Modelling locational price spreads in competitive electricity markets; applications for transmission rights valuation and replication

The restructuring of the electric utilities industry has forcedindustry participants to rethink their approach to a numberof decision processes. To manage risk and plan investment ingeneration assets, as well as to examine the efficient expansionof the current transmission grid, one needs to have a clearunderstanding of the interaction between the grid propertiesand the behaviour of the regional power markets. In this paperwe discuss a fundamental modelling approach which extracts thestochastic properties of electricity prices by modelling theimpact of physical and economic drivers affecting the production,delivery, and consumption of electricity. If the fundamentalinputs are directly observable, we can use historical data tocalibrate the model parameters. In the case of electricity,this simple and abundant set of training data can make a crucialdifference. We present the bid-based stochastic model (BSM) and look intoits application to valuing of financial derivatives, especiallyoptions based on the locational spread in electricity pricebetween two markets. The advantage of the bid-based model isthat one is able to link the capacity of the transmission line,in megawatts, directly to the correlation between electricityprices at the end nodes. This leads us to a valuation methodfor a locational spread option, the financial equivalent ofa physical transmission right. The model represents an improvementover standard spread option formulation in that it accountsfor the effect of the nonlinear flows in the transmission networkon the correlation and distribution of locational prices. Wealso address the question of whether financial transmissionrights can be replicated with a dynamic portfolio of forwardcontracts at the end nodes. This poses the possibility of model-based arbitrage betweenexisting forward markets and the emerging transmission rightsmarkets. Furthermore, it allows users to simulate the effectof transmission outages or expansion. For example, a for-profittransmission provider who is contemplating addition of a newtransmission line between two markets needs to know whetherhe will be able to recover the fixed cost of investing in theline by selling transmission rights to market participants.By calibrating the bid-based model according to current pricelevels and adding the capacity of the new transmission line,the transmission owner can simulate future cash flows and estimatethe profitability of the investment.     

Cyclische Oligomere von (R)-3-Hydroxybuttersäure: Herstellung und strukturelle Aspekte

Cyclic Oligomers of (R)-3-Hydroxybutanoic Acid: Preparation and Structural Aspects The oligolides containing three to ten (R)-3-hydroxybutanoate (3-HB) units (12-through 40-membered rings 1–8 ) are prepared from the hydroxy acid itself, its methyl ester, its lactone (‘monolide’), or its polymer (poly(3-HB), mol. wt. ca. 10⁶ Dalton) under three sets of conditions: (i) treatment of 3-HB ( 10 ) with 2,6-dichlorobenzoyl chloride/pyridine and macrolactonization under high dilution in toluene with 4-(dimethylamino)pyridine (Fig. 3); (ii) heating a solution (benzene, xylene) of the β-lactone 12 or of the methyl ester 13 from 3-HB with the tetraoxadistanna compound 11 as trans-esterification catalyst (Fig. 4); (iii) heating a mixture of poly(3-HB) and toluene-sulfonic acid in toluene/1,2-dichloroethane for prolonged periods of time at ca. 100° (Fig. 6). In all three cases, mixtures of oligolides are formed with the triolide 1 being the prevailing component (up to 50% yield) at higher temperatures and with longer reaction times (thermodynamic control, Figs. 3–6). Starting from rac-β-lactone rac- 12 , a separable 3:1 to 3:2 mixture of the l,u- and the l,l-triolide diasteroisomers rac- 14 and rac- 1 , respectively, is obtained. An alternative method for the synthesis of the octolide 6 is also described: starting from the appropriate esters 15 and 17 and the benzyl ether 16 of 3-HB, linear dimer, tetramer, and octamer derivatives 18–23 are prepared, and the octamer 23 with free OH and CO₂H group is cyclized (→ 6 ) under typical macrolactonization conditions (see Scheme). This ‘exponential fragment coupling protocol’ can be used to make higher linear oligomers as well. The oligolides 1–8 are isolated in pure form by vacuum distillation, chromatography, and crystallization, an important analytical tool for determining the composition of mixtures being ¹³C-NMR spectroscopy (each oligolide has a unique and characteristic chemical shift of the carbonyl C-atom, with the triolide 1 at lowest, the decolide 8 at highest field). The previously published X-ray crystal structures of triolide 1 , pentolide 3 , and hexolide 4 (two forms), as well as those of the l,u-triolide rac- 14 , of tetrolide ent- 2 , of heptolide 5 , and of two modifications of octolide 6 described herein for the first time are compared with each other (Figs. 7–10 and 12–15, Tables 2 and 5–7) and with recently modelled structures (Tables 3 and 4, Fig. 11). The preferred dihedral angles τ₁ to τ₄ found along the backbone of the nine oligolide structures (the hexamer and the larger ones all have folded rings!) are mapped and statistically evaluated (Fig. 16, Tables 5–7). Due to the occurrence of two conformational minima of the dihedral angle O? CO? CH₂? CH (τ₃ = + 151 or ?43°), it is possible to locate two types of building blocks for helices in the structures at hand: a right-handed 3₁ and a left-handed 2₁ helix; both have a ca. 6 Å pitch, but very different shapes and dispositions of the carbonyl groups (Fig. 17). The 2₁ helix thus constructed from the oligolide single-crystal data is essentially superimposable with the helix derived for the crystalline domains of poly(3-HB) from stretched-fiber X-ray diffraction studies. The absence of the unfavorable (E)-type arrangements around the OC? OR bond (‘cis-ester’) from all the structures of (3-HB) oligomers known so far suggests that the model proposed for a poly(3-HB)-containing ion channel (Fig. 2) must be modified.     

