paraphrase
wc.mcq
university_of_new_haven.docxAs directed by the development department of your company, a model to predict the voltage delivered at different current loads that is supplied by the fuel cell has been developed based on the actual performance data for the fuel cell supplied. Two different models are developed to predict the voltage at low current load ranges and moderate current ranges. The Low current load range was identified to be from 0 to 10 Ampere. Similarly, the Moderate Current load range was determined to be from 10 to 20 Amperes, with 20 Amperes being the maximum current draw at which the cell should be used.
The model equations for different current loads are as follows:
· Low Current Loads: 13.915 – 0.418i, being the current load (0-10 amp)
· Moderate Current Loads: 12.695 – 0.238i, i being the current load (10-20 amp)
The fuel cell was assumed to a constant voltage source, VS with some internal resistance, RS. A simple circuit diagram was followed as the basis for creating the model equations. The relationship between the current flowing in the circuit i, VS, and RS was found using simple KVL analysis as follows:
The equation VT = VS – i*RS, was followed to be the base equation and the curve fitting method was employed to find the values for VS and RS. The actual data consisting of the current and terminal voltage values was plotted on a graph, and using the “trend-line” tool for curve fitting in Excel, a linear curve was fitted for the provided points.
The equation of the trend-line gave the initial model equation as: 13.681 – 0.3081i. On comparing this equation with the base equation, the value of y intercept equals VS and the value of x intercept gives RS. Using these initial VS and RS value the values for the Terminal voltage were predicted and compared with the actual voltage values. The absolute value of difference between the actual and predicted values and the square of this difference were found along-with the percentage difference between the same.
The error values were analyzed and it was found that for the current load range between 0-10 Amperes the error values were comparable that the predicted values of the terminal voltage were offset from the trend line by the same distance. Whereas as the current load increased above 10 Amperes the error values changed significantly and were no more in par with the previous error values. Hence this was considered to the first cut-off point and the current range of 0-10 amperes was identified to be the Low current region. The error values for predicted terminal voltage values for current load from 10-20 Amperes were also found to be comparable with each other. However on moving from current of 20 Amperes to 22 Amperes a sudden and abrupt decrease in voltage was observed. Hence this was identified to be the IMAX current load above which load the fuel cell should not be used as it reaches it limiting power.
After identifying the low and moderate current load ranges, separate models for the same were derived using curve fitting and regression tools. The low current load range values were separately plotted on a graph and trend-line was inserted using curve fitting and the model equation for the same was found to be: 13.915 – 0.4018i.
The average error value for the absolute difference between the actual and predicted terminal values was found to be 0.29725 volts and the average of this squared difference was calculated to be 0.10459. The percentage error between the actual and predicted value ranged from 1.31% to a maximum of 4.58%.
Similarly for the moderate current load actual values were plotted and curve fitting was employed on the plotted points and the model equation for the same was found to be: 12.695 – 0.2386i.
The average error value for the absolute difference between the actual and predicted terminal values was found to be 0.0962 volts and the average of this squared difference was calculated to be 0.01069. The percentage error between the actual and predicted value ranged from 0.48% to a maximum of 1.68%.
The IMAX current value lied in the end of the moderate current load range. The predicted terminal voltage for the same was calculated using the model equation for the moderate zone itself and was found to be 7.923 volts compared to the actual value of 8 volts. The percentage error for the same being 0.96% against the allowed percentage error of 6%.
Moderate Current Region Model
High Current Region Model 10.0 12.0 14.0 16.0 18.0 20.0 10.2 10.0 9.4 8.8 8.3 8.0Current, A
Terminal Voltage, volts
Terminal Voltage vs Current
Actual Terminal Voltage (VT)0.0 0.2 0.5 1.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0 28.0 30.0 14.1 14.0 14.2 13.3 12.7 12.1 11.0 10.9 10.2 10.0 9.4 8.8 8.3 8.0 6.88 6.76 6.27 4.649999999999998 3.91
Current, A
Terminal Voltage, volts
Low Current Region Model
Low Current Region Model 0.0 0.2 0.5 1.0 2.0 4.0 6.0 8.0 10.0 14.1 14.0 14.2 13.3 12.7 12.1 11.0 10.9 10.2Current, A
Terminal Voltage, volts
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