A method for recovering missing phase measurement unit (PMU) measurements from a plurality of PMUs is provided. The method comprises: receiving a plurality of obtained PMU measurements from the plurality of PMUs; populating a PMU dataset based on the plurality of obtained PMU measurements; determining a plurality of missing entries within the PMU dataset, wherein each of the plurality of missing entries indicates a missing PMU measurement within the PMU dataset at a particular time; determining a plurality of substitute entries for the plurality of missing entries based on an optimization algorithm that determines differences associated with a missing entry, of the plurality of missing entries, and a first set of PMU measurements, of the plurality of obtained PMU measurements, that are taken immediately prior to the missing entry; and inserting the plurality of substitute entries into the PMU dataset to generate a new PMU dataset.

A method for recovering missing phase measurement unit (PMU) measurements from a plurality of PMUs is provided. The method comprises: receiving a plurality of obtained PMU measurements from the plurality of PMUs; populating a PMU dataset based on the plurality of obtained PMU measurements; determining a plurality of missing entries within the PMU dataset, wherein each of the plurality of missing entries indicates a missing PMU measurement within the PMU dataset at a particular time; determining a plurality of substitute entries for the plurality of missing entries based on an optimization algorithm that determines differences associated with a missing entry, of the plurality of missing entries, and a first set of PMU measurements, of the plurality of obtained PMU measurements, that are taken immediately prior to the missing entry; and inserting the plurality of substitute entries into the PMU dataset to generate a new PMU dataset.

An example welding-type power supply includes: power conversion circuitry configured to convert three-phase input power to welding-type power; a reference node coupled to each winding of the three-phase input power via a corresponding impedance; and a phase detection circuit coupled to the reference node and configured to determine a number of phases connected to the input based on comparing a frequency of a signal at the reference node to a threshold frequency.

An example welding-type power supply includes: power conversion circuitry configured to convert three-phase input power to welding-type power; a reference node coupled to each winding of the three-phase input power via a corresponding impedance; and a phase detection circuit coupled to the reference node and configured to determine a number of phases connected to the input based on comparing a frequency of a signal at the reference node to a threshold frequency.

DeepOPF-V, a deep neural network (DNN)-based voltage-constrained approach for solving an alternating-current optimal power flow (AC-OPF) problem, is used to determine an operating point of an AC electrical power system. DeepOPE-V advantageously uses two DNNs to separately determine voltage magnitudes and voltage phase angles of buses in the system without cross-over operations between the two DNNs. A computation complexity is reduced when compared to using a single DNN for generating both the magnitudes and phase angles, allowing high computation efficiency achieved by DeepOPE-V. Remaining variables of the system are computed based on the determined magnitudes and phase angles. A solution for the operating condition is predicted. A fast post-processing (PP) method is developed to improve the feasibility of the predicted solution. The PP method uses linear adjustment to adjust the predicted solution to improve the solution feasibility while enabling fast execution of the PP method.

DeepOPF-V, a deep neural network (DNN)-based voltage-constrained approach for solving an alternating-current optimal power flow (AC-OPF) problem, is used to determine an operating point of an AC electrical power system. DeepOPE-V advantageously uses two DNNs to separately determine voltage magnitudes and voltage phase angles of buses in the system without cross-over operations between the two DNNs. A computation complexity is reduced when compared to using a single DNN for generating both the magnitudes and phase angles, allowing high computation efficiency achieved by DeepOPE-V. Remaining variables of the system are computed based on the determined magnitudes and phase angles. A solution for the operating condition is predicted. A fast post-processing (PP) method is developed to improve the feasibility of the predicted solution. The PP method uses linear adjustment to adjust the predicted solution to improve the solution feasibility while enabling fast execution of the PP method.

A switching device for controlling power flow on a power line. The device includes a current sensor for measuring primary current on the line, a first voltage sensor for measuring primary voltage on the line at one side of the switching device, and a second voltage sensor for measuring primary voltage on the line at another side of the switching device. An ADC converts measurement signals from the current sensor and the voltage sensors to digital signals, and a PMU calculates magnitude and phase angle synchrophasor data using the current and voltage measurement digital signals and calibration data.

A switching device for controlling power flow on a power line. The device includes a current sensor for measuring primary current on the line, a first voltage sensor for measuring primary voltage on the line at one side of the switching device, and a second voltage sensor for measuring primary voltage on the line at another side of the switching device. An ADC converts measurement signals from the current sensor and the voltage sensors to digital signals, and a PMU calculates magnitude and phase angle synchrophasor data using the current and voltage measurement digital signals and calibration data.

Methods and systems are disclosed for determining active and/or reactive power flows in a distribution line of a distribution network. The determined power flows may be linear in nature, and they may further be used to determine an overall network power flow for the distribution network. Further, the network power flow can be used to determine a voltage magnitude for any distribution bus in the distribution network. The methods and systems are capable of considering a plurality of sensitivity factors that may affect one or more distribution buses.

Techniques and apparatus presented herein are directed toward monitoring an electric power delivery system to detect and locate a power generation event. A power generation event may include a tripped generator, a loss of a transmission line, or other loss of power generation. To detect the event, an analysis engine may receive and monitor input data. A detection signal may be generated based on the input data. Upon detecting the event, the analysis engine may determine a source and propagation of the event through the delivery system. Based on the source and propagation of the event, the analysis engine may determine the location of the event. The analysis engine may generate an overlay with the input data to provide the location and other information about the event to a user such that remedial action can be taken to resolve the event and restore the lost power generation.