Steady-state Stability Analysis Research Articles

Drivers of pattern formation in a predator\u2013prey model with defense in fearful prey

Existence of predator is routinely used to induce fear and anxiety in prey which is well known for shaping entire ecosystem. Fear of predation restricts the development of prey and promotes inducible defense in prey communities for the survival. Motivated by this fact, we investigate the dynamics of a Leslie–Gower predator prey model with group defense in a fearful prey. We obtain conditions under which system possess unique global-in-time solutions and determine all the biological feasible states of the system. Local stability is analyzed by linearization technique and Lyapunov direct method has been applied for global stability analysis of steady states. We show the occurrence of Hopf bifurcation and its direction at the vicinity of coexisting equilibrium point for temporal model. We consider random movement in species and establish conditions for the stability of the system in the presence of diffusion. We derive conditions for existence of non-constant steady states and Turing instability at coexisting population state of diffusive system. Incorporating indirect prey taxis with the assumption that the predator moves toward the smell of prey rather than random movement gives rise to taxis-driven inhomogeneous Hopf bifurcation in predator–prey model. Numerical simulations are intended to demonstrate the role of biological as well as physical drivers on pattern formation that go beyond analytical conclusions.

Probability analysis of steady-state voltage stability considering correlated stochastic variables

The penetration of renewable generation, such as photovoltaic and wind power in power networks will significantly impact the system’s stability in future, due to randomness and intermittency in the natural environment. Moreover, the correlations between renewable generation may enhance the impact on power system's stability. In this paper, cumulant-based maximum entropy method (CMEM) combined with Nataf Transform (NT) is proposed to analyze the steady-state voltage stability problem considering correlations and uncertainties of power injections and consumptions. The proposed methodology is tested on the IEEE 30-node and IEEE 57-node test systems. Taking the results of Monte Carlo method (MCM) as the experimental control group, this paper compares the proposed method with series expansion method (SEM), discusses and analyzes their calculation results and speed under different scenarios, and the results of the comparison prove the validity, accuracy and rapidity of the CMEM.

Exploring the dynamics of a tumor-immune interplay with time delay

With the effect of discrete time delay in deliberation, we propose and analyze a conceptual mathematical model for the tumor-immune interaction. The proposed model is delineated by a system of three coupled non-linear ordinary differential equations (ODEs), namely tumor cells, effector cells and cytokine Interleukin-2 (IL-2). Though simple, the model can have complicated dynamical behaviors. We have discussed the qualitative properties of the mathematical model including existence and positivity of the solutions. We find out tumor-free singular point and interior steady states in our mathematical model. We have studied the local stability analysis of the biological feasible steady states in both of the delayed and non-delayed system. By using transversality condition, we have analyzed Hopf bifurcation by using time delay τ as a bifurcation parameter. We have estimated the length of time delay parameter applying Laplace transformation for preserving the stability of period-1 limit cycle that provides the idea about the mode of action in controlling oscillations in the growth of tumor cells. We performed numerical simulations and explored their biological implications to validate our theoretical analysis. We have also drawn bifurcation diagram of delayed model with reference to the intrinsic growth rate α of tumor cell, deactivation rate d1 of tumor cell, activation rate c2 of effector cell and death rate d2 of effector cell. Theoretical and numerical analysis show that in presence of IL-2 the effector cells can cause the tumor cell population to regress.

Steady-State Stability Analysis of Synchronization Loops in Weak-Grid-Connected Microgrid

The Microgrid (MG) is a flexible system composed of paralleled inverters. When the MG runs in grid-connected mode, the first step is to synchronize with the grid stably. However, the weak grid may interact with the synchronization loops and result in instability issues, where the steady-state instability of the MG coming from the loss of equilibrium points remains to be studied. Concretely, the synchronization loop of each inverter determines the equilibrium point. While, when the paralleled inverters work together, interactions among synchronization loops complicate the steady-state analysis. To recognize the synchronization mechanism and steady-state stability of the MG, a kind of hybrid quasi-static models of synchronization loops in the MG is developed in this paper. Studies show that the stable grid-injected currents of current-controlled inverters (CCIs) in a MG are greatly increased, while the allowed grid-injected power of the voltage-controlled inverter (VCI) are decreased obviously and it is closely dependent on the operating currents of the CCIs. Therefore, it is essential to recognize the operating points of each inverter in a MG considering the steady-state stability. Finally, the simulations are carried out to verify the analysis.

