Variational inequalities with blocking property

The purpose of this paper is to generalize a property of the variational inequality which describes the flow of the Bingham body through a cylinder (see Duvaut and Lions[1], p. 314). We introduce the blocking property and the blocking space for a class of variational inequalities. In the last part of the paper we present some examples, applications and mechanical interpretations of the concepts we have introduced.     

Variational inequalities in stock loan models

This paper develops variational inequality approach to establish optimal stopping problems arising from the pricing of stock loan and capped stock loan models. The valuations of the stock loans and ranges of reasonable values of key parameters such as loan sizes, interest rates, fees for providing such a service and quantity of this automatic termination clause and relationships among these parameters as well as the optimal terminable stopping times are explicitly derived. The paper also gives two numerical samples to portray the results and the difference between stock loan model and capped stock loan model.     

Short-term forecasting of electricity prices in the colombian electricity market

The restructuring of the electricity-generating industry from protected monopoly to an open competitive market has presented producers with a problem scheduling generation: finding the optimal bidding strategy to maximise their profits. In order to solve this scheduling problem, a reliable system capable of forecasting electricity prices is needed. This work evaluates the forecasting capabilities of several modelling techniques for the next-day-prices forecasting problem in the Colombian market, measured in USD/MWh. The models include exogenous variables such as reservoir levels and load demand. Results show that a segmentation of the prices into three intervals, based on load demand behaviour, contribute to an important standard deviation reduction. Regarding the models under analysis, Takagi?Sugeno?Kang models and ARMAX models identified by means of a Kalman filter perform the best forecasting, with an error rate below 6%.     

Strong convergence of subgradient extragradient method with regularization for solving variational inequalities

The paper concerns with the two numerical methods for approximating solutions of a monotone and Lipschitz variational inequality problem in a Hilbert space. We here describe how to incorporate regularization terms in the projection method, and then establish the strong convergence of the resulting methods under certain conditions imposed on regularization parameters. The new methods work in both cases of with or without knowing previously the Lipschitz constant of cost operator. Using the regularization aims mainly to obtain the strong convergence of the methods which is different to the known hybrid projection or viscosity-type methods. The effectiveness of the new methods over existing ones is also illustrated by several numerical experiments.

     

Emission allowances auction for an oligopolistic electricity market operating under cap-and-trade

The authors consider a yearly auction where electricity generating companies (Gencos) bid to receive yearly green house gas (GHG) emission allowances. Gencos sell electricity in an oligopolistic electricity market that clears on an hourly basis and operates under a cap-and-trade emissions regulation scheme. Gencos strategically self-allocate their yearly allowance into hourly allowances that they then use to take part in the hourly electricity market. If a Genco emits above or below its self-allocated allowance for that hour then, in the first case, the hourly deficit is made up by buying an allowance from an external market, whereas in the second the hourly allowance surplus is sold to the external market. Recognising that the levels of power and emissions produced by the Gencos as well as the associated prices throughout the year will be influenced by both the yearly and hourly allowances, the auction maximises an objective function that is equal not only to the total amount bid by the Gencos to obtain allowances but also includes the yearly social welfare. This study proposes an approach that considers all of the above-mentioned points in a coordinated fashion and can be viewed as a mathematical program (the allowance auction) subject to a Nash equilibrium problem (the distribution by each Genco of its yearly allowance into hourly allowances), which in turn is subject to the Cournot?Nash equilibrium conditions of the hourly oligopolistic electricity market.     

Carbon pricing and electricity market reforms in China

As a large emerging economy, China is exploring to establish a carbon-pricing system to mitigate greenhouse gas emissions. The electricity sector which generates the greatest amount of China’s carbon dioxide emissions should be covered by such a carbon-pricing system. The review of the three main stages of China’s electricity market reforms shows that the degree of electricity marketization is relatively low, which might become an obstacle to carbon pricing. This paper develops theoretical and empirical models to analyze the impacts of carbon pricing on electricity supply under two scenarios, namely, marketization and regulation. It is concluded that the electricity market reform is a prerequisite for the development of carbon pricing. Without market-oriented reforms of electricity pricing in China, carbon pricing might lead to a shortage in electricity supply. Potential electricity market reforms to encourage market competition and promote market-oriented electricity pricing are also suggested.     

Dynamic price forecast in a competitive electricity market

Price forecast is a key issue in competitive electricity markets. It provides useful information for the market players and the regulators, in both short and long run. Different approaches have been proposed and implemented. A new dynamic approach for forecasting the market price of electricity in the short term is proposed. The price dates are first clustered according to different types of daily profiles and then, given a proper function representing the trend in price, the set of unknown parameters are identified based on the zeroing of a Lyapunov function. The forecast can be dynamically updated with the latest data available. Higher weight can be attributed to this data in determining the future prices. The proposed approach is validated with reference to real systems in the form of the Italian, New England and New York electricity markets. In addition, an extensive price forecast is provided for the Italian market, an example of a young market that is rather difficult to predict patterns for.     

