Energy and Power
Compared?
Sunday, 22 January 2023
Mark wrote "900 MWh/year" on the whiteboard. The phrase referred to the electricity put on the transmission grid by a small generating station. He went on to compare this to a 50 MW wind farm. I objected that the numbers were not comparable because the first phrase described energy, but the wind farm phrase described power. He countered that, in the first phrase, the h in MWh was canceled by the year in the denominator, so it represented MW, power. We dropped the discussion in order not to break the flow of Mark’s presentation.
The disagreement bothered me for days. Early one morning, as I lay in bed pretending sleep, the disagreement and Mark’s use of the terms energy and power took over my mind. I got up and wrote this essay to clarify what the two expressions mean and whether they can be compared.
“900 MWh/year”
The phrase, applied to a generating station, might mean:
During one year, the station put 900 MWh of electric energy on the grid.
The station generates 900 MWh of electric energy annually.
The station generates 900 MW of electric power (Mark’s interpretation).
The station generates 900 MW of electric power annually.
Both numbers 1 and 2 make good sense because MWh is a unit of energy, and the topic was energy. Number 1 is a statement of fact: during a year’s operation, the station generated 900 MWh electric energy. Number 2 asserts the station’s performance which it may or may not achieve
Number 3 does not specify when the power, a function of time, is generated; but worse, there is an average of 8,766 hours in a year, so "year" cannot cancel "h". Number 4 makes no sense because power is a momentary quantity that has no duration.
My conclusion is that the phrase "900 MWh/year" describes either the generating station’s energy output of the or its output specification.
50 MW wind farm
A wind farm consists of a group of windmills built and operated as a unit. The electricity is collected and put on the transmission grid at one of its nodes. The grid operator treats the wind farm as a generating station, like a coal-fired power plant.
This phrase might mean:
The wind farm was designed to produce 50 MW of electric power.
The maximum amount of electric power the farm will generate is 50 MW.
The farm generates 50 MW of electric power.
The farm provides electricity to 50,000 homes at 1 kW per home.
The farm provides electricity to 17,000 homes.
Numbers 1, 2, and 3 are different ways to describe the maximum electric power the farm should generate. There is no hint of how much electric energy the farm can provide or has provided. Number 1 reports that the farm’s design specification requires it to generate 50 MW. Number 2 asserts that the farm will perform to this specification. Number 3 is an assertion of a fact that is true only when the wind is blowing just right for the windmills to produce maximum power.
Numbers 4 and 5 lean into confusing power with energy. Number 4 asserts an impossibility: the wind mills will operate at full power every moment of every day. (Full power is 50 MW which equals 50,000 kW.) Number 5 recognizes the limitation noted in number 4 by assuming that the farm’s capacity factor is 34%. The capacity factor is the ratio of the average power output to the maximum possible power. A factor of 34% means that, on average, the farm generates 0.34 × 50 = 17 MW. The farm generates anywhere from 0 to 50 MW at any moment. When the wind falls off, some other source must kick in to provide for all 17,000 homes; conversely, when the wind is blowing at the maximum design strength, other generating stations on the grid must reduce their power output.
None of these five interpretations tells us what we need to know about the usefulness of the wind farm. When the wind blows at the maximum speed specified by the design, the farm supplies 50 MW. But it supplies less power at other times, and there is no guarantee the power will be available when it’s needed.
My conclusion is that the phrase "50 MW wind farm" describes either the farm’s maximum power output or its power output specification.
Comparison
Can a valid comparison be made? From the standpoint of physics, the answer is no because it is nonsense to compare energy to power, the rate of change of energy.
However, people who are willing to subsidize the wind farm by overlooking its weather dependence and ignoring a few technical details, can compare the phrases. If they assume a capacity factor of 1⁄3 for the windmills, they might say the wind farm supplies 17 MWh electric energy annually, so "900 MWh/year" describes 53 (= 900/17) times as much electric energy as "50 MW wind farm". You won’t catch me saying such nonsense.
Excellent, George.
If more people understood even the most basic aspects of energy and energy systems, it's not obvious to us solar would exist at all in places like Germany and Rhode Island (where capacity factors are in the low teens averaged over a year).
You are still missing the next and required step into practical application, at a Grid and Electricity Production level, that is.
Which is: the Relationship between Time-of-Production and Time-of-Use.
In the US, for example, we tend to use Electricity the most, and is the most valuable during the Day. So sources that produce during the daytime are most valuable and most fully used during their production time -- typically 100%.
Sources that produce at night tend to run into surplus conditions, as we tend to use less Electricity at night. So even sources such as Coal and Nukes which can run into the 90(s)% Capacity range, are often running surplus and relatively worth less around 1/2 the time.
The alignment of Time-of-Production with Time-of-Use has become so significant, that Capacity Factor(s) are no longer the primary issue -- and a source with low build cost, and low operations/maintenance cost -- even with a relatively poor Capacity Factor (such as Solar at 25%) are now more profitable and in demand that Coal or Nukes, because Solar produces during the high-demand Day Time.