Electricity Spot Prices Research Articles

Stochastic approach to model spot price and value forward contracts on energy markets under uncertainty

The paper deals with a model of electricity spot prices. The proposed dynamics of electricity spot prices is driven by a mean reverting diffusion with jumps having hyperexponential distribution. The analytical formula for the forward contract’s price is derived in a crisp case. Inasmuch as the model parameters are considered to be evaluated imprecisely, their fuzzy counterparts are introduced. With usage of the fuzzy arithmetic, the analytical expression for the forward contract’s price is derived. Several numerical examples highlighting attributes of the fuzzy forward electricity prices are brought out.

ELECTRICITY PRICE FUNDAMENTALS IN HYDROTHERMAL POWER GENERATION MARKETS USING MACHINE LEARNING AND QUANTILE REGRESSION ANALYSIS

A hydrothermal power generation market is characterized by a strong dependence on water reservoir capacity and fossil fuel sources, which causes differences in generation marginal costs and high variability of the electricity spot price. Therefore, this study proposes an empirical approach to identify the price determinants and their effects on price dynamics. This paper presents two methodologies: a machine learning approach and a quantile regression analysis. The first method is used to validate the price determinants through a prediction process, and the second, the quantile regression, to identify the non-linear effects. The most important factors observed are total market demand, water reservoirs capacity for generation, and fossil fuel consumption. The results offer a new perspective about the market structure and spot price volatility.Keywords: electricity prices; hydrothermal power generation markets; machine learning; quantile regression; Gaussian process regression.JEL Classifications: C22, Q41, Q43, Q47DOI: https://doi.org/10.32479/ijeep.11346

Electricity spot price modeling by multi-factor uncertain process: a case study from the Nordic region.

In recent years, the liberalization of energy markets (especially electricity) by many countries has led to much attention being paid to their modeling. The energy market modeling under the framework of probability theory is valuable when the distribution function is close enough to the actual frequency. However, due to the complexity and variability of the world, economic reasons and changing government policies, this assumption is not applicable in some cases. Under such circumstances, we propose an uncertain two-factor model based on uncertain differential equations to evaluate the electricity spot price dynamics. Then, several essential indicators of electricity are investigated and generalized moment estimation for unknown parameters is also provided. Two case studies by using electricity data from the Oslo and Stockholm regions illustrate our approach. We also compare the proposed model with one-factor uncertain model driven by Liu process and the electricity stochastic model. A detailed numerical study illustrates the efficiency of the proposed model to evaluate electricity spot prices.

A feature extraction- and ranking-based framework for electricity spot price forecasting using a hybrid deep neural network

In deregulated electricity markets, reliable electricity market price forecasting is the foundation for making the bidding strategy, operating dispatch control, and hedging volatility risk. However, electricity prices are high-volatile, nonstationary, multi-seasonal, making it difficult to estimate future trends. This paper proposes a hybrid model integrating a deep learning model, feature extraction and feature selection method to forecast short-term electricity prices. In the proposed framework, the ensemble empirical mode decomposition (EEMD) filter is utilized for multi-dimensional sequences, solving hidden characteristic extraction problems. The constructed feature space is identified and ranked under the max-dependency and min-redundancy (MRMR) criterion, improving the accuracy of feature selection. Finally, combining EEMD and MRMR with bidirectional long short-term memory (BiLSTM), a new hybrid framework is designed to improve the efficiency of short-term electricity price forecasting. Case studies on the PJM and New South Wales electricity markets confirm that our model outperforms alternatives on the forecasting accuracy. The average mean absolute percentage error (MAPE) of the proposed model is reduced by 4% to 21% compared to state-of-the-art models for 1-h and 24-h ahead forecasting. The proposed model has achieved relatively higher stability and adaptability in different forecasting steps and can better capture sophisticated fluctuations in electricity prices.

Statistical Analysis of Electricity Prices

The paper presents a statistical analysis of electricity spot prices in a deregulated market in New South Wales, Australia, in the period 10 May, 1996 – 7 March, 1998. It is unusual that a single set of data, such as this, allows one to consider a relatively systematic sequence of statistical problems, each resulting in clear, although not always obvious, solutions. This is the reason why these data and their analysis can be used as a rel atively good base for training in practical statistical analysis. Existing for merly as a report, the material has been used in lecture courses in several universities in Australia and New Zealand.

The effects of wind generation and other market determinants on price spikes

Electricity spot prices have shifted in response to increasing renewable energy infrastructure throughout the United States in recent decades. These shifts manifest as changes in the spot price mean and variance. One major factor influencing the variance of spot prices is the prevalence of price spikes. How renewables influence the magnitude and frequency of price spikes is not well understood. This study examines the influence of wind and additional determinants (load, nuclear generation, natural gas prices, as well as the load-to-capacity ratio) on electricity spot prices in the Electric Reliability Council of Texas system using a multiple regression mixture model framework. We focus on the influence of these determinants on the magnitude of spot prices within a low-price regime and a high-price regime, with the latter representative of price spikes. We also examine how system determinants influence the frequency of occurrence of each regime. We show that increases in wind generation drive average spot prices down in both the low and high price regime. However, system shortfalls of wind generation, particularly during times of high load, result in increased price magnitudes in both regimes, as well as more frequent price spike events.

