Electricity Spot Prices Research Articles

Spikes and Memory in (Nord Pool) Electricity Price Spot Prices

Electricity spot prices are subject to transitory sharp movements commonly referred to as spikes. The paper aims at assessing their effects on model based inferences and predictions, with reference to the Nord Pool power exchange. We identify a spike as a price value which deviates substantially from the normal price, where the latter is defined as the expectation arising from a model accounting for long memory at the zero and at the weekly seasonal frequencies, given the knowledge of the past realizations. Hence, a spike is associated to a time series innovation with size larger than a specified threshold. The latter regulates the robustness of the estimates of the underlying price level and it is chosen by a data driven procedure that focuses on the ability to predict future prices. The normal price is computed by a modified Kalman filter, which robustness the inferences by cleaning the spikes, i.e. shrinking an observation deviating substantially from the normal price towards the one-step-ahead prediction. Our empirical application illustrates the effects of the spikes on the estimates of the parameters governing the persistence of the series; moreover, a real time rolling forecasting exercise is used to establish the amount of cleaning for optimizing the predicting accuracy at different horizons.

Modeling Dependence between European Electricity Markets with Constant and Time-varying Copulas

This paper investigates the dependence between electricity spot markets at the heart of Europe including France, Germany, Austria and Switzerland based on copula models. Ten different copulas with both time invariant and varying parameters are considered. The empirical results show that time-varying Student-t copula is the best model to fit the sample data. The positive of upper and lower dependence indicates that spot electricity prices in France, Germany/Austria and Switzerland tend to move in the same direction. Also, the results indicate that the dependence between European electricity markets is time-varying and asymmetric, which means that traditional models such as Pearson’s correlation are inappropriate to measure the correlations between these markets.

The application of structural electricity models for dynamic hedging

We formulate a general structural model for an energy market in order to analyze the dynamic hedging of contingent claims on spot electricity prices. The electricity price is modeled endogenously using a deterministic function depending on a joint fuels and demand process. We state conditions on the fuels/demand dynamics and the bid stack function under which the electricity forwards are martingales. The martingale property allows us to derive hedging strategies. We find that for liquid power forward contracts our model implies cointegrated forwards. As power forward contracts are not always liquid, we construct an alternative hedging strategy where fuels are used to hedge power based on the marginal fuel according to the merit order of the market. As an example, we use the structural model of Carmona, Coulon and Schwarz and test the performance of our hedging strategies in case of a virtual power plant. Based on an hourly hedging profile, we state a result on how to come from an hourly forwards hedging strategy to a hedging strategy using exchange-traded futures (weekly, monthly, quarterly, etc).

Strategic capacity withholding through failures in the German-Austrian electricity market

In electricity day-ahead markets organized as uniform price auction, a small reduction in supply in times of high demand can cause substantial increases in price. We use a unique data set of failures of generation capacity in the German-Austrian electricity market to investigate the relationship between electricity spot prices and generation failures. Differentiating between strategic and non-strategic failures, we find a positive impact of prices on non-usable marginal generation capacity for strategic failures only. Our empirical analysis therefore provides evidence for the existence of strategic capacity withholding through failures suggesting further monitoring efforts by public authorities to effectively reduce the likelihood of such abuses of a dominant position.

Risk-averse portfolio selection of renewable electricity generator investments in Brazil: An optimised multi-market commercialisation strategy

Investment decisions in renewable energy sources such as small hydro, wind power, biomass and solar are frequently made in the context of enormous uncertainty surrounding both intermittent generation and the highly volatile electricity spot prices that are used for clearing of trades. This paper presents a new portfolio-based approach for selecting long-term investments in small-scale renewable energy projects and matching contracts for the sale of the resulting electricity. Using this approach, we have formulated a stochastic optimisation model that maximises a holding company's risk-averse measure of value. Using an illustrative example representative of investment decisions within the Brazilian electricity system, we investigate the sensitivity of the optimised portfolio composition and commercialisation strategy to contract prices in the free contracting environment and to the decision maker's attitude towards risk. The numerical results demonstrate it is possible to reduce significantly financial risks, such as the price-quantity risk, not only by exploiting the complementarity of the considered renewable sources generation profiles, but also by selecting the optimal mix of commercialisation contracts from different markets. We find that the multi-market strategy generally results in appreciably higher optimal value than single-market strategies and can be applied to a wide range of renewable generators and contracts.

