STATISTICA & APPLICAZIONI - 2013 - Special online issue

Complementarity problems are recognized to be a general computational method for solving economic equilibrium models. There exist various problems describing the energy markets that rely on the complementarity models since they allow to analyze the interactions among different market players. Complementarity models generalize linear and non-linear problems because the Karush-Kuhn-Tucker optimality conditions are one particular instance of a complementarity problem. Moreover, the class of complementarity models is appropriate for modeling spatial price equilibrium, perfect and imperfect completion models, such as Cournot-Nash games, and other many models where both primal and dual variables can be constrained together. The first part of this paper provides a motivation and a description of complementarity models. In the second part, we investigate a capacity expansion problem applied to the restructured Italian electricity market that is currently subject to the European Union Emissions Trading System (EU-ETS). In accordance with the Kyoto Protocol, the EU-ETS aims to reduce greenhouse gas emissions from human activities provoking climate changes. This scheme is now subdivided into three phases and it is based on a cap and trade system that defines the maximum amount of CO2 that can be emitted in each compliance period. Our analysis shows that investments in renewables are mainly conditioned to incentive policies. The solution of the developed model is found by exploiting the mixed complementarity theoretical framework. The model is implemented in GAMS using the PATH solver.

This paper concerns the change of support problem (COSP) for continuos spatial phenomena which are commonly observed at the point and/or area level. A change of the spatial scale can be required for predicting the process of interest at a resolution which is different from the one at which the data are observed or for fusing data coming from several sources and characterized by different spatial resolutions. COSP may be a computationally demanding task as it involves stochastic integration of the continuos spatial process. For this reason, in case of complex models or huge data, Bayesian inference with Markov chain Monte Carlo (MCMC) may become unfeasible and some modeling simplifications may be required. In this paper we present how to manage the COSP through the Integrated Nested Laplace approximation approach (INLA), which is a computationally effective alternative to MCMC for Bayesian inference, and the Stochastic Partial Differential Equation (SPDE) approach, which gains computational benefits by approximating a continuos spatial process as a Gaussian Markov random field (through a basis function representation). An environmental applications regarding particulate matter pollution shows how to obtain spatial predictions at a new spatial resolution without worsening the computational load.

This paper introduces a flexible space-time data fusion model based on latent variables and varying coefficients that can be used to map air quality over large areas such as countries or continents. The model is able to handle point data from ground level monitoring networks and pixel data from remote sensing. As a case study, the model is used to dynamically map the nitrogen dioxide concentration over Europe during 2009.

A deterministic and a stochastic multi-stage portfolio model for a hydropower producer operating in a competitive electricity market is proposed. The producer has to cope with a production function constraint imposing the scheduling of his future production. The portfolio includes its own production, a set of energy contracts for delivery or purchase, including derivatives contracts as forwards with physical delivery to hedge against risks. The goal of our models is to maximise the profit of the producer and reduce the economic risks connected to the fact that energy spot and forward prices are highly volatile. We alternatively derive the forward price by the spot dynamics and model forward dynamics obtaining consistent scenarios. Our results show that forward contracts can be used for hedging purposes. Beyond profit, the convenience of using forward contracts is a more efficient use of the hydroplant, taking advantage of the possibility of pumping water and ending up with a higher final value of the reservoir. Finally, we provide performance measures of our threestage model with respect to deterministic one.

We propose a TransCo model for coordinating transmission expansion planning with competitive generation capacity planning in electricity markets. Our purpose is to provide a tool to simulate the equilibrium interplay regarding strategic decisions of a set of power producers and a single transmission operator. The solution represents an iterative process for defining the optimal transmission expansion program together with a correct guess of the power plants expansion program for each GenCo involved. The composition of new investments in power plants guessed by the TransCo must coincide with the optimal expansion plan defined by each GenCo. We illustrate the methodology by means of an example depicting a zonal electricity market with two zones.