Introducing a train analogy to explain Power Systems 101

(A)  Strengths and weaknesses of Analogies

Analogies are often useful.

It is reasoning by analogies which have produced some of our most successful scientific theories. Isaac Newton compared planets with apples and came up with a theory of gravity. Albert Einstein conducted “thought experiments” of trains travelling close to the speed of light to come up with the theory of relativity.

Of course analogies can also be misleading.

It used to be believed that heavier objects fell faster than lighter objects because it was “obvious” that more force is needed to lift a heavy object. “Obviously” heavier objects have a greater affinity with the earth than lighter objects.

However, so long as the analogy is not pushed too far, carefully chosen analogies are absolutely essential to improve and gain understanding of the physical world and this in turn is essential in order to avoid poor decisions when dealing with technology, and to communicate difficult concepts.

It is now becoming a cliché to state that our electrical power system is in a state of transition.  Everyday our media contains stories of the energy system which has become the major political issue in recent times.

There has been a lot of investment in intermittent renewable energy sources such as wind farms, solar technologies and energy storage devices such as batteries which have now been developed to such an extent that they produce cheaper power than newly installed fossil fuel sources can.

However to do so the technical issues of power intermittency, frequency regulation, voltage control and system strength (fault level) have to solved.  These latter issues, collectively lumped together in power systems parlance as “ancillary services” are not well understood by non-specialists a situation which can and has resulted in poor policy decisions and arbitrary technical rules.

To give a proper explanation of these issues requires explanation of various technical concepts and more than a few mathematical equations, both areas that should be avoided in a blog post if you want to avoid alienating many of your readers.

Accordingly this article will attempt to explain many of these concepts using analogies. However this comes with a warning, although I will attempt to be as conceptually as accurate as possible, the descriptions herein will necessarily be incomplete and experts will most likely be appalled by some of the simplifications which follow below. This is unavoidable, if you want a clear and accurate description of the technicalities it will require some detailed study and some considerable skill in STEM subjects, something that cannot be compressed into a single article.

(B)  Explaining “Power Systems 101” using the analogy of a very long train

The analogy I have chosen is that of a very long train which consists of several engines and several carriages.

The train engines represent the generators on a power system, the carriages represent the loads. Everything is coupled together in the train, as it is in a power system via transmission lines and transformers etc.

The carriages have poor brakes fitted which are always on but which are not strong enough to stop the train. Releasing the brakes is equivalent to switching off a load, reapplying the brakes equivalent to switching on a load.

The train engines jointly control the speed of the train just as generators jointly maintain the power system frequency. If one engine stops or reduces in power the other engines have to increase their power output to compensate the loss of power.

The mass of the train combined with its speed is another name for its inertia. The engines are usually heavier than the carriages, and this is the case for power systems as well, generators usually (up until recently) have more inertia than loads.

This is probably a lot to take in when reading it as prose, so here is a table to summarize:

Train Analogy What this equates to, in Power Systems
Engine (locomotive) Generator
Carriage (with poor brakes applied) Load
Carriage (with brakes released) Load switches off
Speed of the train Power system frequency
Throttle (speed control) Governor control system
Mass of the whole train System inertia
Mass of the engine Generator inertia

The analogies can be pushed further:

Advanced Train Analogy What this equates to, in Power Systems
Transient Stability If an engine is decoupled from the train it will accelerate away from it because it does not have any carriages trying to hold it back. If you had a way of rapidly re-coupling it to the train before it got too far ahead, then everything would return to normal, otherwise the engine would escape (and probably crash!). In power systems the coupling is done by circuit breakers, “escaping” generators is known as pole slipping or transient instability, but if you can rapidly reconnect them before pole slipping occurs; the system is said to be transiently stable.
Load shedding This one is easy, say you suddenly lost a large engine (i.e. it could have run out of fuel). The whole train would start to slow down so to avoid the whole train from slowing down you quickly decouple some carriages. They would slow to a stop, but the rest of the train would return to normal speed and keep going.
Oscillatory (control system) stability With trains and generators it is possible to have poorly tuned speed (i.e. Frequency) control systems which become unstable (i.e. Start “hunting”).

This is known as oscillatory instability which you can imagine as two engines trying to go at different speeds but can’t because they are coupled together (by springs!)  but due to differing time delays in each control system can lead to power surges (oscillations) between the two (or more) engines.

Voltage Control This analogy can be stretched to include power system voltage control (which is very important in power systems) but I won’t go into too much detail on voltage control in this article (maybe next time).

To summarise, if you consider the couplings between train carriages and engines to be springs, the diameter of the spring is analogous to the power system voltage. Stretching the spring shrinks its diameter which is analogous to a reduction in power system voltage levels on transmission lines which occurs when power flows are high through parts of the network.

The Frequency Control Ancillary Services (FCAS) Market We have a long train with several (> 500 ) large engines and several thousand carriages, all linked together with couplings. This gives some idea of the scale of the NEM which is actually relatively small by global standards (though spread out over a very large area).

Controlling the speed of such a long train requires making sure all of the engines control to the same speed. This engineering problem was solved (on railway systems) even before electrical power systems were created. Basically the speed reference set point on every engine is adjusted downwards the faster they go; this reduces the power output which slows down the train.    Eventually equilibrium is reached whereby all engines operate at exactly the same speed; and each engine shares the load reasonably evenly. All achieved with no high speed electronic communications between different generators.

