Last time we completed our description of the end-to-end modelling process. But we noted that there remained many different tricks and tips that were hidden from the layperson.
With that in mind, we promised that in our final instalment in the series we would examine the assumptions and methods that fall into the category of ‘the Dark Arts’ of modelling.
At the outset, we make clear that our intention is to shed light on these often overlooked parts of the modelling process. We want the reader to understand what models can and cannot do, and the ways, means, and devices that together are sometimes used that can make it hard to derive value from modelling exercises. We want to arm you with the basics of ‘Defence against the Dark Arts’.
In the remainder of this article, we explain our thoughts on the top four ‘Dark Arts’ of the modelling process, specifically:
We conclude by setting out how we think about the role of modelling, and the philosophy that underpins our own work in this area.
For capacity expansion, it is necessary to simplify the number of periods (sometimes called time slices or load blocks) over which we model the system. For example, a single day might be represented by 3 time slices: one for each eight-hour period of the day. In turn, this day might represent 30 days, which have similar characteristics. In so doing, 30 * 24 =720 hours could be represented by a mere 3 time slices.
The benefit is that the problem is easier, and so faster, to solve. But the approach of using very few time slices has been limited by the advent of:
It is now the case that unless we use a very large number of time slices, the system that results from the capacity expansion problem is not resilient. The solution is to use more time slices – this is not really an option, unless we are looking at a very simple power system.
Despite this reality, some modellers often want to speed up the process, or do not have access to commercial solvers, and so they resort to use of a crude set of time slices. The outcome can often be a brittle or, on the other hand, massively overbuilt system. When working with a consultant using capacity expansion modelling, it is worth being aware about the assumptions they have made as to time slices – a Dark Art if ever there was one.
One of the powerful aspects of using an optimisation framework for solving models is the ability to impose constraints. It is trivial to add constraints to the model that do the following:
In practice, these constraints are just like any other constraint, such as the supply-demand constraint, or a limit on the amount of generation that can connect in a region. These constraints have the potential to change the outcomes that would have otherwise occurred in their absence.
When these constraints are imposed, the model will do whatever it takes (such as over-building renewable or artificially suppressing thermal generation out-of-the-merit-order) to meet these targets. This will occur regardless of whether the new investment will recover its costs from the energy prices in a potentially over-supplied market. This is not a fault of the least cost expansion model per se – imposing these constraints is to assume they will be met regardless of the cost, and the model is faithfully satisfying the request of the modeller by identifying the cheapest way to meet these requirements.
However, a modeller should know to look for these ‘hidden costs’. Just like the supply-demand constraint, every constraint in the model gives rise to a ‘shadow price’. As explained in our first article, this is the marginal value of alleviating this constraint by one unit on the total system cost. In the case of a renewable target or carbon budget, there is a clear meaning to their associated shadow prices:
Of incredible importance is that, when we invoke these constraints, the prices that fall out of the capacity expansion model assume that there is also a carbon emissions price, and a renewable energy certificate price. And so if we look only at the price that falls out of the model and assume this will be the cost of electricity, we will fail to account for the effect of the assumed carbon and renewable energy certificate prices, or the ‘missing money’ that must be funded outside the wholesale electricity market. These ‘hidden’ prices are often overlooked or forgotten about, but they are critical to understanding how generation recovers its costs. Moreover:
It is critical to be aware of this – otherwise we are not going to factor in the whole cost of policies, and so we may not understand what is required to achieve them.
One of the perennial questions in the sector is whether a least-cost capacity expansion model is the correct way to determine new entry. The alternative, which is used by many advisors, is called ‘market-based new entry’.
The recent surge of market-based new entry
Recent years have seen a surge of market-based new entry in market modelling. We often hear the motivation of using this approach is that new entrant generation built by least-cost capacity expansion models does not seem to earn enough pool revenue to recover its costs. Market-based new entry appears to fix this problem by allowing the modeller to alter the investment path manually until the all new entrants recover their costs.
