Impedance Parameters Estimation of An RLCM Ladder Network Using Subspace and Similarity Transformation Approach

ABSTRACT

Numerous physical systems such as transformers, sensors, and biomaterials are analysed using their equivalent ladder network model. Impedance parameters of a ladder network consist of combinations of resistances, inductances, and capacitances. Accurately determining any device impedance parameters directly from the measured time-domain input-output data is challenging. The use of non-linear optimization algorithms does not always work due to the problem being ill-conditioned. Also, the obtained parameters may not be physically realizable. In this work, the problem is approached from a black-box system identification point of view, followed by a physical parameter extraction step. The necessary current and voltage equations obtained from first principles are utilized to build a physical model in the state-space domain. With the use of a subspace system identification algorithm, the black-box parameter matrices are determined from input-output data, which do not correspond to the physical parameter matrices. However, both sets of parameters can be related through a similarity transformation matrix, leading to the extraction of the physical parameters. The novelty of the approach lies in solving the non-linear parameter estimation problem linearly without initialization. The presence of mutual inductances between various transformer winding sections makes its ladder network the most complex one. Therefore, in this paper, the ladder network model of a transformer winding is considered. As an example of the methodology, a six-section transformer ladder network is simulated and the parameter estimation results are used to validate the proposed algorithm. The same approach can be applied to estimate any other device impedance parameters.

KEYWORDS:

• Impulse response
• Ladder network
• Parameter estimation
• Similarity transformation
• State-space
• System identification
• Time domain analysis
• Transformer winding

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 MATLAB is a registered trademark of The Math Works, Inc.

Additional information

Notes on contributors

Mithun Mondal

Mithun Mondal received the BTech degree in electrical engineering from Dr. MGR University, Chennai, India, in 2009, MTech degree from National Institute of Technology Hamirpur, India, in 2013 and PhD degree from the Department of Electrical Engineering, Indian Institute of Technology Roorkee, India, in 2017. Since 2017, he is working as an assistant professor in Department of Electrical & Electronics Engineering, Birla Institute of Technology & Science Pilani Hyderabad Campus. His research interests are condition monitoring and diagnostic of high voltage apparatus, partial discharge monitoring in transformers, system identification, and application of statistical and digital signal processing techniques in fault localization.

José A. Ramos

José A Ramos received the BS degree in civil engineering from the University of Puerto Rico at Mayagüez, Puerto Rico, in 1978 and the MS and PhD degrees in hydro-systems engineering, specializing in operations research and control theory, from the Georgia Institute of Technology, Atlanta, GA, USA, in 1979 and 1985, respectively. From 1986 to 1990, he was an associate research engineer at United Technologies Optical Systems in West Palm Beach, FL, USA, where he worked on Kalman filtering and target tracking applications for ground-based free electron laser systems. From 1991 to 1993, he was a post doctoral student at the Katholieke Universiteit Leuven in Belgium, sharing responsibilities between the Electrical Engineering Department and the Institute for Land and Water Management, where he worked in the development of subspace-based system identification algorithms for linear, descriptor, bilinear, and 2-D systems, with applications in hydrology. He is currently a professor at Nova Southeastern University, Fort Lauderdale, FL, USA. He has held visiting appointments at the University of Montpellier II in France, the University of Porto in Portugal, the University of Padova in Italy, the University of Poitiers in France, and The University Miguel Hernández de Elche in Spain. His research interests include mathematical modeling and system identification theory, linear and non-linear systems theory, optimization theory, algorithm design, model-based control design, model-based image processing, and stochastic realization theory. Email: [email protected]