Technical memo based on a provided excel sheets
wc.mcqupdated.xlsx_.xlsx
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 10.199999999999999Current, 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 8Current, A
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