We will address the economic fallacy of market-based new entry shortly. However, it is first worth noting that in a market where renewables are built to meet ambitious government renewable constraints or carbon budgets, new entrants will not recover their cost from pool prices alone. This is because of the “missing money” phenomenon discussed in the last section. The least cost expansion model merely exposes this fact, which is either misunderstood or ignored by proponents of market based new entry when communicating their results.
The quasi-economic argument against least-cost capacity expansion
One argument against least-cost new entry is that the decision to build is based on cost rather than price which is what we see in the market. The argument is quasi-economics at its best. It fails to recognise that price is inherently linked to long run marginal cost, and so solving for cost gives us the outcome we seek.
The proponents of market-based new entry fail to recognise that the capacity expansion model solves for cost but also produces prices. These prices are equal to the long-run marginal cost of generation. Taken to its logical conclusion, a market-based new entry proponent would suggest that dispatch also needs to be ‘based on price’. This would involve iterating between different combinations of plant to be dispatched in a given interval until eventually we stumbled upon the same outcome that is yielded by the dispatch engine. Why would we do such a thing, when we can get the answer directly by solving as a linear program?
Market based new entry as a low-quality capacity expansion model
In the absence of constraints, the prices yielded by the least-cost capacity expansion are exactly the level needed so that every technology recovers its costs. In effect this is equivalent to a world where investors build new plant right up until the point where any additional plant would be uneconomic. This is also the common goal shared with market-based new entry.
Put another way, we see the following outcomes:
The key phrase here is ‘at its best’. In reality, the market-based new entry process is trying to solve a very complicated problem with very primitive mathematical machinery. We know that some consultants complete this process manually, with choices being made by an analyst on-the-fly. This is essentially ‘dealer’s choice’ – ie, the outcomes depend on the gut-instinct of the modeller.
Even when an algorithm, or heuristics, are codified in a program, there is no guarantee that the process will converge to an outcome that satisfies both (a) and (b) above. The chances of stumbling on the exact combination of build over the next 25 years that yields prices that walk the tightrope between (a) and (b) above is vanishingly small. This means that there will always be either plants that are not built that should have been, or plants that are built that should not have been.
The computational argument against least-cost capacity expansion
A decade ago, least-cost capacity expansion models took a very long time to solve, and so required very crude chronologies. These models therefore were internally consistent but gave a poor representation of the planning needs of the system. It was not uncommon for these models to lack resilience. Against this backdrop, market-based new entry was an alternative but sometimes necessary evil to provide a meaningful view of the future needs of the power system.
However, in the last decade the speed of solvers has improved dramatically. Gurobi can now solve a least-cost capacity expansion problem with thousands of time slices per year over a 25-year horizon in a matter of hours. It is no longer necessary to stumble around with iteration and primitive heuristics to find a profile of the needs of the system. What was once a helpful tool to plan out the system is now no longer necessary, and there is no basis for it.
Market-based new entry is now a Dark Art
As the system becomes increasingly complex, market-based new entry becomes less and less helpful for planning, resilience testing, and projections of the future needs of the system. For example, when we have been asked to reconcile market-based new entry models against the results of least-cost capacity expansion, we find that there are either large amounts of unserved energy, or many plants that are built that do not recover their costs.
More importantly, the ‘dealer’s choice’ phenomenon means that we cannot easily replicate or reproduce the analysis of other consultants who have used market-based new entry. Outcomes based on choices made in the early hours of the morning by a bleary-eyed analyst as to what plant should get built where, are not consistent with robust modelling practices.
The continued use of these models without recognition of their limitations is surely one of the most prevalent Dark Arts of the sector.
By now it has become clear that there are elements of the market and the power system that are fundamentally challenging to capture. And so not everything can be included in the capacity expansion and operational dispatch models. Many consultants (ourselves included) provide services that alter the outputs of the model in a post-processing step. For example, it is not unusual to add interval-to-interval volatility or ‘noise’ to prices to reflect the patterns we see in the market.
We do not see anything wrong with this, provided it is clear as to what is the effect of this post-processing. Advisors should decompose their results so that the contribution of these post-processing steps can be captured – sometimes they are highly material to their findings.
