High-frequency oscillation(HFO)of gridconnected wind power generation systems(WPGS)is one of the most critical issues in recent years that threaten the safe access of WPGS to the grid.Ensuring the WPGS can damp HFO is...High-frequency oscillation(HFO)of gridconnected wind power generation systems(WPGS)is one of the most critical issues in recent years that threaten the safe access of WPGS to the grid.Ensuring the WPGS can damp HFO is becoming more and more vital for the development of wind power.The HFO phenomenon of wind turbines under different scenarios usually has different mechanisms.Hence,engineers need to acquire the working mechanisms of the different HFO damping technologies and select the appropriate one to ensure the effective implementation of oscillation damping in practical engineering.This paper introduces the general assumptions of WPGS when analyzing HFO,systematically summarizes the reasons for the occurrence of HFO in different scenarios,deeply analyses the key points and difficulties of HFO damping under different scenarios,and then compares the technical performances of various types of HFO suppression methods to provide adequate references for engineers in the application of technology.Finally,this paper discusses possible future research difficulties in the problem of HFO,as well as the possible future trends in the demand for HFO damping.展开更多
Static dipole-dipole magnetic interaction is a classic topic discussed in electricity and magnetism text books. Its dynamic version, however, has not been reported in scientific literature. In this article, the author...Static dipole-dipole magnetic interaction is a classic topic discussed in electricity and magnetism text books. Its dynamic version, however, has not been reported in scientific literature. In this article, the author presents a comprehensive analysis of the latter. We consider two identical permanent cylindrical magnets. In a practical setting, we place one of the magnets at the bottom of a vertical glass tube and then drop the second magnet in the tube. For a pair of suitable permanent magnets characterized with their mass and magnetic moment we seek oscillations of the mobile magnet resulting from the unbalanced forces of the anti-parallel magnetic dipole orientation of the pair. To quantify the observed oscillations we form an equation describing the motion of the bouncing magnet. The strength of the magnet-magnet interaction is in proportion to the inverse fourth order separation distance of the magnets. Consequently, the corresponding equation of motion is a highly nonlinear differential equation. We deploy Mathematica and solve the equation numerically resulting in a family of kinematic information. We show our theoretical model with great success matches the measured data.展开更多
Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and ...Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t0, ∞), and f∈C1 (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results.展开更多
The generalized dispersion equation for longitudinal oscillation in an unmagnetized, collisionless, isotropic and relativistic plasma is derived in the context of nonextensive q-distribution. An analytical expression ...The generalized dispersion equation for longitudinal oscillation in an unmagnetized, collisionless, isotropic and relativistic plasma is derived in the context of nonextensive q-distribution. An analytical expression for the Landau damping is obtained in an ultra-relativistic regime, which is related to q-parameter. In the limit q →1, the result based on the relativistic Maxwellian distribution is recovered. It is shown that the interactions between the wave and particles are stronger and the waves are more strongly damped for lower values of q-parameter. The results are explained by the increased number of superthermal particles or low velocity particles contained in the plasma with the nonextensive distribution.展开更多
The purpose is to design the control method for a single-degree-of-freedom(SDOF)exponentially damped oscillator.Based on the Lyapunov stability theory,sliding mode control and adaptive sliding mode control have been p...The purpose is to design the control method for a single-degree-of-freedom(SDOF)exponentially damped oscillator.Based on the Lyapunov stability theory,sliding mode control and adaptive sliding mode control have been proposed.Sliding control laws and adaptive sliding laws are designed for exponentially damped oscillator respectively in cases that the bound of the external exciting force is known or unknown.The viability and effectiveness of the above control designs have been validated by numerical simulations.展开更多
By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed....By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.展开更多
