Small Signal Stability Analysis Research Articles

Harmonic Sequence Component Model-Based Small-Signal Stability Analysis in Synchronous Machines during Asymmetrical Faults

Power systems are complex and often subject to faults, requiring accurate mathematical models for a thorough analysis. Traditional time-domain models are employed to evaluate the dynamic response of power system elements during transmission system faults. However, only the positive sequence components are considered for unbalanced faults, so the small-signal stability analysis is no longer accurate when assuming balanced conditions for asymmetrical faults. The dynamic phasor approach extends traditional models by representing synchronous machines with harmonic sequence components, making it suitable for an unbalanced condition analysis and revealing dynamic couplings not evident in conventional methods. By modeling electrical and mechanical equations with harmonic sequence components, the study implements an eigenvalue sensitivity analysis and participation factor analysis to identify the variable with significant participation in the critical modes and consequently in the dynamic response of synchronous machines during asymmetric faults, thereby control strategies can be proposed to improve system stability. The article validates the dynamic phasor model through simulations of a single-phase short circuit, demonstrating its accuracy and effectiveness in representing the transient and dynamic behavior of synchronous machines, and correctly identifies the harmonic sequence component with significant participation in the critical modes identified by the eigenvalue sensitivity to the rotor angular velocity and rotor angle.

Control and Stability of Grid-Forming Inverters: A Comprehensive Review

The large integration of inverter-based resources will significantly alter grid dynamics, leading to pronounced stability challenges due to fundamental disparities between inverter-based and traditional energy systems. While grid-following inverters (GFLIs) dominate current inverter configurations, their increased penetration into the grid can result in major stability issues. In contrast, grid-forming inverters (GFMIs) excel over GFLIs by offering features like standalone operation, frequency support, and adaptability in weak grid scenarios. GFMIs, unlike GFLIs, control the AC voltage and frequency at the common coupling point, impacting the inverter dynamic response to grid disturbances and overall stability. Despite the existing literature highlighting differences between GFLIs and GFMIs and their control strategies, a comprehensive review of GFMIs’ stability and the effects of their control schemes on grid stability is lacking. This paper provides an in-depth evaluation of GFMIs’ stability, considering various control schemes and their dynamics. It also explores different types of power system stability, introduces new stability concepts that correspond to power grids with integrated inverters, i.e., resonance and converter-driven stability, and reviews small-signal and transient stability analyses, which are the main two types of GFMI stability studied in the literature. The paper further assesses existing studies on GFMI stability, pinpointing research gaps for future investigations.

An optimal regulation of grid-connected doubly-fed induction generator angular speed and the DC-link voltage

In this work, a linear quadratic regulator controller is utilized to optimize the gains of the machine-side converter and grid-side converter controllers. The DC-link voltage and the rotational speed of the doubly-fed induction generator are optimally regulated by these controls. Additionally, the small-signal stability of the proposed system has been evaluated using the linearized model of the system. The small-signal stability analysis of the designed system has been accomplished through the application of the eigenvalues and participation factors technique. The suggested controller has been tested in a variety of operating conditions under small disturbances. MATLAB/SIMULINK simulation simulations have been used to evaluate the efficacy of the suggested optimal control system. Additionally, the generator-angular speed and DC-link voltage dynamic performances demonstrate the efficacy of the proposed controller. Finally, the robustness of the proposed controller has also been tested and validated using OPAL-RT technology under large perturbations at stator terminal voltage.

