20 research outputs found
Dynamic Incentives for Optimal Control of Competitive Power Systems
Technologisch herausfordernde Transformationsprozesse wie die Energiewende können durch passende Anreizsysteme entscheidend beschleunigt werden. Ziel solcher Anreize ist es hierbei, ein Umfeld idealerweise so zu schaffen, dass das Zusammenspiel aller aus Sicht der beteiligten Wettbewerber individuell optimalen Einzelhandlungen auch global optimal im Sinne eines übergeordneten Großziels ist. Die vorliegende Dissertation schafft einen regelungstechnischen Zugang zur Frage optimaler Anreizsysteme für heutige und zukünftige Stromnetze im Zieldreieck aus Systemstabilität, ökonomischer Effizienz und Netzdienlichkeit. Entscheidende Neuheit des entwickelten Ansatzes ist die Einführung zeitlich wie örtlich differenzierter Echtzeit-Preissignale, die sich aus der Lösung statischer und dynamischer Optimierungsprobleme ergeben. Der Miteinbezug lokal verfügbarer Messinformationen, die konsequente Mitmodellierung des unterlagerten physikalischen Netzes inklusive resistiver Verluste und die durchgängig zeitkontinuierliche Formulierung aller Teilsysteme ebnen den Weg von einer reinen Anreiz-Steuerung hin zu einer echten Anreiz-Regelung. Besonderes Augenmerk der Arbeit liegt in einer durch das allgemeine Unbundling-Gebot bedingten rigorosen Trennung zwischen Markt- und Netzakteuren. Nach umfangreicher Analyse des hierbei entstehenden geschlossenen Regelkreises erfolgt die beispielhafte Anwendung der Regelungsarchitektur für den Aufbau eines neuartigen Echtzeit-Engpassmanagementsystems. Weitere praktische Vorteile des entwickelten Ansatzes im Vergleich zu bestehenden Konzepten werden anhand zweier Fallstudien deutlich. Die port-basierte Systemmodellierung, der Verzicht auf zentralisierte Regeleingriffe und nicht zuletzt die Möglichkeit zur automatischen, dezentralen Selbstregulation aller Preise über das Gesamtnetz hinweg stellen schließlich die problemlose Erweiterbarkeit um zusätzliche optionale Anreizkomponenten sicher
Dynamic Incentives for Optimal Control of Competitive Power Systems
This work presents a real-time dynamic pricing framework for future electricity markets. Deduced by first-principles analysis of physical, economic, and communication constraints within the power system, the proposed feedback control mechanism ensures both closed-loop system stability and economic efficiency at any given time. The resulting price signals are able to incentivize competitive market participants to eliminate spatio-temporal shortages in power supply quickly and purposively
Dynamic Incentives for Optimal Control of Competitive Power Systems
This work presents a real-time dynamic pricing framework for future electricity markets. Deduced by first-principles analysis of physical, economic, and communication constraints within the power system, the proposed feedback control mechanism ensures both closed-loop system stability and economic efficiency at any given time. The resulting price signals are able to incentivize competitive market participants to eliminate spatio-temporal shortages in power supply quickly and purposively
An exponential bound on the number of non-isotopic commutative semifields
We show that the number of non-isotopic commutative semifields of odd order
is exponential in when and is not a power of . We
introduce a new family of commutative semifields and a method for proving
isotopy results on commutative semifields that we use to deduce the
aforementioned bound. The previous best bound on the number of non-isotopic
commutative semifields of odd order was quadratic in and given by Zhou and
Pott [Adv. Math. 234 (2013)]. Similar bounds in the case of even order were
given in Kantor [J. Algebra 270 (2003)] and Kantor and Williams [Trans. Amer.
Math. Soc. 356 (2004)].Comment: 27 pages. Incorporates reviewer comments. To appear in Transactions
of the American Mathematical Societ
Value Distributions of Perfect Nonlinear Functions
In this paper, we study the value distributions of perfect nonlinear
functions, i.e., we investigate the sizes of image and preimage sets. Using
purely combinatorial tools, we develop a framework that deals with perfect
nonlinear functions in the most general setting, generalizing several results
that were achieved under specific constraints. For the particularly interesting
elementary abelian case, we derive several new strong conditions and
classification results on the value distributions. Moreover, we show that most
of the classical constructions of perfect nonlinear functions have very
specific value distributions, in the sense that they are almost balanced.
Consequently, we completely determine the possible value distributions of
vectorial Boolean bent functions with output dimension at most 4. Finally,
using the discrete Fourier transform, we show that in some cases value
distributions can be used to determine whether a given function is perfect
nonlinear, or to decide whether given perfect nonlinear functions are
equivalent.Comment: 28 pages. minor revisions of the previous version. The paper is now
identical to the published version, outside of formattin
Mathematical aspects of the design and security of block ciphers
Block ciphers constitute a major part of modern symmetric cryptography. A mathematical analysis is necessary to ensure the security of the cipher. In this thesis, I develop several new contributions for the analysis of block ciphers. I determine cryptographic properties of several special cryptographically interesting mappings like almost perfect nonlinear functions. I also give some new results both on the resistance of functions against differential-linear attacks as well as on the efficiency of implementation of certain block ciphers
Image sets of perfectly nonlinear maps
We present a lower bound on the image size of a -uniform map, ,
of finite fields, by extending the methods used for planar maps. In the
particularly interesting case of APN maps on binary fields, our bound coincides
with the one obtained by Ingo Czerwinski, using a linear programming method.
We study properties of APN maps of with minimal image set.
In particular, we observe that for even , a Dembowski-Ostrom polynomial of
form is APN if and only if is almost-3-to-1, that is when
its image set is minimal. We show that any almost-3-to-1 quadratic map is APN,
if is even. For odd, we present APN Dembowski-Ostrom polynomials on
with image sizes and .
We present several results connecting the image sets of special APN maps with
their Walsh spectrum. Especially, we show that a large class of APN maps has
the classical Walsh spectrum. Finally, we prove that the image size of a
non-bijective almost bent map contains at most elements.Comment: Minor revision with new references; Theorems 18, 19 are adde