Electricity Spot Prices Research Articles

Robust forecasting of electricity prices: Simulations, models and the impact of renewable sources

In this paper a robust approach to modeling electricity spot prices is introduced. Differently from what has been recently done in the literature on electricity price forecasting, where the attention has been mainly drawn by the prediction of spikes, the focus of this contribution is on the robust estimation of nonlinear SETARX models (Self-Exciting Threshold Auto Regressive models with eXogenous regressors). In this way, parameter estimates are not, or very lightly, influenced by the presence of extreme observations and the large majority of prices, which are not spikes, could be better forecasted. A Monte Carlo study is carried out in order to select the best weighting function for Generalized M-estimators of SETAR processes. A robust procedure to select and estimate nonlinear processes for electricity prices is introduced, including robust tests for stationarity and nonlinearity and robust information criteria. The application of the procedure to the Italian electricity market reveals the forecasting superiority of the robust GM-estimator based on the polynomial weighting function with respect to the non-robust Least Squares estimator. Finally, the introduction of generation from renewable sources in the robust estimation of SETARX processes contributes to the improvement of the forecasting ability of the model.

A study on forecasting electricity production and consumption in smart cities and factories

The electrical power sector must undergo a thorough metamorphosis to achieve the ambitious targets in greenhouse gas reduction set forth in the Paris Agreement of 2015. Reducing uncertainty about demand and, in case of renewable electricity generation, supply is important for the determination of spot electricity prices. In this work we propose and evaluate a context-based technique to anticipate the electricity production and consumption in buildings. We focus on a household with photovoltaics and energy storage system. We analyze the efficiency of Markov chains, stride predictors and also their combination into a hybrid predictor in modelling the evolution of electricity production and consumption. All these methods anticipate electric power based on previous values. The main goal is to determine the best method and its optimal configuration which can be integrated into a (possibly hardware-based) intelligent energy management system. The role of such a system is to adjust and synchronize through prediction the electricity consumption and production in order to increase self-consumption, reducing thus the pressure over the power grid. The experiments performed on datasets collected from a real system show that the best evaluated predictor is the Markov chain configured with an electric power history of 100 values, a context of one electric power value and the interval size of 1.

Modeling the Electricity Spot Price with Switching Regime Semi-Nonparametric Distributions

Spot prices of electricity in liberalized markets feature seasonality, mean reversion, random short-term jumps, skewness and highly kurtosis, as a result from the interaction between the supply and demand and the physical restrictions for transportation and storage. To account for such stylized facts, we propose a stochastic process with a component of mean reversion and switching regime to represent the dynamics of the spot price of electricity and its logarithm. The short-term movements are represented by semi-nonparametric (SNP) distributions, in contrast to previous studies that traditionally assume Gaussian processes. The application is done for the Colombian electricity market, where El Nino phenomenon represents an additional source of risk that should be considered to guarantee long-term supply, sustainability of investments and efficiency of prices. We show that the switching regime model with SNP distributions for the random components outperforms traditional models leading to accurate estimates and simulations, and thus being a useful tool for risk management and policy making.

Uncertainty in Electricity Markets from a Seminonparametric Approach

The spot price of electricity is highly skewed and heavy-tailed, as a result of the interaction of different variables that affect that market. Such characteristics impact the design of power plants with different technologies, fuel prices, and energy demand. This paper introduces the semi-non-parametric (SNP) approach to describe the uncertainty of different variables in an electricity market, reducing the limitations that normality and parametric density functions impose. The selection of probability density functions is achieved in terms of a finite Gram-Charlier expansion fitted by the maximum likelihood criterion. The study case is the Colombian electricity market, where the SNP distribution outperforms the normal distribution for spot price, national energy demand, the climate index ONI, and the series of hydrologic inflows of the system and some rivers. The results show that risk analysis in electricity markets requires the measurement of skewness, kurtosis, and high-order moments. The flexible methodology in our study has directly applications for implementing policies on electricity markets that improve the sustainability indicators of different systems. The particular characteristics of the series under analysis should be considered as a starting point for risk analysis and portfolio choice.

A Hybrid Regression Model for Day-Ahead Energy Price Forecasting

Accurate forecast of the hourly spot price of electricity plays a vital role in energy trading decisions. However, due to the complex nature of the power system, coupled with the involvement of multi-variable, the spot prices are volatile and often difficult to forecast. Traditional statistical models have limitations in improving forecasting accuracies and reliably quantifying the spot electricity price under uncertain market conditions. This paper presents a hybrid model that combines the results from multiple linear regression (MLR) model with an auto-regressive integrated moving average (ARIMA) and Holt-Winters models for better forecasts. The proposed method is tested for the Iberian electricity market data set by forecasting the hourly day-ahead spot price with dataset duration of 7, 14, 30, 90, and 180 days. The results indicate that the hybrid model outperforms the benchmark models and offers promising results under most of the testing scenarios.

