Electricity swing options: Behavioral models and pricing

Electricity swing options are supply contracts for power, which give the owner the right to change the required delivery on short time notice. It gives more flexibility than fixed base load or peak load contracts. The name “option” is a bit misleading, since it gives the owner multiple exercise rights at many different time horizons with exercise amounts on a continuous scale. We look at the problem to determine a rational ask price for such a contract from the viewpoint of the contract seller. The pricing of these contracts differs drastically from the pricing of financial options. First, peculiar properties arise from the non-storability of the underlying (the energy) and therefore the impossibility to hedge with the underlying, hedging is only possible with some future contracts. Second, the behavior of the owner plays an important role. Based on some behavioral model for the option holder, we develop a game-theoretic model, which allows to identify the equilibrium price. Besides some theoretical results, we present some numerical results which clarify the dependence of the asked price on the amount of flexibility offered in the swing option.     

Forecasting the Effects of Television Programming upon Electricity Loads

In Britain, the demand for electricity has been observed to rise sharply at the end of popular television programmes. This presents a serious forecasting problem for the Central Electricity Generating Board in the economic scheduling of standby reserve generation. This report provides some insights into the determinants of the problem and a multivariate forecasting aid through regression analyses on television audience measurements.     

Productivity Indices and Personnel Comparative Assessment in a Multidivisional Corporation

The objective of this study is to explore the determinants and relative performance of manpower in the distribution divisions of the Electricity Utility in Greece. A cross-sectional factor analysis model is proposed for analyzing differences in operating conditions between the divisions; an initial set of variables, which relate to manpower activities, is reduced to some composite dimensions each representing a distinct characteristic of the environment within which personnel activities take place. Regressing personnel along these dimensions an inter-divisional comparison of manning is carried out and some indices of labour-productivity are derived.     

A comment on “Measuring super-efficiency in DEA in the presence of infeasibility”

In a recent paper by Chen [Chen, Y., 2005. Measuring super-efficiency in DEA in the presence of infeasibility. European Journal of Operational Research 161 (1), 447–468], he deals with the infeasibility of super-efficiency DEA models in variable returns to scale (VRS) technology. He provides a necessary and sufficient condition for simultaneous infeasibility of input- and output-oriented super-efficiency DEA models in VRS case, then he claims that both of these models are infeasible only for a rare situation. In this paper, we present some counterexamples and comments to the contention by Chen.     

Application of seasonal SVR with chaotic gravitational search algorithm in electricity forecasting

Hybridization chaotic mapping functions with optimization algorithms into a support vector regression model has been shown its efficient potential to avoid converging prematurely. It is deserved to explore more possibility by hybridizing with other optimization algorithms. Electricity demand sometimes demonstrates a seasonal tendency due to complicate economic activities or climate cyclic nature. This investigation presents a SVR-based electricity forecasting model which applied a novel hybrid algorithm, namely chaotic gravitational search algorithm (CGSA), to improve the forecasting performance. The proposed CGSA employs the chaotic local search by logistic chaotic mapping function in the iteration of the original GSA to search and refine the current best solution. In addition, seasonal mechanism is also applied to deal with seasonal electricity tendency. A numerical example from an existed reference is used to illustrate the forecasting performance of the proposed SSVRCGSA model. The forecasting results indicate that the proposed model yields more accurate forecasting results than ARIMA and TF-ε-SVR-SA models.     

