Minimising the expectation value of the procurement cost in electricity markets based on the prediction error of energy consumption

In this paper, we formulate a method for minimising the expectation value of the procurement cost of electricity in two popular spot markets: {\it day-ahead} and {\it intra-day}, under the assumption that expectation value of unit prices and the distributions of prediction errors for the electricity demand traded in two markets are known. The expectation value of the total electricity cost is minimised over two parameters that change the amounts of electricity. Two parameters depend only on the expected unit prices of electricity and the distributions of prediction errors for the electricity demand traded in two markets. That is, even if we do not know the predictions for the electricity demand, we can determine the values of two parameters that minimise the expectation value of the procurement cost of electricity in two popular spot markets. We demonstrate numerically that the estimate of two parameters often results in a small variance of the total electricity cost, and illustrate the usefulness of the proposed procurement method through the analysis of actual data

Measurement of High Temperature Thermodynamic Propertiesof Several Binary Alkali Silicate Glasses

The method for continuous measurement of the high temperature heat content, developed by W.Oelsen et al. and applied to the glasses by M.Tashiro, was examined and modified in some points. Relations between the temperature and heat contents referred to the standard temperature 25℃, were determined for the some glasses of R(2)O-SiO(2) system, and the specific heats as well as the entropies were calculated. Comparing the results, some views have been obtained relating to the effect of the species and content of alkali ions on the thermodynamic quantities of such glasses