In addition, some post-processing seeks to account for high-impact system events (such as the Callide C explosion) that cannot be meaningfully included in a small number of deterministic model runs. This is not to say that models cannot simulate this type of price impact if we know exactly when and how they happen in the future. In fact, the revenue impact on other assets, which is what most commercial clients are interested in, can even be easily obtained via back-of-the-envelope calculations. The real challenge is to project the frequency with which such events will happen and how the system unfolds immediately following it, which is often highly event-specific and beyond the realm of market simulation models. Including events of this type in a projection of the future and pretending that there is a sophisticated methodology for ‘modelling’ them goes beyond the Dark Arts and verges on the Unforgivable Curses. Market models are not designed to simulate such events – be wary of anyone telling you they can do so.
We have listed here some of the Dark Arts, but in truth there are too many to list. Modellers can always use sleights of hand, and tricks to deceive their audience – the Dark Arts. In my opinion, the problem here stems from our understanding of the purpose of modelling. From my perspective, the purpose of a model is to create a mental latticework on which we can build intuition. When constructed properly, that latticework will remain rigid and so will not simply yield to your gut instincts – it will require that you adhere to its assumptions and logic, and so build your own understanding of the problem. We can change the latticework (through changing assumptions) but that gives rise to a new set of constraints on our logic.
In contrast, when we force models to yield to our own intuition, and to give us the answers that we want, those models lose all meaning. This is why modelling is particularly unhelpful in adversarial processes, where the objective is to show that one model is ‘wrong’ and one is ‘right’. Models were never meant to be ‘wrong’ or ‘right’ – they were meant to inform our thinking.
Sometimes models give us helpful insights, and sometimes they do not. But once problems become sufficiently complex, without them we are left without any sound basis for decision making. The energy industry poses many such problems, where the stakes are high, and the risks are many. We are foolish to leave decision-making to gut instinct alone and not use models, but the more we can learn about those models and understand them, the better our decisions will be. A more informed world is the outcome. Our purpose in discussing this topic is to arm you with the basics of ‘Defence against the dark arts’. This is the information you need to understand both what models cannot do, but more importantly the many powerful questions that can indeed be answered by modelling if we are able to stretch our understanding.
We often hear people talk about volatility in the NEM: ‘the market has been volatile lately’, ‘we’re expecting some volatility this afternoon’, and so on. Moreover, there is a direct connection that is often drawn between volatility and the business case for batteries. But there is no unified view as to what we mean by volatility, and how we can measure it.
In this article, we examine the historical outcomes for three different definitions and attendant measures of volatility. We then seek to answer the question: is the NEM becoming more volatile, and what does this mean for batteries?
Our first measure is an old favourite – the contribution of prices above $300 per MWh to average prices. Chart 1 shows this analysis for all mainland regions of the NEM on a calendar year basis for 2000 to 2024. We note the following:
Chart 1 – Scarcity prices have been rising in importance over the last 5 years
Average prices in bands by region on a calendar year basis, 2010 to 2024
In general, the last 5 years has seen far more value in scarcity pricing across the NEM than at virtually any other period in its history, with the possible exception of 2008 and 2009 in South Australia.
But high prices alone are not the only measure of volatility. People often refer to variability in prices as being a measure of volatility. For example, frequent periods of low prices followed by high prices are often perceived as being volatile periods, particularly because they give rise to the opportunity for energy arbitrage.
How do we measure this type of volatility and how it is changing over time? One way is to examine how a hypothetical price-taking battery would have performed over a given period. Chart 2 shows the calculated trading profit for a 1 MW, 2-hour battery operating with perfect foresight over the period from 2010 to 2024. The height of the bar shows how much a battery could have earned in revenue less the cost of charging.
Maximum energy arbitrage profit available for batteries has been rising steadily, and has seen record levels in NSW and Victoria in 2024. Similarly, the levels seen in Queensland and South Australia have been relatively high.
