Journal articles: 'Steady-state stability limit'

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Indulkar, C. S. "An Exercise for Teaching Transient Stability." International Journal of Electrical Engineering & Education 31, no. 4 (1994): 357–61. http://dx.doi.org/10.1177/002072099403100412.

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An exercise for teaching transient stability In this paper, the transient stability limits of a synchronous machine for various initial loadings have been determined in terms of its steady-state stability limit.

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Hou, Kaiyuan, Zeyu Li, Lei Chen, Deming Xia, Qun Li, and Yong Xiao. "Steady-State Stability of Sending-End System with Mixed Synchronous Generator and Power-Electronic-Interfaced Renewable Energy." Mathematical Problems in Engineering 2020 (April 10, 2020): 1–11. http://dx.doi.org/10.1155/2020/8693245.

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Coupled with the power system through power-electronic interfaces, renewable energies including wind power and photovoltaic can control the power quickly and flexibly. In the steady-state stability analysis, by neglecting the fast dynamics of power-electronic interfaces, the renewable energy power is simplified to a static power injection model and can be described as an algebraic equation in the dynamic process. Based on this simplified model, the steady-state stability of sending-end system with mixed synchronous generator and power-electronic-interfaced renewable energy is studied. By proposing a triangular transformation model based on the classical model of power system, the steady-state stability analysis becomes feasible. The mechanism of steady-state stability is revealed, and the influence of renewable energy on the steady-state stability limit is quantitatively investigated. When the renewable energy power increases, the steady-state stability limit of the sending-end system first increases and then decreases. Reducing the power output of synchronous generator can change for a higher integration limit of renewable energy. Simulation results validate the conclusion.

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Zhang, Wen Chao, Xin Qiao Fan, Yu Long He, Yan Pan, and Yong Lu. "Study on the Steady-State Stability Margin of a Weak Section by Using the Online Data of WAMS." Applied Mechanics and Materials 738-739 (March 2015): 1289–95. http://dx.doi.org/10.4028/www.scientific.net/amm.738-739.1289.

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To realize the on-line quick analysis of the steady-state stability margin for the weak section of a power grid, a method of dividing the important generator groups according to the impact of the system equivalent impedance on the static stability limits of the section is presented. By using the dynamic information provided by the Wide Area Measurement System (WAMS), the center of inertia (COI) of the section of the two sides system is determined. Then the steady-state stability limits of the transmission section and the static stability margin can be calculated. The algorithm is verified by taking the out-play cross-section of West Inner Mongolia as an example, the results show that the static stability power limit and the steady-state stability margin of the section can be obtained accurately according to the presented algorithm. This algorithm can provide an effective analytical method for the online static stability security analysis of a power system.

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Arjona L., M. A., and D. C. Macdonald. "Saturation effects on the steady-state stability limit of turbine-generators." IEEE Transactions on Energy Conversion 14, no. 2 (1999): 133–38. http://dx.doi.org/10.1109/60.766957.

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Haque, M. H. "Determination of Steady-State Voltage Stability Limit Using P-Q Curve." IEEE Power Engineering Review 22, no. 4 (2002): 71–72. http://dx.doi.org/10.1109/mper.2002.4312118.

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Rusilawati, Irrine Budi Sulistiawati, Adi Soeprijanto, and Rony Seto Wibowo. "Determination of Generator Steady State Stability Limit for Multimachine System based on Network Losses Concept." MATEC Web of Conferences 164 (2018): 01041. http://dx.doi.org/10.1051/matecconf/201816401041.

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In the multimachine circumstances, it is difficult to analyze the steady state stability of each generator. In previous research, analysis of the steady state stability limit has been carried out but only look at the stability of the overall system. Therefore, to analyze the stability of each generator, the multimachine system must be changed into a Single Machine to Infinite Bus (SMIB) system by collecting all the loads into one central load in the infinite bus. The method to change from the multimachine system to SMIB system is presented in this paper. The multimachine system is converted into an equivalent impedance (req and xeq) and an equivalent load based on losses concept. After req and xeq is calculated, then by using steady state stability limit concept, the value of the maximum generation of each generator units can be determined. By means of maximum generation is the maximum output power limit that can be generated without causing unstability. ETAP simulation is used to validate the calculation results of the proposed method. The method was applied to units generator in Java Bali system 500 kV.

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Shneer, Seva, and Alexander Stolyar. "Stability and moment bounds under utility-maximising service allocations: Finite and infinite networks." Advances in Applied Probability 52, no. 2 (2020): 463–90. http://dx.doi.org/10.1017/apr.2020.8.

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AbstractWe study networks of interacting queues governed by utility-maximising service-rate allocations in both discrete and continuous time. For finite networks we establish stability and some steady-state moment bounds under natural conditions and rather weak assumptions on utility functions. These results are obtained using direct applications of Lyapunov–Foster-type criteria, and apply to a wide class of systems, including those for which fluid-limit-based approaches are not applicable. We then establish stability and some steady-state moment bounds for two classes of infinite networks, with single-hop and multi-hop message routes. These results are proved by considering the infinite systems as limits of their truncated finite versions. The uniform moment bounds for the finite networks play a key role in these limit transitions.

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E. Mubeen, Samina, Baseem Khan, and R. K. Nema. "Application of Unified Power Flow Controller to Improve Steady State Voltage Limit." IAES International Journal of Robotics and Automation (IJRA) 6, no. 4 (2017): 277. http://dx.doi.org/10.11591/ijra.v6i4.pp277-285.

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<span>This paper utilizes the voltage source model of Unified Power Flow Controller (UPFC) and examines its abilities in mitigating the steady state stability margins of electric power system. It analyzes its behavior for different controls strategies and proposes the most efficient mode of controlling the controller for voltage stability enhancement. A systematic analytical methodology based on the concept of modal analysis of the modified load flow equations is employed to identify the area in a power system which is most prone voltage instability. Also to identify the most effective point of placement for the UPFC, a computer program has been developed using MATLAB. The results of analysis on 14 bus system is presented here as a case study.</span>

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Balasubramaniam, P., M. Prakash, Fathalla A. Rihan, and S. Lakshmanan. "Hopf Bifurcation and Stability of Periodic Solutions for Delay Differential Model of HIV Infection of CD4+T-cells." Abstract and Applied Analysis 2014 (2014): 1–18. http://dx.doi.org/10.1155/2014/838396.

