Publications

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With increasing penetration of variable renewable generation, battery energy storage systems (BESS) are becoming important for power system stability due to their operational flexibility. In this paper, we propose a method for determining the minimum BESS rated power that guarantees security constraints in a grid subject to disturbances induced by variable renewable generation. The proposed framework leverages sensitivity-based inverse uncertainty propagation where the dynamical responses of the states are parameterized with respect to random variables. Using this approach, the original nonlinear optimization problem for finding the security-constrained uncertainty interval may be formulated as a quadratically-constrained linear program. The resulting estimated uncertainty interval is utilized to find the BESS rated power required to satisfy grid stability constraints.

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Structural modularity is critical to solid-state transformer (SST) and solid-state power substation (SSPS) concepts, but operational aspects related to this modularity are not yet fully understood. Previous studies and demonstrations of modular power conversion systems assume identical module compositions, but dependence on module uniformity undercuts the value of the modular framework. In this project, a hierarchical control approach was developed for modular SSTs which achieves system-level objectives while ensuring equitable power sharing between nonuniform building block modules. This enables module replacements and upgrades which leverage circuit and device technology advancements to improve system-level performance. The functionality of the control approach is demonstrated in detailed time-domain simulations. Results of this project provide context and strategic direction for future LDRD projects focusing on technologies supporting the SST crosscut outcome of the resilient energy systems mission campaign.

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This paper presents a visualization technique for incorporating eigenvector estimates with geospatial data to create inter-area mode shape maps. For each point of measurement, the method specifies the radius, color, and angular orientation of a circular map marker. These characteristics are determined by the elements of the right eigenvector corresponding to the mode of interest. The markers are then overlaid on a map of the system to create a physically intuitive visualization of the mode shape. This technique serves as a valuable tool for differentiating oscillatory modes that have similar frequencies but different shapes. This work was conducted within the Western Interconnection Modes Review Group (WIMRG) in the Western Electric Coordinating Council (WECC). For testing, we employ the WECC 2021 Heavy Summer base case, which features a high-fidelity, industry standard dynamic model of the North American Western Interconnection. Mode estimates are produced via eigen-decomposition of a reduced-order state matrix identified from simulated ringdown data. The results provide improved physical intuition about the spatial characteristics of the inter-area modes. In addition to offline applications, this visualization technique could also enhance situational awareness for system operators when paired with online mode shape estimates.

The Cramér-Rao Lower Bound (CRLB) is used as a classical benchmark to assess estimators. Online algorithms for estimating modal properties from ambient data, i.e., mode meters, can benefit from accurate estimates of forced oscillations. The CRLB provides insight into how well forced oscillation parameters, e.g., frequency and amplitude, can be estimated. Previous works have solved the lower bound under a single-channel PMU measurement; thus, this paper extends works further to study CRLB under two-channel PMU measurements. The goal is to study how correlated/uncorrelated noise can affect estimation accuracy. Interestingly, these studies shows that correlated noise can decrease the CRLB in some cases. This paper derives the CRLB for the two-channel case and discusses factors that affect the bound.

Dynamic injection shift factor (DISF) is the linear sensitivity factor that estimates the incremental line flows in a transmission network subject to load disturbances. The DISF provides fast computation of post-disturbance line flows without solving nonlinear equations of power-system dynamics for a given pre-disturbance operating condition. Furthermore, DISF can be utilized to derive other critical sensitivity factors used for fast contingency screening and generation dispatch in real-time markets. However, deriving the DISF analytically is difficult due to nonlinearity of power-system models. In this paper, we propose an approach based on a linear Koopman operator and a data-driven algorithm to construct a representative linear model for generator and network dynamics. The linear model constructed by the proposed approach is utilized to find an analytic expression of the DISF. Then, the DISF provides numerical tools to estimate line flows accurately subject to power injection changes in the network at any instant in time without solving nonlinear power-system equations.

Transient stability control of power systems is based on actions that are taken automatically following a disturbance to ensure that the system remains in synchronism. Examples of such measures include generator rejection and the insertion of dynamic braking resistors. Methods like these are designed to rapidly absorb excess energy or otherwise alter the generation-demand balance at key points in the system. While these methods are often effective, they lack the ability to inject real power to compensate for a deficit. Utility-scale inverter-based resources, particularly energy storage systems, enable bidirectional modulation of real power with the bandwidth necessary to provide synchronizing torque. These resources, and the control strategies they enable, have garnered substantial research interest. This paper provides a critical review of research on real power modulation strategies for transient stability control. The design of these control strategies is heavily informed by the methods used to assess changes in the transient stability margins. Rigorously assessing these changes is difficult because the dynamics of large-scale power systems are inherently nonlinear. The well-known equal-area criterion is physically intuitive, but conceptual extensions are necessary for multi-machine systems. So-called direct methods of transient stability analysis offer a more general alternative; however, these methods require many simplifying assumptions and have difficulty incorporating detailed system dynamics. In this paper, we discuss data-driven methods for offline stability assessment based on Koopman operator theory.

