Electricity Price Model Research Articles

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.

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.

Research on strategy about time‐of‐use pricing and economic operation of power supplier based on Stackelberg game

Demand-side management is an important method to improve the stability of power consumption and the reliability of power grid. In Energy Internet, the power supplier can obtain more detailed data about users' behaviour with numerous smart devices and advanced information network. Here, the utility function of power supplier is established by using the utility function of different users at different times, explicitly taking into account the economic operation's impact. The authors propose a Stackelberg game model to formulate the gaming process between users and power supplier. The authors convert the model into a convex problem to maximum power supplier's benefit, and then calculate the corresponding optimal time-of-use prices, and optimal economic operation power. The simulation results show that the model is effective and has a better result than the traditional profit-only model and non-time-of-use electricity pricing model.

A hybrid model for electricity price forecasting based on least square support vector machines with combined kernel

With the continuous development of the global electricity market, the electricity market needs the electricity price forecasting result to be accurate, and electricity price forecasting also has more profound practical significance. Accurate price forecasting can not only better reflect the operation of the electricity market but also help to make better decisions about the electricity market. However, the electricity price is affected by a variety of uncertain subjective and objective factors, as well as the constraints of the power system, making it more difficult to obtain accurate electricity price forecasting than electricity load forecasting. The kernel function occupies a very important position in a support vector machine (SVM), which is the key to the mature development of SVM theory. When using SVM for classification and regression, the appropriate kernel function is the basis and precondition for obtaining better classification and approximation effects. In this paper, a new combinatorial kernel function that combines RBF and UKF kernel functions is proposed and is applied to a least squares support vector machine (LSSVM), and based on this, a new hybrid model empirical mode (EMD)-Mixed-LSSVM is proposed to forecast electricity price. The hybrid model puts the electricity price data after the noise reduction by the EMD into the LSSVM with the combined kernel function for calculation. In this paper, we forecast the electricity price in Australia and compare the results of EMD-Mixed-LSSVM with other methods. The results show that EMD-Mixed-LSSVM can effectively improve the accuracy of electricity price forecasting.

Study on the Matrix Model of Electricity and Electricity Price

Electric vehicles change the charging time of electric vehicles according to the change of electricity price, so that the electric vehicle can be transferred as a load. The solution of electricity price is different, and its essence is based on definition. The change of electricity price has changed the influence of consumers on electricity demand. It is necessary to study and formulate TOU price according to the actual situation. In this paper, the solution of the power tariff matrix is deeply analyzed, which provides a theoretical basis for the study of TOU price and has practical significance.

Non-linear Pass-Through of the CO2 Emission-Allowance Price onto Wholesale Electricity Prices

This article considers the evidence for threshold effects in the relationship between electricity and emission-permit prices in France and Germany during the second phase of the EU ETS. Specifically, we compare linear and non-linear threshold models of electricity prices using the sample-splitting and threshold estimation approach in Hansen (Econometrica, 64 575–603 2000). We find evidence of non-linear threshold effects in both countries. The estimated carbon-price thresholds are 14.94€ and 12.57€ in France and Germany respectively. The carbon-price threshold in France perfectly matches the well-known carbon spot-price structural break of October 2008. This is not the case for the carbon-price threshold in Germany. Further analysis reveals that carbon prices before October 2008 were not reflected in electricity prices in either country. This is mainly due to uncertainty about the future of the EU ETS that led electricity producers to adopt a wait-and-see attitude. After October 2008, French electricity producers passed the price of emission permits through to electricity prices in a linear way, while their German counterparts did so non-linearly. Finally, we suggest improvements to the design of the EU ETS. Our recommendations are to strengthen the price signal to make it more clear and reliable and provide sufficient incentives for energy transition.

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.

