Appendix D Example n The procedure described in Appendix D is meant to determine a battery’s performance parameters from the data taken during a HPPC test.

Appendix D ExampleAppendix D Example

The procedure described in The procedure described in Appendix D is meant to Appendix D is meant to determine a battery’s determine a battery’s performance parameters from the performance parameters from the data taken during a HPPC test. data taken during a HPPC test. The goal is to determine RThe goal is to determine Ro o and and RRp p with respect to SOC; the time with respect to SOC; the time constant tau also needs to be constant tau also needs to be determined. What is known is Idetermined. What is known is IL L , , Voltage, and A-s with respect to Voltage, and A-s with respect to time. The procedure assumes time. The procedure assumes that an equation for voltage can that an equation for voltage can be created that has Ibe created that has IL , L , IIp p and A-s and A-s its variables. The coefficients will its variables. The coefficients will then be Rthen be Roo, R, Rpp, OCV’, and OCV. , OCV’, and OCV. For this to work, IFor this to work, Ip p will also have will also have to be calculated. The procedure to be calculated. The procedure revolves around an Excel function revolves around an Excel function named LINEST and assumes the named LINEST and assumes the battery model shown.battery model shown.

Start by entering the appropriate labels in an Excel file; column numbers Start by entering the appropriate labels in an Excel file; column numbers go up to twelvego up to twelve

From a HPPC data file carry in From a HPPC data file carry in TimeTime,, I load I load,, A-s A-s, and , and VoltageVoltage

Enter a zero into the first cell of Enter a zero into the first cell of dT/taudT/tau and make a guess for tau, then and make a guess for tau, then use tau in the equation for the second cell of use tau in the equation for the second cell of dT/taudT/tau (be sure to use dollar (be sure to use dollar

signs in front of the tau’s reference)signs in front of the tau’s reference)dT/tau=(tdT/tau=(ti i - t- ti-1i-1)/tau)/tau

Copy the second Copy the second dt/taudt/tau cell and use it to fill in the rest of the column cell and use it to fill in the rest of the column

The The IpIp column can now be filled in; enter a 0 into the first cell, and enter column can now be filled in; enter a 0 into the first cell, and enter the formula for the formula for IpIp from the manual into the second cell from the manual into the second cell

Copy the second cell and use it to fill in the rest of the columnCopy the second cell and use it to fill in the rest of the column

The LINEST function now needs to be set up; enter The LINEST function now needs to be set up; enter OCV’, Rp, Ro, and OCVOCV’, Rp, Ro, and OCV under columns 9-12 and highlight a 5x4 block underneath themunder columns 9-12 and highlight a 5x4 block underneath them

Go to Insert/Function, and click on LINESTGo to Insert/Function, and click on LINEST

The LINEST block needs each cell to be filled in; start by clicking on the The LINEST block needs each cell to be filled in; start by clicking on the square with the red arrow that is across from square with the red arrow that is across from Known_y’sKnown_y’s

Highlight the entire Highlight the entire VoltageVoltage column and hit Enter, this will create an array column and hit Enter, this will create an array for the for the Known_y’sKnown_y’s block block

The The Known_x’sKnown_x’s block is next; click on the square corresponding to that cell block is next; click on the square corresponding to that cell

This time highlight the three columns under This time highlight the three columns under I load, Ip,I load, Ip, and and A-s A-s and hit and hit EnterEnter

Now that the Now that the Known_y’sKnown_y’s and and Known_x’sKnown_x’s cells contain arrays, the cells contain arrays, the ConstConst and and StatsStats cells need filled in cells need filled in

For the purposes of modeling a battery, the last two cells can just have For the purposes of modeling a battery, the last two cells can just have TRUE typed into them; to display the results hit Ctrl-Shift-EnterTRUE typed into them; to display the results hit Ctrl-Shift-Enter

After hitting Ctrl-Shift-Enter the results will appear in the 5x4 block that After hitting Ctrl-Shift-Enter the results will appear in the 5x4 block that was highlightedwas highlighted