Hydro energy management optimization in a deregulated electricity market

When electricity prices were regulated, hydropower optimization often considered only the inflow uncertainty. In a deregulated electricity market, price uncertainty must be also considered in addition to inflow uncertainty. This makes the operation problem more challenging due to inclusion of the objective of minimizing risk. It also makes the objective function nonlinear while the estimation of risk is problematic. For dealing with uncertainty, a set of finite scenarios of inflow or price sequences may form the evolution of information over the stages that are used in optimization algorithms. Such implicit optimization methods can be seen as an extension of deterministic optimization. A disadvantage is the number of scenarios may grow exponentially in multi-stage optimization problems, even with only a few branches at each stage. An explicit method, denoted as the Fletcher-Ponnambalam model (FP), has been recently developed for the first and second moments of the storage state distributions in terms of moments of the inflow distributions. This method provides statistical information on the nature of random behaviour of the system state variables without any discretization and hence suitable for multireservoir problems. Also not considering scenarios makes it computationally inexpensive, as there is little growth to the size of the original problem. In this paper, we introduce the price uncertainty into the FP model; our results indicate that the method could achieve optimum policy considering also the reduction of risk, using the second moment information. Our study is for medium term operations of a single reservoir. The results are compared with corresponding results from simulation and where possible, with the well-known Benders' Decomposition method (BD).     

Unit maintenance scheduling coordination mechanism in electricity market environment

Along with worldwide electricity market deregulation, the traditional approach to unit maintenance scheduling (UMS) is required to make compatible changes for resolving some new challenges. The development of workable coordination mechanism to accord with the market mechanism is under the close concern of the policymaker, the market designer and the market participants. Actually, the key of this problem is both how to treat generation companies equally and how to guarantee the system security during the UMS process. This paper advances the view on UMS in electricity market environment, and identifies that the coordination fairness should include `which plans to be selected for adjustment` and `how to adjust them` simultaneously, of which only the former was comprehensively studied in the past research, however. To ensure the competition fairness thoroughly, a new kind of UMS mechanism with a coordination model is constructed. The transmission capacity constraint and the random line outage are involved in the model in order to make the analysis about the impact of UMS on the system security more reasonable. In addition, the adequate solution for this model and the allocation way about the independent system operator`s income which is created during UMS process have also been discussed. Then the proposed mechanism is applied to a numerical example to show its good features in practical application.     

Social welfare analysis of the iberian electricity market accounting for carbon emission prices

In this study, the authors analyse the social welfare impact of the integration of Portugal and Spain in the Iberian electricity market (MIBEL), taking into account the CO₂ price for emissions trading. They model the impact of emissions trading on the daily clearing prices and generation scheduling, and its effects on the benefits of integration as a whole. They compare the impact of market integration in Portugal and Spain and show that the welfare impact of the MIBEL is dependent on the CO₂ prices. From their analysis, they conclude high CO₂ prices lead to a change in the merit order. Moreover, natural gas is the generation technology that most benefits from transmission constraints and from high CO₂ prices, as in the base case it is mainly used as a peak technology. The authors have also found that increases in the CO₂ prices do not lead to higher profits. Overall, the introduction of the MIBEL will increase social welfare by reducing generation costs and prices.     

Optimal due date quoting for a risk-averse decision-maker under CVaR

This study investigates a due date quoting problem for a project with stochastic duration, taking the decision-maker’s risk attitude into consideration. The project profit is defined as the difference between the price and the cost that is comprised of production cost and earliness–tardiness penalties. In this situation, the due date determination has to be modelled as a stochastic optimisation due to stochastic duration. Conditional value at risk is thus employed as a performance measure to describe the decision-maker’s risk attitude. In fixed price contract, when the unit production cost is not smaller than the unit penalty on earliness, the optimal due date increases with the increase of the degree of a decision-maker’s risk aversion, the unit penalty on delay, and the decrease of the unit penalty on earliness. Besides, when the price is proportional to the due date and the slope is no bigger than the unit penalty on tardiness, the optimal due date is smaller than the result in fixed price. This is because high price for a short due date encourages a decision-maker to quote a small due date. Further, we compare the optimal due date in different parameter setting where the penalty coefficient of earliness is negative or zero, which means there is reward or no penalty on earliness, respectively. Finally, a case study is conducted to validate the effectiveness and efficiency of the proposed model.     