相异成本和广义非线性需求下多寡头古诺模型及应用

在已有的寡头古诺模型基础上进一步扩展,建立了综合考虑竞争者成本差异和市场广义非线性需求的扩展多寡头古诺模型。给出了扩展多寡头古诺模型Nash均衡解的一般求解方法以及两类特殊需求函数下Nash均衡解的解析表达式。接着进一步探讨了模型的性质,重点讨论成本差异对均衡的影响及其与经典模型的异同,并利用模型的结论简单解释若干经济现象。模型性质探讨表明,边际成本差异会对均衡产量及其在各类寡头之间的分配产生重要影响。作为应用,将相关结论应用到以稀土开采管理为代表的稀有资源管理的策略分析上,提出了若干建议。     

Single and multi-period optimal inventory control models with risk-averse constraints

This paper presents some convex stochastic programming models for single and multi-period inventory control problems where the market demand is random and order quantities need to be decided before demand is realized. Both models minimize the expected losses subject to risk aversion constraints expressed through Value at Risk (VaR) and Conditional Value at Risk (CVaR) as risk measures. A sample average approximation method is proposed for solving the models and convergence analysis of optimal solutions of the sample average approximation problem is presented. Finally, some numerical examples are given to illustrate the convergence of the algorithm.     

Australian electricity market and price volatility

Australian Electricity Market has experienced high price volatility since the deregulation in early 1990s. In this exploratory and preliminary analysis of 2010 data from South Australian electricity market we identify and exhibit a number of phenomena which, arguably, contribute to (A) high cost of electricity supply to consumers and (B) volatility in spot prices. These phenomena include: (i) Distinct bidding patterns of some generators occurring in trading intervals corresponding to periods of low, medium and high spot prices, (ii) Low correlation between electricity demand and spot prices on days when spot price spikes are observed, (iii) Failure of the lottery model and associated Markowitz-type optimisation approaches to adequately explain the shifting structure of generators’ bids and (iv) Unexpectedly high contribution to the consumers costs and risks from the relatively small number of trading intervals where spot price spikes were observed.     

BOOK REVIEWS

Book reviewed in this article: Beloved Scientist , by David O. Woodbury. Physics , A Textbook for Colleges , by Oscar M. Stewart. Modern Physics , by Charles E. Dull. Experiments in Organic Chemistry , by E. Wertheim. Dynamical Analogies , by Harry F. Olson, E.E., Ph.D. A Peimer of Electronics , by Don P. Caverly. Applied Mechanics and Heat , by L. Raymond Smith. An Elementary Course in Qualitative Analysis , by William Lloyd Evans, Jesse Erwin Day, and Alfred Benjamin Garrett. Fundamentals of Machines , by John A. Clark. Fundamentals of Machines , by Charles E. Dull. Algebra (Mathematics for Technical Training ), by Paul L. Evans. Geometry with Military and Naval Applications , by Willis F. Kern and James R. Bland. Plane Trigonometry with Tables , by Paul L. Evans. Elementary Applied Electricity , by L. Raymond Smith. Fundamentals of Electricity , Based on Material Developed for the Teaching of Learners and Apprentices of the Carnegie -Illinois Steel Corporation . Rewritten to Conform to the Preinduction Training Course in Fundamentals of Electricity as Prepared by the War Department . Fundamental Jobs in Electricity , by Edgar C. Perry, A. M. and Harry V. Schafebook.     

An integrative modelling approach for understanding competitive electricity markets

A model of the UK Electricity market is presented focusing on the competitive behaviour of buyers and sellers. The model was developed using the OO/DEVS object oriented industry simulation platform and includes as components: generators, suppliers, customers, the electricity pool and the contract market. The motivation and structure of the OO/DEVS platform is described both as a vehicle for systems thinking and as an architecture for integrative modelling, allowing, for example, optimisation and spreadsheet models to exist as objects within an overall strategic simulation model. The actual case-study implementation presented in this paper, was undertaken in collaboration with one of the privatised utilities in the UK.     

