Small Signal Stability Research Articles

Design and Fabrication of an Isolated Two-Stage AC–DC Power Supply with a 99.50% PF and ZVS for High-Power Density Industrial Applications

Power quality in terms of power factor (PF), efficiency, and total harmonic distortions (THDs) is an important consideration in power supplies designed for 5G telecom servers. This paper presents a different magnetic parts design and manufacturing techniques of power supplies, design and selection criteria of switching elements as well as the optimal design of control loops based on small-signal stability modeling and an appropriate stability criterion. The designed telecom power supply consists of the power factor correction (PFC) stage to increase the input power factor and the isolated phase-shift pulse width modulation (PWM) zero-voltage switching (ZVS) DC–DC converter stage to regulate the supply voltage to the specified load value while maintaining a high conversion efficiency. A two-stage outdoor telecom power supply with a power rating of 2 kW was designed and fabricated on a printed circuit board (PCB). The distinct two-stage power components of the power supply were subjected to loss analysis. Furthermore, PSIM simulation and experiments were used to demonstrate the total harmonic distortions (THDs), voltage ripples, power efficiency, and PF performance of the supply current for the proposed power supply under various operating situations. This work produces an industrial high power density power supply with a high PF, low THD and high conversion efficiency which is suitable for telecom power server applications.

Stability analysis and parameter configuration of parallel virtual synchronous generators in microgrid

The current small-signal stability analysis and parameter selection of converters that mimic synchronous generators usually ignore some dynamic characteristics and the changes of steady-state operating points for simplicity. It could only judge the trend of small-signal stability and the analysis result was not accurate enough. Firstly, this paper established a small-signal model that mimics synchronous generators by connecting two isolated converters in parallel, the eigenvalues of the system were calculated and some of their physical meanings were obtained. Following that, in order to demonstrate the relationship of eigenvalues and state variables, the participation factor was calculated. Considering that, there will be some variability of the operating points with the parameters variation. As a function of the system settings, numerous root locus plots were created. For individual eigenvalue close to the real axis, in order to reveal the contribution of different parameters to the oscillation patterns, a separate eigenvalue sensitivity analysis was performed. The rules of the influence are essential to guide the design of parameters and their optimization of isolated converters connected in parallel that mimic synchronous generators.

Power system static and dynamic security studies for the 1st phase of Crete Island Interconnection

The island of Crete is currently served by an autonomous electrical system being fed by oil-fired (Heavy fuel or light Diesel oil) thermal power plants and renewables (wind and PVs). The peak load and annual electric energy consumption are approximately 600 MW and 3 TWh respectively; wind and photovoltaic parks contribute approximately 20% of the electricity needs of the island. Due to the expensive fuel used, the Cretan power system has very high electric energy generation cost compared to the Greek mainland. On the other side the limited size of the system poses severe limitations to the penetration of renewable energy sources, not allowing to further exploit the high wind and solar potential of the island. According to the Ten Year Network Development Plan (TYNDP) of the Greek TSO (Independent Power Transmission Operator S.A. IPTO S.A.), the interconnection of Crete to the mainland Transmission System of Greece will be realized through two links: A 150 kV HVAC link between the Peloponnese and the Crete (Phase I) and a HVDC link connecting the metropolitan area of Athens with Crete (Phase II). The total length of submarine and underground cable of the HVAC link will be approximately 174km; it is at the limits of the AC technology and the longest and deepest worldwide at 150 kV level. A number of studies have been conducted by a joint group of IPTO and Hellenic Electricity Distribution Network Operator (HEDNO) for the design of this interconnection. This paper presents briefly the power system static and dynamic studies conducted for the design of the AC link and its operation. Firstly, the paper presents the main results of the static security study regarding the calculation of the maximum power transfer capability of the link and the selection of the reactive power compensation scheme of the cable. Results from dynamic security analysis studies are also presented. The small-signal stability analysis concludes that a new (intra-area) electromechanical oscillation is introduced to the National System after the interconnection. The damping of the electromechanical oscillations is sufficient; however the operation of power system stabilizers at power plants located both at the mainland and at Crete power system can increase significantly the damping of important oscillation modes. Finally with respect to the risk of loss of synchronism after a significant disturbance in the system of Crete, such as a three-phase fault (“transient stability”)- enough safety margin is estimated by means of Critical Clearing Time calculations.

