SPICE model for lead acid cell

[Daku]

Could some electronics guru please direct me to a SPICE model for a
lead acid cell. I understand that PSpice comes with a model, but I do
not use PSpice, and I hear that the
library is encrypted.

[Robert Macy]

LTspice group had a very active session on this.

the following is from

"sgtwookieusmc" <the...@aol.com>
Date: Mon, November 8, 2010 8:10 am


* V2.0 Helmut Sennewald 02/22/04
*
* Modified from NiMH.lib to simulate sealed lead-acid batteries;
SgtWookie 11/3/2010
*
* Lead-Acid Battery
*------------------------
*
* Possible Parameters
* -------------------
*1 CELLS Number of cells in the battery; 2 = 4.2v, 3=6.35v, 6=12.8v,
etc.
* VCELL nominal cell voltage in volts, e.g. 2.133
* CAPAH cell capacity in Ah(ampere*hours), e.g. 7.2
* R_SER series resistance in Ohms, e.g 0.2
* SOC state of charge (0..1, .9=discharged, .95=50%, 1=full)
* CHEFF charging effeciency, e.g 0.7 means you need 1/0.7 times
the
* ampere*hours to charge fully
* SELFDC self discharge per hour, e.g. 0.000042 if 3%/per month
* TEMPC Battery internal temperature in °C; e.g. 25 = 25°C
*
* I started with an old article from S.C.Hageman about a SPICE model
for
* NIMH batteries. It's the model "NIMH" - PSpice Nickel-Metal-Hydride
* battery discharge simulator. Optimized for 4/5A and AA Standard
Cells
* and discharge rates from 0C to 5C. It's for discharge only.

* First I did some little changes on this discharge model.
* Later, I started with further development to include a charging
model
* for he battery too. The result is the new model NIMH_AA.
* Ext+ Ext-
* ^ ^
* | |
* | |
* | |
* +-------+----------- +/- Cell connections (Floating)
*
*
*
.SUBCKT Batt_SLA Ext+ Ext-
* Soc Rate_d Cells
*
.PARAM CELLS=6
.PARAM VCELL=2.133
.PARAM CAPAH=7.2
.PARAM R_SER=20m
.PARAM SOC=1
.PARAM CHEFF=0.75
.PARAM SELFDC=0.000042
.PARAM TEMPC=25

.IC V(Charge)={SOC}
.NODESET V(Charge)={SOC*CELLS*VCELL}
.PARAM R_DIS={VCELL*CELLS/(SELFDC*CAPAH)}

R_Cell Ext+ Cell+ {R_SER}
V_Sense Ext- Cell- 0
R_dis Cell+ Cell- {R_DIS}

* Charge to voltage translation with E-TABLE
* The last table entry (1.1 -10) together with the clamped reverse
voltage(D2)
* defines the battery voltage in reverse mode. If this entry is
omitted,
* then the battery will clamp to zero volts.
*
* Following table is a rough approximation of a lead-acid battery
E_Cell Cell+ Cell- TABLE { V(SODC) } =
+ (0.0000 {{1.0000*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.0750 {{0.9899*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.1500 {{0.9797*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.2250 {{0.9695*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.3000 {{0.9594*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.3750 {{0.9492*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.4500 {{0.9391*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.5250 {{0.9289*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.6000 {{0.9188*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.6750 {{0.9086*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.7500 {{0.8985*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.8250 {{0.8203*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.8310 {{0.8000*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.8510 {{0.7417*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.9080 {{0.6133*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.9480 {{0.5047*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.9800 {{0.3180*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.9900 {{0.1109*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.9950 {{0.0000*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.9960 {{0.0000*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.9970 {{0.0000*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.9980 {{0.0000*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (0.9990 {{0.0000*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (1.0000 {{0.0000*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})
+ (1.1000 {{-10.0000*CELLS*VCELL}-{{TEMP-25}*0.003*CELLS}})

* Original NiMH table below
*+(0.0 1.3346) (0.0293 1.3042)(0.0426 1.2942) (0.0689 1.2841)
*+(0.13 1.2733) (0.436 1.2633) (0.512 1.2532) (0.580 1.2432)
*+(0.646 1.2331) (0.702 1.2231) (0.7583 1.2130)(8.0324E-01 1.2030)
*+(0.831 1.1929) (0.851 1.1828) (0.908 1.1425) (0.948 1.0919)
*+(0.980 0.987) (0.99 0.9352) (0.995 0.8272) (0.996 0.741)
*+(0.997 0.647)(0.998 0.514) (0.999 0.33) (1.0000 0.0) (1.1 -10)

* Actual rate of discharge by external load.
* E.g. 0.2 means a full battery would last 5hours(=1/0.2).
E_Rate N001 0 VALUE = { IF( (I(V_sense)>0 & V(Cell+,Cell-)>0),
+ I(V_Sense)/CAPAH, CHEFF*I(V_Sense)/CAPAH ) }
R2 N001 Rate_d 1
C1 Rate_d 0 1

* State of charge is actually just a 1 to 1 transform of "Charge"
E_Rate1 Soc 0 TABLE { V(Charge) } = (-1,-1) (1,1)

* Higher capacity for discharge current below 0.2*C
E_LowRate LowRate 0 TABLE { V(Rate_d) } = (0,0) (0.001,0.15) (0.1,0.1)
(0.2,0)
R3 LowRate 0 1G
G_LowRate 0 Charge VALUE = { IF( (I(V_sense)>0 & V(Cell+,Cell-))>0,
+ V(LowRate)*I(V_Sense), 0) }

* Lower capacity for discharge current above 0.2*C
E_LostRate LostRate 0 TABLE { V(Rate_d) } = (0.2,0.0) (1.0,0.1)
(5,0.2)
R5 LostRate 0 1G
G_HighRate Charge 0 VALUE = { IF( I(V_sense)>0 & V(Cell+,Cell-)>0,
+ V(LostRate)*I(V_Sense), 0) }

* The charge model
* Overcharge and discharge clamped with diodes
C_CellCapacity Charge 0 { 3600 * CAPAH * {TABLE (TEMP,
+-99, 0.2,
+-20, 0.46,
+-15, 0.56,
+-10, 0.66,
+-5 , 0.71,
+0 , 0.76,
+5 , 0.83,
+10 , 0.90,
+15 , 0.95,
+20 , 0.98,
+25 , 1.00,
+30 , 1.03,
+35 , 1.05,
+40 , 1.07,
+45 , 1.09,
+99 , 1.10)}}

R1 Charge 0 1MEG
V2 N003 0 0.993
D1 Charge N003 DFULL
D2 0 Charge DREV
G_DisCharge Charge 0 VALUE = { IF( I(V_Sense)>0 ^ (V(Cell+,Cell-)<0),
+ I(V_Sense), I(V_Sense)*CHEFF) }

* State of Discharge = 1-SOC
E_Invert SODC 0 TABLE { V(Soc) } = (-1,2) (0,1) (1,0)
R4 SODC 0 1G

.model DFULL D(Is=1e-6 N={0.02*CELLS} Vj={.15*CELLS})
.model DREV D(Is=1e-8 N={0.02*CELLS} Vj={.15*CELLS})
.ends