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Lars, your expertise is in operational research and optimisation… What exactly are you optimising?

If you’re doing mathematical optimisation like I do, you typically have something you want to improve. We usually focus on specific questions where we can help people. For example, in a project with the National Energy Systems Operator, we worked on how to better plan maintenance outages. Maintenance on different parts of the network means fewer lines are available than usual, which can put the system at risk. The question becomes: how can we schedule as many maintenance outages as possible? Alternatively, how can we make the whole process as cheap as possible while ensuring system stability? The questions we ask are very focused. An example of optimisation is finding the shortest path on a maps app. When it comes to energy markets, we focus on what we lose when setting up a specific market, and how that compares to an ideal, optimal outcome. Right now, there are two competing proposals for how electricity markets could look: a national market and a zonal market. In our research, we might ask: What happens when you have a national market that clears supply and demand first, then balances the system afterwards? How does that compare to a fully zonal market or a system with no market at all? A zonal market might reduce the costs of balancing, but it could also make investments riskier. People often think problems in electricity markets are either purely technical and talk only to engineers, or purely economic and talk only to economists. But both groups are often limited by what they can compute. That’s where mathematical analysis and optimisation help — they push these ideas into the realm of computer models.

From an outsider’s perspective, understanding the link between the technical transmission part of energy systems and the market part can be difficult, especially when talking about balancing costs. Can you explain how these two aspects relate?

Let’s do a thought experiment. Imagine there’s no transmission network because everything is close together. You set up electricity in your house, but you have flatmates and you need to trade with each other. There’s demand, but only one battery or one solar panel, so you have to bid against each other to decide who gets to use the electricity. In this small system, supply has to equal demand. But that’s when things are physically close. Now, if we scale up to a system the size of Great Britain, transmission becomes a big issue – not necessarily speed, but capacity. You have to physically move electricity from point A to point B. If there isn’t enough capacity to transport it, it doesn’t help if someone in one place can produce energy if you cannot transport it. So, the simple equation “supply equals demand” becomes more complicated – it has to be “supply equals demand on the whole transmission system”.  Another analogy is a water system: you need to pump water through pipes from A to B. If the pipes aren’t there or aren’t big enough, you can’t get the water through. Currently, our market works under the fiction that everything is close by. You have a market that sort of pretends capacities on the network don't exist. For example, you could buy electricity in London from someone in Scotland. On paper, that’s fine – you just make sure the amount bought equals what you use. But physically, the system can’t transport that electricity all the way. So, the operator, NESO, has to pay the Scottish producer not to generate, and instead buy electricity somewhere else, like in the south of England. These payments are called balancing costs, and they create a secondary market. In recent years, these balancing costs have grown enormously.

How can we reduce these costs?

There are multiple answers. One answer is to build a bigger network. If we do so, we have lower capacity restrictions and need to do less balancing. The other answer is making the market more local, so that market players can see what zone they are trading in. If they want to trade across zones, they have to pay for the transport. And that’s where zonal pricing comes in. You get different prices in different zones to reflect the fact that there are regions like Scotland, where there’s lots of energy, making it really cheap. However, the southern price becomes higher – we can’t transport everything, and we need some generators in the south of England, which are more expensive. The argument for zonal pricing is that it incorporates capacity constraints, unlike a single national market. But there are drawbacks. People aren’t sure what will happen if the zones change when a new line is built. If zones change as a result, my investment decision might turn out to be bad, because I invested in one zone, and then I get moved into another. And then maybe I don’t invest at all, because it’s uncertain. That’s the type of stuff that is more difficult to capture.

‘You can’t really have fully decentralised control within a single, central market. But having a central entity managing control while “faking” local markets works quite well.’

If we reform our markets, will there still be a central unit that physically controls what electricity resources are used?

