Converting kW/h to kWh for Optimizing Fuel Cell Ramp-Up

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Discussion Overview

The discussion revolves around the conversion of power units from kW/h to kWh in the context of optimizing the ramp-up of a fuel cell. Participants explore the mathematical implications of ramp rates and energy calculations over time, particularly in a simulation model spanning one year.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Ornella describes a modulation ramp of 4% of the nominal power (58.3 kW) per minute and seeks assistance with converting this ramp-up into kWh for her optimization model.
  • One participant suggests that for variable power, the energy should be calculated as the integral over time, while another asserts that the power is constant for their simulation.
  • Another participant proposes that if the ramp is linear, the energy during the ramp can be calculated as the average power multiplied by time, leading to a formula involving half the full power over the ramp time.
  • Ornella later confirms that she calculated the ramp-up time to be 25 minutes and applied the suggested method to find the energy during ramp-up.
  • There is a clarification that energy is measured in kWh, not kW/h, which some participants initially confused.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the power during ramp-up (constant vs. variable) and how to properly calculate energy in this context. While some calculations are confirmed, no consensus is reached on the initial confusion regarding units.

Contextual Notes

There are unresolved aspects regarding the assumptions made about the ramp-up characteristics and the definitions of power and energy in this context.

Ornella
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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
 
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Ornella said:
I simply multiplied the power times one hour and I should get the energy in kWh.
That works for constant power. For variable power you have take its integral over time.
 
A.T. said:
That works for constant power. For variable power you have take its integral over time.
The power is actually constant. I am trying to expand the simulation per every hour of the year. Is it still wrong?
 
Ornella said:
I have a modulation ramp of 4% of the nominal power (58.3 kW) per minute.
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.
 
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
 
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Ornella said:
The power is actually constant.
Than what are you measuring in kW/h?
 
A.T. said:
Than what are you measuring in kW/h?
the energy during the ramp up of my fuel cell
 
Last edited:
Merlin3189 said:
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
Thank you very much! That's what I was looking for!
 
Merlin3189 said:
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.
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!
 
  • #10
Yes you're quite right. My brain must be withering! 25 minutes at 4% per minute is 100%
 
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  • #11
A.T. said:
Then what are you measuring in kW/h?
Ornella said:
the energy during the ramp up of my fuel cell
Energy is measured in kWh, not in kW/h.
 
  • #12
A.T. said:
Energy is measured in kWh, not in kW/h.

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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