arXiv subjects

Georgios B. Giannakis

Publications and source records attributed to Georgios B. Giannakis.

At least 163 records · Page 9Linked to original sources

arXiv2015

Sketch and Validate for Big Data Clustering

In response to the need for learning tools tuned to big data analytics, the present paper introduces a framework for efficient clustering of huge sets of (possibly high-dimensional) data. Building on random sampling and consensus (RANSAC) ideas pursued earlier in a different (computer vision) context for robust regression, a suite of novel dimensionality and set-reduction algorithms is developed. The advocated sketch-and-validate (SkeVa) family includes two algorithms that rely on K-means clustering per iteration on reduced number of dimensions and/or feature vectors: The first operates in a batch fashion, while the second sequential one offers computational efficiency and suitability with streaming modes of operation. For clustering even nonlinearly separable vectors, the SkeVa family offers also a member based on user-selected kernel functions. Further trading off performance for reduced complexity, a fourth member of the SkeVa family is based on a divergence criterion for selecting proper minimal subsets of feature variables and vectors, thus bypassing the need for K-means clustering per iteration. Extensive numerical tests on synthetic and real data sets highlight the potential of the proposed algorithms, and demonstrate their competitive performance relative to state-of-the-art random projection alternatives.

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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.

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arXiv2014

Optimal Dispatch of Residential Photovoltaic Inverters Under Forecasting Uncertainties

Efforts to ensure reliable operation of existing low-voltage distribution systems with high photovoltaic (PV) generation have focused on the possibility of inverters providing ancillary services such as active power curtailment and reactive power compensation. Major benefits include the possibility of averting overvoltages, which may otherwise be experienced when PV generation exceeds the demand. This paper deals with ancillary service procurement in the face of solar irradiance forecasting errors. In particular, assuming that the forecasted PV irradiance can be described by a random variable with known (empirical) distribution, the proposed uncertainty-aware optimal inverter dispatch (OID) framework indicates which inverters should provide ancillary services with a guaranteed a-priori risk level of PV generation surplus. To capture forecasting errors, and strike a balance between risk of overvoltages and (re)active power reserves, the concept of conditional value-at-risk is advocated. Due to AC power balance equations and binary inverter selection variables, the formulated OID involves the solution of a nonconvex mixed-integer nonlinear program. However, a computationally-affordable convex relaxation is derived by leveraging sparsity-promoting regularization approaches and semidefinite relaxation techniques. The proposed scheme is tested using real-world PV-generation and load-profile data for an illustrative low-voltage residential distribution system.

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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.

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arXiv2014

An Efficient Primal-Dual Approach to Chance-Constrained Economic Dispatch

To effectively enhance the integration of distributed and renewable energy sources in future smart microgrids, economical energy management accounting for the principal challenge of the variable and non-dispatchable renewables is indispensable and of significant importance. Day-ahead economic generation dispatch with demand-side management for a microgrid in islanded mode is considered in this paper. With the goal of limiting the risk of the loss-of-load probability, a joint chance constrained optimization problem is formulated for the optimal multi-period energy scheduling with multiple wind farms. Bypassing the intractable spatio-temporal joint distribution of the wind power generation, a primal-dual approach is used to obtain a suboptimal solution efficiently. The method is based on first-order optimality conditions and successive approximation of the probabilistic constraint by generation of p-efficient points. Numerical results are reported to corroborate the merits of this approach.

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arXiv2014

Decentralized Optimal Dispatch of Photovoltaic Inverters in Residential Distribution Systems

Decentralized methods for computing optimal real and reactive power setpoints for residential photovoltaic (PV) inverters are developed in this paper. It is known that conventional PV inverter controllers, which are designed to extract maximum power at unity power factor, cannot address secondary performance objectives such as voltage regulation and network loss minimization. Optimal power flow techniques can be utilized to select which inverters will provide ancillary services, and to compute their optimal real and reactive power setpoints. Leveraging advances in semidefinite relaxation techniques and sparsity-promoting regularizations, such problems can be solved with reduced computational burden and with optimality guarantees. To enable large-scale implementation, a novel algorithmic framework is introduced - based on the so-called alternating direction method of multipliers - by which the optimal power flow problem in this setting can be systematically decomposed into sub-problems that can be solved in a decentralized fashion by the utility and customer-owned PV systems with limited exchanges of information. Since the computational burden is shared among multiple devices and the requirement of all-to-all communication can be circumvented, the proposed optimization approach scales to large distribution networks.