Testing for Market Integration in the Australian National Electricity Market

The National Electricity Market was established in 1998 as a response to the overall liberalization and restructuring of the Australian electricity sector. The wholesale market integration effects of this establishment, however, remain to be systematically examined. We use econometric techniques based on pairwise unit root tests, cointegration analysis and a time varying coefficient model to study the extent of market integration in the physically interconnected regional markets based on daily electricity spot prices. The results from the pairwise unit root tests provide mixed evidence of price convergence while cointegration analysis does not reject the absence of persistent price differences across the physically interconnected regions. The results from the time-varying filtered coefficient model suggest that full market integration has not been achieved yet. We empirically show the presence of significant network losses and constraints across the interregional interconnectors in the NEM. Our findings suggest that convergence in generation and network ownership, coupled with harmonisation of network regulation and regulatory institutional framework, will be increasingly important factors in improving wholesale market integration across all energy-only markets as they experience an increase in the share of renewable energy.

Common long-range dependence in a panel of hourly Nord Pool electricity prices and loads

Equilibrium electricity spot prices and loads are often determined simultaneously in a day-ahead auction market for each hour of the subsequent day. Hence daily observations of hourly prices take the form of a periodic panel rather than a time series of hourly observations. We consider novel panel data approaches to analyse the time series and the cross-sectional dependence of hourly Nord Pool electricity spot prices and loads for the period 2000–2013. Hourly electricity prices and load data are characterized by strong serial long-range dependence in the time series dimension in addition to strong seasonal periodicity, and along the cross-sectional dimension, i.e. the hours of the day, there is a strong dependence which necessarily has to be accounted for in order to avoid spurious inference when focusing on the time series dependence alone. The long-range dependence is modelled in terms of a fractionally integrated panel data model and it is shown that both prices and loads consist of common factors with long memory and with loadings that vary considerably during the day. Due to the competitiveness of the Nordic power market the aggregate supply curve approximates well the marginal costs of the underlying production technology and because the demand is more volatile than the supply, equilibrium prices and loads are argued to identify the periodic power supply curve. The estimated supply elasticities are estimated from fractionally co-integrated relations and range between 0.5 and 1.17 with the largest elasticities being estimated during morning and evening peak hours.

Providing Utility to Utilities: The Value of Information Systems Enabled Flexibility in Electricity Consumption

As the transition to renewable energy sources progresses, the integration of such sources makes electricity production increasingly fluctuate. To contribute to power grid stability, electric utilities must balance volatile supply by shifting demand. This measure of demand response depends on flexibility, which arises as the integration of information systems in the power grid grows. The option to shift electric loads to times of lower demand or higher supply bears an economic value. Following a design science research approach, we illustrate how to quantify this value to support decisions on short-term consumer compensation. We adapt real options theory to the design—a strategy that IS researchers have used widely to determine value under uncertainty. As a prerequisite, we develop a stochastic process, which realistically replicates intraday electricity spot price development. With this process, we design an artifact suitable for valuation, which we illustrate in a plug-in electric vehicle scenario. Following the artifact’s evaluation based on historical spot price data from the electricity exchange EPEX SPOT, we found that real options analysis works well for quantifying the value of information systems enabled flexibility in electricity consumption.

Spatially Explicit Prediction of Wholesale Electricity Prices

Transmission constraints often limit the flow of electricity in a regional transmission network leading to strong interaction effects across different geographically distributed points within the system. In modern wholesale electricity markets, these transmission constraints lead to spatial patterns within the nodal electricity spot prices. This study exploits these spatial patterns to better predict spot prices within a wholesale electricity market. More specifically, we use the latest spatial panel data econometric models to compare within-sample and out-of-sample forecasts against nonspatial panel data models. The spatial panel data approach is explained by demonstrating a simple network optimization model. We find that a dynamic, spatial panel data model provides the best predictions within a forecasting error context. Our results may suggest that the spatial autocorrelation between node prices extends beyond the current market-defined zonal boundaries, which calls into question whether the zonal boundaries accurately reflect the congestion boundaries within the system.

Modeling Positive Electricity Prices with Arithmetic Jump-Diffusions

We propose a mean-reverting electricity spot price model of arithmetic jump-diffusion type yielding positive prices. Based on this approach, we derive the corresponding forward and futures price representations. We further discuss different choices for the stochastic mean level process and investigate the long-term behavior of the spot price. In the second part, we take future information available to the traders into account. The latter is modeled by initially enlarged filtrations with respect to (a) the mean level of the spot, (b) the driving diffusion component and (c) the jump term. We also derive forward and futures price representations under these enlarged filtrations. Finally, we consider the evaluation of options in the proposed models.

