Small Signal Stability Problem Research Articles

Optimal Allocation Strategy of Virtual Inertia and Damping for Improving the Small-signal Stability

The application of the virtual synchronous generator (VSG) control technology to engage the inertia response of renewable energy generation systems is an effective means of coping with the problem of weak inertia in power systems. To deal with the problem of small-signal stability in the weak inertia power system, this paper studies how the strength of virtual inertia and damping affect the small-signal stability, and proposes an optimal allocation strategy of virtual inertia and damping for improving the small-signal stability. The optimal allocation model of virtual inertia is constructed to minimize the energy imbalance of the system under small-signal by selecting the virtual inertia and damping as optimization variables. Regarding the aforementioned model, the evolutionary algorithm is used to obtain the optimal allocation of virtual inertia and damping. Simulations on a virtual synchronized microgrid system show the effectiveness of the proposed strategy in improving small-signal stability.

Analysis of Additional Damping Control Strategy and Parameter Optimization for Improving Small Signal Stability of VSC-HVDC System

The voltage source converter based high voltage direct current (VSC-HVDC) system is based on voltage source converter, and its control system is more complex. Also affected by the fast control of power electronics, oscillation phenomenon in wide frequency domain may occur. To address the problem of small signal stability of the VSC-HVDC system, a converter control strategy is designed to improve its small signal stability, and the risk of system oscillation is reduced by attaching a damping controller and optimizing the control parameters. Based on the modeling of the VSC-HVDC system, the general architecture of the inner and outer loop control of the VSC-HVDC converter is established; and the damping controllers for DC control and AC control are designed in the phase-locked loop and the inner and outer loop control parts respectively; the state-space state model of the control system is established to analyze its performance. And the electromagnetic transient simulation model is built on the PSCAD/EMTDC simulation platform to verify the accuracy of the small signal model. The influence of the parameters of each control part on the stability of the system is summarized. The main control parts affecting stability are optimized for the phenomenon of oscillation due to changes in operation mode occurring on the AC side due to faults and other reasons, which effectively eliminates system oscillation and improves system small signal stability, providing a certain reference for engineering design.

Dynamics and Stability of Power Systems With High Shares of Grid-Following Inverter-Based Resources: A Tutorial

Electric power systems worldwide are undergoing a foundational transition from mechanical-backed generation technologies dominating the resource mixture, primarily synchronous generators, into a hybrid system consisting of periods of a preponderance of power electronics-backed generation technologies, primarily solar photovoltaics and wind power plants and battery storage systems. Almost all current inverter-based resources integrated into bulk power systems are grid-following technology, and there exists a knowledge gap concerning the impacts of large-scale integration of grid-following inverters on power system dynamics, which is a critical aspect of power system planning and operation. This paper serves as a tutorial and addresses the stability and reliability challenges pertinent to the integration of grid-following interfaced inverter-based resources. While considering both small-signal and large-signal stability problems, it demonstrates and explains the underlying interrelated dynamics of electric angle, frequency, and voltage, as well as the impacts that system inertia can have on system stability. Industry-grade electromagnetic transient simulations in Power Systems Computer-Aided Design (PSCAD) are utilized to demonstrate the concepts presented in this paper, and all the computer models have been made available to the public at no cost.

Assessing Maximal Capacity of Grid-Following Converters With Grid Strength Constraints