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This document describes the Power and Energy Storage Systems Toolbox for MATLAB, abbreviated as PSTess. This computing package is a fork of the Power Systems Toolbox (PST). PST was originally developed at Rensselaer Polytechnic Institute (RPI) and later upgraded by Dr. Graham Rogers at Cherry Tree Scientific Software. While PSTess shares a common lineage with PST Version 3.0, it is a substantially different application. This document supplements the main PST manual by describing the features and models that are unique to PSTess. As the name implies, the main distinguishing characteristic of PSTess is its ability to model inverter-based energy storage systems (ESS). The model that enables this is called ess.m , and it serves the dual role of representing ESS operational constraints and the generator/converter interface. As in the WECC REGC_A model, the generator/converter interface is modeled as a controllable current source with the ability to modulate both real and reactive current. The model ess.m permits four-quadrant modulation, which allows it to represent a wide variety of inverter-based resources beyond energy storage when paired with an appropriate supplemental control model. Examples include utility-scale photovoltaic (PV) power plants, Type 4 wind plants, and static synchronous compensators (STATCOM). This capability is especially useful for modeling hybrid plants that combine energy storage with renewable resources or FACTS devices.

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Forced oscillations in power systems are of particular interest when they interact and reinforce inter-area oscillations. This paper determines how a previously proposed inter-area damping controller mitigates forced oscillations. The damping controller modulates active power on the Pacific DC Intertie (PDCI) based on phasor measurement units (PMU) frequency measurements. The primary goal of the controller is to improve the small signal stability of the north south B mode in the North American Western Interconnection (WI). The paper presents small signal stability analysis in a reduced order system, time-domain simulations of a detailed representation of the WI and actual system test results to demonstrate that the PDCI damping controller provides effective damping to forced oscillations in the frequency range below 1 Hz.

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This paper describes the design and implementation of a proof-of-concept Pacific dc Intertie (PDCI) wide area damping controller and includes system test results on the North American Western Interconnection (WI). To damp inter-area oscillations, the controller modulates the power transfer of the PDCI, a ±500 kV dc transmission line in the WI. The control system utilizes real-time phasor measurement unit (PMU) feedback to construct a commanded power signal which is added to the scheduled power flow for the PDCI. After years of design, simulations, and development, this controller has been implemented in hardware and successfully tested in both open and closed-loop operation. The most important design specifications were safe, reliable performance, no degradation of any system modes in any circumstances, and improve damping to the controllable modes in the WI. The main finding is that the controller adds significant damping to the modes of the WI and does not adversely affect the system response in any of the test cases. The primary contribution of this paper, to the state of the art research, is the design methods and test results of the first North American real-time control system that uses wide area PMU feedback.

Inverters using phase-locked loops for control depend on voltages generated by synchronous machines to operate. This might be problematic if much of the conventional generation fleet is displaced by inverters. To solve this problem, grid-forming control for inverters has been proposed as being capable of autonomously regulating grid voltages and frequency. Presently, the performance of bulk power systems with massive penetration of grid-forming inverters has not been thoroughly studied as to elucidate benefits. Hence, this paper presents inverter models with two grid-forming strategies: virtual oscillator control and droop control. The two models are specifically developed to be used in positive-sequence simulation packages and have been implemented in PSLF. The implementations are used to study the performance of bulk power grids incorporating inverters with gridforming capability. Specifically, simulations are conducted on a modified IEEE 39-bus test system and the microWECC test system with varying levels of synchronous and inverter-based generation. The dynamic performance of the tested systems with gridforming inverters during contingency events is better than cases with only synchronous generation.

This report presents a complete listing, as of May 2019, of the damping controller (DCON) project accomplishments including a project overview, project innovations, awards, patent application, journal papers, conference papers, project reports, and project presentations. The purpose of the DCON is to mitigate inter-area oscillations in the WI by active improvement of oscillatory mode damping using phasor measurement unit (PMU) feedback to modulate power flow in the PDCI. The DCON project is the result of a collaboration between Sandia National Laboratories (SNL), Montana Technological University (MTU), Bonneville Power Administration (BPA), and the Department of Energy Office of Electricity (DOE-OE).

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