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arXiv2014

Estimating Traffic and Anomaly Maps via Network Tomography

Mapping origin-destination (OD) network traffic is pivotal for network management and proactive security tasks. However, lack of sufficient flow-level measurements as well as potential anomalies pose major challenges towards this goal. Leveraging the spatiotemporal correlation of nominal traffic, and the sparse nature of anomalies, this paper brings forth a novel framework to map out nominal and anomalous traffic, which treats jointly important network monitoring tasks including traffic estimation, anomaly detection, and traffic interpolation. To this end, a convex program is first formulated with nuclear and $\ell_1$-norm regularization to effect sparsity and low rank for the nominal and anomalous traffic with only the link counts and a {\it small} subset of OD-flow counts. Analysis and simulations confirm that the proposed estimator can {\em exactly} recover sufficiently low-dimensional nominal traffic and sporadic anomalies so long as the routing paths are sufficiently "spread-out" across the network, and an adequate amount of flow counts are randomly sampled. The results offer valuable insights about data acquisition strategies and network scenaria giving rise to accurate traffic estimation. For practical networks where the aforementioned conditions are possibly violated, the inherent spatiotemporal traffic patterns are taken into account by adopting a Bayesian approach along with a bilinear characterization of the nuclear and $\ell_1$ norms. The resultant nonconvex program involves quadratic regularizers with correlation matrices, learned systematically from (cyclo)stationary historical data. Alternating-minimization based algorithms with provable convergence are also developed to procure the estimates. Insightful tests with synthetic and real Internet data corroborate the effectiveness of the novel schemes.

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arXiv2014

Risk-Constrained Microgrid Reconfiguration Using Group Sparsity

The system reconfiguration task is considered for existing power distribution systems and microgrids, in the presence of renewable-based generation and load foresting errors. The system topology is obtained by solving a chance-constrained optimization problem, where loss-of-load (LOL) constraints and Ampacity limits of the distribution lines are enforced. Similar to various distribution system reconfiguration renditions, solving the resultant problem is computationally prohibitive due to the presence of binary line selection variables. Further, lack of closed form expressions for the joint probability distribution of forecasting errors hinders tractability of LOL constraints. Nevertheless, a convex problem re-formulation is developed here by resorting to a scenario approximation technique, and by leveraging the underlying group-sparsity attribute of currents flowing on distribution lines equipped with tie and sectionalizing switches. The novel convex LOL-constrained reconfiguration scheme can also afford a distributed solution using the alternating direction method of multipliers, to address the case where multi-facilities are managed autonomously from the rest of the system.

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arXiv2014

Subspace Learning and Imputation for Streaming Big Data Matrices and Tensors

Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well as the need for {\em real-time} processing of streaming data pose major challenges to this end. In this context, the present paper permeates benefits from rank minimization to scalable imputation of missing data, via tracking low-dimensional subspaces and unraveling latent (possibly multi-way) structure from \emph{incomplete streaming} data. For low-rank matrix data, a subspace estimator is proposed based on an exponentially-weighted least-squares criterion regularized with the nuclear norm. After recasting the non-separable nuclear norm into a form amenable to online optimization, real-time algorithms with complementary strengths are developed and their convergence is established under simplifying technical assumptions. In a stationary setting, the asymptotic estimates obtained offer the well-documented performance guarantees of the {\em batch} nuclear-norm regularized estimator. Under the same unifying framework, a novel online (adaptive) algorithm is developed to obtain multi-way decompositions of \emph{low-rank tensors} with missing entries, and perform imputation as a byproduct. Simulated tests with both synthetic as well as real Internet and cardiac magnetic resonance imagery (MRI) data confirm the efficacy of the proposed algorithms, and their superior performance relative to state-of-the-art alternatives.

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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↗

arXiv2014

Sparsity-leveraging Reconfiguration of Smart Distribution Systems

A system reconfiguration problem is considered for three-phase power distribution networks featuring distributed generation. In lieu of binary line selection variables, the notion of group sparsity is advocated to re-formulate the nonconvex distribution system reconfiguration (DSR) problem into a convex one. Using the duality theory, it is shown that the line selection task boils down to a shrinkage and thresholding operation on the line currents. Further, numerical tests illustrate the ability of the proposed scheme to identify meshed, weakly-meshed, or even radial configurations by adjusting a sparsity-tuning parameter in the DSR cost. Constraints on the voltages are investigated, and incorporated in the novel DSR problem to effect voltage regulation.

