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Recent advancements in research have shown the efficacy of employing sensor measurements, such as voltage and power data, in identifying line outages within distribution grids. However, these measurements inadvertently pose privacy risks to electricity customers by potentially revealing their sensitive information, such as household occupancy and economic status, to adversaries. To safeguard raw data from direct exposure to third-party adversaries, this paper proposes a novel decentralized data encryption scheme. The effectiveness of this encryption strategy is validated via demonstration of its differential privacy attributes by studying the Gaussian differential privacy. Recognizing that the encryption of raw data could affect the efficacy of outage detection, this paper analyzes the performance degradation by examining the Kullback-Leibler divergence between data distributions before and after the line outage. This analysis allows us to further alleviate the performance degradation by designing an innovative detection statistic that accurately approximates the optimal one. Manipulating the variance of this statistic, we demonstrate its ability to approach the optimal detection performance. The proposed privacy-aware detection procedure is evaluated using representative distribution grids and real load profiles, covering 17 distinct outage configurations. Our empirical results confirm the privacy-preserving nature of our approach and show that it achieves comparable detection performance to the optimal baseline., Comment: 12 pages

Line outage identification in distribution grids is essential for sustainable grid operation. In this work, we propose a practical yet robust detection approach that utilizes only readily available voltage magnitudes, eliminating the need for costly phase angles or power flow data. Given the sensor data, many existing detection methods based on change-point detection require prior knowledge of outage patterns, which are unknown for real-world outage scenarios. To remove this impractical requirement, we propose a data-driven method to learn the parameters of the post-outage distribution through gradient descent. However, directly using gradient descent presents feasibility issues. To address this, we modify our approach by adding a Bregman divergence constraint to control the trajectory of the parameter updates, which eliminates the feasibility problems. As timely operation is the key nowadays, we prove that the optimal parameters can be learned with convergence guarantees via leveraging the statistical and physical properties of voltage data. We evaluate our approach using many representative distribution grids and real load profiles with 17 outage configurations. The results show that we can detect and localize the outage in a timely manner with only voltage magnitudes and without assuming a prior knowledge of outage patterns., Comment: 12 pages

We articulate the design imperatives for machine-learning based digital twins for nonlinear dynamical systems subject to external driving, which can be used to monitor the ``health'' of the target system and anticipate its future collapse. We demonstrate that, with single or parallel reservoir computing configurations, the digital twins are capable of challenging forecasting and monitoring tasks. Employing prototypical systems from climate, optics and ecology, we show that the digital twins can extrapolate the dynamics of the target system to certain parameter regimes never experienced before, make continual forecasting/monitoring with sparse real-time updates under non-stationary external driving, infer hidden variables and accurately predict their dynamical evolution, adapt to different forms of external driving, and extrapolate the global bifurcation behaviors to systems of some different sizes. These features make our digital twins appealing in significant applications such as monitoring the health of critical systems and forecasting their potential collapse induced by environmental changes., Comment: 21 pages, 14 figures

Learning the underlying equation from data is a fundamental problem in many disciplines. Recent advances rely on Neural Networks (NNs) but do not provide theoretical guarantees in obtaining the exact equations owing to the non-convexity of NNs. In this paper, we propose Convex Neural Symbolic Learning (CoNSoLe) to seek convexity under mild conditions. The main idea is to decompose the recovering process into two steps and convexify each step. In the first step of searching for right symbols, we convexify the deep Q-learning. The key is to maintain double convexity for both the negative Q-function and the negative reward function in each iteration, leading to provable convexity of the negative optimal Q function to learn the true symbol connections. Conditioned on the exact searching result, we construct a Locally Convex equation Learner (LoCaL) neural network to convexify the estimation of symbol coefficients. With such a design, we quantify a large region with strict convexity in the loss surface of LoCaL for commonly used physical functions. Finally, we demonstrate the superior performance of the CoNSoLe framework over the state-of-the-art on a diverse set of datasets., Comment: 18 pages, 5 figures, conference for NeurIPS 2022