Pricing Electricity Forwards under Future Information on the Stochastic Mean-Reversion Level

We extend the arithmetic multi-factor electricity spot price model proposed by Benth, Kallsen & Meyer-Brandis by adding stochastic mean-level processes to their model and by taking additional information on the future behavior of these mean-level processes into account. The available anticipative information is modeled by an initially enlarged filtration in our paper. We further derive pricing formulas for electricity forwards under future information and investigate the associated information premium.

Managing Volumetric Risk of Long-term Power Purchase Agreements

There exists a negative dependence between wind power production and electricity spot price. 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 using a new generation of 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 a previously published model of the ARMA-GARCH type. 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.

Bayesian estimation of stable CARMA spot models for electricity prices

We develop a Bayesian estimation procedure for the electricity spot price model in Benth et al. (2014). This model incorporates a trend and seasonality component, a stable CARMA process for the price spikes, and an additional Lévy process for mid-range price level changes. Our MCMC algorithm has two advantages over the existing stepwise estimation procedure presented in Benth et al. (2014): First, since our algorithm produces samples from the full posterior distribution over all parameters, we can estimate the parameters much more accurately, which is shown in simulation studies. Second, we can provide accuracy measures as credibility intervals in addition to the point estimates. The approach is quite general, so that it can be adapted also to other similar pricing models. For illustration, we analyse spot and future prices from the EEX using the new Bayesian method and provide estimates for the risk premium together with credibility regions.

A higher-order Markov chain-modulated model for electricity spot-price dynamics

Over the last three decades, the electricity sector worldwide underwent massive deregulation. Power market participants have encountered a growing number of challenges due to competition and other pertinent factors. For most markets at present, electricity is a non-storable commodity and its price is extremely sensitive to changes in supply and demand. The evolution of electricity prices exhibits pronounced mean reversion and cyclical patterns, possesses extreme volatility and relatively frequently occurring spikes, and manifests presence of memory property. These observed features necessitate the development of models aimed to simultaneously capture such price characteristics for forecasting, risk management, and valuation of electricity-driven derivatives. Majority of current research studies examining electricity spot prices are based on one-state models. Such models though may not accurately capture the stylised behaviours of price evolution, especially during periods of sudden spikes driven by the abrupt changes of market sentiments. This paper tackles the modelling and estimation problems under a new paradigm that integrates the deterministic calendar seasons and stochastic factors governing electricity prices with a regime-switching feature. The de-seasonalised component of our proposed model has both the jump and mean-reverting properties to account for spikes and periodic cycles alternating between lower price returns and compensating periods of higher price returns. The parameters of the de-seasonalised model components are also modulated by a higher-order hidden Markov chain (HOHMC) in discrete time. This provides a mechanism to extract latent information from historical data. The HOHMC’s state is interpreted as the “state of the world” resulting from the interaction of various forces impacting the electricity market. Filters are developed to generate optimal estimates of HOHMC-relevant quantities using the observation process, and these provide online estimates of model parameters. Empirical demonstrations using the daily electricity spot prices, compiled by the Alberta Electric System Operator (AESO), show that our HOHMM approach has considerable merits in terms of price data fitting and forecasting metrics. Our proposed framework driven by a hidden Markov chain with a state memory-capturing mechanism provides a powerful alternative to support the pricing of contracts in the electricity markets.

Forecasting performance of time series models on electricity spot markets

PurposeStudy conditions of empirical publications on time series modeling and forecasting of electricity prices vary widely, making it difficult to generalize results. The key purpose of the present study is to offer a comparison of different model types and modeling conditions regarding their forecasting performance.Design/methodology/approachThe authors analyze the forecasting performance of AR (autoregressive), MA (moving average), ARMA (autoregressive moving average) and GARCH (generalized autoregressive moving average) models with and without the explanatory variables, that is, power consumption and power generation from wind and solar. Additionally, the authors vary the detailed model specifications (choice of lag-terms) and transformations (using differenced time series or log-prices) of data and, thereby, obtain individual results from various perspectives. All analyses are conducted on rolling calibrating and testing time horizons between 2010 and 2014 on the German/Austrian electricity spot market.FindingsThe main result is that the best forecasts are generated by ARMAX models after spike preprocessing and differencing the data.Originality/valueThe present study extends the existing literature on electricity price forecasting by conducting a comprehensive analysis of the forecasting performance of different time series models under varying market conditions. The results of this study, in general, support the decision-making of electricity spot price modelers or forecasting tools regarding the choice of data transformation, segmentation and the specific model selection.

