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Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute Shrinkage and Selection Operator (LASSO) approaches by jointly estimating the permutation, resulting in shuffled LS and shuffled LASSO formulations. Existing methods, constrained by the combinatorial complexity of permutation recovery, often address small-scale cases with limited measurements. In contrast, we focus on large-scale SLR, particularly suited for environments with abundant measurement samples. We propose a spectral matching method that efficiently resolves permutations by aligning spectral components of the measurement and feature covariances. Rigorous theoretical analyses demonstrate that our method achieves accurate estimates in both shuffled LS and shuffled LASSO settings, given a sufficient number of samples. Furthermore, we extend our approach to address simultaneous pose and correspondence estimation in image registration tasks. Experiments on synthetic datasets and real-world image registration scenarios show that our method outperforms existing algorithms in both estimation accuracy and registration performance., Comment: This work has been submitted to the IEEE for possible publication

Due to the availability of more comprehensive measurement data in modern power systems, there has been significant interest in developing and applying reinforcement learning (RL) methods for operation and control. Conventional RL training is based on trial-and-error and reward feedback interaction with either a model-based simulated environment or a data-driven and model-free simulation environment. These methods often lead to the exploration of actions in unsafe regions of operation and, after training, the execution of unsafe actions when the RL policies are deployed in real power systems. A large body of literature has proposed safe RL strategies to prevent unsafe training policies. In power systems, safe RL represents a class of RL algorithms that can ensure or promote the safety of power system operations by executing safe actions while optimizing the objective function. While different papers handle the safety constraints differently, the overarching goal of safe RL methods is to determine how to train policies to satisfy safety constraints while maximizing rewards. This paper provides a comprehensive review of safe RL techniques and their applications in different power system operations and control, including optimal power generation dispatch, voltage control, stability control, electric vehicle (EV) charging control, buildings' energy management, electricity market, system restoration, and unit commitment and reserve scheduling. Additionally, the paper discusses benchmarks, challenges, and future directions for safe RL research in power systems.

In this paper, we are interested in solving Network Utility Maximization (NUM) problems whose underlying local utilities and constraints depend on a complex stochastic dynamic environment. While the general model applies broadly, this work is motivated by resource sharing during disasters concurrently occurring in multiple areas. In such situations, hierarchical layers of Incident Command Systems (ICS) are engaged; specifically, a central entity (e.g., the federal government) typically coordinates the incident response allocating resources to different sites, which then get distributed to the affected by local entities. The benefits of an allocation decision to the different sites are generally not expressed explicitly as a closed-form utility function because of the complexity of the response and the random nature of the underlying phenomenon we try to contain. We use the classic approach of decomposing the NUM formulation and applying a primal-dual algorithm to achieve optimal higher-level decisions under coupled constraints while modeling the optimized response to the local dynamics with deep reinforcement learning algorithms. The decomposition we propose has several benefits: 1) the entities respond to their local utilities based on a congestion signal conveyed by the ICS upper layers; 2) the complexity of capturing the utility of local responses and their diversity is addressed effectively without sharing local parameters and priorities with the ICS layers above; 3) utilities, known as explicit functions, are approximated as convex functions of the resources allocated; 4) decisions rely on up-to-date data from the ground along with future forecasts.

In this paper, we present a framework based on differential privacy (DP) for querying electric power measurements to detect system anomalies or bad data. Our DP approach conceals consumption and system matrix data, while simultaneously enabling an untrusted third party to test hypotheses of anomalies, such as the presence of bad data, by releasing a randomized sufficient statistic for hypothesis-testing. We consider a measurement model corrupted by Gaussian noise and a sparse noise vector representing the attack, and we observe that the optimal test statistic is a chi-square random variable. To detect possible attacks, we propose a novel DP chi-square noise mechanism that ensures the test does not reveal private information about power injections or the system matrix. The proposed framework provides a robust solution for detecting bad data while preserving the privacy of sensitive power system data., Comment: 13 pages, 5 figures

Recent research highlights frequent model communication as a significant bottleneck to the efficiency of decentralized machine learning (ML), especially for large-scale and over-parameterized neural networks (NNs). To address this, we present Malcom-PSGD, a novel decentralized ML algorithm that combines gradient compression techniques with model sparsification. We promote model sparsity by adding $\ell_1$ regularization to the objective and present a decentralized proximal SGD method for training. Our approach employs vector source coding and dithering-based quantization for the compressed gradient communication of sparsified models. Our analysis demonstrates that Malcom-PSGD achieves a convergence rate of $\mathcal{O}(1/\sqrt{t})$ with respect to the iterations $t$, assuming a constant consensus and learning rate. This result is supported by our proof for the convergence of non-convex compressed Proximal SGD methods. Additionally, we conduct a bit analysis, providing a closed-form expression for the communication costs associated with Malcom-PSGD. Numerical results verify our theoretical findings and demonstrate that our method reduces communication costs by approximately $75\%$ when compared to the state-of-the-art.

