Electricity Spot Prices Research Articles

An Extended Mean Field Game for Storage in Smart Grids

We consider a stylized model for a power network with distributed local power generation and storage. This system is modeled as a network connection of a large number of nodes, where each node is characterized by a local electricity consumption, has a local electricity production (photovoltaic panels for example) and manages a local storage device. Depending on its instantaneous consumption and production rate as well as its storage management decision, each node may either buy or sell electricity, impacting the electricity spot price. The objective at each node is to minimize energy and storage costs by optimally controlling the storage device. In a noncooperative game setting, we are led to the analysis of a nonzero sum stochastic game with N players where the interaction takes place through the spot price mechanism. For an infinite number of agents, our model corresponds to an extended mean field game. We are able to compare this solution to the optimal strategy of a central planner and in a linear quadratic setting, we obtain and explicit solution to the extended mean field game and we show that it provides an approximate Nash equilibrium for N-player game.

Research on Risk Control under the Background of Electricity Futures Market

In the process of electricity marketization, the electricity futures market is an effective means to avoid the risk of electricity price fluctuations. Based on the background of the electricity futures market, this article first analyzes the physical and market factors of the price fluctuation risk in the electricity market; then, it studies the principle and implementation effects of the power futures hedging function; finally, the manufacturer’s strategy of hedging based on the price difference between the spot price of electricity and the price of forward contracts has been studied in detail. This article believes that the electricity futures market can effectively hedge the spot market risk, and hedging strategies based on the difference between the spot price and the forward price are better.

Estimating fast mean-reverting jumps in electricity market models

Based on empirical evidence of fast mean-reverting spikes, electricity spot prices are often modeledX+Zβas the sum of a continuous Itô semimartingaleXand a mean-reverting compound Poisson processZtβ=∫0t∫ℝxe−β(t−s)p̲(ds,dt) wherep̲(ds,dt) is Poisson random measure with intensityλds⊗dt. In a first part, we investigate the estimation of (λ,β) from discrete observations and establish asymptotic efficiency in various asymptotic settings. In a second part, we discuss the use of our inference results for correcting the value of forward contracts on electricity markets in presence of spikes. We implement our method on real data in the French, German and Australian market over 2015 and 2016 and show in particular the effect of spike modelling on the valuation of certain strip options. In particular, we show that some out-of-the-money options have a significant value if we incorporate spikes in our modelling, while having a value close to 0 otherwise.

Development of electricity prices in the V4 countries and econometric model of forecasting spot electricity prices in Slovakia

In this article, the authors focused on the development of electricity prices on wholesale and retail markets in the Visegrad Four countries (V4). The main goal of the paper is to design an econometric model of predicting spot electricity prices in Slovakia. Therefore, the model of multiple linear regression is used, based on knowledge from the literature and existing studies. The model can be used to predict the possible development of electricity prices depending on several relevant variables - coal prices, gas prices and the share of renewable energy sources. The data were obtained from Eurostat and OECD databases, investment sites, which showed the development of commodity prices on wholesale market, or from power exchanges or a short-term electricity market operator. RStudio software was then used to evaluate created models. The result was price forecasts for further periods, which were also compared with the actual spot prices.

Flexibility from Electric Boiler and Thermal Storage for Multi Energy System Interaction

Active use of heat accumulators in the thermal system has the potential for achieving flexibility in district heating with the power to heat (P2H) units, such as electric boilers (EB) and heat pumps. Thermal storage tanks can decouple demand and generation, enhancing accommodation of sustainable energy sources such as solar and wind. The overview of flexibility, using EB and storage, supported by investigating the nature of thermal demand in a Danish residential area, is presented in this paper. Based on the analysis, curve-fitting tools, such as neural net and similar day method, are trained to estimate the residential thermal demand. Utilizing the estimated demand and hourly market spot price of electricity, the operation of the EB is scheduled for storing and fulfilling demand and minimizing energy cost simultaneously. This demonstrates flexibility and controlling the EB integrated into a multi-energy system framework. Results show that the curve fitting tool is effectively suitable to acknowledge thermal demands of residential area based on the environmental factor as well as user behaviour. The thermal storage has the capability of operating as a flexible load to support P2H system as well as minimize the effect of estimation error in fulfilling actual thermal demand simultaneously.