Distributed energy resources are better for the environment but may cause transformer overload in distribution grids, calling for recovering meter-transformer mapping to provide situational awareness, i.e., the transformer loading. The challenge lies in recovering meter-transformer (M.T.) mapping for two common scenarios, e.g., large distances between a meter and its parent transformer or high similarity of a meter's consumption pattern to a non-parent transformer's meters. Past methods either assume a variety of data as in the transmission grid or ignore the two common scenarios mentioned above. Therefore, we propose to utilize the above observation via spectral embedding by using the property that inter-transformer meter consumptions are not the same and that the noise in data is limited so that all the k smallest eigenvalues of the voltage-based Laplacian matrix are smaller than the next smallest eigenvalue of the ideal Laplacian matrix. We also provide a guarantee based on this understanding. Furthermore, we partially relax the assumption by utilizing location information to aid voltage information for areas geographically far away but with similar voltages. Numerical simulations on the IEEE test systems and real feeders from our partner utility show that the proposed method correctly identifies M.T. mapping.

This paper addresses the problem of real-time monitoring of long-term voltage instability (LTVI) by using local field measurements. Existing local measurement-based methods use Thevenin equivalent parameter estimation that is sensitive to the noise in measurements. For solving this issue, we avoid the Thevenin approach by projecting the power flow equations as circles to develop local static-voltage stability indicator (LS-VSI) that is robust to measurement noises. The proposed method is an attractive option for practical implementation because of its decentralized nature, robustness to noise, and realistic modeling. Next, we utilize LS-VSI to propose a new local dynamic - VSI (LD-VSI) to identify the LTVI triggered by large disturbances and load tap changer dynamics. LD-VSI can identify not only the onset of instability with an alarm but also the voltage collapse point (VCP). Extensive numerical validation comparing LS-VSI with existing methods is presented on IEEE 30-bus and larger test systems like 2000-bus Texas synthetic grid to validate the robustness, accuracy, and situational awareness feature. We also verify the LD-VSI behavior on the Nordic power grid using PSSE dynamic simulation. When compared to existing methods, we observe that LD-VSI is not only more robust to measurement noise but also can identify VCP.

This paper describes how domain knowledge of power system operators can be integrated into reinforcement learning (RL) frameworks to effectively learn agents that control the grid's topology to prevent thermal cascading. Typical RL-based topology controllers fail to perform well due to the large search/optimization space. Here, we propose an actor-critic-based agent to address the problem's combinatorial nature and train the agent using the RL environment developed by RTE, the French TSO. To address the challenge of the large optimization space, a curriculum-based approach with reward tuning is incorporated into the training procedure by modifying the environment using network physics for enhanced agent learning. Further, a parallel training approach on multiple scenarios is employed to avoid biasing the agent to a few scenarios and make it robust to the natural variability in grid operations. Without these modifications to the training procedure, the RL agent failed for most test scenarios, illustrating the importance of properly integrating domain knowledge of physical systems for real-world RL learning. The agent was tested by RTE for the 2019 learning to run the power network challenge and was awarded the 2nd place in accuracy and 1st place in speed. The developed code is open-sourced for public use.

Artificial Intelligence (AI) techniques continue to broaden across governmental and public sectors, such as power and energy - which serve as critical infrastructures for most societal operations. However, due to the requirements of reliability, accountability, and explainability, it is risky to directly apply AI-based methods to power systems because society cannot afford cascading failures and large-scale blackouts, which easily cost billions of dollars. To meet society requirements, this paper proposes a methodology to develop, deploy, and evaluate AI systems in the energy sector by: (1) understanding the power system measurements with physics, (2) designing AI algorithms to forecast the need, (3) developing robust and accountable AI methods, and (4) creating reliable measures to evaluate the performance of the AI model. The goal is to provide a high level of confidence to energy utility users. For illustration purposes, the paper uses power system event forecasting (PEF) as an example, which carefully analyzes synchrophasor patterns measured by the Phasor Measurement Units (PMUs). Such a physical understanding leads to a data-driven framework that reduces the dimensionality with physics and forecasts the event with high credibility. Specifically, for dimensionality reduction, machine learning arranges physical information from different dimensions, resulting inefficient information extraction. For event forecasting, the supervised learning model fuses the results of different models to increase the confidence. Finally, comprehensive experiments demonstrate the high accuracy, efficiency, and reliability as compared to other state-of-the-art machine learning methods., Comment: Presented at AAAI FSS-21: Artificial Intelligence in Government and Public Sector, Washington, DC, USA