Evaluation of a cross-border electricity interconnection: The case of Spain-France

This paper focuses on the economics of a cross-border transmission interconnector. The domestic spot electricity price is modelled as a stochastic process with mean reversion and jumps; it also includes a deterministic part that accounts for hourly and daily sasonalities along with non-working days. The two domestic spot prices are assumed to be correlated. As an illustration of the approach, we consider the particular case of the interconnector between Spain (an ‘electric island’) and France. Domestic prices are first calibrated and then used for simulating the stochastic behavior of the price gap between the two countries. In addition, the actual import/export behavior as a function of the price gap is captured by a Tobit model fitted from observed data. This model is then combined with the simulated price gaps to compute a multiple series of hourly prices and exports/imports of electricity through the interconnector. Drawing on these simulations we derive the probability distributions of revenues and expenses from exports and imports, and also some risk measures. According to our results, the economics of this interconector depends on different domestic seasonalities (hourly and daily), the growing trend of the price gap and some stochastic idiosyncrasies. They call for an expanded link.

The electricity production cost curve during extreme winter weather

This investigation analyzes the characteristics of the largest US wholesale electricity market’s production cost curve and supply curve during the most extreme winter weather event in modern meteorological history. The experience of this event demonstrates that the annual-summer-peak-centric nature of the Northeast US’ PJM capacity planning process does not address the adequacy of supply during the winter. The production cost curve is estimated and compared across recent winter season peak months to understand how large the price responsiveness to load changes can be during extreme winter weather events and how winter weather events can reduce system reliability for a summer-capacity-planning-centric power market. Therefore, PJM and other power pool markets have not considered secondary peak seasons in capacity planning. The shape of the production cost curve discussed herein is a critical component of the structural model and determinant of spot and forward market electricity prices.

The Effect of Mean-Reverting Processes in the Pricing of Options in the Energy Market: An Arithmetic Approach

In this paper we study the effect that mean-reverting components in the arithmetic dynamics of electricity spot price have on the price of a call option on a swap. Our model allows for seasonal effects, spikes, and negative values of the price of electricity. We show that for sufficiently large delivery periods of the swap contract, the error that one makes by neglecting some of the mean-reverting processes affecting the spot price evolution converges to zero. The decay rate is explicitly calculated. This is achieved by exploiting the additive structure of the electricity price process in order to determine an explicit closed-form formula for the price of the call on a swap. The theoretical analysis is then illustrated via a numerical example.

Estimation of time-varying autoregressive stochastic volatility models with stable innovations

A new time-varying autoregressive stochastic volatility model with $$\alpha $$ -stable innovations (TVAR $$\alpha $$ SV) is proposed. This new model for time series data combines a time-varying autoregressive component and a stochastic scaling as known from stochastic volatility models with $$\alpha $$ -stable distributed noise. Hence, the model can cover extreme events better than classical stochastic volatility models. Furthermore, we develop a Gibbs sampling procedure for the estimation of the model parameters. The procedure is based on the estimation strategy by Kim et al. (Rev Econ Stud 65(3): 361–393, 1998) for classical stochastic volatility models, however, the estimation procedure requires a deliberate approximation of $$\alpha $$ -stable distributions by finite mixtures of normal distributions and the application of a simulation smoother for linear Gaussian state space models. A simulation study for the new estimation procedure illustrates the appealing accuracy. Finally, we apply the model to electricity spot price data.

Optimal Hedging Strategies for Options in Electricity Futures Markets

In this paper, we derive optimal hedging strategies for options in electricity futures markets. Optimality is measured in terms of minimal variance and the associated minimal variance hedging portfolios are obtained by a stochastic maximum principle. Our explicit results are particularly useful for electricity retailers, who have sold an option to a client, and now want to hedge the payoff of this option by investing into an electricity futures and into the issued option itself. Another innovative aspect of the paper lies in the derivation of the time dynamics of the stochastic option price process by Malliavin calculus methods and the Clark-Ocone formula. We also apply our theoretical results to several practical examples. Our investigations are based upon the popular arithmetic multi-factor electricity spot price model proposed by Benth, Kallsen & Meyer-Brandis (Appl. Math. Finance 14(2):153-169, 2007).