Chart 2 – Annual operational profit has been rising over the last 10 years
Annual operational profit for 1MW, 2-hour battery, 2010 to 2024
We have described two concepts of volatility, both of which are inherently linked to the concept of battery profit. But there is another more mathematical view of volatility – the concept of variation. Variation is defined as the cumulative interval-to-interval change in a time series. So if we consider the series (10, 20, 5, 40), the cumulative variation is given by:
abs(20-10) + abs(5-20) + abs(40-5) = 10 + 15 + 35 = 60.
We can then take an average of this, which yields 20 per step (ie, 60/3 steps). In the case of the NEM, we can look at the average variation in spot prices for a region, to get an indication of how much prices are rising and falling from one 5-minute interval to the next.
Chart 3 shows the average variation for each mainland region and for each calendar year from 2000 to 2024. To filter out the effect of scarcity pricing, we have capped prices at $500 per MWh, though we note that this does not affect the trend in the results.
Average variation has increased markedly over the last decade. Where previously prices were very stable, there are now regular rises and falls over the course of the day. On average, prices are changing by $15 per MWh every 5-minutes across all regions. Put simply, there is more noise in prices than ever before.
Chart 3 – Variation has been rising steadily over the last 10 years
Average absolute price variation by region on a calendar year basis, 2000 to 2024
This an astonishing result, which confirms what many NEM-watchers, who live and breathe the market have noticed for the last few years, ie, that prices are ‘going up and down’ more and more.
What are the consequences of this rise in variation of prices for batteries? All else being equal, adding noise to a price series increases the opportunity for arbitrage. That said, capturing the low and high points of a noisy price series is harder than capturing the low and high points of a more predictable price series. It follows that:
The third point is particularly relevant, as it speaks to how much of the profitability that we see through backwards looking analysis could have reasonably been captured. Nevertheless, all else being equal, more interval-to-interval volatility is going to improve the business case for batteries, even if they cannot capture the entirety of the available arbitrage revenue.
We have looked at three measures of volatility, and each of them tells a different story about the outlook for batteries. But, regardless of how we define it, there has indeed been an increase in volatility in the market, as demonstrated by the following:
Put simply, the odds have been shifting in favour of battery profitability. However, the immediate question is whether these trends will persist, reverse, or stabilise as the energy transition continues. We will consider this question in a subsequent article.
Last time we spoke about the use of wholesale market models to answer a wide variety of questions across the energy sector. We described the concepts of linear programming, solvers, and even how we derive prices from these tools. We then explained the first step in the modelling process – capacity expansion modelling, which allows us to determine the least-cost combination of generation technologies to meet demand.
But there were some aspects missing from our capacity expansion model, because of the computational complexity of including them. We concluded by foreshadowing the next step in the standard modelling framework, ie, the simulation of real-time dispatch – the subject of this second article.
Having built the arena, the next step is to watch the operation of the system play out. There are three specific factors that we wish to capture in more detail in this process:
We note that there is no reason that a capacity expansion model could not have captured each of these factors, save for the computational burden of doing so. When we have limited time and resources, it makes sense to ‘lock the build’, and examine these other factors in more detail.
The process is to run a time-sequential simulation model, which takes as an input the technologies and capacities from the capacity expansion model. This is a far simpler problem, which can be run many times over with different inputs for demand, renewable energy traces, fuel costs, and any other parameters of interest.
In the remainder of this article, we will examine each of the three factors described above, and how they are handled in the dispatch modelling.
Let us start with the most important, most controversial, of all assumptions: bids from technologies. So often when we try and explain a strange phenomenon in the market, the answer comes back: bidding behaviour. An unexpected price spike to the market price cap – bidding behaviour; counter-price flows on an interconnector – bidding behaviour; high prices for sustained periods on a mild day – bidding behaviour. Indeed, if one is at a loss for explaining a phenomenon, the best bet to avoid embarrassment is to give a sagely shake of the head and appeal to the higher power: ‘bidding behaviour’.
Bids are of such great importance because they collectively give rise to the supply curve that, together with demand, is responsible for price formation. And because demand is highly inelastic – ie, it does not respond to price – it is the supply curve that is responsible for a many of the phenomena in the sector that are otherwise inexplicable.