In this paper, we propose a source coding scheme that represents data from unknown distributions through frequency and support information. Existing encoding schemes often compress data by sacrificing computational efficiency or by assuming the data follows a known distribution. We take advantage of the structure that arises within the spatial representation and utilize it to encode run-lengths within this representation using Golomb coding. Through theoretical analysis, we show that our scheme yields an overall bit rate that nears entropy without a computationally complex encoding algorithm and verify these results through numerical experiments., Comment: This work has been submitted to the IEEE for possible publication

Classical graph matching aims to find a node correspondence between two unlabeled graphs of known topologies. This problem has a wide range of applications, from matching identities in social networks to identifying similar biological network functions across species. However, when the underlying graphs are unknown, the use of conventional graph matching methods requires inferring the graph topologies first, a process that is highly sensitive to observation errors. In this paper, we tackle the blind graph matching problem with unknown underlying graphs directly using observations of graph signals, which are generated from graph filters applied to graph signal excitations. We propose to construct sample covariance matrices from the observed signals and match the nodes based on the selected sample eigenvectors. Our analysis shows that the blind matching outcome converges to the result obtained with known graph topologies when the signal sampling size is large and the signal noise is small. Numerical results showcase the performance improvement of the proposed algorithm compared to matching two estimated underlying graphs learned from the graph signals., Comment: This work has been accepted by the IEEE for possible publication

In this paper, we present a notion of differential privacy (DP) for data that comes from different classes. Here, the class-membership is private information that needs to be protected. The proposed method is an output perturbation mechanism that adds noise to the release of query response such that the analyst is unable to infer the underlying class-label. The proposed DP method is capable of not only protecting the privacy of class-based data but also meets quality metrics of accuracy and is computationally efficient and practical. We illustrate the efficacy of the proposed method empirically while outperforming the baseline additive Gaussian noise mechanism. We also examine a real-world application and apply the proposed DP method to the autoregression and moving average (ARMA) forecasting method, protecting the privacy of the underlying data source. Case studies on the real-world advanced metering infrastructure (AMI) measurements of household power consumption validate the excellent performance of the proposed DP method while also satisfying the accuracy of forecasted power consumption measurements., Comment: Under review in IEEE Transactions on Information Forensics & Security

Stakeholders in electricity delivery infrastructure are amassing data about their system demand, use, and operations. Still, they are reluctant to share them, as even sharing aggregated or anonymized electric grid data risks the disclosure of sensitive information. This paper highlights how applying differential privacy to distributed energy resource production data can preserve the usefulness of that data for operations, planning, and research purposes without violating privacy constraints. Differentially private mechanisms can be optimized for queries of interest in the energy sector, with provable privacy and accuracy trade-offs, and can help design differentially private databases for further analysis and research. In this paper, we consider the problem of inference and publication of solar photovoltaic systems' metadata. Metadata such as nameplate capacity, surface azimuth and surface tilt may reveal personally identifiable information regarding the installation behind-the-meter. We describe a methodology to infer the metadata and propose a mechanism based on Bayesian optimization to publish the inferred metadata in a differentially private manner. The proposed mechanism is numerically validated using real-world solar power generation data., Comment: 10 pages, 6 figures

Deep Reinforcement Learning (DRL) has become a popular method for solving control problems in power systems. Conventional DRL encourages the agent to explore various policies encoded in a neural network (NN) with the goal of maximizing the reward function. However, this approach can lead to infeasible solutions that violate physical constraints such as power flow equations, voltage limits, and dynamic constraints. Ensuring these constraints are met is crucial in power systems, as they are a safety critical infrastructure. To address this issue, existing DRL algorithms remedy the problem by projecting the actions onto the feasible set, which can result in sub-optimal solutions. This paper presents a novel primal-dual approach for learning optimal constrained DRL policies for dynamic optimal power flow problems, with the aim of controlling power generations and battery outputs. We also prove the convergence of the critic and actor networks. Our case studies on IEEE standard systems demonstrate the superiority of the proposed approach in dynamically adapting to the environment while maintaining safety constraints., Comment: This work has been submitted to the IEEE for possible publication

The effective representation, precessing, analysis, and visualization of large-scale structured data over graphs are gaining a lot of attention. So far most of the literature has focused on real-valued signals. However, signals are often sparse in the Fourier domain, and more informative and compact representations for them can be obtained using the complex envelope of their spectral components, as opposed to the original real-valued signals. Motivated by this fact, in this work we generalize graph convolutional neural networks (GCN) to the complex domain, deriving the theory that allows to incorporate a complex-valued graph shift operators (GSO) in the definition of graph filters (GF) and process complex-valued graph signals (GS). The theory developed can handle spatio-temporal complex network processes. We prove that complex-valued GCNs are stable with respect to perturbations of the underlying graph support, the bound of the transfer error and the bound of error propagation through multiply layers. Then we apply complex GCN to power grid state forecasting, power grid cyber-attack detection and localization., Comment: This work has been submitted to the IEEE for possible publication

