Abstract-Phasor measurement units (PMUs) can be effectively utilized for the monitoring and control of the power grid. As the cyber-world becomes increasingly embedded into power grids, the risks of this inevitable evolution become serious. In this paper, we present a risk mitigation strategy, based on dynamic state estimation, to eliminate threat levels from the grid's unknown inputs and potential cyber-attacks. The strategy requires (a) the potentially incomplete knowledge of power system models and parameters and (b) real-time PMU measurements. First, we utilize a dynamic state estimator for higher order depictions of power system dynamics for simultaneous state and unknown inputs estimation. Second, estimates of cyber-attacks are obtained through an attack detection algorithm. Third, the estimation and detection components are seamlessly utilized in an optimization framework to determine the most impacted PMU measurements. Finally, a risk mitigation strategy is proposed to guarantee the elimination of threats from attacks, ensuring the observability of the power system through available, safe measurements. Case studies are included to validate the proposed approach. Insightful suggestions, extensions, and open problems are also posed.
Stochastic partial differential equations (SPDEs) are ubiquitous in engineering and computational sciences. The stochasticity arises as a consequence of uncertainty in input parameters, constitutive relations, initial/boundary conditions, etc. Because of these functional uncertainties, the stochastic parameter space is often high-dimensional, requiring hundreds, or even thousands, of parameters to describe it. This poses an insurmountable challenge to response surface modeling since the number of forward model evaluations needed to construct an accurate surrogate grows exponentially with the dimension of the uncertain parameter space; a phenomenon referred to as the curse of dimensionality.State-of-the-art methods for high-dimensional uncertainty propagation seek to alleviate the curse of dimensionality by performing dimensionality reduction in the uncertain parameter space. However, one still needs to perform forward model evaluations that potentially carry a very high computational burden. We propose a novel methodology for high-dimensional uncertainty propagation of elliptic SPDEs which lifts the requirement for a deterministic forward solver.Our approach is as follows. We parameterize the solution of the elliptic SPDE using a deep residual network (ResNet). In a departure from traditional squared residual (SR) based loss function for training the ResNet, we introduce a physicsinformed loss function derived from variational principles. Specifically, our loss function is the expectation of the energy functional of the PDE over the stochastic variables. We demonstrate our solver-free approach through various examples where the elliptic SPDE is subjected to different types of high-dimensional input uncertainties. Also, we solve high-dimensional uncertainty propagation and inverse problems.
Game-theoretic models have been used to analyze design problems ranging from multi-objective design optimization to decentralized design and from design for market systems (DFMS) to policy design. However, existing studies are primarily analytical in nature, which start with a number of assumptions about the individual decisions, the information available to the players, and the solution concept (generally, the Nash equilibrium). There is a lack of studies related to engineering design, which rigorously evaluate the validity of these assumptions or that of the predictions from the models. Hence, the usefulness of these models to realistic engineering systems design has been severely limited. In this paper, we take a step toward addressing this gap. Using an example of crowdsourcing for engineering design, we illustrate how the analytical game-theoretic models and behavioral experimentation can be synergistically used to gain a better understanding of design situations. Analytical models describe what players with assumed behaviors and cognitive capabilities would do under specified conditions, and the behavioral experiments shed light on how individuals actually behave. The paper contributes to the design literature in multiple ways. First, to the best of our knowledge, it is a first attempt at integrated theoretical and experimental game-theoretic analysis in design. We illustrate how the analytical models can be used to design behavioral experiments, which, in turn, can be used to estimate parameters, refine models, and inform further development of the theory. Second, we present a simple experiment to understand behaviors of individuals in a design crowdsourcing problem. The results of the experiment show new insights on using crowdsourcing contests for design.
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