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.


2. Model Feature

• 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.


3. Concept of the Model

Lead-Acid battery
+
Simplified SPICE Behavioral Model Output
[Spec: C, NS] Characteristics

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.


4. Parameter Settings
Model Parameters:
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)
+ - LEAD-ACID_BATTERY
TSCALE = 1
U1 C = 50 SOC is the initial state of charge in percent
SOC = 1 – e.g. SOC=0 for a empty battery (0%), SOC=1 for a full
NS = 1 charged battery (100%)

(Default values) 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.


5. Lead-Acid Battery Specification (Example)

Nominal Voltage 2.0 [Vdc] /Cell

Capacity 50Ah

Rated Charge 0.1C10A
TSCALE = 1
U1 SOC = 1
Voltage Set 2.23 [Vdc] /Cell
C = 50
NS = 1
Charging Time 24 [hours] @ 0.1C10A
Battery capacity
[Typ.] is input as a
model parameter

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


Measurement Simulation
1.4V 2.6V 210mA
1 2 3

1.2V 2.5V 180mA

1.0V 2.4V 150mA

0.8V 2.3V 120mA
Voltage: 2.23V
0.6V 2.2V 90mA

0.4V 2.1V 60mA
Current: 5A (0.1C10A)
0.2V 2.0V 30mA
>>
0V 1.9V 0A
0s 4s 8s 12s 16s 20s 24s
1 V(X_U1.SOC) 2 V(HI) 3 I(IBATT)/50
(hour)
Time

• Charging Time: 24 [hours] @ 0.1C10A
TSCALE = 3600
U1 C = 50
SOC = 0 SOC=0 means
NS = 1 battery start from 0%
of capacity (empty)


 Simulation Circuit and Setting

PARAMETERS:
rate = 0.1
CAh = 50

Charge Voltage HI
OUT+
OUT-
C1
Vin 10n
2.23V
IBATT
IN+
IN-

0

G1
Limit(V(%IN+, %IN-)/0.1m, 0, rate*CAh )
0
0
A constant current charger at TSCALE = 3600
U1 C = 50
rate of capacity (e.g. 150A) SOC = 0
NS = 1 1 hour intoa second
(in simulation)

*Analysis directives:
.TRAN 0 24 0 25m
.PROBE V(*) I(*) W(*) D(*) NOISE(*)


2.2V

2.0V

0.1C10A

1.8V

0.23C10A
1.6V

0.65C10A
1.0C10A
1.4V
10ms 100ms 1.0s 10s 100s
V(HI) (hour)
Time

TSCALE = 3600
U1 C = 50
SOC = 1 SOC=1 means
NS = 1 battery start from
100% of capacity



PARAMETERS:
rate = 1
CAh = 50
sense
HI

C1
IN+ OUT+ 10n
IN- OUT-
G1 0 0
GVALUE + - LEAD-ACID_BATTERY
limit(V(%IN+, %IN-)/0.1m, 0, rate*CAh ) TSCALE = 3600
U1 C = 50
SOC = 1
0 NS = 1
A constant current discharger at
rate of capacity (e.g. 150A)
TSCALE turns 1 hour into a second(in
simulation), battery starts from 100%
of capacity (fully charged)
.TRAN 0 10 0.02 25m
.STEP PARAM rate LIST 0.1, 0.23, 0.65, 1

2.2
@25C

2.0

Cell Voltage [V]
1.8
0.1C10A
1.0C10A 0.25C10A
1.6
0.6C10A

1.4
1 0.8 0.6 0.4 0.2 0 -0.2
[0-100%]
Capacity [%]

Simulation
1.2
+ - LEAD-ACID_BATTERY Mesurement

(% of Rated Capacity)
1.0
TSCALE = 3600 Simulation
U1 C = 50 0.8

SOC = 1 0.6
NS = 1 0.4
0.2
• Nominal Voltage: 2.0V 0.0
• Capacity: 50Ah 0 1 2 3
Discharge Rate (Multiples of C)



PARAMETERS:
rate = 0.1
CAh = 50
sense
HI

C1
IN+ OUT+ A constant current 10n
IN- OUT- discharger at rate of
G1 capacity (e.g. 150A) 0
GVALUE 0
limit(V(%IN+, %IN-)/0.1m, 0, rate*CAh ) + - LEAD-ACID_BATTERY
TSCALE = 3600
U1 C = 50
0 SOC = 1
NS = 1 1 hour into a second
(in simulation)

.TRAN 0 9.898 0 100m


6. Extend the number of Cell (Example)

Lead-Acid needs
3 cells to reach
this voltage level
Basic Specification
TSCALE = 3600 Voltage - Rated 6.0 [Vdc] /Cell
U1 C = 100
SOC = 1 Capacity 100Ah
NS = 3
Rated Charge 0.1C10A
The number of cells
in series is input as
a model parameter Voltage Set 2.23V*3 [Vdc] /Cell

Charging Time 24 [hours] @ 0.1C10A

Voltage  Rated 6
NS  
Lead - Acid Nominal Voltage 2.0

• The battery information refer to a battery part number MSE-100-6
of GS YUASA.


The battery needs 24 hours to be fully charged
1.4V 7.8V 210mA
1 2 3

1.2V 7.5V 180mA

1.0V 7.2V 150mA

0.8V 6.9V 120mA
Charge Voltage: 6.69V

0.6V 6.6V 90mA

0.4V 6.3V 60mA
Charge Current: 10A (0.1C10A)

0.2V 6.0V 30mA

>>
0V 5.7V 0A
0s 4s 8s 12s 16s 20s 24s
1 V(X_U1.SOC) 2 V(HI) 3 I(IBATT)/100 (hour)
Time

• Charging Current: 10A (0.1C10A)



PARAMETERS:
rate = 0.1
CAh = 100

HI
Charge Voltage
OUT+
OUT-
C1
Vin 10n
6.69V
IBATT
IN+
IN-
0

G1
Limit(V(%IN+, %IN-)/0.1m, 0, rate*CAh )
0
0
TSCALE = 3600
U1 C = 100
SOC = 0
NS = 3
1 hour into a second
(in simulation)

.TRAN 0 24 0 25m


6.6V

6.0V

5.4V

0.1C10A

0.25C10A
4.8V 0.6C10A

1.0C10A

4.2V
10ms 100ms 1.0s 10s 100s
V(HI)
Time (hour)

• Voltage - Rated: 6.0V
• Discharging Current: 10A(0.1C), 23A(0.23C), 65A(0.65C), 100A(1.0C)



Parametric sweep “rate”
for multiple rate
discharge simulation
PARAMETERS:
rate = 1
CAh = 100
sense
HI

C1
IN+ OUT+ 10n
IN- OUT-
G1 0
GVALUE 0
limit(V(%IN+, %IN-)/0.1m, 0, rate*CAh ) + - LEAD-ACID_BATTERY
TSCALE = 3600
U1 C = 100
0 SOC = 1
NS = 3
1 hour into a second
(in simulation)

.TRAN 0 10 0.02 25m
.STEP PARAM rate LIST 0.1, 0.23, 0.65, 1

Simulation Index

Simulations Folder name

1. Charge Time Characteristic................................. Charge_Time
2. Discharge Time Characteristic............................. Discharge_Time
3. Vbat vs. SOC Characteristic.................................. Discharge_SOC
4. Charge Time Characteristic, NS=3....................... Charge_Time(NS)
5. Discharge Time Characteristic, NS=3................... Discharge_Time(NS)


Simple Model of Lead-Acid Battery Model using PSpice

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