Impact of renewable energy (hydro) on electricity prices in Ghana: A tale of the short- and long-run

This study examines the dynamic effects of a hydro-based technology on electricity prices in Ghana. As a counterfactual model, this article also examines the dynamic effects of a thermal-based technology on electricity prices. Given the significance of total electricity expenditure in national and household final consumption expenditure, the findings have important implications on economic-wide welfare. To do this, we estimate a dynamic electricity price model based on the autoregressive distributed lag model. The findings reveal that, the effect of hydro on electricity price is dynamic in nature, and the technology provides better cost advantages than the thermal technology, in terms of reducing end-user tariffs. Though there is an associated risk with relying on the former which could impose a higher cost in the short-term, in the long-term, the effect seems to vanish. Further results show that, the positive pass-through effect of interest rate, exchange rate, and crude oil price to electricity price is gradual and materialises in the long-term. In sum, the task of achieving lower electricity tariffs in the country is multifaceted. Investment in a hydro-based renewable technology is critical as well as investment in demand-side management options. Moreover, prudent macroeconomic policies and structural amendments of the automatic price adjustment formulae are also critical.

A scenario-based optimization of Smart Energy Hub operation in a stochastic environment using conditional-value-at-risk

Besides increasing the installation of distributed generation plants, investigation on multi-carrier energy systems leads recent studies to focus on several aspects of Smart Energy Hub (S. E. Hub) systems. An S. E. Hub incorporates several modules which calculation of optimal size and operation of each have already attracted a great deal of research. Uncertainty in the modeling of these modules is an imperative factor that was not paid attention in S. E. Hub models properly. To build up a more precise framework for S. E. Hubs, here we present a stochastic model for real time electricity and natural-gas prices and electricity demands. In this paper, an S. E. Hub operates in order to minimize a weighted sum function consisting energy bill and penalty for emissions. To have more precise model, we use conditional value at risk (CVaR) technique to control the operational risk of an S. E. Hub when electricity and natural gas are converted to electrical, heating, and cooling energy in its output ports. The proposed optimization method is validated by simulating it on a real office building in Tehran, Iran.

Performance of Electricity Price Forecasting Models: Evidence from Turkey

ABSTRACTIn this article, hourly prices of the Turkish Day Ahead Electricity Market are forecasted by using various univariate electricity price models, then the out-of-sample forecasts are compared with each other and the benchmarks. This article has two main contributions to the literature: Firstly, it provides a factorial Analysis of Variance (ANOVA) as a pre-whitening method of the price series and allows one to work with the stationary residuals series. Secondly, it is the first work, which compares the performances of all important statistical univariate forecast models in the Turkish electricity market. Results indicate the importance of the factorial ANOVA application and the SARIMA model’s success under the given conditions.

Short-Term Electricity Price Forecasting Based on Grey Prediction GM(1,3) and Wavelet Neural Network

Electricity price is a core index that reflects the operation status of the power market, evaluates the efficiency of market competition, and is the basis for decision-making in the electricity market. Electricity price forecasting is of great significance to guide investment, allocate market resources spontaneously, achieve a basic balance of power supply and demand, and meet various service goals. In this paper, a short-term electricity price forecasting method based on a grey forecasting GM(1,3) and wavelet neural network combination model is adopted. Firstly, the power price sequence is decomposed and reconstructed by using the famous MALLAT algorithm of multi-resolution analysis based on wavelet transform theory, and then the final predictive electricity price sequence is obtained by using the BP neural network model. Then the predicted electricity price sequence is used as a relevant factor affecting the future daily electricity price and input to the grey GM(1,3) forecasting model for electricity price forecasting to obtain the final forecasting result. The model training and forecasting based on the 2012 load and price data published by the PJM power market in the United States show that the prediction model established by this method has higher prediction accuracy. Thus, it has important research significance for electricity market price forecasting.

Внешние и внутренние детерминанты рынка электроэнергии: мультимасштабный адаптивный каузальный анализ

The goal of this study is to identify the causal relationships between the electricity price, its demand and the coal price on different time-scales for three markets: the zone Europe-Ural (EU) and Siberia (SI) of the Russian market ATS, and the English market - APX Power UK. The used methodology - multi-scale adaptive causal analysis - includes empirical mode decomposition and Granger causality test. This allows the drilling from the research on the source data level to a more detailed level of the time-series components. Our results show that such well-known stylized facts, as the impact of demand weekly seasonality to the electricity price and co-directional long-term movement of electricity prices and the primary fuels prices is confirmed for ATS EU and APX markets, while for ATS SI we did not find sufficient evidence of these. In practical terms, this suggests the need to take into account various factors for the construction of electricity price models for forecasting and risk management in these markets.