The increasing penetration of renewable resources via power-electronic converters is turning the modern power grid into a multi-converter system (MCS). In an MCS, most renewable resources currently use grid-following converters (GFLCs) for grid synchronization. The increasing integration of renewable resources via GFLCs can cause small-signal stability problems, especially under weak grid conditions. One way to prevent the stability issue is limiting the capacity of GFLCs in an MCS. Thus, it is important to assess the maximal capacity of GFLCs in the MCS while considering small signal stability constraints (SSSCs). This assessment is challenging due to 1) the complexity of assessing the small signal stability resulting from the complicated interaction between the power network and a large number of GFLCs, especially for a heterogeneous GFLCs with unknown inner parameters; 2) the difficulty of finding the optimal solution to the relevant nonlinear optimization problem for maximal capacity assessment. To address these challenges, this paper proposes a semi-definite programming (SDP)-based method to assess the maximal capacity of GFLCs with SSSCs. In the proposed method, we first formulate the SSSCs based on the generalized short-circuit ratio (gSCR), which is a grid strength metric that can significantly reduce the complexity of quantifying small signal stability in an MCS. Then, we convert the formulated gSCR-based nonlinear optimization problem into an SDP that can conveniently find the optimal solution to the maximal capacity of GFLCs and their optimal allocations in the MCS. The efficacy of the proposed method is demonstrated on a 39-bus test system and a practical wind power system.

Computing the Load Margin of Power Systems Using Crow Search Algorithm

Power system operation centers require knowledge of the load level where the system may present instability characteristics. It is common practice to calculate the load margin where the system can collapse in voltage respecting a direction of load growth. However, the increase in load can also cause low damped oscillation modes to appear and cause small-signal stability problems of power systems. This research proposes a Crow Search Algorithm-based method to calculate the load margin of power systems considering small-signal stability and voltage stability requirements. To solve the problem of good initial conditions for the search problem, the Sine Cosine Algorithm was used. The proposed method was evaluated in the IEEE 39-bus system and the results achieved show the effectiveness of the method in determining the load margins quickly.

Comprehensive small-signal stability analysis for master hybrid MMC connected with strong and weak AC systems

The small-signal stability problem of power electronic converters has always been a critical concern for safe operation. This paper conducts a comprehensive analysis of the small-signal stability for the hybrid modular multilevel converter (MMC), which is promising in the application of future over-head-line high-voltage-direct-current transmission. The impacts of the strong and weak AC system connection are comparatively researched through eigenvalue-based analysis. The newly emerging factors that hamper the stability are identified for the weak AC system integration. The work in this paper provides valuable guidance for robust control parameter configuration of the hybrid MMC.

An Estimation-Based Solution to Weak-Grid-Induced Small-Signal Stability Problems of Power Converters

The large-scale deployment of grid-tied power electronic converters in renewable generation, electric motor drives, and energy storage systems speeds up the global energy transition. However, the stability problems faced by power converters in weak grids, which feature large and variable grid impedances, stand as a serious challenge that has puzzled the power electronic community for more than 15 years. Existing solutions to weak-grid-induced small-signal stability problems modify system and/or control parameters so that stable operation is achieved under a certain condition. However, such solutions are problem and application-specific. Therefore, the solutions can hardly be generalized to various operating conditions or stability problems. As such, this article proposes an estimation-based solution that targets multiple weak-grid-induced small-signal stability problems, particularly for converters with grid-supportive services. The essence of the proposed solution lies in the accurate estimation of real grid information rather than the point-of-common-coupling information. For implementation, Kalman filters serve as an estimator. Subsequently, the estimated information is used to design controllers, such as voltage droop, that allow for stable power conversion. Finally, simulation and experimental results validate the effectiveness and generality of the proposed solution.

On the solution of small signal stability of power systems by a block-Krylov subspace algorithm

Iterative methods built on Krylov subspaces for the computation of eigenvalues in small-signal stability problems of power systems have been little explored to date. This computation is one of the most challenging and time-consuming part of the simulation, especially for matrices with clustered eigenvalues and having multiplicity greater than one (named here as CME matrices). This paper proposes a block-Krylov algorithm built on the augmented block Householder Arnoldi method to compute eigenvalues in small-signal stability problems with CME matrices, exploring enlarged subspaces that normally result in less steps to achieve convergence. Both efficiency and robustness are examined through numerical experiments using two power systems and the conventional Arnoldi (unblock) and QR decomposition methods. The results indicate that the block-Krylov algorithm performs better for CME matrices than the other two. On the other hand, it is no longer as efficient on matrices with none or just few clustered and (or) multiple eigenvalues. The proposed block-Krylov algorithm has never been tested in the small-signal stability problem.

