Merchant interconnector projects by generators in the EU: Effects on profitability and allocation of capacity

When building a cross-border transmission line (a so-called interconnector) as a for-profit (merchant) project, where the regulator has required that capacity allocation be done non-discriminatorily by explicit auction, the identity of the investor can affect the profitability of the interconnector project and, once operational, the resulting allocation of its capacity. Specifically, when the investor is a generator (hereafter the integrated generator) who also can use the interconnector to export its electricity to a distant location, then, once operational, the integrated generator will bid more aggressively in the allocation auctions to increase the auction revenue and thus its profits. As a result, the integrated generator is more likely to win the auction and the capacity is sold for a higher price. This lowers the allocative efficiency of the auction, but it increases the expected ex-ante profitability of the merchant interconnector project. Unaffiliated, independent generators, however, are less likely to win the auction and, in any case, pay a higher price, which dramatically lowers their revenues from exporting electricity over this interconnector.electricity markets; regulation; cross-border electricity transmissions; vertical integration; asymmetric auctions; bidding behavior

Analysis of Energy-Based Blended Quasicontinuum Approximations

The development of patch test consistent quasicontinuum energies for multi-dimensional crystalline solids modeled by many-body potentials remains a challenge. The original quasicontinuum energy (QCE) has been implemented for many-body potentials in two and three space dimensions, but it is not patch test consistent. We propose that by blending the atomistic and corresponding Cauchy-Born continuum models of QCE in an interfacial region with thickness of a small number $k$ of blended atoms, a general quasicontinuum energy (BQCE) can be developed with the potential to significantly improve the accuracy of QCE near lattice instabilities such as dislocation formation and motion. In this paper, we give an error analysis of the blended quasicontinuum energy (BQCE) for a periodic one-dimensional chain of atoms with next-nearest neighbor interactions. Our analysis includes the optimization of the blending function for an improved convergence rate. We show that the $\ell^2$ strain error for the non-blended QCE energy (QCE), which has low order $\text{O}(\epsilon^{1/2})$ where $\epsilon$ is the atomistic length scale, can be reduced by a factor of $k^{3/2}$ for an optimized blending function where $k$ is the number of atoms in the blending region. The QCE energy has been further shown to suffer from a O$(1)$ error in the critical strain at which the lattice loses stability. We prove that the error in the critical strain of BQCE can be reduced by a factor of $k^2$ for an optimized blending function, thus demonstrating that the BQCE energy for an optimized blending function has the potential to give an accurate approximation of the deformation near lattice instabilities such as crack growth.Comment: 26 pages, 1 figur

Symmetries of 2-lattices and second order accuracy of the Cauchy-Born model

We show that the Cauchy-Born model of a single-species 2-lattice is second order if the atomistic and continuum kinematics are connected in a novel way. Our proof uses a generalization to 2-lattices of the point symmetry of Bravais lattices. Moreover, by identifying similar symmetries in multispecies pair interaction models, we construct a new stored energy density, using shift gradients but not strain gradients, that is also second order accurate. These results can be used to develop highly accurate continuum models and atomistic/continuum coupling methods for materials such as graphene, hcp metals, and shape memory alloys

Structural versus Behavioral Measures in the Deregulation of Electricity Markets: An Experimental Investigation Guided by Theory and Policy Concerns

We try to better understand the comparative advantages of structural and behavioral measures of deregulation in electricity markets, an eminent policy issue for which the experimental evidence is scant and problematic. In the present paper we investigate theoretically and experimentally the effects of the introduction of a forward market on competition in electricity markets. We compare this scenario with the best alternative, reducing concentration by adding one more competitor by divestiture. Our work contributes to the literature by introducing more realistic cost configurations, teasing apart number and asset effect, and studying numbers of competitors that reflect better the market concentration in the European electricity industries. Our experimental data suggest that introducing a forward market has a positive effect on the aggregate supply in markets with two or three major competitors, configurations typical for both the newly accessed and the old European Union member states. Introducing a forward market also increases efficiency. Our data furthermore suggest, in contrast to previous findings, that the effects of introducing a forward market is stronger than adding one more competitor both in markets with two, and particularly three, producers. Our data thus suggest that the behavioral measure of introducing a forward market is more effective than the structural measure of adding one more competitor by divestiture. Thus competition authorities should, in line with EU law, focus on the behavioral measure of introducing, or at least facilitating the emergence of, forward markets rather than on the structural measure of lowering market concentration by divestiture.economics experiments; market power; competition; forward markets; EU electricity market

Formulation and optimization of the energy-based blended quasicontinuum method

We formulate an energy-based atomistic-to-continuum coupling method based on blending the quasicontinuum method for the simulation of crystal defects. We utilize theoretical results from Ortner and Van Koten (manuscript) to derive optimal choices of approximation parameters (blending function and finite element grid) for microcrack and di-vacancy test problems and confirm our analytical predictions in numerical tests

Sharp entrywise perturbation bounds for Markov chains

For many Markov chains of practical interest, the invariant distribution is extremely sensitive to perturbations of some entries of the transition matrix, but insensitive to others; we give an example of such a chain, motivated by a problem in computational statistical physics. We have derived perturbation bounds on the relative error of the invariant distribution that reveal these variations in sensitivity. Our bounds are sharp, we do not impose any structural assumptions on the transition matrix or on the perturbation, and computing the bounds has the same complexity as computing the invariant distribution or computing other bounds in the literature. Moreover, our bounds have a simple interpretation in terms of hitting times, which can be used to draw intuitive but rigorous conclusions about the sensitivity of a chain to various types of perturbations

Formulation and optimization of the energy-based blended quasicontinuum method

We formulate an energy-based atomistic-to-continuum coupling method based on blending the quasicontinuum method for the simulation of crystal defects. We utilize theoretical results from Van Koten and Luskin [32] and Ortner and Van Koten [24] to derive optimal choices of approximation parameters (blending function and finite element grid) for microcrack and di-vacancy test problems and confirm our analytical predictions in numerical tests