Natural Gas-Fired Power Plants Valuation and Optimisation Under Levy Copulas and Regime-Switching

In this work we analyse a stochastic control problem for the valuation of a natural gas power station while taking into account operating characteristics. Both electricity and gas spot price processes exhibit mean-reverting spikes and Markov regime-switches. The Levy regime-switching model incorporates the effects of demand-supply fluctuations in energy markets and abrupt economic disruptions or business cycles. We make use of skewed Levy copulas to model the dependence risk of electricity and gas jumps. The corresponding HJB equation is the non-linear PIDE which is solved by an explicit finite difference method. The numerical approach gives us both the value of the plant and its optimal operating strategy depending on the gas and electricity prices, current temperature of the boiler and time. The surfaces of control strategies and contract values are obtained by implementing the numerical method for a particular example.

Selected Research Methods

The purpose of this section on research methods and designs is to analyze the contemporary literature in the field of quantitative finance. Fifteen selected research articles were compared and contrasted on how to analyze hedging and price methods for financial assets. In addition, an investigation and evaluation of recent trends with research designs for the use in quantitative finance to develop and establish hedging and pricing techniques will be conducted. The first article investigates modeling asymmetric volatility in the context of research methods explored by Hassan. The second research study involves oil future prices and term structures, whereby understanding the permanent and transitory shocks in oil futures can be accomplished via a structural vector auto-regression model by Zha. The third article of inquiry is by Cao and Guo which involved delta hedging performance methodologies. In the fourth research study, Ankirchner and Heyne suggested how to use research methods using cross hedging with stochastic correlations. In the fifth article, Srinvasan investigated stock market volatility and used different volatility models that are GARCH-types. The sixth peer-review study investigated is by Menkhoff, which involves currency momentum and the use of moving averages. The seventh research article was about how to price currency options and the methods used to determine which volatility model performed the best proposed was by Manzur, Hoque, and Poitras. The eighth scholarly study, which was authored by Jiang, involves foreign exchange markets and the use of a vector error correction model.The ninth intellectual inquiry investigated was on tail risk management and some of the methodologies used when modeling with Value-at-Risk and conditional Value-at-Risk by Kayan, Lee, and Pornrojnangkool. The tenth article explores the hydroelectric power industry and how to incorporate a hedging strategy and test for performance by Fleten, Brathen, and Nissen-Meyer. The eleventh research study investigated was by Frikha and Lemaire involved the gas and electricity spot price using a multi-factor model that can present higher volatility markets. The twelfth scholarly article proposed was by Hinnerich which explores equity swaps and demonstrates how to incorporate a jump diffusion model to capture price dynamics. The thirteenth study relates to derivative pricing using a close-form approximation relying on series expansions by Kristensen and Mele. The fourteenth study in this section involves how to build a trading algorithm system by Moldovan, Moca, and Nitchi. The last article reviewed was by Viebig and Poddig, whereby extreme value theory and copula theory was considered as a way to model multivariate daily return distributions of hedge funds.In the conclusion section of this Depth component a discussion on the synthesis of the relevant research related to research design used in quantitative finance was conducted. Comments on how to approach the research design with a focus on establishing hedging and pricing strategies of financial assets was shown. The intent of this section was to explore some of the tools developed in statistical analysis that enable researchers in quantitative finance to evaluate different hedging and pricing strategies. With a better research design and the use of advanced statistical methods researchers and practitioners can evaluate their financial modeling performance more accurately.Within the conclusion section each of the fifteen research articles mentioned above will be summarized in the framework of research methods that can promote social change. In addition to the summary of these research studies, some questions are explored to provide possible investigational paths.

Risk Management and Portfolio Optimization for Gas- and Coal-Fired Power Plants in Germany: A Multivariate GARCH Approach

We investigate the hedging effectiveness of energy derivatives traded at the European Energy Exchange (EEX), which can be used for mitigating the risk exposure of gas- and coal-fired power plants in Germany. Our aim is to identify the optimum forward contract for simultaneously hedging power output and fuel input price risk. The optimum hedging contract for each commodity is identified with the help of a multivariate GARCH model (D-BEKK model). We find that it is more prudent to hedge the spot electricity and coal prices with long-term contracts, whereas for natural gas prices there is evidence that short-term futures enable higher hedging effectiveness. Further, with all futures contracts available we construct portfolios and compare the hedging performance with that of the individual futures contracts. More specifically, we first identify the point at which the combination of spot and forward prices gives the maximum reduction of risk exposure and then investigate the impact of time-varying risk premiums on the spot-forward price relationship. Finally, we compute portfolio weights for different risk levels that reveal the optimal mix of spot and futures contracts. The results show that electricity and coal both produce negative returns, whereas for natural gas we are able to construct economically viable portfolios, albeit with low returns.

