1. EDPE_2013 Dubrovnik, Croatia 1 Problem of Obtaining Boost Converter Bifurcation Model for Hysteretic Behaviour Željko Stojanović Department of Electrical Engineering Polytechnic of Zagreb zeljko.stojanovic@tvz.hr Denis Pelin, Krešimir Predrijevac Faculty of Electrical Engineering University of Osijek pelin@etfos.hr

2. EDPE_2013 Dubrovnik, Croatia 2 Contents Introduction Boost converter physical realisation and measurements Simulation Comparison of simulation results and measurements Two-parameters bifurcation diagrams Conclusions

3. EDPE_2013 Dubrovnik, Croatia 3 Boost converter physical realisation and measurements Schematic of the experimental boost converter

4. EDPE_2013 Dubrovnik, Croatia 4 Boost converter physical realisation and measurements Increasing of input voltage E Decreasing of input voltage E Steady-state response Input voltage E [V] Period-117.0–22.5 Period-222.5–23.1 Period-623.10–23.45 Chaos23.45–24.28 Period-424.28–24.55 Period-824.55–24.64 Chaos24.64–25.57 Period-525.57–25.86 Chaos25.86–26.80 Period-626.80–26.98 Chaos>26.98 Steady-state response Input voltage E [V] Period-317.18–23.02 Period-623.02–23.38 Chaos23.38–24.02 Period-424.02–24.39 Period-824.39–24.59 Chaos24.59–25.53 Period-525.53–25.83 Chaos25.83–26.62 Period-626.62–26.98 Steady state responses The same sequence for both directions of change Different sequence for both directions of change => Hysteresis! }{ } {

5. EDPE_2013 Dubrovnik, Croatia 5 Simulation

6. EDPE_2013 Dubrovnik, Croatia 6 Simulation

7. EDPE_2013 Dubrovnik, Croatia 7 Comparison of simulation results and measurements Correspondence of measured and simulated steady-states for decreasing of input voltage E. Steady-state response Input voltage E [V] MeasuringSimulation Period-3to 23 V22.5–23.05 Period-623.00–23.2723.03–23.22 Period-9–23.22–23.32 Chaos23.27–24.0723.32–24.06 Period-424.07–24.4224.06–24.32 Period-824.42–24.4924.32–24.50 Chaos24.49–25.4724.50–25.46 Period-525.47–25.6825.46–25.70 Chaos25.68–26.6325.70–26.66 Period-626.63–26.8526.66–26.76 Chaos26.85–2726.76–27

8. EDPE_2013 Dubrovnik, Croatia 8 Comparison of simulation results and measurements One-parameter bifurcation diagram inductor current versus input voltage. Correspondence of measured and simulated results for decreasing of input voltage E.

9. EDPE_2013 Dubrovnik, Croatia 9 Two-parameters bifurcation diagrams Two-parameters bifurcation diagram of input voltage and initial inductor current with constant initial capacitor voltage. Simulation results does not match measured results.

10. EDPE_2013 Dubrovnik, Croatia 10 Two-parameters bifurcation diagrams Two-parameters bifurcation diagram of initial capacitor voltage and initial inductor current with constant input voltage. Simulation results does not match measured results.

11. EDPE_2013 Dubrovnik, Croatia 11 Conclusions Bifurcation model is valid for only one direction of input voltage varying. Change of two bifurcation parameter at the same time does not improve bifurcation model. The next step is investigation of influence of ramp input voltage on bifurcation model.

12. EDPE_2013 Dubrovnik, Croatia 12 Thank you! Questions please.