Q:

Confused about unit of kilowatt hours

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?

A:

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.

A:

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.

