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• Geoff Russell

# Modelling grids and telling fibs

Updated: Jun 4, 2022

Claims that we can move to 100 percent renewable electricity are based on mathematical models; as is climate science. But you can test climate models. For example, you can run them backwards and see if they can produce past climates; they can. But what about models of electricity grids? How do you test those? What exactly is a grid model? Do you need to be a geek to understand them? Happily, you can get an intuitive understanding just by thinking about everyday problems. Please read on!

A modest understanding of models will enable you to understand the otherwise puzzling content in the most recent IPCC assessment report (AR6 Working Group III) (p.6-4):

Economic, regulatory, social, and operational challenges increase with higher shares of renewable electricity and energy. The ability to overcome these challenges in practice is not fully understood. {high confidence}

The bit in brackets, the tag "{high confidence}", tells you how much faith the IPCC authors have in the preceding claim. I added the emphasis (bold font).

Let's unpack the quoted paragraph.

The first sentence is a concise way of saying that going from 20 percent renewable electricity to 40 percent is easier than going from 40 to 60 percent, and going from 60 to 80 percent is harder again. And the last 20 percent? Nobody has ever done it. In April 2020 the organisation in charge of Australia's grid(s) (Australia's Energy Market Operator -- AEMO) published a "Renewable Integration Study: Stage 1". The "Stage 1" subtitle is revealing.

During the month ending 24th May 2022, the Australian National Electricity Market got 30.4% from renewables; with the South Australian connected grid getting about double that; so we haven't got to the pointy end of the problem yet.

The second sentence, the bold one, in the IPCC paragraph says politely that we don't know how to build a fully renewable electricity powered grid.

What? Fully two decades after Germany began its Energiewende (energy transformation), the IPCC authors still reckon there are unsolved problems. And they are not alone. The International Energy Agency's Net Zero by 2050 plan bets big on wind and solar, but also recommends a doubling of current global nuclear capacity with a cessation of premature closures. It also understands that totally renewable grids are both uncertain and will increase electricity costs compared to a doubling of nuclear capacity.

This post will explain the "challenges", which are what glass-half-full people call the things that glass-half-empty people call "problems". It will explain what models are by reference to a very common problem; packing stuff into a van. We are all really good as such problems; even if some of us are less good than others!

###### Models in plain English

Models are just simplified mathematical descriptions of the world. But I want to explain how models work without maths, so here's a first example.

Think of a mini-van with a 3 cubic metre carrying capacity. The simplest model of the van uses the capacity and ignores any other attribute;

Model 1. The van has a carrying capacity of 3 cubic metres.

This model ignores the shape of the van; one of the most important features!

With our simple model we can assert that our van can carry any collection of items with an aggregate volume less than 3 cubic metres. This assertion will be reasonable if our items are books or small rectangular boxes. But it will fail if we are talking about floorboards or furniture.

When a model fails, we typically enhance it with more salient details.

Model 2.

Originally our model was a single sentence.

1. Our van can carry 3 cubic metres of stuff.

1. Our van can carry 3 cubic metres of stuff,

2. But nothing longer than 2.1 metres,

3. And nothing higher than 0.8 metres

4. And nothing wider than 1.8 metres

Our original model is a bit like those models of our global energy system that claim we can power our civilisation with sunshine by noting that the amount of energy we generate with all our fossil fuels is less than the amount of energy in the sunshine hitting the planet's surface each day.

Real models can get very complicated. A bus driver scheduling model might have tens of thousands of variables and a thousand constraints. Variables are things we can change. If we are packing books in the van, than the number of books is a variable and when we use the model to solve problems an answer will be the number of each type of book we can pack. The first model had one constraint; dealing with capacity. Our enhanced model added three constraints on width, height and length. Once we added those, do we really still need the capacity constraint? Yes; because some irregular shapes could have those maximum lengths but with a much smaller capacity.

Our enhanced model still sucks, but it's better than the first one!

A good model would be able to predict whether or not some collection of objects would fit in our van.