This paper proposes a model-free Volt-VAR control (VVC) algorithm via the spatio-temporal graph ConvNet-based deep reinforcement learning (STGCN-DRL) framework, whose goal is to control smart inverters in an unbalanced distribution system. We first identify the graph shift operator (GSO) based on the power flow equations. Then, we develop a spatio-temporal graph ConvNet (STGCN), testing both recurrent graph ConvNets (RGCN) and convolutional graph ConvNets (CGCN) architectures, aimed at capturing the spatiotemporal correlation of voltage phasors. The STGCN layer performs the feature extraction task for the policy function and the value function of the reinforcement learning architecture, and then we utilize the proximal policy optimization (PPO) to search the action spaces for an optimum policy function and to approximate an optimum value function. We further utilize the low-pass property of voltage graph signal to introduce an GCN architecture for the the policy whose input is a decimated state vector, i.e. a partial observation. Case studies on the unbalanced 123-bus systems validate the excellent performance of the proposed method in mitigating instabilities and maintaining nodal voltage profiles within a desirable range., Comment: This work has been submitted to the IEEE for possible publication

Volt-VAR and Volt-Watt functionality in photovoltaic (PV) smart inverters provide mechanisms to ensure system voltage magnitudes and power factors remain within acceptable limits. However, these control functions can become unstable, introducing oscillations in system voltages when not appropriately configured or maliciously altered during a cyberattack. In the event that Volt-VAR and Volt-Watt control functions in a portion of PV smart inverters in a distribution grid are unstable, the proposed adaptation scheme utilizes the remaining and stably-behaving PV smart inverters and other Distributed Energy Resources to mitigate the effect of the instability. The adaptation mechanism is entirely decentralized, model-free, communication-free, and requires virtually no external configuration. We provide a derivation of the adaptive control approach and validate the algorithm in experiments on the IEEE 37 and 8500 node test feeders.

Volt-VAR and Volt-Watt control functions are mechanisms that are included in distributed energy resource (DER) power electronic inverters to mitigate excessively high or low voltages in distribution systems. In the event that a subset of DER have had their Volt-VAR and Volt-Watt settings compromised as part of a cyber-attack, we propose a mechanism to control the remaining set of non-compromised DER to ameliorate large oscillations in system voltages and large voltage imbalances in real time. To do so, we construct control policies for individual non-compromised DER, directly searching the policy space using an Adam-based augmented random search (ARS). In this paper we show that, compared to previous efforts aimed at training policies for DER cybersecurity using deep reinforcement learning (DRL), the proposed approach is able to learn optimal (and sometimes linear) policies an order of magnitude faster than conventional DRL techniques (e.g., Proximal Policy Optimization).

The proliferation of smart meters has resulted in a large amount of data being generated. It is increasingly apparent that methods are required for allowing a variety of stakeholders to leverage the data in a manner that preserves the privacy of the consumers. The sector is scrambling to define policies, such as the so called `15/15 rule', to respond to the need. However, the current policies fail to adequately guarantee privacy. In this paper, we address the problem of allowing third parties to apply $K$-means clustering, obtaining customer labels and centroids for a set of load time series by applying the framework of differential privacy. We leverage the method to design an algorithm that generates differentially private synthetic load data consistent with the labeled data. We test our algorithm's utility by answering summary statistics such as average daily load profiles for a 2-dimensional synthetic dataset and a real-world power load dataset., Comment: 13 pages, 13 figures

The Differential Privacy (DP) literature often centers on meeting privacy constraints by introducing noise to the query, typically using a pre-specified parametric distribution model with one or two degrees of freedom. However, this emphasis tends to neglect the crucial considerations of response accuracy and utility, especially in the context of categorical or discrete numerical database queries, where the parameters defining the noise distribution are finite and could be chosen optimally. This paper addresses this gap by introducing a novel framework for designing an optimal noise Probability Mass Function (PMF) tailored to discrete and finite query sets. Our approach considers the modulo summation of random noise as the DP mechanism, aiming to present a tractable solution that not only satisfies privacy constraints but also minimizes query distortion. Unlike existing approaches focused solely on meeting privacy constraints, our framework seeks to optimize the noise distribution under an arbitrary $(\epsilon, \delta)$ constraint, thereby enhancing the accuracy and utility of the response. We demonstrate that the optimal PMF can be obtained through solving a Mixed-Integer Linear Program (MILP). Additionally, closed-form solutions for the optimal PMF are provided, minimizing the probability of error for two specific cases. Numerical experiments highlight the superior performance of our proposed optimal mechanisms compared to state-of-the-art methods. This paper contributes to the DP literature by presenting a clear and systematic approach to designing noise mechanisms that not only satisfy privacy requirements but also optimize query distortion. The framework introduced here opens avenues for improved privacy-preserving database queries, offering significant enhancements in response accuracy and utility., Comment: Accepted for publication in the journal Cybersecurity (https://cybersecurity.springeropen.com/)