Application of the largest Lyapunov exponent and non-linear fractal extrapolation algorithm to short-term load forecasting

Precise short-term load forecasting (STLF) plays a key role in unit commitment, maintenance and economic dispatch problems. Employing a subjective and arbitrary predictive step size is one of the most important factors causing the low forecasting accuracy. To solve this problem, the largest Lyapunov exponent is adopted to estimate the maximal predictive step size so that the step size in the forecasting is no more than this maximal one. In addition, in this paper a seldom used forecasting model, which is based on the non-linear fractal extrapolation (NLFE) algorithm, is considered to develop the accuracy of predictions. The suitability and superiority of the two solutions are illustrated through an application to real load forecasting using New South Wales electricity load data from the Australian National Electricity Market. Meanwhile, three forecasting models: the gray model, the seasonal autoregressive integrated moving average approach and the support vector machine method, which received high approval in STLF, are selected to compare with the NLFE algorithm. Comparison results also show that the NLFE model is outstanding, effective, practical and feasible.     

An Interactive,Graphical Approach to Linear Financial Models

Early attempts to utilize linear algebraic (L.P.) techniques in financial planning met with little success. This was probably due to a misunderstanding of the process by which financial and corporate plans were formulated. The planning process is now better understood and the use of computer-based models is well accepted. However current modelling systems perform only simple arithmetic evaluations. There is a prima facie case for re-examining linear algebraic methods to exploit the considerable amount of information which is available within a plan. This paper describes the work done in the South of Scotland Electricity Board to develop an interactive financial modelling system.     

Functions of event variables of a random system with complete connections

In applications it often occurs that the experimenter is faced with functions of random processes. Suppose, for instance, that he only can draw partial or incomplete information about the underlying process or that he has to classify events for the sake of efficiency. We assume that the underlying process is a random system with complete connections (which contains the Markovian case as a special one) satisfying some basic properties, and that a mapping operates on the event space. With these two elements we construct in Section 2 a new random system with complete connections which inherits the properties of the old one (Theorem 2.2.3). In Section 3 we prove a weak convergence theorem (Theorem 3.4.4) in the theoretical framework of the so-called distance diminishing models, which gives a straightforward application in Section 4 to conditional probabilities related to partially observed events (Theorems 4.1.3). Finally we prove a Shannon-McMillan-type theorem (Theorem 4.2.3) finding application to classification procedures.     

Electricity price forecasting accounting for renewable energies: optimal combined forecasts

Electricity price forecasting is an interesting problem for all the agents involved in electricity market operation. For instance, every profit maximisation strategy is based on the computation of accurate one-day-ahead forecasts, which is why electricity price forecasting has been a growing field of research in recent years. In addition, the increasing concern about environmental issues has led to a high penetration of renewable energies, particularly wind. In some European countries such as Spain, Germany and Denmark, renewable energy is having a deep impact on the local power markets. In this paper, we propose an optimal model from the perspective of forecasting accuracy, and it consists of a combination of several univariate and multivariate time series methods that account for the amount of energy produced with clean energies, particularly wind and hydro, which are the most relevant renewable energy sources in the Iberian Market. This market is used to illustrate the proposed methodology, as it is one of those markets in which wind power production is more relevant in terms of its percentage of the total demand, but of course our method can be applied to any other liberalised power market. As far as our contribution is concerned, first, the methodology proposed by García-Martos et al (2007 and 2012) is generalised twofold: we allow the incorporation of wind power production and hydro reservoirs, and we do not impose the restriction of using the same model for 24?h. A computational experiment and a Design of Experiments (DOE) are performed for this purpose. Then, for those hours in which there are two or more models without statistically significant differences in terms of their forecasting accuracy, a combination of forecasts is proposed by weighting the best models (according to the DOE) and minimising the Mean Absolute Percentage Error (MAPE). The MAPE is the most popular accuracy metric for comparing electricity price forecasting models. We construct the combination of forecasts by solving several nonlinear optimisation problems that allow computation of the optimal weights for building the combination of forecasts. The results are obtained by a large computational experiment that entails calculating out-of-sample forecasts for every hour in every day in the period from January 2007 to December 2009. In addition, to reinforce the value of our methodology, we compare our results with those that appear in recent published works in the field. This comparison shows the superiority of our methodology in terms of forecasting accuracy.     