But our sucky model doesn't understand how things fit together, or not. It also doesn't say anything about weights. Three cubic metres of steel is going to weigh 24 tonnes and bust any normal van.

Models are used to predict or plan things. If you can predict then you can usually plan. Our van model might suck for some things, but it can probably be used to predict the number of vans we need if we were a publisher producing a specified number of different sized books we need to ship each day. In the real world, the model would have more constraints, but adding these would tend to obscure the forest with trees we don't need.

Does a model have to represent reality accurately to be useful? Definitely not. The only thing that matters is that a model gives good enough predictions for the job at hand. For example, in many physics models, the size of the moon doesn't matter, so these models typically pretend it's a "point source"; meaning something with mass but no size. Models don't have to be accurate to be good!

###### Models of our electricity grid

Electrical grids can be modelled in many ways; depending on what you want to predict or plan. We'll discuss three levels of model which I'll call simple, operational and physical. Keep in mind that I'm trying to make really complicated things a little comprehensible in useful ways. I'm not trying to describe any real-world models!

At the simple level, which might be used for planning, a model would look at the maximum electricity demand during the last decade. You could use that to get a rough estimate of the number of PV panels, wind turbines and gas generators required. You can calculate stuff like this in your head for simple fact-checking. For example, the South Australian electricity grid had a maximum power demand of 3,147 megawatts at 7.30 pm on the 19th of December 2019 (during a 4-day heatwave). That's late in the evening; just one hour before sunset. Any planner would be thinking that South Australia would need backup power of at least 3,147 megawatts and that it might be needed for at least 4-6 hours because that historical maximum demand could well occur again and occur during periods of little or no wind and little or no PV output.

An enhanced, but still simple, model would look at the profile of electricity demand, hour by hour, over a decade or two and more precisely try to think about the required backup capacity. If you have the data, you can test your model by postulating an amount of any technology mix you like and just check that it will meet the demand on every hour of your data. With this more complex model, you might guess that you don't actually need 3,147 megawatts of backup power, because the output of wind farms is never zero. So you might guess that you only need 2,747 watts because you can always count on at least 400 watts of wind power.

Once we've explained another couple of model levels we'll be able to explain the challenges noted in the quote from the IPCC report.

###### Operational models

The next level of model is far more complex and I've called it "operational". This is the kind of model that is used on Australia's electricity grid many times each day. Here's how the process works. The electricity operator (AEMO) predicts the power required in 5 minutes time. All the attached generators then bid to supply as much power (electricity) as they have available. If they are down for maintenance, then they don't bid. Once the bids are in, a complex mathematical model with a bunch of equations works to select the cheapest set of bids to match what is required. Really. That's what happens ... and it happens all day ever day and every 5 minutes; this is because the amount of electricity generated has to match very closely the amount required. If a million Australians arrive home at 5.30 and turn their kettles on, then another power station has to be added to meet the increased demand. It is of course, highly automated; meaning computers are doing the bidding ... and deciding the auction outcome.

The "what is required" referred to above isn't just about having enough electricity. That's the easy bit.

Additional characteristics of the model relate to the quality of the electricity. This is just a shorthand for the ability of the mix of chosen generators to cope with problems; like losing transmission lines or whole power plants or unanticipated demand surges or (these days) clouds blocking the sunshine temporarily.

These operational features are far too complex to be accurately modelled by 5-minute models, so rules of thumb and experience are part of the mix. Suppose you want 3000 megawatts of power and your algorithm chooses 3 x 1000 megawatt coal plants to do the job. How will that choice cope if you lose one of the three (via some catastrophic failure ... it happens)? I won't flesh out the detail, but when that one plant fails, the huge loss of available electricity would crash the entire grid. If instead, you chose 6 x 500-megawatt plants, then losing one would be a problem, but the grid would probably cope; because the second or so that it took for the frequency to drop would be long enough to blackout a few suburbs briefly and bring backup power onto the grid; assuming you have such power. Having standby power is just part of the job. My examples here are trivial compared to the actual calculations required by models to choose generators for a 5-minute block. But they give the flavour of the process.

