Technical memo based on a provided excel sheets

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Definiing current regions

Terminology Units
VT Terminal Voltage Volts (v)
VS Constant Voltage Source Volts (v)
RS Internal Resistance ohms
RL External Resistance ohms
VT Current A
Initial Curve Fitting for full data
y intercept x intercept
VS RS
13.681 0.3081
Fuel Cell PEM-15 Performance Data Predicted Values
Current Actual Terminal Voltage (VT) Current Predicted Terminal Voltage (VT)
Amps Volts Amps Volts Absolute difference I(Actual-predicted)I Square of Absolute Difference Percentage Error
0 14.1 0 13.681 0.419 0.175561 2.97% Low Current Region
0.2 14 0.2 13.61938 0.38062 0.1448715844 2.72%
0.5 14.2 0.5 13.52695 0.67305 0.4529963025 4.74%
1 13.3 1 13.3729 0.0729 0.00531441 0.55%
2 12.7 2 13.0648 0.3648 0.13307904 2.87%
4 12.1 4 12.4486 0.3486 0.12152196 2.88%
6 11 6 11.8324 0.8324 0.69288976 7.57%
8 10.9 8 11.2162 0.3162 0.09998244 2.90%
10 10.2 10 10.6 0.4 0.16 3.92% Cut Off Point
12 10 12 9.9838 0.0162 0.00026244 0.16% Moderate Current Region
14 9.4 14 9.3676 0.0324 0.00104976 0.34%
16 8.8 16 8.7514 0.0486 0.00236196 0.55%
18 8.3 18 8.1352 0.1648 0.02715904 1.99%
20 8 20 7.519 0.481 0.231361 6.01% Maximum Current Draw
22 6.88 22 6.9028 0.0228 0.00051984 0.33% Sudden Voltage Drop Occurs at this point for should not be used
24 6.76 24 6.2866 0.4734 0.22410756 7.00%
26 6.27 26 5.6704 0.5996 0.35952016 9.56%
28 4.65 28 5.0542 0.4042 0.16337764 8.69%
30 3.91 30 4.438 0.528 0.278784 13.50%

Terminal Voltage vs Current

Actual Terminal Voltage (VT)

0 0.2 0.5 1 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 14.1 14 14.2 13.3 12.7 12.1 11 10.9 10.199999999999999 10 9.4 8.8000000000000007 8.3000000000000007 8 6.88 6.76 6.27 4.6500000000000004 3.91

Current, A

Terminal Voltage, volts

Low Current Region Model

Curve Fitting for Low Current Range
y intercept x intercept
VS RS
13.915 0.4018
Fuel Cell PEM-15 Performance Data Predicted Values
Current Actual Terminal Voltage (VT) Current Predicted Terminal Voltage (VT)
Amps Volts Amps Volts Absolute difference I(Actual-predicted)I Square of Absolute Difference Percentage Error
0 14.1 0 13.915 0.185 0.034225 1.31%
Rs VT 0.2 14 0.2 13.83464 0.16536 0.0273439296 1.18%
0.4 0.5 14.2 0.5 13.7141 0.4859 0.23609881 3.42%
ohms 12.31 1 13.3 1 13.5132 0.2132 0.04545424 1.60%
2 12.7 2 13.1114 0.4114 0.16924996 3.24%
volts 4 12.1 4 12.3078 0.2078 0.04318084 1.72%
6 11 6 11.5042 0.5042 0.25421764 4.58%
i 8 10.9 8 10.7006 0.1994 0.03976036 1.83%
10 10.2 10 9.897 0.303 0.091809 2.97%
Vs 4.0
13.92
volts Amps
I, A VT, V0lts RL, ohms
4 12.3078 3076.95
0 13.915 ERROR:#DIV/0!
0.2 13.83464 69173.2
0.5 13.7141 27428.2
1 13.5132 13513.2
2 13.1114 6555.7
4 12.3078 3076.95
6 11.5042 1917.3666666667
8 10.7006 1337.575
10 9.897 989.7

Internal Voltage Vs volts

Low Current Region Model

Low Current Region Model 0 0.2 0.5 1 2 4 6 8 10 14.1 14 14.2 13.3 12.7 12.1 11 10.9 10.199999999999999

Current, A

Terminal Voltage, volts

Internal Resistance, Rs

Moderate Current Region Model

Curve Fitting for Moderate Current Range
y intercept x intercept
VS RS
12.695 0.2386
Fuel Cell PEM-15 Performance Data Predicted Values
Current Actual Terminal Voltage (VS) Current Predicted Terminal Voltage (VT)
Amps Volts Amps Volts Absolute difference I(Actual-predicted)I Square of Absolute Difference Percentage Error
10 10.2 10 10.309 0.109 0.011881 1.07%
Rs VT 12 10 12 9.8318 0.1682 0.02829124 1.68%
0.2 14 9.4 14 9.3546 0.0454 0.00206116 0.48%
ohms 9.83 16 8.8 16 8.8774 0.0774 0.00599076 0.88%
18 8.3 18 8.4002 0.1002 0.01004004 1.21%
volts 20 8 20 7.923 0.077 0.005929 0.96%
i
Vs 12.0
12.70
volts Amps
I, A VT, V0lts RL, ohms
12 9.8318 819.3166666667
10 10.309 1030.9
12 9.8318 819.3166666667
14 9.3546 668.1857142857
16 8.8774 554.8375
18 8.4002 466.6777777778
20 7.923 396.15

Internal Voltage Vs volts

Moderate Current Region Model

High Current Region Model 10 12 14 16 18 20 10.199999999999999 10 9.4 8.8000000000000007 8.3000000000000007 8

Current, A

Terminal Voltage, volts

Internal Resistance, Rs

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