A grid-forming approach utilizing DC bus dynamics for low inertia power systems with HVDC applications

While power electronic converters, such as voltage source converters (VSCs), are crucial for the operation of converter-dominated renewables and their integration with the electricity grid, their reliance on VSCs can pose a challenge. The limited inertia of these sources can lead to a deterioration of the rate of change of frequency, potentially causing power system stability issues. A grid-forming approach utilizing dc-link dynamics is one of the attractive alternatives to achieve grid synchronization and support grid frequency. Existing grid-forming control schemes, which assume a constant or virtually constant dc source, rely on a fixed physical dc-link capacitor. Nonetheless, the inertia support from such a capacitor is brief, owing to its limited energy storage capability. Consequently, enhancing inertia becomes imperative; otherwise, it may result in an increased rate of change of voltage on the dc side, potentially leading to issues with protection, undesirable interactions, and system instability. This paper proposes a new grid-forming control strategy that considers a virtual capacitor to achieve grid synchronization while simultaneously providing the network with inertia response services during power imbalances. Moreover, including a virtual resistor in the controller effectively attenuates power and dc voltage oscillations. Simulations using Simulink and small signal stability analysis are conducted to validate the efficacy of the proposed controller.

Small Signal Modelling and Stability Analysis of a Grid Connected Inverted Based Microgrid

Objectives: This work focuses on the stability analysis of grid connected microgrids. It considers the impact of load disturbance and grid voltage change on voltage and current levels, as well as reactive and active power responses, is analysed. Methods: A comprehensive small-signal state-space model is developed for an inverter-based microgrid, incorporating submodules of inverters, phase-locked loops (PLLs), and LCL filters. The model is linearized around a stable operating point, and eigenvalue analysis is performed and validated through MATLAB/Simulink simulations. A current controller operating in the d-q frame is proposed to enhance stable power conversion and maintain microgrid stability. Findings: The proposed model and control strategy demonstrate the microgrid's ability to maintain transient voltage stability under severe dynamic conditions. During a 10% grid voltage fluctuation, the microgrid exhibits stable active and reactive power responses, with currents and voltages at the point of common coupling stabilizing within 0.2 seconds. Furthermore, when a 25 kVA active load is disconnected, the microgrid effectively manages the power transition, maintaining stable operation with minimal deviations in key parameters. The current controller simplifies AC current control, integrating active power management from solar input, DC-link voltage stability, and reactive power control. Novelty: The novelty lies in the comprehensive analysis of transient voltage stability in grid-connected microgrids under grid voltage fluctuations and load disturbances, areas that have received limited attention in previous research. By developing a detailed small-signal state-space model incorporating PLL and LCL filter dynamics and proposing a robust control strategy with the current controller, this study offers new insights into enhancing the resilience and reliability of grid-connected microgrids during transient events. Keywords: Microgrid, Small Signal Stability, Voltage Source Inverter, State Space model, Eigen Values

Dynamic impact of hybrid wind-solar photovoltaic power injection on small signal stability of Nigerian 11kV power system using Self Organizing Map neural network

Power industry reorganization, legislation on greenhouse gas emissions and inadequate conventional generation capacity encourage the idea of incorporating Distributed Generation (DG) into the distribution networks as unconventional sources of power generation. High penetration of DG has further increased the complexity of the analysis of small signal stability because the variability of renewable energy sources affects the stability of power system. Therefore, this research work investigates the effect of wind and solar photovoltaic power injection on small signal stability of Nigerian 11 kV power network. Wind and solar photovoltaic were modelled using probabilistic methods and output power at twenty-one different locations within Nigeria was computed. Using the real and reactive power data of the network, Self-Organizing Map (SOM) neural network was trained and tested for the assessment of the small signal stability of the distribution network before and after the injection of renewable power in python virtual environment. The integration of hybrid wind-solar PV distributed generation at 30 %, 60 %, 90 % and 100 % into the studied 11 kV power distribution network improved its small signal stability by 1.4 %, 2.1 %, 2.5 % and 3.2 % respectively. Moreover, increase in the injection of power gotten from wind and solar sources reduces the oscillation frequency of the system from 1.39 Hz to 1.01 Hz and increases the damping from 4.6 % to 13.2 %. Reactive power increment in the range of 5 %-20 % improved the small signal stability of the system by the range 2.4 %-7 %. This improvement will translate to better power transfer capability of the network.

