Rotor Swing Research Articles

Transient synchronous stability analysis and enhancement control strategy of a PLL-based VSC system during asymmetric grid faults

The stability of a voltage source converters (VSC) system based on phase-locked loop (PLL) is very important issue during asymmetric grid faults. This paper establishes a transient synchronous stability model of a dual-sequence PLL-based VSC system during low voltage ride-through by referring to the equivalent rotor swing equation of synchronous generators. Based on the model, the synchronization characteristics of the VSC system under asymmetric grid faults are described, and the interaction mechanisms, as well as the transient instability phenomena of positive and negative sequence PLL during asymmetric faults are explained. Using the equal area criterion, the influences of sequence control switching action, detection delay, and interaction between the positive and negative sequence PLL on the transient synchronous stability of the VSC system are analyzed, respectively. In addition, a transient stability assessment criterion based on the critical fault clearance angle and time and an enhancement control strategy based on the improved positive and negative sequence PLL are proposed. Finally, the analytical results are validated through simulation and experiments.

Solar-PV inverter for the overall stability of power systems with intelligent MPPT control of DC-link capacitor voltage

This paper demonstrates the controlling abilities of a large PV-farm as a Solar-PV inverter for mitigating the chaotic electrical, electromechanical, and torsional oscillations including Subsynchronous resonance in a turbogenerator-based power system. The oscillations include deviations in the machine speed, rotor angle, voltage fluctuations (leading to voltage collapse), and torsional modes. During the night with no solar power generation, the PV-plant switches to PV-STATCOM mode and works as a Solar-PV inverter at its full capacity to attenuate the oscillations. During full sun in the daytime, on any fault detection, the PV-plant responds instantly and stops generating power to work as a Solar-PV inverter. The PV-farm operates in the same mode until the oscillations are fully alleviated. This paper manifests the control of the DC-link capacitor voltage of the Solar-PV inverter with a bacterial foraging optimization-based intelligent maximum power point tracking controller for the optimal control of active and reactive power. Kundur’s multi-machine model aggregated with PV-plant is modeled in the Matlab/Simulink environment to examine the rotor swing deviations with associated shaft segments. The results for different test cases of interest demonstrate the positive outcomes of deploying large PV-farms as a smart PV-STATCOM for controlling power system oscillations.

Transient Stability Analysis and Improved Control Strategy for DC-Link Voltage of DFIG-Based WT During LVRT

In this paper, the transient stability for dc-link voltage of doubly-fed induction generator (DFIG)-based wind turbine (WT) is studied in detail during low voltage ride-through (LVRT). Firstly, referring to the rotor swing equation of synchronous generator (SG), the nonlinear large-signal model of dc-link voltage is established. In addition, the damping power, static slip power, and dynamic slip power are derived. Consequently, the transient performance of dc-link voltage under the different operation conditions of DFIG is revealed during LVRT. Furthermore, the instability form of dc-link voltage with the moving process of equivalent power angle is analyzed by the energy function of dc-link voltage. In addition, the impacts of dc voltage control loop's parameter, the active current of the stator, and the slip on the stabilization process of dc-link voltage are studied. Analysis result indicates that the insufficient damping and large unbalanced power would deteriorate the transient behavior and steady-state level of dc-link voltage. Therefore, an additional damping and slip power feedforward control strategy is proposed, which can make the transition process of dc-link voltage smoother and significantly improve the voltage steady-state level. Finally, simulation and experimental results validate the effectiveness of theoretical analysis.

Transient Synchronization Stability Improvement Control Strategy for Grid-Connected VSC Under Symmetrical Grid Fault

Under grid fault, the grid-connected voltage source converters (VSCs) have the risk of transient synchronization instability during low voltage ride through. Based on the equivalent rotor swing equation of VSC, this letter proposes an improved transient synchronization stability control strategy, which improves the existence of equilibrium points and transient synchronization behaviors of the VSC system. Thus, the transient synchronization stability of grid-connected VSC can be significantly enhanced. The simulation and experimental results demonstrate the validity of the proposed strategy.

