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I have a simulation software which shows energy consumption at 30 minutes timestep. If a system consumes 0.06 kWh at 6am, and 0.09 kWh at 630am, how to calculate the energy consumption between 6-7am? Can I assume it is the average of both timestep? Does finer timestep, eg. 10 minutes interval returns a different result?

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I think you are getting power and energy confused, so I'll quickly define them before giving an answer.

Energy energy is a measure of how much potential for work exists. If you had a battery, it contains a certain amount of energy. Once that energy is used, the battery is "dead" and must be recharged (or thrown away). This is usually measured in Joules (J) or kilowatt-hours (kWh).

Power is the rate at which energy is being used. For example, for a fan to blow air it must be continuously consuming energy. One joule per second is called a Watt (W). 1000W is a kilowatt (kW).

If an appliance consumed a constant 1000W for one hour, it would have consumed 1kWh. 1kWh could also be consumed by an appliance consuming a constant 100W for 10hours: in general the energy is the integral of the power over time.

If your software returns energy consumption values (kWh) for 30 minute timesteps, that means that it is (presuming it is designed sanely) integrating the power over every 30 minute timestep. For your specific example, that means that between 6 and 7am the system consumed 0.15kWh of energy.

A 10 minute timestep would have resulted in 6 values that added up to 0.15kWh, assuming that you have set up your model to achieve step-size independence. If you set your timestep to 10 minutes and you get a different value, then you should probably view your 30 minute results with suspicion, but that is an entirely different topic.

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In SI units the measure of "amount" of electrical energy is the Joule.
Energy is a measure of "work done".
Energy can be (and often is) expressed in terms of 'rate of doing work'.
The rate at which work is done or at which energy is supplied or utilised is also named "Power".
Work done = 'rate of doing work' x time period involved
= Power x time (involved)

So 1 Joule of energy = 1 Watt of power for 1 Second = 1 W.s 1 Joule is a small amount of energy compared to typical usage so a larger multiple is used of 1 kWh
= 1000 Watts work rate x 3600 seconds
= 3,600,000 Joule = 1 MJ = 1 kWh

kWh (KiloWatt hours) is a typical unit of "amount" for electrical energy use for eg heaters, motors, lighting etc.

SO if you operate at a power level of 120 Watts from 6am to 6.30 am you will consume 120 Watts x 1/2 hour = 60 Watt hours = 0.060 kWh.

180 Watts from 6:30am to 7am = 180 x 1/2 Hour = 90 Wh = 0.090 kWh.

As kWh = amount of energy, successive figures can be added.
So 0.060 kWh + 0.090 kWh = 0.150 kWh.

Key summary:

Energy = Joule or Watt-hour (W.h) or KiloWatt hour (KWh)

Energy = Watts of power x period used

Energy = W1.T1 + W2.T2 + .... WnTn

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