A state space three-phase multilimb transformer model in the time domain: fast periodic steady state analysis

In this contribution, a state space three-phase multilimb transformer model is proposed and applied to the computation of fast and efficient periodic steady state solutions. The model takes into account the physical dimensions at different regions of the magnetic core and the effects of nonlinear saturation and winding electrical connections, respectively. The full transformer electromagnetic model is represented by a set of algebraic and ordinary differential equations (ODEs), solved in the time domain by the fourth order Runge-Kutta integration method. A case study is presented to illustrate and demonstrate the potential of the proposed transformer model. The periodic steady state solution is efficiently obtained in the time domain by a Newton procedure for the acceleration of the convergence of the state variables to the limit cycle.

[1]  E. C. Cherry.  The Duality between Interlinked Electric and Magnetic Circuits and the Formation of Transformer Equivalent Circuits , 1949 .

[2]  G. R. Slemon,et al.  Equivalent circuits for transformers and machines including non-linear effects , 1953 .

[3]  R. D. Slater,et al.  Representation of magnetisation curves by exponential series , 1973 .

[4]  T. H. Barton,et al.  Three Phase Transformer Transients , 1974 .

[5]  N. L. Diseko,et al.  A method of simulating linear and nonlinear resonant phenomena associated with transformer feeders , 1980 .

[6]  M. A. Rahman,et al.  Digital Simulation of Magnetizing Inrush Currents in Three-Phase Transformers , 1986, IEEE Power Engineering Review.

[7]  J. Milias-Argitis,et al.  An incremental transformer model for the study of harmonic overvoltages in weak AC/DC systems , 1988 .

[8]  Adam Semlyen,et al.  Investigation of the Inrush Phenomenon a Quasi-Stationary Approach in the Harmonic Domain , 1989, IEEE Power Engineering Review.

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

[10]  Jos Arrillaga,et al.  General frame of reference for analysis of harmonic distortion in systems with multiple transformer nonlinearities , 1989 .

[11]  C.M. Arturi.  Transient Simulation and Analysis of Three-Phase Five-Limb Step-Up Transformer Following an Out-of-Phase Synchronization , 1991, IEEE Power Engineering Review.

[12]  F. de Leon,et al.  Reduced order model for transformer transients , 1992 .

[13]  Jos Arrillaga,et al.  Simulation of multilimb power transformers in the harmonic domain , 1992 .

[14]  Jos Arrillaga,et al.  Generalised modelling of power transformers in the harmonic domain , 1992 .

[15]  X. S. Chen,et al.  Digital model for transient studies of a three-phase five-legged transformer , 1992 .

[16]  S. Lu,et al.  FEM analysis of DC saturation to assess transformer susceptibility to geomagnetically induced currents , 1993 .

[17]  F. de Leon,et al.  Complete transformer model for electromagnetic transients , 1994 .

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

[19]  S. S. Venkata,et al.  A three-phase three-winding core-type transformer model for low-frequency transient studies , 1997 .

[20]  Bruce A. Mork,et al.  Five-legged wound-core transformer model: derivation, parameters, implementation and evaluation , 1999 .

[21]  C. Perez-Rojas.  Fitting saturation and hysteresis via arctangent functions , 2000 .

[22]  Aurelio Medina,et al.  Fast periodic steady state solution of systems containing thyristor switched capacitors , 2000, 2000 Power Engineering Society Summer Meeting (Cat. No.00CH37134).

[23]  Aurelio Medina,et al.  Efficient computation of the periodic steady-state solution of systems containing nonlinear and time-varying components: application to the modeling of TCRs , 2000, Ninth International Conference on Harmonics and Quality of Power. Proceedings (Cat. No.00EX441).