuration for both poker transistors and GTO PHH inverters , 1984, 1984 IEEE Power Electronics Specialists Conference.

[11]  R.M. Nelms,et al.  Simulation of transmission line transients using a personal computer , 1988, IEEE Conference Record of the 1988 Eighteenth Power Modulator Symposium.

[12]  Fernando L. Alvarado,et al.  Testing of Trapezoidal Integration With Damping for the Solution of Power Transient Problems , 1983, IEEE Power Engineering Review.

[13]  K Strunz,et al.  Modeling Guidelines and a Benchmark for Power System Simulation Studies of Three-Phase Single-Stage Photovoltaic Systems , 2011, IEEE Transactions on Power Delivery.

[14]  F. F. Kuo.  Network analysis by digital computer , 1966 .

[15]  A. M. Gole,et al.  Dynamic system equivalents: A survey of available techniques , 2009, 2009 IEEE Power & Energy Society General Meeting.

[16]  Leon O. Chua,et al.  Practical Numerical Algorithms for Chaotic Systems , 1989 .

[17]  Aurelio Medina,et al.  Periodic Steady State Assessment of Microgrids with Photovoltaic Generation Using Limit Cycle Extrapolation and Cubic Splines , 2018 .

[18]  T. Aprille,et al.  A computer algorithm to determine the steady-state response of nonlinear oscillators , 1972 .

[19]  Jose R. Marti,et al.  Suppression of numerical oscillations in the EMTP power systems , 1989 .

[20]  Hermann W. Dommel,et al.  Digital Computer Solution of Electromagnetic Transients in Single-and Multiphase Networks , 1969 .

[21]  G. W. Chang,et al.  Harmonic Analysis in Frequency and Time Domain , 2013, IEEE Transactions on Power Delivery.

[22]  A. Medina,et al.  Computation of the Steady-State Solution of Nonlinear Power Systems by Extrapolation to the Limit Cycle Using a Discrete Exponential Expansion Method , 2010 .

[23]  Soham Chakraborty,et al.  New Numerical Integration Methods for Simulation of Electromagnetic Transients , 2018 .

[24]  Aurelio Medina,et al.  Computation of the periodic steady state in systems with nonlinear components using a hybrid time and frequency domain methodology , 1995 .

[25]  Wenjie Wang,et al.  A Novel PV Array Connection Strategy with PV-buck Module to Improve System Efficiency , 2018, 2018 International Power Electronics Conference (IPEC-Niigata 2018 -ECCE Asia).