Distributed learning for optimal allocation of synchronous and converter-based generation

Motivated by the penetration of converter-based generation into the electrical grid, we revisit the classical log-linear learning algorithm for optimal allocation {of synchronous machines and converters} for mixed power generation. The objective is to assign to each generator unit a type (either synchronous machine or DC/AC converter in closed-loop with droop control), while minimizing the steady state angle deviation relative to an optimum induced by unknown optimal configuration of synchronous and DC/AC converter-based generation. Additionally, we study the robustness of the learning algorithm against a uniform drop in the line susceptances and with respect to a well-defined feasibility region describing admissible power deviations. We show guaranteed probabilistic convergence to maximizers of the perturbed potential function with feasible power flows and demonstrate our theoretical findings via simulative examples of power network with six generation units.Comment: 7 pages, 3 figure

Power Flow Control In Hybrid Ac/Dc Microgrids

Microgrid structures allow for more efficient utilization of renewable resources as well as autonomous operation. Ideally, a centralized controller would be available to allow for an optimizer to take all components into account so that they may collaboratively work towards a shared goal. To this end, a centralized optimization method was developed called the squared slack interior point method. The novelty of this method is that it incorporates the fraction to bound rule to alleviate the known ill-conditioning introduced by utilizing squared slack variables to handle inequality constraints. In addition, this method also allows for inequality constraint violations to be quantified in the same manner that equality constraints are quantified. The proposed method is found to quickly and accurately calculate the optimal power flow and reject solutions that violate the inequality constraints beyond some specified tolerance. Where centralized information is not available, a decentralized method is required. In this method, constrained game theoretical optimization is utilized. However, due to unknown information about remote loads, inconsistent solution among players result in overloaded generators. To alleviate this issue, two perturbation methods are introduced. The first is overload feedback and the second is the perturb and observe squeeze method. In both methods, the goal is to adjust voltage angles and magnitudes to locally manage generator output. Both methods are found to rapidly drive overloaded sources back within their desired tolerances. Moreover, the game theoretical approach is found to have poor performance in the absence of shared load information among players. It is determined that the localized optimizers should be removed to reduce cost and that the operating condition should be perturb starting from the most recently available power flow calculation or starting from the nominal value. Also, to manage voltage stability in the absence of communication, a Hamiltonian approach is implemented for the voltage source rectifier. This approach resulted in a highly stable voltage and a fast response to large step changes. The method was able to maintain the reference dc output at unity power factor while not requiring any information about loading or interconnection

Data-Driven Stealthy Injection Attacks on Smart Grid

Smart grid cyber-security has come to the forefront of national security priorities due to emergence of new cyber threats such as the False Data Injection (FDI) attack. Using FDI, an attacker can intelligently modify smart grid measurement data to produce wrong system states which can directly affect the safe operation of the physical grid. The goal of this thesis is to investigate key research problems leading to the discovery of significant vulnerabilities and their impact on smart grid operation. The first problem investigates how a stealthy FDI attack can be constructed without the knowledge of system parameters, e.g., line reactance, bus and line connectivity. We show how an attacker can successfully carry out an FDI attack by analysing subspace information of the measurement data without requiring the system topological knowledge. In addition, we make a critical observation that existing subspace based attacks would fail in the presence of gross errors and missing values in the observed data. Next, we show how an attacker can circumvent this problem by using a sparse matrix separation technique. Extensive evaluation on several benchmark systems demonstrates the effectiveness of this approach. The second problem addresses the scenario when an attacker may eavesdrop but only has access to a limited number of measurement devices to inject false data. We show how an attack can be constructed by first estimating the hidden system topology from measurement data only and then use it to identify a set of critical sensors for data injection. Extensive experiments using graph-theoretic and eigenvalue analyses demonstrate that the estimated power grid structure is very close to the original grid topology, and a stealthy FDI attack can be carried out using only a small fraction of all available sensors. The third problem investigates a new type of stealthy Load Redistribution (LR) attack using FDI which can deliberately cause changes in the Locational Marginal Price (LMP) of smart grid nodes. To construct the LR-FDI attack, the Shift factor is estimated from measurement and LMP data. Finally, the impact of the attacks on the state estimation and the nodal energy prices is thoroughly investigated

Two-Stage Stochastic Semidefinite Programming: Theory, Algorithms, and Application to AC Power Flow under Uncertainty

