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).