1. Modeling and Simulation of Nickel-Cadmium Batteries during Discharge Giuliano S. Sperandio Cairo L. Nascimento Jr. Geraldo J. Adabo Prof. Master Program in Aeronautical Eng. (ITA-EMBRAER) Instituto Tecnológico de Aeronáutica (ITA) Brazil

2. Introduction Electrical batteries are essential components of an aircraft. Main uses: –to start the propulsion engines, –to provide power during electrical emergencies. The knowledge of the battery dynamics is important for the aircraft designers. Virtual Aircraft Project.

3. Introduction Battery manufacturers provide DATA: voltage curves over time considering –constant room temperature T, –constant discharge current I, –battery initially fully charged. Battery manufacturers DO NOT provide MODELS.

4. Objective Produce a mathematical model to be used for simulation of the battery discharge during eletrical emergencies when: –the discharge current is not constant, –the battery is not fully charged. using the data provided by the battery manufacturer to adjust the model parameters.

5. Ni-Cd Battery Model U(t) = f(DOD(t),I(t),T(t)) U(t) = battery voltage DOD(t) = Depth of Discharge I(t) = discharge current T(t) = temperature

6. Ni-Cd Battery ParameterValue Capacity50 Ah Total cell number20 Nominal cell voltage1.2 V Total voltage24 V

7. Ni-Cd Battery Discharge Curve (T)

8. Ni-Cd Battery Discharge Curve (I)

9. Battery Data Extraction At least 50 points were manually captured for each curve. A polynomial function was fitted to each curve. problem: how to select the order of the polynomial? In each case, a polynomial function was used to interpolate and extrapolate the curve to U=0.

10. Ni-Cd Battery Model

11. Ni-Cd Battery Discharge Curve (T)

12. Ni-Cd Battery Discharge Curve (I)

13. Ni-Cd Paatero's Battery Model adapted from a lead-acid battery model, 17 parameters.

14. Ni-Cd Paatero's Battery Model

15. Ni-Cd Battery Model: R 2 Index -20 °C0 °C20 °C40 °C 10 A-0.080-0.275-0.565-0.473 50 A0.9510.9700.8960.883 100 A0.8670.8660.8960.924 200 A0.8040.8810.8950.975 500 A0.2390.7620.8170.993

16. Model Modification Proposal Paatero's model considers the battery capacity constant. The battery capacity is influenced by the discharge current and the room temperature. Idea: to model the battery capacity as a function of the room temperature T and the discharge current I.

17. Battery Capacity

19. Battery Model Modification Proposal Model the battery capacity using:

20. Modified Ni-Cd Battery Model

21. Ni-Cd Battery Model: R 2 Index -20 °C0 °C20 °C40 °C 10 A0.9700.9950.9750.954 50 A0.9910.9880.9870.961 100 A0.9880.9890.9910.975 200 A0.9850.9860.9840.989 500 A0.9170.9560.9660.938

22. SIMULINK Simulation

23. Case: constant current load

24. Model Simulation

25. Case: Constant power load

26. Model Simulation

27. Case: Constant resistance load

28. Model Simulation

29. Conclusions Proposal of a procedure to generate a Ni- Cd battery discharge model. The results show that the proposed battery model fits the data well over a large range of discharge currents and room temperatures. Use of the model to simulate battery discharge with different load types.

30. Future Research Comparison of the simulation results for emergency situations with experimental data. Proposal and validation of a model for the charging phase of aircraft batteries. Proposal and validation of a model for battery aging (capacity degradation).