Moving estimates test with time varying bandwidth

In this paper, we consider the problem of testing for parameter changes in time series models based on a moving estimates (ME) test. It is widely accepted that detecting some changes, for instance, those caused by temporary parameter shifts by the existing cusum test is difficult. A MV test with a fixed bandwidth has been developed to circumvent the defect, but the test still does not perform well under certain conditions. Motivated by this, we propose a MV test with a time varying bandwidth to outperform the original test. In order to illustrate our findings, we have provided simulation results.     

Searching for targets who want to be found

The paper reports some simulation results for models of the types of search that might be conducted by a rescue helicopter when looking for a walker who is lost in the desert and wants to be found. The walker has a smaller speed than the helicopter, but the walker can detect the helicopter at a greater distance than the helicopter can detect the walker. Possible search strategies include those in which the helicopter flies in a decreasing spiral or sweeps back and forth across a region. The walker may remain stationary, move randomly or walk towards the helicopter when he hears it. Simulation work suggests the types of strategies that may do best.     

基于概念的数学系统及其结构

随着科学技术的发展，应用定量分析的数学方法已从自然科学发展到社会科学、思堆科学．为了处理这些问题的需要，许多学者建立了多种数学模型和数学方法，这些模型和方法都直接或间接地涉及到概念，因此归纳并研究基于概念的数学方法显得很有必要。本文应用系统的方法，尝试络出数学系境的概念，并建立了基于概念的数学系统及其结构的一般方法，期望更多的学者予以关注和研究。     

Irreducibility and emergence in complex systems and the quest for alternative insights

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. Henri Poincaré In this essay, we briefly survey the contemporary scientific and philosophical debates on emergence and conclude that this notion has become a dilemma. We argue that the reason for this dilemma is metaphysical. Subsequently, we investigate some fundamental philosophical methods in science, such as Cartesian reduction and objectivism, as the main sources of scientific drawbacks. Eventually, we suggest some refinements in philosophical methods for improvement of scientific insight and propose the method of transcendentionism as a metaphysical panacea to encounter the dilemma of emergence. © 2011 Wiley Periodicals, Inc. Complexity, 17,10–18, 2011     

Multistage stochastic demand-side management for price-making major consumers of electricity in a co-optimized energy and reserve market

In this paper, we take an optimization-driven heuristic approach, motivated by dynamic programming, to solve a class of non-convex multistage stochastic optimization problems. We apply this to the problem of optimizing the timing of energy consumption for a large manufacturer who is a price-making major consumer of electricity. We introduce a mixed-integer program that co-optimizes consumption bids and interruptible load reserve offers, for such a major consumer over a finite time horizon. By utilizing Lagrangian methods, we decompose our model through approximately pricing the constraints that link the stages together. We construct look-up tables in the form of consumption-utility curves, and use these to determine optimal consumption levels. We also present heuristics, in order to tackle the non-convexities within our model, and improve the accuracy of our policies. In the second part of the paper, we present stochastic solution methods for our model in which, we reduce the size of the scenario tree by utilizing a tailor-made scenario clustering method. Furthermore, we report on a case study that implements our models for a major consumer in the (full) New Zealand Electricity Market and present numerical results.     

A Non‐Gaussian Ornstein–Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing

A mean‐reverting model is proposed for the spot price dynamics of electricity which includes seasonality of the prices and spikes. The dynamics is a sum of non‐Gaussian Ornstein–Uhlenbeck processes with jump processes giving the normal variations and spike behaviour of the prices. The amplitude and frequency of jumps may be seasonally dependent. The proposed dynamics ensures that spot prices are positive, and that the dynamics is simple enough to allow for analytical pricing of electricity forward and futures contracts. Electricity forward and futures contracts have the distinctive feature of delivery over a period rather than at a fixed point in time, which leads to quite complicated expressions when using the more traditional multiplicative models for spot price dynamics. In a simulation example it is demonstrated that the model seems to be sufficiently flexible to capture the observed dynamics of electricity spot prices. The pricing of European call and put options written on electricity forward contracts is also discussed.