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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Spectral Clustering-Based Partitioning of Large-Scale Power Electronics-Based Power Systems for Small-Signal Stability Analysis

The nodal admittance matrix (NAM)-based approach is well-suited for small-signal stability analysis of large-scale power electronics-based power systems (PEPSs), as it preserves the system structure through its admittance matrix. Previous studies have explored partitioning such systems into subareas and interconnections to reduce computational burden; however, they lacked a formal algorithmic procedure for determining feasible partitions. While several grid partitioning methods, such as those based on graph theory or machine learning, exist in the literature, they cannot be directly applied to NAM-based analysis due to differing objectives and constraints. Here, this paper addresses this gap by presenting a systematic, step-by-step procedure for applying a spectral partitioning algorithm that yields a division of the system into subareas suitable for NAM-based analysis. The computational complexity of the proposed method is also derived to demonstrate its efficiency and justify the practicality of the resulting subarea decomposition. The performance of the partitioning method is evaluated by applying the spectral clustering-derived subareas and interconnections to the NAM-based partitioning approach on a 140-bus system. Computational times for the full-system and partitioned NAM analyses are compared using MATLAB. Additionally, PSCAD simulations of the complete system and partitioned subareas are carried out to verify the effectiveness of the proposed method.

Nupur [Univ. of Tennessee, Knoxville, TN (United S↗
DOE OSTI2024

Partitioning of Large-Scale Power Electronics-Based Power Systems for Small-Signal Stability Analysis

The nodal admittance matrix (NAM)-based approach is suitable for analyzing the small-signal stability of large-scale power electronics-based power systems (PEPSs) as it preserves the system structure by utilizing the admittance matrix. Previously, NAM-based area partition has been proposed, which divides the system into various subareas and interconnections for easier analysis of the low-dimension matrix compared to the entire system-based high-dimension matrix. However, no partition algorithm has been presented for the NAM-based area partition method. This paper focuses on implementing the spectral partitioning algorithm for partitioning large-scale PEPSs into a low-dimension matrix to reduce the computation complexity of the analysis. These spectral components facilitate data transformation into a new space, enabling the application of traditional clustering methods like k-means. To evaluate the performance of the partitioning method, the subareas and interconnections obtained from the spectral clustering algorithm are incorporated into the NAM-based area partition method for a large system with 140 buses. The computational times of the original method, where the NAM-based criterion is directly applied to the entire system, are compared with those of the NAM-based partition method in MATLAB. PSCAD simulations of the whole system and the obtained subareas are conducted to validate the effectiveness of the proposed algorithm.

Nupur, Nupur↗
DOE OSTI2021

Nodal Admittance Matrix Based Area Partition Method for Small-Signal Stability Analysis of Large-Scale Power Electronics Based Power Systems

In power electronics-based power systems (PEPSs), small-signal stability is an important factor for system design and operation, where the impedance-based approach is often used. However, unlike small-scale PEPSs with simple and straightforward impedance models, it would take much more efforts to derive the large-scale PEPSs impedance model, which is very complicated and sometimes may get wrong results due to the elimination of right-half plane (RHP) poles during the impedance aggregation process. To simplify the derivation procedure and analyze the small-signal stability of large-scale PEPSs, this paper proposes a nodal admittance matrix (NAM) based area partition method. In this method, the large-scale PEPS is divided into several sub-areas, and the stability is analyzed within the sub-area first, and then the interconnection stability among these sub-areas is analyzed. The proposed method is scalable and can help to locate the weakest areas/converters that may cause instability in the whole system. In this paper, the concept of the proposed method and its application to an example system are introduced. Experimental results are also given to validate the effectiveness of the proposed method.

Qiao, Liang↗
DOE OSTI2022

Comparative Small-Signal Stability Analysis of Grid-Forming and Grid-Following Inverters in Low-Inertia Power Systems: Preprint

Inverter-based resources (IBRs) are gradually replacing conventional fossil energy in modern power systems, which could make the system susceptible due to insufficient inertia, especially when moving towards a 100% inverter-based power grid. Grid-forming (GFM) and grid-following (GFL) controls are two common inverter control algorithms. However, the corresponding stability issues along with a comparative study on low-inertia power systems should still be investigated. This paper focuses on small-signal stability and conducts a comprehensive analysis of GFM and GFL controls, with emphases on the interactions between synchronous generators and IBRs. The detailed modeling of GFM and GFL inverters, and synchronous generators (SGs) are established. The coupling mechanism of IBRs and SGs is then conducted through participation factor analysis. The impacts of critical parameters on system stability are finally identified. The theoretical analyses are validated through time-domain simulation in MATLAB/Simulink.