But what bidding assumptions should we use? Bids can vary from day to day, hour to hour and, even in some cases, minute to minute because of rebidding. Although it is entirely possible to reconstruct outcomes given historical bids, making projections about future bidding behaviour is far more complex. This is particularly the case in an environment where the technology capacity mix is changing, eg, when new plants are rapidly entering the system, or older plants are retiring.
The Holy Grail of bidding assumptions is some mechanism for determining how plants will bid in their capacity in any future world, whether that world be defined by:
Despite many claims to the contrary, no such mechanism exists. Yes, it is possible to create bids based on rules, or game-theoretic frameworks, but in the end they all result in the same outcome – players will bid some proportion (potentially none) of their capacity at a level that exceeds their short-run marginal cost. Some typical assumptions are as follows.
Approach 1: Contract bidding:
Players will bid in their contracted level of output at SRMC, but will then bid all remaining output with some mark-ups. A problem with this outcome is that we must assume a contract level. How contracting changes with changes in market conditions and the change of asset ownership will be difficult to forecast for every plant into the future, and so requires us to make assumptions. In effect, we are still assuming a supply curve.
Approach 2: Game theoretic bidding:
Players are assumed to bid based on the assumption of maximising their profit, subject to the strategies of other players. The assumption is that by iterating between players and giving them opportunities to change their bids, we will converge to a Nash-equilibrium (ie, a world where nobody has a reason to change their bids unilaterally). This is not mathematically correct – there is no assurance of convergence to a single Nash equilibrium given the way the supply curve is represented – and it drastically increases the computational overhead of the exercise, slowing down run times and forcing the modeller to make simplifications in other parts of the model. Moreover, the assumption that generators seek outcomes that are Nash is elegant but unrealistic. As one of my old colleagues was fond of saying: ‘I’ve never seen a rebid reason that says ‘Seeking Nash Equilibrium’.
Approach 3: Using historical, or other assumed profile of, bids:
In this case, Players are assumed to bid their capacity in at levels based on recent outcomes. This approach suffers from the weakness that the bids are once again being driven by the world we know and understand, and may not align with future changes in contracting behaviour, portfolio changes, or other developments of the system.
There seem to be no good solutions – one must choose their poison. At one time or another, we have used each of the above methods depending on the task at hand. But in general we have found that the approaches that limit the computational complexity (ie, Approaches 1 and 3) are more favourable, because they allow us to investigate different sensitivities to the supply curve. In addition, using historical information tends to provide a helpful reference point for any such discussion. For example, we can ask the question of ‘what happens if more generation is bid in at the market price cap than historically’, or ‘what if batteries start to bid more generation at a lower bid band’.
Regardless, there is no way to avoid the challenge that at its core we are making assumptions about future behaviours and that as the power system changes, the current information set we have will become more out of date.
In addition, we recognise that all existing models are poor at capturing the type of volatility (ie, instances of super-high prices well in excess of the $300 – $500 range) that are so important to market outcomes. This is because volatility occurs in the actual market due to unexpected transient factors such as system constraints (ie, temporary local FCAS constraints due to the risk of islanding), occasional bidding behaviours that are often quickly outcompeted by competitor responses, and unexpected major events such as an explosion at a major unit or lightning strike on a transmission line. Put simply, the reason why super high prices are difficult to forecast is not because the market model is not “good enough” (eg, 30-minute vs 5-minute resolution) but because the modeller cannot systematically forecast transient market disturbances. Where these super high price volatilities are included, they typically occur through post-processing of results, such as adding some historical “noise” component – it is not an outworking of the model. This is a clear limitation of market modelling. Our advice is to be aware of this limitation and be suspicious of anyone who tells you they have a model that can forecast this type of volatility.
One of the benefits of ‘locking the build’ is that we can simultaneously unlock large amounts of computational power to capture other factors. This can come in the form of more runs of the model (see next section), or in the form of increased fidelity of representation of the system.
There are three, and potentially many more, ways that this computational windfall is spent. The first is the inclusion of operational plant limitations, such as ramp rate and minimum stable level constraints. Historically ramp rates were generally of limited importance because of the relatively small amounts of ramping required across the system. But with the advent of renewables – in particular solar – minimum stable levels in the middle of the day and ramping on either side of the morning and evening peaks have become more and more important. Dispatch models can easily capture the inter-temporal restrictions on generation caused by limited plant flexibility, and so the benefits of fast-ramping technologies are more evident.