Managing volumetric risk of long-term power purchase agreements

A negative dependence between wind power production and electricity spot price exists. This is an important fact to consider for risk management of long-term power purchase agreements (PPAs). In this study we investigate this dependence by constructing a joint model using constant as well as time-varying copulas. We propose to use score-driven models as marginal model for the spot price of electricity as these are more robust to extreme events compared to ARMA–GARCH models. We apply the new model to pricing and risk management of PPAs and benchmark it against the ARMA–GARCH specification. Our comparison shows that the score-driven model results in a statistically significant improvement of predicting the Value-at-Risk (VaR), which is of high importance for risk management of long-term PPAs. Further, comparing constant and time–varying copulas we find that all time-varying copulas are significantly better than their constant counterparts at predicting the VaR, hence time–varying copulas should be used in risk management of PPAs.

Characterizing the Volatility of Wholesale Electricity Spot Prices in Australia

Understanding the volatility dynamics of electricity markets is important in evaluating the deregulation experience and in pricing electricity futures. This paper introduced an approach to portray the volatility of electricity price. We first introduced the Integrated Volatility (IV) and Quadratic Variation (QR) theory to define the volatility. Based on the theories, two nonparametric methods, i.e. Classical Realized Volatility (RV) and Realized Bi-power Volatility (RBV) were adopted to respectively measure the electricity price volatility with half-hour resolution in High-Frequency (HF) environment, using historical data from Victoria, Australia. By comparing the characterizing performance, the RBV method exhibited more superior effect. Next, the paper separated the total volatility into jump and continuous components based on Z jump test and the distinct dynamics of the Jump Volatility (JV) and Continuous Volatility (CV) were also analyzed.

Assessing the impact of renewable energy sources on the electricity price level and variability – A quantile regression approach

The literature on renewable energy sources indicates that an increase of the intermittent wind and solar generation affects significantly the distribution of electricity prices. In this article, the influence of two types of renewable energy sources (wind and solar photo voltaic) on the level and variability of German electricity spot prices is analyzed. The quantile regression models are built to estimate the merit order effect for different quantiles of electricity prices. The results indicate that both types of renewable generations have a similar, negative impact on the price level, approximated by the price median. When the price volatility, measured by the inter-quantile range (IQR), is considered, the outcomes show that wind and solar influence prices differently. Conditional on the level of the total demand, the wind generation would either increase (when the demand is low) or decrease (when the demand is high) the IQR. Meanwhile, the increase of solar power stabilizes the price variance for moderate demand level. Thus, policy supporting the development and integration of RES should search for a balance between the wind and solar power.

Deep reinforcement learning–based approach for optimizing energy conversion in integrated electrical and heating system with renewable energy

With advanced information technologies applied in integrated energy systems (IESs), controlling the energy conversion has become an effective method for improving grid flexibility and reducing the operating cost of IESs. This study proposes a dynamic energy conversion strategy for the energy management of an IES with renewable energy, which considers the system operator’s (SO) operating cost. Deep reinforcement learning (DRL) is used to illustrate the hierarchical decision-making process, in which the dynamic energy conversion problem is formulated as a discrete finite Markov decision process, and proximal policy optimization (PPO) is adopted to solve the decision-making problem. Using DRL, the SO can adaptively decide the wind power conversion ratio during the online learning process, where the uncertainties of customers’ load demand profiles, flexibility of spot electricity prices, and wind power generation are addressed. Simulations show that the proposed PPO-based renewable energy conversion algorithm can effectively reduce the SO’s operating cost.