grid-following↗
DOE OSTI2026

Analytical small-signal stability analysis of low-inertia power system frequency response considering secondary frequency regulation

Modern power systems are increasingly vulnerable to frequency instability as inverter-based resources (IBRs) replace synchronous machines and reduce system rotational inertia. Existing small-signal frequency stability assessment methods are either computationally intensive, relying on simulation-driven approaches, or lack analytical stability regions that explicitly account for secondary frequency response (SFR). This paper introduces new analytical frameworks that enable evaluation small-signal frequency stability while explicitly incorporating tunable IBR and SFR parameters. Using Kharitonov’s theorem with an overbounding approach, explicit small-signal stability criteria are derived. In addition, based on Białas’ criterion and Hurwitz matrix, analytical stability regions are established to reveal feasible design spaces for SFR and IBR parameters tuning. Extensive Matlab/Simulink-based simulations validate the accuracy and computational efficiency of the proposed methods, demonstrating that coordinated tuning of SFR and IBR parameters can substantially enhance system resilience. By bridging analytical rigor with practical tunability, this work provides an analytical framework for assessing small-signal frequency stability in low-inertia grids, supporting the real-time, scalable, and resilient operation of sustainable power systems.

14 SOLAR ENERGY↗
DOE OSTI2021

Small-Signal Stability Analysis of Low-Inertia Power Grids with Inverter-Based Resources and Synchronous Condensers: Preprint

With the potential environmental impacts of conventional fossil fuels and the technology advances of grid interactive power electronics, inverter-based resources (IBRs) are playing a crucial role in modern power grids. However, due to the lack of physical inertia, IBRs are vulnerable to system disturbances. Further, conventional grid-following (GFL) inverters cannot actively establish the frequency and voltage, which could not be a appropriate solution for 100% inverter-based power grids. Grid-forming (GFM) control, as an emerging inverter control function, has drawn great attention in recent years, while it is still under development and pre-mature for large-scale field deployment. A potential solution for gradually transitioning into a 100% inverter-based power grid is to combine both IBRs and synchronous machines into a mixed generation portfolio. More importantly, synchronous machines can be operated as synchronous condensers (SCs) until they are retired. It is also worth mentioning that the stability analysis is of great importance to ensure the smooth transition from existing power grids to 100% inverter-based system, which is the main focus of this work with detailed modeling and modal analysis.

100% renewable↗
DOE OSTI2024

Holistic Small-Signal Stability Analysis for Large-Scale Inverter-Intensive Power Systems with Coupled and Full-Order Dynamics from Control Systems and Power Networks

The increasing penetration of inverter-based resources (IBRs) into the existing power systems introduces tremendous benefits for enhanced sustainability but also poses inevitable challenges in terms of insufficient inertia, potential instability, and complex network dynamics, among others. However, the additional coupling introduced by the interactions among gridfollowing (GFL) and grid-forming (GFM) IBRs and the other components (i.e., synchronous generators [SGs], loads, and network, etc.) has not been clearly explored. A holistic, scalable, and quantitative stability analysis framework with the control systems and power networks is still missing. Here, in this paper, to fill in the technical gaps, a holistic small-signal model of the entire system with both rotating generation units and IBRs is established. An extended power flow model with operation dynamics from both generator control schemes and power networks is proposed to provide the varying steady-state operating points for small-signal modeling. The proposed method is compared with MATLAB solvers, and the results show that the proposed approach has a minimum calculation time, which can be less than 12 seconds for a large-scale power system with up to 2,000 buses. Furthermore, a quantitative method is developed to identify the impacts of IBRs on system performance with emphases on the potential stability issues with GFL IBRs, additional benefits of employing GFM IBRs, the feasibility of replacing SGs with GFM IBRs, and the impact of penetration level of different kinds of generation units. Finally, a field island power system is used to verify the proposed approach, and hardware-in-the-loop (HIL) tests are provided to further demonstrate the effectiveness of the proposed analysis.