Innovation and market regulation: evidence from the European electricity industry

This paper studies the effects of changes in the level of product market regulation on the industry-level innovation intensity in the EU electricity sector during years 1990–2009. In order to test the impact of deregulatory policies on the propensity to innovate in energy technologies, we match data on R&D budgets and European Patent Office patent applications from International Energy Agency and Eurostat Databases with the Organisation for Economic Co-operation and Development indexes of product market regulation. The analysis addresses innovations in the traditional electricity-related technologies, but keeping aside renewable energy technologies. Findings show an increase in patenting activities following market deregulation, measured along three factors: entry barriers, public ownership and vertical integration. In particular, econometric results suggest that policies aimed at reducing vertical integration – i.e. to unbundle networks from energy generation and supply – have a positive impact on innovation activity. Results are robust to the introduction of controls for country-level public R&D expenditures in the electricity field.     

Parameter optimisation using genetic algorithm for support vector machine-based price-forecasting model in National electricity market

The parameter selection is very important for successful modelling of input-output relationship in a function approximation model. In this study, support vector machine (SVM) has been used as a function approximation tool for a price series and genetic algorithm (GA) has been utilised for optimisation of the parameters of the SVM model. Instead of using single time series, separate time series for each trading interval has been employed to model each day-s price profile, and SVM parameters of these separate series have been optimised using GA. The developed model has been applied to two large power systems from National electricity market (NEM) of Australia. The forecasting performance of the proposed model has been compared with a heuristic technique, a linear regression model and the other reported works in the literature. Effect of price volatility on the performance of the models has also been analysed. Testing results show that the proposed GA-SVM model has better forecasting ability than the other forecasting techniques.     

A possibilistic approach for designing hybrid cellular manufacturing systems

In this paper, a hybrid cellular manufacturing (HCM) system is presented in which the main sources of uncertainty, e.g. the demands of parts and unit costs are treated as fuzzy numbers in the form of possibilistic distributions. The basic concept of HCM is that high variation in demand might disturb cell efficiency, so forming cells with only those parts that have stable demand, will profit. Thus, to design stable and robust manufacturing cells, a two-phase method is proposed in which a fuzzy adaptive ranking method is first applied to identify those parts with low and non-repetitive demands (i.e. the special parts) which will then be assigned to a functional cell. Afterwards, an interactive possibilistic programming model is applied to cell formation of remaining regular parts while considering both part sequences and multiple routes. To show the capability and usefulness of the proposed method, an illustrative example is also provided. Finally, concluding remarks are reported.     

Robust optimisation for risk-averse multi-period inventory decision with partial demand distribution information

We study robust multi-period inventory decisions for risk-averse managers with incomplete demand information for products with a short life cycle. The three inventory models we developed aim respectively to maximise expected profit, maximise conditional value-at-risk-based profit, and balance between the two objectives. We formulate each objective into an associated robust counterpart model under the assumption of ellipsoid distribution and again under the box distribution. The ellipsoid distribution-based robust model can be mathematically transformed into a non-linear programming which can be solved by finding solutions to some second-order cone programs, while the box distribution-based model can be converted into a general piecewise linear optimisation problem. We prove that the transformed versions are equivalent to the original ones and that both transformed models can be solved efficiently. Numerical examples are given to demonstrate the practicability of the proposed approach for dealing with uncertain demands. We find that the proposed optimisation approaches are robust under both the ellipsoid and box distributions. Finally, sensitivity analysis on the risk-averse degree and optimism index is conducted to validate the proposed models and solution approaches.     

Complex dynamics of Cournot game with bounded rationality in an oligopolistic electricity market

In order to accurately simulate the dynamic decision-making behaviors of market participants, a novel dynamic Cournot game model with bounded rationality of electricity market that considers the constraints of realistic power networks is proposed in this paper. This model is represented by discrete difference equations embedded within the optimization problem of consumption benefits. The Nash equilibrium of electricity market and its stability are quantitatively analyzed. It is found that there are different Nash equilibriums with different market parameters corresponding to different operating conditions of power network, i.e. congestion and non-congestion, and even in some cases there is no Nash equilibrium at all. Numerical simulations with the 2-node and IEEE 30-node systems are carried out to evaluate the dynamic behaviors of electricity market, especially the periodic and chaotic behaviors when the market parameters are beyond the stability region of Nash equilibrium.     

CO2 price effects on the electricity market and greenhouse gas emissions levels: an application to the Spanish market

Clean Technologies and Environmental Policy - This research proposes an empirical method to estimate the impact on the wholesale electricity market of an increase in the price of CO2 emission...     

Risk management of generators' strategic bidding in dynamic oligopolistic electricity market using optimal control

Here, the risk-constrained generation decision in a dynamic oligopolistic electricity market using stochastic optimal control is studied. In this formulation, the generation competition process is modelled as a dynamic feedback system, taking into account the system demand variation and generators' adaptive behaviours. Using the proposed framework, the risk-constrained strategic bidding is investigated with stochastic optimal control. Two common methods of risk management are discussed: the min-max regret technique and the mean-variance technique. It is found that the risk-constrained decision always results in less generation