Positive Damping Research Articles

Mechanism analysis on a type of limit induced oscillation for single‐machine infinite‐bus system of PMSG with positive damping

AbstractThe mechanism of oscillations that occur in the system connected to renewable energy sources is complex, generally including negative damping oscillation, limit induced oscillation etc. Combining with the dynamic characteristics of the low‐dimensional system after limit working, this paper analyses the mechanism of a type of limit induced oscillation that occurs when the output of the DC voltage outer loop continuously touches the limit for single‐machine infinite‐bus system of permanent magnet synchronous generator with positive damping under a large disturbance. Specific study as follows: firstly, a non‐smooth state space model of single‐machine infinite‐bus system of permanent magnet synchronous generator with nonlinear state limit (clarified as a Filippov system) is established. Secondly, the small disturbance characteristics of the system are analysed when the limit does not work. Thirdly, the piecewise dynamic description of the system is analysed with the limit working, and the reason that the final contraction of the system to an eight‐dimensional manifold is explained based on mathematical derivation and physical characteristics. Finally, the characteristics of equilibrium point of the system in a low‐dimensional manifold are analysed when the limit continuously working, revealing that the existence of a pair of conjugate unstable eigenvalues in the low‐dimensional system is the reason of system oscillation.

A comparison of static and rotordynamic characteristics for two types of liquid annular seals with and without helical grooved stator

Less leakage is a benefit of parallel grooved liquid seals (labyrinth seals). But researches show that the liquid seal with parallel grooves on the rotor harms the rotor stability. The seal with helical grooves on stator performs well in terms of rotordynamics, and its leakage is sensitive to the rotating speed. To make use of the advantages of both seals and improve seal stability, based on the Smooth-stator/Parallel Grooved-rotor (SPG) liquid seal, a Helical Grooved-stator/Parallel Grooved-rotor (HGPG) liquid seal is designed. To evaluate two liquid seals’ leakage, rotordynamic characteristics and drag power loss, a transient computational fluid dynamics-based method is employed. This method is based on the multi-frequency elliptical-orbit rotor whirling model and the mesh deformation technique. The published experimental data of the leakage and rotordynamic force coefficients for an SPG liquid seal are used to validate the accuracy and dependability of the current method. Seal leakage and force coefficients are presented and compared for the SPG liquid seal and the HGPG liquid seal at various pressure drops. The influences of parallel groove depth on the leakage and rotordynamic properties for the HGPG liquid seals at two rotational speeds (2000, 6000 r/min) are analyzed. The numerical findings demonstrate that the novel HGPG liquid seal has a lower leakage flow rate (by ∼22.3%) than the traditional SPG liquid seal. There is an optimal parallel groove depth that minimizes leakage. The presented novel HGPG liquid seal significantly improves rotordynamic stability, due to the similar effective stiffness and the obviously larger positive effective damping. Reducing parallel groove depth can increase the positive effective damping. In terms of leakage and rotordynamic characteristics, the novel HGPG liquid seal is a better seal design for liquid turbomachinery.

Characteristic analysis and mitigation strategy for SSCI in series-compensated DFIG-based wind farm controlled by a virtual synchronous generator

