Maximum loading problems using stochastic nonlinear programming and confidence intervals

Abstract

This paper presents a stochastic non-linear program (S-NLP) with a confidence interval constraint. The problem extends the conventional maximum loading problem to include randomness Vnd uncertainty in system loading levels.The problem restricts the 99% confidence interval of the loading level to be within a pre-specified amount of the mean. The paper presents solutions when the confidence interval is restricted to be within 15, 20, and 25% of the mean.The proposed solution methodology is tested using the IEEE 30 bus system and results are compared against solutions found using Monte Carlo Simulations. Each of the Monte Carlo Simulations consist of 10,000 samples.

Modelling the growth and ethanol production of Brettanomyces bruxellensis at different glucose concentrations

“…For the last three conditions with 163, 176 and 214 g l −1 glucose concentrations, a third phase was included which models the presence of a critical product that shows inhibition effect stopping substrate consumption, biomass growth and ethanol production. For kinetic parameters estimation, a Simplex method was used, and final values were reached in just one or two interactions (Schellenberg et al. 2005).…”

Modeling of yeast Brettanomyces bruxellensis growth at different acetic acid concentrations under aerobic and anaerobic conditions

“…The confidence interval [24,25] for the parameters Y x/s a 1 K s and K i were obtained by a statistical method [26,27], which includes a parameter sensitivity analysis of the model [28]: The individual confidence limits of each parameter estimate at probability level (1 -a t ) were obtained with the expressions below: …”