Being inherently fragile, power systems may not return back to equilibrium after contingency. Fast second-scale dynamics implies that automatic emergency response is required to prevent this from happening. Power electronic components in the form of HVDC lines, FACTS devices and renewable inverters can save the facilitate the arrest of instability and prevent the system from collapsing.
We have developed novel algorithms for synthesis of emergency control systems exploiting the flexibility of power electronic components. Specificically, opportunity for fast reallocation of virtual storage on renewable generators, reconfiguration of network topology, remedial rerouting of power flows via FACTS enabled structural control.
Power system components are often described by nonlinear differential algebraic equation (DAE) models. These models are hard to analyze using conventional Lyapunov function techniques. There are no universal scalable approaches for constructing attraction basin estimates and designing nonlinear control systems.
We have been new techniques for certification of stability of DAE systems based on establishing contraction metrics. These techniques allowed to develop new approaches for certifying transient stability and estimating robustness of trajectories to parameter uncertainty and stochastic noise.
Direct energy methods are the only alternative to simulations for transient stability analysis and are currently used by a number of system operators around the world. Despite many decades of research these methods still rely on NP-hard algorithms and cannot be applied directly to standard models.
We proposed an alternative approach based on more general Lyapunov functions.This technique is based solely on convex optimization algorithms, extends to wider range of models, and is less conservative in comparison to classical energy methods.
Regions of safe and stable operating conditions are generally non-convex. Their non-trivial shape is responsible for NP-hardness of many critical decision-making processes in power systems: optimal resource allocation, risk assessment, emergency control.
We use modern analysis and optimization techniques to construct inner approximations of the feasibility sets of simple convex shape suitable for real-time computations. Resulting approximations are then used for security assessment in the presence of renewable generation, design of optimal remedial actions and other time-critical applications.
Heavily loaded grids may experience a voltage instability resulting in blackout in most dramatic scenarios. Stability margin of safe operating points depends on the dynamic response of the loads that are difficult to model due to inherent uncertainty and lack of observability.
To address this problem, we developed novel robust stability certificates based on structured Lyapunov functions. These certificates provide mathematical guarantees that an operating point is stable for any load response. Safe regions identified with the approach can be naturally used for security assessment and emergency control.
Modern power systems are protected against failures of any individual component (N-1 security), so blackouts are usually triggered by simultaneous failures of at least 2 components (N-2 contingency). Identification of dangerous N-2 contingencies is very challenging due to large number of possible pairs of lines and generators.
We invented a unique filtering technique for selection of dangerous contigencies that allows fast screening of safe scenarios with zero missing rate guarantees. On medium sized models the algorithm leads to thousand fold acceleration of the selection process and allows real-time blackout risk assessment.
Interconnection of independent single-source microgrids allows for sharing of resources and can dramatically reduce the costs of operation. However, such a system is prone to instabilities arising due to competition of multiple master (voltage source) inverters interacting through a strong networks with electromagnetic delays.
We have elucidated the origins of instability, used singular perturbation theory to derive more accurate dynamic equations, and developed simple simple interconnection rules that guarantee stability even in the presence of uncertainty.
More than 1 billion people in the world are still lacking power access and won't likely get access to main power grids in the next decades. Low voltage dc microgrids provide a unique opportunity for improving the lifes of those communities. However, the approaches to system design and operation have to be revisited to make them truly affordable.
We have proposed the concept of ad hoc microgrids composed of modular source and load components that can be interconnected in arbitrary manner without pre-planning. Simple design rules guarantee existence of equilibrium and transient stability of the system after switching events. Distributed secondary controls allow for optimal power sharing.
High penetration levels of distributed generation may result in reversal of power flow in modern distribution grids. We have shown that reversed power flow may result in appearance of new previously unobserved operating equilibria.
The resulting solutions are generally low-voltage and undesirable for normal operation. However, the system may get trapped in the new equilibria during the post-fault recovery. We have proposed new algorithms for identification of all the solutions, as well as special emergency control actions that can help maintain stability and enable adoption of high levels of clean renewable energy.
Introduction of high penetrations of distributed photovoltaic resources like roof-top panel causes a lots of headaches to the utilities and forces them to rethink how to operate distribution grids that were not designed with distributed generation in mind. Flexibility of power electronics circuits on individual inverters can be naturally leveraged to support the reactive power in the system.
We have explored several strategies for controlling the photovoltaic inverters and demonstrated that their reactive power capabilities can be naturally used to both supporting the voltage levels and reducing the losses. The centralized control strategies can be formulated as simple convex optimization problems, while the decentralized control achieves strong improvement effect even without prior coordination.