Wide area damping controller(WADC) is usually utilized to damp interarea low frequency oscillation in power system. However, conventional WADC design method neglects the influence of signal transmission delay and damp...Wide area damping controller(WADC) is usually utilized to damp interarea low frequency oscillation in power system. However, conventional WADC design method neglects the influence of signal transmission delay and damping performance of WADC designed by the conventional method may deteriorate or even has no effect when signal transmission delay is beyond delay margin, an index that denotes delay endurance degree of power system. Therefore, a new design method for WADC under the condition of expected damping factor and required signal transmission delay is presented in this work. An improved delay margin with less conservatism is derived by adopting a new Lyapunov-Krasovskii function and more compact bounding technique on the derivative of Lyapunov-Krasovskii functional. The improved delay margin, which constructs the correlation of damping factor and signal transmission delay, can be used to design WADC. WADC designed by the proposed method can ensure that power system satisfies expected damping factor when WADC input signal is delayed within delay margin. Satisfactory test results demonstrate the effectiveness of the proposed method.展开更多
The benefits of using experiments in physics classes are widely discussed in the literature, but sometimes experimental setups are not available. In this paper we present different ways of using experiments in physics...The benefits of using experiments in physics classes are widely discussed in the literature, but sometimes experimental setups are not available. In this paper we present different ways of using experiments in physics classes based on the Arduino board, since it involves low cost materials and can be built by the own students in several cases. In this work we addressed the well known damped harmonic oscillator and performed the data acquisition through the Arduino board, a LDR (Light Dependent Resistor), a infrared photodiode sensor and a computer. The setup of the proposed experiment and the technical details related to assembly are discussed in a clear way in order to be reproduced by anyone interested in the subject. We found a significant difference in the results obtained through the LDR and the photodiode. The later has given better results and has reproduced a regular decay in the amplitude of the oscillator even when the experiment was performed in a highly illuminated room. The Arduino board, alongside the referred peripherals, has shown great potential for building low cost experimental setups to be used in physics classes, both for expositive and hands on approaches.展开更多
Oscillations and their damping were investigated for plant stems of Cyperus alternifolius L., Equisetum hyemale L., Equisetum fluviatile L., Juncus effuses L., Stipa gigantea Link, and Thamnocalamus spathaceus (Franc...Oscillations and their damping were investigated for plant stems of Cyperus alternifolius L., Equisetum hyemale L., Equisetum fluviatile L., Juncus effuses L., Stipa gigantea Link, and Thamnocalamus spathaceus (Franch.) Soderstr. With the exception of T. spathaceus, mechanical damping of the oscillation of individual plant stems, even without side organs, leaves or inflorescences, is quite effective. Our experiments support the hypothesis that embedding stiff sclerenchymatous elements in a more compliant parenchymatous matrix provides the structural basis for the dissipation of mechanical energy in the plant stem. As an application the naturally occurring structures were mimicked in a compound material made from hemp fabrics em- bedded in polyurethane foam, cured under pressure. Like its natural model it shows plastic deformability and viscoelastic be- haviour. In particular the material is characterized by a remarkably high shock absorption capacity even for high impact loads.展开更多
In this paper, a powerful analytical method, called He’s homotopy perturbation method is applied to obtaining the approximate periodic solutions for some nonlinear differential equations in mathematical physics via V...In this paper, a powerful analytical method, called He’s homotopy perturbation method is applied to obtaining the approximate periodic solutions for some nonlinear differential equations in mathematical physics via Van der Pol damped non-linear oscillators and heat transfer. Illustrative examples reveal that this method is very effective and convenient for solving nonlinear differential equations. Comparison of the obtained results with those of the exact solution, reveals that homotopy perturbation method leads to accurate solutions.展开更多
This paper presents the effect of the high voltage direct current (HVDC) transmission system based on voltage source converter (VSC) on the sub synchronous resonance (SSR) and low frequency oscillations (LFO) in power...This paper presents the effect of the high voltage direct current (HVDC) transmission system based on voltage source converter (VSC) on the sub synchronous resonance (SSR) and low frequency oscillations (LFO) in power system. Also, a novel adaptive neural controller based on neural identifier is proposed for the HVDC which is capable of damping out LFO and sub synchronous oscillations (SSO). For comparison purposes, results of system based damping neural controller are compared with a lead-lag controller based on quantum particle swarm optimization (QPSO). It is shown that implementing adaptive damping controller not only improves the stability of power system but also can overcome drawbacks of conventional compensators with fixed parameters. In order to determine the most effective input of HVDC system to apply supplementary controller signal, analysis based on singular value decomposition is performed. To evaluate the performance of the proposed controller, transient simulations of detailed nonlinear system are considered.展开更多
