Matematično programiranje in trg električne energije

diplomsko delo

Mojca Bračič (Author), Drago Bokal (Mentor)

Abstract

V diplomskem delu je predstavljena osnovna teorija matematičnih programov. V začetnem delu so zajeti predvsem pojmi in izreki, v povezavi s konveksnimi in konkavnimi funkcijami na konveksni množici, ki vodijo do pomembnih ugotovitev, povezanih z lokalnimi in globalnimi ekstremi. Ti izreki so pomembni v matematičnem programiranju, saj ob določenih posebnih predpostavkah, kot sta konveksnost in linearnost, omogočajo preprostejše načine iskanja optimalne rešitve danega programa. Kot pomemben primer matematičnega programiranja je predstavljen linearen program in njegov dual. Opisan je postopek pretvorbe linearnega programa v dualni program in izrek o dualnosti, ki pravi, da imata primarni in dualni program enaki optimalni vrednosti kriterijske funkcije, če optimalna rešitev obstaja. Prav tako je opisana ekonomska vloga dualnih spremenljivk in z njimi povezane senčne cene. Predstavljeni so Kuhn-Tuckerjevi pogoji za optimalnost rešitve matematičnega programa, ki so potrebni pogoji za lokalni ekstrem in pri posebnih predpostavkah zadostni pogoji za globalni ekstrem. V drugem delu sledi kratka predstavitev trga električne energije in njegovih udeležencev. Predstavljeni so modeli proizvajalcev, odjemalcev, trgovcev in borza električne energije. Pomembni vprašanji, s katerima se proizvajalci, odjemalci in trgovci soočajo, sta, koliko energije kupiti (prodati) z dvostranskimi pogodbami in koliko na borzi električne energije. Običajno se za daljše obdobje udeleženci odločijo za dvostranske pogodbe, ki zagotavljajo zadostno količino električne energije po nespremenjenih cenah, kar pa nujno ne prinaša maksimalnega dobička. V primerih povečanega povpraševanja oz. padca cen električne energije se zatekajo k nakupu na organiziranem trgu. Opisani so matematični programi, ki maksimirajo dobiček posameznih udeležencev, glede na dane omejitve.

Keywords

matematika;programiranje;električna energija;trg;linearno programiranje;dualni program;senčne cene;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2009
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[M. Bračič]
UDC:	51(043.2)
COBISS:	16809992
Views:	3066
Downloads:	408
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	MATHEMATICAL PROGRAMMING AND ELECTRICITY MARKETS
Secondary abstract:	In this diploma thesis, we present a theoretical basis of mathematical programming. At the beginning, we describe notation and theorems related to convex and concave functions on convex sets, which is the basis of important results about local and global extremes. These theorems are important in mathematical programming, because they allow for more efficient methods of finding the optimal solution of a mathematical program, under suitable convexity and linearity assumptions. Next, we present an important basic case of mathematical programming that is linear program and its dual program, including a procedure of how to find the dual of normal linear program and the dual theorem, which says if the optimal value exists, it's the same for both the primal and the dual program. We also present the economical interpretation of the dual variables as shadow prices. At the end of the theoretical part, we describe the Kuhn-Tucker conditions. These are the necessary conditions for local optimality for a mathematical program. Under suitable restrictions, they are also sufficient conditions for global optimality. In the second part of this diploma thesis, we continue with a short presentation of electricity markets and their participants. We describe the viewpoints of the main participants including producers, consumers, energy service companies, and a pool operator. A decision problem that we investigate is how much energy to buy (sell) with bilateral contracts and how much energy to buy from or sell in the power pool. It turns out that participants decide on bilateral contracts in longer terms, because of their reliability and fixed price in advance, but this does not necessarly give the maximal profit. In case of lower prices in the power pool and increased demand for electrical energy, the participants decide to buy energy from or sell it in the pool. According to this, we describe mathematical programs that maximize profits for all participants under certain constraints.
Secondary keywords:	Mathematical programming;linear programming;shadow price;dual problem;electricity market;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	62 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	17718