Spot electricity price forecasting in Indian electricity market using autoregressive-GARCH models

In this study we investigate Spot electricity price forecasting performance of Autoregressive-GARCH models on Indian spot electricity price series. Hourly spot electricity price data for each of the five regions of Indian Electricity market from 1st of October 2010 to 15th November 2013 is used for the study to evaluate forecasting performance of the calibrated models. The conditional mean and conditional variance equations are estimated and one-step-ahead forecasts with a rolling window is performed. The fact that India being the only country in the world having power exchanges in-spite of demand outstripping supply and peak power shortage even to this day, further emphasizes the significance and criticality of spot electricity price forecasting from a power market participant's perspective and its practical relevance for Open access consumers in India.

Simulation of volatility modulated Volterra processes using hyperbolic stochastic partial differential equations

We propose a finite difference scheme to simulate solutions to a certain type of hyperbolic stochastic partial differential equation (HSPDE). These solutions can in turn estimate so called volatility modulated Volterra (VMV) processes and L\'{e}vy semistationary (LSS) processes, which is a class of processes that have been employed to model turbulence, tumor growth and electricity forward and spot prices. We will see that our finite difference scheme converges to the solution of the HSPDE as we take finer and finer partitions for our finite difference scheme in both time and space. Finally, we demonstrate our method with an example from the energy finance literature.

A Note on the Normalization of Spanish Electricity Spot Prices

Merit order of renewable generation has produced an increasing, relevant number of zero values in Spanish electricity spot prices since 2010, in contrast with the rest of markets which rarely present zero values. This letter shows that existing methodologies for normalizing the price distribution fail to yield a proper normalization. This letter proposes a new algorithm based on Nataf transformation which addresses this issue and ensures a correct normalization. Numerical results validate the proposed algorithm.

Intra-day electro-thermal model predictive control for polygeneration systems in microgrids

This paper is framed within the context of intra-day optimal control of polygeneration systems and storage connected to microgrids. In particular, the paper proposes an optimal control strategy that accounts for both electrical and thermal processes taking place in multi-building energy networks. To this end, the proposed optimal control strategy, based on the use of a Model Predictive Control, has been developed with the aim of providing optimal resource set-points for the coming 24 h. The proposed approach takes into account: day-ahead and spot prices of electricity, resource prices in terms of fuel cost and shut-down, start-up costs as well as the presence of electrical and thermal storage. The ability of this thermo-electric optimal control strategy is then demonstrated through simulations considering three case studies, namely: (a)fixed electricity price, (b)electricity spot-price and (c)different seasonal cases. The paper also studies the shaving of peaks through the use of optimally sized units in a system with the proposed method.

Using clustering techniques to provide simulation scenarios for the smart grid

The objective of this work is to obtain characteristic daily profiles of consumption, wind generation and electricity spot prices, needed to develop assessments of two different options commonly regarded under the smart grid paradigm: residential demand response, and small scale distributed electric energy storage. The approach consists of applying clustering algorithms to historical data, namely using a hierarchical method and a self-organizing neural network, in order to obtain clusters of diagrams representing characteristic daily diagrams of load, wind generation or electricity price. These diagrams are useful not only to analyze different scenarios of combined existence, but also to understand their individual relative importance. This study enabled also the identification of a probable range of variation around an average profile, by defining boundary profiles with the maximum and minimum values of any cluster prototypes.

Interconnecting an isolated electricity system to the European market: The case of Malta

The long-term European Union (EU) energy policy increasingly requires member countries to reform existing power systems, including those of small island states. These are commonly isolated electricity systems that rely heavily on imported fossil fuels. Interconnections with mainland power systems are an alternative to offset the exposure to volatile fuel prices. This paper studies the 200-MW (MW) subsea transmission cable between the EU island member state of Malta and Sicily that was inaugurated on April 2015. Our main purpose is to examine whether and to what extent Malta's vulnerability to distinct oil price scenarios can be overcome with this new interconnector. We describe the process used to simulate the merit order for both Malta's isolated and interconnected electric generation setup. The algorithm used provides the average electricity spot price and economic scarcity rent of electricity imports and exports. The main finding is that the Malta-Sicily interconnector does not necessarily lower electricity prices for Malta's consumers. However, some scenarios, notably the incorporation of natural gas in Malta's future generation portfolio, achieve win–win situations for both consumer and supplier. The Malta case study shows that cable impacts depend on the installed generation capacity, oil price, and market design.

Strategic Capacity Withholding Through Failures in the German-Austrian Electricity Market

In electricity day-ahead markets organized as uniform price auction, a small reduction in supply in times of high demand can cause substantial increases in price. We use a unique data set of failures of generation capacity in the German-Austrian electricity market to investigate the relationship between electricity spot prices and generation failures. Differentiating between strategic and non-strategic failures, we find a positive impact of prices on non-usable marginal generation capacity for strategic failures only. Our empirical analysis therefore provides evidence for the existence of strategic capacity withholding through failures suggesting further monitoring efforts by public authorities to effectively reduce the likelihood of such abuses of a dominant position.