The oscillatory behavior of solutions of a class of second order nonlinear differential equations with damping is studied and some new sufficient conditions are obtained by using the refined integral averaging techniq...The oscillatory behavior of solutions of a class of second order nonlinear differential equations with damping is studied and some new sufficient conditions are obtained by using the refined integral averaging technique. Some well known results in the literature are extended. Moreover, two examples are given to illustrate the theoretical analysis.展开更多
In this article, we will establish sufficient conditions for the interval oscillation of fractional partial differential equations of the form It is based on the information only on a sequence of subintervals of the t...In this article, we will establish sufficient conditions for the interval oscillation of fractional partial differential equations of the form It is based on the information only on a sequence of subintervals of the time space rather than whole half line. We consider f to be monotonous and non monotonous. By using a generalized Riccati technique, integral averaging method, Philos type kernals and new interval oscillation criteria are established. We also present some examples to illustrate our main results.展开更多
Forced and damped oscillators appear in the mathematical modelling of many problems in pure and applied sciences such as physics, engineering and celestial mechanics among others. Although the accuracy of the T-functi...Forced and damped oscillators appear in the mathematical modelling of many problems in pure and applied sciences such as physics, engineering and celestial mechanics among others. Although the accuracy of the T-functions series method is high, the calculus of their coefficients needs specific recurrences in each case. To avoid this inconvenience, the T-functions series method is transformed into a multistep method whose coefficients are calculated using recurrence procedures. These methods are convergent and have the same properties to the T-functions series method. Numerical examples already used by other authors are presented, such as a stiff problem, a Duffing oscillator and an equatorial satellite problem when the perturbation comes from zonal harmonics J2.展开更多
The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity is obtained by making a specific coordinate transformation and by using the method of time-dependent invariant.
In this study, homotopy perturbation method and parameter expanding method are applied to the motion equations of two nonlinear oscillators. Our results show that both the (HPM) and (PEM) yield the same results for th...In this study, homotopy perturbation method and parameter expanding method are applied to the motion equations of two nonlinear oscillators. Our results show that both the (HPM) and (PEM) yield the same results for the nonlinear problems. In comparison with the exact solution, the results show that these methods are very convenient for solving nonlinear equations and also can be used for strong nonlinear oscillators.展开更多
This paper presents a comprehensive stability analysis of the dynamics of the damped cubic-quintic Duffing oscillator. We employ the derivative expansion method to investigate the slightly damped cubic-quintic Duffing...This paper presents a comprehensive stability analysis of the dynamics of the damped cubic-quintic Duffing oscillator. We employ the derivative expansion method to investigate the slightly damped cubic-quintic Duffing oscillator obtaining a uniformly valid solution. We obtain a uniformly valid solution of the un-damped cubic-quintic Duffing oscillator as a special case of our solution. A phase plane analysis of the damped cubic-quintic Duffing oscillator is undertaken showing some chaotic dynamics which sends a signal that the oscillator may be useful as model for prediction of earth- quake occurrence.展开更多
The time dependence of probability and Shannon entropy of a modified damped harmonic oscillator is studied by using single and double Gaussian wave functions through the Feynman path method. We establish that the damp...The time dependence of probability and Shannon entropy of a modified damped harmonic oscillator is studied by using single and double Gaussian wave functions through the Feynman path method. We establish that the damped coefficient as well as the system frequency and the distance separating two consecutive waves of the initial double Gaussian function influences the coherence of the system and can be used to control its decoherence.展开更多