Integration and convergence in European electricity markets

This paper investigates the degree of integration among markets using wholesale electricity prices, which arises from the link between the long-run dynamics of fuel prices and electricity prices. We address the question of whether European electricity markets have experienced convergence patterns in recent years, using the stochastic definitions of convergence and common trend based on cointegration analysis. We apply a vector error correction model to a representative sample of electricity spot prices of European markets, including those of Italy, France, the Netherlands, Poland, and the integrated market of Germany and Austria. We analyze both the long- and the short-run system properties, studying their persistence profiles. The short-run analysis reveals the non-significance of adjustment coefficients of the market prices in the Netherlands and Poland. Moreover, the Netherlands Granger causes Poland and the integrated market of German and Austria, but the reverse is not true. A unidirectional Granger causality is also found for France and Germany and Austria toward Italy. Given the cointegrating equilibrium, all country-specific price dynamics converge toward the steady state, but most of the exogenous shocks have permanent effects. Forecast error variance decomposition analysis clearly highlights that orthogonalized shocks largely affect the variance of neighboring markets.

Radioinactive: Do nuclear power plant outages in France affect the German electricity prices?

Do nuclear power plant outages in France affect the German electricity prices? In the case of the extensive inspections from October 2016 to February 2017 in 12 French nuclear power plants: Yes. This capacity shock increased the French electricity spot market price on average by 27.1%. The German-Austrian electricity spot market price was affected through cross-border trade. Due to increased electricity exports from Germany to France, the German-Austrian electricity spot market price increased on average by 3.2%. Moreover, due to decreased electricity imports from France to Germany, the German-Austrian electricity spot price increased on average by 7.6%. These results derive from a quasi-experimental approach based on coarsened exact matching, where the exogenous nature of the capacity shock is exploited as a random treatment in order to identify causal effects.

Grid-connected hydrogen production via large-scale water electrolysis

A techno-economic analysis was performed for large-scale hydrogen production plants (4000–40,000 kgH2/day or approximately 10–100 MW). Two electricity pricing schemes in 8 different geographical locations were considered. The analysis included five Canadian provinces with flat rates and real-time pricing for the wholesale markets in Germany, California, and Ontario. Under flat-rate pricing, the levelized cost of hydrogen produced via water electrolysis ranged from, for example, $4.21 to $4.71/kgH2 in Québec. For wholesale electricity markets, an operational strategy was developed that aims to identify if a posted price is high or low based on historical electricity spot prices. The electricity cost can be reduced by 4%–9% in Germany and by 15%–31% in Ontario and California at a capacity factor of 0.9 by implementing such operational strategy. Electrolytic hydrogen production in Ontario combined with underground storage was found to be the cheapest in the three wholesale electricity markets, resulting in a levelized cost of hydrogen of $2.93–$3.22/kgH2 for alkaline electrolysis and $2.66–$3.54/kgH2 for proton exchange membrane electrolysis. Compared to steam methane reforming at $2.5–$2.8/kgH2 (without carbon capture), the electrolytic hydrogen cost is 6%–27% higher. However, this cost becomes comparable to that from steam methane reforming once carbon capture and storage are included in the analysis. Our results suggest that maximizing the use of the electrolytic systems via high capacity factors can be favorable, especially under integration with wholesale electricity markets.

Short-Term Forecasting of Electricity Spot Prices Containing Random Spikes Using a Time-Varying Autoregressive Model Combined With Kernel Regression

Forecasting spot prices of electricity is challenging because it not only contains seasonal variations, but also random, abrupt spikes, which depend on market conditions and network contingencies. In this paper, a hybrid model has been developed to forecast the spot prices of electricity in two main stages. In the first stage, the prices are forecasted using autoregressive time varying (ARXTV) model with exogenous variables. To improve the forecasting ability of the ARXTV model, the price variations in the training process have been smoothened using the wavelet technique. In the second stage, a kernel regression is used to estimate the price spikes, which are detected using support vector machine based model. In addition, mutual information technique is employed to select appropriate input variables for the model. A case study is carried out with the aid of price data obtained from the Australian energy market operator. It is demonstrated that the proposed hybrid method can accurately forecast electricity prices containing spikes.