Forecasting performance of time series models on electricity spot markets: a quasi-meta-analysis

PurposeEmpirical publications on the time series modeling and forecasting of electricity prices vary widely regarding the conditions, and the findings make it difficult to generalize results. Against this background, it is surprising that there is a lack of statistics-based literature reviews on the forecasting performance when comparing different models. The purpose of the present study is to fill this gap.Design/methodology/approachThe authors conduct a comprehensive literature analysis from 2000 to 2015, covering 86 empirical studies on the time series modeling and forecasting of electricity spot prices. Various statistics are presented to characterize the empirical literature on electricity spot price modeling, and the forecasting performance of several model types and modifications is analyzed. The key issue of this study is to offer a comparison between different model types and modeling conditions regarding their forecasting performance, which is referred to as a quasi-meta-analysis, i.e. the analysis of analyses to achieve more general findings independent of the circumstances of single studies.FindingsThe authors find evidence that generalized autoregressive conditional heteroscedasticity models outperform their autoregressive–moving-average counterparts and that the consideration of explanatory variables improves forecasts.Originality/valueTo the best knowledge of the authors, this paper is the first to apply the methodology of meta-analyses in a literature review of the empirical forecasting literature on electricity spot markets.

A Novel Hybrid BND-FOA-LSSVM Model for Electricity Price Forecasting

Accurate electricity price forecasting plays an important role in the profits of electricity market participants and the healthy development of electricity market. However, the electricity price time series hold the characteristics of volatility and randomness, which make it quite hard to forecast electricity price accurately. In this paper, a novel hybrid model for electricity price forecasting was proposed combining Beveridge-Nelson decomposition (BND) method, fruit fly optimization algorithm (FOA), and least square support vector machine (LSSVM) model, namely BND-FOA-LSSVM model. Firstly, the original electricity price time series were decomposed into deterministic term, periodic term, and stochastic term by using BND model. Then, these three decomposed terms were forecasted by employing LSSVM model, respectively. Meanwhile, to improve the forecasting performance, a new swarm intelligence optimization algorithm FOA was used to automatically determine the optimal parameters of LSSVM model for deterministic term forecasting, periodic term forecasting, and stochastic term forecasting. Finally, the forecasting result of electricity price can be obtained by multiplying the forecasting values of these three terms. The results show the mean absolute percentage error (MAPE), root mean square error (RMSE) and mean absolute error (MAE) of the proposed BND-FOA-LSSVM model are respectively 3.48%, 11.18 Yuan/MWh and 9.95 Yuan/MWh, which are much smaller than that of LSSVM, BND-LSSVM, FOA-LSSVM, auto-regressive integrated moving average (ARIMA), and empirical mode decomposition (EMD)-FOA-LSSVM models. The proposed BND-FOA-LSSVM model is effective and practical for electricity price forecasting, which can improve the electricity price forecasting accuracy.

A Joint Model for Electricity Spot Prices and Wind Penetration with Dependence in the Extremes

This article analyses the dependence between electricity spot prices and the wind penetration index in the European energy market. The wind penetration index is given by the ratio of the wind energy production divided by the total electricity production. We find that the wind penetration has an impact on the intensity of the spike occurrences in the electricity prices, and we formulate a joint model for electricity prices and wind penetration and calibrate it to recent data. We then use the new joint model in an application where we assess the impact of the modelling assumptions on the potential income of an electricity distributor who buys electricity from a wind farm operator.

Electricity price subsidy or carbon-trading subsidy: which is more efficient to develop photovoltaic power generation from a government perspective?