The market layer is more or less an artificial construct compared to the physical network. Even in a zonal market, physical control probably stays centralised. For example, on the east coast of the United States, they use what’s called nodal pricing – they divide the system into many nodes, each with its own price, but control remains central. You can’t really have fully decentralised control within a single, central market. But having a central entity managing control while “faking” local markets works quite well. At NESO’s control room, for instance, there are teams for different regions of Great Britain, one of which focuses on Scotland. But the overall control still happens within the central unit.

Yet, in a report for the Catapult network, you and Professor Chris Dent argue that in the future, control will need to be, to an extent, decentralised. Why did you recommend this? 

Simply because in the future, we will likely rely on many smaller units. This isn’t about the day-ahead timescale that current market reforms focus on, but much shorter periods where algorithms decide which resources should react to changing demand. A lot depends on what our algorithms can do. If we develop better algorithms that can manage all these units centrally, more countries will be able to keep control centralised. But if the math shows it’s better to solve the coordination problem between numerous lower-level control centres on these short timescales, then the system might be run in a more decentralised way. In the report, we mainly wanted to point out that a single centralised system isn’t necessarily what will work in the future. At the moment, it seems like the decentralised option might be better. This is partly what motivates my research – determining where the lines are that define which methods work best for which systems.

As the energy system changes, we need to deal with the problem of “inertia”. Can you explain what this is and what the solutions to this problem might be? How does this link to the market discussions?

This is something market designers have mostly ignored over the last 30 or 40 years. In the mathematical models that underpin markets, inertia simply doesn’t exist. It’s treated as an extra system feature – a separate market. The core market model doesn’t care what type of generator you are; it only says: you provide this amount of energy at this price, and that’s all it wants to know. An analogy I like is riding an electric bike – if the motor suddenly cuts out, you coast for a bit before you need to start pedalling again. Without inertia, you’d just stop immediately and fall. If that happened, your reaction time to fix a problem would be much shorter. A nuclear or hydro plant is physically connected to the grid frequency through its rotating turbines. If the frequency changes, the turbines keep spinning, providing inertia. Most renewables don’t have this rotating mass at a fixed speed. A wind turbine spins, but not at a fixed speed; a solar panel doesn’t spin at all. Instead, these generators use electronic components to adjust electricity output based on the grid frequency. This makes them very reactive and unable to provide the same extent of inertia. Solutions are technological: we might manage to simulate inertia electronically and improve how renewables respond to frequency changes, or add devices like flywheels to the system to provide mechanical inertia. If you have enough hydro and nuclear power, you have all the inertia you need.

Lars, you mentioned that part of your motivation is drawing the lines that determine which solutions work best in which systems. How did you come to specialise in energy optimisation?

How did I come to this? In my PhD, I did pure maths – focused on geometry, and related to optimisation. But I was always interested in specific examples. I liked looking at concrete mathematical objects and trying to determine whether they exist or not. I wasn’t so interested in whether, at the mathematical limit, something just might exist. I realised that, in geometry, not many people shared this interest in specific, concrete problems. But people in applied optimisation did. Their approach was more like: we have this specific problem, do whatever you want to solve it. At the time, I did a lot of work on gas networks and gas markets, and that’s where I came into these energy questions, where I now have quite a bit of dedicated application knowledge.  My work on COVID-19, which you have seen, was different – I had no background in epidemiological models, and my colleagues had to explain them to me, although I was mainly working on optimisation problems that sit on top of the models. But in that case, I didn’t have the same depth of knowledge as I do in energy systems. In energy markets, a big issue is that our models often don’t capture the underlying physics, or even the actual market rules. We often assume markets are convex and that we understand them completely. In a convex model, the gap between the real market and the idealised one is zero. That assumption usually works well. But as soon as you introduce rules that make the market non-convex, you get different results. Gaps appear between the model and reality. So, what we often try to do is take a non-convex problem and approximate it with a convex one, as closely as possible, because convex problems are much easier to work with and better understood. If you can show that the convex version of your problem is close enough to the non-convex version, then you're good to go, and you don't have to worry. So that's why convexity comes up, and that's the more methodological research that we are doing.

