Battery Parameter Extraction from Data

Open Model

This example shows optimization of the Battery block's parameters to fit data defined over different temperatures. It uses the MATLAB® optimization function fminsearch. Other products available for performing this type of parameter fitting with Simscape™ Electrical™ models are the Optimization Toolbox™ and Simulink® Design Optimization™. These products provide predefined functions to manipulate and analyze blocks using GUIs or a command line approach.

Strategy

Fit output voltage curves for a Battery to data using a 4 step procedure:

Optimize parameters in the Battery Main dialog tab.
Optimize parameters in the Battery Dynamics dialog tab.
Optimize nominal voltage and internal resistance in the Battery Temperature Dependence dialog tab.
Optimize temperature dependent charge dynamics parameters in the Battery Temperature Dependence dialog tab.

Data and Block Setup

The MATLAB data file, BatteryParameterizationData.mat, stores Battery data as an array of structures. Each structure contains 5 fields: v (voltage), i (current), t (time), SOC0 (initial state of charge) and T (temperature). Scope save the output voltage as structure data, out.Vo.signals.values.

Initial Parameter Specification

Starting values for fminsearch can be estimated using a combination of Battery block defaults and data sheet values

List of parameters and initial values prior to optimization

	 Vnom =   3.6
	   R1 = 0.045
	   AH =   2.7
	   V1 =   3.4
	  AH1 =   1.4
	  Rp1 = 0.006
	 tau1 =   200
	Vnom_T2 =   3.8
	R1_T2 = 0.055
	V1_T2 =   3.6
	Rp1_T2 = 0.006
	tau1_T2 =   200

Since fminsearch is an unconstrained nonlinear optimizer that locates a local minimum of a function, varying the initial estimate will result in a different solution set.

Plot Data Versus Battery Output Using Initial Parameters

Load single cell Battery model and set parameters

Sum of Squares of Error Calculation

BatteryParameterizationCostFunction is the function to be minimized by fminsearch. This function returns a sum of squares of error for the difference between the Battery output voltage and the data. If an invalid parameter value is supplied by fminsearch, the catch statement returns a large value for the error.

Optimize Main Tab Dialog Parameters Without Charge Dynamics (Step 1)

Optimized parameters for the battery main dialog tab are:
	 Vnom =   3.6999
	   R1 = 0.050299
	   AH =   2.6033
	   V1 =   3.5265
	  AH1 =      1.4

Optimize Charge Dynamics Parameters (Step 2)

Optimized parameters for the Battery, including charge dynamics, are:
	 Vnom =    3.699931
	   R1 =  0.05019736
	   AH =    2.603326
	   V1 =    3.526493
	  AH1 =         1.4
	  Rp1 = 0.005029392
	 tau1 =     109.691

Optimize Temperature Dependent Parameters (Step 3)

Optimized temperature dependent parameters for the Battery are:
	Vnom_T2 =   3.9003
	R1_T2 = 0.081404
	V1_T2 =   3.8133

Optimize Charge Dynamics Parameters for Second Temperature (Step 4)

Optimized temperature dependent parameters for the Battery, including charge dynamics, are:
	Vnom_T2 =    3.900266
	R1_T2 =  0.07979468
	V1_T2 =    3.813256
	Rp1_T2 = 0.007920818
	tau1_T2 =    160.2999