The goal of this paper is to propose and analyze a differentially private randomized mechanism for the $K$-means query. The goal is to ensure that the information received about the cluster-centroids is differentially private. The method consists in adding Gaussian noise with an optimum covariance. The main result of the paper is the analytical solution for the optimum covariance as a function of the database. Comparisons with the state of the art prove the efficacy of our approach., Comment: 5 pages, 3 figures, preprint

In this work, we study how to implement a distributed algorithm for the power method in a parallel manner. As the existing distributed power method is usually sequentially updating the eigenvectors, it exhibits two obvious disadvantages: 1) when it calculates the $h$th eigenvector, it needs to wait for the results of previous $(h-1)$ eigenvectors, which causes a delay in acquiring all the eigenvalues; 2) when calculating each eigenvector, it needs a certain cost of information exchange within the neighboring nodes for every power iteration, which could be unbearable when the number of eigenvectors or the number of nodes is large. This motivates us to propose a parallel distributed power method, which simultaneously calculates all the eigenvectors at each power iteration to ensure that more information could be exchanged in one shaking-hand of communication. We are particularly interested in the distributed power method for both an eigenvalue decomposition (EVD) and a singular value decomposition (SVD), wherein the distributed process is proceed based on a gossip algorithm. It can be shown that, under the same condition, the communication cost of the gossip-based parallel method is only $1/H$ times of that for the sequential counterpart, where $H$ is the number of eigenvectors we want to compute, while the convergence time and error performance of the proposed parallel method are both comparable to those of its sequential counterpart.

The underlying theme of this paper is to explore the various facets of power systems data through the lens of graph signal processing (GSP), laying down the foundations of the Grid-GSP framework. Grid-GSP provides an interpretation for the spatio-temporal properties of voltage phasor measurements, by showing how the well-known power systems modeling supports a generative low-pass graph filter model for the state variables, namely the voltage phasors. Using the model we formalize the empirical observation that voltage phasor measurement data lie in a low-dimensional subspace and tie their spatio-temporal structure to generator voltage dynamics. The Grid-GSP generative model is then successfully employed to investigate the problems pertaining to the grid of data sampling and interpolation, network inference, detection of anomalies and data compression. Numerical results on a large synthetic grid that mimics the real-grid of the state of Texas, ACTIVSg2000, and on real-world measurements from ISO-New England verify the efficacy of applying Grid-GSP methods to electric grid data., Comment: 15 Pages, under review in IEEE Transactions on Signal Processing

In federated learning, models are learned from users' data that are held private in their edge devices, by aggregating them in the service provider's "cloud" to obtain a global model. Such global model is of great commercial value in, e.g., improving the customers' experience. In this paper we focus on two possible areas of improvement of the state of the art. First, we take the difference between user habits into account and propose a quadratic penalty-based formulation, for efficient learning of the global model that allows to personalize local models. Second, we address the latency issue associated with the heterogeneous training time on edge devices, by exploiting a hierarchical structure modeling communication not only between the cloud and edge devices, but also within the cloud. Specifically, we devise a tailored block coordinate descent-based computation scheme, accompanied with communication protocols for both the synchronous and asynchronous cloud settings. We characterize the theoretical convergence rate of the algorithm, and provide a variant that performs empirically better. We also prove that the asynchronous protocol, inspired by multi-agent consensus technique, has the potential for large gains in latency compared to a synchronous setting when the edge-device updates are intermittent. Finally, experimental results are provided that corroborate not only the theory, but also show that the system leads to faster convergence for personalized models on the edge devices, compared to the state of the art., Comment: 31 pages, 5 figures. Codes available at this url {https://github.com/REIYANG/FedBCD}. To appear in AAAI 2021

Fast-acting smart inverters that utilize preset operating conditions to determine real and reactive power injection/consumption can create voltage instabilities (over-voltage, voltage oscillations and more) in an electrical distribution network if set-points are not properly configured. In this work, linear distribution power flow equations and droop-based Volt-Var and Volt-Watt control curves are used to analytically derive a stability criterion using \lyapnouv analysis that includes the network operating condition. The methodology is generally applicable for control curves that can be represented as Lipschitz functions. The derived Lipschitz constants account for smart inverter hardware limitations for reactive power generation. A local policy is derived from the stability criterion that allows inverters to adapt their control curves by monitoring only local voltage, thus avoiding centralized control or information sharing with other inverters. The criterion is independent of the internal time-delays of smart inverters. Simulation results for inverters with and without the proposed stabilization technique demonstrate how smart inverters can mitigate voltage oscillations locally and mitigate real and reactive power flow disturbances at the substation under multiple scenarios. The study concludes with illustrations of how the control policy can dampen oscillations caused by solar intermittency and cyber-attacks., Comment: Accepted for IET Renewable Power Generation

