Simple Model of Lead-Acid Battery Model using PSpice

Lead-Acid Battery Simplified SPICE Behavioral Model

All Rights Reserved Copyright (C) Bee Technologies Corporation 2013 1

Contents

1. Benefit of the Model

2. Model Feature

3. Concept of the Model

4. Parameter Settings

5. Lead-Acid Battery Specification (Example)

5.1 Charge Time Characteristic

5.2 Discharge Time Characteristic

5.3 Vbat vs. SOC Characteristic

6. Extend the number of Cell (Example)

6.1 Charge Time Characteristic, NS=3

6.2 Discharge Time Characteristic, NS=3

Simulation Index


1. Benefit of the Model

• The model enables circuit designer to predict and optimize Lead-

Acid battery runtime and circuit performance.

• The model can be easily adjusted to your own Lead-Acid battery

specifications by editing a few parameters that are provided in the

datasheet.

• The model is optimized to reduce the convergence error and the

simulation time.


• This Lead-Acid Battery Simplified SPICE Behavioral Model is for users who

require the model of a Lead-Acid Battery as a part of their system.

• The model accounts for Battery Voltage(Vbat) vs. Battery Capacity Level

(SOC) Characteristic, so it can perform battery charge and discharge time at

various current rate conditions.

• As a simplified model, the effects of cycle number and temperature are

neglected.

2. Model Feature


3. Concept of the Model


Lead-Acid battery

Simplified SPICE Behavioral Model

[Spec: C, NS]

Adjustable SOC [ 0-1(100%) ]

+

-

• The model is characterized by parameters: C which represent the battery

capacity and SOC which represent the battery initial capacity level.

• Open-circuit voltage (VOC) vs. SOC is included in the model as an analog

behavioral model (ABM).

• NS (Number of Cells in series) is used when the Lead-acid cells are in series

to increase battery voltage level.

Output Characteristics

-+

U1

LEAD-ACID_BATTERY

SOC = 1NS = 1

TSCALE = 1C = 50

4. Parameter Settings

C is the amp-hour battery capacity [Ah]

– e.g. C = 1, 50, or 100 [Ah]

NS is the number of cells in series

– e.g. NS=1 for 1 cell battery, NS=2 for 2 cells battery (battery voltage is double from 1 cell)

SOC is the initial state of charge in percent

– e.g. SOC=0 for a empty battery (0%), SOC=1 for a full charged battery (100%)

TSCALE turns TSCALE seconds(in the real world) into a

second(in simulation)

– e.g. TSCALE=60 turns 60s or 1min (in the real world) into a second(in simulation), TSCALE=3600 turns 3600s or 1h into a second.

• From the Lead-Acid Battery specification, the model is characterized by setting

parameters C, NS, SOC and TSCALE.


Model Parameters:

(Default values)

-+

U1

LEAD-ACID_BATTERY

SOC = 1

NS = 1

TSCALE = 1

C = 50

5. Lead-Acid Battery Specification (Example)

• The battery information refer to a battery part number MSE Series of GS YUASA.


Battery capacity

[Typ.] is input as a

model parameter

Nominal Voltage 2.0 [Vdc] /Cell

Capacity 50Ah

Rated Charge 0.1C10A

Voltage Set 2.23 [Vdc] /Cell

Charging Time 24 [hours] @ 0.1C10A

Time

0s 4s 8s 12s 16s 20s 24s

1 V(X_U1.SOC) 2 V(HI) 3 I(IBATT)/50

0V

0.2V

0.4V

0.6V

0.8V

1.0V

1.2V

1.4V1

1.9V

2.0V

2.1V

2.2V

2.3V

2.4V

2.5V

2.6V2

0A

30mA

60mA

90mA

120mA

150mA

180mA

210mA3

>>

-+

U1

LEAD-ACID_BATTERY

SOC = 0NS = 1

TSCALE = 3600C = 50

5.1 Charge Time Characteristic


• Charging Time: 24 [hours] @ 0.1C10A

(hour)

Measurement Simulation

SOC=0 means

battery start from 0%

of capacity (empty)

Current: 5A (0.1C10A)

Voltage: 2.23V

PARAMETERS:rate = 0.1CAh = 50

0

Vin

2.23VIBATT

0

C110n

HI

IN-

OUT+

OUT-

IN+

G1Limit(V(%IN+, %IN-)/0.1m, 0, rate*CAh )

0

-+

U1

LEAD-ACID_BATTERY

SOC = 0NS = 1

TSCALE = 3600C = 50

5.1 Charge Time Characteristic Simulation Circuit and Setting

*Analysis directives:

.TRAN 0 24 0 25m

.PROBE V(*) I(*) W(*) D(*) NOISE(*)


Charge Voltage

A constant current charger at

rate of capacity (e.g. 150A)

1 hour into a second

(in simulation)

-+

U1

LEAD-ACID_BATTERY

SOC = 1NS = 1

TSCALE = 3600C = 50

Time

10ms 100ms 1.0s 10s 100s

V(HI)

1.4V

1.6V

1.8V

2.0V

2.2V

5.2 Discharge Time Characteristic


(hour)