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This paper deals with stability and Hopf bifurcation analyses of a mathematical model of HIV infection ofCD4+T-cells. The model is based on a system of delay differential equations with logistic growth term and antiretroviral treatment with a discrete time delay, which plays a main role in changing the stability of each steady state. By fixing the time delay as a bifurcation parameter, we get a limit cycle bifurcation about the infected steady state. We study the effect of the time delay on the stability of the endemically infected equilibrium. We derive explicit formulae to determine the stability and direction of the limit cycles by using center manifold theory and normal form method. Numerical simulations are presented to illustrate the results.

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Rusilawati. "Menentukan Batas Kestabilan Steady State Sistem Jawa Bali 500 kV menggunakan Pendekatan Model Single Machine to Infinite Bus." ALINIER: Journal of Artificial Intelligence & Applications 1, no. 1 (2020): 1–12. http://dx.doi.org/10.36040/alinier.v1i1.2517.

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The indicator of the power system operation stability can be seen from the power balance between the load demand and the generator output power. The Single Machine to Infinite Bus (SMIB) system that can actually represent the operation of a single machine system in a multimachine system can be used to analyze each generator unit stability. This paper present a fairly simple method to determine the generator steady state stability limit on the Jawa Bali 500 kV system using an SMIB system approach consider the load configuration changes in the system. The Radial Basis Function Neural Network (RBFNN) is applied to simplify the determination of the generator steady state stability limit that changes every time a load configuration changes. The simulation results carried out on the Java Bali system 500 kV 29 bus 10 generators can be seen that the steady state stability limit of each generator unit tends to decrease with the increasing of loading value and the further of load distance from the generator.  Keseimbangan daya antara kebutuhan beban dengan pembangkitan generator merupakan salah satu ukuran kestabilan operasi sistem tenaga listrik., Untuk menganalisis kestabilan setiap unit generator dalam sistem multimachine harus dilakukan pada sistem Single Machine to Infinite Bus (SMIB) yang secara aktual dapat mewakili keadaan sistem single machine tersebut dalam sebuah sistem multimachine. Dalam paper ini digunakan suatu metode sederhana untuk menentukan batas kestabilan steady state setiap unit generator pada sistem multimachine Jawa Bali 500 kV menggunakan pendekatan model sistem SMIB dengan memperhatikan perubahan konfigurasi peletakan beban dalam sistem. Untuk memudahkan penentuan batas kestabilan steady state generator yang selalu berubah setiap saat terjadi perubahan peletakan beban, diaplikasikan salah satu model jaring syaraf tiruan yaitu Radial Basis Function Neural Network (RBFNN). Dari hasil simulasi yang dilakukan pada sistem Jawa Bali 500 kV 29 bus 10 generator dapat diketahui bahwa batas kestabilan steady state setiap unit generator cenderung menurun dengan semakin meningkatnya nilai pembebanan dan semakin jauhnya jarak beban dari pembangkit.

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DE LA FUENTE, LORENZO, DAVID INGRAM, CLIVE MINGHAM, DEREK CAUSON, and XIAO-YI HE. "ENHANCING STABILITY OF LATTICE-BOLTZMANN SIMULATIONS VIA NEW BOUNDARY CONDITIONS." International Journal of Modern Physics C 14, no. 01 (2003): 29–40. http://dx.doi.org/10.1142/s0129183103004176.

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A new boundary condition is developed to enhance numerical stability for moving walls in lattice-Boltzmann simulations. It includes a population "adjustment" procedure at boundaries which allows stable simulations closer to the theoretical limit of τ = 0.5. Couette and lid-driven cavity flow simulations show improved velocity profiles, lower stable relaxation timestep τ and higher Reynolds number Re limits. The new method needs fewer timesteps to achieve steady-state.

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Zheng, Hui Ping, Yu Long Yang, Shu Yong Song, Xin Yuan Liu, Min Xue, and Wen Chao Zhang. "Research on Generator Tripping Value of Security and Stability Control." Applied Mechanics and Materials 494-495 (February 2014): 1795–800. http://dx.doi.org/10.4028/www.scientific.net/amm.494-495.1795.

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In this paper, the problem of the excessive generator tripping value of security and stability control after occurrence of the N-2 fault in the Shentou-Yantong transmission line of Shanxi DaTong Regional grid is studied. And the principle of security and stability control measures based on equal area criterion is analyzed. The reason leading to excessive generator-tripping value of security and stability control after the occurrence of the N-2 fault in Shentou-Yantong region is figured out, and it is that the steady-state stability limit of transmission section decreases and the accelerator power cannot be released. Finally, the results of theoretical analysis are verified by simulations. The simulation results indicate that too large generator-tripping value of security and stability control is mainly caused by decrease of the steady-state stability limit of the transmission section after occurrence of the fault in Datong. The conclusions in the paper have referential significance for the study on similar power concentrated send-out systems.

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Golov, V. P., D. N. Kormilitsyn, and O. S. Sukhanova. "Transmitted power limit of controlled high voltage transmission line for modes on steady-state stability boundary." Vestnik IGEU, no. 2 (April 30, 2023): 28–35. http://dx.doi.org/10.17588/2072-2672.2023.2.028-035.

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The use of series compensation devices is one of the methods to increase the capacity of a power transmission line. In addition, the use of controlled series compensation devices affects the steady-state stability of the electric power system. It is also widely known that automatic excitation control of generators has a positive effect on the stability of the system. Thus, it is reasonable to analyze the influence of the adjustable parameters of the controlled series compensation device on the line capacity when considering modes at the boundaries of the stability regions, taking into account automatic excitation controllers on synchronous generators of the power plant. Methods of mathematical modeling of the electric power system, the theory of long-distance power lines and electromechanical transients, methods of analyzing the stability of electric power systems are used. The original software in the C ++ programming language is used as a modeling tool. The authors have selected the regulation laws parameters of controlled series compensation device and automatic excitation controller, provided that steady-state stability is maintained. The stability regions of the electric power-engineering system under study are constructed depending on the tuning parameters of the considered devices. A technique is proposed to select the coefficients of complex regulation of the devices to increase the capacity of a high-voltage power transmission line. The proposed method of the complex selection of regulation coefficients of controlled devices provides the possibility of obtaining their optimal values in a controlled electric power system to ensure stability.

