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So I am a little confused on how to deal with the Kilowatt hours unit of power, I have only ever used Kilowatts and I have to design a residential fuel cell used as a backup generator for one day. The average power consumption of a US household is 8,900 kW-hr per year and 25 kW-hr per day and approximate 1 kW-hr per hour. Does this mean that the power output of my fuel cell is 1 kW and if I wanted to use it for the entire day would it have to be designed to be 25 kW? |
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What RedGrittyBrick said in his comment is correct, but as you need to understand $kWh$ I'll try to explain a bit more. There are two main things you need to take into account: the total energy in your fuel cell (in $kWh$) and the maximum power it can deliver (in $kW$). Power is the rate at which energy is used. In electricity, $1W$ is equal to $1V times 1A$, so 1kW is equivalent to $220V$ at about $4.5A$ and $1kWh$ is that amount of power used for 1 hour. A $1kWh$ battery can deliver $1kW$ for 1 hour, or $0.5kW$ for 2 hours, etc. It does get problematic though, if we try to deliver more power over a shorter time. Batteries can only deliver so much current. For example, a $1kWh$ battery is unlikely to be able to supply $60kW$ for 1 minute. It may not be able to supply the full current required, or at those high currents it may not be able to supply it for the expected time. If your fuel cell has to last a day, then it obviously needs to store enough energy to last that time. So, if your average use is $1kW$, then you need a $24kWh$ fuel cell to go the distance. But your usage will not be constant during the day. At some time most appliances may be switched off, but at other times you may turn on heaters or airconditioners, etc, and use lots of power. The power used by appliances can also vary a lot. A laser printer can use $1kW$ while printing, but only $10W$ in standby. Your fuel cell has to be able to deliver the maximum current required under the worst circumstances. On top of all that, the above is only valid if you are using DC appliances - and I have not noticed any of those recently... If your appliances run AC you also need to allow for things like the "power factor". So you need to know a lot more than just the power or energy usage. |
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A kilowatt is a unit of power, which has the dimensions of energy over time. A kilowatt-hour, then, has dimensions of energy. As a simple example, if you wanted to charge up a battery so as to operate a 1,000-watt (DC) heater for one hour, you'd need one kilowatt-hour of energy (assuming the mythical world of perfectly efficient batteries, lossless wires, etc.) In terms of SI units, this is 1000 J/s $\times$ 3600 s = 3.6 MJ. |
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The average power output is about 1kW (which is the same as 1KW-hour per hour). The energy capacity required for 1 day's operation at this power level is 25 kW-hours. |
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OK, I think you have it right, in the context and scope of the question, the fuel cell should be able to deliver 1Kw, and do it all day. From a more practical interpretation, the problem is under-specified. You need to know the peak load. What is the highest power the house needs? It might sometimes draw 5Kw, maybe 20Kw. Your fuel cell should be able to handle that. But the homework did not mention that. So set the fuel cell to deliver 1Kw all the time. It will produce 24Kw-Hrs in a day. |
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A kilowatt-hour is a unit of energy. It's the energy of one kilowatt for one hour. Which is equivalent to the energy of 2 kilowatts for half an hour, 4 kilowatts for quarter of an hour, or 2 kilowatts for quarter of an hour plus 1 kilowatt for half an hour. A house might use 24kWh in a day. But that doesn't mean 1kW continuous output would meets needs, hour by hour. It just means that 1kW continuous output would produce equivalent energy to the household consumption. It would only meet the house's needs, if the household demand were perfectly constant at 1kW power. To meet power needs and energy needs, you need three things:
Your question doesn't have enough information on points 2 and 3 to specify the fuel cell. A 1kW fuel cell, if it could run continuously for 24 hours, would produce equivalent energy to a household that needs 24 kWh in a day - because the household's mean power requirement is 1kW, the same output as the fuel cell. So the house would not be energy-independent; but it would be some sort of self-sufficient, as long as it could export its surplus at times of surplus, and import extra power at times of deficit. In such a case, it would on average have zero net imports (but it would have N kWh of absolute imports each day, and N kWh of absolute exports each day, where N is some number between 0 and 24). |
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Kilowatt-hours is not a unit of power, it is a unit of energy. I think the easiest way to clarify this may be to think in terms of energy and power and try to avoid terms like kilowatt-hours per hour.
Answer 1A fuel-cell with a power output of 1042 Watt operated for a day will deliver the 25 kWh of energy you mention. (Assuming you have a hydrogen-cylinder delivery man who visits regularly with fresh supplies) It will not allow you to use a kettle. It may not allow you to turn all the lights on and watch TV Answer 2It may help if you translate everything into SI units 1 kW is 1,000 Watts of power So your target house uses 90,000,000 Joules in a day. If the rate of energy usage is constant and never varies you can supply that amount of energy at a constant rate of 1,042 Joules per second (otherwise known as 1,042 Watts or just over 1 kW) A typical kettle for boiling drinking water needs over 2 kW of power. Answer 3I eat 2,500 kCalories in 24 hours. (10,460,000 Joules) That is an average of 121 Joules every second. However I don't eat a tiny speck of food every second 24 hours a day. I spend some of that time sleeping and on activities where I do not necessarily want to concurrently eat blueberry pie at that rate. |
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