The proliferation of virtual synchronous generator (VSG) technology within series-compensated double-fed induction generator (DFIG)-based wind farms is substantially hampered by the attendant risk of subsynchronous control interaction (SSCI), resulting in a significant research deficiency on systematic control interaction analysis and the development of mitigation strategies. The paper proposes an advanced active disturbance rejection control (ADRC) framework, incorporating real-time compensation mechanisms to mitigate the inadequate suppression efficacy attributable to the VSG's diminished output impedance. Initially, the mathematical expression for the VSG output impedance is rigorously deduced, and the positive damping attributes of the VSG in relation to SSCI are elucidated from the perspective of underlying mechanistic principles. Subsequently, the suppressive mechanism of SSCI by the ADRC is revealed in the context of VSG involvement, and the consequent augmentation of SSCI attributed to PI control is systematically derived. In immediate succession, the quanta of oscillation and inductive cross-coupling are encapsulated as the system's aggregate disturbance, thereby streamlining the ADRC to its primary order configuration, permitting the utilization of an extended state observer (ESO) for the dynamic estimation of said disturbance. Furthermore, a fractional-order filter function is instituted to engineer an augmented ESO, which refines the output voltage of the grid-side converter. Concurrently, a meticulous discourse on the rectification strategy for the proposed ESO parameters and its stability ensues. Ultimately, the efficacy of the mechanism analysis, alongside the robustness of the proffered control strategy for SSCI mitigation under diverse perturbation conditions, is corroborated via impedance evaluation and time-domain simulation.

Modal effects of span-layout types on coupled flutter of long-span suspension bridges

This study provides a theoretical explanation for a perplexing experimental phenomenon observed frequently in suspension bridge flutter testing, where the flutter critical wind speed (Ucr) predicted by two-dimensional (2D) section model testing is higher than that predicted by three-dimensional (3D) full aeroelastic model testing. Six long-span suspension bridges with either a single simply supported span or multiple continuously supported spans were taken as research examples, then the comparative studies on the flutter critical wind speeds, flutter frequencies, modal energy ratios and aerodynamic damping corresponding to 2D and 3D coupled flutter states were carried out to illustrate the flutter modal effects. The research findings indicate that the Ucr of 2D testing being higher than that of 3D testing is an inherent characteristic for single-span simply-supported suspension bridges, which can be attributed to the prominent aerodynamic negative damping associated with 2nd-order vertical bending mode. However, due to the aerodynamic positive damping associated with 3rd-order vertical bending mode, the Ucr of 2D testing is consistently lower than that of 3D testing in the cases of multi-spans continuously-supported suspension bridges. Additionally, to eliminate unsafe 2D evaluations, a reasonable modal matching principle is recommended for section model testing of single-span simply-supported suspension bridges.

Analysis of Factors Affecting Sub-Synchronous Oscillation in Doubly-Fed Wind Power Grid-Connected System Based on Impedance Sensitivity and Research on Suppression Strategy

Aiming at the matter of sub-synchronous oscillation (SSO) of the doubly-fed induction generator (DFIG) series compensation capacitors grid connection, a SSO suppression strategy based on adding damping controllers in rotor-side converter (RSC) is put forwarded. Considering the control parameters of power and current control loops of RSC, the equivalent impedance model of DFIG series compensation grid connection (SCGC) is established, and then combined with the equivalent RLC resonant circuit of the system, the mechanism and factors of SSO are analyzed by impedance method. Calculating the impedance sensitivity of the system impedance to parameters by sensitivity analysis method, so as to identify the leading factor affecting the SSO characteristics of wind power system. Combined with the stability criterion of system impedance characteristics, the parameters are adjusted to meliorate system stability. Based on the leading factor affecting the SSO and the mechanism of the SSO, the damping controllers are added in the RSC to supply positive damping for the system to eliminate the negative damping brought by the RSC and rotor resistance, thus suppressing the SSO of the system. The validity of the put forwarded suppression strategy is proved through PSCAD/EMTDC simulation.

Numerical Investigation of Classic Flutter Mechanism Under Circumferentially Non-Uniform Inlet Condition