The second change in the dispatch modelling is the use of outages. Now here we face a conundrum: how is one best placed to capture the effect of outages, given that they are a random variable. In some studies, such as reliability modelling, we are not just interested in one realisation of outages, but in the distribution of outcomes across many potential different outage traces. Such modelling often involves rerunning the same model hundreds or even thousands of times to build a picture of the distribution of unserved energy. Here again we see the benefits of the dispatch model being simpler and faster – we can spend the computational windfall on running many different simulations, rather than just one.
But what if we are restricted to just one simulation? It would seem that in this world, we need some concept of a ‘normal’ outage pattern. This is indeed the approach that is taken by most modellers. For example, some modellers derate all capacity uniformly over the course of the year. However, this averaging approach tends to crimp volatility further, because it does not capture the extreme events which occur when outages are greater than their long-term average. We have typically adopted the approach of examining many different outage profiles and selecting the median profile according to a metric of the frequency of extreme events. Regardless of the approach adopted, it is important to understand the degree to which outages are affecting outcomes, because a single sustained outage at the wrong time can lead to a massive impact on reliability.
These factors tend to provide more granular results, because they impose additional constraints. All else being equal:
When all is said and done, these many different factors can give a great deal more shape to prices, as well as leading to different marginal costs or prices being observed in the system.
We have described using the computational windfall from locking the build that comes out of the capacity expansion model to increase the complexity of dispatch. But another way to spend that windfall is by running our dispatch models many times. This is particularly important when we want to understand how random factors influence outcomes.
We can look at many different potential realisations of a random variable, to understand not just a single point estimate of outcomes, but an entire distribution. This can help us answer questions like:
The key here is to create the inputs – ie, the weather and demand traces – that will feed into these simulations. In the National Electricity Market, the market operator publishes a range of traces for demand and weather going back 13 years. But we can go further using historical data sets such as the MERRA-2 data set to create a longer history. The challenge is always to ensure that the weather and demand conditions are correlated. For example, it would be a mistake to use temperature from 2011, but wind data from 2022. The two would be misaligned with the potential for outcomes like high output from wind farms occurring at the same time as high temperature outcomes in summer. In general, the solution here is to ensure that all the trace variables are aligned, and so it is not possible to ‘mix and match’ traces without compromising the value of the exercise.
In the event that a model requires even more data than is historically available, the solution is to create synthetic data, which preserves the relationships between the variables, but which is generated using probabilistic machine learning or some other suitable technique. For more information about this type of approach, we refer the reader to Probabilistic Deep Learning by Oliver Dürr and Beate Sick.
Once we have run the model across all the available data, we can look at the distribution of outcomes and see how much additional information has been revealed. In our opinion, this type of ‘stress testing’ is massively underapplied across the sector. And even when it is applied, for example in reliability studies, not enough analysis occurs of the distribution of outcomes. As more and more data sets become available, and the system gets more and more dependent on random factors, this type of approach will become increasingly powerful.
So we now have an end-to-end modelling process. But even after two articles, we have barely scratched the surface of the process. The power system is a complex beast, and a model that seeks to simulate its operation will be similarly intricate.
This intricacy can sometimes lead modellers to avoid talking about the fine details of their modelling and, in some instances, to use modelling to justify poor decisions.
With this in mind, we think that the most helpful tool for someone trying to engage with, or commission, energy market modelling is a guide to some of these tricks. In our final instalment of this series, we therefore examine the assumptions and methods – the Dark Arts – that your modeller would rather not talk about. Our intention in doing so is to arm you with the basics of ‘Defence against the dark arts’. This is the information you need to understand both what models cannot do, but more importantly the many powerful questions that can indeed be answered by modelling if we are able to stretch our understanding.