Many businesses run models like this to schedule activities. I used to work in transport scheduling and our models were far more complex. But we didn't run them every 5 minutes, because they took hours or days to run! A model that can run in 5 minutes might look really complex to a person, but not to a computer. It probably (only!) has hundreds of constraints. Airline scheduling models, for example, may have many thousands of constraints. The statements in the model, corresponding to the van statements above, are equations and they themselves are generated by software during the heavily automated bidding process.

###### Physical models

The last level of model is the most complex; physical. Meaning that the model really aims to accurately represent reality; or at least the physics and chemistry of that reality. If a fire destroys an electrical transmission line, then a couple of things happen. First, the electricity delivered by that line stops. You can model that at the previous level, operational. But the more important thing is the way the voltage and current change. Have you ever seen a jug short circuit and seen the flame and smoke as it fails? A surge of electricity will (these days) trip a circuit breaker and save you from a life-threatening shock. A physical model would predict the height of the surge in current, whereas an operational model would just predict the current vanishing as the circuit breaker did its job.

A fire taking out a transmission line requires rather more circuit protection than your jug. To build that protection you need a physical model which will predict very precisely what will happen. The job of the model is to calculate the "fault current" ... the surge that follows the event. Managing problems and potential problems is a far bigger job than merely scheduling generators.

Think about it this way. Suppose you drop a bowling ball vertically down onto a trampoline. It will bounce up and down for a while and gradually stop. A physical model will predict how long that process will take and probably predict the height of each successive bounce. An operational model will probably just tell you that the bouncing will stop within 10 seconds.

Physical models of grids are used to model changes in the structure and the way those changes will affect the capacity of the grid to handle failures.

###### Using the right level of model for your claims

Over the past decade or two, there have been frequent claims about how easy, feasible or cheap it would be to replace current electricity grids, composed of big thermal power plants, with generators based on wind, sunshine and either batteries and/or water (hydroelectricity). Probably the most famous of these claims come from a multi-author team led by Mark Jacobson at Stanford in the US entitled: "Low-cost solution to the grid reliability problem with 100% penetration of intermittent wind, water, and solar for all purposes". Similar studies and claims have been made in the Australian context, for example, here's one from 2013 by University of NSW researchers.

All these studies use models which fall into the simple category.

They might look complex to a layperson, but they are utterly trivial to a power engineer familiar with physical and operational models.

For example, all these studies make a "copper plate" assumption. What's that? It assumes that you can always get electricity from where it is generated to where you need it. That's the equivalent of pretending that all the hard parts of grid construction and management don't exist. It's as if your entire grid sits on a copper plate that allows unconstrained flows of electricity as required. There's nothing wrong with such assumptions if you moderate your claims based on them appropriately. Does Jacobson's title make humble and moderate claims based on his simple model?

One team in the UK tested the Jacobson model in the UK context by including a little more of what would go into a real operational model. Their appropriately titled "Real-World Challenges with a Rapid Transition to 100% Renewable Power Systems" fell a long way short of being a full operational model let alone a physical one, but it still found fatal problems:

Up to 9% of annual demand could remain unmet, causing frequent black-outs during times of low wind and solar availability despite a high level of interconnection to neighboring networks ...

By now you may be starting to understand the caution in the IPCC quote we started with.

###### Challenges

The AEMO Renewable Integration Study, mentioned above, discusses, among other things, the increasing complexity of running physical modelling for analysing the capacity of the grid to handle failures. Already, with small amounts of renewable generation, there are challenges (aka problems). It describes one:

For example, running a single contingency in an EMT [this is a physical model] study takes thousands of times longer than a single contingency in an RMS [a much simplified physical model] dynamic study, with 50 times the computing resources.