The impact of renewable energy forecast errors on imbalance volumes and electricity spot prices

This paper contributes to the general consideration of whether a policy of incentivising system operators to improve the quality and market availability of forecasts for renewable energy outputs would be beneficial. Using data from the German electricity market, we investigate the effect of wind and solar energy forecasts errors on imbalance volumes and subsequent spot electricity prices. We use ordinary least squares regression, quantile regression and autoregressive moving averages to identify these relationships using variables that have a quarter-hourly data granularity. The results show that higher wind and solar forecast errors increase the absolute values of imbalance volumes and that these can pass through into higher spot prices. We find that wind forecast errors in Germany impact spot prices more than solar forecasting errors. Policy incentives to improve the accuracy and availability of renewable energy forecasts by the system operators should therefore be encouraged.

The merit order effect of wind and river type hydroelectricity generation on Turkish electricity prices

The environmental concerns and dependency on gas imports push Turkish policy makers to find ways of increasing the share of renewable sources in electricity generation. Providing incentives for renewable energy in the form of feed-in-tariffs is one of the measures to achieve this goal. Basing on the data of Turkish electricity market operator, we quantified the magnitude of the price effects of wind and river type hydro generations on hourly average of day-ahead prices. We find that wind and river type hydro plants reduced the spot electricity prices during the period of 2012–2017, and despite these resources get the same incentives, their impacts on the spot prices and price volatility are different: this can be useful for a more comprehensive cost benefit analysis aimed at differentiating incentive schemes. The paper also discusses possible underlying reasons of these different impacts such as high seasonality of hydro generation and volatility of wind generation. Finally, we show that, assuming more than 75% of the price reductions were reflected into the consumer prices in Turkey, the net impact of wind and river type hydro generation on final consumer prices would be negative. This finding contributes to the discussions on renewable energy incentive mechanisms.

MCMC calibration of spot‐prices models in electricity markets

AbstractThe calibration of some stochastic differential equation used to model spot prices in electricity markets is investigated. As an alternative to relying on standard likelihood maximization, the adoption of a fully Bayesian paradigm is explored, that relies on Markov chain Monte Carlo (MCMC) stochastic simulation and provides the posterior distributions of the model parameters. The proposed method is applied to one‐ and two‐factor stochastic models, using both simulated and real data. The results demonstrate good agreement between the maximum likelihood and MCMC point estimates. The latter approach, however, provides a more complete characterization of the model uncertainty, an information that can be exploited to obtain a more realistic assessment of the forecasting error. In order to further validate the MCMC approach, the posterior distribution of the Italian electricity price volatility is explored for different maturities and compared with the corresponding maximum likelihood estimates.

Replacing Flat Rate Feed-In Tariffs for Rooftop Photovoltaic Systems With a Dynamic One to Consider Technical, Environmental, Social, and Geographical Factors

A flat rate feed-in tariff (FiT) is a traditional incentive offered by many utilities around the world to encourage their customers to invest in electricity generation from renewable sources such as rooftop photovoltaic systems (RPVs). It is designed by financial techniques that mostly consider the initial capital cost and electricity spot price. However, such an incentive cannot help the utilities to address the technical challenges in networks with large renewable penetration. In this paper, a dynamic FiT is designed based on the value of electricity, hosting capacity, ambient temperature, and time of day (ToD). The developed method uses fuzzy logic to convert these parameters into a time-varying FiT. This FiT will specifically support utilities that experience challenges in the electrification of remote areas or observe excessive stress on their networks at demand peak periods. The proposed FiT encourages the rural customers to install RPVs while discouraging the urban customers from installing RPVs without battery storages. The performance of the developed FiT is validated numerically and its capability is evaluated by analyzing the annual revenue, net present value, and payback periods.

