Abstract
In this paper, bond graphs are employed to develop a novel mathematical model of conventional switched-mode DC-DC converters valid for both continuous and discontinuous conduction modes. A unique causality bond graph model of hybrid models is suggested with the operation of the switch and the diode to be represented by a modulated transformer with a binary input and a resistor with fixed conductance causality. The operation of the diode is controlled using an if-then function within the model. The extracted hybrid model is implemented on a boost and buck converter with their operations to change from CCM to DCM and to return to CCM. The vector fields of the models show validity in a wide operational area and comparison with the simulation of the converters using PSPICE reveals high accuracy of the proposed model, with the normalised root means square error and the maximum absolute error remaining adequately low. The model is also experimentally tested on a buck topology.
Keywords
References
- 1. (1995). ‘Discontinuities in a bond graph framework’. Journal of the Franklin Institute. 332, 2, 141-154 Google Scholar
- 2. (2010). Bond Graph Methodology: Development and Analysis of Multidisciplinary Dynamic System Models. London:Springer Google Scholar
- 3. (2012). ‘Bond-graph-based fault detection and isolation for hybrid system models’. Systems and Control Engineering. 226, 6, 742-760 Google Scholar
- 4. (1993). ‘Analysis and characterisation of hybrid systems with bond-graphs’. Proceedings Systems Man and Cybernetics Conference SMC. 264-269 Google Scholar
- 5. (2001). ‘Bond graph modeling of power converters with switches commutating by pairs’. Proceedings Conference on Bond Graph Modeling and Simulation (ICBGM). SCS Publishing, 2-7 Google Scholar
- 6. (2002). ‘Analysis of the bond graph model of hybrid physical systems with ideal switches’. Journal of Systems and Control Engineering. 216, 1, 47-63 Google Scholar
- 7. (2000).
‘A mathematical criteria to determine the valid modes of a hybrid system’.
IFAC Symposium on Power Plants & Power Systems Control ,Brussels, Belgium Google Scholar - 8. (1977). ‘A general unified approach to modelling switching dc-todc converters in discontinuous conduction mode’. Proceedings of the IEEE Power Electronics Specialists Conference. 36-57 Google Scholar
- 9. (1993). ‘Why a unique causality in the elementary commutation cell bond graph model of a power electronics converter’. Proceedings of IEEE Systems Man and Cybernetics Conference – SMC. 257-263 Google Scholar
- 10. (1993). ‘Bond graph modelling of commutation phenomena in power electronics circuit’. Proceedings International Conference on Bond Graph Modelling (ICBGM). 132-136 Google Scholar
- 11. (1994). ‘On the modeling of PWM converters for large signal analysis in discontinuous conduction mode’. IEEE Transactions on Power Electronics. 9, 5, 487-496 Google Scholar
- 12. (2008). ‘Open-loop control methods for interleaved DCM/CCM boundary boost PFC converters’. IEEE Transactions on Power Electronics. 23, 4, 1649-1657 Google Scholar
- 13. (1990). System Dynamics: A Unified Approach. 2nd ed., New York:Wiley-Interscience Google Scholar
- 14. (1993). ‘Design consideration for power factor correction boost converter operating at the boundary of continuous conduction mode and discontinuous conduction mode’. Proceedings 8th Annual Applied Power Electronics Conference and Exposition. 267-273 Google Scholar
- 15. (2011). ‘A comparison between bond graphs switching modelling techniques implemented on a boost dc-dc converter’. Proceedings International Telecommunications Energy Conference (INTELEC). 1-7 Google Scholar
- 16. (2009). ‘Hybrid modelling and control of a synchronous DC-DC converter’. International Journal of Power Electronics. 1, 4, 414-433 Abstract, Google Scholar
- 17. (2001). ‘Averaged modelling of PWM converters operating in discontinuous conduction mode’. IEEE Transactions on Power Electronics. 16, 4, 482-492 Google Scholar
- 18. (1998). ‘A theory of discontinuities in physical system models’. Journal of the Franklin Institute. 335, 3, 401-439 Google Scholar
- 19. (1990). ‘Comparison between state space averaging and PWM switch for switch mode power supply analysis’. Proceedings of the IEEE Southern Tier Technical Conference. 15-21 Google Scholar
- 20. (2013). ‘Practical inputs for maturity model of sliding mode control concepts in power electronics domain’. International Journal of Power Electronics. 5, 2, 145-164 Abstract, Google Scholar
- 21. (1961). Analysis and Design of Engineering Systems. Cambridge, MA:MIT Press Google Scholar
- 22. (2009). ‘Generalised bond graph model of a rotating machine’. International Journal of Power Electronics. 1, 4, 397-413 Abstract, Google Scholar
- 23. (2005a). ‘Modelling of switched mode power converters using bond graph’. IEE Proceedings on Electric Power Applications. 51-60 Google Scholar
- 24. (2005b). ‘Modelling of switching systems in bond graphs using the concept of switched power junctions’. Journal of the Franklin Institute. 342, 2, 131-147 Google Scholar
- 25. (1991a). ‘Simulation of system models containing zero-order causal paths–I: classification of zero-order causal paths’. Journal of the Franklin Institute. 328, 959-979 Google Scholar
- 26. (1991a). ‘Simulation of system models containing zero-order causal paths–II: numerical implications of class 1 zero-order causal paths’. Journal of the Franklin Institute. 328, 981-1004 Google Scholar
- 27. (1990a). ‘Simplified analysis of PWM converters using model of PWM switch part I: continuous conduction mode’. IEEE Transactions on Aerospace and Electronic Systems. 26, 3, 490-496 Google Scholar
- 28. (1990b). ‘Simplified analysis of PWM converters using model of PWM switch II: discontinuous conduction mode’. IEEE Transactions on Aerospace and Electronic Systems. 26, 3, 497-505 Google Scholar