Abstract Over recent years, the aeroelastic problem of fan blades has become significantly serious due to the demand for high performance of aero-engines. To explore the aeroelastic issue of flutter, fan instability is represented by the aerodynamic damping. When the inlet condition is uniform, aerodynamic damping is mainly caused by the temporal factor, and the classic flutter usually does not occur due to the usage of mistuning. However, with the existence of circumferentially non-uniform components in the distorted inflow, aerodynamic damping is also affected by the spatial factor, which may alter the occurrence mechanism of classic flutter. To investigate this issue, the full-annulus 3D (three-dimensional) unsteady calculation is conducted on a transonic fan NASA Rotor 67 with a typical circumferential distortion inflow. As demonstrated by the energy method for the rotor blades at each nodal diameter, the coefficients of aerodynamic damping contain an interval value rather than a fixed datum. Some of the blades have positive damping, and others are negative. The positive and negative aerodynamic damping is determined by the relative position between the rotor blade and the distorted region in the circumferential direction. Furthermore, a fast calculation method based on the fundamental principle regarding flow periodicity is developed to obtain the aerodynamic damping at different nodal diameters under non-uniform inlet conditions.

Suppression method of ultralow-frequency oscillation under ambient excitation in hydro-dominant power systems

Ultralow-frequency oscillations (ULFOs) have frequently occurred in hydro-dominant power systems in recent years. These phenomena seriously threaten the safe and stable operation of power systems. Therefore, measures that can effectively suppress ULFO need to be taken. Currently, the hydropower unit governor can enhance the dynamic stability and dampening oscillations of a system through adjusting the proportional–integral–derivative parameters. However, modifying these parameters can affect the primary frequency regulation performance, which compromises the assurance of grid frequency quality. This study proposes a switching type of hydro generator governor based on the local damping contribution rate to address the aforementioned problems. The approach incorporates the energy structure into the classical governor model, calculates the local damping contribution rate, and enables automatic switching of the hydro generator governor parameters based on positive and negative local damping contributions. This way allows for segmented control with different parameter settings, which enables the system to effectively consider the damping characteristics of ULFO while maintaining primary frequency regulation performance. It can also accurately and efficiently suppress the ULFO. The proposed method is verified through arithmetic analysis conducted on a 16-machine 5-zone system and an actual grid system. Simulation results demonstrate the effectiveness of the method.

Conditions of Existence and Uniqueness of Limit Cycle for Grid-Connected VSC With PLL

This paper investigates the large disturbance stability of single voltage source converter (VSC) connected to the infinite bus system through the transmission line. One conservative stable region is obtained via the direct method of Lyapunov. Based on the Poincaré Theorem, it is interesting to find there might exist limit cycle between the obtained stable boundary and the angle of unstable equilibrium point (UEP). Accordingly, the nonlinear damping effect on the system stability is defined, and one limit cycle exists when the positive and negative damping effect over one period is mutually balanced. A conservative existence condition of limit cycle is further derived by constructing a proper piece-wise curve to approximate one specified unstable system trajectory. The derived analytical existence condition can directly predict the limit cycle without numerical simulations. Finally, the paper also proves that the studied dynamic system has at most one limit cycle, and if it exists, it is unstable.

Flutter Suppression Effects of Movable Vertical Stabilizers on Suspension Bridges With Steel Box Girders

As the combination of springs and vertical stabilizers, the movable downward vertical central stabilizer (MDVCS) is proposed to further control the nonlinear flutter of super long‐span suspension bridges in this paper. A series of flutter suppression tests of closed‐box girders and twin‐box steel girders with various MDVCSs are conducted. Based on the coupled flutter theoretical method, the sensitivity analysis of two important parameters including the height and stiffness of MDVCS are carried out to compare their nonlinear flutter control mechanism. The results show that the flutter critical wind speed (Ucr) of the closed‐box girder continued to increase with the decrease of the height of the DVCS and the increase of spring stiffness, whereas the Ucr of the twin‐box girder increased at first and then decreased. The cubic polynomial function and quadratic Holliday function are suitable to modify the correction coefficients of Ucr for the closed‐box girder with various stiffnesses and heights of MDVCS, while the Lorentz peak‐value function and cubic polynomial function are suitable to modify the Ucr of the twin‐box girder. Furthermore, the MDVCS significantly changes the rules of two positive and negative aerodynamic damping ratios for the closed‐box girder and two negative aerodynamic damping ratios for the twin‐box girder. Besides, the peak vertical displacement amplitudes of the box girder are about half of the MDVCS, since both the height and stiffness of MDVCS alter the elliptical radius of vertical phase planes to affect the limit cycle oscillation of soft flutter, especially for the leeward MDVCS for the twin‐box girder.

