A combined modeling approach for wind power feed-in and electricity spot prices
Introduction
Renewable electricity generation has been considerably growing throughout the past 10–15 years in some countries, like e.g. Germany, and wind energy has strongly contributed to this boost. This development is mainly driven by renewable promotion schemes, whereby guaranteed feed-in-tariffs have been most successful to stimulate investments in renewable energies (see Ragwitz and Held, 2007). These investments receive their income from the sold electricity on the basis of the installed renewable promotion scheme and not from the electricity sold on spot markets with highly volatile prices. However, the influence of electricity generated by renewable energy sources on the spot market price is gaining importance with increasing shares of renewable energy feed-in (see Ryu et al., 2010). The electricity feed-in from renewable resources reduces the remaining system load, which has to be satisfied by conventional power capacities. As the renewable feed-in shifts market prices along the merit-order curve of power plants, this effect is often called the merit-order-effect of renewable energies (see Sensfuss et al., 2008, Menanteau et al., 2003). The following figures for the German electricity system illustrate the impact of renewable feed-in especially based on wind energy: wind energy capacities in Germany amounted to approx. 26 GW in 2010, which corresponds to more than 30% of the maximum load of the year. The maximum feed-in of wind power equaled to 21.5 GW in 2010. Considering a minimum load of 40 GW (see Saint-Drenan et al., 2009), this means that in times with strong wind about 50% of the minimum load are served by wind power, which replaces the adequate amount of conventional capacities. Thus, it is obvious that the feed-in from wind energy has significant impact on spot market prices.
Several modeling approaches exist to analyze and predict spot market electricity prices. Within fundamental models the consideration of renewable feed-in, especially wind power feed-in, is plausible and evident, as all fundamental data has to be taken into account. Financial models are often favored to model electricity prices for a short and midterm planning horizon. These models try to explain electricity prices by deterministic and stochastic patterns. As the feed-in from wind energy is more and more of crucial importance in electricity price modeling also financial models have to integrate this new uncertain parameter in the modeling approach. Up to now, hardly any financial or time-series modeling approach exists, which explicitly model the wind power feed-in and which incorporates this uncertain parameter in an integrated time-series or financial model for electricity spot prices. Therefore this paper presents an analysis of the wind power feed-in (in Germany), proposes a modeling approach for wind power feed-in and presents an integrated approach which simulates electricity spot prices under consideration of wind power feed-in within a financial modeling approach.
The combined modeling of wind power feed-in (WPF) and electricity spot prices is existential, if specific energy technologies, which rely on wind power, are economically evaluated based on market prices. E.g. if investments in wind power plants or energy storages are assessed under liberalized market conditions, appropriate wind power feed-in series and electricity price paths will be necessary to carry out the economic evaluation. For the evaluation of wind power plants simulated prices and WPF series are required, if an evaluation approach based on market prices instead of fixed feed-in tariffs is used.
Due to the market premium mechanism of the latest renewable energy legislation in Germany, wind power plant operators have also the opportunity to sell their power output directly on the electricity spot market. In this case they receive grants (market and management premiums) additionally to their earnings on the spot market (see EEG, 2012). These earnings and the funding premiums can be applied to a market evaluation. However, if a market evaluation should also consider the uncertainty of prices and WPF, a multistage stochastic optimization approach is necessary. This is not only relevant for wind power plant evaluation, but also for other technologies, such as storage or gas power plants. To carry out the stochastic optimization, a large number of price and WPF simulations, describing all possible developments of these parameters, can be reduced to a stochastic tree and applied to the optimization.
Besides, if a deterministic evaluation approach is applied for the evaluation of wind power plants or energy storages, a model for WPF and electricity prices is also useful. As historical data of both parameters is only available for a limited time-period, the combined modeling and simulation of these parameters can deliver the necessary time series for future years. These data series can also consider the extension of installed capacities of wind power in the coming decades.