Stability and bifurcation of collective dynamics in phase oscillator populations with general coupling.

The Kuramoto model serves as an illustrative paradigm for studying the synchronization transitions and collective behaviors in large ensembles of coupled dynamical units. In this paper, we present a general framework for analytically capturing the stability and bifurcation of the collective dynamics in oscillator populations by extending the global coupling to depend on an arbitrary function of the Kuramoto order parameter. In this generalized Kuramoto model with rotation and reflection symmetry, we show that all steady states characterizing the long-term macroscopic dynamics can be expressed in a universal profile given by the frequency-dependent version of the Ott-Antonsen reduction, and the introduced empirical stability criterion for each steady state degenerates to a remarkably simple expression described by the self-consistent equation [Iatsenko et al., Phys. Rev. Lett. 110, 064101 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.064101]. Here, we provide a detailed description of the spectrum structure in the complex plane by performing a rigorous stability analysis of various steady states in the reduced system. More importantly, we uncover that the empirical stability criterion for each steady state involved in the system is completely equivalent to its linear stability condition that is determined by the nontrivial eigenvalues (discrete spectrum) of the linearization. Our study provides a new and widely applicable approach for exploring the stability properties of collective synchronization, which we believe improves the understanding of the underlying mechanisms of phase transitions and bifurcations in coupled dynamical networks.

The analysis of power system steady-state aperiodic stability with electronic generation

One of the main directions of electric power industry development all over the world is the use of distributed small generation, both based on carbon fuel resources with synchronous communication between sources when they are connected to electric networks, and renewable energy sources working in the electric network through frequency-converting devices (electronic generation). The latter leads to the inevitable mass use of inverters in existing AC electric networks. The objectives of this investigation are to study the impact of electronic generation on the modes and stability of existing electric networks and power systems, the formation of requirements for the characteristics of electronic generation control, which minimize the coordination of relay protection and automation with electronic generation in the electric network, as well as increase the reliability of the general electrical mode. The article presents the results study of the steady-state aperiodic stability of the power system with electronic generation, the requirements for their steady-state characteristics and control in the power system.

EIGENVALUE METHOD AND LINEARIZATION FOR THE STEADY STATE STABILITY ANALYSIS OF JAMSHORO THERMAL POWER PLANT (JTPP)

Electrical power system without interruption is the need of every consumer. Therefore, supplying electrical power which must be efficient, reliable and secure from any disturbance is the priority of power supply companies. But, due to changes in weather conditions and continuous load variations, small disturbances arise which may lead to severe disturbance. All electrical generating stations are interconnected, so a failure in any one unit can affect other generating units, therefore analysis is compulsory to solve the problem in the least time, and avoid a further big loss. Analysis of steady-state stability or transient stability plays a key role in a power system which helps to understand the behavior of a dynamic system. The stability problem is concerned with the behavior of the generating station when the system puts on either small or large disturbance. In this work, the steady-state stability (SSS) analysis of the Jamshoro thermal power plant (JTPP) is analyzed by using the eigenvalue method and linearization technique at four different reheat gain values. We develop a nonlinear mathematical model of JTPP and discuss its linearized form, and examine the behavior of the system stability using eigenvalues. The eigenvalue method analyzes the behavior of synchronous machine when system load varies continually. Numerical values of eigenvalues consist of either real part or real as well as imaginary parts. These eigenvalues help to understand the stability of the system, as to whether the system is stable or not.

