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All sources NASA NTRS DOE OSTI

DOE OSTI2023

Examining the Feasibility of Modeling the Inner Current Loop of a Grid-Following Inverter in the Phasor-Based Solver

Historically, when modeling a grid-following (GFL) inverter in the phasor domain, the fast inner current loop is typically ignored. To achieve a more accurate modeling, the authors have attempted to model the inner current loop in the phasor domain, but experienced significant numerical stability issues. This paper conducts a detailed analysis and provides insight into the feasibility of modeling the inner current loop of a GFL inverter in the phasor domain. It points out that: a) because of the neglection of the inverter filter dynamic, the bandwidth of the inner current loop becomes infinite with typical parameters in the phasor domain, resulting in an inaccurate representation of the actual inner current loop, whose bandwidth is typically between 600 Hz to 2 kHz, and b) the relatively large simulation time step in the phasor simulation causes numerical stability issues when simulating such an inner current loop with an infinite bandwidth. Detailed electromagnetic (EMT) and phasor modeling, and frequency response analysis are performed to explain this phenomenon. The findings of this paper explain why it is inappropriate to model the fast current loop of a GFL inverter in the phasor domain.

Mohiuddin, Sheik Mohammad↗

NASA NTRS2013

Development of a Phasor Diagram Creator to Visualize the Piston and Displacer Forces in an Advanced Stirling Convertor

The steady state, nearly sinusoidal behavior of the components in a Free Piston Stirling Engine allows for visualization of the forces in the system using phasor diagrams. Based on Newton's second law, F=ma, any phasor diagrams modeling a given component in a system should close if all of the acting forces have been considered. Since the Advanced Stirling Radioisotope Generator (ASRG), currently being developed for future NASA deep space missions, is made up of such nearly sinusoidally oscillating components, its phasor diagrams would also be expected to close. A graphical user interface (GUI) has been written in MATLAB by taking user input data, passing it to Sage, a 1-D thermodynamic modeling program used to model the Stirling convertor, running Sage and then automatically plotting the phasor diagrams. Using this software tool, the effect of varying different Sage inputs on the phasor diagrams was determined. The parameters varied were piston amplitude, hot end temperature, cold end temperature, operating frequency, and displacer spring constant. By using these phasor diagrams, better insight can be gained as to why the convertor operates the way that it does.

Saha, Dipanjan↗

NASA NTRS2013

Development of a Phasor Diagram Creator to Visualize the Piston and Displacer Forces in an Advanced Stirling Convertor

The steady-state, nearly sinusoidal behavior of the components in a free-piston Stirling engine allows for visualization of the forces in the system using phasor diagrams. Based on Newton's second law, F = ma, any phasor diagrams modeling a given component in a system should close if all of the acting forces have been considered. Since the Advanced Stirling Radioisotope Generator (ASRG), currently being developed for future NASA deep space missions, is made up of such nearly sinusoidally oscillating components, its phasor diagrams would also be expected to close. A graphical user interface (GUI) has been written in MATLAB (MathWorks), which takes user input data, passes it to Sage (Gedeon Associates), a one-dimensional thermodynamic modeling program used to model the Stirling convertor, runs Sage, and then automatically plots the phasor diagrams. Using this software tool, the effect of varying different Sage inputs on the phasor diagrams was determined. The parameters varied were piston amplitude, hot-end temperature, cold-end temperature, operating frequency, and displacer spring constant. These phasor diagrams offer useful insight into convertor operation and performance.