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Antonelli, P. L., S. F. Rutz, and V. S. Sabău. "A Transient-State Analysis of Tyson's Model for the Cell Division Cycle by Means of KCC-Theory." Open Systems & Information Dynamics 09, no. 03 (2002): 223–38. http://dx.doi.org/10.1023/a:1019752327311.

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The transient-state stability analysis for the trajectories of Tyson's equations for the cell-division cycle is given by the so-called KCC-Theory. This is the differential geometric theory of the variational equations for deviation of whole trajectories to nearby ones. The relationship between Lyapunov stability of steady-states and limit cycles is throughly examined. We show that the region of stability (where, in engineering parlance, the system is “hunting”) encloses the Tyson limit cycle, while outside this region the trajectories exhibit a periodic behaviour.

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Nagamori, Yuichi, Naoyuki Uchida, and Kazuo Fujibayashi. "High Speed Searching of Steady State Stability Limit for Preventive Control of Power System." IEEJ Transactions on Power and Energy 130, no. 9 (2010): 795–801. http://dx.doi.org/10.1541/ieejpes.130.795.

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Sghir, Radhouane, and Mnaouar Chouchane. "Prediction of the nonlinear hysteresis loop for fluid-film bearings by numerical continuation." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 4 (2014): 651–62. http://dx.doi.org/10.1177/0954406214538618.

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A nonlinear dynamic model of a short journal bearing is used to predict the steady-state motion of the journal and its successive bifurcations in the neighbourhood of the stability critical speed. Numerical continuation is applied to determine the branch of equilibrium point and its bifurcation into stable or unstable limit cycles. It has been found that the unstable limit cycles undergo a single limit point bifurcation whereas the stable limit cycles undergo two successive limit point bifurcations. Thus, the bi-stability domain, the potential jumping from small to large motion and the hysteresis loop motion are predicted.

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HADŽIĆ, MAHIR, and GERHARD REIN. "On the small redshift limit of steady states of the spherically symmetric Einstein–Vlasov system and their stability." Mathematical Proceedings of the Cambridge Philosophical Society 159, no. 3 (2015): 529–46. http://dx.doi.org/10.1017/s0305004115000511.

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AbstractFamilies of steady states of the spherically symmetric Einstein–Vlasov system are constructed, which are parametrised by the central redshift. It is shown that as the central redshift tends to zero, the states in such a family are well approximated by a steady state of the Vlasov–Poisson system, i.e., a Newtonian limit is established where the speed of light is kept constant as it should be and the limiting behavior is analysed in terms of a parameter which is tied to the physical properties of the individual solutions. This result is then used to investigate the stability properties of the relativistic steady states with small redshift parameter in the spirit of recent work by the same authors, i.e., the second variation of the ADM mass about such a steady state is shown to be positive definite on a suitable class of states.

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Hoof, Simon. "Dynamic Monopolistic Competition." Journal of Optimization Theory and Applications 189, no. 2 (2021): 560–77. http://dx.doi.org/10.1007/s10957-021-01843-w.

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AbstractI study a dynamic variant of the Dixit–Stiglitz (Am Econ Rev 67(3), 1977) model of monopolistic competition by introducing price stickiness à la Fershtman and Kamien (Econometrica 55(5), 1987). The analysis is restricted to bounded quantity and price paths that fulfill the necessary conditions for an open-loop Nash equilibrium. I show that there exists a symmetric steady state and that its stability depends on the degree of product differentiation. When moving from complements to perfect substitutes, the steady state is either a locally asymptotically unstable (spiral) source, a stable (spiral) sink or a saddle point. I further apply the Hopf bifurcation theorem and prove the existence of limit cycles, when passing from a stable to an unstable steady state. Lastly, I provide a numerical example and show that there exists a stable limit cycle.

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Epureanu, B. I., F. M. Montoya, and C. L. Garcia. "Centerless Grinding Systems Stability." Journal of Manufacturing Science and Engineering 121, no. 2 (1999): 157–62. http://dx.doi.org/10.1115/1.2831199.

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In this paper, the steady state dynamics of a centerless grinding machine and work piece has been examined. A model of a centerless grinding system which allows both the deflection of the work piece center and the deformation of the grinding machine frame has been developed. Two instabilities are demarcated • work piece surface generation instability, and • grinding process instability. Both the generation and the grinding stability of self-excited vibrations are investigated. Stability limits are defined using the characteristic equations of the system. The main factors that influence the limit of stability of the machine, and the transversal profile of the work piece have been shown to be • the relative position of the grinding wheel, regulating wheel and support blade of the work piece; • the width of the grinding wheel; • the harmonic response of the grinding machine frame.

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Sawicki, Jerzy T., and T. V. V. L. N. Rao. "Cavitation Effects on the Stability of a Submerged Journal Bearing." International Journal of Rotating Machinery 10, no. 3 (2004): 227–32. http://dx.doi.org/10.1155/s1023621x04000247.

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A computational procedure for the mechanism of shear between the liquid sublayer and air cavity in the cavitation zone of a submerged journal bearing is presented here. Using the mass conservation principle, Elrod's universal equation is modified to take into consideration the shear of the air cavity in the cavitation region. Results of steady state and transient response for the submerged journal bearing using the present approach are compared with the universal equation based on the striated flow in the cavitation region. At steady state, the angular extent of cavitation region predicted by the present approach is higher than that predicted by Elrod's model and the limit cycle journal transient response using the present approach predicts higher eccentricity ratios.

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Kara, F., and D. Vassalos. "Time Domain Computation of the Wave-Making Resistance of Ships." Journal of Ship Research 49, no. 02 (2005): 144–58. http://dx.doi.org/10.5957/jsr.2005.49.2.144.

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The Ship Stability Research Centre, Department of Naval Architecture and Marine Engineering, The Universities of Glasgow and Strathclyde, Scotland, UKA linearized three-dimensional potential flow formulation in time domain is applied to calculate wave-making resistance of ships in calm water. Steady-state perturbation potentials for resistance are obtained as the steady-state limit of the surge radiation impulse response function using the transient free surface source distribution over the body surface. Five different vessels are used to validate the present numerical approximation. The results, including steady-state wave-making resistance, sinkage force, trim moment, and wave profile along the waterline, are compared with other published numerical and experimental results.