Singular Perturbation and Small-Signal Stability for Inverter Networks

This article examines small-signal stability of electrical networks composed dominantly of three-phase grid-following inverters. We show that the mere existence of a high-voltage power flow solution does not necessarily imply small-signal stability; this motivates us to develop a framework for stability analysis that systematically acknowledges inverter dynamics. We identify a suitable time-scale decomposition for the inverter dynamics, and using singular perturbation theory, obtain an analytic sufficient condition to verify small-signal stability. Compared to the alternative of performing an eigenvalue analysis of the full-order network dynamics, our analytic sufficient condition reduces computational complexity and yields insights on the role of network topology and constitution as well as inverter-filter and control parameters in small-signal stability. Numerical simulations for a radial network validate the approach and illustrate the efficiency of our analytic conditions for designing and monitoring grid-tied inverter networks.

A method for monitoring the load margin of power systems under load growth variations

The load margin is an important safety measure used in operation centers to assess the voltage stability of power systems. Usually this measure is calculated considering a single load growth direction and voltage stability requirements. However, oscillation modes with low damping rates can compromise the small-signal stability of power systems and different load growth directions can also affect load margin estimates. Thus, these two factors must be considered to provide adequate load margin for power system operation. This paper proposes a load margin monitoring scheme based on Artificial Neural Networks (ANN) considering voltage stability requirements and small-signal stability and load growth variations. Thus, the power system operator will have real-time load margin information considering voltage stability requirements and small-signal stability requirements. ANN uses as input data the voltage magnitude and voltage angle measurements provided by Phasor Measurement Units (PMUs) installed in system buses. A method to select a reduced set of buses for the monitoring system is proposed and evaluated. Case studies are presented and the results achieved provide indications of the applicability of the proposed scheme in the real-time operation of power systems.

Accurate Small-Signal Modeling and Stability Analysis of Wide-Input Buck Converter Considering Modulation Waveform Ripples

Buck converters are widely used in consumer electronics, electric vehicles, and dc microgrids. Small-signal models are necessary tools to design high-quality controllers. However, most of them neglect modulation waveform ripples, which introduces significant errors under high-bandwidth controls. Recently, two models explain the influences of nondifferentiable modulation waveform ripples by their left-side derivatives at crossing points. However, this conclusion is built on the premise that infinite sideband components caused by switching have been considered, which largely complicates these models. The accurate small-signal model with finite sideband components is proposed for nondifferentiable modulation waveform ripples in this article. Based on it, the stable working region and control design of wide-input high-bandwidth Buck converters are talked about. Simulations and experiments validate the accuracy and effectiveness of the proposed model.

Inertia Emulation and Fast Frequency-Droop Control Strategy of a Point-to-Point VSC-HVdc Transmission System for Asynchronous Grid Interconnection

This article proposes a novel inertia emulation and fast frequency-droop (IEFF) control strategy for a point-to-point voltage source converter-based high voltage direct current (VSC-HVdc) transmission system. It allows asynchronous ac grid synchronization in forms of inertial and fast frequency-droop responses provided to “both” sides of the VSC-HVdc interconnected grids, different from the historically reported schemes only providing these responses to one grid. Under the IEFF scheme, the power-regulating VSC (PR-VSC) station emulates a synchronous generator directly through its active power control, whereas the dc-voltage-regulating VSC (DR-VSC) station employs a dc voltage/frequency droop control to convey its connected grid frequency communication-free to the remote PR-VSC for inertial and fast frequency-droop oriented power variations. To avoid the clash of the PR-VSC IEFF and DR-VSC IEFF control under simultaneous frequency events in the asynchronous grids, a novel frequency support mode selection scheme is designed to effectively prioritize the IEFF support with a higher frequency gradient. The key parameters of the IEFF controller are optimized through small signal stability analysis. The effectiveness of the proposed IEFF scheme is verified through controller hardware-in-the-loop experiments. The results show that the proposed IEFF scheme effectively promotes synchronization and enhances overall frequency stability for the two interconnected asynchronous grids.

