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This paper is concerned with the complex task of identifying the type and cause of the events that are captured by distribution-level phasor measurement units (D-PMUs) in order to enhance situational awareness in power distribution systems. Our goal is to address two fundamental challenges in this field: a) scarcity in measurement locations due to the high cost of purchasing, installing, and streaming data from D-PMUs; b) limited prior knowledge about the event signatures due to the fact that the events are diverse, infrequent, and inherently unscheduled. To tackle these challenges, we propose an unsupervised graph-representation learning method, called GraphPMU, to significantly improve the performance in event clustering under locationally-scarce data availability by proposing the following two new directions: 1) using the topological information about the relative location of the few available phasor measurement units on the graph of the power distribution network; 2) utilizing not only the commonly used fundamental phasor measurements, bus also the less explored harmonic phasor measurements in the process of analyzing the signatures of various events. Through a detailed analysis of several case studies, we show that GraphPMU can highly outperform the prevalent methods in the literature., Comment: 10 pages, 8 figures, Submitted to IEEE Trans. on Smart Grid

Community resilience in the face of natural hazards relies on a community's potential to bounce back. A failure to integrate equity into resilience considerations results in unequal recovery and disproportionate impacts on vulnerable populations, which has long been a concern in the United States. This research investigated aspects of equity related to community resilience in the aftermath of Winter Storm Uri in Texas which led to extended power outages for more than 4 million households. County level outage and recovery data was analyzed to explore potential significant links between various county attributes and their share of the outages during the recovery and restoration phases. Next, satellite imagery was used to examine data at a much higher geographical resolution focusing on census tracts in the city of Houston. The goal was to use computer vision to extract the extent of outages within census tracts and investigate their linkages to census tracts attributes. Results from various statistical procedures revealed statistically significant negative associations between counties' percentage of non-Hispanic whites and median household income with the ratio of outages. Additionally, at census tract level, variables including percentages of linguistically isolated population and public transport users exhibited positive associations with the group of census tracts that were affected by the outage as detected by computer vision analysis. Informed by these results, engineering solutions such as the applicability of grid modernization technologies, together with distributed and renewable energy resources, when controlled for the region's topographical characteristics, are proposed to enhance equitable power grid resiliency in the face of natural hazards.

Convergence bidding, a.k.a., virtual bidding, has been widely adopted in wholesale electricity markets in recent years. It provides opportunities for market participants to arbitrage on the difference between the day-ahead market locational marginal prices and the real-time market locational marginal prices. Given the fact that convergence bids (CBs) have a significant impact on the operation of electricity markets, it is important to understand how market participants strategically select their CBs in real-world. We address this open problem with focus on the electricity market that is operated by the California ISO. In this regard, we use the publicly available electricity market data to learn, characterize, and evaluate different types of convergence bidding strategies that are currently used by market participants. Our analysis includes developing a data-driven reverse engineering method that we apply to three years of real-world data. Our analysis involves feature selection and density-based data clustering. It results in identifying three main clusters of CB strategies in the California ISO market. Different characteristics and the performance of each cluster of strategies are analyzed. Interestingly, we unmask a common real-world strategy that does not match any of the existing strategic convergence bidding methods in the literature. Next, we build upon the lessons learned from the existing real-world strategies to propose a new CB strategy that can significantly outperform them. Our analysis includes developing a new strategy for convergence bidding. The new strategy has three steps: net profit maximization by capturing price spikes, dynamic node labeling, and strategy selection algorithm. We show through case studies that the annual net profit for the most lucrative market participants can increase by over 40% if the proposed convergence bidding strategy is used., Comment: IEEE Transactions on Power Systems

Convergence bidding has been adopted in recent years by most Independent System Operators (ISOs) in the United States as a relatively new market mechanism to enhance market efficiency. Convergence bidding affects many aspects of the operation of the electricity markets and there is currently a gap in the literature on understanding how the market participants strategically select their convergence bids in practice. To address this open problem, in this paper, we study three years of real-world market data from the California ISO energy market. First, we provide a data-driven overview of all submitted convergence bids (CBs) and analyze the performance of each individual convergence bidder based on the number of their submitted CBs, the number of locations that they placed the CBs, the percentage of submitted supply or demand CBs, the amount of cleared CBs, and their gained profit or loss. Next, we scrutinize the bidding strategies of the 13 largest market players that account for 75\% of all CBs in the California ISO market. We identify quantitative features to characterize and distinguish their different convergence bidding strategies. This analysis results in revealing three different classes of CB strategies that are used in practice. We identify the differences between these strategic bidding classes and compare their advantages and disadvantages. We also explain how some of the most active market participants are using bidding strategies that do not match any of the strategic bidding methods that currently exist in the literature.