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Wang, Yuanzhen, Aiping Sun, Zhengji Li, Zhuo Wang, Yue Liu та Xinliang Xu. "Predicted optimization of β _N limit for steady-state scenario with double transport barriers in HL-2M tokamak". Plasma Physics and Controlled Fusion 64, № 5 (2022): 055002. http://dx.doi.org/10.1088/1361-6587/ac55f7.

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Abstract The equilibria of the HL-2M tokamak, designed for steady-state operation with reversed magnetic shear and double transport barriers, are calculated using TOQ code, and the n = 1 linear ideal magnetohydrodynamic (MHD) stability of the equilibria is investigated using GATO code. To improve the beta ( β N ) limit, the MHD stability of the equilibria with different heights of internal transport barrier (ITB) and edge transport barrier (ETB) is simulated. The simulation results indicate that the ITB drives low m globalized modes while the ETB drives high m edge localized modes, and thus a moderate barrier height ratio is beneficial to MHD stability. By adjusting the heights of both barriers with different plasma shapes, as well as different locations and widths of ITBs, optimal equilibria with improved MHD stability are achieved, which always have a moderate barrier height ratio unless the ITB is extremely wide or very close to the edge. In ideal-wall conditions, when the ITB is wide enough or very close to the edge, β N limits could exceed six, or even reach seven in some special cases. Increasing elongation and triangularity, broadening the ITB, as well as moving the ITB to a large minor radius, can contribute to the optimization of the β N limit, especially when combined with the stabilizing effect from an ideal wall.

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SISWANTO, Agus. "Steady State Stability Limit Assessment when Wind Turbine Penetrated to the Systems using REI Approach." PRZEGLĄD ELEKTROTECHNICZNY 1, no. 6 (2019): 53–57. http://dx.doi.org/10.15199/48.2019.06.10.

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Sladen, J. A., R. D. D'Hollander, and J. Krahn. "The liquefaction of sands, a collapse surface approach." Canadian Geotechnical Journal 22, no. 4 (1985): 564–78. http://dx.doi.org/10.1139/t85-076.

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Recent large-scale slides occurring during the hydraulic placement of an artificial island berm in the Beaufort Sea resulted from the liquefaction of the berm sand. Subsequent laboratory tests and back analyses have led to advancements in the understanding of the liquefaction potential of sand. Analyses of undrained triaxial tests, undertaken to measure steady state parameters, suggest that there is a "collapse surface" in three-dimensional void ratio – shear stress – normal stress space. A necessary condition for liquefaction is that the soil state lie on this surface. This collapse surface concept is fundamentally an extension of the steady state concepts proposed by others, and in many respects follows the principles of critical state soil mechanics. Replotted published tests support the concept. Parameters used to describe the position of the surface are termed collapse parameters. These can be converted into parameters analogous to Mohr–Coulomb failure parameters and can therefore be used in conventional limit equilibrium stability analyses. Utilizing these parameters overcomes limitations inherent in previously proposed undrained steady state analysis methods. These concepts also provide a basis for a rational explanation of the Beaufort Sea hydraulic fill slides. Key words: liquefaction, sand, hydraulic fill, slope stability, steady state testing.

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Liu, Jia, and Yun Kang. "Spatiotemporal dynamics of a diffusive predator–prey model with fear effect." Nonlinear Analysis: Modelling and Control 27 (May 14, 2022): 1–22. http://dx.doi.org/10.15388/namc.2022.27.27535.

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This paper concerned with a diffusive predator–prey model with fear effect. First, some basic dynamics of system is analyzed. Then based on stability analysis, we derive some conditions for stability and bifurcation of constant steady state. Furthermore, we derive some results on the existence and nonexistence of nonconstant steady states of this model by considering the effect of diffusion. Finally, we present some numerical simulations to verify our theoretical results. By mathematical and numerical analyses, we find that the fear can prevent the occurrence of limit cycle oscillation and increase the stability of the system, and the diffusion can also induce the chaos in the system.

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Miao, Haixing, Joe Bentley, Hendra Nurdin, and Yanbei Chen. "Fundamental quantum limit for linear measurements with instability." Applied Physics Letters 122, no. 13 (2023): 134001. http://dx.doi.org/10.1063/5.0139740.

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The fundamental quantum limit, or the quantum Cramér-Rao bound, defines the sensitivity limit for quantum measurements. For linear measurement systems, such as gravitational-wave detectors, it is inversely proportional to the noise spectrum of the dynamical variable that couples to the measured signal. Defining a physically meaningful spectrum, however, requires that the system is stable and a steady state exists. We relax such a stability requirement and prove that the fundamental quantum limit can be derived simply by considering the open-loop dynamics in the Fourier domain.

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Xing, Da Peng, Jia Li, and Da Qiang Qiu. "A New Estimation Method of Transient Voltage Stability Limit Clearing Time." Advanced Materials Research 971-973 (June 2014): 1051–54. http://dx.doi.org/10.4028/www.scientific.net/amr.971-973.1051.

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Critical clearing time index is one of the indices to assess transient voltage stability. At present it is mainly calculated based on the instantaneous value after transient voltage instability or the steady state valueafer fault clearing time. So a new method to estimate the critical clearing time is presented which is correspongding to the induction motor minimum slipvalue in the fault. It can forecasttransient voltage instability,and has higher precision comparing whithquik criterion and analytical method. The simulation results of IEEE 30-bus system verify the effectiveness of the stated method. .CLC number: TM 73 Document code: A Article ID: 000-3673(2013)00-0000-00

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Podymaka, Valeriy. "DYNAMIC CONDITIONS OF COMPENSATED SYNCHRONOUS MACHINE." Science Journal Innovation Technologies Transfer, no. 2019-4 (September 1, 2019): 76–82. http://dx.doi.org/10.36381/iamsti.4.2019.76-82.

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The dynamic behavior of synchronous machine with longitudinal-transverse excitement by maintenance of the rotor overhang corner as equal zero are considered. The given condition is named as compensated and correspond with full compensation of transverse armature reaction by magnetizing force of transverse excitement winding. In such machine is absented the limit of steady-state overload, but active and reactive components of load current are concurrent as projections of load current image vector on orthogonal axes of machine inductor. The research aim is a determination of steady-state stability criterion of compensated synchronous machine working on powerful electrical system. The researches are organized in assumption of inductor current invariance and at neglect of stator windings time constant. The electromagnetic moment expression of longitudinal-transverse excitement synchronous machine in compensated work condition is received as a result of analysis of the spatial vector diagrams and equations. The expression analysis has allowed to find the criterion of rotor creepage stability and to examine the steady-state stability of the machine in different work conditions. It is shown that machines stability factor is defined by not only the reactive power of machine short circuit, but also associated reactive power.