Sustained oscillations on low frequencies is a regularly observed phenomenon in large scale power systems that can compromise their stability and contribute to wear and tear of equipment. Several mechanisms can cause these oscillations, and PMU technologies provide an opportunity to quickly identify and fix the underlying problem.
We are developing algorithms that process the PMU data and point to the mechanism and source of oscillations. Diagnostics of the mechanism of the sustained oscillations is performed based on Kurtosis - higher order statistical indicator sensitive to nonlinear effects. The source of forced oscillations can be identified by comparing the natural to the observed response of individual generators.
Estimation of generator/power plant parameters is a complicated but important task essential for ensurance of stable power system operations. Traditional approaches are focused on mean values of parameters and provide little insight in the confidence intervals and accuracy of the predictions.
We have proposed a Bayesian approach to estimation of generator parameters that can provide a full posterior distribution of uncertain quantities. The algorithm is based on particle filter techniques and paves the path for more systematic uncertainty quantification in power systems.
Power systems are never truly stationary and are always fluctuating in stochastic manner. These fluctuations are typically viewed as nuisance. However, their statistics captures a lot of useful information about the current state of the system and the changes the system experiences.
We have proposed a number of approaches for detecting the statistical precursors of instability: approach of Hopf or saddle-node bifurcations. Later, we have broadly extended the approach to allow for full power flow Jacobian reconstruction purely from correlation function estimates.
Intriguing morphologies and surface patterns in nature at different scales from wrinkles on skins of mammalians, plants, and fruits to crumpled membranes of blood cells have inspired a big body of research in soft matter instabilities. In this project, we extend the application of soft matter instabilities to kinetic energy harvesting.
Conventional vibratory energy harvesters usually suffer from narrow bandwidth and are very inefficient at small scale for low frequency harvesting. Here, to improve the harvesting effectiveness, we propose to exploit surface instability or in general instability in layered composites, e.g. wrinkling, where intriguing morphological patterns with large strain are formed under compressive loads. The induced large strains which are independent of the excitation frequency, could be exploited to give rise to large strains in an attached piezoelectric layer to generate charge and, hence energy.
Uncertainty in parameters is inevitable with any physical device mainly due to manufacturing tolerances, defects, and environmental effects; hence, optimization under uncertainty is consequential for effective harvesting. All optimization studies in energy harvesting have focused on expectation optimization that is not appropriate for many practical applications.
Here we have proposed and formulated a new optimization strategy; optimization for the worst-case scenario (minimum power). This is particularly useful when there is a minimum power requirement for the self-powered device. We have shown harvesters thus optimized are much more robust to uncertainties.
Purposeful inclusion of nonlinearity, in particular the bistable potential, into energy harvesting devices has been the focus of tremendous research efforts in the recent years. However, recent research has proven that the bistable harvester is effective only when the vibration intensity is just enough to trigger interwell oscillations.
We have proposed a novel adaptive bistable system with variable potential height. We have shown that a bistable system whose potential barrier changes following a buy-low-sell-high strategy outperforms its linear and conventional bistable counterparts, and is much more robust to changes in excitation statistics. More recently we have also introduced novel strategies for driving the nonlinear systems to the most energy effective attractors.
Every little bit counts toward energy efficiency, including catching what would be lost to stray mechanical vibrations. Current research into harvesting of vibrational energy aims to exploit nonlinearity for effective energy harvesting, but one of the key challenges in designing such harvesters is the immense range of possible nonlinearities.
Rather than focusing on specific nonlinearities, we have studied the fundamental limits, and have shown that for a simple vibratory system, this limit forms into a simple non-resonant harvesting strategy called buy-low-sell-high, for any generic excitation statistics. A harvester following this strategy outperforms the linear and conventional nonlinear harvesters.
Classical Shannon capacity limits the spectral efficiency, and more broadly channel capacity of linear systems with additive noise. However, as the signal to noise ratio is increased the nonlinear effects start to come into play. Their effect on fundamental limits to channel capacity is still poorly understood.
In a series of papers we have demonstrated that the traditional Kerr nonlinearity observed in fiber optical channels does not result in significant reduction in channel capacity in comparison to linear channels. Moreover, carefully designed nonlinearity with regenerative effect can increase the capacity well beyond Shannon limit.
The polarization properties of light are now actively exploited in modern coherent fiber-optic communication systems for transmission of infor- mation. The possibility to control, regenerate and manipulate pulse polarization by purely optical means would have major impact in the field, enabling development of new generation of high speed optical communication systems.
In a series of works we have analyzed the phenomenon of polarization rotation in optical fibers with co- and counter-propagating beams. We have developed a theoretical description of the polarization attraction phenomenon, derived stability regions and proposed a possible technological realization of all-optical polarizers.