In real life decision problems, one almost always is confronted with uncertainty and risk. For practical optimization problems this is manifested by unknown parameters within the input data, or, an inexact knowledge about the system description itself. In case the uncertain problem data is governed by a known probability distribution, stochastic programming offers a variety of models hedging against uncertainty and risk. Most widely employed are two-stage models, who admit a recourse structure: The first-stage decisions are taken before the random event occurs. After its outcome, a recourse (second-stage) action is made, often but not always understood as some "compensation''. In the present thesis, the optimization problems that involve parameters which are not known with certainty are semidefinite programming problems. The constraint sets of these optimization problems are given by intersections of the cone of symmetric, positive semidefinite matrices with either affine or more general equations. Objective functions, formally, may be fairly general, although they often are linear as in the present thesis. We consider risk neutral and risk averse two-stage stochastic semidefinite programs with continuous and mixed-integer recourse, respectively. For these stochastic optimization problems we analyze their structure, derive solution methods relying on decomposition, and finally apply our results to unit commitment in alternating current (AC) power systems. Furthermore, deterministic unit commitment in AC power transmission systems is addressed. Beside traditional unit commitment constraints, the physics of power flow are included. To gain globally optimal solutions a recent semidefinite programming (SDP) approach is used which leads to large-scale semidefinite programs with discrete variables on top. As even the SDP relaxation of these programs is too large for being handled in an all-at-once manner by general SDP solvers, it requires an efficient and reliable method to tackle them. To this end, an algorithm based on Benders decomposition is proposed. With power demand (load) and in-feed from renewables serving as sources of uncertainty, two-stage stochastic programs are set up heading for unit commitment schedules which are both cost-effective and robust with respect to data perturbations. The impact of different, risk neutral and risk averse, stochastic criteria on the shapes of the optimal stochastic solutions will be examined. To tackle the resulting two-stage programs, we propose to approximate AC power flow by semidefinite relaxations. This leads to two-stage stochastic mixed-integer semidefinite programs having a special structure. To solve the latter, the L-shaped method and dual decomposition have been applied and compared.Betrachtet man reale Entscheidungsprobleme, die also der Wirklichkeit entstammen, so ist man fast immer mit Unsicherheiten und Risiken konfrontiert. Für konkrete Optimierungsprobleme äußert sich dies sowohl in Form von ungewissen Parametern in den Eingangsdaten, als auch durch eine unzureichende Kenntnis über die Systembeschreibung selbst. Handelt es sich um zufallsbehaftete Eingangsdaten, dessen Verteilung bekannt ist, so stellt die Stochastische Optimierung eine Vielzahl von Modellen bereit - allesamt mit dem Ziel sich gegen Unsicherheiten und Risiken abzusichern. Die am Häufigsten verwendeten stochastischen Modelle sind zweistufige Modelle. Diese gestatten folgende Kompensationsstrategie: Eine Erststufenentscheidung wird getroffen bevor das Zufallsereignis eintritt. Nach Realisierung des Zufalls können Korrekturmaßnahmen (zweite Stufe) ergriffen werden, welche häufig, aber nicht immer, als "Kompensation" verstanden werden. Die vorliegende Arbeit behandelt Semidefinite Programme, dessen Parameter nicht mit Sicherheit bekannt sind. Der Zulässigkeitsbereich dieser Optimierungsprobleme entsteht aus dem Durchschnitt affiner oder auch allgemeinerer Gleichungen mit dem Kegel der symmetrisch und positiv semidefiniten Matrizen. Die Zielfunktion kann relativ allgemein sein, wird aber häufig, wie es auch in dieser Arbeit der Fall ist, als linear angenommen. Es werden risikoneutrale und risikoaverse zweistufige stochastische semidefinite Optimierungsprobleme mit jeweils stetiger und gemischt-ganzzahliger Kompensation betrachtet. Wir analysieren die Struktur dieser stochastischen Optimierungsprobleme, leiten dekompositionsbasierte Lösungsverfahren her und wenden unsere Resultate auf das Problem der optimalen Kraftwerkseinsatzplanung in Wechselstromnetzen an. Ferner beschäftigt sich diese Arbeit mit der deterministischen Kraftwerkseinsatzplanung in Wechselstromnetzen. Neben den traditionellen technischen Bedingungen an die einzelnen Kraftwerke wird auch die Physik des Wechselstroms berücksichtigt. Um global optimale Lösungen zu erhalten wird eine auf Semidefinite Programmierung (SDP) basierende Lösungsstrategie benutzt. Dieser Ansatz resultiert in einem umfangreichen semidefiniten Programm, welches zusätzlich diskrete Entscheidungsvariablen enthält. Da selbst die SDP Relaxierung dieses Optimierungsproblems zu groß ist um es mittels gängiger SDP Löser auf einmal zu lösen, wird eine effiziente und zuverlässige Methode benötigt. Es wird ein Algorithmus basierend auf dem Dekompositionsprinzip von Benders vorgeschlagen. Ausgehend vom Energiebedarf (Last) und der Einspeisung der erneuerbaren Energien als Unsicherheitsquelle, wird ein zweistufiges stochastisches Optimierungsproblem formuliert. Das Ziel ist es, einen Kraftwerkseinsatzplan zu finden, der wirtschaftlich effektiv und robust gegenüber Veränderungen in den Daten ist. Es werden die Auswirkungen des risikoneutralen und risikoaversen Ansatzes auf die stochastische Lösung untersucht und miteinander verglichen. Um die resultierenden zweistufigen Programme zu lösen wird das Wechselstromnetz mit Hilfe des SDP Ansatzes approximiert. Dies führt zu zweistufigen stochastischen gemischt-ganzzahligen semidefiniten Programmen mit spezieller Struktur. Als Lösungsmethoden wurden die L-shaped Methode und die duale Dekomposition verwendet