Supply function equilibria on the electricity market

Overview & Synopsis

This thesis studies the dynamic of the day ahead electricity market. The first chapter focuses on building a theoretical model : by considering ramping costs for power plants, that is costs associated with the time derivative of production, and adding a physical argument about production, it is possible to introduce demand shocks in continuous time by using Ito processes while keeping a tractable model. We obtain economic predictions from it that are notably different from the existing literature : in the case of a linear demand, linear costs, and quadratic ramping costs, we obtain a unique Nash equilibria, in contrast with the continuum of equilibria, and this equilibria gets steeper with increasing ramping costs as well as increasing uncertainty about demand, in order to absorb demand shocks more as price variations than quantity variations so as to minimise the ramping costs incurred. We then study those predictions empirically.To do so, we first describe in a methodological chapter how we can study those predictions on the data we possess : hourly aggregate supply and demand functions on the french day-ahead market as well as spatial hourly weather data over the entire french territory. The first step is to define a way to compare these functions to one another. Those functions are badly caracterized by parametric curves, we propose a way to define points that we consider comparable on those curves : the maximum value of the non parametric estimation of the first derivative of the functions, and the two maximum of the estimation of the second derivative. It amounts to noting that all of the functions are S-curves, and that by defining those points 98% of the variance between curves can be captured. The second step consists in estimating the uncertainty related to the weather : France has a large part of electrified heating systems, thus the demand for electricity is very sensitive to changes in temperature. We note that weather forecasts that are available when producers bid on the market are limited by their numerical methods and that the more the weather varies spatially, the worst it performs. We therefore introduce spatial autocorrelation as a measure of this uncertainty. Finally, in the third and last chapter, we combine these ingredients to test the theoretical predictions : is uncertainty driving steeper bids on the markets ? We have to introduce a last ingredient : a measure of the information available to producers on demand as a whole when they bid, in addition to the weather contribution isolated in chapter 2. We validate our predictions when it comes to weather uncertainty, but obtain more nuanced results for the full demand uncertainty. We face two types of such uncertainty : one on the prices, the other on quantity. However, our model, most notably with its assumption of a linear demand, is unable to distinguish theoretically those two types of shocks. We measure empirically that those shocks have opposite effects on the slope of the aggregate supply functions, and interpret this as a limit of the model that asks for a non linear extension to be built in order to explore those effects in more detail.