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Hetzler, H., D. Schwarzer, and W. Seemann. "Steady-state stability and bifurcations of friction oscillators due to velocity-dependent friction characteristics." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 221, no. 3 (2007): 401–12. http://dx.doi.org/10.1243/14644193jmbd80.

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This article presents an analytical investigation on stability and bifurcation behaviour due to an exponential and a generalized friction characteristics in the sliding domain of a simple friction oscillator, which is commonly referred to as ‘mass-on-a-belt’ oscillator. The friction is described by a friction coefficient which depends on the relative velocity between the two tribological partners. The standard way of examining the steady-state only gives very rough insight in the behaviour and is not able to provide further informations about the steady-state's basin of attraction or about limit-cycles. It is found that the system may undergo bifurcations of Hopf type. Hereby, the character of the bifurcations strongly depends on the parameters of the friction characteristic.

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THAOKAR, R. M., and V. KUMARAN. "Stability of fluid flow past a membrane." Journal of Fluid Mechanics 472 (November 30, 2002): 29–50. http://dx.doi.org/10.1017/s0022112002001751.

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The stability of fluid flow past a membrane of infinitesimal thickness is analysed in the limit of zero Reynolds number using linear and weakly nonlinear analyses. The system consists of two Newtonian fluids of thickness R* and HR*, separated by an infinitesimally thick membrane, which is flat in the unperturbed state. The dynamics of the membrane is described by its normal displacement from the flat state, as well as a surface displacement field which provides the displacement of material points from their steady-state positions due to the tangential stress exerted by the fluid flow. The surface stress in the membrane (force per unit length) contains an elastic component proportional to the strain along the surface of the membrane, and a viscous component proportional to the strain rate. The linear analysis reveals that the fluctuations become unstable in the long-wave (α→0) limit when the non-dimensional strain rate in the fluid exceeds a critical value Λt, and this critical value increases proportional to α2 in this limit. Here, α is the dimensionless wavenumber of the perturbations scaled by the inverse of the fluid thickness R*−1, and the dimensionless strain rate is given by Λt = (γ˙*R*η*/Γ*), where η* is the fluid viscosity, Γ* is the tension of the membrane and γ˙* is the strain rate in the fluid. The weakly nonlinear stability analysis shows that perturbations are supercritically stable in the α→0 limit.

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Wang, Liqiu, and Tianliang Yang. "Numerical Simulation of Multiplicity and Stability of Mixed Convection in Rotating Curved Ducts." International Journal of Rotating Machinery 2005, no. 2 (2005): 168–78. http://dx.doi.org/10.1155/ijrm.2005.168.

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A numerical study is made on the fully developed bifurcation structure and stability of the mixed convection in rotating curved ducts of square cross-section with the emphasis on the effect of buoyancy force. The rotation can be positive or negative. The fluid can be heated or cooled. The study reveals the rich solution and flow structures and complicated stability features. One symmetric and two symmetric/asymmetric solution branches are found with seventy five limit points and fourteen bifurcation points. The flows on these branches can be symmetric, asymmetric, 2-cell, and up to 14-cell structures. Dynamic responses of the multiple solutions to finite random disturbances are examined by the direct transient computation. It is found that possible physically realizable fully developed flows evolve, as the variation of buoyancy force, from a stable steady multicell state at a large buoyancy force of cooling to the coexistence of three stable steady multicell states, a temporal periodic oscillation state, the coexistence of periodic oscillation and chaotic oscillation, a chaotic temporal oscillation, a subharmonic-bifurcation-driven asymmetric oscillating state, and a stable steady 2-cell state at large buoyancy force of heating.

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32

Díaz-Araujo, Marcolino, Aurelio Medina, Rafael Cisneros-Magaña, and Amner Ramírez. "Periodic Steady State Assessment of Microgrids with Photovoltaic Generation Using Limit Cycle Extrapolation and Cubic Splines." Energies 11, no. 8 (2018): 2096. http://dx.doi.org/10.3390/en11082096.

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This paper proposes a fast and accurate time domain (TD) methodology for the assessment of the dynamic and periodic steady state operation of microgrids with photovoltaic (PV) energy sources. The proposed methodology uses the trapezoidal rule (TR) technique to integrate the set of first-order differential algebraic equations (DAE), generated by the entire electrical system. The Numerical Differentiation (ND) method is used to significantly speed-up the process of convergence of the state variables to the limit cycle with the fewest number of possible time steps per cycle. After that, the cubic spline interpolation (CSI) algorithm is used to reconstruct the steady state waveform obtained from the ND method and to increase the efficiency of the conventional TR method. This curve-fitting algorithm is used only once at the end part of the algorithm. The ND-CSI can be used to assess stability, power quality, dynamic and periodic steady state operation, fault and transient conditions, among other issues, of microgrids with PV sources. The results are successfully validated through direct comparison against those obtained with the PSCAD/EMTDC simulator, widely accepted by the power industry.

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Mukherjee, Debasis. "Fear induced dynamics on Leslie-Gower predator-prey system with Holling-type IV functional response." Jambura Journal of Biomathematics (JJBM) 3, no. 2 (2022): 49–57. http://dx.doi.org/10.34312/jjbm.v3i2.14348.

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This paper analyzes the effect of fear in a Leslie-Gower predator-prey system with Holling type IV functional response. Firstly, we show positivity and boundedness of the system. Then we discuss the structure of the positive equilibrium point, dynamical behavior of all the steady states and long term survival of all the populations in the system. It is shown that fear factor has an impact on the prey and predator equilibrium densities. We have shown the occurrence of transcritical bifurcation around the axial steady state. The presence of a Hopf bifurcation near the interior steady state has been developed by choosing the level of fear as a bifurcation parameter. Furthermore, we discuss the character of the limit cycle generated by Hopf bifurcation. A global stability criterion of the positive steady state point is derived. Numerically, we checked our analytical findings.

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Sommer III, H. Joseph, John M. Cimbala, and David G. Miller. "Self-Excited Limit Cycle Yaw Oscillation Instability of External Sling Payloads with Dual-Point Suspension During Level Flight." Journal of the American Helicopter Society 60, no. 4 (2015): 1–10. http://dx.doi.org/10.4050/jahs.60.042008.