Furthermore, an electricity price modeling including WPF effects allows analyses of changes in the future price structure. These analyses can be not only essential for power plant investors, but also for energy policy makers, as they can adjust their policies regarding market design and renewable energy funding with a better knowledge of possible price effects resulting from their actions. All these arguments necessitate a combined modeling of WPF and electricity spot prices with the help of stochastic processes, as it is introduced in this paper. Thereby, it is important to mention that an adequate modeling of both parameters has to capture also their correlation, as the electricity prices and WPF series are correlated due to the so-called merit order effect of wind power.
The paper is structured as follows: the next section gives an overview of the uncertainty in wind power generation and quantifies its impact on the electricity spot prices that is related to the merit-order effect of wind energy. Section 4.2 focuses on the simulation of wind power feed-in (WPF) based on the hourly utilization of the overall wind power capacity installed in Germany. Thereby the focus will be set on the removal of deterministic patterns, such as seasonality, and on the modeling of stochastic properties of the hourly capacity utilization series. The autoregressive behavior of the stochastic part of the capacity utilization will be captured by a recursive method simulating the change rate of the next capacity utilization level by its preceding values. After generating the stochastic component, the time-series will be reseasonalized to receive final capacity utilization series representing the hourly WPF of a year. The hourly WPF series will be used in Section 4.3 to extend the simulation of electricity prices considering the short-term impact of WPF. Thereby, an already existing electricity model will be shortly described, before the focus is set on model extensions integrating the impacts of WPF. The description of the extended electricity price model will be followed by the results section, in which simulated WPF and electricity price series will be compared with original series to determine in-sample performance of the simulation models. In the conclusions the main outcome is summarized and further work is presented that can be carried out in that area.
Section snippets
Impacts of wind power feed-in on electricity prices
The effect of wind power feed-in on electricity prices has been analyzed in various papers (see Ray et al., 2010). In general it can be distinguished between model based analysis (see Sensfuss et al., 2008, Weigt, 2009, Delarue et al., 2008, Bode and Groscurth, 2006, de Miera et al., 2008) and statistical analysis. Main goal of the statistical approaches is to quantify the price spread of market prices with a high and a low wind power feed-in (see Jonsson et al., 2010, Neubarth et al., 2006).
Literature about wind power and electricity price modeling—differences in this approach
The merit order effect described above is appropriately integrated into a model for electricity wholesale prices. An existing time-series model for electricity prices is extended by a component, which models the wind power feed-in (WPF) and incorporates the price reduction effect of simulated WPF series into the price modeling. This is a novel approach, as there exists hardly any paper focusing on combined modeling of wind power feed-in and electricity whole prices. However, there are several
Integrated approach for modeling wind power feed-in and electricity prices
A combined approach for modeling a wind power feed-in (WPF) and electricity spot prices is introduced in the following. Focusing on the relationship between WPF and prices, especially on the price reduction effect of WPF on electricity prices (see Section 2). In the combined modeling approach historical electricity prices and WPF series are used to calibrate the model components, which in turn are applied to generate simulated prices and WPF series. But before each model component is described
Results
Based on the combined modeling approach described above, 100 simulation runs are carried out delivering WPF series and electricity prices. The WPF series are generated via multiplying the capacity utilization series by the installed capacity of the analyzed year. For future years, the expected installed capacity has to be estimated, so that WPF series for these years can be generated.
Besides, different electricity price series are produced with the two electricity model versions. As already
Conclusions and future research
Wind power generation and feed-in have a significant impact on electricity wholesale prices. Especially in hours with high electricity demand a high WPF leads to an immense price reduction, as the WPF avoids the dispatch of power plants with high variable costs, such as gas turbines. Extending the analysis of Sensfuss et al. (2007) about the merit order effect, we have shown that this effect is load dependent, which means that with growing residual load the price reduction induced by wind power
Acknowledgments
The paper results from the work of the young investigator group “New methods for energy market modeling” of Dominik Möst. The young investigator group received financial support by the concept for the future of Karlsruhe Institute of Technology within the framework of the German Excellence Initiative.
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