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arXiv2014

Distributed Optimal Power Flow for Smart Microgrids

Optimal power flow (OPF) is considered for microgrids, with the objective of minimizing either the power distribution losses, or, the cost of power drawn from the substation and supplied by distributed generation (DG) units, while effecting voltage regulation. The microgrid is unbalanced, due to unequal loads in each phase and non-equilateral conductor spacings on the distribution lines. Similar to OPF formulations for balanced systems, the considered OPF problem is nonconvex. Nevertheless, a semidefinite programming (SDP) relaxation technique is advocated to obtain a convex problem solvable in polynomial-time complexity. Enticingly, numerical tests demonstrate the ability of the proposed method to attain the globally optimal solution of the original nonconvex OPF. To ensure scalability with respect to the number of nodes, robustness to isolated communication outages, and data privacy and integrity, the proposed SDP is solved in a distributed fashion by resorting to the alternating direction method of multipliers. The resulting algorithm entails iterative message-passing among groups of consumers and guarantees faster convergence compared to competing alternatives

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arXiv2014

Efficient Decentralized Economic Dispatch for Microgrids with Wind Power Integration

Decentralized energy management is of paramount importance in smart microgrids with renewables for various reasons including environmental friendliness, reduced communication overhead, and resilience to failures. In this context, the present work deals with distributed economic dispatch and demand response initiatives for grid-connected microgrids with high-penetration of wind power. To cope with the challenge of the wind's intrinsically stochastic availability, a novel energy planning approach involving the actual wind energy as well as the energy traded with the main grid, is introduced. A stochastic optimization problem is formulated to minimize the microgrid net cost, which includes conventional generation cost as well as the expected transaction cost incurred by wind uncertainty. To bypass the prohibitively high-dimensional integration involved, an efficient sample average approximation method is utilized to obtain a solver with guaranteed convergence. Leveraging the special infrastructure of the microgrid, a decentralized algorithm is further developed via the alternating direction method of multipliers. Case studies are tested to corroborate the merits of the novel approaches.

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arXiv2014

Moving-Horizon Dynamic Power System State Estimation Using Semidefinite Relaxation

Accurate power system state estimation (PSSE) is an essential prerequisite for reliable operation of power systems. Different from static PSSE, dynamic PSSE can exploit past measurements based on a dynamical state evolution model, offering improved accuracy and state predictability. A key challenge is the nonlinear measurement model, which is often tackled using linearization, despite divergence and local optimality issues. In this work, a moving-horizon estimation (MHE) strategy is advocated, where model nonlinearity can be accurately captured with strong performance guarantees. To mitigate local optimality, a semidefinite relaxation approach is adopted, which often provides solutions close to the global optimum. Numerical tests show that the proposed method can markedly improve upon an extended Kalman filter (EKF)-based alternative.

eess.SY↗

arXiv2014

Embedding Graphs under Centrality Constraints for Network Visualization

Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of structural network properties. The present paper advocates two graph embedding approaches with centrality considerations to comply with node hierarchy. The problem is formulated first as one of constrained multi-dimensional scaling (MDS), and it is solved via block coordinate descent iterations with successive approximations and guaranteed convergence to a KKT point. In addition, a regularization term enforcing graph smoothness is incorporated with the goal of reducing edge crossings. A second approach leverages the locally-linear embedding (LLE) algorithm which assumes that the graph encodes data sampled from a low-dimensional manifold. Closed-form solutions to the resulting centrality-constrained optimization problems are determined yielding meaningful embeddings. Experimental results demonstrate the efficacy of both approaches, especially for visualizing large networks on the order of thousands of nodes.

stat.ML↗

arXiv2014

Optimal Dispatch of Photovoltaic Inverters in Residential Distribution Systems

Low-voltage distribution feeders were designed to sustain unidirectional power flows to residential neighborhoods. The increased penetration of roof-top photovoltaic (PV) systems has highlighted pressing needs to address power quality and reliability concerns, especially when PV generation exceeds the household demand. A systematic method for determining the active- and reactive-power set points for PV inverters in residential systems is proposed in this paper, with the objective of optimizing the operation of the distribution feeder and ensuring voltage regulation. Binary PV-inverter selection variables and nonlinear power-flow relations render the novel optimal inverter dispatch problem nonconvex and NP-hard. Nevertheless, sparsity-promoting regularization approaches and semidefinite relaxation techniques are leveraged to obtain a computationally feasible convex reformulation. The merits of the proposed approach are demonstrated using real-world PV-generation and load-profile data for an illustrative low-voltage residential distribution system.

math.OC↗

arXiv2013

Robust Optimal Power Flow with Wind Integration Using Conditional Value-at-Risk

Integrating renewable energy into the power grid requires intelligent risk-aware dispatch accounting for the stochastic availability of renewables. Toward achieving this goal, a robust DC optimal flow problem is developed in the present paper for power systems with a high penetration of wind energy. The optimal dispatch is obtained as the solution to a convex program with a suitable regularizer, which is able to mitigate the potentially high risk of inadequate wind power. The regularizer is constructed based on the energy transaction cost using conditional value-at-risk (CVaR). Bypassing the prohibitive high-dimensional integral, the distribution-free sample average approximation method is efficiently utilized for solving the resulting optimization problem. Case studies are reported to corroborate the efficacy of the novel model and approach tested on the IEEE 30-bus benchmark system with real operation data from seven wind farms.

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