Stability Analysis in a Direct-Current Shipboard Power System with Parallel Permanent Magnet Synchronous Generators and Supercapacitor Integration

This paper investigates the small-signal stability of a DC shipboard power system (SPS) with the integration of a supercapacitor. As an efficient energy storage solution, supercapacitors can not only provide rapid energy response to sudden power demand spikes, effectively mitigating load fluctuations, but also enhance the system’s resilience to disturbances. In the context of the parallel operation of two Permanent Magnet Synchronous Generators (PMSGs), the inclusion of supercapacitors may alter the system’s dynamic behaviors, thereby affecting its small-signal stability. This paper develops the small-signal model of SPS and explores the small-signal model under various power distribution strategies in the parallel operation of diesel generator sets. Through the calculation of eigenvalues and influence factors, the system’s oscillation modes are analyzed, and key parameters affecting the stability of the DC distribution system are identified. Furthermore, this paper meticulously examines the specific impacts of electrical and control parameter variations on the system’s small-signal stability. Simulation experiments validate the accuracy of the small-signal stability analysis after supercapacitor integration into SPS.

Slow-Interaction Converter-Driven Stability in the Distribution Grid: Small-Signal Stability Analysis With Grid-Following and Grid-Forming Inverters

Slow-Interaction Converter-Driven Stability in the Distribution Grid: Small-Signal Stability Analysis With Grid-Following and Grid-Forming Inverters

Small-Signal Stability Analysis of Three-Phase Four-Wire System Integrated With Single-Phase PV Inverters Considering Phase to Phase Coupling

Small-Signal Stability Analysis of Three-Phase Four-Wire System Integrated With Single-Phase PV Inverters Considering Phase to Phase Coupling

A Small-Signal Stability Analysis Method Based on Minimum Characteristic Locus and Its Application in Controller Parameter Tuning

A small-signal stability analysis method based on minimum characteristic locus (MCL) was recently proposed by the authors. The method is found to be particularly useful in analyzing various oscillation modes in a unified way. The present work continues this line of research. After providing a brief review of the basic principle of MCL method, the paper proceeds to show the mathematical relationship between the stability margin obtained using an MCL method, and that obtained by traditional modal analysis method. Next, a sensitivity analysis procedure is proposed to study quantitatively the effects of control parameters on the stability of the system. Third, the properties of the so-called exciter mode are explained in detail, in particular, explicit formulas of exciter mode frequency and power system stabilizer (PSS) critical gain are derived. Finally, taking PSS4B as an example, a controller parameter tuning method is proposed. The effectiveness and practicability of the proposed method are verified by case studies of Kundur's four-machine-two-area system and China's Yunnan power grid.

Analysis and control of large-signal stability with storage in small scale islanded AC microgrids

The analysis of small-signal stability in AC microgrids has yielded numerous findings. However, investigating large-signal stability remains a major difficulty and has received limited attention in research. The article presents the establishment of a non-linear reduced-order model for small-scale AC microgrids with storage. The model considers the changes in converter structure that occur during large disturbances. Next, we will analyse the system’s stability under large-signal conditions and identify the underlying unstable mechanism. The impact of limitation links on system stability is significant, as they result in structural changes. The proposal of “virtual synchronous damping control” (VSD) aims to improve the stability of AC microgrids by addressing the issues caused by an unstable mechanism. The validation of the proposed analysis and control methods are demonstrated by examining relevant case studies in MATLAB/Simulink.

Low-frequency oscillations damping with doubly-fed induction generators embodying grid-forming control with hardware-in-the-loop simulation

The integration of wind power generation into modern power systems necessitates the development of advanced control strategies to enhance grid stability and reliability. Among these strategies, grid-forming control has emerged as a promising solution, enabling converter-interfaced generation technologies to provide services traditionally supplied by conventional generation. This paper specifically addresses the challenge of low-frequency oscillations damping in power systems incorporating Doubly-Fed Induction Generators embodying grid-forming control. In this paper, two low-frequency oscillations damping strategies are proposed and tested, designed to complement a doubly-fed induction generator grid-forming control strategy. The first, called POD-Q, uses reactive power; while the second, POD-P, acts on the active power injection. Both strategies are analyzed through small-signal stability analysis and experimental testing. For the small-signal stability analysis, a dynamic model of a conventional system with a certain penetration of doubly-fed induction generation has been employed. Experimental results are obtained within a real-time simulation environment, using the hardware-in-the-loop technique to communicate a real controller board with the real-time simulator. The results indicate that the POD-P strategy is more efficient in low-frequency oscillations damping compared to a synchronous generator with a conventional power system stabilizer and also in comparison to the POD-Q strategy. However, both proposed strategies have demonstrated improvements in low-frequency oscillations damping.