Solar distribution feeders are commonly used in solar farms that are integrated into distribution substations. In this paper, we focus on a real-world solar distribution feeder and conduct an event-based analysis by using micro-PMU measurements. The solar distribution feeder of interest is a behind-the-meter solar farm with a generation capacity of over 4 MW that has about 200 low-voltage distributed photovoltaic (PV) inverters. The event-based analysis in this study seeks to address the following practical matters. First, we conduct event detection by using an unsupervised machine learning approach. For each event, we determine the event's source region by an impedance-based analysis, coupled with a descriptive analytic method. We segregate the events that are caused by the solar farm, i.e., locally-induced events, versus the events that are initiated in the grid, i.e., grid-induced events, which caused a response by the solar farm. Second, for the locally-induced events, we examine the impact of solar production level and other significant parameters to make statistical conclusions. Third, for the grid-induced events, we characterize the response of the solar farm; and make comparisons with the response of an auxiliary neighboring feeder to the same events. Fourth, we scrutinize multiple specific events; such as by revealing the dynamics to the control system of the solar distribution feeder. The results and discoveries in this study are informative to utilities and solar power industry., Comment: 5 pages, 6 figures, IEEE ISGT2021

Distribution-level phasor measurement units, a.k.a, micro-PMUs, report a large volume of high resolution phasor measurements which constitute a variety of event signatures of different phenomena that occur all across power distribution feeders. In order to implement an event-based analysis that has useful applications for the utility operator, one needs to extract these events from a large volume of micro-PMU data. However, due to the infrequent, unscheduled, and unknown nature of the events, it is often a challenge to even figure out what kind of events are out there to capture and scrutinize. In this paper, we seek to address this open problem by developing an unsupervised approach, which requires minimal prior human knowledge. First, we develop an unsupervised event detection method based on the concept of Generative Adversarial Networks (GAN). It works by training deep neural networks that learn the characteristics of the normal trends in micro-PMU measurements; and accordingly detect an event when there is any abnormality. We also propose a two-step unsupervised clustering method, based on a novel linear mixed integer programming formulation. It helps us categorize events based on their origin in the first step and their similarity in the second step. The active nature of the proposed clustering method makes it capable of identifying new clusters of events on an ongoing basis. The proposed unsupervised event detection and clustering methods are applied to real-world micro-PMU data. Results show that they can outperform the prevalent methods in the literature. These methods also facilitate our further analysis to identify important clusters of events that lead to unmasking several use cases that could be of value to the utility operator., Comment: 8 pages, 12 figures, R1 IEEE Trans. on SmartGrid

Topology identification (TI) in distribution networks is a challenging task due to the limited measurement resources and therefore the inevitable need to use pseudo-measurements that are often inaccurate. To address this issue, a new method is proposed in this paper to integrate harmonic synchrophasors into the TI problem in order to enhance TI accuracy in distribution networks. In this method, topology identification is done jointly based on both fundamental synchrophasor measurements and harmonic synchrophasor measurements. This is done by formulating and then solving a mixed-integer linear programming (MILP) problem. Furthermore, an analysis is provided to capture the number of and the location of harmonic sources and sensors that are needed to ensure full observability. The benefits of the proposed TI scheme are compared against those of the traditional scheme that utilizes only the fundamental measurements. Finally, through numerical simulations on the IEEE 33-Bus power system, it is shown that the proposed scheme is considerably accurate compared to the traditional scheme in topology identification.

A new data-driven method is proposed to detect events in the data streams from distribution-level phasor measurement units, a.k.a., micro-PMUs. The proposed method is developed by constructing unsupervised deep learning anomaly detection models; thus, providing event detection algorithms that require no or minimal human knowledge. First, we develop the core components of our approach based on a Generative Adversarial Network (GAN) model. We refer to this method as the basic method. It uses the same features that are often used in the literature to detect events in micro-PMU data. Next, we propose a second method, which we refer to as the enhanced method, which is enforced with additional feature analysis. Both methods can detect point signatures on single features and also group signatures on multiple features. This capability can address the unbalanced nature of power distribution circuits. The proposed methods are evaluated using real-world micro-PMU data. We show that both methods highly outperform a state-of-the-art statistical method in terms of the event detection accuracy. The enhanced method also outperforms the basic method.

