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Let $T$ be a bounded linear operator on a Banach space $X$. We give new necessary and sufficient conditions for $T$ to be Drazin or Koliha-Drazin invertible. All those conditions have the following form: $T$ possesses certain decomposition property and zero is not an interior point of some part of the spectrum of $T$. In addition, we study operators $T$ satisfying Browder\textquoteright s theorem, or a-Browder\textquoteright s theorem, by means of some relationships between diferent parts of the spectrum of $T$.

Recently, the volatility associated with marginal prices has increased due to large scale integration of renewable generation. Price volatility is undesirable from a consumer perspective. To address this issue, we present a framework for hedging that uses duality theory for quantifying the amount of demand-side flexibility required for constraining marginal prices to the consumers maximum willingness to pay for electricity. Using our formulation, we investigate the ability of an Energy Storage System (ESS), as a demand-side flexibility source, to hedge against electricity price volatility across a multi-time period horizon while accounting for its inter-temporal constraints. Additionally, we analyze the economical benefit that operating the ESS under information forecasts brings to the consumers., Comment: Submitted to IEEE Power and Energy Society General Meeting 2019

Evaluating new technological developments for energy systems is becoming more and more complex. The overall application environment is a continuously growing and interconnected cyber-physical system so that analytical assessment is practically impossible to realize. Consequently, new solutions must be evaluated in simulation studies. Due to the interdisciplinarity of the simulation scenarios, various heterogeneous tools must be connected. This approach is known as co-simulation. During the last years, different approaches have been developed or adapted for applications in energy systems. In this paper, two co-simulation approaches are compared that follow generic, versatile concepts. The tool mosaik, which has been explicitly developed for the purpose of co-simulation in complex energy systems, is compared to the High Level Architecture (HLA), which possesses a domain-independent scope but is often employed in the energy domain. The comparison is twofold, considering the tools' conceptual architectures as well as results from the simulation of representative test cases. It suggests that mosaik may be the better choice for entry-level, prototypical co-simulation while HLA is more suited for complex and extensive studies.

Locational Marginal Price (LMP) is a dual variable associated with supply-demand matching and represents the cost of delivering power to a particular location if the load at that location increases. In recent times it become more volatile due to increased integration of renewables that are intermittent. The issue of price volatility is further heightened during periods of grid congestion. Motivated by these problems, we propose a market design where, by constraining dual variables, we determine the amount of demand-side flexibility required to limit the rise of LMP. Through our proposed approach a price requesting load can specify its maximum willingness to pay for electricity and through demand-side flexibility hedge against price volatility. For achieving this, an organizational structure for flexibility management is proposed that exhibits the coordination required between the Distribution System Operator (DSO), an aggregator and the price requesting load. To demonstrate the viability of our proposed formulation, we run an illustrative simulation under infinite and finite line capacities.

A class of data integrity attack, known as false data injection (FDI) attack, has been studied with a considerable amount of work. It has shown that with perfect knowledge of the system model and the capability to manipulate a certain number of measurements, the FDI attacks can coordinate measurements corruption to keep stealth against the bad data detection. However, a more realistic attack is essentially an attack with limited adversarial knowledge of the system model and limited attack resources due to various reasons. In this paper, we generalize the data attacks that they can be pure FDI attacks or combined with availability attacks (e.g., DoS attacks) and analyze the attacks with limited adversarial knowledge or limited attack resources. The attack impact is evaluated by the proposed metrics and the detection probability of attacks is calculated using the distribution property of data with or without attacks. The analysis is supported with results from a power system use case. The results show how important the knowledge is to the attacker and which measurements are more vulnerable to attacks with limited resources., Comment: Accepted in the 43rd Annual Conference of the IEEE Industrial Electronics Society (IECON 2017)

Understanding smart grid cyber attacks is key for developing appropriate protection and recovery measures. Advanced attacks pursue maximized impact at minimized costs and detectability. This paper conducts risk analysis of combined data integrity and availability attacks against the power system state estimation. We compare the combined attacks with pure integrity attacks - false data injection (FDI) attacks. A security index for vulnerability assessment to these two kinds of attacks is proposed and formulated as a mixed integer linear programming problem. We show that such combined attacks can succeed with fewer resources than FDI attacks. The combined attacks with limited knowledge of the system model also expose advantages in keeping stealth against the bad data detection. Finally, the risk of combined attacks to reliable system operation is evaluated using the results from vulnerability assessment and attack impact analysis. The findings in this paper are validated and supported by a detailed case study., Comment: Submitted to IEEE Transactions on Smart Grid on August 14th, 2017

We shall say that a bounded linear operator $T$ acting on a Banach space $X$ admits a generalized Kato-Riesz decomposition if there exists a pair of $T$-invariant closed subspaces $(M,N)$ such that $X=M\oplus N$, the reduction $T_M$ is Kato and $T_N$ is Riesz. In this paper we define and investigate the generalized Kato-Riesz spectrum of an operator. For $T$ is said to be generalized Drazin-Riesz invertible if there exists a bounded linear operator $S $ acting on $X$ such that $TS=ST$, $STS=S$, $ TST-T$ is Riesz. We investigate generalized Drazin-Riesz invertible operators and also, characterize bounded linear operators which can be expressed as a direct sum of a Riesz operator and a bounded below (resp. surjective, upper (lower) semi-Fredholm, Fredholm, upper (lower) semi-Weyl, Weyl) operator. In particular we characterize the single-valued extension property at a point $\lambda_0\in{\mathbb C}$ in the case that $\lambda_0-T$ admits a generalized Kato-Riesz decomposition., Comment: 24 pages. arXiv admin note: text overlap with arXiv:1603.07880

Let ${\bf R}$ denote any of the following classes: upper (lower) semi-Fredholm operators, Fredholm operators, upper (lower) semi-Weyl operators, Weyl operators, upper (lower) semi-Browder operators, Browder operators. For a bounded linear operator $T$ on a Banach space $X$ we prove that $T=T_M\oplus T_N$ with $T_M \in {\bf R}$ and $T_N$ quasinilpotent (nilpotent) if and only if $T$ admits a generalized Kato decomposition ($T$ is of Kato type) and $0$ is not an interior point of the corresponding spectrum $\sigma_{\bf R}(T)=\{\lambda \in \mathbb{C}: T-\lambda \notin {\bf R}\}$. In addition, we show that every non-isolated boundary point of the spectrum $\sigma_{\bf R}(T)$ belongs to the generalized Kato spectrum of $T$., Comment: 25 pages

We study the generalized Drazin invertibility as well as the Drazin and ordinary invertbility of an operator matrix (A C \\ 0 B) acting on a Banach or on a Hilbert space. As a consequence some recent results are extended., Comment: 12 pages

Given a (not necessarily continuous) homomorphism between Banach algebras $\T\colon\A\to\B$, an element $a\in\A$ will be said to be B-Fredholm (respectively generalized B-Fredholm) relative to $\T$, if $\T(a)\in \B$ is Drazin invertible (respectively Koliha-Drazin invertible). In this article, the aforementioned elements will be characterized and their main properties will be studied. In addition, perturbation properties will be also considered., Comment: 17 pages, original research article