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1SPW 2012ENNEAD LLC

Complex Modeling ofLi-Ion Cells in Series and

Batteries in Parallel within SatelliteEPS Time Dependent Simulations

Patrick Bailey, ENNEAD, LLC

Aerospace Space Power WorkshopApril 16-19, 2012

Manhattan Beach, CA

2SPW 2012ENNEAD LLC

Dr. Patrick G. BaileyENNEAD, LLCP.O. Box 201

Los Altos, CA 94023-0201

ennead@sbcglobal.netwww.padrak.com/ennead/

14 Years Nuclear Reactor Safety (USAF, LANL, EPRI)25 Years Lockheed (Martin), LMSSC

Retired, Available, EnthusiasticBS, UC Berkeley

PhD, MIT

3SPW 2012ENNEAD LLC

Abstract

A presentation is made of the advanced models and various results that have been obtained tosimulate complex Lithium Ion (LiIon) battery behavior within any satellite Electric Power Systems(EPS). The battery cell behavior is modeled by the publically available Quallion Lithium Ion battery cellmodel, whose voltage behavior is defined to be a complicated function of the cell current, the celltemperature, and the cell state-of-charge. A battery is defined to be composed of a series of cells,whose individual properties in each cell at any given time may be different. The overall EPS battery isthen composed of a number of such batteries connected in parallel. The simulation model allows theproperties of each individual cell in the overall EPS battery to be individually different (for example,each cell at a different state-of-charge and at a different temperature), and each cell can be degradedor dropped out of the battery at any given time. Simulation results are shown for the cases of bothcharging and discharging, to illustrate the effects of varying the temperature between cells, and theeffects of changing the state-of-charge between cells. Studies are also included that show the effectson the overall EPS battery voltage when the individual battery cells are not fully charged (to 100%state-of-charge) during recharging or during rebalancing. In addition, results are shown as cells aredegraded and dropped from operation.

These models and results are very important for complex EPS simulations and predictions. Theinability of cells stacked in series to fully rebalance during recharging can lead to battery voltages lowerthan planned or designed for, and can result in EPS performance that is much less than expected ordesired. Such battery models are planned to be included in the Power Tools Suite (PTS) system ofcodes and tools used at Lockheed Martin Space Systems Company. These models are already beingused in the Satellite EPS Transient Code (Sat-Tran) that has been independently developed byENNEAD LLC for satellite EPS transient simulation, operation, validation, and prediction.

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The Problem

Need for accurate computer simulations of EPS

Time-Dependent Behavior over Mission Life

Many Solar Array Cell Types, Char.s, Models

Many Battery Cell Types, Char.s, Models

Many EPS Designs (architectures, batt. domin., etc.)

Need capabilities for each, including:

• Sizing / Proposals

• Design / with and without Margins

• On Orbit Verification and Planning

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The Solution

Lumped Parameter Models, No Fast C/L/Z Transients

Accurate for 10 second time steps and above

Many Simple Spreadsheets (no generalizations)

A Few General Simulation Packages:

MATLAB & Simulink [Simplistic, Proprietary]

Lockheed Martin Power Tools Suite (PTS) [Proprietary]

ENNEAD Time Dependent Simulations (TDS) [Available]

Models and Results for Verification and Validation

Detailed Documentation

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EPS Simulation - PTS

Time-Dependent Simulation Code for EPS DetailedDynamic Simulations

For Proposals, Sizing, Design

Detailed Battery, Solar Array, Non-Linear Models

Lumped Parameter Models (1 minute time steps)

Excel VB Macros (Same as C++ or FORTRAN)

80,000+ Lines of Code – User Friendly Interfaces

Easily Expandable

Many IECEC Papers and SPW Presentations:

www.padrak.com/pts_pgb/ [Publically released]

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EPS Simulation – PTS (IECEC 2004)

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EPS Simulation – PTS (IECEC 2004)

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EPS Simulation - PTS (IECEC 2004)

-0.5-0.4

-0.3-0.2

-0.10

0.10.2

0.30.6

10

0.2

0.4

0.6

0.8

1

20.000

22.000

24.000

26.000

28.000

30.000

32.000

34.000

36.000

38.000

Ba

tter

yV

olt

ag

e

Discharge Rate (C Fraction)Depth of Discharge

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.000 1.100 1.200 1.300 1.400 1.500 1.600 1.700

Battery Model Examples:

Solar Array Model Examples:

* Other EPS components have similar models!

