arXiv subjects

Vassilis Kekatos

Publications and source records attributed to Vassilis Kekatos.

68 records · Page 4Linked to original sources

arXiv2016

Ergodic Energy Management Leveraging Resource Variability in Distribution Grids

Contemporary electricity distribution systems are being challenged by the variability of renewable energy sources. Slow response times and long energy management periods cannot efficiently integrate intermittent renewable generation and demand. Yet stochasticity can be judiciously coupled with system flexibilities to enhance grid operation efficiency. Voltage magnitudes for instance can transiently exceed regulation limits, while smart inverters can be overloaded over short time intervals. To implement such a mode of operation, an ergodic energy management framework is developed here. Considering a distribution grid with distributed energy sources and a feed-in tariff program, active power curtailment and reactive power compensation are formulated as a stochastic optimization problem. Tighter operational constraints are enforced in an average sense, while looser margins are enforced to be satisfied at all times. Stochastic dual subgradient solvers are developed based on exact and approximate grid models of varying complexity. Numerical tests on a real-world 56-bus distribution grid and the IEEE 123-bus test feeder relying on both grid models corroborate the advantages of the novel schemes over their deterministic alternatives.

eess.SY↗

arXiv2016

Scalable Electric Vehicle Charging Protocols

Although electric vehicles are considered a viable solution to reduce greenhouse gas emissions, their uncoordinated charging could have adverse effects on power system operation. Nevertheless, the task of optimal electric vehicle charging scales unfavorably with the fleet size and the number of control periods, especially when distribution grid limitations are enforced. To this end, vehicle charging is first tackled using the recently revived Frank-Wolfe method. The novel decentralized charging protocol has minimal computational requirements from vehicle controllers, enjoys provable acceleration over existing alternatives, enhances the security of the pricing mechanism against data attacks, and protects user privacy. To comply with voltage limits, a network-constrained EV charging problem is subsequently formulated. Leveraging a linearized model for unbalanced distribution grids, the goal is to minimize the power supply cost while respecting critical voltage regulation and substation capacity limitations. Optimizing variables across grid nodes is accomplished by exchanging information only between neighboring buses via the alternating direction method of multipliers. Numerical tests corroborate the optimality and efficiency of the novel schemes.

math.OC↗

arXiv2015

Voltage Regulation Algorithms for Multiphase Power Distribution Grids

Time-varying renewable energy generation can result in serious under-/over-voltage conditions in future distribution grids. Augmenting conventional utility-owned voltage regulating equipment with the reactive power capabilities of distributed generation units is a viable solution. Local control options attaining global voltage regulation optimality at fast convergence rates is the goal here. In this context, novel reactive power control rules are analyzed under a unifying linearized grid model. For single-phase grids, our proximal gradient scheme has computational complexity comparable to that of the rule suggested by the IEEE 1547.8 standard, but it enjoys well-characterized convergence guarantees. Adding memory to the scheme results in accelerated convergence. For three-phase grids, it is shown that reactive injections have a counter-intuitive effect on bus voltage magnitudes across phases. Nevertheless, when our control scheme is applied to unbalanced conditions, it is shown to reach an equilibrium point. Yet this point may not correspond to the minimizer of a voltage regulation problem. Numerical tests using the IEEE 13-bus, the IEEE 123-bus, and a Southern California Edison 47-bus feeder with increased renewable penetration verify the convergence properties of the schemes and their resiliency to grid topology reconfigurations.

eess.SY↗

arXiv2015

Online Censoring for Large-Scale Regressions with Application to Streaming Big Data

Linear regression is arguably the most prominent among statistical inference methods, popular both for its simplicity as well as its broad applicability. On par with data-intensive applications, the sheer size of linear regression problems creates an ever growing demand for quick and cost efficient solvers. Fortunately, a significant percentage of the data accrued can be omitted while maintaining a certain quality of statistical inference with an affordable computational budget. The present paper introduces means of identifying and omitting "less informative" observations in an online and data-adaptive fashion, built on principles of stochastic approximation and data censoring. First- and second-order stochastic approximation maximum likelihood-based algorithms for censored observations are developed for estimating the regression coefficients. Online algorithms are also put forth to reduce the overall complexity by adaptively performing censoring along with estimation. The novel algorithms entail simple closed-form updates, and have provable (non)asymptotic convergence guarantees. Furthermore, specific rules are investigated for tuning to desired censoring patterns and levels of dimensionality reduction. Simulated tests on real and synthetic datasets corroborate the efficacy of the proposed data-adaptive methods compared to data-agnostic random projection-based alternatives.