The adoption of blockchain for Transactive Energy has gained significant momentum as it allows mutually non-trusting agents to trade energy services in a trustless energy market. Research to date has assumed that the built-in Byzantine Fault Tolerance in recording transactions in a ledger is sufficient to ensure integrity. Such work must be extended to address security gaps including random bilateral transactions that do not guarantee reliable and efficient market operation, and market participants having incentives to cheat when reporting actual production/consumption figures. Work herein introduces the Electron Volt Exchange framework with the following characteristics: 1) a distributed protocol for pricing and scheduling prosumers' production/consumption while keeping constraints and bids private, and 2) a distributed algorithm to prevent theft that verifies prosumers' compliance to scheduled transactions using information from grid sensors (such as smart meters) and mitigates the impact of false data injection attacks. Flexibility and robustness of the approach are demonstrated through simulation and implementation using Hyperledger Fabric., Comment: Accepted for Applied Energy

The increasing penetration of DER with smart-inverter functionality is set to transform the electrical distribution network from a passive system, with fixed injection/consumption, to an active network with hundreds of distributed controllers dynamically modulating their operating setpoints as a function of system conditions. This transition is being achieved through standardization of functionality through grid codes and/or international standards. DER, however, are unique in that they are typically neither owned nor operated by distribution utilities and, therefore, represent a new emerging attack vector for cyber-physical attacks. Within this work we consider deep reinforcement learning as a tool to learn the optimal parameters for the control logic of a set of uncompromised DER units to actively mitigate the effects of a cyber-attack on a subset of network DER.

This applied research paper introduces a novel framework for integrating hardware security and blockchain functionality with grid-edge devices to establish a distributed cyber-security mechanism that verifies the provenance of messages to and from the devices. Expanding the idea of Two Factor Authentication and Hardware Root of Trust, this work describes the development of a Cryptographic Trust Center(TM) (CTC(TM)) chip integrated into grid-edge devices to create uniform cryptographic key management. Product managers, energy system designers, and security architects can utilize this modular framework as a unified approach to manage distributed devices of various vendors, vintages, and sizes. Results demonstrate the application of CTC(TM) to a blockchain-based Transactive Energy (TE) platform for provisioning of cryptographic keys and improved uniformity of the operational network and data management. This process of configuring, installing, and maintaining keys is described as Eco-Secure Provisioning(TM) (ESP(TM)). Laboratory test results show the approach can resolve several cyber-security gaps in common blockchain frameworks such as Hyperledger Fabric., Comment: 2021 North American Power Symposium

The notion of graph filters can be used to define generative models for graph data. In fact, the data obtained from many examples of network dynamics may be viewed as the output of a graph filter. With this interpretation, classical signal processing tools such as frequency analysis have been successfully applied with analogous interpretation to graph data, generating new insights for data science. What follows is a user guide on a specific class of graph data, where the generating graph filters are low-pass, i.e., the filter attenuates contents in the higher graph frequencies while retaining contents in the lower frequencies. Our choice is motivated by the prevalence of low-pass models in application domains such as social networks, financial markets, and power systems. We illustrate how to leverage properties of low-pass graph filters to learn the graph topology or identify its community structure; efficiently represent graph data through sampling, recover missing measurements, and de-noise graph data; the low-pass property is also used as the baseline to detect anomalies., Comment: 11 pages, 5 figures

K-12 engineering outreach has typically focused on elementary electrical and mechanical engineering or robot experiments integrated in science or math classes. In contrast, we propose a novel outreach program focusing on communication network principles that enable the ubiquitous web and smart-phone applications. We design outreach activities that illustrate the communication network principles through activities and team competitions in physical education (PE) as well as story writing and cartooning in English Language Arts (ELA) classes. The PE activities cover the principles of store-and-forward packet switching, Hypertext Transfer Protocol (HTTP) web page download, connection establishment in cellular wireless networks, as well as packet routing in Software-Defined Networking (SDN). The proposed outreach program has been formatively evaluated by K-12 teachers. A survey for the evaluation of the impact of the outreach program on the student perceptions, specifically, the students' interest, self-efficacy, utility, and negative stereotype perceptions towards communication network engineering, is also presented.