Small-Signal Stability Analysis and Improvement in Multi-Converter Grid-Tied System Based on Gerschgorin Disc Theorem

The integration of a large number of voltage source converters (VSCs) into the power grid decreases the small-signal stability of the power system. When several VSCs with different control parameters are simultaneously connected to the power grid to form a multi-converter grid-tied system, the potential destabilizing factors increase. Thus, parameter optimization for stability-weakest parameters that have the greatest impact on the system stability becomes more significant in addressing small-signal stability issues. This paper first proposes a stability evaluation function based on the Gerschgorin disc theorem, which can assess the stability of the multi-converter grid-tied system. Then a parameter sensitivity method is proposed to identify the stability-weakest parameters. Finally, an iterative calculation-based parameter optimization method is developed to regulate the identified stability-weakest parameters. Hence, the parameter optimization technique in this research can improve the system stability without requiring eigenvalue solutions and has the merit of low computational complexity. Simulation results based on both the MATLAB/Simulink (2023a) and the RT-LAB (OPAL-RT 5700) platform of a multi-converter grid-tied system validate the correctness of the theoretical analysis and the effectiveness of the parameter optimization method.

Supercapacitor‐based coordinated synthetic inertia scheme for voltage source converter‐based HVDC integrated offshore wind farm

AbstractA supercapacitor‐based coordinated synthetic inertia (SCSI) scheme for a voltage source converter‐based HVDC (VSC‐HVDC)‐integrated offshore wind farm (OWF) is proposed. The proposed SCSI allows the OWF to provide a designated inertial response to an onshore grid. Under the SCSI scheme, a supercapacitor is added to the DC side of each wind turbine generator via a bidirectional DC/DC converter, varying its voltage along with the offshore frequency to synthesise the desired inertial response. The HVDC grid side VSC employs a DC voltage/frequency droop control to convey the onshore frequency information to DC voltage without communication. Meanwhile, the wind farm side VSC regulates the offshore frequency to couple with the conveyed onshore frequency, considering voltage drop across the DC cables. An offshore frequency switching algorithm is incorporated to avoid undesired SCSI maloperation under offshore faults. The key parameters of the proposed SCSI are optimised through a small signal stability analysis. The effectiveness of the SCSI scheme is evaluated using a modified IEEE 39‐bus test system. The results show that the proposed SCSI scheme can provide required inertial support from WTG‐installed supercapacitors to the onshore grid through the VSC‐HVDC link, significantly improving the onshore frequency stability.

Impedance-Based AC/DC Terminal Modeling and Analysis of the MMC-BTB System

Impedance-based small-signal stability analysis is widely applied in practical engineering with modular multilevel converters (MMCs). However, the deficiencies of existing impedance models (IMs) and the idealized extension for the single MMC influence the analyses in multiterminal systems. In this paper, these gaps are filled by focusing on an MMC-based back-to-back system. To obtain the steady-state harmonics of the system, a numerical method is initially proposed based on Newton–Raphson iteration in the frequency domain. Then, by substituting the shared terminal dynamics with active or passive devices, theoretical AC/DC IMs based on typical control loops with pure time delays are directly established via multiharmonic linearization. Further aided by the derived IMs, two neglected aspects in the current literature are investigated, including the influence of power transformers on low-frequency impedance characteristics and the rationality of using simplified IMs for high-frequency resonance studies. The stability of interlinking systems needs to be comprehensively analyzed at both AC and DC terminals. The analyses help to position the instability source, obtain the stability margin, and guide the supplementary control strategy. All IMs and analyses are verified via frequency scans and simulations in PSCAD.