The Small-Signal Stability of Offshore Wind Power Transmission Inspired by Particle Swarm Optimization

Voltage source converter-high-voltage direct current (VSC-HVDC) is the mainstream technology of the offshore wind power transmission, which has been rapidly developed in recent years. The small-signal stability problem is closely related to offshore wind power grid-connected safety, but the present study is relatively small. This paper established a mathematical model of the doubly fed induction generator (DFIG) integrated into the IEEE9 system via VSC-HVDC in detail, and small-signal stability analysis of offshore wind farm (OWF) grid connection is specially studied under different positions and capacities. By selecting two load nodes and two generator nodes in the system for experiments, the optimal location and capacity of offshore wind power connection are obtained by comparing the four schemes. In order to improve the weak damping of the power system, this paper presents a method to determine the parameters of the power system stabilizer (PSS) based on the particle swarm optimization (PSO) algorithm combined with different inertia weight functions. The optimal position of the controller connected to the grid is obtained from the analysis of modal control theory. The results show that, after joining the PSS control, the system damping ratio significantly increases. Finally, the proposed measures are verified by MATLAB/Simulink simulation. The results show that the system oscillation can be significantly reduced by adding PSS, and the small-signal stability of offshore wind power grid connection can be improved.

Small signal stability analysis due to the development of renewable energy generators in Sulawesi electricity

The problem of small signal stability is one of the main problems in the current power system because the purpose of operating the system is close to the limit. Small signal stability is important because small disturbances in the form of non-dampened electromechanical oscillations have limited the power flow limit in a steady state, so the oscillation will affect the operating system in a security and quality review. The entry of renewable energy in the Sulawesi interconnection system certainly has an impact on system stability and the emergence of electromechanical oscillations. An estimated 75 MW of power will come from the PLTB that will be built in Sidrap and 62.5 MW in Jeneponto. This study aims to analyze small signal stability due to the development of EBT generators on the Sulawesi interconnection system through eigenvalue characteristics and participation factors. The PLTB that will be integrated in the Sulawesi system certainly affects power flow which has an impact on small signal stability.

Modeling and Control Parameters Design for Grid-Connected Inverter System Considering the Effect of PLL and Grid Impedance

Small-signal stability problems often occur when the inverter for renewable energy generation is connected to weak grid. A small-signal transfer function integrated model reflecting the interaction of grid impedance, phase locked-loop (PLL), and current control loop is established in this paper. Based on the established model, the oscillation mechanism of the grid-connected inverter system is revealed: the inductance current flowing through the grid impedance can produce a voltage disturbance, which will eventually affect the inductance current through PLL and current control loop. Therefore, the loop composed of the grid impedance and PLL can easily lead to the oscillation of the grid-connected inverter system under weak grid condition. To suppress the oscillation, a control parameters design method of the grid-connected inverter is proposed. Without changing the control method, the proposed control parameters design method can ensure the stable operation of the grid-connected inverter system under the very weak grid condition when the short-circuit ratio (SCR) is 2. Finally, the experimental results verify the correctness of the stability analysis and the effectiveness of the control parameters design method proposed in this paper.

