I have the chance to collaborate with a number of Ph.D. and M.Sc. students for their thesis work, who focus their research on challenging methodological and applied topics.
Let me describe here briefly their field of research and expertise:
- Julija Tastu – Short-term wind power forecasting: probabilistic and space-time aspects (DTU Compute)
- Claire Vincent – Predictability of wind fluctuations at large wind farms
- Tryggvi Jonsson – Optimal participation of renewable energy in deregulated energy markets
- Pierre-Julien Trombe – Modeling and forecasting of wind power generation – Regime-switching approaches
- Marco Zugno – Impact of stochastic generation on the dynamics of electricity markets
- Karsten Capion – (2009) – Optimal charging of electric-drive vehicles in a market environment (with Peter Meibom and Trine Kristoffersen)
- Philip D. Andersen – (2009) – Optimal operation of a wind-storage power system under market conditions (with Henrik Madsen)
- Marco Zugno and Paolo Giabardo – (2008) – Competitive bidding and stability analysis in electricity markets using control theory (with Henrik Madsen)
- Tryggvi Jonsson – (2008) – Forecasting of electricity prices accounting for wind power predictions (with Henrik Madsen)
Julija is looking at how we may be able to improve wind power forecasts based on extensive knowledge and modeling of the spatio-temporal characteristics of the wind power fields. The main potential practical application of her research may be the increase in accuracy of short-term point forecasts of wind power production, as well as an increase in skill of related probabilistic forecasts. Among other things, she has described the space-time structure of forecast error fields over Denmark, and how they are conditioned upon prevailing winds over the country.
Claire is looking at how we may better understand, model and forecast events with low and high wind (power) variability at large offshore wind farms, by combining meteorological and statistical perspectives. This problem is uterly difficult, since near-coastal offshore wind dynamics are the result of the combination of complex meteorological processes which are not all understood today. Among other things, she has shown how to employ nonparametric and nonstationary spectral analysis techniques for defining climatologies of wind dynamics, with application in the North and Batic Seas.
Claire completed her PhD project in March 2011. She is now a post-doc at Risø National Laboratory, being awarded a prestigious 3-year grant from the Danish Agency for Science, Technology and Innovation.
Tryggvi concentrates on the market aspects of wind power integration, developing the necessary insight for optimal trading of wind energy in liberalized electricity markets. Based on his demonstration that wind power forecasts have a significant impact on day-ahead prices, the sign of regulation, and eventually the magnitude of regulation penalties, he has developed a suite of methods and tools permitting to forecast the market dynamics accounting for the additional effect of the forecasted wind power generation. In parallel, he is looking of strategic bidding and decision-making under uncertainty.
Even though the headline of his Ph.D. sounds very general, Pierre-Juien has mainly been focusing on wind energy and heat dynamics in buildings. He has developed a deep understanding of regime-switching modeling techniques with observable and unobservable regime sequences for the modeling of offshore wind power fluctuations. He is also looking at how weather radar images may permit a classification of such regimes, with potential use in future forecasting methods. Among other things, he has shown how the variance in wind (power) dynamics may be captured and analysed using Markov-switching AR-GARCH models.
Marco puts particular emphasis on the interaction between wind power and market dynamics. More than just considering statistical relationship, he has shown how to model electricity markets as closed-loop systems, the dynamics of which are jointly influenced by strategic behaviour of the market participants and stochasticity in the energy generation. In parallel, he has proposed some optimal bidding strategies based on a fully probabilistic view of the problem, or looked at strategic bidding for generic wind-storage systems. Another interesting piece he has carried on has consisting in showing how wind power generation in Germany may significantly affect the whole European electricity network.
Electric drive vehicles (EDVs) could become widespread within the coming decades as a solution to the many problems related to liquid fuels consumption. These vehicles interact with the electricity system and offers, unlike most other electricity consumption, flexibility in demand, since it to a large extent can be decided when the vehicles should be charged. Deciding on an optimal charging plan for electric drive vehicles requires knowledge of electricity prices and driving patterns. A simple model minimizing costs for a fleet operator charging all vehicles in Western Denmark was developed. The model only addressed the day-ahead spot market.
The problem of finding an optimal charging pattern is complicated by the fact that prices are affected by change in demand caused by the charging. Using linear regression on historical data the relationship between price and demand was investigated in an attempt to find dP=dQ (i.e. how much price changes with a change in demand). After correcting for long term effects (fuel prices etc.) a coefficient of 0.1174 DKK/MWh2 was found, but a linear model failed to model the complex relationship between price and demand, especially at extreme loads. A non-linear model was proposed which defined dP=dQ as a function of the squared deviation of the price from some mean price. The parameters were estimated by fitting the solution of the differential equation (a tan-function) visually to the data. Drive patterns were obtained from statistical survey data in a novel approach using a slightly modified version of the k-means clustering algorithm. EDVs were modeled as a set of standard vehicles. Each
standard vehicle represented a number of real world vehicles with identical driving patterns. This allowed for a realistic treatment of battery charge levels. Both battery electric vehicles and plug-in hybrid electric vehicles (PHEVs) were modeled
A set of scenarios were investigated. In the baseline scenario with 300.000 EDVs 75% of charging takes place at night. Day time charging is primarily used for PHEVs to limit liquid fuels consumption. Peak electricity demand remained almost constant. The charging adds about 200 MW of base load consumption at night and gives rise to an overall average price increase of 20 DKK/MWh, while reducing the price variance. DVs compete with each other for cheap electricity, leading to increased marginal charging costs of adding more EDVs. The possibility to shift consumption between days is limited due to the fleet operators contractual obligations to the users. It was found that very little discharging from the vehicle to the grid (V2G) was provided in general. Price differences are most of the time too small for this and the battery wear cost and incurred losses limit the profitability considerably. While EDVs may be used to increase base load consumption their role as energy storage is limited as long as batteries costs remain high.