Saha, Dipanjan↗

DOE OSTI2020

Local Phasor-Based Control of DER Inverters for Voltage Regulation on Distribution Feeders

We introduce a new control paradigm termed Phasor-Based Control (PBC) to coordinate Distributed Energy Resources (DER) for improved voltage regulation and other objectives. PBC is a multi-layer control framework where the state of the distribution grid is represented by voltage phasors, and Phasor Measurement Units (PMUs) measure the state at critical points in the distribution grid. In the PBC paradigm, a supervisory controller (S-PBC) sets phasor targets which local controllers track. In this paper, we propose a Proportional Integral (PI) implementation for the local control layer (LPBC), to regulate real and reactive power output of distributed inverters to track a voltage phasor target computed by the supervisory layer. We tune the PI controller gains offline with a genetic algorithm that yields better performance than the Ziegler-Nichols method. We benchmark the proposed L-PBC controller against droop volt-var control (DVVC) and observe improved voltage regulation in simulation on the IEEE 13 node unbalanced test feeder (IEEE 13NF). Furthermore, by means of numerical simulation we observe the response of the L-PBC controllers to small and large grid disturbances. Simulations on larger feeders, IEEE 123-node and 647-node, demonstrate challenges with tuning controllers in setups with different amounts of power-voltage coupling.

42 ENGINEERING↗

DOE OSTI2021

Local Power-Voltage Sensitivity and Thevenin Impedance Estimation from Phasor Measurements

This paper describes how to use voltage phasor measurements to produce a sensitivity matrix that describes how real and reactive power injections at a node on a distribution network affect the local voltage magnitude and angle. Rather than estimating the sensitivity directly, the voltage phasor measurements and power commands/measurements are used to estimate the unbalanced, three-phase Thevenin impedance. The Thevenin impedance estimation is conducted using recursive least squares on temporal difference measurements. The Thevenin impedance and voltage phasor measurement are then used to build the local power-voltage sensitivity matrix with the closed form expression for the Jacobian of the power flow manifold. Hardware-in-the-loop simulations with phasor measurement units providing real phasor measurements are used to evaluate the recursive temporal difference Thevenin impedance estimation and Thevenin-based power-voltage sensitivity methods.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Phasor-Domain Modeling of Inverter Based Resources Considering Unbalanced Grid Faults

A significant increase in inverter-based distributed energy resources (DERs) is expected in distribution systems of the near future. The latest phasor modeling approach of DERs with emerging control technologies can capture relevant dynamics in large-scale three-phase distribution systems with unbalanced construction. However, there is a lack of appropriate phasor models to deal with unbalanced fault scenarios. As such, this paper describes per-phase phasor modeling approach appropriate for unbalanced grid disturbance studies in distribution systems with high penetration of DERs. The overall modeling performance of representative DERs is simulated in phasor domain GridLAB-D environment and validated against controller hardware-in-the loop (CHIL) testing or electromagnetic transient (EMT) based switching model simulation in PSCAD with test cases including different unbalanced grid faults. The high accuracy retained from the simulation verifies the effectiveness of the proposed phasor modeling approach considering interactions between positive and negative sequence signals.

Chen, Zhe↗

NASA NTRS1990

Precise synchronization of phasor measurements in electric power systems

Phasors representing positive sequence voltages and currents in a power network are in the most important parameters in several monitoring, control, and protection functions in interconnected electric power networks. Recent advances in computer relaying have led to very efficient and accurate phasor measurement systems. When the phasors to be measured are separated by hundreds of miles, it becomes necessary to synchronize the measurement processes, so that a consistent description of the state of the power system can be established. Global Positioning System (GPS) transmissions offer an ideal source for synchronization of phasor measurements. The concept and implementation of this technique are described. Several uses of synchronized phasor measurements are also described. Among these are improved state estimation algorithms, state estimator enhancements, dynamic state estimates, improved control techniques, and improved protection concepts.

Phadke, Arun G.↗

DOE OSTI2021

Comparison of Electromagnetic Transient and Phasor-based Simulation for the Stability of Grid-Forming-Inverter-based Microgrids

The increasing interest in studying feeder-level, inverter-based microgrids requires appropriate simulation methods that can effectively simulate the dynamics of distribution feeders that typically have thousands of nodes. To examine the accuracy of phasor-based simulation for the stability of feeder-level, inverter-based microgrids, a comparative study between electromagnetic transient (EMT) and phasor-based simulation was conducted. Case studies of a two-inverter small microgrid and a modified version of the IEEE 34-Node Test System that has seven grid-forming inverters show that phasor-based simulation agrees well with EMT simulation when the P-f droop gains of grid-forming inverter controllers are within normal ranges. However, under extremely high P-f droop gains, phasor-based simulation can result in over-optimistic stability results. This study provides insight into the applicability of phasor-based simulation for the stability of feeder-level, inverter-based microgrids.