Synergy of adaptive super-twisting method (ASTM) and game-theory algorithm (GTA) for dynamic stability improvement of interconnected grids

In this research work, a proposed technique of adaptive super-twisting method (ASTM) and game-theory algorithm (GTA) is presented. The proposed technique is applied to improve the dynamic stability of UPFC-based tidal energy resource. The impact of UPFC-based tidal energy resource on the power network is significantly recognized to support the demands supply and to enhance the dynamic performance. UPFC is able to control and enhance the power flow, voltage profile, power angle profile, and transmission lines loadability. The proposed technique has been optimally tuned to control the operational parameters of UPFC-based tidal energy resource. Both scenarios of single machine connected to infinite-bus grid, and multi-machine system are considered. The dynamic modelling of underlined system is done by d–q axis reference modelling. The analysis of steady-state stability is represented by the dynamic response specifications with stability discussion to evaluate the system performance. The simulations, including modelling, analysis and results, are carried out to confirm the entire stability of underlined systems. It has been confirmed the superb characteristics of proposed technique on interconnected UPFC-based tidal energy resource to power systems. The results of concerned scenarios have been emphasized that the proposed technique outperforms other well-established techniques. It is consolidated that UPFC-based tidal energy resource with proposed technique achieves significant performance and strengthened response. Therefore, the proposed solution can be offered as a favourable technique for enhancing the dynamic performance of power systems.

Developed analytical expression for current harmonic distortion of the PV system’s inverter in relation to the solar irradiance and temperature

This paper deals with modeling and simulation of the total harmonic distortion of the current (THDI) dispatched from the inverter and connected to nonlinear load. The change of THDI was examined in relation to the ambient temperature (T) and solar irradiance (G). The developed model is being used to extract parameters for a given THDI as a function of temperature and solar radiation. This study outlines the working principle of photovoltaic (PV) panel as well as PV array. Off-grid PV system is modeled by using Matlab/Simulink program, and detailed analytical study has been carried out in this work. The design, modeling and simulation of this study are performed from 50 up to 988 W/m2 for solar irradiance. Harmonic components have negative effects on the steady-voltage stability of the PV system. Therefore, analytical expression is needed for steady-state stability analysis in order to reduce negative effects. Hence, two analytical expressions of THDI were obtained by two new different methods which are statistical package for the social sciences program and genetic expression programming. Eventually, two different methods have been verified by the Matlab/Simulink program in order to find out THDI and demonstrated the effectiveness of the proposed strategy. As a result of this study, it is observed that input current THDI of nonlinear load is too high at low irradiance. It is suggested that active harmonic filters should be used at low irradiance in order to produce better quality energy and avoid damages in the PV system.

Statistical Steady-State Stability Analysis for Transmission System Planning for Offshore Wind Power Plant Integration

This paper presents a statistical steady-state stability analysis for transmission system planning studies in order to identify operational issues inherent in the integration of offshore wind power plants. It includes normal and contingency operation. This study considers the integration of a 1000-MW offshore wind power plant into the FirstEnergy/PJM service territory in the U.S. Great Lakes region as a case study and uses a realistic computer model of the U.S. Eastern Interconnection, a 63,000-bus test system. The results show the utility of this statistical analysis tool and its effectiveness in identification of the operational impacts as a result of the integration of offshore wind power plant.

A General Steady-State Voltage Stability Analysis for Hybrid Multi-Infeed HVDC Systems

As large-scale offshore wind farms are integrated into the power grid, a hybrid multi-infeed HVDC (HMIDC) system including both LCC-HVDC and VSC-HVDC links is facing a critical steady-state voltage stability problem which mainly stems from a weak AC system under high-level DC power injections. To overcome this challenge, this paper proposes a general steady-state voltage stability analysis to accurately measure the critical voltage stability point of HMIDC systems. In this paper, a typical HMIDC system is firstly modeled as a general dual-infeed system composed of an LCC-HVDC, a VSC-HVDC, and a virtual equivalent voltage source behind a virtual equivalent impedance at the AC side. Then a hybrid power sensitive factor (HPSF) is established to indicate the critical voltage stability point with the consideration of dynamic power-voltage characteristics of HVDC links, as well as operational changes in AC system (e.g. dynamics of excitation voltage control in generator and network topology change). Finally, a general voltage stability index, called hybrid generalized short circuit ratio (HGSCR), is further derived to effectively explain the critical voltage stability point of HMIDC systems. Moreover, multiple comparative studies with existing voltage stability indices are conducted in this paper to verify the effectiveness of the proposed general steady-state voltage stability analysis by using both PSCAD/EMTDC™ power flow and time-domain simulations.