Optimal Fractional Order BELBIC to Ameliorate Small Signal Stability of Interconnected Hybrid Power System

The small signal stability of power systems integrated with fallback large‐scale distributed energy resources is of utmost importance during the perturbation conditions. Among the various renewable resources in power systems: photovoltaic, fuel cell, wind turbine, diesel engine, aqua electrolyser, battery, ultra‐capacitor, and flywheel is becoming more favored in last decades. AGC, a main control system of frequency modulation, must correctly alleviate the low frequency oscillations caused by the perturbation and variable output power of renewable resources. In this regard, FOBELBIC is here introduced to enhance the damping capability of AGC. Since both the frequency and tie‐line power oscillations must be concomitantly alleviated, the small signal stability problem has been multi‐objectively formulated. Due to the exploration capability of MOALO, it has been chosen to extract the optimal parameters of FOBELBIC. Furthermore, MOPSO, MOBA, and NSGA‐II have been studied to demonstrate the capability of MOALO. To verify and validate the damping performance of suggested controller, it has been evaluated in three‐area reconstructed power system under the load perturbations as well as wind speed and sun radiation variations, and at the same time compared with BELBIC and PID controllers. Finally, the simulation results have evidently confirmed the damping the performance of MOALO‐based FOBELBIC to enhance the small signal stability of hybrid power system. © 2019 American Institute of Chemical Engineers Environ Prog, 38:e13146, 2019

The impact of DG’s location on the small signal stability of the distribution network

The distribution network has been integrated with more and more distributed generations. Most of these generations are inverter based photo-voltaic plant or DFIG based wind farm. As the proportion of these renewable energies goes high, the stability problems, especially the small signal stability problems gain attention from researchers. Literatures have conducted on the single machine infinite bus system of them, focusing mostly on their dynamic characteristics. This paper analyses the impact of DG’s location on the small signal stability of the distribution network, which includes DGs, network and dynamic load. The conclusion is drawn from the modal analysis, and is verified by time domain simulation.

Small signal stability criteria for descriptor form power network model

ABSTRACT This work considers the problem of small signal stability of a lossless power network by representing its mathematical model in descriptor form. A stability criterion is derived by constructing two orthogonal projectors corresponding to the system model. These projectors are then used in (i) constructing a Lyapunov function and (ii) deriving another criterion to identify the presence of poles (finite) of the system to the right of a given vertical line in the complex plane. The latter criterion is required to analyse whether the dominant low-frequency electro-mechanical modes, that cause oscillatory instability in the power network, settle down within a specified time limit. Using the derived criteria, linear matrix inequality feasibility problems are formulated to analyse small signal instability and oscillatory instability. Power network examples, including an IEEE benchmark system, are considered to demonstrate the developed approach.

Harmonic Stability in Power Electronic-Based Power Systems: Concept, Modeling, and Analysis

The large-scale integration of power electronic-based systems poses new challenges to the stability and power quality of modern power grids. The wide timescale and frequency-coupling dynamics of electronic power converters tend to bring in harmonic instability in the form of resonances or abnormal harmonics in a wide frequency range. This paper provides a systematic analysis of harmonic stability in the future power-electronic-based power systems. The basic concept and phenomena of harmonic stability are elaborated first. It is pointed out that the harmonic stability is a breed of small-signal stability problems, featuring the waveform distortions at the frequencies above and below the fundamental frequency of the system. The linearized models of converters and system analysis methods are then discussed. It reveals that the linearized models of ac–dc converters can be generalized to the harmonic transfer function, which is mathematically derived from linear time-periodic system theory. Lastly, future challenges on the system modeling and analysis of harmonic stability in large-scale power electronic based power grids are summarized.

Coordination of Adaptive Neuro Fuzzy Inference System (ANFIS) and Type-2 Fuzzy Logic System-Power System Stabilizer (T2FLS-PSS) to Improve a Large-scale Power System Stability