The potential of chatGPT in digital learning: A Review

Digital education is an activity that monitors developments in the digital world in everyday life. increase literacy, develop critical thinking abilities and skills. Digital education functions as a digital reference for students to guide their learning activities. The aim of this research is to reviewing one of the digital learning resources for students. The research design uses high-quality literature from mature articles. proceedings, which are currently available on Google Scholar for 2019–2022. The research results show that the use of GPT chat as a reference source for learning students' intellectual tasks. Additionally, many GPT Chat user interface issues were also mentioned. In education, this applies to both positive and negative damping contributions. GPT chat is useful for learning, especially as a substitute for one of the digital learning resources for students.

Corrected complex torque coefficient method for synchronization stability analysis of grid‐connected VSC

AbstractSub‐synchronous oscillation of grid‐connected voltage source converter (VSC) dominated by phase locked loop (PLL) is an important stability issue in nowadays power systems. The complex torque coefficient method has been used to investigate the issue because of its advantage of giving insights into source of damping and contributions of different components on damping. However, it is found that the classic complex torque coefficient method is not entirely applicable for stability analysis of VSC because of the proportional term in PLL. This paper proposes a corrected complex torque coefficient method and defines synchronous and damping coefficients. Based on the proposed method, a small‐signal stability criterion is obtained, in which the system stability depends on the sign of corrected damping coefficient. The impacts of different elements on system damping can be quantitatively evaluated through the method. It is drawn that current control loop and line dynamics contribute negative damping, whereas power control loop contributes positive damping. Moreover, the impacts of operating conditions and controller parameters on damping of different elements are analysed. The eigenvalue analyses and electromagnetic transient simulations have verified the theoretical analysis.

An investigation into the modal effect mechanism of multi-mode coupled flutter with modality-driven method

Modal coupled effects concealed in the semblance of flutter dominated by torsional modes have an uncertain impact on the flutter characteristics of long-span bridges, making it challenging to fully comprehend the underlying physics of three-dimensional flutter. Consequently, this research has investigated the composition of flutter modality and its related modal effect mechanism through experimental and theoretical analyses. Initially, the actual flutter modality and its compositions were ascertained through full-bridge aeroelastic tests on four suspension bridges with main spans exceeding 1750 m. Subsequently, the practical modality-driven flutter analysis was developed to measure the impact of each natural mode, particularly the higher-order mode, on the flutter performance through modal-generated aerodynamic damping. Next, the genetic algorithm was introduced in this method to enhance the convergence robustness. Finally, a systematic investigation was conducted to examine the evolution of modal effects with changes in the main spans. The results of full-bridge aeroelastic tests indicate that the flutter pattern is predominantly formed by the first-order symmetric torsional mode, the first-order symmetric heaving mode, and the second-order symmetric heaving mode. In terms of modal participation and modal aerodynamic damping contribution, the second-order mode governs the flutter heaving modality but has a smaller impact on the flutter performance compared to the first-order mode. The first-order torsional mode and the first-order heaving mode provide continuously increasing positive damping and continuously decreasing negative damping respectively, while the aerodynamic damping provided by the second-order heaving mode exhibits a turning phenomenon as wind velocities increase due to the system frequency approaching the second-order natural frequency. The genetic algorithm can effectively address potential occurrences of non-convergence or switching phenomena in numerical calculations.