The growing integration of distributed energy resources (DERs) in distribution grids raises various reliability issues due to DER's uncertain and complex behaviors. With a large-scale DER penetration in distribution grids, traditional outage detection methods, which rely on customers report and smart meters' last gasp signals, will have poor performance, because the renewable generators and storages and the mesh structure in urban distribution grids can continue supplying power after line outages. To address these challenges, we propose a data-driven outage monitoring approach based on the stochastic time series analysis with a theoretical guarantee. Specifically, we prove via power flow analysis that the dependency of time-series voltage measurements exhibits significant statistical changes after line outages. This makes the theory on optimal change-point detection suitable to identify line outages. However, existing change point detection methods require post-outage voltage distribution, which is unknown in distribution systems. Therefore, we design a maximum likelihood estimator to directly learn the distribution parameters from voltage data. We prove that the estimated parameters-based detection also achieves the optimal performance, making it extremely useful for fast distribution grid outage identifications. Furthermore, since smart meters have been widely installed in distribution grids and advanced infrastructure (e.g., PMU) has not widely been available, our approach only requires voltage magnitude for quick outage identification. Simulation results show highly accurate outage identification in eight distribution grids with 14 configurations with and without DERs using smart meter data., Comment: 12 pages, 12 figures. arXiv admin note: substantial text overlap with arXiv:1811.05646

Ensuring the stability of power systems is gaining more attraction today than ever before, due to the rapid growth of uncertainties in load and renewable energy penetration. Lately, wide area measurement system-based centralized controlling techniques started providing a more flexible and robust control to keep the system stable. But, such a modernization of control philosophy faces pressing challenges due to the irregularities in delays of long-distance communication channels and response of equipment to control actions. Therefore, we propose an innovative approach that can revolutionize the control strategy for damping down low frequency oscillations in transmission systems. Proposed method is enriched with a potential of overcoming the challenges of communication delays and other non-linearities in wide area damping control by leveraging the capability of the reinforcement learning technique. Such a technique has a unique characteristic to learn on diverse scenarios and operating conditions by exploring the environment and devising an optimal control action policy by implementing policy gradient method. Our detailed analysis and systematically designed numerical validation prove the feasibility, scalability and interpretability of the carefully modelled low-frequency oscillation damping controller so that stability is ensured even with the uncertainties of load and generation are on the rise.

Power systems face increasing challenges on reliable operations due to the widespread distributed generators (DGs), e.g., rooftop PV system in the low voltage (LV) distribution grids. Characterizing the hosting capacity (HC) is vital for assessing the total amount of distributed generations that a grid can hold before upgrading. For analyzing HC, some methods conduct extensive simulations, lacking theoretical guarantees and can time-consuming. Therefore, there are also methods employing optimization over all necessary operation constraints. But, the complexity and inherent non-convexity lead to non-optimal solutions. To solve these problems, this paper provides a constructive model for HC determination. Based on geometrically obtained globally optimal HC, we construct HC solutions sequentially according to realistic constraints, so that we can obtain optimal solution even with non-convex model. For practical adaption, we also consider three-phase unbalance condition and parallel computation to speed-up. We validated our method by extensive numerical results on IEEE standard systems, such as 8-bus and 123-bus radial distribution grids, where the global optimums are obtained and performance illustrations are demonstrated.

Load forecasting has long been recognized as an important building block for all utility operational planning efforts. Over the recent years, it has become ever more challenging to make accurate forecasts due to the proliferation of distributed energy resources, despite the abundance of existing load forecasting methods. In this paper, we identify one drawback suffered by most load forecasting methods: neglect to thoroughly address the impact of input errors on load forecasts. As a potential solution, we propose to incorporate input modeling and uncertainty quantification to improve load forecasting performance via a two-stage approach. The proposed two-stage approach has the following merits. (1) It provides input modeling and quantifies the impact of input errors, rather than neglecting or mitigating the impact, a prevalent practice of existing methods. (2) It propagates the impact of input errors into the ultimate point and interval predictions for the target customer's load to improve predictive performance. (3) A variance-based global sensitivity analysis method is further proposed for input-space dimensionality reduction in both stages to enhance the computational efficiency. Numerical experiments show that the proposed two-stage approach outperforms competing load forecasting methods in terms of both point predictive accuracy and coverage ability of the predictive intervals., Comment: 9 pages, 4 figures, journal