Du, Wei↗

DOE OSTI2020

75 Years of Drift: The changing meaning of phasor [History]

The origin of what electrical engineers call a phasor diagram is explored, and traced to a treatise by William Thomson (later Lord Kelvin) and Peter Tait. The diagram was mechanical in origin, and gave a geometrical way to visualize and calculate the interactions of sinusoidal motions. Originally, the words radius vector were used in association with the diagram. Later authors used vector. As work on electromagnetic fields expanded, the word phasor was introduced to replace it. That change came about as a result of a deliberate effort (in 1944) to have a clear and unambiguous term of art. Since then, the meaning of the word has changed, and the geometrical interpretation has fallen out of favor. Unfortunately, clarity and unambiguity have suffered as a result. Newer meanings are examined. The measurement of phase angle in the electric power system is described. An Appendix on the work of Steinmetz shows that he did not favor the phasor representation.

Vector, Phasor, Phasor Measurement Unit↗

DOE OSTI2023

Comparison of Electromagnetic Transient and Phasor Dynamic Simulations: Implications for Inverter Dominated Systems

The simulation of very high shares of inverter-based resources in power systems has begun to draw into question the validity of phasor domain tools in capturing relevant dynamics. Electromagnetic transient simulators can capture the dynamics of power electronics with substantially smaller time steps, but are computationally expensive. This work contrasts the results of phasor domain and electromagnetic transient tools for simulations on a validated model of the Maui power system operating at very high inverter-based resource shares with near zero voltage forming devices. The results show that the phasor domain tool predicts optimistic stability with fewer voltage forming elements on the network, and loses computational stability before the electromagnetic transient tool. As the electromagnet transient model is of the entire system, and system-wide discrepancies are observed, this case study of a physical power system highlights the potential need for system-wide detailed modeling during periods of very high shares of inverter-based resources and few voltage forming devices.

electromagnetic transient-domain↗

DOE OSTI2021

An overview of continuous and discrete phasor analysis of binned or time-gated periodic decays

Time-resolved analysis of periodically excited luminescence decays by the phasor method in the presence of time gating or binning is revisited. Analytical expressions for discrete configurations of square gates are derived and the locus of the phasors of such modified periodic single-exponential decays is compared to the canonical universal semicircle. The effects of IRF offset, decay truncation and gate shape are also discussed. Finally, modified expressions for the phase and modulus lifetimes are provided for some simple cases. A discussion of a modified phasor calibration approach is presented.

42 ENGINEERING↗

DOE OSTI2021

Continuous and discrete phasor analysis of binned or time-gated periodic decays

The time-resolved analysis of periodically excited luminescence decays by the phasor method in the presence of time-gating or binning is revisited. Analytical expressions for discrete configurations of square gates are derived, and the locus of the phasors of such modified periodic single-exponential decays is compared to the canonical universal semicircle. The effects of instrument response function offset, decay truncation, and gate shape are also discussed. Finally, modified expressions for the phase and modulus lifetimes are provided for some simple cases. A discussion of a modified phasor calibration approach is presented, and an illustration of the new concepts with examples from the literature concludes this work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Iterative Linearization for Phasor-Defined Optimal Power Dispatch