Study of Modified Flux-Coupling-Type SFCLs For Stability Improvement of a Multi-Machine Power System Based On Energy Function

This paper investigates modified flux-coupling-type superconducting fault current limiters (SFCLs) for enhancing the transient stability of a multi-machine power system (MMPS). The clustering architecture of the MMPS with the modified SFCLs is presented, and the transient energy function (TEF) of the MMPS is established. Through clarifying the potential influence of the modified SFCLs, theoretical analysis signifies that the modified SFCLs can reduce the transient energy accumulation during the fault-feeding period, and increase the transient stability margin of the MMPS. Using MATLAB/Simulink, a benchmark IEEE 9-bus system with the SFCLs is modeled, and the simulation analysis of the generator rotor swing behaviors is carried out. Varying the resistive-inductive parameters and altering the positions of the SFCLs are considered, and the TEF method is applied to gain quantitative effects. The simulation findings in different scenarios testify the correctness of the theoretical analysis. The presence of the SFCLs can availably reduce the generator rotor oscillating and restrain the transient energy changing, and meanwhile, an extension of the critical clearance time is achieved for the MMPS.

Modelling and Transient Synchronization Stability Analysis for PLL-Based Renewable Energy Generator Considering Sequential Switching Schemes

The synchronization characteristics of phase-locked loop (PLL) based renewable energy generators (REG) are considerably sensitive to the grid condition and the inner sequential switching actions of their control system, especially suffered from grid faults. In this article, the general output characteristics of REG systems are investigated considering the nonlinear behaviour of PLL. In addition, general sequential switching control schemes for the entire grid fault process are introduced. Then, to physically determine and theoretically analyze the transient synchronization stability of REG systems, the synchronization model of a REG system for different fault stages is built and presented in the form of rotor swing equations, which are similar to those of a synchronous generator (SG). The proposed model was able to deduce the characteristics of virtual torque, virtual inertia, and virtual damping coefficient of the REG system, and identify the coupling relationship between the angular frequency/magnitude states of the terminal voltage of the REG system during the synchronization process. Thus, the synchronization stability criteria were proposed based on those of the SG, in which the transient instability phenomenon and mechanism for different fault stages is physically explained by the deduced equal area criteria. Finally, the analysis was verified by simulations and experiments.

Transient Stability of Power Systems Integrated With Inverter-Based Generation

The fundamental mechanism of transient stability of the conventional power system can be physically understood with the rotor swing dynamics of synchronous generators (SGs). The basic factor affecting the transient stability is the power-angle relationship among the SGs. The integration of a large number of inverter-based generations (IBGs) into the power system inevitably changes the original power-angle relationship, therefore leading to a more complicated transient stability mechanism. In this letter, the impact of IBG on the power system transient stability is analytically investigated. It is shown that the connection of IBG changes the original power-angle relationship into a nonsinusoidal curve, introduces a limit on the peak of the rotor swing, and therefore brings about a new bottleneck for the transient stability.

Stiffness Model and Experimental Study of Hydrostatic Spindle System considering Rotor Swing

For high-end CNC machine tools, the stiffness of the spindle system is one of the most important performance indicators. In this paper, the hydrostatic motorized spindle system of a grinding machine is taken as the research object, and a two-degree-of-freedom stiffness model of the spindle system considering rotor swing is proposed. The stiffness of the spindle system under different excitation frequencies is analyzed, and the contributions of the stiffness of two bearings to the stiffness of the spindle system are evaluated. The vibration test on the spindle system is implemented through the hammering method. The vibration responses of the spindle system are obtained, and the stiffness of the spindle system is identified. The results show that the test results of the stiffness of the spindle system are in good agreement with the theoretical calculation, with an average error of about 14.21%. The research in this paper can provide theoretical and data support for bearing design and stiffness evaluation of a hydrostatic spindle system.

