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Phase retrieval is a prevalent problem in digital signal processing and experimental physics that consists of estimating a complex signal from magnitude measurements. This paper expands the classical phase retrieval framework to electric power systems with unknown network models and limited access to observations of voltage magnitudes, active power injections, and reactive power injections. The proposed method recovers the phase angles and the power-phase angle submatrices of the AC power flow Jacobian matrix. This is made possible by deriving topology and parameter-free expressions for the structural symmetries of the power flow Jacobian that do not depend on the phase angles. These physical laws provide structural constraints for the proposed phase retrieval method. The paper then presents sufficient conditions for guaranteed recovery of the voltage phase angles, which also depend solely on voltage magnitudes, active power injections, and reactive power injections. The method offers two significant benefits: both estimating the voltage phase angles and recovering the power flow Jacobian matrix, a basis for approximating the power flow equations. Simulations on widely studied open-source test networks validate the findings., Comment: The 14th ACM International Conference on Future Energy Systems (ACM e-Energy 2023)

Voltage phase angle measurements are often unavailable from sensors in distribution networks and transmission network boundaries. Therefore, this paper addresses the conditions for estimating sensitivities of voltage magnitudes with respect to complex (active and reactive) electric power injections based on sensor measurements. These sensitivities represent submatrices of the inverse power flow Jacobian. We extend previous results to show that the sensitivities of a bus voltage magnitude with respect to active power injections are unique and different from those with respect to reactive power. The classical Newton-Raphson power flow model is used to derive a novel representation of bus voltage magnitudes as an underdetermined linear operator of the active and reactive power injections; parameterized by the bus power factors. Two conditions that ensure the existence of unique complex power injections given voltage magnitudes are established for this underdetermined linear system, thereby compressing the solution space. The first is a sufficient condition based on the bus power factors. The second is a necessary and sufficient condition based on the system eigenvalues. We use matrix completion theory to develop estimation methods for recovering sensitivity matrices with varying levels of sensor availability. Simulations verify the results and demonstrate engineering use of the proposed methods., Comment: 14 pages, 10 figures. Code corresponding to this work is publicly available at https://github.com/samtalki/PowerSensitivities.jl

To improve the resilience of electric distribution systems, this paper proposes a stochastic multi-period mixed-integer linear programming model that determines where to underground distribution lines and how to coordinate mobile generators in order to serve critical loads during extreme events. The proposed model represents the service restoration process using the linearized DistFlow approximation of the AC power flow equations as well as binary variables for the undergrounding statuses of the lines, the configurations of switches, and the locations of mobile generators during each time period. The model also enforces a radial configuration of the distribution network and considers the transportation times needed to reposition the mobile generators. Using an extended version of the IEEE 123-bus test system, numerical simulations show that combining the ability to underground distribution lines with the deployment of mobile generators can significantly improve the resilience of the power supply to critical loads.

Distributed energy resources behind the meter and automation systems enable traditional electricity consumers to become prosumers (producers/consumers) that can participate in peer-to-peer exchange of electricity and in retail electricity markets. Emerging prosumers can provide benefits to the system by exchanging energy and energy-related services. More importantly, they can do so in a more honest and more competitive way than the traditional producer/consumer systems. We extend the traditional Cournot model to show that the dual nature of prosumers can lead to more competitive behavior under a game theoretic scenario. We show that best response supply quantities of a prosumer are usually closer to the competitive level compared to those of a producer., Comment: 8 pages

Collecting, analyzing and gaining insight from large volumes of data is now the norm in an ever increasing number of industries. Data analytics techniques, such as machine learning, are powerful tools used to analyze these large volumes of data. Synthetic data sets are routinely relied upon to train and develop such data analytics methods for several reasons: to generate larger data sets than are available, to generate diverse data sets, to preserve anonymity in data sets with sensitive information, etc. Processing, transmitting and storing data is a key issue faced when handling large data sets. This paper presents an "On the fly" framework for generating big synthetic data sets, suitable for these data analytics methods, that is both computationally efficient and applicable to a diverse set of problems. An example application of the proposed framework is presented along with a mathematical analysis of its computational efficiency, demonstrating its effectiveness., Comment: 13 pages, 3 figures

The area of building energy management has received a significant amount of interest in recent years. This area is concerned with combining advancements in sensor technologies, communications and advanced control algorithms to optimize energy utilization. Reinforcement learning is one of the most prominent machine learning algorithms used for control problems and has had many successful applications in the area of building energy management. This research gives a comprehensive review of the literature relating to the application of reinforcement learning to developing autonomous building energy management systems. The main direction for future research and challenges in reinforcement learning are also outlined., Comment: 17 pages, 3 figures