stat.AP↗

arXiv2014

Stochastic Reactive Power Management in Microgrids with Renewables

Distribution microgrids are being challenged by reverse power flows and voltage fluctuations due to renewable generation, demand response, and electric vehicles. Advances in photovoltaic (PV) inverters offer new opportunities for reactive power management provided PV owners have the right investment incentives. In this context, reactive power compensation is considered here as an ancillary service. Accounting for the increasing time-variability of distributed generation and demand, a stochastic reactive power compensation scheme is developed. Given uncertain active power injections, an online reactive control scheme is devised. This scheme is distribution-free and relies solely on power injection data. Reactive injections are updated using the Lagrange multipliers of a second-order cone program. Numerical tests on an industrial 47-bus microgrid and the residential IEEE 123-bus feeder corroborate the reactive power management efficiency of the novel stochastic scheme over its deterministic alternative, as well as its capability to track variations in solar generation and household demand.

math.OC↗

arXiv2014

Online Energy Price Matrix Factorization for Power Grid Topology Tracking

Grid security and open markets are two major smart grid goals. Transparency of market data facilitates a competitive and efficient energy environment, yet it may also reveal critical physical system information. Recovering the grid topology based solely on publicly available market data is explored here. Real-time energy prices are calculated as the Lagrange multipliers of network-constrained economic dispatch; that is, via a linear program (LP) typically solved every 5 minutes. Granted the grid Laplacian is a parameter of this LP, one could infer such a topology-revealing matrix upon observing successive LP dual outcomes. The matrix of spatio-temporal prices is first shown to factor as the product of the inverse Laplacian times a sparse matrix. Leveraging results from sparse matrix decompositions, topology recovery schemes with complementary strengths are subsequently formulated. Solvers scalable to high-dimensional and streaming market data are devised. Numerical validation using real load data on the IEEE 30-bus grid provide useful input for current and future market designs.

stat.ML↗

arXiv2014

Electricity Market Forecasting via Low-Rank Multi-Kernel Learning

The smart grid vision entails advanced information technology and data analytics to enhance the efficiency, sustainability, and economics of the power grid infrastructure. Aligned to this end, modern statistical learning tools are leveraged here for electricity market inference. Day-ahead price forecasting is cast as a low-rank kernel learning problem. Uniquely exploiting the market clearing process, congestion patterns are modeled as rank-one components in the matrix of spatio-temporally varying prices. Through a novel nuclear norm-based regularization, kernels across pricing nodes and hours can be systematically selected. Even though market-wide forecasting is beneficial from a learning perspective, it involves processing high-dimensional market data. The latter becomes possible after devising a block-coordinate descent algorithm for solving the non-convex optimization problem involved. The algorithm utilizes results from block-sparse vector recovery and is guaranteed to converge to a stationary point. Numerical tests on real data from the Midwest ISO (MISO) market corroborate the prediction accuracy, computational efficiency, and the interpretative merits of the developed approach over existing alternatives.

stat.ML↗

arXiv2014

Grid Topology Identification using Electricity Prices

The potential of recovering the topology of a grid using solely publicly available market data is explored here. In contemporary whole-sale electricity markets, real-time prices are typically determined by solving the network-constrained economic dispatch problem. Under a linear DC model, locational marginal prices (LMPs) correspond to the Lagrange multipliers of the linear program involved. The interesting observation here is that the matrix of spatiotemporally varying LMPs exhibits the following property: Once premultiplied by the weighted grid Laplacian, it yields a low-rank and sparse matrix. Leveraging this rich structure, a regularized maximum likelihood estimator (MLE) is developed to recover the grid Laplacian from the LMPs. The convex optimization problem formulated includes low rank- and sparsity-promoting regularizers, and it is solved using a scalable algorithm. Numerical tests on prices generated for the IEEE 14-bus benchmark provide encouraging topology recovery results.

cs.LG↗

arXiv2013

Risk-Aware Management of Distributed Energy Resources

High wind energy penetration critically challenges the economic dispatch of current and future power systems. Supply and demand must be balanced at every bus of the grid, while respecting transmission line ratings and accounting for the stochastic nature of renewable energy sources. Aligned to that goal, a network-constrained economic dispatch is developed in this paper. To account for the uncertainty of renewable energy forecasts, wind farm schedules are determined so that they can be delivered over the transmission network with a prescribed probability. Given that the distribution of wind power forecasts is rarely known, and/or uncertainties may yield non-convex feasible sets for the power schedules, a scenario approximation technique using Monte Carlo sampling is pursued. Upon utilizing the structure of the DC optimal power flow (OPF), a distribution-free convex problem formulation is derived whose complexity scales well with the wind forecast sample size. The efficacy of this novel approach is evaluated over the IEEE 30-bus power grid benchmark after including real operation data from seven wind farms.

math.OC↗

arXiv2013

Monitoring and Optimization for Power Grids: A Signal Processing Perspective

The smart grid vision is to revitalize the electric power network by leveraging the proven sensing, communication, control, and machine learning technologies to address pressing issues related to security, stability, environmental impact, market diversity, and novel power technologies. Significant effort and investment have been committed to architect the necessary infrastructure by installing advanced metering systems and establishing data communication networks throughout the grid. Signal processing methodologies are expected to play a major role in this context by providing intelligent algorithms that fully exploit such pervasive sensing and control capabilities to realize the vision and manifold anticipated benefits of the smart grid. In this feature article, analytical background and relevance of signal processing tools to power systems are delineated, while introducing major challenges and opportunities for the future grid engineering. From grid informatics to inference for monitoring and optimization tools, energy-related issues are shown to offer a fertile ground for signal processing growth whose time has come.