This paper presents a new approach for determining the effective control signals for damping of oscillations by using fuzzy logic based Interline Power Flow Controller [IPFC]. The IPFC performance is tested with PI co...This paper presents a new approach for determining the effective control signals for damping of oscillations by using fuzzy logic based Interline Power Flow Controller [IPFC]. The IPFC performance is tested with PI controllers in comparison with fuzzy logic based controller on Modified Phllips-Heffron Model of Single Machine Infinite Bus System to achieve improved damping performance by selecting effective control signals such as deviation in pulse width modulation index of voltage series converter 1 in line 1, pulse width modulation index of voltage series converter 2 in line 2, deviation in phase angle of the injected voltage of convertor 1, injected voltage phase angle deviation of convertor 2. Investigations reveal that coordinated tuning of Interline Power Flow Controller with Fuzzy Logic Controller provides the robust dynamic performance. The Fuzzy Logic Based Interline Power Flow Controller [IPFC] is designed with simple fuzzy rules to coordinate the additional damping signal. The proposed controllers for IPFC are able to achieve improved designed performance of the power system. Validity of effective control signals has been done by eigen value analysis.展开更多
基金supported in part by the Fundamental Research Funds for the Central Universities under Grant 2682023CX019National Natural Science Foundation of China under Grant U23B6007 and Grant 52307141Sichuan Science and Technology Program under Grant 2024NSFSC0115。
文摘High-frequency oscillation(HFO)of gridconnected wind power generation systems(WPGS)is one of the most critical issues in recent years that threaten the safe access of WPGS to the grid.Ensuring the WPGS can damp HFO is becoming more and more vital for the development of wind power.The HFO phenomenon of wind turbines under different scenarios usually has different mechanisms.Hence,engineers need to acquire the working mechanisms of the different HFO damping technologies and select the appropriate one to ensure the effective implementation of oscillation damping in practical engineering.This paper introduces the general assumptions of WPGS when analyzing HFO,systematically summarizes the reasons for the occurrence of HFO in different scenarios,deeply analyses the key points and difficulties of HFO damping under different scenarios,and then compares the technical performances of various types of HFO suppression methods to provide adequate references for engineers in the application of technology.Finally,this paper discusses possible future research difficulties in the problem of HFO,as well as the possible future trends in the demand for HFO damping.
文摘Static dipole-dipole magnetic interaction is a classic topic discussed in electricity and magnetism text books. Its dynamic version, however, has not been reported in scientific literature. In this article, the author presents a comprehensive analysis of the latter. We consider two identical permanent cylindrical magnets. In a practical setting, we place one of the magnets at the bottom of a vertical glass tube and then drop the second magnet in the tube. For a pair of suitable permanent magnets characterized with their mass and magnetic moment we seek oscillations of the mobile magnet resulting from the unbalanced forces of the anti-parallel magnetic dipole orientation of the pair. To quantify the observed oscillations we form an equation describing the motion of the bouncing magnet. The strength of the magnet-magnet interaction is in proportion to the inverse fourth order separation distance of the magnets. Consequently, the corresponding equation of motion is a highly nonlinear differential equation. We deploy Mathematica and solve the equation numerically resulting in a family of kinematic information. We show our theoretical model with great success matches the measured data.
文摘Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t0, ∞), and f∈C1 (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results.
文摘This paper investigates a class of even order functional differential equations with damped term,and derives two new oscillatory criteria of solution.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10963002)the International S & T Cooperation Program of China and Jiangxi Province (Grant No. 2009DFA02320)+1 种基金the Program for Innovative Research Team of Nanchang Universitythe National Basic Research Program of China (Grant No. 2010CB635112)
文摘The generalized dispersion equation for longitudinal oscillation in an unmagnetized, collisionless, isotropic and relativistic plasma is derived in the context of nonextensive q-distribution. An analytical expression for the Landau damping is obtained in an ultra-relativistic regime, which is related to q-parameter. In the limit q →1, the result based on the relativistic Maxwellian distribution is recovered. It is shown that the interactions between the wave and particles are stronger and the waves are more strongly damped for lower values of q-parameter. The results are explained by the increased number of superthermal particles or low velocity particles contained in the plasma with the nonextensive distribution.