Forecasting electricity spot price for Nord Pool market with a hybridk‐factor GARMA–LLWNN model

AbstractThis paper proposes a new hybrid approach, based on the combination of parametric and nonparametric models by adopting wavelet estimation approach, to model and predict the price electricity for Nord Pool market. Our hybrid methodology consists into two steps. The first step aims at modeling the conditional mean of the time series, using a generalized fractional model withk‐factor of Gegenbauer termed thek‐factor GARMA model; the parameters of this model are estimated using the wavelet approach based on the discrete wavelet packet transform (DWPT). The second step aims at estimating the conditional variance, so we adopt the local linear wavelet neural network (LLWNN) model. The proposed hybrid model is tested using the hourly log‐returns of electricity spot price from the Nord Pool market. The empirical results were compared with the predictions of the ARFIMA–LLWNN, thek‐factor GARMA–FIGARCH and the individual LLWNN models. It is shown that the proposed hybridk‐factor GARMA–LLWNN model outperforms all other competing methods. Hence it is a robust tool in forecasting time series.

Managing electricity price modeling risk via ensemble forecasting: The case of Turkey

There are two ways of managing market price risk in electricity day ahead markets, forecasting and hedging. In emerging markets, since hedging possibilities are limited, forecasting becomes the foremost important tool to manage spot price risk. Despite the existence of great diversity of spot price forecasting methods, due to the unique characteristics of electricity as a commodity, there are still three key forecasting challenges that a market participant has to take into account: risk of selection of an inadequate forecasting method and transparency level of the market (availability level of public data) and country-specific multi-seasonality factors. We address these challenges by using a detailed market-level data from the Turkish electricity day-ahead auctions, which is an interesting research setting in that it presents a number of challenges for forecasting. We reveal the key distinguishing features of this market quantitatively which then allow us to propose individual and ensemble forecasting models that are particularly well suited to it. This forecasting study is pioneering for Turkey as it is the very first to focus specifically on electricity spot prices since the country's day-ahead market was established in 2012. We also suggested applicable policy and managerial implications for both regulatory bodies, market makers and participants.

Economic Evaluation of Maintenance Strategies for Offshore Wind Turbines Based on Condition Monitoring Systems

An offshore wind farm’s cost of energy is, to a large extent, driven by operation and maintenance costs. Through the optimization of the maintenance strategies for offshore wind farms, the Levelized Cost of Energy (LCOE) will be further reduced, which will ceteris paribus lead to a higher competitiveness of offshore wind farms with other energy sources. This study pro-poses an event-based simulation of an offshore wind farm comprising 400 MW. The aim of the model is to minimize the total cost, and thus to maximize the revenues from the wind farm. Therefore, corrective, condition-based, and scheduled maintenance strategies are compared, and constraints, such as weather conditions and service team shifts, are taken into consideration. When hourly electricity spot prices are applied instead of feed-in tariffs, results show that weekly scheduled maintenance on a Saturday dayshift (starting at 8 am) is the most cost-efficient scenario. Condition monitoring systems have been found to be advantageous and are set as a standard application regarding the turbines. The impact of scheduled maintenance frequency, the distance between the offshore site and the coast, the interest rate, and altering reliability data are further analyzed.

Analysis of Distribution Locational Marginal Prices

Low-voltage distribution networks are emerging as an increasingly important component of power system operations due to the deployment of distributed renewable resources (e.g., rooftop solar supply) and the need to mobilize the flexibility of consumers that are connected to the low-voltage grid. The pricing of electric power at distribution nodes follows directly from the theory of spot pricing of electricity. However, in contrast to linearized lossless models of transmission networks, an intuitive understanding of prices at the distribution level presents challenges due to voltage limits, reactive power flows, and losses. In this paper, we present three approaches toward understanding distribution locational marginal prices by decomposing them: 1) through a duality analysis of the problem formulated with a global power balance constraint; 2) through a duality analysis of a second-order cone program relaxation; and 3) through an analysis of the impact of marginal losses on price. We discuss the relative strengths and weaknesses of each approach in terms of computation and physical intuition, and demonstrate the concepts on a 15-bus radial distribution network.