Stability and neimark - sacker bifurcation for a discrete system of one - scroll chaotic attractor with fractional order

This present work investigates the dynamical behaviors of a new form of fractional order three dimensional system with a chaotic attractor of the one-scroll structure and its discretized counterpart. Firstly, existence and parametric conditions for local stability analysis of steady states of the model are addressed. Then the bifurcation theory is applied to investigate the presence of Neimark - Sacker (NS) bifurcations at the coexistence steady state taking the time delay as a bifurcation parameter in the discrete fractional order system. Also the trajectories, phase diagrams, limit cycles, bifurcation diagrams, attractors for period - 1, 2, 3, 4, 5 and a chaotic attractor with one scroll are exhibited for biologically meaningful sets of parameter values in the discretized system. Finally, several numerical examples are presented to assure the validity of the theoretical results and further rich dynamics of the model is explored as well.

Steady-State Stability of Sending-End System with Mixed Synchronous Generator and Power-Electronic-Interfaced Renewable Energy

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.

Steady State Stability Analysis and Improvement using Eigenvalues and PSS: A Case Study of a Thermal Power Plant in Jamshoro, Pakistan

The efficient handling and distribution of electrical power consist one of the most complex and appealing research problems. Due to the interconnection of different power plants and intensity of load, which gradually changes due to continuous change in load on generating units, careful treatment of the small disturbances in a power system which may lead to severe disturbance is necessary. Stability is an essential part in electrical power system operation and control. The stability problem is related with the behavior of synchronous machine after the power system is subjected to trouble. This work presents Steady State Stability (SSS) analysis of a Jamshoro Thermal Power Plant (JTPP) by using eigenvalue analysis of the different cases by varying load at three different positions. A mathematical model has been used for the JTPP with real data in order to examine the behavior of the system and to find the eigenvalues. A Simulink model of the JTTP for waveform analysis in MATLAB/Simulink has been used without and with Power System Stabilizer (PSS). Numerical quantification of the eigenvalues under the examined cases categorizes the stability of the system. The waveforms of the system are analyzed, and in cases of instability, the proposed procedure utilizing PSS helps in maintaining the system’s usual working conditions. The eigenvalue analysis and simulation results show the behavior of synchronous machines when loading changes gradually. The existing system becomes stable after more swings, whereas by using PSS in the existing system, stable regimes are attained in less time. The obtained results demonstrate the effectiveness of the proposed solution for SSS examination and securing of the disturbances of the JTPP.

A Mathematical Model for the Eradication of Anopheles Mosquito and Elimination of Malaria

A mathematical model to eliminate malaria by breaking the life cycle of anopheles mosquito using copepods at larva stage and tadpoles at pupa stage was derived aimed at eradicating anopheles pupa mosquito by introduction of natural enemies “copepods and tadpoles” (an organism that eats up mosquito at larva and pupa stage respectively). The model equations were derived using the model parameters and variables. The stability analysis of the free equilibrium states was analyzed using equilibrium points of Beltrami and Diekmann’s conditions for stability analysis of steady state. We observed that the model free equilibrium state is stable which implies that the equilibrium point or steady state is stable and the stability of the model means, there will not be anopheles adult mosquito in our society for malaria transmission. The ideas of Beltrami’s and Diekmann conditions revealed that the determinant and trace of the Jacobian matrix were greater than zero and less than zero respectively implying that the model disease free equilibrium state is stable. Hence, the number of larva that transforms to pupa is almost zero while the pupa that develop to adult is zero meaning the life-cycle is broken at the larva and pupa stages with the introduction of natural enemy. Maple was used for the symbolic and numerical solutions.