What does this mean? "Running a single contingency" means testing a single possible event that might challenge the stability of the grid. Note ... "thousands of times longer". Put simply, even with current low levels of intermittent renewables, AEMO can't test the grid's response to too many types of problems; they have to guess the most likely scenarios and test for them. In short, they are flying blind.

This kind of challenge is happening elsewhere.

During August 2020, California, noted for its aggressive wind and solar deployment, suffered a bunch of blackouts; big ones. There were about 50,000 blackouts in California during 2018 and 2019, but the big ones in 2020 were deadly serious. The January 2021 report on the causes stated:

2. In transitioning to a reliable, clean, and affordable resource mix, resource planning targets have not kept pace to ensure sufficient resources that can be relied upon to meet demand in the early evening hours. This made balancing demand and supply more challenging during the extreme heat wave.

So it's not only Australia that is having problems, despite Jacobson's low cost "solutions" to the grid reliability problems.

The AEMO Renewable Integration Study doesn't only highlight problems running physical models, it also describes how their operational models are floundering. I'll follow this quote with some plainer English, but here's what they say:

Without constraints to stipulate these limits, the [5-minute planning] process cannot automatically keep the system above these minimum levels. Instead, AEMO’s control room must monitor these limits and intervene in the dispatch process to avoid the limits being breached.

What does the first sentence mean? We know from our simple van model what a constraint is. In the van model, defining constraints to deal with combinations of odd-shaped products is really hard. So we probably don't even try; we just get a person with a brain. People are pretty good with packing problems; well some people are! What AEMO is saying here is that they don't know how to modify their operational models to handle some of the problems that variable renewables are throwing up. So they are intervening manually to solve problems. Using people with brains; power engineers.

###### Old grids, new grids

Our current electricity grids are designed for large thermal power plants. They are like buses or trains in a transport system. The distribution system of poles and wires delivers electricity in one direction; from the source to the consumer. It was trivial for the French to bolt nuclear power plants into such a system. Nuclear plants are also thermal (heat-based) power plants. The nuclear part just provides heat, the turbines and generators use the same physics as those of coal or gas plants. You don't have to think about vastly expanded transmission grids, batteries, synthetic inertia, smart grids, virtual power plants, rebuilding and redesigning the distribution system, physical modelling difficulties and all of the other things people hope will patch the holes in the system.

Globally we have started rolling out wind and solar plants with absolutely no idea of the end game; how to finish the job. The engineers are just following orders and doing their best to make it up as they go and keep the lights on, but it's becoming increasingly hard. In the Australian grid, intervention to manually adjust for problems used to happen a handful of times annually. The count of manual interventions had risen to 229 by 2019/20 as reported in the RIS; and it's rising.

The most crucial part of managing change in a large system is to have a method of testing what you are about to do. Intermittent renewables are making this extremely hard and in ways that few non-technical people will be familiar with. Let me give an example. Consider your car's SATNAV. It finds the shortest path between two points on a map. The algorithm for this is typically taught in Computing 101 or included as homework in a tertiary maths course. The interesting thing about it is that it doesn't matter much if your map is big or small, the problem is still manageable with very little computing power.

Now think about finding the shortest path to visit 50 locations. This sounds misleadingly like more of the same, except that it isn't. It's called the Travelling Salesman Problem and has exercised mathematicians and supercomputers for decades. As the number of locations rises, the computing power required increases exponentially. Sometimes problems which sound the same as simple problems turn out to be really hard.

Building physical models of grids is like that. As more and more small, but significant, generators are added to a grid, the complexity rises; exactly as AEMO states in the RIS.

The AEMO 2022 Integrated System Plan (Draft) predicts a need for 10,000 km of additional transmission lines as a result of wind and solar requirements. The amount of power capacity of their heavily renewable plan will be about 6 times higher than a traditional plan where coal and gas were simply swapped out for nuclear plants and the grid functioned in the traditional way. But they still envisage 9 gigawatts of gas turbines to hold the system up during "long dark and still weather periods". They also have a list of "risks". Some are called "technical", meaning they are relying on technology that is predicted rather than exists; there are also supply chain risks; and transmission build risks.