Optimisation of the damping properties of steel structures using adhesively bonded joints

AbstractAdhesives offer both good damping properties and very high strengths. The possibilities for using the positive damping properties in particular to optimise dynamically stressed steel structures have rarely been explored to date. In this paper, comprehensive numerical and experimental investigations are presented. In numerical investigations on dynamically loaded, representative steel structures, the potential for damping of structures by adhesively bonded joints is analysed. Numerical investigations show that the vibration amplitudes of adhesively bonded structures are more than 95 % lower than those of welded reference structures in the relevant resonance case. Based on this, the damping properties of adhesively bonded tubular steel joints in a scale relevant for construction industry were experimentally investigated. Different geometry and test boundary conditions are investigated in a parameter study. The loss factor of tubular joints is a maximum of 0.38, which is relevant for steel construction. Based on the results of experimental investiga‐tions, a methodology is presented for the analytic determination of the damp‐ing properties of adhesively bonded tubular joints for various specimen ge‐ometries and stress boundary conditions. For this purpose, dimensional anal‐ysis is carried out using the Buckingham Pi Theorem.

Estimation of Wideband Multi-Component Phasors Considering Signal Damping.

Harmonic and interharmonic content in power system signals is increasing with the development of renewable energy generation and power electronic devices. These multiple signal components can seriously degrade power quality, trip thermal generators, cause oscillations, and threaten system stability, especially the interharmonic tones with positive damping factors. The first step to mitigate these adverse effects is to accurately and quickly monitor signal features, including frequency, damping factor, amplitude, and phase. This paper proposes a concise and robust index to identify the number of modes present in the signal using the singular values of the Hankel matrix and discusses the scope of its application by testing the influence of various factors. Next, the simplified matrix pencil theory is employed to estimate the signal component frequency and damping factor. Then their estimates are considered in the modified least-squares algorithm to extract the wideband multi-component phasors accurately. Finally, this paper designs a series of scenarios considering varying signal frequency, damping factor, amplitude, and phase to test the proposed algorithm thoroughly. The results verify that the proposed method can achieve a maximum total vector error of less than 1.5%, which is more accurate than existing phasor estimators in various signal environments. The high accuracy of the proposed method is because it considers both the estimation of the frequency number and the effect of signal damping.

Post critical characteristics of a side-box steel concrete composite girder: Experimental investigation and mechanism analysis

The present study is aimed to investigate the post-critical behavior of a side-box steel-concrete composite girder under varying wind angles of attack, by conducting a series of section model testing with single-degree and two-degrees of freedom. The essence of flutter, as well as the adverse impact of vortex shedding lock-in on exacerbating post-critical flutter responses, was revealed in detail. The results indicate that the coupled motion of flutter for the prototype composite girder can be characterized as a supercritical Hopf bifurcation with significant phase shifting between motions. The circular character of the limit cycle oscillation (LCO) expressed in the phase diagram is altered to a non-circular form due to the apparent aerodynamic stiffness nonlinearity within a wide range of wind speeds. Interestingly, the coupling vibration between vortex-induced vibrations (VIV) and flutter, i.e., VIV-flutter coupling vibration is observed for the prototype girder, due to the evolution of total damping ratio concave shape with wind speed. Two mitigation countermeasures, i.e., a L-shaped skirt plate and a sharpened wind fairing, were proposed to improve the aeroelastic stability, caused by a significant increase in uncoupled positive aerodynamic damping and alternation of VIV-flutter coupling. In addition, the specific effects of structural damping on the VIV-flutter coupling were discussed in detail.