Optimal power flow with small signal stability constraints

En grandes sistemas de potencia interconectados el problema de estabilidad ante pequeños disturbios recibe atención debido a las oscilaciones ocasionales o a la variación en la demanda del mismo, para esto se incorpora al problema de optimización matemática de flujos óptimos de potencia una restricción de estabilidad ante pequeños disturbios, la cual se basa en el teorema de Lyapunov modelada como un problema de programación semidefinida, la cual dicta que su matriz P sea positiva definida y simétrica para garantizar la estabilidad del sistema, la solución se hace mediante el método de optimización matemática punto interior con ayuda del software AMPL, A Modeling Language for Mathematical Programming, donde se hará la simulación sobre el sistema de prueba del Institute of Electrical and Electronics Engineers (IEEE), Western System Coordinating Council o WSCC que consta de 9 nodos y 3 máquinas modificado para este propósito.

Analysis of Internal Control Loop Interactions in VSCs: An Individual Design Perspective

This paper addresses the interactions among the control loops of voltage-sourced converters (VSCs) embedded in high-voltage direct current(HVDC) systems and the impact of these interactions on the performance of individual control loops. Furthermore, this paper proposes a method to design the individual control loops, rather than the interconnected control system, such that the overall system stability is ensured in the presence of interactions. This paper addresses three aspects of the impact of control loop interactions on the overall control system of the VSC including stability, transient response, and steady-state response. To illustrate the impact of interactions on the VSC small-signal stability, stability regions of the interconnected control loops are obtained and compared against those of the various individual control loops. Then, a novel formulation of the VSC stability criterion is presented, and the small-gain theorem is utilized to determine a range of stabilizing gains for the interconnected control system. Moreover, new indices using the infinity norm are introduced to evaluate the impact of interactions on the transient response of the VSC. Finally, the DC gain of a certain set of transfer functions is used to assess the impact of control loops interactions on the set-point tracking capability of the VSC

A Nonlinear Adaptive Stabilizing Control Strategy to Enhance Dynamic Stability of Weak Grid-Tied VSC System

Large scale renewable energy systems interfaced with voltage source converters (VSCs) experience several challenging issues when integrated to weak grids. One of the specific issue i.e. control loop interaction of vector-controlled VSC under high grid impedance leads to several instability mechanism ultimately resulting in unwanted tripping of the VSC unit. As a countermeasure, a unique nonlinear adaptive stabilizing control (NASC) technique has been proposed in this paper to enhance the dynamic stability of the VSC during such scenarios. A small-signal model is developed first to examine the instability mechanism of VSC connected to weak grids under abnormal operating conditions and varying set points of the power controller. The dominant modes are identified from the analysis and a stabilizing controller is developed based on adaptive dynamic surface control philosophy for enhancing its stability. The proposed controller has been proved to be uniformly ultimately bounded using Lyapunov analysis. Besides, the stabilizing mechanism of VSC is analyzed with the proposed controller by performing small-signal stability analysis of the entire system. The efficacy of the proposed control scheme is demonstrated by performing numerical simulations in MATLAB 2017a and conducting experimental validations in controller-hardware-in-the Loop (CHIL) platform.

Self-Synchronizing Cascaded Inverters With Virtual Oscillator Control

In this article, we introduce a decentralized communication-free control strategy to synchronize and control an arbitrary number of series-connected inverters delivering power to islanded loads. The proposed approach reduces wiring complexity, streamlines installation, and eliminates single points of failure in cascaded inverter systems. We focus on three-phase power stages that are composed of three full-bridge inverters on the ac side. The proposed controller at each module takes the form of a digitally implemented virtual oscillator controller (VOC), which uses the inverter current as a feedback signal and in turn modulates the ac voltage amplitude and frequency. Power and voltage sharing among modules can be adjusted on-the-fly via oscillator setpoints at each converter controller. We take advantage of the superior transient performance of VOC over the conventional droop-based controllers, which in turn yields a high-performance series-connected inverter system with fast responsiveness. A system model is put forward to analyze small-signal stability and provide a control design framework. Finally, experiments on a system of five series-connected inverters substantiate the proposed approach.