Adaptive Command-Filtered Backstepping Control for Virtual Synchronous Generators

Distributed energy sources are usually interfaced to the grid using power electronic converters, and lack of inertia in inverter dominated microgrids can affect the system stability. This paper presents a new method for virtual synchronous generator (VSG) control in order to solve the low system inertia and support the grid frequency problem. In this paper, the VSG based on electromagnetic transient characteristics is improved and an adaptive command filter back-stepping controller is designed. Firstly, the rotor swing equation and power part are modeled to complete the controller design for achieving system stability in the islanded, grid-connected and transition modes. In addition, a limited-amplitude command filter is used to deal with computational complexity and nonlinear saturation problems in the design process. Secondly, projection operator, and adaptive inertia and damping control are introduced to reduce the modeling error and disturbance caused by changing parameters. This ensures the boundedness of the estimated value and further improves the frequency response, especially in the transition mode. Finally, simulation results show that the proposed controller is more effective than the traditional control method for achieving power stability and frequency improvement.

Coordinated Control of DC Grid and Offshore Wind Farms to Improve Rotor-Angle Stability

This paper proposes a coordinated control strategy for voltage source converter (VSC) based dc grids and offshore wind farms connected by the dc grids. The strategy could enhance the stability of the onshore synchronous power system subjected to disturbances. Based on the mathematical model of dc grid connected power system and control Lyapunov function, the active and reactive control law for onshore VSC stations is presented. And to maintain the power balance of dc grid and reduce the rotor swing of wind turbines, the windfarms’ power modulation and distribution method is given. A layered control structure to implement the proposed strategy which combines the dc grids and windfarms control is also put forward. Simulations are run in a modified New England 39-bus system by DIgSILENT/Power Factory to validate the effectiveness of the proposed scheme.

Enhancement of Power System Transient Response by Control of HVDC Converter Power

This paper examines enhancement of power system stability by control of real power which is injected into or taken from the AC system by the high-voltage direct current (HVDC) converter in transmission systems with HVDC transmission. It also investigates the influence of transient converter reactive power following a severe system disturbance with clearance together with the effect of system dynamic loads on system transient response. First, a new algorithm for damping power system oscillations which is based on modulation of active power injected into a node of the power system is described. The algorithm is based on the direct Lyapunov method which is used to process signals for supplementary control of an HVDC converter to damp AC system electromechanical oscillations to enhance power system stability. The algorithm is formulated to minimize time of dissipation of turbine-generator rotor oscillation energy which results from incidence andclearance of a system disturbance. The relationship between rotor slip and locally measured quantities is used in formulating the control strategy. The performance of a benchmark multimachine system with and without optimal HVDC converter control to enhance damping and power system stability is then illustrated. This is extended to include transient link reactive power which is consumed by the AC system by the converter in controlling rotor swing due to a severe transmission system disturbance with clearance, and the effect dynamic loads have on dynamic response of the system following a severe system disturbance.

Experimental study of squirrel-caged damper structure for superconducting generator

In this paper a double-layer damper is developed which will consist of a squirrelcaged warm damper and a cylindrical cold damper as a part of a 70-MW superconducting generator development project. To evaluate the characteristics of unbalance current capability, magnetic shielding and damping for rotor swing, a one-half scale rotor model is constructed and an experimental study is made. From analysis of the experimental results, design guidelines have been developed and the FEM magnetic field analysis technique is refined. The main results are summarized as follows: 1 The squirrel-caged warm damper has sufficient capability against negative sequence current; 2 Damping characteristics can be designed to be effective near the rotor swing frequency; 3 Flux shielding at low frequencies corresponding to quick response excitation is sufficiently small so as not to prevent field flux change; and 4 Magnetic field can be analyzed by the refined FEM field analysis technique which now takes into account the effects of the rotor end region by estimating the end resistance based on the eddy current flow path.