Increased wind power capacities are expected to be installed all around Europe, and also in rapidly developing countries such as China, India or Brazil. A disadvantage of wind power in comparison to easily dispatchable generation is its variability and limited predictability, which reduces its unit value in a market environment. Indeed, the unit value of wind generation on an electricity market is in general reduced by 20%. In parallel, one traditionally thinks that electricity storage cannot be used at the large-scale. However, the decrease in storage prices makes it possible to envisage the installation of storage capacities at a wind farm in a near future, either for dampening short-term power fluctuations, or for increasing the value of wind power on a market. The aim of this project is to develop stochastic optimization methods for the optimal operation of a combined wind-storage system, and to evaluate the resulting benefits, both in terms of reduced variability of the wind farm output and in terms of increased unit value of wind generation.
In a first stage, the study will focus on determining the best way of representing stochasticity in the wind farm ouput from wind power forecasts and information on their uncertainty. In parallel, it will be necessary to review potential storage devices and study their operation strategies. The stochastic optimization problem to be solved for optimal operation of the combined wind-storage power systems will then have to be formulated, and appropriate methods applied for solving this problem. The methodology developed will be used for simulating the participation of a real-world wind farm in the Scandinavian Nord Pool electricity market.
The process of deregulation that has involved electricity markets in the recent years has opened the way for several interesting research topics. This thesis addresses one of the most fascinating ones among them: the study of strategic bidding and the analysis of its consequences in terms of market stability. The problem faced is twofold. From the generators’ point of view, it is of interest to develop bidding strategies aimed to optimize the individual profits, given their costs of production, the evolution of energy demand and the response of the other players in the market. On the other hand, the point of view of the society is addressed by analyzing the behavior and the stability of the market when these strategies are applied.
In this thesis, two competition models are considered in analyzing electricity markets: the Cournot and the Linear Supply Function (LSF) models. In the former one, the supply bid is assumed to be in the form of a quantity representing the amount of energy that each generator is going to dispatch to the market. In the latter framework, instead, the bid is in the form of a linear function relating the quantity to the relative price the producers are willing to sell the energy at. In both the cases, the problem is tackled by means of optimal control theory and the approach used is the same. First, a dynamic closed loop system is built in order to model electricity markets’ competition, in which each generator aims to optimize its prots in the next bidding round. Then, an optimal strategy is developed with the goal of maximizing the individual prots over a longer horizon. This multi step strategy is derived analytically in the Cournot framework and numerically in the LSF competition model, namely through the use of the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm. The simulations performed show that a generator can increase its prots by employing the multi-step strategy; both in the Cournot and the LSF frameworks. On the other hand, the analysis of the social consequences of strategic bidding gives dierent results in the two competition models. In the Cournot framework, the society benets when the generators become more strategic. In the LSF competition model, instead, the social welfare decreases when players bid more strategically. Furthermore, sensitivity analysis are performed in order to evaluate the effects of changes in the market demand on both the individual generators and on the society.
Besides these analysis in a deterministic framework, the work is aimed to develop stochastic versions of these models. The closed loop dynamic systems are modified in order to account for wind power generation, which brings uncertainty into the system. Then, optimal strategies are developed with the aim of maximizing the expectation of the profits over more days. Again, the convenience of switching to the multi step strategy is shown in both the competition models for the generators, while a benefit for the society is veried, again, only in the Cournot framework. The stochastic models allow also the assessment of the consequences of the introduction of wind power in electricity generation markets. The results obtained in both the Cournot and the LSF frameworks show that switching to wind power generation is convenient both for the generators and for the society.
For players in deregulated energy markets such as Nord Pool and EEX, price forecasts are paramount when it comes to designing bidding strategies and are an important aid in production planning. In addition, price forecasts can be of great value for grid operators who are responsible for keeping the grid in balance. It is a known fact that electricity prices on Nord Pool spot market are, in the long run, mainly influenced by the level of water in the reservoirs of the Norwegian and Swedish hydropower plants. However, changes in the water level happen slowly and are therefore not a matter of great relevance when forecasts are made for the prices at the Nord Pool spot market on a relatively short horizon. In this thesis, the effects of predicted wind power production on the spot prices in Nord Pool Western Danish price area (DK-1) are investigated. Moreover, ways of including the predicted wind power production in a forecasting model not only for the mean spot price in DK-1, but also the full distribution of the prices, are explored. It turns out that the effects of forecasted wind power production on the spot price is substantial and even more effects can be found with small modifications. The forecasting model constructed consists of three mains parts. The first part accounts for the effects of external factors on the prices while the second one is a dynamic model of the spot prices that accounts for the effects found be the first model. The final layer adds valuable information about the uncertainty or the distribution of the prices. Combined these models give reliable non-parametric description to the full distribution of the spot prices. Given the result of this thesis, it is very likely that the same methodology will give good results when forecasting the prices on other electricity pools. It is expected that the approach will be highly beneficial both for pools where wind power penetration is relatively high, and for markets with other characteristics, such as regulation markets.