Traditional models of communication channels assume independent propagation of individual signals. However, in nonlinear channels, the signals interact with each other and the form of interaction may depend on the alphabet symbol pattern.
We have studied a simple but realistic model of signal interactions within fiber optical channel. For this system specific three symbol patterns have the highest error rate and their frequency should be suppressed in encoding. Specific algorithms for optimal encoding were proposed and analyzed.
Carbon dioxide capture and storage in deep saline aquifiers is a viable technology that allows for reduction in emissions even without immediate replace of fossil-fueled power plants. At the same time, there is still a very limited understanding of the hihgly nonlinear carbon sequestration phenomenon, in particular the rates of mixing and the role of convective instabilities.
In collaboration with experimental groups, I have studied the characteristics of the convective density driven Rayleigh instability occuring in Hele Shaw setup. Unlike classical instabilities that have been studied for almost a century, the unique features of this system is miscible nature of the liquids that leads to dissolution of initial fingers.
Formation of air bubbles following air entrapment is a complicated though very common process occuring on every nonequilibrium water-air surfaces. The final stage of this process - bubble neck pinch-off is charactherzed by singular growth of pressure and extremely fast development on shape instabilities.
Although the initial growth of instability is a relatively well-understood process, the final stages of the dynamics have been poorly understood until our paper. We have developed a unique approach based on conformal mapping capable of predicting the evolution of the neck cross-section shape and demonstrated that the neck actually separates into two before final collapse. The results were in a good agreement with high-speed camera experiments.
Lipid bilayer vesicles are composed of liquid membrane surrounding a liquid drop. They are a natural transport vehicle in many cellular processes and also actively used for artificial drug delivery. When subjected to external flow they experience a very rich dynamics.
We have developed an analytic reduced model for dynamics of nearly-spherical vesicles and shown that it accurately reproduces the phase diagram of experimentally observed motion types. Moreover, it can be used to predict the statistical properties of the wrinkling dynamics observed during buckling instability.
Addition of small concenctrations of flexible polymer molecules can dramatically reduce the viscosity of the liquids. This effect is actively used to reduce the fluid drag in pipes, however its microscopic origins are still poorly understood.
We have developed a theoretical description of nonequilibrium and nonlinear dynamics of individual polymer molecules exposed to external shear flows. Our theory predicts multiple statistical properties of motions, such as tumbling time distribution, probability of different orientation etc. Most of the predictions have been successfully confirmed by experimental groups.
Turbulent mixing of inertial particles like droplets is a process that occurs frequently in nature (for example during rain formation) and in engineering (for example in internal combustion engines). Unlike passive tracers, inertial particles do not follow Lagrangian trajectories, and tend to cluster due to random centrifugal process. This is an inherently stochastic process that is hard to characterize using conventional deterministic approaches.
We have developed a theoretical description for two aspects of this process. First, we have derived the fractal dimension of the resulting clusters for Markovian stochastic flows. Second, we have characterized the dynamics during the caustic formation events when the local concentration experiences explosive growth.
Random motion of particles, in viscoelastic media, for example motion of individual proteins on the membranes is very sensitive to the environment. It's statistical properties can be naturally used to probe the medium and test hypotheses about its composition. However, traditional approaches have been focused on simple second-order characteristics like (anomalous) diffusion coefficient.
We have proposed a non-conventional measure based on displacement kurtosis that is sensitive to nonlinear interactions that the particle experience. It can distinguish between different mechanisms characterized by the same diffusion coefficient and naturally detect lipid rafts and other membrance constituents.
Markov Chain Monte Carlo algorithms are the most popular strategies for sampling from complicated probability distributions. Most popular versions of these algorithms rely on the detailed balance principle, also referred to as "reversibility" of the Markov Chain. Although reversibility is a sufficient condition that leads to relatively simple step acceptance rules, it restricts the class of algorithms and limits their performance.
We have explored the idea of breaking reversibility/detailed balance and proposed simple strategies for breaking detailed balance of a given reversible chain. The procedure of breaking detailed balance can be interpreted as either lifting the chain in a higher dimensional space or introducing memory in otherwise Markovian dynamics.
Non-equilibrium irreversible processes increase the entropy of the universe, but do so in a temporally non-steady manner. While the second law of thermodynamics guarantees that the average increase is positive, the exact amounts of entropy produced in a given period are stochastic and have a finite probability of being negative. Understanding these flucutations of entropy is essential for describing processes occuring on micro and nano-scales.
We have proposed a systematic approach for calculation of entropy production for systems in non-equilibrium steady state experiencing weakly nonlinear or linear fluctuations. Our results were illustrated on an example polymer molecule in shear flow system.