Real-Time Pricing of Smart Grid Based on Piece-Wise Linear Functions

In a power grid system, utility is a measure of the satisfaction of users' electricity consumption; cost is a monetary value of electricity generated by the supplier. The utility and cost functions represent the satisfaction of different users and the supplier. Quadratic utility, logarithmic utility,and quadratic cost functions are widely used in social welfare maximization models of real-time pricing. These functions are not universal; they have to be discussed in detail for individual models. To overcome this problem, a piece-wise linear utility function and a piece-wise linear cost function with general properties are proposed in this paper. By smoothing the piece-wise linear utility and cost functions, a social welfare maximization model can be transformed into a differentiable convex optimization problem. A dual optimization method is used to solve the smoothed model. Through mathematical deduction and numerical simulations, the rationality of the model and the validity of the algorithm are verified as long as the elastic and cost coefficients take appropriate values. Thus, different user types and the supplier can be determined by selecting different elastic and cost coefficients.     

Effects of drug-polymer dispersions on solubility and <Emphasis Type="Italic">in vitro</Emphasis> diffusion of artemisinin across a polydimethylsiloxane membrane

Artemisinin(ART) is a sesquiterpene lactone with an endo-peroxide bridge that is thought to be responsible for its antimalarial activity.It has low oral bioavailability because of aqueous insolubility,which leads to local toxicity at the site of aggregation.The present work focused on increasing its solubility and evaluating its permeation across a model membrane to mimic transdermal delivery that bypasses the hepatic metabolism.For this purpose,physical mixtures(PM),solid dispersions(SD) and lyophilized dispersions(LD) with different drug-polymer ratios(1:0.5,1:1,1:2,1:4 and 1:9) were prepared using the hydrophilic polymer polyvinylpyrrolidone(PVP).Drug-polymer dispersions were characterized using X-ray diffraction(XRD) and Fourier transform infrared spectroscopy(FTIR).Solubility was measured in three solvents:de-ionized water,phosphate buffered saline(PBS) and methanol.The toluene-water partition coefficient was evaluated and compared with the literature and calculated logP values.In vitro diffusion of ART was studied across a polydimethylsiloxane membrane from a saturated solution of drug-polymer dispersions.XRD patterns showed a gradual decrease in crystallinity of ART with increasing polymer concentration,while FTIR confirmed no interactions between ART and PVP.Solubility was increased up to 4-,5-and 8-fold for LD in water,PBS and methanol,respectively.The logP for toluene-water was 2.65 ± 0.3,which is in good agreement with literature and calculated logP values.Permeation was enhanced,which is attributed to the decrease in crystallinity and increase in wettability of the drug.The ART flux was significantly higher than that of pure ART(0.12 ± 0.01) with increasing PVP concentration for SD and LD formulations.In conclusion,drug-polymer dispersions with PVP improve the pharmaceutical properties of ART in the order LD>SD>PM.