A Novel Online Inductance Identification of Traction Network and Adaptive Control Method for Cascaded H-Bridge Converter

The grid-tied cascaded H-bridge (CHB) converter may become unstable, especially for the traction onboard application where the grid impedance may gradually vary as the train moves. In order to overcome this weakness, a small-signal stability-based adaptive control strategy is proposed in this article, where the parameter of the current-inner-loop controller is adaptively regulated according to the online grid inductance identification (GII) result. In the proposed control structure, there is only one control parameter needed to be regulated online, which is based on the estimated value of the grid inductance. In this article, the grid inductance is estimated by injecting the specific harmonic current. With the corresponding harmonic current regulator, stable and sustained harmonic current can be injected, which is beneficial to mitigate the fierce fluctuation of the GII result. The GII algorithm is made up of three parts, including the analog low-pass filter, the sliding discrete Fourier transform, and the digital composite filter, which can suppress the switching noise, the low-frequency grid harmonics, and the grid frequency deviation. With the proposed adaptive control strategy, the CHB can ensure small-signal stability wherever it is connected. All these theoretical analyses are verified by the experiment.

Small-Signal Modeling and Controller Parameters Tuning of Grid-Forming VSCs With Adaptive Virtual Impedance-Based Current Limitation

The adaptive virtual impedance (VI) control emerges as an attractive solution to limit the current of grid-forming voltage-source converters (GFM-VSCs) during grid faults. Yet, the adaptive VI-based current limitation relies on the detection of the current magnitude, which introduces nonlinear dynamics that challenges the controller parameters tuning of GFM-VSCs. This article develops the small-signal model of GFM-VSCs with adaptive VI-based current limitation, from which, the dynamic impact of the adaptive VI is explicitly revealed. Considering such impact, a holistic controller parameters tuning method for GFM-VSC is proposed to guarantee the small-signal stability of the system. Simulation and experimental tests are performed to verify the effectiveness of the theoretical analysis and the proposed parameters tuning method.

Intelligent Coordinated Control of PID-SMES and AVR based on Hybrid PSO-DE for Small Signal Stability Enhancement

Dynamic disturbances in the electric power system occur due to changes in the load that can change important parameter values, this results in loss of synchronization in multi-machine power systems, so a controller in the power system is needed to maintain a stable condition during dynamic disturbances. In this final project, a Proportional Integral Differential (PID)-Superconducting Magnetic Energy Storage (SMES) controller is useful for supplying or absorbing active power when there is a load change so that the frequency can be maintained continuously, and an Automatic Voltage Regulator (AVR) is in charge of regulating the voltage on the system. The PID controller in SMES is useful for setting the output parameters of SMES. Hybrid Differential Evolution - Particle Swarm Optimization (DE-PSO) optimization method is used to optimize the oscillation damping process. The results indicate that the use of PID SMES and AVR optimized using the DE-PSO hybrid algorithm has a better response. In the Suralaya generator unit, the overshoot is -0.0001395 pu, and the settling time is 12.4 seconds by using the optimal controller. Meanwhile, when it is not using the additional controller, the overshoot is -0.0004228 pu, and the settling time is more than 16 seconds.

Dynamic Performance Evaluation of the Secondary Control in Islanded Microgrids Considering Frequency-Dependent Load Models

Performance analysis is challenging in modern power distribution networks due to the increasing penetration of distributed energy resources (DERs) interfaced by voltage source converters (VSCs). Parameter uncertainty, black-box models of the components, and low inertia are some of the issues that must be addressed. The latter can represent high vulnerabilities to sudden load changes in a microgrid (MG). Additionally, the islanded operation represents a challenge for inverter-based (DERs), where secondary control must regulate the microgrid frequency and voltage to its nominal values. When a secondary control strategy is implemented, it is necessary to validate its performance under several conditions. Most existing research papers focus on the microgrid’s small-signal and transient stability. At the same time, little has been done on the influence of the load model on voltage stability. This type of analysis is required to ensure an adequate transition between the grid-connected and stand-alone modes. This paper provides a voltage stability analysis of a microgrid, considering secondary control based on receding horizon and frequency-dependent load models. Simulation results demonstrate the robust performance of the secondary control and validate the importance of considering or adapting voltage stability indices to ensure adequate microgrid performance.