Peer-to-peer (P2P) energy trading has emerged as a next-generation energy management mechanism for the smart grid that enables each prosumer of the network to participate in energy trading with one another and the grid. This poses a significant challenge in terms of modeling the decision-making process of each participant with conflicting interest and motivating prosumers to participate in energy trading and to cooperate, if necessary, for achieving different energy management goals. Therefore, such decision-making process needs to be built on solid mathematical and signal processing tools that can ensure an efficient operation of the smart grid. This paper provides an overview of the use of game theoretic approaches for P2P energy trading as a feasible and effective means of energy management. As such, we discuss various games and auction theoretic approaches by following a systematic classification to provide information on the importance of game theory for smart energy research. Then, the paper focuses on the P2P energy trading describing its key features and giving an introduction to an existing P2P testbed. Further, the paper zooms into the detail of some specific game and auction theoretic models that have recently been used in P2P energy trading and discusses some important finding of these schemes., Comment: 38 pages, single column, double space

Strategic bidding problems in electricity markets are widely studied in power systems, often by formulating complex bi-level optimization problems that are hard to solve. The state-of-the-art approach to solve such problems is to reformulate them as mixed-integer linear programs (MILPs). However, the computational time of such MILP reformulations grows dramatically, once the network size increases, scheduling horizon increases, or randomness is taken into consideration. In this paper, we take a fundamentally different approach and propose effective and customized convex programming tools to solve the strategic bidding problem for producers in nodal electricity markets. Our approach is inspired by the Schmudgen's Positivstellensatz Theorem in semi-algebraic geometry; but then we go through several steps based upon both convex optimization and mixed-integer programming that results in obtaining close to optimal bidding solutions, as evidenced by several numerical case studies, besides having a huge advantage on reducing computation time. While the computation time of the state-of-the-art MILP approach grows exponentially when we increase the scheduling horizon or the number of random scenarios, the computation time of our approach increases rather linearly.

Participating in demand response programs is a promising tool for reducing energy costs in data centers by modulating energy consumption. Towards this end, data centers can employ a rich set of resource management knobs, such as workload shifting and dynamic server provisioning. Nonetheless, these knobs may not be readily available in a cloud data center (CDC) that serves cloud tenants/users, because workloads in CDCs are managed by tenants themselves who are typically charged based on a usage-based or flat-rate pricing and often have no incentive to cooperate with the CDC operator for demand response and cost saving. Towards breaking such "split incentive" hurdle, a few recent studies have tried market-based mechanisms, such as dynamic pricing, inside CDCs. However, such mechanisms often rely on complex designs that are hard to implement and difficult to cope with by tenants. To address this limitation, we propose a novel incentive mechanism that is not dynamic, i.e., it keeps pricing for cloud resources unchanged for a long period. While it charges tenants based on a Usage-based Pricing (UP) as used by today's major cloud operators, it rewards tenants proportionally based on the time length that tenants set as deadlines for completing their workloads. This new mechanism is called Usage-based Pricing with Monetary Reward (UPMR). We demonstrate the effectiveness of UPMR both analytically and empirically. We show that UPMR can reduce the CDC operator's energy cost by 12.9% while increasing its profit by 4.9%, compared to the state-of-the-art approaches used by today's CDC operators to charge their tenants.

Burstable billing is widely adopted in practice, e.g., by colocation data center providers, to charge for their users, e.g., data centers, for data transferring. However, there is still a lack of research on what the best way is for a user to manage its workload in response to burstable billing. To overcome this shortcoming, we propose a novel method to optimally respond to burstable billing under demand uncertainty. First, we develop a tractable mathematical expression to calculate the 95th percentile usage of a user, who is charged by provider via burstable billing for bandwidth usage. This model is then used to formulate a new bandwidth allocation problem to maximize the user's surplus, i.e., its net utility minus cost. Additionally, we examine different non-convex solution methods for the formulated stochastic optimization problem. We also extend our design to the case where a user can receive service from multiple providers, who all employ burstable billing. Using real-world workload traces, we show that our proposed method can reduce user's bandwidth cost by 26% and increase its total surplus by 23%, compared to the current practice of allocating bandwidth on-demand.

In order to reduce the energy cost of data centers, recent studies suggest distributing computation workload among multiple geographically dispersed data centers, by exploiting the electricity price difference. However, the impact of data center load redistribution on the power grid is not well understood yet. This paper takes the first step towards tackling this important issue, by studying how the power grid can take advantage of the data centers' load distribution proactively for the purpose of power load balancing. We model the interactions between power grid and data centers as a two-stage problem, where the utility company chooses proper pricing mechanisms to balance the electric power load in the first stage, and the data centers seek to minimize their total energy cost by responding to the prices in the second stage. We show that the two-stage problem is a bilevel quadratic program, which is NP-hard and cannot be solved using standard convex optimization techniques. We introduce benchmark problems to derive upper and lower bounds for the solution of the two-stage problem. We further propose a branch and bound algorithm to attain the globally optimal solution, and propose a heuristic algorithm with low computational complexity to obtain an alternative close-to-optimal solution. We also study the impact of background load prediction error using the theoretical framework of robust optimization. The simulation results demonstrate that our proposed scheme can not only improve the power grid reliability but also reduce the energy cost of data centers.