Decentralized optimization has found a significant utility in recent years, as a promising technique to overcome the curse of dimensionality when dealing with large-scale inference and decision problems in big data. While these algorithms are resilient to node and link failures, they however, are not inherently Byzantine fault-tolerant towards insider data injection attacks. This paper proposes a decentralized robust subgradient push (RSGP) algorithm for detection and isolation of malicious nodes in the network for optimization non-strongly convex objectives. In the attack considered in this work, the malicious nodes follow the algorithmic protocols, but can alter their local functions arbitrarily. However, we show that in sufficiently structured problems, the method proposed is effective in revealing their presence. The algorithm isolates detected nodes from the regular nodes, thereby mitigating the ill-effects of malicious nodes. We also provide performance measures for the proposed method., Comment: 6 pages, 2 figures, 8th IFAC Workshop on Distributed Estimation and Control in Networked Systems

In recent years, many Blockchain based frameworks for transacting commodities on a congestible network have been proposed. In particular, as the number of controllable grid connected assets increases, there is a need for a decentralized, coupled economic and control mechanism to dynamically balance the entire electric grid. Blockchain based Transactive Energy (TE) systems have gained significant momentum as an approach to sustain the reliability and security of the power grid in order to support the flexibility of electricity demand. What is lacking in these designs, however, is a mechanism that physically verifies all the energy transactions, to keep the various inherently selfish players honest. In this paper, we introduce a secure peer-to-peer network mechanism for the physical validation of economic transactions cleared over a distributed ledger. The framework is $\textit{secure}$ in the sense that selfish and malicious agents that are trying to inject false data into the network are prevented from adversely affecting the optimal functionality of the verification process by detecting and isolating them from the communication network. Preliminary simulations focusing on TE show the workings of this framework., Comment: 8 pages, 5 figures, submitted to The 2020 American Control Conference

This work proposes a framework to generate synthetic distribution feeders mapped to real geo-spatial topologies using available OpenStreetMap data. The synthetic power networks can facilitate power systems research and development by providing thousands of realistic use cases. The location of substations is taken from recent efforts to develop synthetic transmission test cases, with underlying real and reactive power in the distribution network assigned using population information gathered from United States 2010 Census block data. The methods illustrate how to create individual synthetic distribution feeders, and groups of feeders across entire ZIP Code, with minimal input data for any location in the United States. The framework also has the capability to output data in \OpenDSS format to allow further simulation and analysis., Comment: North American Power Symposium 2019

Power systems often rely on natural gas pipeline networks to supply fuel for gas-fired generation. Market inefficiencies and a lack of formal coordination between the wholesale power and gas delivery infrastructures may magnify the broader impact of a cyber-attack on a natural gas pipeline. In this study we present a model that can be used to quantify the impact of cyber-attacks on electricity and gas delivery operations. We model activation of cyber-attack vectors that attempt to gain access to pipeline gas compressor controls using a continuous-time Markov chain over a state space based on the gas operator Industrial Control System firewall zone partition. Our approach evaluates the operating states and decision-making in the networks using physically realistic and operationally representative models. We summarize these models, the sequence of analyses used to quantify the impacts of a cyber-incident, and propose a Monte Carlo simulation approach to quantify the resulting effect on the reliability of the bulk power system by the increase in operational cost. The methodology is applied to a case study of interacting power, gas, and cyber test networks.

This paper considers a new framework to detect communities in a graph from the observation of signals at its nodes. We model the observed signals as noisy outputs of an unknown network process, represented as a graph filter that is excited by a set of unknown low-rank inputs/excitations. Application scenarios of this model include diffusion dynamics, pricing experiments, and opinion dynamics. Rather than learning the precise parameters of the graph itself, we aim at retrieving the community structure directly. The paper shows that communities can be detected by applying a spectral method to the covariance matrix of graph signals. Our analysis indicates that the community detection performance depends on a `low-pass' property of the graph filter. We also show that the performance can be improved via a low-rank matrix plus sparse decomposition method when the latent parameter vectors are known. Numerical experiments demonstrate that our approach is effective., Comment: Single column format, 32 pages, 9 figures

A significant portion of the literature on fault localization assumes (more or less explicitly) that there are sufficient reliable measurements to guarantee that the system is observable. While several heuristics exist to break the observability barrier, they mostly rely on recognizing spatio-temporal patterns, without giving insights on how the performance are tied with the system features and the sensor deployment. In this paper, we try to fill this gap and investigate the limitations and performance limits of fault localization using Phasor Measurement Units (PMUs), in the low measurements regime, i.e., when the system is unobservable with the measurements available. Our main contribution is to show how one can leverage the scarce measurements to localize different type of distribution line faults (three-phase, single-phase to ground, ...) at the level of sub-graph, rather than with the resolution of a line. We show that the resolution we obtain is strongly tied with the graph clustering notion in network science., Comment: Accepted in IEEE SmartGridComm 2018 Conference

