A power grid is a complex system connecting electric power generators to consumers through power transmission and distribution networks across a large geographical area. System monitoring is necessary to ensure the reliable operation of power grids, and state estimation is used in system monitoring to best estimate the power grid state through analysis of meter measurements and power system models. Various techniques have been developed to detect and identify bad measurements, including interacting bad measurements introduced by arbitrary, nonrandom causes. At first glance, it seems that these techniques can also defeat malicious measurements injected by attackers.In this article, we expose an unknown vulnerability of existing bad measurement detection algorithms by presenting and analyzing a new class of attacks, called false data injection attacks, against state estimation in electric power grids. Under the assumption that the attacker can access the current power system configuration information and manipulate the measurements of meters at physically protected locations such as substations, such attacks can introduce arbitrary errors into certain state variables without being detected by existing algorithms. Moreover, we look at two scenarios, where the attacker is either constrained to specific meters or limited in the resources required to compromise meters. We show that the attacker can systematically and efficiently construct attack vectors in both scenarios to change the results of state estimation in arbitrary ways. We also extend these attacks to generalized false data injection attacks, which can further increase the impact by exploiting measurement errors typically tolerated in state estimation. We demonstrate the success of these attacks through simulation using IEEE test systems, and also discuss the practicality of these attacks and the real-world constraints that limit their effectiveness.

False data injection attacks against state estimation in electric power grids

A power grid is a complex system connecting electric power generators to consumers through power transmission and distribution networks across a large geographical area. System monitoring is necessary to ensure the reliable operation of power grids, and state estimation is used in system monitoring to best estimate the power grid state through analysis of meter measurements and power system models. Various techniques have been developed to detect and identify bad measurements, including the interacting bad measurements introduced by arbitrary, non-random causes. At first glance, it seems that these techniques can also defeat malicious measurements injected by attackers.In this paper, we present a new class of attacks, called false data injection attacks, against state estimation in electric power grids. We show that an attacker can exploit the configuration of a power system to launch such attacks to successfully introduce arbitrary errors into certain state variables while bypassing existing techniques for bad measurement detection. Moreover, we look at two realistic attack scenarios, in which the attacker is either constrained to some specific meters (due to the physical protection of the meters), or limited in the resources required to compromise meters. We show that the attacker can systematically and efficiently construct attack vectors in both scenarios, which can not only change the results of state estimation, but also modify the results in arbitrary ways. We demonstrate the success of these attacks through simulation using IEEE test systems. Our results indicate that security protection of the electric power grid must be revisited when there are potentially malicious attacks.

The development of a trustworthy smart grid requires a deeper understanding of potential impacts resulting from successful cyber attacks. Estimating feasible attack impact requires an evaluation of the grid's dependency on its cyber infrastructure and its ability to tolerate potential failures. A further exploration of the cyber-physical relationships within the smart grid and a specific review of possible attack vectors is necessary to determine the adequacy of cybersecurity efforts. This paper highlights the significance of cyber infrastructure security in conjunction with power application security to prevent, mitigate, and tolerate cyber attacks. A layered approach is introduced to evaluating risk based on the security of both the physical power applications and the supporting cyber infrastructure. A classification is presented to highlight dependencies between the cyber-physical controls required to support the smart grid and the communication and computations that must be protected from cyber attack. The paper then presents current research efforts aimed at enhancing the smart grid's application and infrastructure security. Finally, current challenges are identified to facilitate future research efforts.

Cyber–Physical System Security for the Electric Power Grid

Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the “bible of computer algebra”, gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany oneor two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.

Modern computer algebra

It is often appealing to assume that existing solutions can be directly applied to emerging engineering domains. Unfortunately, careful investigation of the unique challenges presented by new domains exposes its idiosyncrasies, thus often requiring new approaches and solutions. In this paper, we argue that the “smart” grid, replacing its incredibly successful and reliable predecessor, poses a series of new security challenges, among others, that require novel approaches to the field of cyber security. We will call this new field cyber-physical security. The tight coupling between information and communication technologies and physical systems introduces new security concerns, requiring a rethinking of the commonly used objectives and methods. Existing security approaches are either inapplicable, not viable, insufficiently scalable, incompatible, or simply inadequate to address the challenges posed by highly complex environments such as the smart grid. A concerted effort by the entire industry, the research community, and the policy makers is required to achieve the vision of a secure smart grid infrastructure.