With more distributed energy resources (DERs) connected to distribution grids, better monitoring and control are needed, where identifying the topology accurately is the prerequisite. However, due to frequent re-configurations, operators usually cannot know a complete structure in distribution grids. Luckily, the growing data from smart sensors, restricted by Ohm law, provides the possibility of topology inference. In this paper, we show how line parameters of Ohm equation can be estimated for topology identification even when there are hidden nodes. Specifically, the introduced learning method recursively conducts hidden-node detection and impedance calculation. However, the assumptions on uncorrelated data, availability of phasor measurements, and a balanced system, are not met in practices, causing large errors. To resolve these problems, we employ Cholesky whitening first with a proof for measurement decorrelations. For increasing robustness further, we show how to handle practical scenarios when only measurement magnitudes are available or when the grid is three-phase unbalanced. Numerical performance is verified on multi-size distribution grids with both simulation and real-world data., Comment: 11 pages, 15 figures, journal

The Phasor measurement unit (PMU) measurements are mandatory to monitor the power system's voltage stability margin in an online manner. Monitoring is key to the secure operation of the grid. Traditionally, online monitoring of voltage stability using synchrophasors required a centralized communication architecture, which leads to high investment cost and cyber-security concerns. The increasing importance of cyber-security and low investment cost have recently led to the development of distributed algorithms for online monitoring of the grid that are inherently less prone to malicious attacks. In this work, a novel distributed non-iterative voltage stability index (VSI) is proposed by recasting the power flow equations as circles. The online computations of VSI are simultaneously performed by the processors embedded at each bus in the smart grid with the help of PMUs and communication of voltage phasors between neighboring buses. The distributed nature of the index enables the real-time identification of the critical bus of the system with minimal communication infrastructure. The effectiveness of the proposed distributed index is demonstrated on IEEE test systems and contrasted with existing methods to show the benefits of the proposed method in speed, interpretability, identification of outage location, and low sensitivity to noisy measurements.

Grid topology and line parameters are essential for grid operation and planning, which may be missing or inaccurate in distribution grids. Existing data-driven approaches for recovering such information usually suffer from ignoring 1) input measurement errors and 2) possible state changes among historical measurements. While using the errors-in-variables (EIV) model and letting the parameter and topology estimation interact with each other (PaToPa) can address input and output measurement error modeling, it only works when all measurements are from a single system state. To solve the two challenges simultaneously, we propose the PaToPaEM framework for joint line parameter and topology estimation with historical measurements from different unknown states. We improve the static framework that only works when measurements are from one single state, by further treating state changes in historical measurements as an unobserved latent variable. We then systematically analyze the new mathematical modeling, decouple the optimization problem, and incorporate the expectation-maximization (EM) algorithm to recover different hidden states in measurements. Combining these, PaToPaEM framework enables joint topology and line parameter estimation using noisy measurements from multiple system states. It lays a solid foundation for data-driven system identification in distribution grids. Superior numerical results validate the practicability of the PaToPaEM framework.

The growing integration of distributed energy resources (DERs) in urban distribution grids raises various reliability issues due to DER's uncertain and complex behaviors. With a large-scale DER penetration, traditional outage detection methods, which rely on customers making phone calls and smart meters' "last gasp" signals, will have limited performance, because the renewable generators can supply powers after line outages and many urban grids are mesh so line outages do not affect power supply. To address these drawbacks, we propose a data-driven outage monitoring approach based on the stochastic time series analysis from micro phasor measurement unit ($\mu$PMU). Specifically, we prove via power flow analysis that the dependency of time-series voltage measurements exhibits significant statistical changes after line outages. This makes the theory on optimal change-point detection suitable to identify line outages via $\mu$PMUs with fast and accurate sampling. However, existing change point detection methods require post-outage voltage distribution unknown in distribution systems. Therefore, we design a maximum likelihood-based method to directly learn the distribution parameters from $\mu$PMU data. We prove that the estimated parameters-based detection still achieves the optimal performance, making it extremely useful for distribution grid outage identifications. Simulation results show highly accurate outage identification in eight distribution grids with 14 configurations with and without DERs using $\mu$PMU data., Comment: 9 pages