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This work developed and verified a computational model to predict self-excited limit cycle yaw oscillation (SELCYO) instability of external sling payloads carried under aircraft with dual-point suspension. Inverted-V and inverted-Y slings during steady-state level flight are discussed. The primary goal was to provide a design tool for comparison of the onset of SELCYO between alternate sling geometries. The computational model incorporates steady-state aerodynamic loading during level flight based on scale-model wind tunnel testing. Scale-model sling tests of the onset of SELCYO in the same wind tunnel were used for validation. Predictions of cargo hook load for a full-size HMMWV-M1025 payload carried by inverted-V slings are compared to V-22 Osprey flight-test data. Predictions of stability indicate that stiffer slings are generally more stable, and inverted-V slings are significantly more stable than inverted-Y slings. Small differences between right and left front sling leg lengths caused by rigging error can significantly reduce stability.

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ROTENBERRY, JAMES M., and ANTONMARIA A. MINZONI. "THE STABILITY OF SPATIALLY NONHOMOGENEOUS STEADY STATES IN A TUBULAR CHEMICAL REACTOR." International Journal of Bifurcation and Chaos 03, no. 06 (1993): 1477–86. http://dx.doi.org/10.1142/s0218127493001161.

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We study the axial heat and mass transfer in a highly diffusive tubular chemical reactor in which a simple reaction is occurring. The steady state solutions of the governing equations are studied using matched asymptotic expansions, the theory of dynamical systems, and by calculating the solutions numerically. In particular, the effect of varying the Peclet and Damköhler numbers (P and D) is investigated. A simple expression for the approximate location of the transition layer for large Peclet number is derived and its accuracy tested against the numerical solution. The stability of the steady states is examined by calculating the eigenvalues and eigenfunctions of the linearized equations. It is shown that a Hopf bifurcation of the CSTR model (i.e., the limit as the P approaches zero) can be continued up to order 1 in the Peclet number. Furthermore, it is shown numerically that for appropriate values of the Peclet number, the Damköhler number, and B (the heat of reaction) these Hopf bifurcations merge with the limit points of an "S–shaped" bifurcation curve in a higher order singularity controlled by the Bogdanov–Takens normal form. Consequently, there must exist a finite amplitude, nonuniform, stable periodic solution for parameter values near this singularity. The existence of higher order degeneracies is also explored. In particular, it is shown for D ≪ 1 that no value of P exists where two pairs of complex conjugate eigenvalues of the steady state solutions can cross the imaginary axis simultaneously.

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SISWANTO, Agus. "Steady-State Stability Limit (SSSL) Assessment when Wind Turbine Penetration to South Sulawesi System Using ANN." PRZEGLĄD ELEKTROTECHNICZNY 1, no. 11 (2021): 53–58. http://dx.doi.org/10.15199/48.2021.11.09.

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De Dier, B., F. Walraven, R. Janssen, P. Van Rompay, and V. Hlavacek. "Bifurcation and Stability Analysis of a One-Dimensional Diffusion-Autocatalytic Reaction System." Zeitschrift für Naturforschung A 42, no. 9 (1987): 994–1004. http://dx.doi.org/10.1515/zna-1987-0912.

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Results of a numerical analysis of a set of one-dimensional reaction -diffusion equations are presented. The basis of these equations is a model scheme of chemical reactions, involving auto-and cross-catalytic steps (“Brusselator”). The steady state problem is solved numerically, fully exploiting the properties of recently developed continuation codes. Bifurcation diagrams are constructed for zero flux boundary conditions. For a relatively large diffusivity of initial species the Brusselator displays a huge number of dissipative steady state structures. At low system lengths a mechanism of perturbed bifurcation may be percieved. Bifurcations coincide with turning points of asymmetric solution branches. Completely isolated solutions prove to exist as well. For the problem without limited diffusion of the initial species, a careful bifurcation analysis show s the existence of a number of higher order bifurcations. At some of these points asymmetric profiles emanate from other asymmetric structures. Bifurcation points and limit points do not necessarily coincide. Stability analysis shows that relatively few steady states are stable. Especially symmetric solutions are found to be stable.

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Nur, Ashida Salim, Salehan Ab. Samah Mohamad, Mohamad Hasmaini, Mat Yasin Zuhaila, and Fadilah Ab Aziz Nur. "Implementation of graphical user interface to observe and examine the frequency and rotor angle stability of a power system due to small disturbances." Indonesian Journal of Electrical Engineering and Computer Science (IJEECS) 17, no. 2 (2020): 606–14. https://doi.org/10.11591/ijeecs.v17.i2.pp606-614.

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The aim of this research is to anticipate the stability status of a power system when the system is exposed to a change in frequency and rotor angle due to small disturbances. The proposed study was implemented on the IEEE Reliability Test System 1979 (IEEE RTS-79) which contains 24 buses, 38 transmission lines and 32 generators. Steady state stability limit of a system refers to the maximum amount of power that is permissible through the system without loss of its steady state stability. This research proposes the development of a Graphical User Interface (GUI) to observe the frequency and rotor angle stability due to the effect of small disturbances using the One Machine Infinite Bus (OMIB) technique. This proposed technique could ease the power system utility especially the power system operation to observe and examine the system frequency and rotor angle stability due to small disturbances. The findings from this research has proven that the proposed technique to observe the frequency and rotor angle stability due to small disturbances has successfully been developed using a GUI.

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Golov, V. P., A. V. Kalutskov, D. N. Kormilitsyn, and O. S. Sukhanova. "Aperiodic steady-state stability criterion of electric power system with controlled series compensation on 200 kV line." Vestnik IGEU, no. 6 (December 28, 2020): 14–24. http://dx.doi.org/10.17588/2072-2672.2020.6.014-024.