14 SOLAR ENERGY↗
DOE OSTI2023

Quantitative Small-Signal Stability Analysis of Grid-Forming Inverters in Large-Scale Power Systems

In this paper, the challenges induced by the integration of inverter-based resources (IBRs) into existing power systems are discussed. Although the grid-forming (GFM) control has been used to enhance system performance in multiple sections of electric power systems (e.g., transmission and distribution systems, microgrids, among others), the coupling mechanism between GFM inverter and various types of other components in modern power systems should be clearly explored. Existing analyses mainly focus on qualitative investigations that verify the effectiveness of deploying GFM inverters for stability enhancement. A holistic system-level quantitative analysis is still missing to verify the detailed benefits of GFM inverters and their interactions with other generation units (e.g., synchronous generators [SGs], conventional grid-following [GFL] inverters, synchronous condensers, among others). To fill in the technical gaps, a holistic small-signal model of the entire system with both rotating generation units and IBRs is established along with the customized power flow analysis for varying steady-state operating points. Further, a quantitative method is proposed to identify the impacts of GFM inverters on system performance with an emphasis on a quantifiable stability margin and a complete modal analysis at the system level. Finally, a realistic test system is used to verify the proposed approach.

grid-following↗
DOE OSTI2021

Detecting and Analyzing Power System Disturbances in PMU Data with the Open-Source Archive Walker Tool

As the number of Phasor Measurement Units (PMUs) deployed in power systems increases, so do the archives of synchrophasor measurements stored by utilities. Significant value can be extracted from these archives by using them to support studies such as frequency response analysis, small-signal stability analysis, and power plant model validation. To better enable utilities to perform these studies, the open-source Archive Walker tool was developed. This tool examines PMU data for grid disturbances and periods of interest. Once identified, the data can be further analyzed inside Archive Walker or exported to specialty tools. In this paper, the various disturbance detectors available in Archive Walker are described, and its interactions with other openly-available tools are highlighted.

Follum, James D.↗
DOE OSTI2026

Control Parameter Sensitivity Study for Inverter-Based-Resource Dominated Grids: A Small Signal Stability Approach and Framework

The growing adoption of renewable energy is driving the prevalence of inverter-based resources (IBRs) within power grids. Future power grids will integrate both grid-following IBRs (GFM-IBRs) and grid-forming IBRs (GFL-IBRs) alongside synchronous generators. Therefore, it is crucial to perform stability studies that account for all components and especially control interactions related to IBRs. Extensive research has performed to study the IBR-related stability, however, the sensitivity study of IBRs' control parameters on system stability has not been adequately studied yet, especially from a systematic way. Therefore, this paper conducts a small signal stability analysis for a generic grid with multiple types of resources and develops an analytical framework for assessing the sensitivity of control parameters affecting stability margins. To achieve that, the non-autonomous reduced-order non-linear dynamic model is developed for a generic power system with multiple synchronous generator-based resources (SGBRs), GFM-IBRs, and GFL-IBRs. Based on the analytic model, a systematic framework for parametric sensitivity on systems' asymptotic stability is developed. A parameter sensitivity analysis based on eigenvalue methods is proposed. The impact of the droop controllers of GFM-IBRs, PQ-dispatch and the PLL controller of GFL-IBR on the system asymptotic stability is discussed. This sensitivity study is aiming to provide deep insights on control parameters' impact on system stability, and gives direction for parameter tuning in case of instability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Impact of Increased Inverter Penetration on Power System Small-Signal Stability: Preprint

The transformation of the power system to include more distributed energy resources (DER) implies an increase in the number of inverter-based resources deployed on the grid. Envisioning future scenarios, this paper presents a small-signal stability analysis for a power grid comprising synchronous generators and inverter-based resources. Three types of inverter control are considered: grid following, droop-controlled grid forming, and virtual oscillator control grid forming. Although small-signal stability of power systems is a widely studied topic, systematic analysis of mixed machine-inverter systems with detailed control models at various inverter penetration levels are limited. This paper addresses the gap with numerical simulations tailored to the IEEE 39-bus system. Results show the system may become unstable at high inverter penetration level of grid-following inverters, and grid-forming inverter control can potentially improve system stability, thereby enabling very high level of DERs.

