modeling and simulation of nickel-cadmium batteries during discharge giuliano s. sperandio cairo l....
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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
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.
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.
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.
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
Ni-Cd Battery
Parameter Value
Capacity 50 Ah
Total cell number 20
Nominal cell voltage 1.2 V
Total voltage 24 V
Ni-Cd Battery Discharge Curve (T)
Ni-Cd Battery Discharge Curve (I)
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.
Ni-Cd Battery Model
Ni-Cd Battery Discharge Curve (T)
Ni-Cd Battery Discharge Curve (I)
Ni-Cd Paatero's Battery Model
• adapted from a lead-acid battery model,
• 17 parameters.
Ni-Cd Paatero's Battery Model
Ni-Cd Battery Model: R2 Index
-20 °C 0 °C 20 °C 40 °C
10 A -0.080 -0.275 -0.565 -0.473
50 A 0.951 0.970 0.896 0.883
100 A 0.867 0.866 0.896 0.924
200 A 0.804 0.881 0.895 0.975
500 A 0.239 0.762 0.817 0.993
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.
Battery Capacity
Battery Capacity
Battery Model Modification Proposal
iIhgfeIdTc
TbaTIC
arctan),(
• Model the battery capacity using:
Modified Ni-Cd Battery Model
Ni-Cd Battery Model: R2 Index
-20 °C 0 °C 20 °C 40 °C
10 A 0.970 0.995 0.975 0.954
50 A 0.991 0.988 0.987 0.961
100 A 0.988 0.989 0.991 0.975
200 A 0.985 0.986 0.984 0.989
500 A 0.917 0.956 0.966 0.938
SIMULINK Simulation
SIMULINK Simulation
Case: constant current load
Model Simulation
Model Simulation
Case: Constant power load
Model Simulation
Model Simulation
Case: Constant resistance load
Model Simulation
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.
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).