A simulation framework for electricity markets
Keywords: real-world applications
game theory
analytic results
network constraints
auction mechanism
numerical optimization

Electricity Markets are paramount to the economy of any country and therefore lie at the foundation of society. These markets are usually very complex when compared to traditional financial markets due to the physical nature of the asset traded, difficulty of storage and distribution. Supply and demand balancing, network constraints, renewable energy influx, desire of participants to maximise their own profits, their risk aversion, fuel costs required for production, and the market clearing mechanism, do not exhaust the list of factors that influence the market outcome, but are perhaps the most important ones. The market outcome includes the prices and quantities allocated whose understanding is of great importance for market regulators and market participants alike.
This work is focused on improving the fundamental understanding of the Spot Electricity Markets which lie at the core of Electricity Trading and represent the majority of trading volume. In particular we focus on Day Ahead Auctions which represent the vast majority of Spot Electricity trading, due to the difficulty of storing electricity, coupled with uncertainty in demand and production patterns. Every market has its own peculiarities and, we consider as a case study the Central Western European (CWE) Day Ahead Auction (DAA) for the period of 01/01/2019−31/12/2019. The Central Western European market includes Austria, Belgium, Germany, France and the Netherlands.
Following an introductory chapter, due to the lack of full and complete network constraints historical data, Chapter 2 is focused on the reconstruction of historical network constraints, that are a key input in any fundamental model considering the electricity grid’s structure. Further, network constraints may impose price decoupling between countries, which is of great interest to practitioners, academics and regulators. The task is very challenging due to the input data being very large and sparse. We reconstruct the network constraints data, known as the Power Transmission Distribution Factors (PTDFs) and Remaining Available Margins (RAMs), by first recovering the underlying time dependent signals known as the Generation Shift Keys (GSKs) and Phase Angles (PAs), and the electricity grid characteristics, via a mathematical optimisation problem that is solved by exploiting problem structure. The second step maps GSKs and PAs to the network constraints via the electricity grid characteristics. Our reconstruction achieves good in- and out-of- sample relative errors when compared to a naive approach.
With the network constraints available, and by obtaining the cost and capacity characteristics of suppliers, in Chapter 3 we formulate a fundamental model to resolve for the zonal prices and quantities assigned to each participant, based on a simplification of the CWE market clearing mechanism, known as the Social Welfare Maximisation Problem (SWM). We also propose a novel market clearing mechanism which we call the Total Cost Minimisation Problem, because as we show, the prices are generally much lower and the total cost of supplying electricity is guaranteed to be lower by definition. Solving the Cost Minimisation problem is more challenging than solving the SWM, due to zonal prices appearing as explicit variables, but we obtain strong (but partial) analytical results to aid numerical solutions and provide efficient numerical algorithms. For both clearing mechanisms, demand is considered as inflexible, and producers bid marginal prices linear in the quantities produced. Since as expected, the SWM better represents the target data, this is further used as the market clearing mechanism. We consider the case when producers truthfully bid (TB) their cost curves, which is usually assumed by the regulators and many academic papers. However, we also consider the case of players trying to maximise their own profit, tand thus forming a Game Theoretic (GT) framework. For our CWE case study, both GT and TB models generally give an accurate representation of the actual price outcomes. Further, we define a method based on simple hypothesis testing to identify if and when the players are bidding strategically (gaming). We show that in fact, while for a large majority of times we cannot say with high confidence whether the players are bidding strategically or bidding truthfully, the number of times we are confident that players are gaming is much higher than the number of times we are confident that the players are bidding truthfully. Our results show that, in general, strategic bidding appears to be especially pronounced at peak demand hours: between 8am − 1pm and 5pm − 9pm. A different regime, where renewable energy influx appears to dominate the price action is also identified and this effect is generally more pronounced at off-peak morning hours (0am − 6am). Our model can thus be used as a fundamental approach for market outcome and price prediction, understanding the impact various fundamental factors on the price, understanding of producers’ behaviour, and identifying if and when players are not bidding truthfully. These are all of interest to academics, market participants, and regulators.