Grid Integration of a Renewable Energy System: Modeling and Analysis

This paper presents a study to perform a steady state stability analysis with integrating a wind turbine to a standard power network, where an open source software is used to model the system. The IEEE 9 bus system is simulated using the OpenModelica software. The steady state stability analysis study of the system is performed with and without using automatic voltage regulator AVR and speed governor GOV controllers. The steady state impact of integrating a wind turbine is investigated. Moreover, the voltage dependency of the wind turbine power is examined. The significance of the analysis results provided by the OpenModelica software is discussed.

A thermodynamic Lyapunov Approach to the Stability Analysis of a Nonlinear Irreversible Process Having Multiplicity

Following the second law of thermodynamics, the entropy is always created in irreversible processes such as reacting systems, etc. Under certain operating conditions, the reaction system can be operated with multiple steady states (also called the steady state multiplicity behavior). This behavior is considered for the illustration of the stability analysis of all possible steady states by Lyapunov methods using thermodynamics. More precisely, a novel symmetric storage function (or Lyapunov function candidate) is proposed on the basis of the so-called (non-symmetric) thermodynamic availability function. The acid-catalyzed hydration of 2-3-epoxy-1-propanol to glycerol subject to steady state multiplicity is used for further technical developments. The results are discussed with the inclusions of the simulations.

A Minimal HIV-AIDS Infection Model with General Incidence Rate and Application to Morocco Data

We study the global dynamics of a SICA infection model with general incidence rate. The proposed model is calibrated with cumulative cases of infection by HIV–AIDS in Morocco from 1986 to 2015. We first prove that our model is biologically and mathematically well-posed. Stability analysis of different steady states is performed and threshold parameters are identified where the model exhibits clearance of infection or maintenance of a chronic infection. Furthermore, we examine the robustness of the model to some parameter values by examining the sensitivity of the basic reproduction number. Finally, using numerical simulations with real data from Morocco, we show that the model predicts well such reality.

Liquid flowing downward in parallel pipes with evaporation

Two basic flow patterns are possible for evaporating liquid flowing downwards in a vertical pipe: co-current downward flow of liquid and gas and counter current flow where the liquid flows downward while the gas flows in the upward direction. For an assembly of parallel pipes with a common upper plenum and a common bottom manifold numerous different flow configurations can take place within the parallel pipes.Analysis of the various flow configurations is presented. The analysis contains steady state solutions, stability analysis and transient simulations. Specific examples for single and two parallel pipes are detailed. The analysis is restricted to low flow rates and low heat fluxes where it is possible to obtain counter current gas liquid flow.It is shown that for parallel pipes many of the steady state solutions are unstable. The transient simulations are consistent with the linear stability analysis.

Assessing the Integration of Large-Scale Solar PV to a Nine-Bus Power System

Solar energy has numerous promising features which also includes CO2 reduction. The adoption of large-scale solar PV ensures that demand can be satisfied by utilising renewable energy and reduces the dependency on the conventional non-renewable energy resources. Bringing this energy to widespread consumers requires transmission medium. However, controlling and bringing the harvested energy to the homes and industries is a task which needs attention. According to the various researches, it is deduced that the implementation of large-scale solar PV will have a marked effect on the grid which may lead to instability. The main obstacle to implementation is the distribution and transmission of energy to the recipients. In this study, the efforts are put to design the large-scale solar PV suitable for Malaysia using Pvsyst designing algorithm and the designed LSS PV is studied in a power system analysis tool to analyse the potential difference variation in different buses when connected to the nine-bus power system. Three solar PV models were selected based on their efficiency; among them two best PV model were obtained by conducting PVSyst simulation. The power output respect to time obtained from the simulation is used as inputs for conducting steady state stability analysis on nine bus power system to understand the voltage fluctuations when the LSSPV is integrated to the power system.