abstract: The large distributed electric power system is a hierarchical network involving the transportation of power from the sources of power generation via an intermediate densely connected transmission network to a large distribution network of end-users at the lowest level of the hierarchy. At each level of the hierarchy (generation/ trans- mission/ distribution), the system is managed and monitored with a combination of (a) supervisory control and data acquisition (SCADA); and (b) energy management systems (EMSs) that process the collected data and make control and actuation de- cisions using the collected data. However, at all levels of the hierarchy, both SCADA and EMSs are vulnerable to cyber attacks. Furthermore, given the criticality of the electric power infrastructure, cyber attacks can have severe economic and social con- sequences. This thesis focuses on cyber attacks on SCADA and EMS at the transmission level of the electric power system. The goal is to study the consequences of three classes of cyber attacks that can change topology data. These classes include: (i) unobservable state-preserving cyber attacks that only change the topology data; (ii) unobservable state-and-topology cyber-physical attacks that change both states and topology data to enable a coordinated physical and cyber attack; and (iii) topology- targeted man-in-the-middle (MitM) communication attacks that alter topology data shared during inter-EMS communication. Specically, attack class (i) and (ii) focus on the unobservable attacks on single regional EMS while class (iii) focuses on the MitM attacks on communication links between regional EMSs. For each class of attacks, the theoretical attack model and the implementation of attacks are provided, and the worst-case attack and its consequences are exhaustively studied. In particularly, for class (ii), a two-stage optimization problem is introduced to study worst-case attacks that can cause a physical line over ow that is unobservable in the cyber layer. The long-term implication and the system anomalies are demonstrated via simulation. For attack classes (i) and (ii), both mathematical and experimental analyses sug- gest that these unobservable attacks can be limited or even detected with resiliency mechanisms including load monitoring, anomalous re-dispatches checking, and his- torical data comparison. For attack class (iii), countermeasures including anomalous tie-line interchange verication, anomalous re-dispatch alarms, and external contin- gency lists sharing are needed to thwart such attacks. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2015

Magisterská práce se zabývá stochastickou optimalizací síťových úloh. Teoretická část pokrývá tři témata - teorii grafů, optimalizaci a progressive hedging algoritmus. V rámci optimalizace je hlavní část věnována stochastickému programování a dvoustupňovému programování. Progressing hedging algoritmus zahrnuje také metodu přiřazování scénářů a modifikaci obecného algoritmu na dvou stupňové úlohy. Praktická část je věnována modelům na reálných datech z oblasti svozu odpadu v rámci České republiky. Data poskytl Ústav procesního inženýrství.

Optimalizace toku v síti je klasickou aplikací matematického programování. Tyto modely mají, mimo jiné, široké uplatnění také v logistice, kde se tak snažíme docílit optimálního rozdělení dopravy, např. vzhledem k maximalizaci zisku, či minimalizaci nákladů. Toto pojetí ovšem často problém idealizuje, poněvadž předpokládá existenci jediného rozhodovatele. Takový přístup je možný ve striktně organizovaných sítích jako např. v logistických sítích přepravních společností, železničních sítích či armádním zásobování. Úloha ''Traffic Assignment Problem'' (TAP) se zaměřuje na dopady teorie her na optimalizaci toku, tj. zkoumá vliv více rozhodovatelů na celkové využití sítě. V práci se zaobíráme úlohou TAP s působením náhodných vlivů, k čemuž využíváme metod stochastické a vícestupňové optimalizace. Dále zkoumáme možnosti zlepšení stávajícího využití sítě za rozhodnutí autoritativního rozhodovatele, kterému je umožněn zásah do samotné struktury sítě, k čemuž využíváme víceúrovňové programování.

We consider a class of periodic preventive maintenance (PM) optimization problems, for a single piece of equipment that deteriorates with time or use, and can be repaired upon failure, through corrective maintenance (CM). We develop analytical and simulation-based optimization models that seek an optimal periodic PM policy, which minimizes the sum of the expected total cost of PMs and the risk-averse cost of CMs, over a finite planning horizon. In the simulation-based models, we assume that both types of maintenance actions are imperfect, whereas our analytical models consider imperfect PMs with minimal CMs. The effectiveness of maintenance actions is modeled using age reduction factors. For a repairable unit of equipment, its virtual age, and not its calendar age, determines the associated failure rate. Therefore, two sets of parameters, one describing the effectiveness of maintenance actions, and the other that defines the underlying failure rate of a piece of equipment, are critical to our models. Under a given maintenance policy, the two sets of parameters and a virtual-age-based age-reduction model, completely define the failure process of a piece of equipment. In practice, the true failure rate, and exact quality of the maintenance actions, cannot be determined, and are often estimated from the equipment failure history. We use a Bayesian approach to parameter estimation, under which a random-walk-based Gibbs sampler provides posterior estimates for the parameters of interest. Our posterior estimates for a few datasets from the literature, are consistent with published results. Furthermore, our computational results successfully demonstrate that our Gibbs sampler is arguably the obvious choice over a general rejection sampling-based parameter estimation method, for this class of problems. We present a general simulation-based periodic PM optimization model, which uses the posterior estimates to simulate the number of operational equipment failures, under a given periodic PM policy. Optimal periodic PM policies, under the classical maximum likelihood (ML) and Bayesian estimates are obtained for a few datasets. Limitations of the ML approach are revealed for a dataset from the literature, in which the use of ML estimates of the parameters, in the maintenance optimization model, fails to capture a trivial optimal PM policy. Finally, we introduce a single-stage and a two-stage formulation of the risk-averse periodic PM optimization model, with imperfect PMs and minimal CMs. Such models apply to a class of complex equipment with many parts, operational failures of which are addressed by replacing or repairing a few parts, thereby not affecting the failure rate of the equipment under consideration. For general values of PM age reduction factors, we provide sufficient conditions to establish the convexity of the first and second moments of the number of failures, and the risk-averse expected total maintenance cost, over a finite planning horizon. For increasing Weibull rates and a general class of increasing and convex failure rates, we show that these convexity results are independent of the PM age reduction factors. In general, the optimal periodic PM policy under the single-stage model is no better than the optimal two-stage policy. But if PMs are assumed perfect, then we establish that the single-stage and the two-stage optimization models are equivalent. / text