Electricity price modelling with stochastic volatility and jumps: An empirical investigation

Over the past few years, the electricity derivatives market has experienced a substantial growth in the volume of trade and the diversity of available products. This has led to a rich data environment that requires more sophisticated and accurate modelling approaches for electricity spot prices. This paper deals with an analysis of continuous-time stochastic volatility jump-diffusion processes in the context of pricing of futures contracts written on electricity spots. We formulate a variety of models which aim to capture the most prominent characteristics and stylised facts of the electricity spot market including mean reversion, seasonality, extreme volatility, and spikes. The proposed modelling framework extends the existing models by incorporating mean reversion, stochastic volatility, and jumps in both the underlying spot price process and its volatility. The modelling parameters are estimated using the Markov Chain Monte Carlo (MCMC) technique for the Australian electricity market. We find that incorporating stochastic volatility and jumps in both the underlying electricity spot price and its volatility is absolutely essential to accurately fit the observed electricity spot prices. We derive futures prices in a semi-closed form and confirm flexibility of the proposed models by their ability to fit the observed spot and futures prices in the Australian electricity market.

Carbon pass-through rates on spot electricity prices in Australia

This study assesses the impact of the Australian Carbon Pricing Mechanism (CPM) on electricity prices in the National Electricity Market (NEM). An econometric model is designed to examine the influence of short-run marginal costs, electricity demand and emission intensities on carbon pass-through to spot electricity prices. Our sample period from July 2009 to June 2016 allows us to analyse three different sub-periods in order to quantify pass-through effects: the period before the CPM, the period when the pricing mechanism was effective, as well as the period after its repeal. Therefore, our study allows a comprehensive evaluation of the effect of carbon pricing on the Australian electricity spot market. Our results demonstrate a high degree of carbon costs pass-through across the considered markets, while the increase in electricity prices typically exceeds carbon costs, in particular for the markets in New South Wales, Queensland and South Australia. Furthermore, we find a negative relationship between carbon pass-through rates and emission intensities in the regional markets: pass-through rates were relatively low for Victoria that is characterised by electricity generation from fossil fuels and high emission intensities, while they were the highest for South Australia, a market with the lowest emission intensities and a higher share of renewable energy generation. We also find that for most markets, emission intensities were only reduced by a relatively small margin during the tax period and electricity prices have never reverted back to their pre-tax levels after the repeal of the tax. • The impact of the Carbon Pricing Mechanism (CPM) on Australian spot electricity prices is examined. • Results demonstrate that consumers were bearing the costs of carbon rather than generators. • Carbon costs pass-through estimates range from 100% to 290% across regional markets. • Evidence for a minor reduction in emission intensities during the CPM period is found. • Spot prices did not revert back to their pre-CPM levels after abolishment of the CPM.

Effective Management of Energy Consumption during the COVID-19 Pandemic: The Role of ICT Solutions

This research tackles effective and functional management practices in energy consumption using advanced technological solutions to mitigate unexpected events. This study specifically focuses on the recent COVID-19 pandemic that led to a reduction in energy consumption and therefore meddled with the project management’s status quo for the energy sources. Moreover, this research analyzes the role of information and communication technology (ICT) solutions in energy management before and after the recent coronavirus pandemic turmoil. This study also examined the role and place of sustainable energy resources in the effective management of energy consumption during the COVID-19 pandemic. The main purpose of this research is to demonstrate how the recent coronavirus pandemic affected energy consumption and energy prices in many countries and how it paved the way for the new ICT in managing energy consumption. This study elaborated a model to show how these changes evolved in selected European Union (EU) Member States. It turns out that adjusted electricity consumption, as well as the average daily spot electricity prices for the baseload power in the EU countries, declined, and this trend is likely to continue in the next years to come. Due to the COVID-19 pandemic, substantial changes in the economy led to reduced office space usage, cutting commuting and business trips, and bringing commercial travel almost to a halt, further shifting the energy balance towards renewable energy sources (RES). Besides, it becomes apparent that ICT solutions used in maintaining and superintending the energy balance are gaining popularity and wide recognition worldwide and will help pave the way towards modern and smart high-renewables grids.

A Multivariate High-Order Markov Model for the Income Estimation of a Wind Farm

The energy produced by a wind farm in a given location and its associated income depends both on the wind characteristics in that location—i.e., speed and direction—and the dynamics of the electricity spot price. Because of the evidence of cross-correlations between wind speed, direction and price series and their lagged series, we aim to assess the income of a hypothetical wind farm located in central Italy when all interactions are considered. To model these cross and auto-correlations efficiently, we apply a high-order multivariate Markov model which includes dependencies from each time series and from a certain level of past values. Besides this, we used the Raftery Mixture Transition Distribution model (MTD) to reduce the number of parameters to get a more parsimonious model. Using data from the MERRA-2 project and from the electricity market in Italy, we estimate the model parameters and validate them through a Monte Carlo simulation. The results show that the simulated income faithfully reproduces the empirical income and that the multivariate model also closely reproduces the cross-correlations between the variables. Therefore, the model can be used to predict the income generated by a wind farm.