41 EE - Solar Energy Technologies Office (EE-4S)↗
DOE OSTI2022

Small-Signal Stability Support from Dynamically Configurable Grid-Forming/Following Inverters for Distribution Systems: Preprint

As the penetration of inverter-based resources (IBRs) continues to increase in modern power systems, system stability is challenged by the insufficient inertia induced by IBRs; hence, there is a need to develop various methods to address the potential instabilities. In this paper, grid-forming (GFM) and grid-following (GFL) controls are implemented for inverters with flexible-mode transitions between them. The operation mode transition between GFM and GFL controls is adopted as an additional degree of control flexibility to adjust the small signal stability margin. Further, a holistic and detailed small signal model of the entire system with the dynamics from both synchronous generators (SGs) and IBRs is derived. The effectiveness of the proposed work in adjusting the system small signal stability margin is validated by conducting case studies with varying penetration levels of IBRs. A test system with one SG and five inverters was implemented in MATLAB/Simulink to demonstrate the effectiveness of the proposed approach. Index Terms - grid-following control, grid-forming control, operation mode transition, small-signal stability analysis

grid-following control↗
DOE OSTI2024

Advanced grid-forming (GFM) inverter controls, modeling and system impact study for inverter dominated grids

Our main goals in this project are to understand: 1) the stability of the power system with very high penetration of PV or other inverter-based resources (IBR), 2) the interactions among IBRs and traditional generators, and 3) the impact of the GFM inverters on bulk power system. To achieve these goals, we took a holistic research and development approach. First, an impedance-based large system modeling and stability analysis tool was developed to aid the large IBR system small-signal stability analysis. Second, consensus-based control and transient overload ride through were developed to control and coordinate multiple GFM inverters in a large system to maintain transient stability during big grid events. Third, high fidelity electromagnetic transient (EMT) IBR models were developed and integrated into a large reduced WECC model to study the system impact from IBRs. Lastly, extensive validation tests of the GFM control which was developed in this project and implemented in two 1MW commercial solar inverters were performed using different validation platforms, e.g., control hardware-in-the-loop (CHIL) platform, power hardware- in-the-loop (PHIL) platform, and a real PV plant.

14 SOLAR ENERGY↗
DOE OSTI2021

Impact of Increased Inverter-Based Resources on Power System Small-Signal Stability

The transformation of the power system to include more distributed energy resources (DER) implies an increase in the number of inverter-based resources deployed on the grid. Envisioning future scenarios, this paper presents a small-signal stability analysis for a power grid comprising synchronous generators and inverter-based resources. Three types of inverter control are considered: grid following, droop-controlled grid forming, and virtual oscillator control grid forming. Although small-signal stability of power systems is a widely studied topic, systematic analysis of mixed machine-inverter systems with detailed control models at various inverter levels are limited. This paper addresses the gap with numerical simulations tailored to the IEEE 39-bus system. Results show the system may become unstable at high inverter level of grid-following inverters, and grid-forming inverter control can potentially improve system stability, thereby enabling very high level of DERs.

grid-following inverter↗
DOE OSTI2023

A Stability Analysis Tool for Bulk Power Systems Using Black-Box Models of Inverter-Based Resources

This paper presents a small-signal stability analysis tool for large-scale power systems with high penetration of inverter-based resources (IBRs). Firstly, a network transfer function matrix (NTFM), which represents the information of the system topology, transmission lines, loads, IBRs locations, etc., is derived to model the entire power system network. Secondly, small-signal perturbation method is applied to obtain the sequence impedance/admittance models of the block-box IBRs considering the frequency cross-coupling effects. With the obtained NTFM as well as IBR models, a multi-input, multi-output (MIMO) feedback system is constructed, and the generalized Nyquist criterion (GNC)-based stability method is employed to analyze the stability of the entire power system. Furthermore, based on the developed stability analysis method, sensitivity analysis is conducted on an unstable case to identify which parameter has a high impact on the system stability. As a result, different test cases based on a modified IEEE 14- bus system as well as a reduced 240-bus WECC system are studied to verify the proposed stability analysis tool.

42 ENGINEERING↗
DOE OSTI2022

A Stability Analysis Tool for Bulk Power Systems Using Black-Box Models of Inverter-based Resources

This paper presents a small-signal stability analysis tool for large-scale power systems with high penetration of inverter-based resources (IBRs). Firstly, a network transfer function matrix (NTFM), which represents the information of the system topology, transmission lines, loads, IBRs locations, etc., is derived to model the entire power system network. Secondly, small-signal perturbation method is applied to obtain the sequence impedance/admittance responses of IBRs considering the frequency cross-coupling effects. With the obtained NTFM as well as IBRs' models, a multi-input, multi-output (MIMO) feedback system is constructed, and the generalized Nyquist criterion (GNC)-based stability method is employed to analyze the stability of the entire power system. Different testing cases based on a modified IEEE-14 bus system are leveraged to verify the proposed stability analysis tool.

Sun, Dongsen↗