Neise Risk Management in Stochastic Integer Programming

With Application to Dispersed Power Generation
1. Auflage 2008
ISBN: 978-3-8348-9536-3
Verlag: Vieweg & Teubner
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 107 Seiten, Web PDF

Reihe: Mathematics and Statistics

I am deeply grateful to my advisor Prof. Dr. Rüdiger Schultz for his untiring - couragement. Moreover, I would like to express my gratitude to Prof. Dr. -Ing. - mund Handschin and Dr. -Ing. Hendrik Neumann from the University of Dortmund for inspiration and support. I would like to thank PD Dr. René Henrion from the Weierstrass Institute for Applied Analysis and Stochastics in Berlin for reviewing this thesis. Cordial thanks to my colleagues at the University of Duisburg-Essen for motivating and fruitful discussions as well as a pleasurable cooperation. Contents 1 Introduction 1 1. 1 Stochastic Optimization. . . . . . . . . . . . . . . . . . . . . . . 3 1. 1. 1 The two-stage stochastic optimization problem . . . . . . 3 1. 1. 2 Expectation-based formulation. . . . . . . . . . . . . . . 5 1. 2 Content and Structure. . . . . . . . . . . . . . . . . . . . . . . . 6 2 RiskMeasuresinTwo-StageStochasticPrograms 9 2. 1 Risk Measures. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2. 1. 1 Deviation measures. . . . . . . . . . . . . . . . . . . . . 10 2. 1. 2 Quantile-based risk measures . . . . . . . . . . . . . . . 11 2. 2 Mean-Risk Models . . . . . . . . . . . . . . . . . . . . . . . . . 12 2. 2. 1 Results concerning structure and stability . . . . . . . . . 13 2. 2. 2 Deterministic equivalents. . . . . . . . . . . . . . . . . . 22 2. 2. 3 Algorithmic issues – dual decomposition method . . . . . 26 3 StochasticDominanceConstraints 33 3. 1 Introduction to Stochastic Dominance . . . . . . . . . . . . . . . 33 3. 1. 1 Stochastic orders for the preference of higher outcomes . . 34 3. 1. 2 Stochastic orders for the preference of smaller outcomes . 38 3. 2 Stochastic Dominance Constraints . . . . . . . . . . . . . . . . . 42 3. 2. 1 First order stochastic dominanceconstraints. . . . . . . . 43 3. 2. 2 Results concerning structure and stability . . . . . . . . . 44 3. 2. 3 Deterministic equivalents. . . . . . . . . . . . . . . . . . 51 3. 2. 4 Algorithmic issues . . . . . . . . . . . . . . . . . . . . .

Zielgruppe

Research

Autoren/Hrsg.

Neise, Frederike

Inhaltsverzeichnis

Risk Measures in Two-Stage Stochastic Programs.- Stochastic Dominance Constraints induced by Mixed-Integer Linear Recourse.- Application: Optimal Operation of a Dispersed Generation System.- Conclusion and Perspective.

Leseproben

4 Application: Optimal Operation of a Dispersed Generation (S. 69-70)

System In this chapter we apply the introduced theories and algorithms to an optimization problem from power planning. We consider a dispersed generation system which is run by a German utility. We aim at an optimal operation with respect to technical constraints, the supply of thermal an electric demand, and the minimization of operational costs.

4.1 A Dispersed Generation System

A dispersed generation (DG) system is a combination of several power and/or heat generating units with a low capacity compared to conventional nuclear or coal- .red power stations. The single units, which can be installed decentrally, next to the consumers, are linked via communication networks and considered as one power producing system, also called Virtual Power Plant ([AKKM02, HBU02, IR02]). A de.nition can be found in [AAS01]. As reported in former studies (see e.g., [HNNS06]), the operation of dispersed generation units as one system is economically superior to the autarkic operation of each single unit.

Dispersed generation units can be combined heat and power (CHP) units which produce heat and power simultaneously, for example fuel cells, gas motors, or gas turbines, as well as units gaining power from renewable resources like wind turbines, hydroelectric power plants, or photovoltaic devices. Usually, also boilers are included to supply load peaks of heat. Furthermore, DG systems are often equipped with thermal storages and also with cooling devices to exhaust excessive heat. Electric storages are not considered here because either their capacity is too big to be used in DG systems or they store energy only for such a short time that it is not relevant for optimization.

Instead, we assume that electric energy can always be sold completely and imported if production does not meet demand. DG systems gain more and more importance today because of several reasons ([Neu04]). On the one hand they are preferable over custom power plants because of their high overall efficiency – installation next to consumers avoids transportation costs ([BHHU03]) – as well as the comparably low investments needed. They show a high .exibility which enables the operator to react immediately and to supply sudden load peaks, for example.

Furthermore, the energy generation with dispersed generation is environmentally friendly compared to convential power generation. On the other hand the current political development promotes the installation of dispersed generation units. For example, the pending nuclear phaseout has to be compensated ("Gesetz zur geordneten Beendigung der Kernenergienutzung zur gewerblichen Erzeugung von Elektrizität", AtG-E). Moreover, the usage of renewable resources is encouraged by the"Erneuerbare Energien Gesetz" (EEG), where it is stated that power generation from renewable resources should be increased to 20 % of the whole power production in 2020.

Furthermore, the "Kraft-Wärme-Kopplungsgesetz" (KWKG) dictates that CO2 emissions should be reduced by at least 20 million tons until 2010 (based on the emissions of 1998) by an increase of the installed CHP capacity. Additionally, the power generation with CHP units is subsidized. Last but not least many of the existing generation capacities are out-aged and will have to be replaced in the next years ([MMV05]). This stimulates a discussion of new trends, efficiency improvements, and the development of innovative techniques in power generation. The optimal operation of a DG system requires complex decisions ([Han02]) which are substantially influenced by uncertainty.

Über Autor(innen)

Dr. Frederike Neise gained a PhD in Mathematics from the University of Duisburg-Essen studying two-stage stochastic programming and its application to the optimal management of dispersed generation systems. She currently works as a gas market analyst with E.ON Ruhrgas AG.