With the recent bout of load shedding, everyone’s been writing about electricity. The problem is that many people get things wrong, or apply conventions which are less useful than they think.
The basics
Electricity is fundamentally about the flow of electrons. You may say that it is also about magnetic fields, but most of the terminology you’ll be seeing in the articles about load shedding is about making electrons move. Now, electrons are very small, so it makes sense to count them in big groups rather than individually. In the SI system, the coulomb (C) is defined as exactly 6.241×1018 electrons. You can think of this as equivalent to something like a truckload of coal. Since every material we work with has many electrons already, just having them is not particularly useful. Electrons can do useful things when they are in motion. When there is a flow of electrons in a conductor, this is referred to as current and measured in ampere (A). 1 A = 1 C/s, although technically the ampere is the base unit and the coulomb is the derived unit in SI, so 1 C = 1 A⋅s . To continue our analogy, if coulomb is like “truckloads”, ampere would be “truckloads per day”.
Flowing electrons can be harnessed to do work in the same way that a flowing river can be harnessed. The rate at which they can do work is related not only to how fast they are flowing (the current) but also to the potential difference (measured in volts, V) between the end points. In a river, this would be the pressure. Work is measured in joules (J), which is also the unit of energy. The rate at which work is done (also called the power) is measured in watt (W). 1 W = 1 J/s. For a constant current (DC), the power is the product of the current and the potential difference. This means that 1 W = 1 V⋅A. This is approximately true for power supplied by batteries. For a thoroughly mixed metaphorical space, let’s say that energy (J) is like a distance and power (W) is like a speed.
It gets a little more complicated if the current is not constant. The kind of electricity Eskom supplies is sinusoidally varying (AC), which means that we need to distinguish the “apparent power” and the “real power”. This Wikipedia page is a pretty good resource for this idea. The calculation doesn’t change the units in SI, although there are conventions which I will discuss a bit later.
In terms of the load shedding, W is the unit that will be used to talk about the amount of load to be shed. Load in this context is the same as power.
Orders of magnitude
Some of the SI units discussed above are not sized reasonably for everyday use. For instance, a 100 W lightbulb burning for one day will consume 8 640 000 J of energy. For this reason the SI has prefixes for different orders of magnitude. I can choose to express the energy consumed by that lightbulb as 8.64 MJ to save space. It’s anyone’s guess why the load shedding limits are reported in MW rather than GW. Why say 1000 MW when you could have said 1 GW?
The problem of time
In the discussion above, I have restricted myself to the SI system. The SI unit of time is the second (s), and all the units which reference time are built using the second. Time calculations are tricky, because of the fact that there are 60 seconds in a minute and 60 minutes in an hour. Those factors aren’t powers of 10, so they don’t fit smoothly into the decimal system that SI uses. This means that in various industries, the quantities discussed above have been measured using different time units. For instance, your electricity bill probably specifies your electricity usage using the “kWh”, which is the energy used by a 1 kW device operating for 1 hour. Notice that this is the same dimensional combination as the joule. 1 kWh = 1 kW⋅h and 1 J = 1 W⋅s. In fact, 1 kWh = 3.6 GJ, so there’s no real nead for the kWh, even in terms of easy magnitudes. The real difference boils down to the difficulties of manipulating factors of 60.
When measuring the storage capacity of batteries, one will mostly see A⋅h being used rather than the dimensionally-similar C. Smallish batteries like AAs typically have capacity of around 10 kC (meaning that this is the number of electrons they can push around a circuit), but you are more likely to see that reported as 3000 mAh. I believe this is again due to the problems of time calculation, as there shouldn’t be much other difference between using A⋅h instead of A⋅s.
The kWh is such a popular unit of energy that it is even used for derived rates. People will report the average energy production of the Jasper solar facility as 180 000 MW-hours annually rather than saying that it will produce 648 TJ per year or produce at a rate of 20.5 MW on average over a year
Conventions
There are people reading this who will object viscerally to the calculation above, especially if they have been in the electricity industry. There are certain conventions regarding units which are widespread but don’t really make much sense from a dimensional point of view. One of them is that electrical energy is measured primarily in the kWh family of units, while the joule is restricted to other forms of energy. They would say that it is not proper to report the energy production of that solar plant in TJ as that sounds more like the energy supplied by fuel.
Similarly, if you refer to the discussion about power calculations for time-varying current, there are people who insist on saying V⋅A is different from W rather than saying apparent power is different from real power and using W for both.
Peaks and averages
The last confusing thing about talking of energy is in being clear about peaks and averages. To continue the car analogy, it is pretty clear when someone says that they will travel 100 km in 1 hour that they will average 100 km/h but that they probably spent some of the time above that speed and may even have hit 160 km/h at some point. Remembering that the distance is like energy and that speed is like power, we can say that the 774 PJ of energy SA used in 2010 according to Wolfram Alpha means that we averaged 24.5 GW for that year. Why do we have a problem if Eskom has around 41 GW of generating capacity? For one thing, not all that capacity is on line at once. Due to various factors Eskom only has about 24 GW of generating capacity on line right now. Of course, the other problem is that peak demand is more than average demand. The load shedding of 4 November 2014 happened on a day where there was 28 GW of demand, leaving Eskom 4 GW short.
While I’m on this topic, let’s also explain the somewhat confusing fact that the Jasper solar energy plant I linked to earlier reports “Size: 96 MW-DC installed capacity; 75 MW-AC net generation, Electricity Production: approximately 180,000 MW-hours annually”. We translated that last number to 20.5 MW. So what’s happening between the 96 MW and the 20 MW? The 96 MW is what the panels will produce when they have 1 MW/m² of solar irradiation. In SA, we have more like 1.2 MW/m², so they’ll see more than that at peak production. This is a bit like the maximum speed in the book that came with your car. Often you can get better than that if you run at the coast or use better fuel than they tested with. The 75 MW is pretty clear, that’s the amount of AC power they will deliver under the same conditions as the 96 MW was calculated. This includes the use of the station of its own power and conversion losses. Of course, the sun is only available part of the day, and the light is not as strong for the whole day either. There is also maintenance and other stoppages, which cuts the effective rate of production down to the 20 MW number. This final number divided by the “nameplate capacity” of 96 MW is known as the capacity factor, and 20 % is about par for the course for solar.
Wrap-up
So there you have it – this should enable you to decipher the different terms used in articles talking about electrical energy (and perhaps to do some research about that battery backup for your power at home). My last word on the matter is that you should be on the lookout for common misperceptions about units, like that kWh for some reason means kW/h instead of kW⋅h. Hopefully the discussion above will show you why kW/h doesn’t make any kind of sense.
Leave a Reply