Development and validation of a high-performance liquid chromatographic method using fluorimetric detection for the determination of the diarrhetic shellfish poisoning toxin okadaic acid without chlorinated solvents

A modification of the high-performance liquid chromatographic method with fluorimetric detection method for the determination of diarrhetic shellfish poisoning toxins was developed to completely avoid the use of dangerous chlorinated solvents. The method was validated for the toxin okadaic acid (OA) over a period of 6 months where 12 calibrations were performed and 72 samples were analyzed. Analysis of toxic and non-toxic mussels, clams and scallops demonstrated its selectivity. Linearity was observed in the tested range of interest for monitoring purposes of edible shellfish, from the limit of detection (0.3 microg OA/g hepatopancreas) to 13 microg OA/g hepatopancreas. Intra-assay precision of the method was 7% RSD at the quantification limit (0.97 microg OA/g hepatopancreas at S/N=10). Accuracy was tested in triplicate recovery experiments from OA-spiked shellfish where recovery ranged from 92 to 106% in the concentration range of 0.8 to 3.6 microg OA/g hepatopancreas. Useful information on critical factors affecting calibration and reproducibility is also reported. Good correlation (R=0.87) was observed between the results of the method and those of the method of Lee, after the analysis of 45 samples of mussels from the galician rias.     

Symmetry reductions and exact solutions of shallow water wave equations

In this paper we study symmetry reductions and exact solutions of the shallow water wave (SWW) equation $$u_{xxxt} + \alpha u_x u_{xt} + \beta u_t u_{xx} - u_{xt} - u_{xx} = 0,$$ whereα andβ are arbitrary, nonzero, constants, which is derivable using the so-called Boussinesq approximation. Two special cases of this equation, or the equivalent nonlocal equation obtained by settingu _x =U, have been discussed in the literature. The caseα=2β was discussed by Ablowitz, Kaup, Newell and Segur (Stud. Appl. Math.,53 (1974), 249), who showed that this case was solvable by inverse scattering through a second-order linear problem. This case and the caseα=β were studied by Hirota and Satsuma (J. Phys. Soc. Japan,40 (1976), 611) using Hirota's bi-linear technique. Further, the caseα=β is solvable by inverse scattering through a third-order linear problem. In this paper, a catalogue of symmetry reductions is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole (J. Math. Mech,18 (1969), 1025). The classical Lie method yields symmetry reductions of (1) expressible in terms of the first, third and fifth Painlevé transcendents and Weierstrass elliptic functions. The nonclassical method yields a plethora of exact solutions of (1) withα=β which possess a rich variety of qualitative behaviours. These solutions all like a two-soliton solution fort < 0 but differ radically fort > 0 and may be viewed as a nonlinear superposition of two solitons, one travelling to the left with arbitrary speed and the other to the right with equal and opposite speed. These families of solutions have important implications with regard to the numerical analysis of SWW and suggests that solving (1) numerically could pose some fundamental difficulties. In particular, one would not be able to distinguish the solutions in an initial-value problem since an exponentially small change in the initial conditions can result in completely different qualitative behaviours. We compare the two-soliton solutions obtained using the nonclassical method to those obtained using the singular manifold method and Hirota's bi-linear method. Further, we show that there is an analogous nonlinear superposition of solutions for two (2+1)dimensional generalisations of the SWW Equation (1) withα=β. This yields solutions expressible as the sum of two solutions of the Korteweg-de Vries equation.     