Power systems all over the world are experiencing rapid and profound change. The last decade has seen an inexorable rise in the penetration of renewable generation technologies, ie, wind and solar farms. In the past, these technologies accounted for only a small fraction of total electricity supply. But now they are a critical part of our power system, and their significance will only continue to grow. These are profound changes that have consequences for every part of the energy sector.
Against this backdrop, there is now more focus than ever on how we can better understand the outlook for the power system. Despite their many detractors, wholesale market models are in widespread use across the sector – we seek to use these models to answer a wide variety of questions, including:
Despite their shortcomings, models of the future power system provide us with the power to design, understand, and stress test potential system configurations without having to touch the physical system. Tools such as PLEXOS and Gurobi are now in widespread use across the energy sector.
Notwithstanding the widespread use of wholesale market models, we have learned through our work in the energy sector that there is sometimes limited understanding of how these models work, their strengths and weaknesses, and how they can be adapted to fit different purposes. People regularly use the term ‘black box’ to describe wholesale market models. This term tends to be associated with results that cannot be explained, poor visibility of the linkage between inputs and outputs, and a lack of consistency across scenarios and sensitivities.
The problem is that all too often, wholesale market models are used to produce a single, highly aggregated answer. An entire study can be boiled down to a single result: a price of $72 per MWh, a capacity factor of 15 per cent, or even in some instances an answer such as ‘Yes’ or ‘No’. Indeed, we have heard about modelling studies where advisors refuse to provide more detailed information, usually on the grounds that such information leads to ‘greater scrutiny’. This type of approach enshrines the black box view of the system into our thinking, disempowers decision-makers, and undermines the role and power of modelling.
But the ‘black box’ can be opened. One of the powerful elements of the models that are used in the electricity sector is that they provide us with virtually endless data that can allow us to understand outcomes better, to dig deeper into the operation of the system, and to build, challenge, and refine our intuition. Models can help us understand mechanisms that drive the outcomes we care about. For example, over the last few years the industry has developed an increasingly sophisticated understanding of wind droughts, and their interaction with firming needs. This in turn has led us to understand the significance of the availability of gas-fired generation, and the importance of constraints on the availability of gas.
Similarly, models have shown us that as we see increasing penetration of batteries, the short, sharp periods of high demand in summer that were previously the major driver of high prices will give way to longer periods of energy shortfalls in winter. To understand the solutions to these energy shortfalls, we have used models to answer the question: what is the best combination of resources to respond to wind droughts? We have learned that batteries alone cannot provide the energy we need to endure these periods. Modelling has helped us build our intuition about these events, and challenge ‘gut instinct’ which is wrong at least as often as it is right.
With this context in mind, we have prepared a three-part series on understanding how energy market modelling works. We seek to open the black box, and describe how these models work at a detailed level. We cannot hope to describe everything, but we will endeavour to shine a light onto some aspects of their operation that are often overlooked, avoided, and (in some cases) hidden from decision-makers.
The series is divided into three parts:
In this article, we consider (1).
When it comes to long-term modelling of the system, the biggest question is how the players/generators that make up that system will change into the future. Given a starting point, where we have a set of existing generators, we want to answer questions like:
These models are sometimes referred to as ‘LTs’ standing for Long Term models. They work by taking a set of assumptions (described below), formulating the problem as a linear program, and using a mathematical solver to identify the least cost combination of new and existing generation that can satisfy demand.
Linear programming is a branch of mathematics that seeks to find the optimal solution to specific classes of problems, ie, ones where all the variables and constraints are linear functions. It is important to understand what we mean here by optimal – this word has a very precise meaning. In linear programming, we define a function (hereafter the ‘objective function’) that we seek to minimise or maximise. In a capacity expansion problem the objective function is the total cost of operating the power system – a function we seek to minimise. The optimal value of the objective function is achieved with the lowest cost combination of generation investment and dispatch and any other variables that we might consider, which satisfies all the constraints, such as meeting demand and delivering policy targets. We use a solver, such as Gurobi, to find this optimal combination that yields the least-cost solution to the objective function. For those who are interested, a good introduction to linear programming can be found in Linear and Integer Optimization by Sierksma and Zwols.