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Currently there is a need to synchronize operation of the electric power system in the remote areas and increase of existing lines transmission capacity. The construction of new power transmission lines involves high economic expenditures. Well-known papers consider the issues of application of controlled series compensation devices only for long-distance power transmission lines with voltage of 500 kV and higher to increase the transmission capacity and the level of stability. The aim of the study is to increase the stability and the limit of the transmitted power when controlled series compensation devices are installed on 220 kV lines. It is necessary to develop a criterion of aperiodic steady-state stability of an electric power system with a 220 kV-controlled power transmission line. Methods of mathematical modeling of electric power system, the theory of long-distance power transmission lines and electromechanical transients, and methods of analyzing electric power system stability were used. A.M. Lyapunov’s first approximation method was used to develop a simplified mathematical model. We applied the developed software as a simulation tool. An analysis was carried out to study the influence of series compensation devices regulation coefficients on the aperiodic steady-state stability of the electric power system and the transmission capacity of 220 kV power transmission lines. A change in the modulus of voltage drop at the power transmission and the angle characteristics under the influence of the regulation coefficients of the series compensation device was revealed. A criterion of aperiodic steady-state stability has been developed for systems of this kind with controlled series compensation. It differs from traditional ones by considering the changes in the voltage drop in the power transmission and it allows more accurate estimation of the proximity to the stability threshold. An assessment of aperiodic steady-state stability according to the formulated criterion for an electric power system with a controlled series compensation device on a 220 kV line was obtained. The values of the control coefficients of the series compensation device have been determined. No violation of the steady-state stability occurs under the given values. The results can be used to solve the issues of increasing the transmission capacity of transmission lines to improve the stability of the system.

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Stribersky, A., and P. S. Fancher. "The Nonlinear Behavior of Heavy-Duty Truck Combinations With Respect to Straightline Stability." Journal of Dynamic Systems, Measurement, and Control 111, no. 4 (1989): 577–82. http://dx.doi.org/10.1115/1.3153094.

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A comparison of the nonlinear stability behavior of the steady state straight line motion of truck combinations with and without a second trailer is shown. These investigations have been done by applying bifurcation theory. Stability boundaries in the parameter space and the corresponding bifurcation solutions are given. Depending on the loading conditions, unstable and also stable limit cycles have been found. Particular emphasis is given to the influence of the frictional coupling between tire and road on the nonlinear stability behavior of these vehicles.

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Lee, Jeong-Bae, and Kyung-Woong Kim. "Effects of Synchronous Vibration of Bearing on Stability of Externally Pressurized Air Journal Bearings." Journal of Tribology 121, no. 4 (1999): 830–35. http://dx.doi.org/10.1115/1.2834142.

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An active control of bearing is proposed as a new method to improve the stability characteristics of the externally pressurized air journal bearing and the results of numerical investigations of the stability characteristics of the actively controlled air journal bearing are presented. The synchronous control, where the bearing center whirls with the same frequency as the journal center with respect to the position in the steady state, is proposed as a control algorithm of the active air bearing. The step jump method is used to calculate the locus of the journal center which whirls or vibrates relative to the whirling bearing. The stability characteristics of the high speed rotor supported by actively controlled bearing system for zero steady-state eccentricity are investigated for various phase difference between the bearing and journal. It is shown that the stability of the air bearing can be greatly increased by the controlled synchronous motion of the bearing, and there is an optimum phase difference, which gives the maximum stability limit of the system.

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JI, HANGJIE, and THOMAS P. WITELSKI. "Steady states and dynamics of a thin-film-type equation with non-conserved mass." European Journal of Applied Mathematics 31, no. 6 (2019): 968–1001. http://dx.doi.org/10.1017/s0956792519000330.

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We study the steady states and dynamics of a thin-film-type equation with non-conserved mass in one dimension. The evolution equation is a non-linear fourth-order degenerate parabolic partial differential equation (PDE) motivated by a model of volatile viscous fluid films allowing for condensation or evaporation. We show that by changing the sign of the non-conserved flux and breaking from a gradient flow structure, the problem can exhibit novel behaviours including having two distinct classes of co-existing steady-state solutions. Detailed analysis of the bifurcation structure for these steady states and their stability reveals several possibilities for the dynamics. For some parameter regimes, solutions can lead to finite-time rupture singularities. Interestingly, we also show that a finite-amplitude limit cycle can occur as a singular perturbation in the nearly conserved limit.

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43

Ishak, Muhammad Izhar, Hirohiko Ogino, and Yoshio Yamamoto. "Numerical Simulation Analysis of an Oversteer In-Wheel Small Electric Vehicle Integrated with Four-Wheel Drive and Independent Steering." International Journal of Vehicular Technology 2016 (June 30, 2016): 1–12. http://dx.doi.org/10.1155/2016/7235471.

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Similar to conventional vehicle, most in-wheel small EVs that exist today are designed with understeer (US) characteristic. They are safer on the road but possess poor cornering performance. With recent in-wheel motor and steer-by wire technology, high cornering performance vehicle does not limit to sport or racing cars. We believe that oversteer (OS) design approach for in-wheel small EV can increase the steering performance of the vehicle. However, one disadvantage is that OS vehicle has a stability limit velocity. In this paper, we proposed a Four-Wheel Drive and Independent Steering (4WDIS) for in-wheel small EV with OS characteristic. The aim of implementing 4WDIS is to develop a high steer controllability and stability of the EV at any velocity. This paper analyses the performance of OS in-wheel small EV with 4WDIS by using numerical simulation. Two cornering conditions were simulated which are (1) steady-state cornering at below critical velocity and (2) steady-state cornering over critical velocity. The objective of the simulation is to understand the behavior of OS in-wheel small EV and the advantages of implementing the 4WDIS. The results show that an in-wheel small EV can achieve high cornering performance at low speed while maintaining stability at high speed.

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44

De La Torre Juárez, M., and F. H. Busse. "Stability of two-dimensional convection in a fluid-saturated porous medium." Journal of Fluid Mechanics 292 (June 10, 1995): 305–23. http://dx.doi.org/10.1017/s0022112095001534.

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The range of existence and the stability of spatially periodic solutions has been studied for steady and oscillatory two-dimensional convection in a fluid-saturated porous medium. We have analysed the limit where viscous effects are dominant and Darcy's law can be applied. A Galerkin method has been used to obtain the steady and the centrosymmetric oscillatory solutions that appear in nonlinear convection at Rayleigh numbers up to 20 times the critical value. Their stability boundaries to arbitrary infinitesimal perturbations have been obtained. Above a given Rayleigh number stable oscillatory solutions are possible at wavenumbers close to the critical values. The stability of this oscillatory state with respect to infinitesimal perturbations of any wavenumber has also been studied. The resulting temporal dynamics in the different unstable regimes is briefly discussed. We show the existence of 3:1 spatial resonances of the steady roll solutions and the existence of stable centrosymmetric and non-centrosymmetric oscillatory solutions.