APPLICATION OF ARIMA MODELLING FOR THE FORECASTING OF SOLAR, WIND, SPOT AND OPTIONS ELECTRICITY PRICES: THE AUSTRALIAN NATIONAL ELECTRICITY MARKET

This study aims to develop autoregressive integrated moving average (ARIMA) models to predict the solar, wind, spot and options pricing over the next two years, with historical data being used in a univariate manner to understand market behaviour in terms of trends. The assessment is made in the context of the Australian National Electricity Market (ANEM). The ARIMA models predict the future values of the monthly solar, wind, spot and options prices for various Australian states using time-series data from January 2006 to March 2018. The results show increases from 30.46–40.42% for the spot electricity prices and from 14.80–15.13% for the options electricity prices in the ANEM with a two-year horizon. The results further show that wind prices are expected to increase by an average of 5.43%. However, the results also show that the average solar electricity prices will decrease by 67.7%.Keywords: Electricity pricing, ARIMA model, Forecasting.JEL Classifications: C22, E37, Q47DOI: https://doi.org/10.32479/ijeep.7785

BRIM: An Accurate Electricity Spot Price Prediction Scheme-Based Bidirectional Recurrent Neural Network and Integrated Market

For the benefit from accurate electricity price forecasting, not only can various electricity market stakeholders make proper decisions to gain profit in a competitive environment, but also power system stability can be improved. Nevertheless, because of the high volatility and uncertainty, it is an essential challenge to accurately forecast the electricity price. Considering that recurrent neural networks (RNNs) are suitable for processing time series data, in this paper, we propose a bidirectional long short-term memory (LSTM)-based forecasting model, BRIM, which splits the state neurons of a regular RNN into two parts: the forward states (using the historical electricity price information) are designed for processing the data in positive time direction and backward states (using the future price information available at inter-connected markets) for the data in negative time direction. Moreover, due to the fact that inter-connected power exchange markets show a common trend for other neighboring markets and can provide signaling information for each other, it is sensible to incorporate and exploit the impact of the neighboring markets on forecasting accuracy of electricity price. Specifically, future electricity prices of the interconnected market are utilized both as input features for forward LSTM and backward LSTM. By testing on day-ahead electricity prices in the European Power Exchange (EPEX), the experimental results show the superiority of the proposed method BRIM in enhancing predictive accuracy in comparison with the various benchmarks, and moreover Diebold-Mariano (DM) shows that the forecast accuracy of BRIM is not equal to other forecasting models, and thus indirectly demonstrates that BRIM statistically significantly outperforms other schemes.

Cointegration Analysis of the Convergence Process in the European Electricity Markets

This paper investigates the degree of integration among markets using wholesale electricity prices. The reason arises from the link between the long-run dynamic of fuel prices and electricity prices. We address the question of whether European electricity markets have experienced convergence patterns in the last years using the stochastic definitions of convergence and common trend based on co-integration analysis. We apply a Vector Error Correction model to a representative sample of electricity spot prices of European markets, including those of Italy, France, the Netherlands, Poland, and the integrated market of Germany and Austria. We analyze both the long- and the short-run of system properties, studying their persistence profiles. The short-run analysis reveals the non–significance of adjustment coefficients of the market prices in the Netherlands and Poland. Moreover, the Netherlands Granger causes Poland and the integrated market German and Austria, but the reverse is not true. A unidirectional Granger causality has been found also for France and Germany and Austria toward Italy. Given the cointegrating equilibrium, all country-specific price dynamics converge toward the steady state, but most of the exogenous shocks have permanent effects. Forecast Error Variance Decomposition analysis clearly highlights that orthogonalized shocks largely affect the variance of neighboring markets.