Optimal power flow (OPF) problems, which dispatch power targets to controllable generating units across a network, must generally account for non-convex constraints on power flow. Furthermore, adapting those problems so as to make them solvable with convex optimization techniques is an area of much academic and operational interest. In this paper, we present a method for solving OPF as a quadratic program by iteratively refining and re-initializing a linearized model of power flow based on the outputs of an associated nonlinear solver. The linear model on which we demonstrate this method is an adapted version of an approximation designed for use with unbalanced distribution networks. As an important benefit, the model allows for the explicit inclusion of nodal voltage phasor values in both the OPF problem's objective and its constraints, which opens the door to the idea of phasor-based control (PBC) design. We show in simulations on the IEEE 13-node test feeder that our method quickly converges to a set of phasor targets that are sufficiently precise for use in operations at the distribution level.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Dynamic Model of Back-to-Back Converter for System Level Phasor Simulation

The power system is expected to evolve rapidly with increasing deployment of power electronic interface and conditioning systems, microgrids, and hybrid AC/DC grids. Among power electronic systems, back-to-back (BTB) converters can be a powerful interface to integrate microgrids and networked microgrids. However, in system level dynamic simulations for synchronous machine dominated system with BTB converters, a detailed electromagnetic sinusoidal models is not warranted as these simulations are focused on electromechanical transients. This paper focus on developing a simple phasor model for back- to-back converters that can be easily integrated into powerflow solvers to facilitate large-scale power system simulations. The model is implemented using C++ language and integrated into GridLAB-D software as a potential new capability. The GridLAB-D phasor domain model is validated against the electromagnetic transient (EMT) simulation of the detailed switching model. Simulation results show that the phasor model successfully captures the dominant dynamics of the converters.

Mahmood, Hisham↗

NASA NTRS2013

Development and Integration of an Advanced Stirling Convertor Linear Alternator Model for a Tool Simulating Convertor Performance and Creating Phasor Diagrams

A simple model of the Advanced Stirling Convertors (ASC) linear alternator and an AC bus controller has been developed and combined with a previously developed thermodynamic model of the convertor for a more complete simulation and analysis of the system performance. The model was developed using Sage, a 1-D thermodynamic modeling program that now includes electro-magnetic components. The convertor, consisting of a free-piston Stirling engine combined with a linear alternator, has sufficiently sinusoidal steady-state behavior to allow for phasor analysis of the forces and voltages acting in the system. A MATLAB graphical user interface (GUI) has been developed to interface with the Sage software for simplified use of the ASC model, calculation of forces, and automated creation of phasor diagrams. The GUI allows the user to vary convertor parameters while fixing different input or output parameters and observe the effect on the phasor diagrams or system performance. The new ASC model and GUI help create a better understanding of the relationship between the electrical component voltages and mechanical forces. This allows better insight into the overall convertor dynamics and performance.

Metscher, Jonathan F.↗

NASA NTRS2013

Development and Integration of an Advanced Stirling Convertor Linear Alternator Model for a Tool Simulating Convertor Performance and Creating Phasor Diagrams

Metscher, Jonathan F.↗

DOE OSTI2021

Hardware-In-the-Loop Benchmarking Setup for Phasor Based Control Validation

Phasor Based Control is a novel approach to controlling Distributed Energy Resources that aims at relieving various constraints that arise in the distribution grid. It is a two-layer control system with a supervisory control that coordinates distributed controllers to reach voltage phasor targets. The distributed controllers use local synchrophasor measurements and operate as feedback controllers. This control method is currently under development with several algorithms being under consideration for both the central and distributed components. In this report, we present the experimental setup that was prepared to prototype a hardware implementation and validate the control method in Hardware-In-the-Loop.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Phasor Based Control with the Distributed, Extensible Grid Control Platform

This paper describes how to implement Phasor Based Control (PBC) using the Distributed, Extensible Grid Control (DEGC) Platform. PBC is a novel method for controlling distributed energy resources (DER) that coordinates a centralized optimization with distributed feedback controllers to enforce voltage phasor targets. DEGC is an open source software and communication platform designed for general DER control. We deployed PBC at Lawrence Berkeley Lab's FLEXLAB test site, conducting multiple hardware-in-the-loop test runs. Here, we describe how DEGC was used to implement PBC on hardware, and results demonstrating successful deployment.

24 POWER TRANSMISSION AND DISTRIBUTION↗