This paper studies an acceleration technique for incremental aggregated gradient ({\sf IAG}) method through the use of \emph{curvature} information for solving strongly convex finite sum optimization problems. These optimization problems of interest arise in large-scale learning applications. Our technique utilizes a curvature-aided gradient tracking step to produce accurate gradient estimates incrementally using Hessian information. We propose and analyze two methods utilizing the new technique, the curvature-aided IAG ({\sf CIAG}) method and the accelerated CIAG ({\sf A-CIAG}) method, which are analogous to gradient method and Nesterov's accelerated gradient method, respectively. Setting $\kappa$ to be the condition number of the objective function, we prove the $R$ linear convergence rates of $1 - \frac{4c_0 \kappa}{(\kappa+1)^2}$ for the {\sf CIAG} method, and $1 - \sqrt{\frac{c_1}{2\kappa}}$ for the {\sf A-CIAG} method, where $c_0,c_1 \leq 1$ are constants inversely proportional to the distance between the initial point and the optimal solution. When the initial iterate is close to the optimal solution, the $R$ linear convergence rates match with the gradient and accelerated gradient method, albeit {\sf CIAG} and {\sf A-CIAG} operate in an incremental setting with strictly lower computation complexity. Numerical experiments confirm our findings. The source codes used for this paper can be found on \url{http://github.com/hoitowai/ciag/}., Comment: 22 pages, 3 figures, 3 tables. Accepted by Computational Optimization and Applications, to appear

We propose and analyze a new stochastic gradient method, which we call Stochastic Unbiased Curvature-aided Gradient (SUCAG), for finite sum optimization problems. SUCAG constitutes an unbiased total gradient tracking technique that uses Hessian information to accelerate con- vergence. We analyze our method under the general asynchronous model of computation, in which each function is selected infinitely often with possibly unbounded (but sublinear) delay. For strongly convex problems, we establish linear convergence for the SUCAG method. When the initialization point is sufficiently close to the optimal solution, the established convergence rate is only dependent on the condition number of the problem, making it strictly faster than the known rate for the SAGA method. Furthermore, we describe a Markov-driven approach of implementing the SUCAG method in a distributed asynchronous multi-agent setting, via gossiping along a random walk on an undirected communication graph. We show that our analysis applies as long as the graph is connected and, notably, establishes an asymptotic linear convergence rate that is robust to the graph topology. Numerical results demonstrate the merits of our algorithm over existing methods., Comment: to appear in CDC 2018, 17 pages, 2 figures

In this paper we introduce a continuous time multi stage stochastic optimization for scheduling generating units, their commitment, reserve capacities and their continuous time generation profiles in the day-ahead wholesale electricity market. Our formulation approximates the solution of a variational problem, in which the balance, generation capacity and ramping constraints are in continuous time. Due to the greater accuracy of our representation of ramping events this approach improves the system reliability and lowers the real-time cost., Comment: Accepted for the 2018 IEEE Power System Computation Conference

We propose a new algorithm for finite sum optimization which we call the curvature-aided incremental aggregated gradient (CIAG) method. Motivated by the problem of training a classifier for a d-dimensional problem, where the number of training data is $m$ and $m \gg d \gg 1$, the CIAG method seeks to accelerate incremental aggregated gradient (IAG) methods using aids from the curvature (or Hessian) information, while avoiding the evaluation of matrix inverses required by the incremental Newton (IN) method. Specifically, our idea is to exploit the incrementally aggregated Hessian matrix to trace the full gradient vector at every incremental step, therefore achieving an improved linear convergence rate over the state-of-the-art IAG methods. For strongly convex problems, the fast linear convergence rate requires the objective function to be close to quadratic, or the initial point to be close to optimal solution. Importantly, we show that running one iteration of the CIAG method yields the same improvement to the optimality gap as running one iteration of the full gradient method, while the complexity is $O(d^2)$ for CIAG and $O(md)$ for the full gradient. Overall, the CIAG method strikes a balance between the high computation complexity incremental Newton-type methods and the slow IAG method. Our numerical results support the theoretical findings and show that the CIAG method often converges with much fewer iterations than IAG, and requires much shorter running time than IN when the problem dimension is high., Comment: Final version submitted to Allerton Conference 2017 on Oct 8, 2017

As the distribution grid moves toward a tightly-monitored network, it is important to automate the analysis of the enormous amount of data produced by the sensors to increase the operators situational awareness about the system. In this paper, focusing on Micro-Phasor Measurement Unit ($\mu$PMU) data, we propose a hierarchical architecture for monitoring the grid and establish a set of analytics and sensor fusion primitives for the detection of abnormal behavior in the control perimeter. Due to the key role of the $\mu$PMU devices in our architecture, a source-constrained optimal $\mu$PMU placement is also described that finds the best location of the devices with respect to our rules. The effectiveness of the proposed methods are tested through the synthetic and real $\mu$PMU data., Comment: This article is submitted to IEEE Transaction on Power System and is currently under the review process