Analytical investigation of factors affecting small-signal stability of grid-connected VSC

This paper provides an analytical investigation of the small-signal stability of the grid-connected voltage source converter (VSC) as well as the impacts of the system resistances. The dynamic model of the studied system is first established, and the characteristic function is derived from the linearized model. Based on the characteristic function, the analytical relationships between the system resistances and the dominated pole are obtained utilizing the analytical sensitivity approach. It is found that the line resistance can provide positive damping for the oscillation mode, improving the system stability, while the converter resistance will worsen the system stability. Generally, the line resistance has an evident more substantial impact on the stability of the grid-connected VSC than the converter resistance. The stability analysis results of the grid-connected VSC conducted by ignoring the system resistances are conservative. Ulteriorly, the characteristic function is simplified by neglecting the system resistances, and a sufficient and analytical stability criterion is established from the simplified characteristic function using the Routh Judgement. It exhibits the constraint condition among controller parameters, electrical distance and operation conditions for ensuring system stability. Moreover, the power transmission limitation of the converter affected by the controller parameters and electrical distance is obtained from the derived stability criterion. The small perturbation analysis and electromagnetic transient simulation give a demonstration to the analysis.

Synchronization Stability Enhancement of Grid-Following Converter Under Inductive Power Grid

The loss of synchronization (LOS) is a main issue for dynamic behavior of grid-following converter (GFC) under inductive power grid. This letter reveals the underlying mechanism of insufficient damping or even negative damping during grid disturbance, and analyzes how the initial speed of angle-difference between PLL output and grid voltage affects the synchronization stability. Then a synchronization stability enhancement scheme to add a positive damping and a reverse angular frequency during transient process is proposed in this letter.

Polynomial stabilizations for wave equations with positive definite kernels and boundary frictional damping

This paper is concerned with stabilizations of wave equations with variable coefficients, subject to positive definite kernels and boundary frictional damping. Here, the memory kernel can be sign‐varying and the boundary of the domain does not need to satisfies the “geometric control condition.” Under some appropriate assumptions on memory kernel, we establish the polynomial stabilizations. Meanwhile, the decay result shows that the memory damping plays the dominant role in the stabilizations of the system with both memory damping and boundary frictional damping.

Multi-coupled biomimetics for tire noise reduction

To explore ways of reducing tire noise, a 205/55R16 KR10 semi-steel radial tire was used as the research object. Vibration noise and aerodynamic noise were analyzed using the modal transfer vector method and the computational fluid dynamics method respectively. The cat’s paw pads can swivel left to right when walking, which dampens vibrations. The left-right pivoting characteristics of the cat’s paw pads are successfully transplanted into the tire by opening asymmetric bypass tube grooves in the tread to form a bionic tire. The results showed that the bionic tire can effectively decrease vibration noise. However, without considering the bypass tube’s resonant muffler acoustic noise reduction, the bionic tire increased aerodynamic noise. According to the multi-coupling bionic concept, the shark scale shield structure is coupled based on the bionic tire, and the shark-like structure is targeted at the sound source to form a multi-coupled bionic tire. Characterized by the left and right pendulum positive damping motion of the cat’s paw pad as well as the non-smooth damping structure of the shark scale shield, the multi-coupled bionic tire jointly reduced the tire vibration noise and aerodynamic noise.

Adaptive Inertia and Damping Coordination (AIDC) Control for Grid-Forming VSG to Improve Transient Stability

Different from the conventional synchronous generator, the virtual inertia and damping control parameters for the inverter-based virtual synchronous generator (VSG) provide more flexibility for stable operation and dynamic performance optimization. However, the operation control principle is still unclear regarding how to coordinate virtual inertia and damping considering both frequency stability and transient synchronization stability. In this paper, an Adaptive Inertia and Damping Coordination (AIDC) control strategy is proposed for grid-forming VSGs to improve transient stability. The proposed AIDC strategy adaptively adjusts the virtual inertia and damping coefficients based on real-time conditions of operation frequency deviation and its rate of change of frequency (RoCoF). The virtual inertia is designed to dynamically increase in the accelerated area and decrease in the decelerated are, and the virtual damping coefficient is designed to increase and enlarge the positive virtual damping effect during the whole accelerated/decelerated transient process. In addition, the proposed AIDC strategy is realized through the practical arctan-function control method with limited boundaries, which can assist engineers. The effectiveness of the proposed AIDC strategy is validated through hardware-in-the-loop experiments.