Stability tool for electric power systems with a high penetration of electronic power converters

The increasing use of electronic converters is making possible the development of more sustainable, efficient, and reliable electric power systems, but it is also introducing new challenges that need to be addressed. Power system stability is one of them since the converter multiscale coupling between control loops and the mutual effects of multiple converters make the traditional approaches and specialized software available not fully adequate. In this context, this paper presents a software tool called CSTEP capable of carrying out small- and large-signal stability analysis for electric power systems strongly dominated by electronic converters. By utilizing the tool description, the paper provides the reader with a systematic methodology to obtain the system dynamic representation, and with some software tools for the analysis of the large and small-signal stability. Finally, the validity and functionality of CSTEP have been tested with the implementation of three use cases: a simple ac use case to illustrate the application of the system algorithm step by step, an IEEE 5-bus use case to validate the tool with already established commercial software and a more realistic system based on a medium voltage CIGRÉ benchmark to highlight the potential applications of the tool. The results show that, unlike existing tools that simplify or neglect the electric part of the grid (filters, line impedances, etc.), CSTEP can predict power system instabilities caused by the interactions of fast control loops of electronic converters with the electric part.

Small-Signal Stability Analysis of the Power System Based on Active Support of Renewable Energy VSCs

With the large-scale renewable energy access to the power system, the voltage source converters (VSCs) in the system are gradually increasing. The system inertia is weakened, which leads to the decrease in frequency supportability and affects the stability of the power system. After adopting active support control, VSC-based renewable energy units have inertia supportability similar to traditional synchronous generators (SGs), which can improve the frequency stability of the power system. This article is intended to the control strategy based on active support of renewable energy. Small-signal stability of a two-zone system with different control strategies for VSCs under different conditions is analyzed. At the same time, the dynamic adjustment effect of different parameters on active support control is considered, and frequency stability of a two-zone system with inertial flexible control is improved. In this article, the basic principle of active support control is expounded in detail. Compared with PQ-control and droop-control, it is verified that active support control has good frequency supportability. The small-signal model of VSCs for active support and two-machine system is established. Combined with the simulation system, the influence of virtual inertia and damping coefficient on system stability is verified.

Evaluation and Adjustment Based on Broad Learning System for Small Signal Stability Analysis of Power System Integrated with Wind Farms

Evaluation and Adjustment Based on Broad Learning System for Small Signal Stability Analysis of Power System Integrated with Wind Farms

VSC-HVDC Robust LMI Optimization Approaches to Improve Small-Signal and Transient Stability of Highly Interconnected AC grids

VSC-HVDC Robust LMI Optimization Approaches to Improve Small-Signal and Transient Stability of Highly Interconnected AC grids by Yankai Xing 1 , Elkhatib Kamal 1, Bogdan Marinescu 1* , Florent Xavier 2 1 Ecole Centrale de Nantes, LS2N-CNRS, 1 rue de la No¨e, Nantes, France2 R&D Division, RTE, Paris La D´efense, France * Author to whom correspondence should

A Hybrid Power Sharing Control to Enhance the Small Signal Stability in DC Microgrids

Low-frequency power oscillations pose serious problems to the operation of Distributed Generations (DGs) equipped with droop control. This paper presents a new hybrid power-sharing control for damping low-frequency power and current oscillations in DC microgrids. The proposed control consists of a decentralized droop control together with a centralized average current sharing control. A small-signal equivalent model is analytically derived for the proposed hybrid control and is incorporated into the DC microgrid model. The parameters of the PI controllers involved in the average current sharing control units are tuned individually to achieve a satisfactory performance in a stand-alone operation of DGs with a local load. The contributions of control signals contained in the hybrid control signal to the damping characteristic are analyzed. The dynamic response of the DC microgrid under a variety of disturbance scenarios is investigated. The power-sharing accuracy of the proposed control is also examined under the investigated scenarios. The method performance is also investigated for the oscillations caused by constant-power loads. Sensitivity analyses are conducted to evaluate the impact of the loading level and line parameters on the damping ratio associated with the dominant low-frequency modes. The effectiveness of the control method is examined in case of losing a number of communication links. The impact of the delay in the communication links on the method performance is also examined. The simulations are conducted on a multi-source DC microgrid, and the results are verified in the OPAL-RT real-time simulator.