The power flow (PF) problem is a fundamental problem in power system engineering. Many popular solvers face challenges, such as convergence issues. One can try to rewrite the PF problem into a fixed point equation, which can be solved exponentially fast. But, existing methods have their own restrictions, such as the required AC network structure or bus types. To remove these restrictions, we employ the circle geometry per-bus via rectangular coordinate representation to embed our physical knowledge of operation point selection in PV curves. Each iteration of the algorithm consists of finding intersections of circles, which can be computed efficiently with high numerical accuracy. Such analysis also helps in visualizing PV curve to always select the high voltage solution. We compare the performance of our fixed point algorithm with existing state-of-the-art methods, showing that the proposed method can correctly find the solutions when other methods cannot. In addition, we empirically show that the fixed point algorithm is much more robust to bad initialization points than the existing methods., Comment: Submitted to IEEE Transactions on Control of Network Systems

There is an increasing need for monitoring and controlling uncertainties brought by distributed energy resources in distribution grids. For such goal, accurate multi-phase topology is the basis for correlating measurements in unbalanced distribution networks. Unfortunately, such topology knowledge is often unavailable due to limited investment, especially for \revv{low-voltage} distribution grids. Also, the bus phase labeling information is inaccurate due to human errors or outdated records. For this challenge, this paper utilizes smart meter data for an information-theoretic approach to learn the topology of distribution grids. Specifically, multi-phase unbalanced systems are converted into symmetrical components, namely positive, negative, and zero sequences. Then, this paper proves that the Chow-Liu algorithm finds the topology by utilizing power flow equations and the conditional independence relationships implied by the radial multi-phase structure of distribution grids with the presence of incorrect bus phase labels. At last, by utilizing Carson's equation, this paper proves that the bus phase connection can be correctly identified using voltage measurements. For validation, IEEE systems are simulated using three real data sets. The simulation results demonstrate that the algorithm is highly accurate for finding multi-phase topology even with strong load unbalancing condition and DERs. This ensures close monitoring and controlling DERs in distribution grids., Comment: 17 pages, 18 figures

For accommodating more electric vehicles (EVs) to battle against fossil fuel emission, the problem of charging station placement is inevitable and could be costly if done improperly. Some researches consider a general setup, using conditions such as driving ranges for planning. However, most of the EV growths in the next decades will happen in the urban area, where driving ranges is not the biggest concern. For such a need, we consider several practical aspects of urban systems, such as voltage regulation cost and protection device upgrade resulting from the large integration of EVs. Notably, our diversified objective can reveal the trade-off between different factors in different cities worldwide. To understand the global optimum of large-scale analysis, we add constraint one-by-one to see how to preserve the problem convexity. Our sensitivity analysis before and after convexification shows that our approach is not only universally applicable but also has a small approximation error for prioritizing the most urgent constraint in a specific setup. Finally, numerical results demonstrate the trade-off, the relationship between different factors and the global objective, and the small approximation error. A unique observation in this study shows the importance of incorporating the protection device upgrade in urban system planning on charging stations.

High impedance fault (HIF) has been a challenging task to detect in distribution networks. On one hand, although several types of HIF models are available for HIF study, they are still not exhibiting satisfactory fault waveforms. On the other hand, utilizing historical data has been a trend recently for using machine learning methods to improve HIF detection. Nonetheless, most proposed methodologies address the HIF issue starting with investigating a limited group of features and can hardly provide a practical and implementable solution. This paper, however, proposes a systematic design of feature extraction, based on an HIF detection and classification method. For example, features are extracted according to when, how long, and what magnitude the fault events create. Complementary power expert information is also integrated into the feature pools. Subsequently, we propose a ranking procedure in the feature pool for balancing the information gain and the complexity to avoid over-fitting. For implementing the framework, we create an HIF detection logic from a practical perspective. Numerical methods show the proposed HIF detector has very high dependability and security performance under multiple fault scenarios comparing with other traditional methods.