306 Control Lab. Prof. Kung, Chung-Chun

Lithium Battery (18650 type)

Battery Equivalent Circuit Model Analysis Battery Parameter Identification Battery Parameter Modeling Model-Based State of Charge Estimator Lithium Battery Modeling Steps

Li-ion Battery Equivalent Circuit Model (I) z(t)State of Charge V oc (z)Open-Circuit Voltage (V) R I (z)Total Internal Resistance (Ω) I(t)Load Current (A) V t (t)Terminal Voltage (V) QNQN Nominal Capacity (Ah) State of Charge Equation:Output Equation: Coulomb Counting Method Total Internal Resistance:

Li-ion Battery Equivalent Circuit Model (II) z(t)State of Charge V oc (z)Open-Circuit Voltage (V) V p (t)Polarization Voltage (V) RIRI Total Internal Resistance (Ω) RpRp Polarization Resistance (Ω) CpCp Polarization Capacitance (Ω) I(t)Load Current (A) V t (t)Terminal Voltage (V) Q max Max available Capacity (Ah) State of Charge Equation:Model Equation:

“..., the useful voltage delivered by the cell is reduced by polarization and the internal IR drop. It is only at very low operating currents, where polarization and the IR drop are small, that the cell may operate close to the open-circuit voltage and deliver most of the theoretically available energy.” From: Thomas B. Reddy, Handbook of Batteries. Li-ion Battery Equivalent Circuit Model (II)

Battery Equivalent Circuit Model Analysis Battery Parameter Identification Battery Parameter Modeling Model-Based State of Charge Estimator Lithium Battery Modeling Steps

Li-ion Battery Equivalent Circuit Model (II) Battery Model Parameter (V oc (z)) Estimation :

Internal Resistance versus State of Charge: Li-ion Battery Equivalent Circuit Model (III) Using ICR18650H

Li-ion Battery Equivalent Circuit Model (III) Internal Resistance (Normalized) versus Cycle Number: Using ICR18650H

Li-ion Battery Equivalent Circuit Model (III) Polarization Resistance versus State of Charge: Using ICR18650H

Li-ion Battery Equivalent Circuit Model (III) Polarization Resistance (Normalized) versus Cycle Number: Using ICR18650H

Li-ion Battery Equivalent Circuit Model (III) Polarization Capacitance versus State of Charge: Using ICR18650H

Li-ion Battery Equivalent Circuit Model (III) Polarization Capacitance (Normalized) versus Cycle Number: Using ICR18650H

Battery Equivalent Circuit Model Analysis Battery Parameter Identification Battery Parameter Modeling Model-Based State of Charge Estimator Lithium Battery Modeling Steps

Polynomial Equation:

Battery Equivalent Circuit Model Analysis Battery Parameter Identification Battery Parameter Modeling Model-Based State of Charge Estimator Lithium Battery Modeling Steps

Model-Based State of Charge Estimator (nonlinear observer)

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