The first row of values are coefficients for a linear equation where The first row of values are coefficients for a linear equation where VoltageVoltage is the dependent variable and is the dependent variable and I load, Ip, and A-sI load, Ip, and A-s are the independent are the independent

variables; variables; OCV’OCV’ goes with goes with A-sA-s, , RpRp with with IpIp, , RoRo with with I loadI load, and, and OCV OCV is the is the “b” value“b” value

Voltage=(A-s)(OCV’)+( Ip)(Rp)+(I load)(Ro)+ OCVVoltage=(A-s)(OCV’)+( Ip)(Rp)+(I load)(Ro)+ OCV

Use the voltage formula in the first cell of Use the voltage formula in the first cell of Estimated V loadEstimated V load Voltage=(A-s)(OCV’)+( Ip)(Rp)+(I load)(Ro)+ OCVVoltage=(A-s)(OCV’)+( Ip)(Rp)+(I load)(Ro)+ OCV

Copy the first cell to fill in the rest of the column, remember that the Copy the first cell to fill in the rest of the column, remember that the coefficients in the formula need to have a dollar sign in frontcoefficients in the formula need to have a dollar sign in front

Fill in the Fill in the V errorV error column by taking the difference between the measured column by taking the difference between the measured voltage and estimated voltage; if the formula is good the errors should be voltage and estimated voltage; if the formula is good the errors should be

smallsmall

The third cell down in the leftmost column of the results is the rThe third cell down in the leftmost column of the results is the r22 value, value, this number indicates the accuracy of the formula; the formula is perfect this number indicates the accuracy of the formula; the formula is perfect if rif r22 is equal to one, and the battery manual requires that r is equal to one, and the battery manual requires that r22 be >0.995 be >0.995

The rest of the cells give more statistics on the formula that LINEST The rest of the cells give more statistics on the formula that LINEST created, but they will not be used in this applicationcreated, but they will not be used in this application

Tau affects all of the results, but in the beginning it was only guessed; to Tau affects all of the results, but in the beginning it was only guessed; to get the correct value, adjust tau so that it gives the maximum value of rget the correct value, adjust tau so that it gives the maximum value of r22, ,

then consider that the true valuethen consider that the true value

For this example 9.4 was the best value for tau; changing tau by 0.1 For this example 9.4 was the best value for tau; changing tau by 0.1 caused changes in rcaused changes in r22 as small as 1x10 as small as 1x10-6-6

Sometimes there is “noisy data” in the Sometimes there is “noisy data” in the VoltageVoltage column; a bad cell can be column; a bad cell can be edited out by setting it equal to the corresponding calculated valueedited out by setting it equal to the corresponding calculated value

Excel must be in “Iteration” mode for the editing strategy to work; this Excel must be in “Iteration” mode for the editing strategy to work; this mode can be set by choosing Tools/Options/Calculation and checking the mode can be set by choosing Tools/Options/Calculation and checking the

appropriate boxappropriate box

Two charts can be made, the first is of Two charts can be made, the first is of V errorV error vs. vs. TimeTime

The second chart is of Measured and Estimated Voltage vs. time; both The second chart is of Measured and Estimated Voltage vs. time; both charts can be used to graphically see how well the LINEST formula follows charts can be used to graphically see how well the LINEST formula follows

the measured datathe measured data

This procedure needs to be done for each This procedure needs to be done for each pulse profile in a HPPC test. To save effort, pulse profile in a HPPC test. To save effort, copy the results of each profile into a separate copy the results of each profile into a separate Excel file (be sure to use Copy/Paste Excel file (be sure to use Copy/Paste Special/Values). Then for a new pulse, paste Special/Values). Then for a new pulse, paste in Time, I load, A-s, and Voltage into the old in Time, I load, A-s, and Voltage into the old setup; LINEST should recalculate on its own.setup; LINEST should recalculate on its own.

Once all the resistance values are in their own Once all the resistance values are in their own file, plot them with respect to SOC. From this, file, plot them with respect to SOC. From this, polynomials can be created that can be polynomials can be created that can be plugged into PNGV models.plugged into PNGV models.