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Conversion kW/h to kWh

  1. Feb 4, 2016 #1
    Hi everyone,

    I am working on a mathematical optimization model for a fuel cell.
    Currently I am facing a problem with the ramp-up of the cell.
    I have a modulation ramp of 4% of the nominal power (58.3 kW) per minute.
    My constraint in the model has to be in kWh (I have to precise that my model is a hourly simulation during one year).
    Concerning the conversion of the power in other constraints (as for FC capacity constraint) I simply multiplied the power times one hour and I should get the energy in kWh.
    But for the ramp-up constraint I am really struggling with the conversion.
    Anyone that has an idea how to obtain it?

    Thanks in advance for any help.
    Ornella
     
  2. jcsd
  3. Feb 4, 2016 #2

    A.T.

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    That works for constant power. For variable power you have take its integral over time.
     
  4. Feb 4, 2016 #3
    The power is actually constant. I am trying to expand the simulation per every hour of the year. Is it still wrong?
     
  5. Feb 4, 2016 #4

    Merlin3189

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    Maybe:
    At the start you are drawing no current. Every minute you can increase your power draw by 4% of 58.3kW (= 2.332kW)
    After 15min you are drawing the full rated power of 58.3kW.
     
  6. Feb 4, 2016 #5

    Merlin3189

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    If you are looking at energy, then, provided the ramp is a straight line (as it usually seems to be),
    energy during ramp = average power x time = 1/2 full power * ramp time. = 0.5 x 58.3 x 0.25 kWh
     
  7. Feb 4, 2016 #6

    A.T.

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    Than what are you measuring in kW/h?
     
  8. Feb 4, 2016 #7
    the energy during the ramp up of my fuel cell
     
    Last edited: Feb 4, 2016
  9. Feb 4, 2016 #8
    Thank you very much! That's what I was looking for!
     
  10. Feb 4, 2016 #9
    I actually found out the time for ramp up to be 25 min.

    0.04/min * 60 min/h * 58 kW = 139.9 kW/h
    58.3 kW / 139.92 = 0.42 h = 25 min
    Then I applied the method as you said.
    0.5 * 58.3 * 0.42 = 12.5 kWh
    Thanks again!
     
  11. Feb 4, 2016 #10

    Merlin3189

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    Yes you're quite right. My brain must be withering! 25 minutes at 4% per minute is 100%
     
  12. Feb 4, 2016 #11

    A.T.

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    Energy is measured in kWh, not in kW/h.
     
  13. Feb 4, 2016 #12
    I was trying to obtain the energy during the actual time of ramp-up. But I solved my problem.
    Thanks anyways.
     
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