SOC=1 means

battery start from

100% of capacity

0.1C10A

0.23C10A

0.65C10A

1.0C10A

HI

0

00IN-

OUT+

OUT-

IN+

G1

limit(V(%IN+, %IN-)/0.1m, 0, rate*CAh )GVALUE

PARAMETERS:

rate = 1CAh = 50

C1

10n

sense

-+

U1

LEAD-ACID_BATTERY

SOC = 1NS = 1

TSCALE = 3600C = 50

5.2 Discharge Time Characteristic Simulation Circuit and Setting


.TRAN 0 10 0.02 25m

.STEP PARAM rate LIST 0.1, 0.23, 0.65, 1



A constant current discharger at

rate of capacity (e.g. 150A) TSCALE turns 1 hour into a second(in

simulation), battery starts from 100%

of capacity (fully charged)

1.4

1.6

1.8

2.0

2.2

-0.200.20.40.60.81

Cell

Vo

ltag

e [V

]

Capacity [%]

-+

U1

LEAD-ACID_BATTERY

SOC = 1NS = 1

TSCALE = 3600C = 50

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 1 2 3

(% o

f R

ate

d C

apacity

)

Discharge Rate (Multiples of C)

Mesurement

Simulation

5.3 Vbat vs. SOC Characteristic


• Nominal Voltage: 2.0V

• Capacity: 50Ah

0.1C10A


Simulation

0.25C10A

0.6C10A

1.0C10A

[0-100%]

@25C

PARAMETERS:

rate = 0.1CAh = 50

HI

0

00

IN-

OUT+

OUT-

IN+

G1


C1

10n

sense

-+

U1

LEAD-ACID_BATTERY

SOC = 1NS = 1

TSCALE = 3600C = 50

5.3 Vbat vs. SOC Characteristic Simulation Circuit and Setting



.TRAN 0 9.898 0 100m


A constant current

discharger at rate of

capacity (e.g. 150A)


(in simulation)

-+

U1

LEAD-ACID_BATTERY

SOC = 1NS = 3

TSCALE = 3600C = 100

Voltage - Rated 6.0 [Vdc] /Cell

Capacity 100Ah

Rated Charge 0.1C10A

Voltage Set 2.23V*3 [Vdc] /Cell

Charging Time 24 [hours] @ 0.1C10A

6. Extend the number of Cell (Example)

• The battery information refer to a battery part number MSE-100-6

of GS YUASA.


The number of cells

in series is input as

a model parameter

Basic Specification

Lead-Acid needs

3 cells to reach

this voltage level

0.2

6

Acid-Lead

VoltageNominal

RatedVoltageNS

Time

0s 4s 8s 12s 16s 20s 24s

1 V(X_U1.SOC) 2 V(HI) 3 I(IBATT)/100

0V

0.2V

0.4V

0.6V

0.8V

1.0V

1.2V

1.4V1

5.7V

6.0V

6.3V

6.6V

6.9V

7.2V

7.5V

7.8V2

0A

30mA

60mA

90mA

120mA

150mA

180mA

210mA3

>>


• Charging Current: 10A (0.1C10A)


(hour)

The battery needs 24 hours to be fully charged

Charge Current: 10A (0.1C10A)

Charge Voltage: 6.69V

PARAMETERS:rate = 0.1CAh = 100

0

Vin

6.69VIBATT

0

C110n

HI

IN-

OUT+

OUT-

IN+

G1Limit(V(%IN+, %IN-)/0.1m, 0, rate*CAh )

0

-+

U1

LEAD-ACID_BATTERY

SOC = 0NS = 3

TSCALE = 3600C = 100


Simulation Circuit and Setting


.TRAN 0 24 0 25m



Charge Voltage


(in simulation)

Time

10ms 100ms 1.0s 10s 100s

V(HI)

4.2V

4.8V

5.4V

6.0V

6.6V

• Voltage - Rated: 6.0V

• Discharging Current: 10A(0.1C), 23A(0.23C), 65A(0.65C), 100A(1.0C)

6.2 Discharge Time Characteristic, NS=3


(hour)

0.1C10A

0.25C10A

0.6C10A

1.0C10A

6.2 Discharge Time Characteristic, NS=3 Simulation Circuit and Setting


.TRAN 0 10 0.02 25m

.STEP PARAM rate LIST 0.1, 0.23, 0.65, 1



Parametric sweep “rate”

for multiple rate

discharge simulation


(in simulation)

HI

0

00

IN-

OUT+

OUT-

IN+

G1


PARAMETERS:

rate = 1CAh = 100

C1

10n

sense

-+

U1

LEAD-ACID_BATTERY

SOC = 1NS = 3

TSCALE = 3600C = 100

Simulation Index


Simulations Folder name

1. Charge Time Characteristic.................................

2. Discharge Time Characteristic.............................

3. Vbat vs. SOC Characteristic..................................

4. Charge Time Characteristic, NS=3.......................

5. Discharge Time Characteristic, NS=3...................

Charge_Time

Discharge_Time

Discharge_SOC

Charge_Time(NS)

Discharge_Time(NS)

Technology

Simple Model of Lead-Acid Battery Model using PSpice