It is not quite that simple, the speed control systems need to be tuned to prevent control system oscillations (hunting), and it is natural that generators of different sizes to respond differently to changes in frequency (speed). E.g. larger units tend to be slower to respond than smaller units. However, subject to these technical details, the problem of managing the power system frequency was solved more than 150 years ago when several engines were first linked together to create trains of higher power, and then the technique was extended to electrical power systems.

(C)  A critique of some recent developments in FCAS, using this train analogy

I originally wrote this as a single article on LinkedIn here.

On WattClarity it has been separated into two for easier readability and as both parts address a different audience, with the second piece here.

 Bruce Miller is an Electrical Engineer from a High Voltage Power systems background. He has experience in design, commissioning and project management and the development of mathematical and software tools. He currently manages a team of highly skilled engineering and software specialists who carry out planning, technical and commercial studies for clients to assist them in obtaining low cost, clean energy which is safe and reliable. You can find Bruce on LinkedIn here.

9 Commentson "Introducing a train analogy to explain Power Systems 101"

1. Thanks for the article Bruce, just one quibble in the advanced analogy I would alter the Transient Stability section to say:
“If an engine is decoupled from the train it will accelerate away from it because it does not have any carriages trying to hold it back. If you had a way of rapidly re-coupling it to the train before it got too far ahead, then everything would return to normal, otherwise the engine would escape (and probably crash!). In power systems the coupling is done by magnetic field between the generator rotor and its stator, “escaping” generators is known as pole slipping or transient instability, but if you can rapidly reconnect them before pole slipping occurs; the system is said to be transiently stable.
This should not be confused with circuit breakers suddenly opening causing the generator to unload while the turbine has steam passing through it. The sudden loss of load could cause the turbine and generator to over-speed with catastrophic results due to centrifugal force. Consequently turbines are fitted with over speed trip mechanisms which shut off steam flow to the turbine and release valves which exhaust the steam already in the turbine to atmosphere.”
Unfortunately text colour and cross-outs don’t translate to this comments field so if any of it is unclear I can forward it in a Word doc. P.S. I am a former power station operator so am more familiar with steam than electrical parts of the system.
Regards,
Shane O’Loughlin

• Thanks Shane, I generally agree. However I should point out a sustained fault which doesn’t get cleared will also cause the generator to unload with likely catastrophic results.
Fortunately faults are usually cleared within a fraction of a second.

2. Thanks Shane, I generally agree. However I should point out a sustained fault which doesn’t get cleared will also cause the generator to unload with likely catastrophic results.
Fortunately faults are usually cleared within a fraction of a second.

3. While some analogies are useful in gaining various insights into the behaviors of a complex system like for example Relativity, this is because what is being describe is beyond our normal experience. Clever people grappling with such concepts can extend their sophisticated understand this way. However, I fail to see why one would want to help those who want to stick their busy beaks into matters which in fact they actuality have nothing to contributed. If someone can’t understand the the system dynamics of a grid using the normal explanations using the appropriate mathematical equations with the correct solutions I think it best that they stay out of the discussion. I am dismayed to read about what I call the democratization of complex technology. I have been lucky enough to spend a working life dealing with various complex technologies that the public has never tried to understand and I would hope it should remain that way. As the clever people of this world do their level best to design, build and run complex systems I fail to understand why they need to taking into account the thoughts and opinions of the what I would like to call the stupid people. There was, once upon a time, nothing more boring than a bunch of power stations supply a grid in the mind of most of the public. All people cared about was that that it should keep working and they did not have to pay too much for the power. While the genie has partly got out of the lamp lets not do any more to let any more out.

• Thanks Ken, I think the Duke of Wellington had similar views on democracy

• You are kind in ONLY suggesting The Duke of Wellington might share my views – there are others that I would not align myself with for other reason who also thought that the democracy can go to far. On a more technical basis I think your analogy would be fine for a DC grid. But with an AC grid there needs to be two degrees of freedom (voltage and power) and the linear motion of a train only allows for one degree. But, trying to shoe-horn your idea a bit further if you had an engine (loco) to pull a number of carriages (cars in US Nomenclature) and that that train set was coupled to a much bigger train set by a rather long and electric “tow rope” (that could take compression as well as tension) then that might serve to explain the stability problems of South Australia as far as the interconnections are concerned. But your analogy works well for the control of governors and the various types of feeds (1 to 5) of the inverters associated with wind turbines. Some loco just set to a fixed throttle (diesel injector stroke) setting, while some locos with their “cruse controls” are set to a certain speed. But some of the very long ore train had delays of more than 30 seconds on the their brake air lines – not sure how that can be worked into the story. And I am not sure how you can work the quadrature current into the train analogy when dealing with the excitation of a particular alternator.

• Hi Ken, I generally agree with your observations. Part of the reason I didn’t dwell too much on the voltage side of things was because it doesn’t fit too neatly into the train analogy, and I also wanted to talk about system frequency issues. However, please stay tuned, I do have a voltage analogy in the works which will be published in the next few weeks.

4. Add in the solar and wind in generation please to the train . What sort of Engine /carriage will that be? a ship’s wind sail on the a special carriage ? and solar would be solar cells on top of an electric driven carriage?

Simon

5. In theory Simon. The engine does not care where the power comes from. The power source is determined by politics and economics.