基金National Natural Science Foundation of China(No.11802338)
文摘The purpose is to design the control method for a single-degree-of-freedom(SDOF)exponentially damped oscillator.Based on the Lyapunov stability theory,sliding mode control and adaptive sliding mode control have been proposed.Sliding control laws and adaptive sliding laws are designed for exponentially damped oscillator respectively in cases that the bound of the external exciting force is known or unknown.The viability and effectiveness of the above control designs have been validated by numerical simulations.
文摘By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.
基金Project(51007042) supported by the National Natural Science Foundation of China
文摘Wide area damping controller(WADC) is usually utilized to damp interarea low frequency oscillation in power system. However, conventional WADC design method neglects the influence of signal transmission delay and damping performance of WADC designed by the conventional method may deteriorate or even has no effect when signal transmission delay is beyond delay margin, an index that denotes delay endurance degree of power system. Therefore, a new design method for WADC under the condition of expected damping factor and required signal transmission delay is presented in this work. An improved delay margin with less conservatism is derived by adopting a new Lyapunov-Krasovskii function and more compact bounding technique on the derivative of Lyapunov-Krasovskii functional. The improved delay margin, which constructs the correlation of damping factor and signal transmission delay, can be used to design WADC. WADC designed by the proposed method can ensure that power system satisfies expected damping factor when WADC input signal is delayed within delay margin. Satisfactory test results demonstrate the effectiveness of the proposed method.
文摘The benefits of using experiments in physics classes are widely discussed in the literature, but sometimes experimental setups are not available. In this paper we present different ways of using experiments in physics classes based on the Arduino board, since it involves low cost materials and can be built by the own students in several cases. In this work we addressed the well known damped harmonic oscillator and performed the data acquisition through the Arduino board, a LDR (Light Dependent Resistor), a infrared photodiode sensor and a computer. The setup of the proposed experiment and the technical details related to assembly are discussed in a clear way in order to be reproduced by anyone interested in the subject. We found a significant difference in the results obtained through the LDR and the photodiode. The later has given better results and has reproduced a regular decay in the amplitude of the oscillator even when the experiment was performed in a highly illuminated room. The Arduino board, alongside the referred peripherals, has shown great potential for building low cost experimental setups to be used in physics classes, both for expositive and hands on approaches.
文摘Oscillations and their damping were investigated for plant stems of Cyperus alternifolius L., Equisetum hyemale L., Equisetum fluviatile L., Juncus effuses L., Stipa gigantea Link, and Thamnocalamus spathaceus (Franch.) Soderstr. With the exception of T. spathaceus, mechanical damping of the oscillation of individual plant stems, even without side organs, leaves or inflorescences, is quite effective. Our experiments support the hypothesis that embedding stiff sclerenchymatous elements in a more compliant parenchymatous matrix provides the structural basis for the dissipation of mechanical energy in the plant stem. As an application the naturally occurring structures were mimicked in a compound material made from hemp fabrics em- bedded in polyurethane foam, cured under pressure. Like its natural model it shows plastic deformability and viscoelastic be- haviour. In particular the material is characterized by a remarkably high shock absorption capacity even for high impact loads.
文摘In this paper, a powerful analytical method, called He’s homotopy perturbation method is applied to obtaining the approximate periodic solutions for some nonlinear differential equations in mathematical physics via Van der Pol damped non-linear oscillators and heat transfer. Illustrative examples reveal that this method is very effective and convenient for solving nonlinear differential equations. Comparison of the obtained results with those of the exact solution, reveals that homotopy perturbation method leads to accurate solutions.
