Steady-state Stability Analysis Research Articles

SPECTRAL THEORY AND FUNCTIONAL CALCULI IN THE REFLEXIVE BANACH SPACES

The design and assessment of closed loop control systems must include accurate and stable accuracy analysis and simulation. An overview of the significance of closed loop control systems and its uses in several engineering disciplines is given in this paper. The paper then explores the different techniques used for evaluating the accuracy and stability of closed loop control systems, including steady-state error analysis, stability analysis, and simulation techniques. It also discusses the design and tuning of control algorithms to optimize the performance of the system, and identifies the different factors that can affect the accuracy and stability of closed loop control systems, such as sensor noise, model inaccuracies, and environmental disturbances.

Analysis of steady-state dynamics and stability of particle dampers considering the friction effect

This study analyzes the steady-state dynamics and stability of a structure with a particle damper considering the friction effect between the particle and container, with a focus on whether the system can maintain stable-state motion for an extended period. The determination of friction’s contribution and the maximum allowable gap clearance for steady-state motion is demonstrated through the solution of motion of the primary structure with a particle damper subjected to low-frequency vibration conditions. Additionally, stability analysis is conducted to assess if initial disturbances cause deviations from the original stable state and identify necessary parameters for stability when the system parameters are uncertain. Analytical descriptions for the stability of the system are derived. The effects of friction on the dynamics and stability regions of the particle dampers are systematically revealed, where the theoretical and numerical models are mutually verified and supported by the cases of previous studies. Results show that the inclusion of the rolling friction effect will disrupt the steady-state motion as gap clearance approaches the optimal value. As the coefficient of rolling friction increases, the stability region’s area gradually decreases with a notable leftward shift of its right boundary. This shift ultimately leads to a leftward shift in the optimal vibration reduction curve. In the range of gap clearance variation allowing for steady-state motion with two symmetrical impacts per cycle, the relative velocity of the particle is more effective and intuitive to reveal the vibration reduction mechanism of particle dampers than other perspectives such as momentum, energy, and phase.

Time Evolution of the Densities of Three Species Interacting in the Same Ecosystem and the Stability Analysis of Steady States for a Reaction–Diffusion PDE Model

This paper investigates the trends of three different species interacting in the same ecosystem. The study is conducted on the ecosystem which consists of a prey S1 and two predators S2 and S3 in such a way that S2 is a predator of S1 and S3 is a predator of both S1 and S2. In addition, S1 and S2 share the same food which is the main food for S1 and the alternative food for S2. A system of three simultaneous nonlinear partial differential equations is used to represent this situation. The local stability of all constant equilibrium points is discussed after showing their feasibility. In addition, a condition for which a coexisting constant equilibrium point is asymptotically globally stable is also investigated. The results showed that the system has eight constant equilibrium points. Five of them are unstable, while the three remaining are asymptotically locally stable under some conditions on the parameters that are involved in the model.

Exploring Hopf-bifurcations and endemic bubbles in a tuberculosis model with behavioral changes and treatment saturation.

To manage risks and minimize the transmission of contagious diseases, individuals may reduce their contact with each other and take other precautions as much as possible in their daily lives and workplaces. As a result, the transmission of the infection reduces due to the behavioral changes. These behavioral changes are incorporated into models by introducing saturation in disease incidence. In this article, we propose and analyze a tuberculosis model that incorporates saturated exogenous reinfection and treatment. The stability analysis of the model's steady states is rigorously examined. We observe that the disease-free equilibrium point and the endemic equilibrium point (EEP) are globally asymptotically stable if the basic reproduction number (R0) is less than 1 and greater than 1, respectively, only when exogenous reinfection is not present (p=0) and when treatment is available for all (ω=0). However, even when R0 is less than 1, tuberculosis may persist at a specific level in the presence of exogenous reinfection and treatment saturation, leading to a backward bifurcation in the system. The existence and direction of Hopf-bifurcations are also discussed. Furthermore, we numerically validate our analytical results using different parameter sets. In the numerical examples, we study Hopf-bifurcations for parameters such as β, p, α, and ω. In one example, we observe that increasing β leads to the loss of stability of the unique EEP through a forward Hopf-bifurcation. If β is further increased, the unique EEP restores its stability, and the bifurcation diagram exhibits an interesting structure known as an endemic bubble. The existence of an endemic bubble for the saturation constant ω is also observed.

Modelling the Dynamics of Multi-strain COVID-19 Transmission

It is on record that rolling out COVID-19 vaccines has been one of the fastest for any vaccine production worldwide. Despite this prompt action taken to mitigate the transmission of COVID-19, the disease persists. One of the reasons for the persistence of the disease is that the vaccines do not confer immunity against the infections. Moreover, the virus-causing COVID-19 mutates, rendering the vaccines less effective on the new strains of the disease. This research addresses the multi-strains transmission dynamics and herd immunity threshold of the disease. Local stability analysis of the disease-free steady state reveals that the pandemic can be contained when the basic reproduction number, R 0 is brought below unity. The results of numerical simulations also agree with the theoretical results. The herd immunity thresholds for some of the vaccines against COVID-19 were computed to guide the management of the disease. This model can be applied to any strain of the disease.

