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.     

Amorphous drug nanosuspensions. 1. Inhibition of Ostwald ripening

Amorphous drug nanosuspensions are prone to particle growth due to Ostwald ripening. By incorporating a second component of extremely low aqueous solubility, Ostwald ripening can be inhibited. These studies indicate that to inhibit ripening, the drug/inhibitor mixture (in the particles) must form a single phase. The drug/inhibitor mixture can be characterized by the interaction parameter chi using the Bragg-Williams theory, in which single phase mixtures are obtained for chi < 2. The chi parameter can be calculated from the (crystalline) solubility of the drug in the inhibitor, provided the inhibitor is a liquid, and the melting entropy and temperature of the drug.     

Amorphous drug nanosuspensions. 3. Particle dissolution and crystal growth

In the present paper, we have studied particle dissolution and crystal growth of the poorly water soluble drug felodipine, using fluorescence as a probe for the amount of crystalline material. Dissolution kinetics is essentially diffusion-controlled, while the rate of crystal growth is significantly slower compared to the diffusion-controlled limit. The deviation from diffusion control was characterized by the effective length, lambda, related to the kinetics of a surface integration process. Amorphous nanoparticles may be highly unstable in the presence of small amounts of crystalline particles. This is due to the fact that the molecular solubility from the amorphous nanoparticles often is at least an order of magnitude higher than the corresponding crystalline solubility. In a mixed system where crystalline nanoparticles have been added to an amorphous nanosuspension, the bulk will have a monomer concentration intermediate between the amorphous and crystalline solubilities, and is thus supersaturated with respect to the crystalline particles while being undersaturated with respect to the amorphous particles. As a consequence, the amorphous particles spontaneously dissolve, while crystalline particles grow, in a combined process which is similar to Ostwald ripening. By knowing the parameters describing dissolution and crystal growth, respectively, it was possible to simulate the outcome of controlled seeding experiments, where a small amount of crystalline nanoparticles was added to a dispersion of amorphous nanoparticles. A good agreement between model calculations and experiments was obtained including how the crystal growth rate varied with the amounts of added crystalline seeds.     

Amorphous drug nanosuspensions. 2. Experimental determination of bulk monomer concentrations

A simple turbidimetric method was developed to measure the bulk concentration of drug in nanosuspensions. The bulk concentrations measured were in the range from 1 microM to 1 mM. The accuracy of the method was checked by determination of the bulk concentration of crystalline nanosuspensions, i.e., the crystalline solubility, which compared favorably to solubilities measured by a conventional method. Results obtained for amorphous nanosuspensions agreed with predictions using a theory describing the relative solubility between a supercooled liquid and a crystal. Further, it was found that the bulk concentration in Ostwald ripening inhibited amorphous nanosuspensions and could be lowered by incorporation of higher amounts of the inhibitor, in agreement with predictions using the Bragg-Williams theory of nonideal solutions.