Effect of excitation capacitors on transient performance of reluctance generators

The transient responses of a reluctance generator connected to an infinite power system excited by a bank of terminal capacitances are compared to those when load excitation is used. A mathematical model is developed to simulate the machine with its terminal capacitor. With the aid of a least-square-error method, this model is used to optimize the machine parameters. The capacitance excitation requirements for different load conditions are then computed using a steady-state model. The comparison of the transient responses shows that the terminal-capacitor excitation method has several advantages over the load excitation method. It reduces the first rotor swing and gives more damping to the subsequent rotor oscillations. It also increases the critical fault-clearing time and hence the transient stability limits. In addition, it suppresses all power frequency torque oscillations, which are quite pronounced when load excitation is used. >

Effect of Fault Clearing and Damper Modelling on Excitation and Decay of Vibrations in Generator Shafts Following Severe Disturbances on the System Supply

The paper examines the effect damper circuit modelling and the current interruption process has on amplitude and decay of torsional vibrations in turbine-generator shafts following severe supply network disturbances. A phase-variable model of a synchronous-generator with up to 2 direct-axis and 3 quadrature-axis dampers where fault current is cleared at fault current zeros is employed to calculate generator airgap torque which results from a severe disturbance on the electrical supply. Using airgap torque, effective amplitude of torque excitation acting on the generator rotor for each eigenfrequency is determined by Fourier analysis. Amplitude of torsional vibration at each shaft section for each modal frequency is then calculated. Shaft torque at each shaft location for each modal frequency is thereby deduced. These components, together with the steady-state component (and that due to rotor swing), are summed as absolute values for all modal frequencies to yield approximate peak torque at critical locations along the shaft following each disturbance. Approximate peak shaft torque estimated by frequency domain analysis is compared in some instances with peak torque predicted by solution of exact differential equations. Presented results illustrate amplitude of torque excitation and shaft torques as a function of fault clearing time for L-L-L and L-L high-voltage system short-circuits, and effect reactive power and system resistance has on damping predominant torsional vibrations in the shaft.

FAST ACCURATE TRANSIENT STABILITY SIMULATIONS

ABSTRACT The paper describes a Simultaneous Implicit (SI) approach for transient stability simulations based on an iterative technique using traingularised admittance matrix [1]. The reduced saliency of generator in the subtransient state is taken advantage of to speed up the algorithm. Accordingly, generator differential equations, except rotor swing, contain voltage proportional to fluxes in the main field, dampers and a hypothetical winding representing deep flowing eddy currents, as state variables. The simulation results are validated by comparison with two independent methods viz. Runge-Kutta simulation for a simplified system and a method based on modelling damper windings using conventional induction motor theory[2].

Analysis of Continuum and Reduced Shaft Models in Evaluating Turbine-Generator Shaft Torsional Response following Severe Disturbances on the System Supply

ABSTRACT The paper examines use of continuum and reduced models of turbine-generator shafts in evaluating torque response following incidence and clearance of severe disturbances on the system supply. Using airgap torque which results from incidence and clearance of system disturbances at fault current zeros, torque excitation which acts along the active length of the generator rotor for each torsional vibration is determined by Fourier analysis. Amplitude of torsional vibration at each shaft cell for each modal vibration is determined from the torque prime mover and generator shaft sections of interest for each modal vibration is then calculated. These components, together with the steady-state component (and that due to rotor swing), are summed as absolute values to give approximate peak torque at critical shaft sections. Presented results illustrate torque excitation and shaft torque estimated from continuum, simple and stiffness-adjusted shaft models as a function of fault clearing time following L-L-L and L-L high voltage disturbances with clearance. Effect of employing continuum and reduced shaft models in estimating time constants for decay of predominant shaft torsional vibrations and on peak energy of the vibrations is illustrated. The effect saturation of the stator leakage reactance has on torque response following sustained stator-terminal L-L-L and L-L short-circuits at full-load and no-load and following worst-case synchronisation is also illustrated. 66O MW and 1000 MW two-pole machines are analysed.

Concept of synchronous generator stability

The conventional ideas concerning power-system stability are briefly outlined. Some ways in which the automatic voltage regulator and velocity-sensitive governor have modified these ideas by showing their effects qualitatively on alternator swing curves are indicated. They indicate that overall stability cannot with certainty be assessed from the first rotor swing, and the paper concludes by showing how, for some particular system conditions, the machine control devices modify transient stability.