‘People who are sceptical about zonal pricing – especially in Scotland – don’t really argue with the claim that it would reduce balancing costs. Their concern is that the uncertainty around how the rules are set up will make it harder to invest. That, for me, is fascinating.’

Having published on the topic of non-convexity in electricity markets, can you explain why these markets are not convex? Is it because energy flows are directional, and because the production of electricity doesn’t increase linearly but in discrete increments from each resource?

Yeah, sort of. Let’s bring it back to the example of maintenance. In the maintenance problem, you need to decide whether you do maintenance or not. That’s a very discrete decision, but you also need to take into account what accidents or other faults could happen in the system, and incorporate that into your planning. You get into this discrete, non-convex situation. Or take another example: imagine a water system where water flows from high to low. Once it’s low, it can’t go back up again. In an electricity system, you have potentials, which work similarly. In the model, you often assume a linear relationship between the difference in potential and the resulting flow. But typically, that relationship is non-linear. That’s where you get into non-convexity, and that’s where market questions start to appear.

Along with ClimateXChange, the Royal Society of Edinburgh and your colleagues from the Electricity Markets Research Hub, you co-organised the first Scottish Forum on Future Electricity Markets. What topics at the Forum were you particularly interested in as a mathematician, and how do they link to Scotland’s position within the reforming UK market?

The standard models show that zonal pricing would reduce balancing costs. So, we can ask optimisation questions, like how exactly we should draw the zonal boundaries, or how to get the highest welfare impact with just a few zones. But what I found particularly interesting, for my thinking and my research, was the question of investment risk. People who are sceptical about zonal pricing – especially in Scotland – don’t really argue with the claim that it would reduce balancing costs. Their concern is that the uncertainty around how the rules are set up will make it harder to invest. That, for me, is fascinating. Is it the model that makes investors sceptical of zonal pricing? Or is it more of a gut feeling stemming from a recognition that the models themselves can’t handle this uncertainty?  The question for me is what models they should be using, how we can evaluate them and how policymakers can assess and quantify the risk that people won’t invest because of these unknowns.  You could frame the main outcome of the Forum like this: some people have relatively simple mathematical models that say zonal pricing is great; others say, “Well, there are unknowns,” and that makes us cautious. You have to acknowledge that those unknowns exist – and then make a decision anyway. The evidence-based view becomes blurred. It turns into: do I trust the gut feeling, or do I trust these nice but clearly simplified studies? I find this fascinating, but I don’t yet have an answer for how to properly integrate that kind of uncertainty into our models to give policymakers better support.

Do you personally think that, even in a zonal market, it will be possible to create the right arrangements and securities so that people feel confident enough to invest?

Well, there are systems, like the US nodal pricing model, that operate with much more uncertainty, and people still invest. So I think it’s doable. But at the same time, I’m not sure whether they would invest more or less if the market were centralised, and by how much.

If we flip the argument against zonal pricing, could it actually lead, in the long run, to more investment in places where electricity is less abundant, simply because of regional price differences?

Yeah, that’s the idea, or the hope, behind a zonal system. In the short term, it reduces balancing costs. In the long term, the hope is that it incentivises investment, not just in supply, but also in demand. And that’s where the Scottish situation becomes really interesting. The question is: do you see Scotland’s role mainly as producing energy more cheaply than anywhere else in the UK and making sure it gets transported there? Or do you think the future for Scotland is to generate cheap energy and use it right here?

And what do you think?

I don’t know. Many vocal people at the moment are those impacted on the industrial side, not the consumer side – for them, it makes sense to want to produce electricity cheaply and sell it somewhere else for a profitable price. We haven’t heard from that many people who are thinking about what Scotland could do with its cheap electricity.

Interviewer: Jan Žižka