The structure type of Re2Te5, a new [M6X14] cluster compound

Re₂Te₅ crystallizes in a new structure type, having space group Pbca (No. 61) with a = 13.003(5), b = 12.935(7), c = 14.212(5) Å, Z = 12. All atoms are in the general positions 8(c), apart from one Te atom which occupies the special position 4(a) in a center of symmetry. The Re atoms are arranged in octahedral [Re₆] clusters and all the atoms in general positions can be grouped as {[Re₆Te₈]Te₆} complexes. The centers of these units and the Te atom in 4(a) are arranged like a slightly distorted rock salt structure. The Te atoms can be replaced by Se atoms up to at least 40%. Re₂Te₅ and Re₂Se₂Te₃ reveal a semiconductor-like electric behavior which is accounted for by the chemical bonding.     

Generalized roof duality

The roof dual bound for quadratic unconstrained binary optimization is the basis for several methods for efficiently computing the solution to many hard combinatorial problems. It works by constructing the tightest possible lower-bounding submodular function, and instead of minimizing the original objective function, the relaxation is minimized. However, for higher-order problems the technique has been less successful. A standard technique is to first reduce the problem into a quadratic one by introducing auxiliary variables and then apply the quadratic roof dual bound, but this may lead to loose bounds.We generalize the roof duality technique to higher-order optimization problems. Similarly to the quadratic case, optimal relaxations are defined to be the ones that give the maximum lower bound. We show how submodular relaxations can efficiently be constructed in order to compute the generalized roof dual bound for general cubic and quartic pseudo-boolean functions. Further, we prove that important properties such as persistency still hold, which allows us to determine optimal values for some of the variables. From a practical point of view, we experimentally demonstrate that the technique outperforms the state of the art for a wide range of applications, both in terms of lower bounds and in the number of assigned variables.     

Preparation,Crystal Structure and Properties of Spirophosphoranes Derived from Hydroxycarboxylic Acid Azides

Abstract

Spirophosphoranes are produced by reaction of 2–phenyl–1,3,2–dioxaphospholane with both 2- and 3–hydroxycarboxylic acid azides, whereas 1–phenyl–phospholane yields spirophosphoranes only upon reaction with the former. The structures of two spirophosphoranes have been determined by X-ray analysis.     

Synthesis and X-Ray Crystal Structure of an Annelated Spirophosphorane

Abstract

Reaction of the 2-azidoalcohol 1 with 2-phenyl1-1,3,2-dioxaphospholane leads to a 4:1 mixture of the pentacoordinate phosphorane 3 and the diazadiphosphetidine 4. In solution, these compounds are in equilibrium, presumably involving the not detectable iminophosphorane 2. A single X-ray analysis carried out on 3 proves the structure of this type of compound which has been postulated earlier as intermediate in the synthesis of aziridines from azidoalcohols^1,2     

Hot Branching Dynamics in a Light‐Harvesting Iron Carbene Complex Revealed by Ultrafast X‐ray Emission Spectroscopy

Iron N‐heterocyclic carbene (NHC) complexes have received a great deal of attention recently because of their growing potential as light sensitizers or photocatalysts. We present a sub‐ps X‐ray spectroscopy study of an Fe^IINHC complex that identifies and quantifies the states involved in the deactivation cascade after light absorption. Excited molecules relax back to the ground state along two pathways: After population of a hot ³MLCT state, from the initially excited ¹MLCT state, 30 % of the molecules undergo ultrafast (150 fs) relaxation to the ³MC state, in competition with vibrational relaxation and cooling to the relaxed ³MLCT state. The relaxed ³MLCT state then decays much more slowly (7.6 ps) to the ³MC state. The ³MC state is rapidly (2.2 ps) deactivated to the ground state. The ⁵MC state is not involved in the deactivation pathway. The ultrafast partial deactivation of the ³MLCT state constitutes a loss channel from the point of view of photochemical efficiency and highlights the necessity to screen transition‐metal complexes for similar ultrafast decays to optimize photochemical performance.