Structural price model for coupled electricity markets

We propose a new structural model that can compute the electricity spot and forward prices in two coupled markets with limited interconnection and multiple fuels. We choose a structural approach in order to represent some key characteristics of electricity spot prices such as their link to fuel prices, consumption level and production fleet. With this model, explicit formulas are also available for forward prices and other derivatives. We give some illustrative results of the behaviour of spot, forward and transmission rights prices.

Econometric modeling of regional electricity spot prices in the Australian market

Wholesale electricity markets are increasingly integrated via high voltage interconnectors, and inter-regional trade in electricity is growing. To model this, we consider a spatial equilibrium model of price formation, where constraints on inter-regional flows result in three distinct equilibria in prices. We use this to motivate an econometric model for the distribution of observed electricity spot prices that captures many of their unique empirical characteristics. The econometric model features supply and inter-regional trade cost functions, which are estimated using Bayesian monotonic regression smoothing methodology. A copula multivariate time series model is employed to capture additional dependence — both cross-sectional and serial — in regional prices. The marginal distributions are nonparametric, with means given by the regression means. The model has the advantage of preserving the heavy right-hand tail in the predictive densities of price. We fit the model to half-hourly spot price data in the five interconnected regions of the Australian national electricity market. The fitted model is then used to measure how both supply and price shocks in one region are transmitted to the distribution of prices in all regions in subsequent periods. Finally, to validate our econometric model, we show that prices forecast using the proposed model compares favorably with those from some benchmark alternatives.

Stochastic Modeling of Wind Derivatives in Energy Markets

We model the logarithm of the spot price of electricity with a normal inverse Gaussian (NIG) process and the wind speed and wind power production with two Ornstein–Uhlenbeck processes. In order to reproduce the correlation between the spot price and the wind power production, namely between a pure jump process and a continuous path process, respectively, we replace the small jumps of the NIG process by a Brownian term. We then apply our models to two different problems: first, to study from the stochastic point of view the income from a wind power plant, as the expected value of the product between the electricity spot price and the amount of energy produced; then, to construct and price a European put-type quanto option in the wind energy markets that allows the buyer to hedge against low prices and low wind power production in the plant. Calibration of the proposed models and related price formulas is also provided, according to specific datasets.

An economic feasibility assessment of decoupled energy storage in the UK: With liquid air energy storage as a case study

This work assesses the economic feasibility of adopting decoupled energy storage technologies in the UK, using a methodology to optimize the size of individual components for charging, storing and discharging energy. Such technologies, including pumped hydro and compressed air energy storage, are likely to become more important in the future energy system. In this paper we consider liquid air energy storage as a case study - a technology that has the potential to provide multiple balancing and ancillary services to the electricity grid, as well as to obtain revenues through energy price arbitrage. Based on the UK’s half-hourly electricity spot price in 2015, the developed numeric model calculates the revenue streams of a liquid air energy storage system from providing reserve service and arbitrage every half hour. Results from the genetic algorithm give the optimal sizes for the liquefaction, storage and recovery units, to maximize the net present value and allow us to calculate other economic objectives. Our model results suggest that the profitability of a liquid air energy storage system can be improved by either introducing waste heat into the system or increasing system scale. The payback period could vary from 25.7 years to 5.6 years for a 200 MW system, with the use of waste heat ranging from 0 °C to 250 °C.

Photovoltaic and wind power feed-in impact on electricity prices: The case of Germany

The aim of the paper is to quantify the impact of increasing renewable energy sources (RES), especially wind generation and photovoltaic feed-in, on electricity prices in Germany, with a view to investigating the well-known merit order effect.To explore the dynamics of the merit order effect at an hourly resolution, we use the SURE methodology for carrying out an empirical analysis based on hourly historical data for the Germany electricity market between 2012 and 2015.Our main empirical findings confirm that increasing the share of wind generation and photovoltaic feed-in induces a sharp fall in electricity spot prices. Moreover, this impact varies throughout the 24 h of the day due to the dynamics of electricity demand and the intermittency of wind and solar photovoltaic feed-in.

Research on Cointegration Relationship Between the Electric Spot Markets and Future Markets

The electricity market is a complex nonlinear system, which not only follows the basic rules of market economy, but also is affected by the power system. This paper considers the non-stationarity of electricity futures and spot electricity price, and puts forward a forecasting model of futures electricity price by means of a cointegration theory to carry out an empirical research on the dynamic relationship between the electric spot markets and future markets. The research results show that there is a long-term equilibrium cointegration relationship between the spot electricity price and futures electricity price, and the combination of long-term relationship and short-term dynamic in time series of electricity price is realized, and a higher forecasting accuracy is obtained.