Forward price and fitting of electricity Nord Pool market under regime-switching two-factor model

Jump in electricity prices is often due to shock in electricity demand or shock in existing electricity supplies, which can be caused by sudden changes in temperature or production and system failure. Since jumps in electricity dynamics are directly related to the regime switch, we model them via the chain itself and consider a regime switching model for electricity spot price dynamic. Next, we determine an equivalent measure by Esscher transform and through it we evaluate the electricity forwards and risk premium. We apply expectation maximization algorithm to estimate parameters of the model. Furthermore, we use the real data of Nord Pool market to calibration of the proposed model. Using the characteristic function of model, we obtain a closed-form for forward contracts of Nord Pool market. Finally, we provide forward surfaces which show the months, quarters and seasons-ahead prices.

Markets for Efficient Decarbonization: Revisiting Market Regulation and Design

In the 1980s, some seminal works such as markets for power: an analysis of Electric Utility Deregulation by Joskow and Schmalensee and Spot Pricing of Electricity by Schweppe et al. set the foundations for electric system restructuring toward a fully liberalized, marginal price-based market environment in which generators and end users trade. Even then, it was clear that the task was not going to be easy, but an increasingly and always significant portion of the industry and academic thought that it was at least possible. More than three decades after the first markets were implemented, the entire power sector community continues to discuss the suitability of relying on short-term market prices as an efficient signal to drive investments, especially in the current context in which not only traditional generators but also end users can decide to invest in energy supply resources, and an increasing amount of new generation investments have zero or close to zero variable costs, which some people see as a threat to the short-term market paradigm.

Electricity Spot Prices Forecasting Based on Ensemble Learning

Efficient modeling and forecasting of electricity prices are essential in today’s competitive electricity markets. However, price forecasting is not easy due to the specific features of the electricity price series. This study examines the performance of an ensemble-based technique for forecasting short-term electricity spot prices in the Italian electricity market (IPEX). To this end, the price time series is divided into deterministic and stochastic components. The deterministic component that includes long-term trends, annual and weekly seasonality, and bank holidays, is estimated using semi-parametric techniques. On the other hand, the stochastic component considers the short-term dynamics of the price series and is estimated by time series and various machine learning algorithms. Based on three standard accuracy measures, the results indicate that the ensemble-based model outperforms the others, while the random forest and ARMA are highly competitive.

Short-Term Forecasting for the Electricity Spot Prices With Extreme Values Treatment

Nowadays, modeling and forecasting electricity spot prices are challenging due to their specific features, including multiple seasonalities, calendar effects, and extreme values (also known as jumps, spikes, or outliers). This study aims to provide a comprehensive analysis of electricity price forecasting by comparing several outlier filtering techniques followed by various modeling frameworks. To this end, extreme values are first treated with five different filtering techniques and are then replaced by four different outlier replacement approaches. Next, the spikes-free series is divided into deterministic and stochastic components. The deterministic component includes long-term trend, yearly and weekly seasonalities, and bank holidays and is estimated through parametric and nonparametric approaches. On the other hand, the stochastic component accounts for the short-run dynamics of the price time series and is modeled using different univariate and multivariate models. The one-day-ahead out-of-sample forecast results for the Italian Power Exchange (IPEX), obtained for a whole year, suggest that the outliers pre-filtering give a high accuracy gain. In addition, multivariate modeling for the stochastic component outperforms univariate models.

Large scale and rooftop solar generation in the NEM: a tale of two renewables strategies

Solar generation has increased dramatically over recent years, breaking world records of meeting 100% of the electricity demand on occasion in Australia’s National Electricity Market (NEM). Solar output variability coupled with rooftop solar impact on demand as a behind-the-meter resource poses challenges to electricity price stability. Using 30-minute intraday data, we investigate how electricity spot prices are impacted by the rapid uptake of large-scale and rooftop solar generation in the NEM. We find that, on average, both large-scale and rooftop solar generation depress the level of spot prices and positively impact price volatility. However, over 30-minute intervals, we find that solar generation tends to increase electricity prices in the early morning and in the evening due to the high cost of traditional fossil-fuelled generators required to meet the lost output when the sun is below the horizon. While large-scale solar generation typically smooths spot price volatility, rooftop solar tends to increase it, reflecting the dominance of axis-tracking systems in the former and north-facing systems in the latter. The increasing incidences of variable renewable energy curtailment undermine the merit order effect in the middle of the day but with the benefit of reducing price variability. Moreover, solar generation impact on electricity prices differs substantially across seasons. Our results stress the need for policy adjustment to increase the correlation between solar output and electricity demand through small-scale renewable energy schemes and state-based policies, rooftop solar curtailment, dynamic feed-in tariffs, and two-sided market reform.