文摘This paper presents the effect of the high voltage direct current (HVDC) transmission system based on voltage source converter (VSC) on the sub synchronous resonance (SSR) and low frequency oscillations (LFO) in power system. Also, a novel adaptive neural controller based on neural identifier is proposed for the HVDC which is capable of damping out LFO and sub synchronous oscillations (SSO). For comparison purposes, results of system based damping neural controller are compared with a lead-lag controller based on quantum particle swarm optimization (QPSO). It is shown that implementing adaptive damping controller not only improves the stability of power system but also can overcome drawbacks of conventional compensators with fixed parameters. In order to determine the most effective input of HVDC system to apply supplementary controller signal, analysis based on singular value decomposition is performed. To evaluate the performance of the proposed controller, transient simulations of detailed nonlinear system are considered.
文摘The oscillatory behavior of solutions of a class of second order nonlinear differential equations with damping is studied and some new sufficient conditions are obtained by using the refined integral averaging technique. Some well known results in the literature are extended. Moreover, two examples are given to illustrate the theoretical analysis.
文摘In this article, we will establish sufficient conditions for the interval oscillation of fractional partial differential equations of the form It is based on the information only on a sequence of subintervals of the time space rather than whole half line. We consider f to be monotonous and non monotonous. By using a generalized Riccati technique, integral averaging method, Philos type kernals and new interval oscillation criteria are established. We also present some examples to illustrate our main results.
文摘Forced and damped oscillators appear in the mathematical modelling of many problems in pure and applied sciences such as physics, engineering and celestial mechanics among others. Although the accuracy of the T-functions series method is high, the calculus of their coefficients needs specific recurrences in each case. To avoid this inconvenience, the T-functions series method is transformed into a multistep method whose coefficients are calculated using recurrence procedures. These methods are convergent and have the same properties to the T-functions series method. Numerical examples already used by other authors are presented, such as a stiff problem, a Duffing oscillator and an equatorial satellite problem when the perturbation comes from zonal harmonics J2.
文摘The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity is obtained by making a specific coordinate transformation and by using the method of time-dependent invariant.
文摘In this study, homotopy perturbation method and parameter expanding method are applied to the motion equations of two nonlinear oscillators. Our results show that both the (HPM) and (PEM) yield the same results for the nonlinear problems. In comparison with the exact solution, the results show that these methods are very convenient for solving nonlinear equations and also can be used for strong nonlinear oscillators.
文摘This paper presents a comprehensive stability analysis of the dynamics of the damped cubic-quintic Duffing oscillator. We employ the derivative expansion method to investigate the slightly damped cubic-quintic Duffing oscillator obtaining a uniformly valid solution. We obtain a uniformly valid solution of the un-damped cubic-quintic Duffing oscillator as a special case of our solution. A phase plane analysis of the damped cubic-quintic Duffing oscillator is undertaken showing some chaotic dynamics which sends a signal that the oscillator may be useful as model for prediction of earth- quake occurrence.
文摘The time dependence of probability and Shannon entropy of a modified damped harmonic oscillator is studied by using single and double Gaussian wave functions through the Feynman path method. We establish that the damped coefficient as well as the system frequency and the distance separating two consecutive waves of the initial double Gaussian function influences the coherence of the system and can be used to control its decoherence.
文摘This paper presents a new approach for determining the effective control signals for damping of oscillations by using fuzzy logic based Interline Power Flow Controller [IPFC]. The IPFC performance is tested with PI controllers in comparison with fuzzy logic based controller on Modified Phllips-Heffron Model of Single Machine Infinite Bus System to achieve improved damping performance by selecting effective control signals such as deviation in pulse width modulation index of voltage series converter 1 in line 1, pulse width modulation index of voltage series converter 2 in line 2, deviation in phase angle of the injected voltage of convertor 1, injected voltage phase angle deviation of convertor 2. Investigations reveal that coordinated tuning of Interline Power Flow Controller with Fuzzy Logic Controller provides the robust dynamic performance. The Fuzzy Logic Based Interline Power Flow Controller [IPFC] is designed with simple fuzzy rules to coordinate the additional damping signal. The proposed controllers for IPFC are able to achieve improved designed performance of the power system. Validity of effective control signals has been done by eigen value analysis.