Photovoltaic (PV) power generation has high investment costs and long payback periods. Therefore, during early deployment, subsidies are fundamental and necessary to accelerate its development. We consider the question of how to promote PV industry development and which supporting policy is more efficient in accelerating adoption. Based on real options method, we establish a subsidy efficiency model for electricity price subsidies and carbon-trading subsidies under two sources of uncertainty power demand for PV and the investment cost-reduction probability. This study aims to compare the two forms of subsidies from the perspective of promoting immediate investment and maximizing the subsidy policy efficiency for the government (minimizing the unit carbon-mitigation cost) and advance relevant policy proposals. An example of China is provided to test the effectiveness of the model and to illustrate the implications of the solutions. The results show that a carbon-trading subsidy is better than an electricity price subsidy and that it is essential to improve the demand for the power produced by the PV power-generation projects. Lower market risk and driving technology progress are both conducive to improving the subsidy efficiency. This study also provides a meaningful reference for governments worldwide to formulate subsidy programs to support PV power-generation projects.

A space-time random field model for electricity forward prices

Abstract Stochastic models for forward electricity prices are of great relevance nowadays, given the major structural changes in the market due to the increase of renewable energy in the production mix. In this study, we derive a spatio-temporal dynamical model based on the Heath-Jarrow-Morton (HJM) approach under the Musiela parametrization, which ensures an arbitrage-free model for electricity forward prices. The model is fitted to a unique data set of historical price forward curves. As a particular feature of the model, we disentangle the temporal from spatial (maturity) effects on the dynamics of forward prices, and shed light on the statistical properties of risk premia, of the noise volatility term structure and of the spatio-temporal noise correlation structures. We find that the short-term risk premia oscillates around zero, but becomes negative in the long run. We identify the Samuelson effect in the volatility term structure and volatility bumps, explained by market fundamentals. Furthermore we find evidence for coloured noise and correlated residuals, which we model by a Hilbert space-valued normal inverse Gaussian Levy process with a suitable covariance functional.

Periodic Heteroskedastic RegARFIMA Models for Daily Electricity Spot Prices

Although the main interest in the modelling of electricity prices is often on volatility aspects, we argue that stochastic heteroskedastic behaviour in prices can only be modelled correctly when the conditional mean of the time series is properly modelled. In this paper we consider different periodic extensions of regression models with autoregressive fractionally integrated moving average disturbances for the analysis of daily spot prices of electricity. We show that day-of-the-week periodicity and long memory are important determinants for the dynamic modelling of the conditional mean of electricity spot prices. Once an effective description of the conditional mean of spot prices is empirically identified, focus can be directed towards volatility features of the time series. For the older electricity market of Nord Pool in Norway, it is found that a long memory model with periodic coefficients is required to model daily spot prices effectively. Further, strong evidence of conditional heteroskedasticity is found in the mean corrected Nord Pool series. For daily prices at three emerging electricity markets that we consider (APX in The Netherlands, EEX in Germany and Powernext in France) periodicity in the autoregressive coefficients is also established, but evidence of long memory is not found and existence of dynamic behaviour in the variance of the spot prices is less pronounced. The novel findings in this paper can have important consequences for the modelling and forecasting of mean and variance functions of spot prices for electricity and associated contingent assets.

Forecasting Models of Electricity Prices

This book contains the successful invited submissions [1,2,3,4,5,6,7,8,9,10,11] to a Special Issue of Energies on the subject area of “Forecasting Models of Electricity Prices”.

Electricity price modeling with stochastic time change

In this paper, we develop a novel approach to electricity price modeling, based on the powerful technique of stochastic time change. This technique allows us to incorporate the characteristic features of electricity prices (such as seasonal volatility, time varying mean reversion and seasonally occurring price spikes) into the model in an elegant and economically justifiable way. The stochastic time change introduces stochastic as well as deterministic (e.g., seasonal) features in the price process' volatility and in the jump component.We specify the base process as a mean reverting jump diffusion and the time change as an absolutely continuous stochastic process with seasonal component. The activity rate of the stochastic time change can be related to the factors that influence supply and demand. Here we use the temperature as a proxy for the demand and hence, as the driving factor of the stochastic time change, and show that this choice leads to realistic price paths. We derive properties of the resulting price process and develop the model calibration procedure. We calibrate the model to the historical EEX power prices and apply it to generating realistic price paths by Monte Carlo simulations. We show that the simulated price process matches the distributional characteristics of the observed electricity prices in periods of both high and low demand.