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Cyber–Physical Security of a Smart Grid Infrastructure

The availability of large datasets is crucial for the development of new power system applications and tools; unfortunately, very few are publicly and freely available. We designed an end-to-end generative framework for the creation of synthetic bus-level time-series load data for transmission networks. The model is trained on a real dataset of over 70 Terabytes of synchrophasor measurements spanning multiple years. Leveraging a combination of principal component analysis and conditional generative adversarial network models, the scheme we developed allows for the generation of data at varying sampling rates (up to a maximum of 30 samples per second) and ranging in length from seconds to years. The generative models are tested extensively to verify that they correctly capture the diverse characteristics of real loads. Finally, we develop an open-source tool called LoadGAN which gives researchers access to the fully trained generative models via a graphical interface.

Generation of Synthetic Multi-Resolution Time Series Load Data

We consider a problem of guessing, wherein an adversary is interested in knowing the value of the realization of a discrete random variable $X$ on observing another correlated random variable $Y$. The adversary can make multiple (say, $k$) guesses. The adversary's guessing strategy is assumed to minimize $\alpha$-loss, a class of tunable loss functions parameterized by $\alpha$. It has been shown before that this loss function captures well known loss functions including the exponential loss ($\alpha=1/2$), the log-loss ($\alpha=1$) and the $0$-$1$ loss ($\alpha=\infty$). We completely characterize the optimal adversarial strategy and the resulting expected $\alpha$-loss, thereby recovering known results for $\alpha=\infty$. We define an information leakage measure from the $k$-guesses setup and derive a condition under which the leakage is unchanged from a single guess.

Evaluating Multiple Guesses by an Adversary via a Tunable Loss Function

In The paper above [1] , published in the April 2019 issue of the IEEE Transactions on Information Theory, the following change is noted. The affiliations of the authors were listed incorrectly due to a production error. The affiliations should be listed as follows: The authors were with the School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287 USA, while performing their research for [1] .

Corrections to “Fine Asymptotics for Universal One-to-One Compression of Parametric Sources”

This work addresses the cooperation facilitator (CF) model, in which network nodes coordinate through a rate limited communication device. For multiple-access channel (MAC) encoders, the CF model is known to show significant rate benefits, even when the rate of cooperation is negligible. Specifically, the benefit in MAC sum-rate, as a function of the cooperation rate CCF , sometimes has an infinite slope at CCF = 0 when the CF enables transmitter dependence where none was possible otherwise. This work asks whether cooperation through a CF can yield similar infinite-slope benefits when dependence among MAC transmitters has no benefit or when it can be established without the help of the CF. Specifically, this work studies the CF model when applied to relay nodes of a single-source, single-terminal, diamond network comprising a broadcast channel followed by a MAC. In the relay channel with orthogonal receiver components, careful generalization of the partial-decode-forward/compress-forward lower bound to the CF model yields sufficient conditions for an infinite-slope benefit. Additional results include derivation of a family of diamond networks for which the infinite-slope rate-benefit derives directly from the properties of the corresponding MAC studied in isolation.

On the Benefit of Cooperation in Relay Networks

We study the problem of localizing multiple sources of forced oscillations (FOs) and estimating their characteristics, including frequency, phase, and amplitude, using noisy PMU data. We assume sparsity in the number of locations, and for each location, we model the input FO as a sum of a few unknown sinusoids. This allows us to obtain a sparse linear model in the frequency domain that relates measurements and the unknown input locations at frequencies of the unknown sinusoidal terms. We determine these frequencies by thresholding the empirical spectrum of the noisy data. Finally, we cast the location recovery problem as an $\ell_{1}$-regularized least squares problem in the complex domain-i.e., complex-LASSO (linear shrinkage and selection operator). We numerically solve this optimization problem using the complex-valued coordinate descent method and show its efficiency on the IEEE 68-bus, 16 machine and WECC 179-bus, 29-machine systems.

Oliver Kosut

Papers

Generation of Synthetic Multi-Resolution Time Series Load Data

Evaluating Multiple Guesses by an Adversary via a Tunable Loss Function

Corrections to “Fine Asymptotics for Universal One-to-One Compression of Parametric Sources”

On the Benefit of Cooperation in Relay Networks

A Complex-LASSO Approach for Localizing Forced Oscillations in Power Systems