A solver is a piece of software that implements a combination of different algorithms to find the optimal combination of variables that yields the optimal value of the objective function. Now here I must make a confession – to me most solvers have become so sophisticated that they are themselves a black box. Companies like Gurobi have invested decades in making their software faster and faster, and able to solve broader and broader classes of optimisation problems. Open an introductory textbook to optimisation, and you will find a description of solver algorithms that bears almost no resemblance to what commercial solvers are doing.
The critical point is that we do not (in general) need to know how a solver works to understand how to run the power system. All we need to know is that the outputs of the solver yield the very best solution possible to running the system. It is of course highly valuable to be able to understand how these tools work, but it is not essential to decision-making. All we need to remember is that the outputs of the solver, are the least cost way of operating the system. A pilot need not understand the millions of lines of code that help fly a plane, provided he understands the interaction between his actions, the controls, and the effect on the plane itself.
So we have decided that we want to find the least cost combination of generation to satisfy demand. What information do we need to do this in the power system? The standard array of inputs are as follows:
Beyond this there are two additional overarching assumptions that are of critical importance:
A discount rate that can be applied uniformly across all time periods in the model, to translate costs in one time period into costs in another time period.
At this point, the reader may be asking the question: why have we made no assumptions about the new capacity of generation, when existing plants will retire, the amount of generation from different sources, or the flows on interconnectors. Aren’t these the very things that we are interested in studying?
Indeed, these variables – these decisions – are our focus. But it is for precisely that reason that we have not assumed values for them. Instead, we leave it up to the solver to search and find the optimal combination of these ‘decision variables’ that yields the optimal outcome. The decision variables are:
Without constraints, a linear program is trivial. But we know that there are constraints on the operation of the power system that cannot be violated, whether it be because of the laws of physics, operational restrictions on plants, or some policy objective.
There are many constraints that we could consider, but for the most part they fall into four broad categories:
Generation + Net Imports = Demand – Unserved Energy
Generation <= Capacity
Minimum Flow <= Flow <= Maximum Flow
Generation <= Max Half-hourly Output for a given trace
In addition, there are a wide variety of additional constraints that we could add to this list, including storage constraints for batteries and hydro assets, emissions budgets, and limits on the acceptable level of unserved energy. But for the most part, the vast majority of constraints in a capacity expansion model are shown above.
Having defined our objective (ie, to minimise cost), chosen our input parameters, and implemented our constraints, the next step is to hand our problem to our solver to give us the answer. But what is the answer? Many people often assume that the answer is the value of the objective function, ie, the total cost of operating the system over the time horizon. But is this really that helpful? In fact what we are often more interested in are the values of the decision variables that yield this optimal value. We want to know what we should build, when we should retire existing plant, and how all of these facilities should be operated. Put simply, it is the value of the decision variables that are of most interest.
There is also a trick here – it turns out that when we solve a linear program we get some additional variables for free. In particular, every constraint yields a special value, called a dual variable or ‘shadow price’, that represents the effect of alleviating that constraint by an infinitesimal value. In the case of the Supply-Demand constraints, this shadow price has a very particular economic interpretation – it is the additional cost to the system of an additional megawatt-hour of demand. In microeconomic terms, it is the marginal cost of an additional unit of supply.
In a workably competitive market, this can be thought of as being the price yielded by a capacity expansion model. When the marginal cost of building a new plant is higher than the shadow price of the supply demand constraint (ie, the price) a new plant will remain unbuilt. But when the price exceeds the marginal cost, the new plant will be built. This is a desirable characteristic of the model, as it says new plants will be built up to the point where they make an economic profit, but not beyond that point.
So now we have a means of planning out the system. We have a model that can help us project the new plants that will be built economically, the old plants that will be similarly retired, and how all these plants will work together to ensure supply meets demand. But there have been simplifications along the way – for example, we have not accounted for the following:
One might ask why we did not simply account for these factors in our capacity expansion model. The answer is that were we to do so, the computational complexity would be prohibitive – the problem is simply too big to solve in one go, or even in large chunks. It is for this reason that the next step in a standard modelling framework is to simulate real-time dispatch – the subject of Part 2 in this series.