Small-Signal Stability Analysis of MMC-HVDC System Based on Hybrid Passivity

Small-Signal Stability Analysis of MMC-HVDC System Based on Hybrid Passivity

Research on power system small signal stability analysis and correction based on LightGBM algorithm

Research on power system small signal stability analysis and correction based on LightGBM algorithm

Probabilistic Small Signal Stability Analysis with Wind Power Based on Maximum Entropy Theory

The probability parameters for the small signal stability in a system are studied to quantify the impact of uncertain wind power on system stability. With the increase in the scale of wind power access systems, how to more efficiently and accurately obtain the probability of small signal stability is worthy of further investigation. Therefore, this work proposes an analysis method of probabilistic small signal stability (PSSS) based on maximum entropy (ME) theory for studying power systems with uncertain wind power from doubly fed induction generators (DFIGs). Firstly, the sensitivity of the eigenvalues to the variable power is obtained by linearization. Then, when the probability characteristic for wind is known, the probability characteristic for the system critical eigenvalues is approximated using the ME method and the derived sensitivity. The proposed ME method is used in the analysis of the PSSS for power systems with different wind power penetration scales in case studies. Compared to the probability function for the eigenvalue obtained by the conventional series expansion method, the proposed method has excellent accuracy and sufficient efficiency in analysing the PSSS for a system with uncertain wind power.

Advanced Single-Phase PLL-Based Transfer Delay Operators: A Comprehensive Review and Optimal Loop Filter Design

In recent years, several research works have addressed and developed the phase-locked loop (PLL) in single-phase grid-connected converters with different structures and properties. Each has merits and demerits, such as a complex structure, high computational burden, and slow transient response. This paper aims to comprehensively review advanced single-phase PLLs based on transport delay operators to realize signal orthogonality. A deep insight into the PLLs’ small-signal modeling, main characteristics, stability analysis, and loop filter design are provided in this paper. The main advantages and drawbacks are explained for each type of PLL in terms of different performance indexes, such as settling time, estimation error, and ripples in the estimated grid information. This paper also aims to provide optimal tuning and design of the loop filter gains from the large-signal model point of view, including all the nonlinearities, adopting the stochastic optimization method. All simulations are implemented using the MATLAB/Simulink 2018b environment to validate all theoretical analyses of this paper. The sampling and nominal frequencies are set to be 100 kHz and 50 Hz throughout all the simulation studies.

Real-time validation of RoCoF – Enhancing advanced coordinated control strategy for voltage unbalance mitigation implementing demand side management

The absence of rotational masses in converter-interfaced microgrids has led to a reduction in system inertia. As a consequence, the stability of modern microgrids is at risk, especially in the case of unbalanced systems, resulting in significant issues such as an increase in the rate of change of frequency (RoCoF), disturbances in the nominal frequency, and unfavourable voltage unbalances. This research article introduces an advanced concept centered around a virtual synchronous generator designed to enhance RoCoF performance. This is achieved through the implementation of a positive and a negative (PN) - sequence controller scheme in coordination with demand side management to ensure that RoCoF remains within the limit of 2 Hz/s according to IEEE Standard 1547–2018 and the voltage unbalance factor (VUF) adheres to the established standard of 2 % according to IEC 61,000–3–13. The behaviour of the proposed control strategy during transient conditions has also been demonstrated. The framework of the virtual synchronous generator is utilized in this paper to demonstrate the influence of damping coefficient and moment of inertia on the low inertia system's frequency and transient response where it has been established that greater inertia and damping are essential for their enhancement. The study also conducts a small signal stability analysis to assess the effects of various parameters on system stability. Furthermore, the real-time efficacy of the coordinated control methodology based on virtual inertia has been experimentally verified using OPAL-RT simulator. The simulation and experimental results, both provide evidence of the successful performance of the proposed approach in realizing efficient RoCoF enhancement and VUF mitigation.