10SPW 2012ENNEAD LLC

EPS Simulation - PTS (IECEC 2011)

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EPS Simulation – Using Excel

No s/w application license

Ease of use

Ease of expansion, debugging, verification

Use of VB Function Macros (e.g. Get V from many models)

Stacked functions for various EPS components/types

Function V_Batt_G(soc, curr, temp, age) as Double

… Code …

V_Batt_G = The Result

End Function

12SPW 2012ENNEAD LLC

EPS Simulation - TDS

Time-Dependent Simulation Code for EPS DetailedDynamic Simulations

Developed Independently within ENNEAD LLC

Detailed Battery, Solar Array, Non-Linear Models

Lumped Parameter Models (1 minute time steps)

Excel VB Macros – No Computer App. License Needed

Complex Solar Array and Battery Designs

User Friendly Interfaces

Easily Expandable

Available Now for Various Applications

13SPW 2012ENNEAD LLC

Solar Array Simulation

Simple Wing:

One Cell. N cells in series. M strings in parallel.

Many such wings.

General Wing:

Same cells per string. Many strings in parallel.

Variable number of cells per string, and strings.

Many such wings.

Allows multiple spectral cells for higher SA .

14SPW 2012ENNEAD LLC

Battery Simulation

Simple Battery:

One Cell. N cells in series. M stacks in parallel.

Many such batteries.

General Battery:

Any cells per stack. Many stacks in parallel.

Variable number of cells per stack, and stacks.

Many such batteries.

Allows detailed SOC calculations.

Allows detailed chg. rebalancing simulation

Different: Types, SOCs, Currents, Temperatures, etc.

15SPW 2012ENNEAD LLC

Detailed Battery Simulation

Different Cell Types, Different SOCs, Different Temps

Variable # Cells per Stack, and Variable # Stacks

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Detailed Battery Sim. Looks Easy… Not!

Example:

Given Battery Charging Current

Calculate Current Split into Stacks

Calculate Cell Properties

Calculate Cell New SOCs

Calculate Cell New Impedances

Compare Cell Old to New Impedances

Iterate if Necessary

Converge to Current Splits and Cell New SOCs

17SPW 2012ENNEAD LLC

Sample Detailed Battery Simulations

Sci-Fi LiIon Battery Cell V vs. SOC, 5 Ah Capacity,

2.5 V Full, with V/I and V/T Corrections

(Enlarged to show effects in the results)

30 minute simulation time (1 min. T steps)

Simulation Cases: (Max SOC = 110%)

• 1 – Constant Current Charge

• 2 – Constant Current Discharge

• 3 – Constant Current Cycles

• 4 - Sample Orbit Current Cycles

• Can Cause Cell Dropouts Anytime

18SPW 2012ENNEAD LLC

Chosen Battery Cell Model VCell @ I=0

Sci-Fi User Chosen Cell Model (Normalized)

19SPW 2012ENNEAD LLC

Chosen Battery Cell Model (V/I, V/T)

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Chosen Battery Model

Same Cell Types, Different SOCs, Same Temps

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Chosen Battery Cell Initial SOCs

User Chosen Stack, Cell, and SOCs

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Given Time Dependent Input Data

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Case 1 – Constant Charge

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Case 1 – Constant Charge

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Case 1 – Constant Charge

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Case 1 – Constant Charge

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Case 2 – Constant Discharge

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Case 2 – Constant Discharge

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Case 2 – Constant Discharge

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Case 2 – Constant Discharge

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Case 3 – Const. Current Cycles

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Case 3 – Const. Current Cycles

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Case 3 – Const. Current Cycles

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Case 3 – Const. Current Cycles

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Case 4 – Sample Orbit Current Cycles

36SPW 2012ENNEAD LLC

Case 4 – Sample Orbit Current Cycles

37SPW 2012ENNEAD LLC

Case 4 – Sample Orbit Current Cycles

38SPW 2012ENNEAD LLC

Case 4 – Sample Orbit Current Cycles

39SPW 2012ENNEAD LLC

Conclusions

Excel allows easy, fast, large, accurate simulations.

EPS Time Dependent Simulation is needed for sizing,

proposals, design mods, and on-orbit validations.

PTS (LM) and TDS are available for general EPS use.

TDS includes detailed (cell) SA and Battery modeling.

Battery cells need to be modeled for individual SOC

and other parameter effects.

Battery cell “not full” recharging and cell drop-outs

are very important in EPS design and use.

Time Dependent Simulations can predict EPS behavior.

40SPW 2012ENNEAD LLC

Q/A

Dr. Patrick G. Bailey

ennead@sbcglobal.net

www.padrak.com/ennead/