###### Summary

I hope I've shone a little light on the cautious statement in the IPCC report with which we began. If you read all of the report you'll detect a range of views; given the big list of authors, this isn't surprising. Some engineers love leaping into the unknown, going on grand quests. Others shudder, perhaps because they've lived through one or more such revolutions, or perhaps they are just conservative in nature.

Claims that moving to renewables is trivial and simple are common among people who don't know anything about grids or computational complexity or electromagnetic transients. They aren't too common among real experts.

###### Appendix: Solar PV and wind turbine growth rates have been trending down for the past decade

Global growth rates of solar panels have been declining since 2011 (see graph) and will be further challenged by China's covid lockdowns and the US Administration's trade restrictions on polysilicon as a result of China's treatment of Uyghur and other Muslim groups.

###### Appendix: Public Transport and rooftop solar

There's an interesting transport analogy to what is currently happening in our electricity system.

We could have a transport system based mostly on walking/cycling and mass transit, but we don't. That's not quite true; many cities are dominated by precisely these kinds of systems. The French gilet jaunes protests of 2021 reminded people who lived in Paris with its nuclear-powered underground that rural people didn't have that luxury. Places like Australia and the US are dominated by large houses and the associated urban sprawl and automobiles.

Rooftop PV panels are to electricity what motor cars are to transport.

As rooftop systems grow in size and increase in penetration, they require a total redesign of the distribution infrastructure; the poles and wires. This is analogous to cars. As car density rises, the same thing happened (and continues to happen) with roads. Roads needed to be wider and more robust; with traffic lights and traffic managers. An electricity grid where many people have 6-10 kilowatts of solar panels on their roofs needs not just a redesign, but a rebuild. The AEMO Renewable Integration Study makes that clear with the growing number of thermal overload issues at different levels of the distribution system. "Thermal overload" is geek-speak for things getting too hot. When you have more electricity flowing in a wire than it was designed for, then you need a thicker wire! Think Crocodile Dundee ... that's not a wire ... etc. And as solar panel size and density increases further, people want batteries. These make them self-sufficient in electricity in the same way private cars do with transport. The impact of this transformation on the mining sector is already being felt ... as a global boom. The ABC 4-Corners program Digging In presented some of the impacts. It would be fine if we could open the new battery mines on the disused sites of fossil fuel mines, but you have to open the mines where you have the material required; so the vast expansion in mining will be over and above existing mine sites. The boom is already happening and it is global with many countries, including Australia, getting ready to expand mining onto the ocean floor.

###### Appendix: Inverters

Most people get frustrated by the constant churn of plugs on phones. Wouldn't it be nice if all phones used the same charging plugs? How hard can that be?

Solar panels and wind farms connect to the grid via "Inverters". These are rather more complex than a phone plug but serve to match the electrical requirements of one side of the connection with the other. Think about your computer again. What does it do when the power spikes? You know, those times when your house lights vary in brightness, fade in and out, during a storm. Your computer just stops. Of course it does. It needs to protect itself from damage. What do your solar panels do if they detect a strange variation in the power grid? They cut out ... or do they? Think about it. When you have a grid with a little power coming from a few panels, then if those panels cut out, everything is fine. But as the percentage of panels rises, the simple strategy of cutting out in response to a problem becomes a recipe for bringing down the entire grid. Think about it. A tree hits a power line, there is a voltage surge, some panels close by disconnect, causing a further change in voltage which is detected by other panels which also cut out. It can ripple right through the system. Inverters have to be much much smarter to handle problems without causing them.

In December 2020, Australia published a new technical standard for Inverters; this is for manufacturers telling them the specifications they need to comply with to make the electronics which connect renewables to the grid. The RIS also reports that an estimated 40% of current inverters don't meet the last set of specifications (2015). Twenty years in and we are still fixing design specifications which could crash the entire grid.