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45

Yang, S. M., and G. J. Sheu. "On the Spillover of Steady State Unbalance Response of a Rotating Shaft Under Velocity Feedback." Journal of Vibration and Acoustics 128, no. 2 (2005): 143–47. http://dx.doi.org/10.1115/1.2149391.

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It has been stated that a uniform rotating shaft in the Rayleigh beam model has only a finite number of critical speeds and precession modes. This paper presents a controller design of optimal sensor/actuator location and feedback gain for steady state unbalance response of a rotating shaft operating in a speed range. For systems under order-limit constraint such that only part of the precession modes can be included in the reduced-order controller design, the system stability can be evaluated. The example of a hinged-hinged rotating shaft is employed to illustrate the controller design of velocity feedback in collocated and noncollocated senor/actuator configuration. Analyses show that the reduced-order controller not only guarantees the closed loop system stability but also effectively suppress the unbalance response.

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46

Ashida Salim, Nur, Mohamad Salehan Ab. Samah, Hasmaini Mohamad, Zuhaila Mat Yasin, and Nur Fadilah Ab Aziz. "Implementation of graphical user interface to observe and examine the frequency and rotor angle stability of a power system due to small disturbances." Indonesian Journal of Electrical Engineering and Computer Science 17, no. 2 (2020): 606. http://dx.doi.org/10.11591/ijeecs.v17.i2.pp606-614.

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<span lang="EN-GB">The aim of this research is to anticipate the stability status of a power system when the system is exposed to a change in frequency and rotor angle due to small disturbances. The proposed study was implemented on the IEEE Reliability Test System 1979 (IEEE RTS-79) which contains 24 buses, 38 transmission lines and 32 generators. Steady state stability limit of a system refers to the maximum amount of power that is permissible through the system without loss of its steady state stability. This research proposes the development of a Graphical User Interface (GUI) to observe the frequency and rotor angle stability due to the effect of small disturbances using the One Machine Infinite Bus (OMIB) technique. This proposed technique could ease the power system utility especially the power system operation to observe and examine the system frequency and rotor angle stability due to small disturbances. The findings from this research has proven that the proposed technique to observe the frequency and rotor angle stability due to small disturbances has successfully been developed using a GUI.</span>

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THEISEN, E. A., M. J. VOGEL, C. A. LÓPEZ, A. H. HIRSA, and P. H. STEEN. "Capillary dynamics of coupled spherical-cap droplets." Journal of Fluid Mechanics 580 (May 21, 2007): 495–505. http://dx.doi.org/10.1017/s0022112007005514.

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Centre-of-mass motions of two coupled spherical-cap droplets are considered. A model with surface tension and inertia that accounts for finite-amplitude deformations is derived in closed form. Total droplet volume λ and half-length L of the tube that connects the droplets are the control parameters. The model dynamics reside in the phase-plane. For lens-like droplets λ < 1, and for any L there is a single steady state about which the droplets vibrate with limit-cycle behaviour. For λ>1, the symmetric state loses stability (saddle point) and new antisymmetric steady states arise about which limit-cycle oscillations occur. These mirror states – big-droplet up or big-droplet down – are also stable. In addition, there are large finite-amplitude ‘looping’ oscillations corresponding to limit cycles that enclose both steady states in the phase-plane. All three kinds of oscillations are documented in an experiment that sets the system into motion by ‘kicking’ one of the droplets with a prescribed pressure-pulse. Model predictions for frequencies are consistent with observations. Small-amplitude predictions are placed in the wider context of constrained Rayleigh vibrations. A model extension to account for the small but non-negligible influence of viscosity is also presented.

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Nishi, Hajime. "Study of the Steady-State Stability Limit in the Two-Machines Connected to an Infinite Bus System." IEEJ Transactions on Power and Energy 121, no. 2 (2001): 210–16. http://dx.doi.org/10.1541/ieejpes1990.121.2_210.

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VERRI, MAURIZIO. "ASYMPTOTIC STABILITY OF TRAVELING WAVES IN SOLID-PROPELLANT COMBUSTION UNDER THERMAL RADIATION." Mathematical Models and Methods in Applied Sciences 09, no. 09 (1999): 1279–305. http://dx.doi.org/10.1142/s0218202599000567.

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The steady burning stability of solid propellants under thermal radiation with volumetric absorption is investigated. The combustion model we are dealing with includes the classical assumptions of quasiplanarity of all spatial variations, quasisteadiness of the gas phase and surface reaction. However, the stability analysis requires neither assuming a specific pyrolysis law nor formulating a specific flame submodel as long as the surface mass production and heat feedback satisfy some general properties, which are indeed observed experimentally. The existence of a steady state (traveling wave) solution is proved, and a dispersion relationship for its asymptotic stability is derived by conveniently transforming the problem into an evolution equation in a Banach space. The fully opaque burning surface limit and the case of transparent burning surface with exponential volumetric absorption are examined in details. The resulting stability regions in a proper parameter space are given and, finally, existence and stability of bifurcating time-periodic solutions are discussed.

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KOPPERT, MARC, STILIYAN KALITZIN, DEMETRIOS VELIS, FERNANDO LOPES DA SILVA, and MAX A. VIERGEVER. "DYNAMICS OF COLLECTIVE MULTI-STABILITY IN MODELS OF MULTI-UNIT NEURONAL SYSTEMS." International Journal of Neural Systems 24, no. 02 (2014): 1430004. http://dx.doi.org/10.1142/s0129065714300046.

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In this study, we investigate the correspondence between dynamic patterns of behavior in two types of computational models of neuronal activity. The first model type is the realistic neuronal model; the second model type is the phenomenological or analytical model. In the simplest model set-up of two interconnected units, we define a parameter space for both types of systems where their behavior is similar. Next we expand the analytical model to two sets of 90 fully interconnected units with some overlap, which can display multi-stable behavior. This system can be in three classes of states: (i) a class consisting of a single resting state, where all units of a set are in steady state, (ii) a class consisting of multiple preserving states, where subsets of the units of a set participate in limit cycle, and (iii) a class consisting of a single saturated state, where all units of a set are recruited in a global limit cycle. In the third and final part of the work, we demonstrate that phase synchronization of units can be detected by a single output unit.

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Journal articles on the topic 'Steady-state stability limit'

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