In this paper, a stochastic model with regime switching is developed for solar photo-voltaic (PV) power in order to provide short-term probabilistic forecasts. The proposed model for solar PV power is physics inspired and explicitly incorporates the stochasticity due to clouds using different parameters addressing the attenuation in power.Based on the statistical behavior of parameters, a simple regime-switching process between the three classes of sunny, overcast and partly cloudy is proposed. Then, probabilistic forecasts of solar PV power are obtained by identifying the present regime using PV power measurements and assuming persistence in this regime. To illustrate the technique developed, a set of solar PV power data from a single rooftop installation in California is analyzed and the effectiveness of the model in fitting the data and in providing short-term point and probabilistic forecasts is verified. The proposed forecast method outperforms a variety of reference models that produce point and probabilistic forecasts and therefore portrays the merits of employing the proposed approach., Comment: Manuscript submitted to IEEE transactions on Sustainable Energy . Extension of conference paper : R. Ramakrishna and A. Scaglione, A Compressive Sensing Framework for the analysis of Solar Photo-Voltaic Power, in Conference Record of the Fiftieth Asilomar Conference on Signals, Systems and Computers, 2016

We consider the problem of optimally utilizing $N$ resources, each in an unknown binary state. The state of each resource can be inferred from state-dependent noisy measurements. Depending on its state, utilizing a resource results in either a reward or a penalty per unit time. The objective is a sequential strategy governing the decision of sensing and exploitation at each time to maximize the expected utility (i.e., total reward minus total penalty and sensing cost) over a finite horizon $L$. We formulate the problem as a Partially Observable Markov Decision Process (POMDP) and show that the optimal strategy is based on two time-varying thresholds for each resource and an optimal selection rule for which resource to sense. Since a full characterization of the optimal strategy is generally intractable, we develop a low-complexity policy that is shown by simulations to offer near optimal performance. This problem finds applications in opportunistic spectrum access, marketing strategies and other sequential resource allocation problems.

This work provides new insights on the convergence of a locally connected network of pulse coupled oscillator (PCOs) (i.e., a bio-inspired model for communication networks) to synchronous and desynchronous states, and their implication in terms of the decentralized synchronization and scheduling in communication networks. Bio-inspired techniques have been advocated by many as fault-tolerant and scalable alternatives to produce self-organization in communication networks. The PCO dynamics in particular have been the source of inspiration for many network synchronization and scheduling protocols. However, their convergence properties, especially in locally connected networks, have not been fully understood, prohibiting the migration into mainstream standards. This work provides further results on the convergence of PCOs in locally connected networks and the achievable convergence accuracy under propagation delays. For synchronization, almost sure convergence is proved for $3$ nodes and accuracy results are obtained for general locally connected networks whereas, for scheduling (or desynchronization), results are derived for locally connected networks with mild conditions on the overlapping set of maximal cliques. These issues have not been fully addressed before in the literature.

Enabling low power wireless devices to adopt Nyquist sampling at high carriers is prohibitive. In spectrum sensing, this limit calls for an analog front-end that can sweep different bands quickly, in order to use the available spectrum opportunistically. In this paper we propose a new framework that allows to optimize a sub-Nyquist sampling front-end to combine the benefits of optimum sequential sensing with those of Compressive Spectrum Sensing (CSS). The sensing strategy we propose is formulated as a sequential utility optimization problem. The utility function decreases linearly with the number of measurements (accrued to make a decision) and increases as a function of the signal components binary states. The optimization selects the best linear combinations of sub-bands to mix, in order to accrue maximum utility. The structure of the utility represents the trade-off between exploration, exploitation and risk of making an error, that is characteristic of the spectrum sensing problem. We first present the analog front-end architecture, and then map the measurement model into the abstract optimization problem proposed, and analyzed, in the remainder of the paper. We characterize the optimal policy under constraints on the sensing matrix and derive the approximation factor of the greedy approach. Numerical simulations showcase the benefits of combining opportunistic spectrum sensing with sub-Nyquist sampling., Comment: submitted to IEEE Transactions on Cognitive Communications and Networking

Opinion dynamics have fascinated researchers for centuries. The ability of societies to learn as well as the emergence of irrational {\it herding} are equally evident. The simplest example is that of agents that have to determine a binary action, under peer pressure coming from the decisions observed. By modifying several popular models for opinion dynamics so that agents internalize actions rather than smooth estimates of what other people think, we are able to prove that almost surely the actions final outcome remains random, even though actions can be consensual or polarized depending on the model. This is a theoretical confirmation that the mechanism that leads to the emergence of irrational herding behavior lies in the loss of nuanced information regarding the privately held beliefs behind the individuals decisions., Comment: 23 pages; 7 figures