math.OC↗

arXiv2012

Distributed Robust Power System State Estimation

Deregulation of energy markets, penetration of renewables, advanced metering capabilities, and the urge for situational awareness, all call for system-wide power system state estimation (PSSE). Implementing a centralized estimator though is practically infeasible due to the complexity scale of an interconnection, the communication bottleneck in real-time monitoring, regional disclosure policies, and reliability issues. In this context, distributed PSSE methods are treated here under a unified and systematic framework. A novel algorithm is developed based on the alternating direction method of multipliers. It leverages existing PSSE solvers, respects privacy policies, exhibits low communication load, and its convergence to the centralized estimates is guaranteed even in the absence of local observability. Beyond the conventional least-squares based PSSE, the decentralized framework accommodates a robust state estimator. By exploiting interesting links to the compressive sampling advances, the latter jointly estimates the state and identifies corrupted measurements. The novel algorithms are numerically evaluated using the IEEE 14-, 118-bus, and a 4,200-bus benchmarks. Simulations demonstrate that the attainable accuracy can be reached within a few inter-area exchanges, while largest residual tests are outperformed.

stat.ML↗

arXiv2011

Sparse Volterra and Polynomial Regression Models: Recoverability and Estimation

Volterra and polynomial regression models play a major role in nonlinear system identification and inference tasks. Exciting applications ranging from neuroscience to genome-wide association analysis build on these models with the additional requirement of parsimony. This requirement has high interpretative value, but unfortunately cannot be met by least-squares based or kernel regression methods. To this end, compressed sampling (CS) approaches, already successful in linear regression settings, can offer a viable alternative. The viability of CS for sparse Volterra and polynomial models is the core theme of this work. A common sparse regression task is initially posed for the two models. Building on (weighted) Lasso-based schemes, an adaptive RLS-type algorithm is developed for sparse polynomial regressions. The identifiability of polynomial models is critically challenged by dimensionality. However, following the CS principle, when these models are sparse, they could be recovered by far fewer measurements. To quantify the sufficient number of measurements for a given level of sparsity, restricted isometry properties (RIP) are investigated in commonly met polynomial regression settings, generalizing known results for their linear counterparts. The merits of the novel (weighted) adaptive CS algorithms to sparse polynomial modeling are verified through synthetic as well as real data tests for genotype-phenotype analysis.

cs.LG↗

arXiv2011

Robust Clustering Using Outlier-Sparsity Regularization

Notwithstanding the popularity of conventional clustering algorithms such as K-means and probabilistic clustering, their clustering results are sensitive to the presence of outliers in the data. Even a few outliers can compromise the ability of these algorithms to identify meaningful hidden structures rendering their outcome unreliable. This paper develops robust clustering algorithms that not only aim to cluster the data, but also to identify the outliers. The novel approaches rely on the infrequent presence of outliers in the data which translates to sparsity in a judiciously chosen domain. Capitalizing on the sparsity in the outlier domain, outlier-aware robust K-means and probabilistic clustering approaches are proposed. Their novelty lies on identifying outliers while effecting sparsity in the outlier domain through carefully chosen regularization. A block coordinate descent approach is developed to obtain iterative algorithms with convergence guarantees and small excess computational complexity with respect to their non-robust counterparts. Kernelized versions of the robust clustering algorithms are also developed to efficiently handle high-dimensional data, identify nonlinearly separable clusters, or even cluster objects that are not represented by vectors. Numerical tests on both synthetic and real datasets validate the performance and applicability of the novel algorithms.

stat.ML↗

arXiv2011

From Sparse Signals to Sparse Residuals for Robust Sensing

One of the key challenges in sensor networks is the extraction of information by fusing data from a multitude of distinct, but possibly unreliable sensors. Recovering information from the maximum number of dependable sensors while specifying the unreliable ones is critical for robust sensing. This sensing task is formulated here as that of finding the maximum number of feasible subsystems of linear equations, and proved to be NP-hard. Useful links are established with compressive sampling, which aims at recovering vectors that are sparse. In contrast, the signals here are not sparse, but give rise to sparse residuals. Capitalizing on this form of sparsity, four sensing schemes with complementary strengths are developed. The first scheme is a convex relaxation of the original problem expressed as a second-order cone program (SOCP). It is shown that when the involved sensing matrices are Gaussian and the reliable measurements are sufficiently many, the SOCP can recover the optimal solution with overwhelming probability. The second scheme is obtained by replacing the initial objective function with a concave one. The third and fourth schemes are tailored for noisy sensor data. The noisy case is cast as a combinatorial problem that is subsequently surrogated by a (weighted) SOCP. Interestingly, the derived cost functions fall into the framework of robust multivariate linear regression, while an efficient block-coordinate descent algorithm is developed for their minimization. The robust sensing capabilities of all schemes are verified by simulated tests.

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