Traditional protection schemes face significant challenges when applied to microgrids with high penetrations of renewables with inverter-based resources (IBRs). The proliferation of advanced sensing and communication technologies has generated copious data, offering an opportunity to overcome these limitations using data-driven machine learning approaches. This work proposes a novel approach based on a support vector machine (SVM) for detecting faults within a 100% renewable microgrid. The approach encompasses a systematic offline training stage for the development of a linear SVM-based fault detection algorithm. This process covers offline data collection from the microgrid under study, the extraction of features such as positive- and negative-sequence components and the total harmonic distortion of the voltage and current measurements of the relays, and the design of the linear SVM-based classifier. During the online implementation, however, different classifiers can exhibit asynchronicity in detecting the fault inception at different subcycle-to-cycle period-level delays. To circumvent this asynchronicity issue, a separate algorithm is developed for each relay to estimate the fault inception time as close to the real fault time. The performance of the proposed SVM-based synchronized fault detection method is evaluated using online time-domain simulation studies on a microgrid test system. The results corroborate the reliability of the fault detection scheme when tested under various fault cases (fault types, locations, and impedances) and non-fault cases during both grid-tied and islanded operation modes.

The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over 45 literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Applications. Funding: This work was supported by the U.S. Department of Energy (DOE) Advanced Grid Modeling project, Coordinated Planning and Operation of Water and Power Infrastructures for Increased Resilience and Reliability. Incorporation of the PolyhedralRelaxations Julia package was supported by Los Alamos National Laboratory’s Directed Research and Development program under the project Fast, Linear Programming-Based Algorithms with Solution Quality Guarantees for Nonlinear Optimal Control Problems [Grant 20220006ER]. All work at Los Alamos National Laboratory was conducted under the auspices of the National Nuclear Security Administration of the U.S. DOE, Contract No. 89233218CNA000001. This work was also authored in part by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the U.S. DOE, Contract No. DE-AC36-08GO28308. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0233 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0233 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Tensor factorization methods have recently gained increased popularity. A key feature that renders tensors attractive is the ability to directly model multi-relational data. In this work, we propose ParaSketch, a parallel tensor factorization algorithm that enables massive parallelism, to deal with large tensors. The idea is to compress the large tensor into multiple small tensors, decompose each small tensor in parallel, and combine the results to reconstruct the desired latent factors. Prior art in this direction entails potentially very high complexity in the (Gaussian) compression and final combining stages. Adopting sketching matrices for compression, the proposed method enjoys a dramatic reduction in compression complexity, and features a much lighter combining step. Moreover, theoretical analysis shows that the compressed tensors inherit latent identifiability under mild conditions, hence establishing correctness of the overall approach. Numerical experiments corroborate the theory and demonstrate the effectiveness of the proposed algorithm.

Joint analysis of data from multiple information repositories facilitates uncovering the underlying structure in heterogeneous datasets. Single and coupled matrix-tensor factorization (CMTF) has been widely used in this context for imputation-based recommendation from ratings, social network, and other user-item data. When this side information is in the form of item-item correlation matrices or graphs, existing CMTF algorithms may fall short. Alleviating current limitations, we introduce a novel model coined coupled graph-tensor factorization (CGTF) that judiciously accounts for graph-related side information. The CGTF model has the potential to overcome practical challenges, such as missing slabs from the tensor and/or missing rows/columns from the correlation matrices. A novel alternating direction method of multipliers (ADMM) is also developed that recovers the nonnegative factors of CGTF. Our algorithm enjoys closed-form updates that result in reduced computational complexity and allow for convergence claims. A novel direction is further explored by employing the interpretable factors to detect graph communities having the tensor as side information. The resulting community detection approach is successful even when some links in the graphs are missing. Results with real data sets corroborate the merits of the proposed methods relative to state-of-the-art competing factorization techniques in providing recommendations and detecting communities.

Tensor factorization methods have gained increased popularity in the data mining community. A key feature that renders tensors attractive is the essential uniqueness (identifiability) of their decomposition into latent factors: this is crucial for explanatory data analysis – model uniqueness makes interpretations well grounded. In this work, we propose ParaSketch, a distributed tensor factorization algorithm that enables massive parallelism, to deal with large tensors. The idea is to compress/sketch the large tensor into multiple small tensors, decompose each small tensor, and combine the results to reconstruct the desired latent factors. Prior art in this direction entails potentially very high complexity in the (Gaussian) compression and final combining stages. Utilizing sketching matrices for compression, the proposed method greatly reduces compression complexity, and features much simpler combining. Moreover, theoretical analysis shows that the compressed tensors inherit latent identifiability under mild conditions, hence establishing correctness of the overall approach. Our approach to establish identifiability for the sketched tensor is original, and of interest in its own right.

We investigate the degrees of freedom (DoF) of the downlink of a cellular relay network. In this network, two base stations transmit to two mobile stations via relays due to the absence of a direct communication link. Each base station and mobile station is equipped with $M$ antennas. Each base station has two messages; one to each mobile station, and uses two relays to transmit to the mobile stations. The relays are half duplex, decode-and-forward and equipped with $N$ antennas each. We consider two configurations of the relays; shared and dedicated relays. In the shared relays configuration, the system has two relays that are used by both base stations. Whereas, in the dedicated relays configuration, each base station has two dedicated relays, i.e., the system has four relays. We consider all possible relaying schemes where the base stations can use the relays either simultaneously or alternately. We derive an upper bound on the DoF achievable by each relaying scheme as a function of the ratio between $N$ and $M$. Furthermore, we propose an achievable scheme that uses interference alignment to achieve the upper bound on the DoF for the shared relays configuration, and for all values of $M$ and $N$ except for $1<;\frac{N}{M}<;\frac{5}{2}$ in the dedicated relays configuration.

In this paper we investigate the degrees of freedom of a cellular relay network that consists of two base stations, two mobile stations and four decode-and-forward relays. The base stations and the mobile stations are equipped with M antennas each, whereas the relays are equipped with N antennas each. In addition, each base station has an independent message to each mobile station. The relays are used to froward the messages from the base stations to the mobile station as there is no direct link. We consider three different relaying architectures where the two relays associated with each base station simultaneously or alternately transmit their messages. We derive an upper bound on the degrees of freedom achievable by each relaying architecture as a function of the ratio between N and M. Furthermore, we propose an achievable scheme that uses interference alignment to achieve the upper bound on the DoF for all values of M and N except for 1 ≤ N/M ≤ 5/2.