Continuous Reduced-Order Dynamic Model Based on Energy Balancing for Inductive Power Transfer Systems

Wenli Shi, Jianning Dong, Thiago B. Soeiro, Junjun Deng, Calvin Riekerk, Pavol Bauer

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
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Resonant circuits are commonly used in inductive power transfer (IPT) systems for the charging of electric vehicles because of the high power efficiency. Transient behaviors of the resonant circuits, which play a significant role in the design and analysis of IPT systems, are cumbersome to model analytically because of the high-order. This article develops a reduced-order continuous dynamic model based on the energy interactions among the resonant tanks. By applying the proposed energy balancing method (EBM), the order of the dynamic model is reduced to half of the number of the passive components in the resonant circuits. To show the accuracy of the EBM, the dynamics of a series-series (SS) compensated IPT system are modeled using Laplace phasor transformation (LPT) and EBM separately and the results are compared. The order of the EBM is found to be one-fourth of that of the LPT method. The sensitivity of the EBM to the switching frequency is discussed when the zero voltage switching turn-on operation is attained. Besides, to prove the advantage of reducing the order of the dynamic model, model predictive controls (MPCs) based on EBM and LPT are developed. The transient performances of the MPC controllers are simulated and the control inputs are applied to an experimental setup. Finally, experiments are conducted to verify the accuracy of the proposed EBM under zero and nonzero conditions and the effectiveness of the developed MPC controller.

Original languageEnglish
Article number9721577
Pages (from-to)9959-9971
Number of pages13
JournalIEEE Transactions on Power Electronics
Issue number8
Publication statusPublished - 2022

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • inductive power transfer
  • electric vehicles
  • reduced-order dynamic model
  • resonant circuits
  • model predictive control


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