<p align="LEFT">Intelligent control included ANFIS and type-2 fuzzy (T2FLS) controllers grown-up rapidly and these controllers are applied successfully in power system control. Meanwhile, small signal stability problem appear in a large-scale power system (LSPS) due to load fluctuation. If this problem persists, and can not be solved, it will develop blackout on the LSPS. How to improve the LSPS stability due to load fluctuation is done in this research by coordinating of PSS based on ANFIS and T2FLS. The ANFIS parameters are obtained automatically by training process. Meanwhile, the T2FLS parameters are determined based on the knowledge that obtained from the ANFIS parameters. Input membership function (MF) of the ANFIS is 5 Gaussian MFs. On the other hand, input MF of the T2FLS is 3 Gaussian MFs. Results show that the T2FLS-PSS is able to maintain the stability by decreasing peak overshoot for rotor speed and angle. The T2FLS-PSS makes the settling time is shorter for rotor speed and angle on local mode oscillation as well as on inter-area oscillation than conventional/ ANFIS-PSS. Also, the T2FLS-PSS gives better performance than the other PSS when tested on single disturbance and multiple disturbances.</p>

Stability Analysis of Aircraft Power Systems Based on a Unified Large Signal Model

Complex power electronic conversion devices, most of which have high transmission performance, are important power conversion units in modern aircraft power systems. However, these devices can also affect the stability of the aircraft power system more and more prominent due to their dynamic and nonlinear characteristics. To analyze the stability of aircraft power systems in a simple, accurate and comprehensive way, this paper develops a unified large signal model of aircraft power systems. In this paper, first the Lyapunov linearization method and the mixed potential theory are employed to analyze small signal and large signal stability, respectively, and then a unified stability criterion is proposed to estimate small and large signal stability problems. Simulation results show that the unified large signal model of aircraft power systems presented in this paper can be used to analyze the stability problem of aircraft power systems in an accurate and comprehensive way. Furthermore, with simplicity, universality and structural uniformity, the unified large signal model lays a good foundation for the optimal design of aircraft power systems.

Alleviation SSR and Low Frequency Power Oscillations in Series Compensated Transmission Line using SVC Supplementary Controllers

In this work, supplementary sub-synchronous damping controllers (SSDC) are proposed for damping sub-synchronous oscillations in power systems with series compensated transmission lines. Series compensation have extensively been used as effective means of increasing the power transfer capability of a transmission lines and improving transient stability limits of power systems. Series compensation with transmission lines may cause sub-synchronous resonance (SSR). The eigenvalue investigation tool is used to ascertain the existence of SSR. It is shown that the addition of supplementary controller is able to stabilize all unstable modes for T-network model. Eigenvalue investigation and time domain transient simulation of detailed nonlinear system are considered to investigate the performance of the controllers. The efficacies of the suggested supplementary controllers are compared on the IEEE first benchmark model for computer simulations of SSR by means of time domain simulation in Matlab/Simulink environment. Supplementary SSDC are considered in order to compare effectiveness of SSDC during higher loading in alleviating the small signal stability problem.

Self-Tuning Control for Synchronous Machine Stabilization

A small-signal stability problem of a synchronous generator influencing a power grid was studied. A thorough theoretical analysis of a simplified linearized model of the synchronous generator connected to an infinite bus was carried out. The described analysis pointed out disadvantages of the conventional linear power system stabilizer. In contrast to the conventional, an original self-tuning power system stabilizer was developed. This stabilizer compacts a linear quadratic regulator and a recursive least square identification method. The study involving numerical simulations and laboratory experiments reveals encouraging results with displayed advantages and feasibility of this novel approach in considered applications. DOI: http://dx.doi.org/10.5755/j01.eee.21.4.12773

New Eigenvalue Method for Power System Stability Analysis

The most widely adopted methodology for the analysis of power system small signal stability relies on the approach in the frequency domain, i.e. to linearize the system equation to obtain a linear model as well as the system matrix of which the eigenvalues can be calculated to determine the system stability. However, we often have high order of system matrix and thus it will be undesirable to calculate and analyze all the system eigenvalues. This paper is to explore the problem of small signal stability for power system and the main purpose is to find out the worst-damped mode of system eigenvalues and thus to alleviate the effort for computing and analyzing all the system eigenvalues. The developed algorithm is to be tested on a sample power system to validate the feasibility of the proposed new eigenvalue calculation method.