Primena Lagranžove optimizacije na problematiku proizvodnje energije iz obnovljivih izvora

The apparent increase of ecological awareness during the previous decade has led to the need for adaptation of numerous areas of everyday human lives, so they fit the newly developed environmental tendencies. One of the areas in which this necessity was prominent was the power engineering, where, above all, the understanding of production systems was affected, with the turnabout regarding the distancing from the conventional sources and inclining towards the more acceptable renewable sources taking place. However, alongside the undeniable ecological sustainability of these sources, the financial sustainability of their utilization needs to be considered as well, which is why the subject of this paper is the minimization of costs of energy production in these capacities, if the fictious demand area needed to be supplied. It was assumed that this area is separated from transmission and distribution network, with the sole source of energy for the analyzed consumption being the wind, solar and hydro power plants, located in the close vicinity of the examined area. As the objective of the optimization, performed by the method of Lagrange multipliers, the appropriate apportioning of the generation powers in these plants for every hour during the year was selected, so the total yearly costs of supplying the demand were as low as possible. Also, considering the currently promoted methods intended for encouragement of the potential investors to proceed with the projects that encompass renewable sources, the different cases for which the share of renewables included in the feed-in tariff was varied. Finally, in order to provide the full insight into the optimization procedure, for the randomly selected hour of the year and share of feed-in tariff in the generation capacities, the process of calculation of production powers in the described plants and multipliers needed for application of the selected optimization technique was enclosed.