MW to MWh Conversion – Understanding the Difference

A watt (or kilowatt or megawatt) is a measure of power. Power is the rate of energy transfer. For example, a watt is defined as 1 joule per second, where you can think of a joule as one nicely measured packet of energy.

Watt-hours (or kilowatt-hours or megawatt-hours) is just another way of measuring energy. A kWh is one kW of power flowing for one hour, which is 1000 joules going by every second for one hour. Since there are 3600 seconds in a hour, 1 kWh is therefore exactly the same as 3.6 Mj. The electric grid deals with large power levels and large energy transfers, so that discipline has evolved to express energy in MWh and kWh because that is more directly relevant to how they transfer and store energy.

I didn't look at your link, but what I remember from the Beacon Power flywheels is that each one is rated for 100 kWh. The 100 kWh is stored by spinning large and heavy flywheels in vacuum on magnetic bearings. During normal operation, the flywheel speed goes from its maximum to half that, which means from full to 1/4 of the flywheel's total energy. If I remember right, the 100 kWh figure is the difference between the two normal operating extremes.

I think the discrepancy between 20 MW and the 100 kWh of individual flywheels is that they are referring to a large plant with many flywheels.

25 kWh transferred over 5 minutes is 25 kWh transferred over 1/12 hour, which is 300 kW continuously for 1/12 hour. So yes, your last sentence is correct.

The term "watt-hour" (Wh) is often not correctly understood. Watt (W) is a unit of power. Energy is measured in Joules (J) and is related to power by $$ E = {P_\text{avg}}\times \Delta t, $$ where \$\Delta t\$ is time in question and \$P_\text{avg}\$ is the average power spent during that time.

With only two measurements, one at the start and one at the end, the best guess is that the average power was $$ P_\text{avg} = \frac{P_\text{start} + P_\text{end}}{2} $$

Notice that "watt-hours" is power multiplied with time, so it is a measure of energy. This is what power companies really sell you, and what they should charge you for; though that's for some reason not always the case.

Joules is the same as a "watt-second", so $$ 1\;\text{Wh} = (1\;\text{W})\times(1\;\text{h}) = (1\;\text{W})\times(3,600\;\text{s}) = 3,600\;\text{J}=3.6\;\text{kJ} $$

Sidenote

If you know calculus, then a more accurate formula for the relationship between power and energy is $$ E = \int_{t_\text{start}}^{t_\text{end}} P(t)\;dt, $$ or even $$ P(t) = \frac{dE(t)}{dt}, $$ which says that power is the rate-of-change of energy consumption. You can make use of this, if you know the sample-rate of your measurements, for instance by using an ADC from a micro-controller. If the time between samples is dt, then the total energy can be calculated by:

loop() {
  current = currentADC.sample();
  voltage = voltageADC.sample();
  time = time_now();
  dt = time - time_last;
  power = current * voltage;
  energy += power * dt;
  time_last = time;
}