Is Power Consumption (kWh and kW) a Linear Function?

Your question is a little confusing. KWH = KW x hours applies to any load. You only need to know 2 of the 3 values associated with a particular load to get you answer.

1000 x 1 hr = 1 kwh. 1 w x 1000 hrs = 1 kwh.

Suppose that I know the monthly kWh consumed by a circuit (the load are some motors, pumps, lights) 350,000 kWh. For this same month the total kW consumed are 500 kW. If I want to know how much of this 350,000 kWh are generated by 50 kW of this load, can I use kWh = (50 kW * 350,000 kWh) / 500Kw ; in order to get an estimation, don't has to be exact.

Thanks.

That would give you an estimate.

Hi,

For this same month the total kW consumed are 500 kW.

We can't calculate the total KW consumption. It can be said as normal or constant KW. The formula is applicable only when the load is constant & it acts 24 hours a day.

yes, it is a ratio of the partial power demand to the full power demand times the energy usage, on average. Keep in mind the energy usage is a a total over a long period of time, not a peak usage when the particular demand of concern is in operation.

If all the loads on the circuit has the same running hour that will be applicable. But in case of different running, it will give / mis lead someone who would conduct an analysis.

Thus the relationship of a load to a given total consumption

Y = (Z * Estimated Operating Hours) / X

"Y" (% from total consumption "X")

"Z" (kW which is a part of "X")

"X" (kWh total energy consumption)

The energy is only linear if all the loads are running, not only for the same number of hours, but at a consistant load. For example, part of the time a 50 hp motor might be fully loaded and part of the time it might only be running with no load or light load on it. If the equipment were running fully loaded all of the time, then you could make your assumption and it would be pretty valid. Otherwise, it is pretty much a guess. There are lots of meter devices available that can record both kW and kWh and send the data to an energy management system or building management system and then you could can allocate energy (and cost) to particular pieces of equipment.

In general, I'd say "no" that you cannot do this even as an estimate. The exception would be if everything on the circuit runs all the time, but that is very unusual. Pump motors, for example, often cycle on and off, and some (such as a sump pump) only operate under unusual circumstances. Perhaps your 50 kW motor only operates 5% of the time and you have a 20 kW motor than runs continuously. The 20 kW motor would then consume far more kWhs than your 50 kW motor.

KW is Power, while kWh is Work. Two different things.

The only thing you can calculate is the equivalent time the full power has been drawn.

Time in hours = kWh / kW

If you consumed 1000 kWh at a constant rate of 100 kW, then the time is:

Time in hours = 1000 kWh / 100 kW = 10 hours.

If your system is longer in operation, then the average power drawn is not 100 kW.

This leads to the next calculation:

Say you used 1000 kWh over a time of 20 hours, then the average kW is:

kW = kWh / h = 1000 kWh / 20 h = 50 kW average power usage.

Regards

Rolf

Castel, perhaps relating the two terms to other understood quantities will be of help to you in this query:

Cars usually have a speedometer to show how fast you are going at the moment,and an odometer to log how far you went in total.

Think of the speedometer as kW, and the odometer as kWh. Now insert the speedometer/odometer terms into your query and you will be able to get that there is the same direct relationship between the two, but it is rarely linear.