Steady-State Angle Stability Analysis of Parallel Grid-Forming Converters in Current Saturation Mode

Grid-forming converters (GFCs) usually operate in parallel to supply power to unknown loads. Nevertheless, unknown loads may lead to overcurrent, causing parallel GFCs to enter the current saturation mode (CSM). The steady-state angle stability of parallel GFCs in CSM is crucial for ensuring reliable operation under unknown loads, yet this issue has not been studied previously. This paper presents a novel power model for parallel GFCs in CSM and conducts the first-ever investigation of steady-state angle stability in this context. The analysis results reveal that the steady-state angle stability of the equilibrium points (EPs) under overall inductive load is opposite to that under overall capacitive load. Specifically, it is shown that the EP with even power allocation is unstable, and the parallel GFCs will transition to the EP with circulating currents in the presence of overall capacitive loads. Eventually, all the capacity of GFCs is occupied by the circulating currents, failing to supply voltage to the loads. The proposed model and analysis are validated through experimental results, highlighting the significant risk of power supply failure for parallel GFCs in CSM and providing general guidance for the operation of GFCs in parallel.

System Studies to Assess Preparedness of the Zambian Electrical Grid for the Energy Transition Through Integration of Large-Scale Variable Renewable Energy Sources

Zambia still faces significant challenges in her quest to become a middle-income nation by 2030. Some of these issues include low access to clean energy technologies, low electrification rates and limited infrastructure to transport electricity. Moreover, for a country that is predominantly hydropower dependent with an 85% share, climate change induced droughts contributed to approximately a 30% power deficit in 2020 owing to reduction in the hydropower generation capacity. Two years down the line the situation has not changed much with load management anticipated to commence in the fourth quarter of 2022 with an average outage duration of 6 hours a day countrywide. However, with approximately 3000 sunshine hours per annum and an average solar insolation of 5.5 kWh/m2/day and great wind resource potential (~6 to 11 m/s) for utility scale wind power in some parts of the country at heights between 80 and 200 m above sea level (A.S.L), Zambia has potential to benefit from its immense renewable resources endowment to accelerate electricity access and decarbonization of the power sector. In 2019, RES4Africa alongside Enel Foundation and with technical expertise from CESI conducted an optimal technical-economic penetration of variable renewable energy sources (VRES) in Zambia. This study had limitations as it did not tackle site-specific geospatial mapping of VRES, nor did it delve into technical system studies to include steady state and dynamic stability analyses for the Zambian power grid owing to the large-scale VRES penetration. With this motivation in research gap, a systematic methodology was developed by the author for the potential of conducting renewable energy penetration system studies for the Zambian integrated power system for the year 2025 and 2030. Thereafter, the potential sites were mapped using QGIS before applying the formulated modelling methodology on the Zambian grid to conduct steady state and dynamic stability studies for the various scenarios and study cases (i.e., 2025 base, 2025 peak demand with VRES, 2025 peak solar, 2025 peak VRES). The results obtained using Power factory Dig SILENT modelling, and simulation software are presented as system steady state, short circuit, system inertia estimation and dynamic stability analyses. The results obtained for each scenario were compared to the base case i.e., before connecting the proposed VRES projects. Further, investigation of system adequacy and security were performed through contingency analysis. The 2025 steady state analysis for the peak VRES case revealed that the loading of the transmission lines was below 100%. With the proposed VRES projects contributing to about 68% of the total system generation under this condition, the results showed huge reduction in loadings of the transmission lines from the major power plants i.e., Kariba North and Kafue Gorge Power plants when compared to the base case results. The 2025 system inertia analysis for the peak VRES case showed a reduction in the system inertia by approximately 68.5% compared to the base case. This is because the dispatch to serve the grid load in this scenario prioritized VRES over hydropower. The 2025 short circuit analysis revealed that the largest decrease in the fault level was Kariba North Bank and Kafue gorge power stations under peak VRES condition with a reduction of 6kA owing to all the machines being switched off at Kariba North from the initial 6 while Kafue Gorge upper had 2 running machines from the initial 6 in the base case. On the other hand, an overall increase in short circuit levels was experienced across the network for the Peak demand case with VRES. In the dynamic stability analysis, fault ride through (FRT) studies were conducted to ensure that VRES plants stay connected when the AC grid voltage is temporarily reduced or increased due to a fault or large load change in the grid. Moreover, the study demonstrated that for all 2025 study cases, a general increase in rate of change of frequency (RoCoF) values was observed with increased VRES integration. However, all RoCoF values obtained were well below the 1Hz/s threshold as stipulated in the Zambian transmission grid code with both frequency nadir and zenith values being well within the 50±2.5% limits.Seeing that a large share of grid demand will be met by VRES in 2025, 2030 and beyond, detailed future research must go towards utilization of machine learning and artificial intelligence in nowcasting and day ahead short-term forecasts. This has the potential to optimize both system operations during dispatch and energy market trading both local and regional.

A simplified model design of MMC-HVDC transmission system for steady state and transient stability analyses

A simplified model of a modular multilevel converter (MMC) implemented on a high voltage direct current (HVDC) transmission system is presented in this study for the analyses of steady-state and transient stabilities. The simplified model design’s goal is to reduce the complicated modeling of the MMC circuit as well as the simulation time of the analysis. The validity of the model design has been examined using the PSCAD/EMTDC simulation program, where the simulation outcomes of the detailed model and the simplified model are contrasted. It has been established that the simplified model is accurate enough and that simulation time can be substantially decreased. It is concluded that the suggested model design is very significant as a simplified model for analyzing the steady state and transient stabilities of MMC-HVDC transmission system.

Process Performance and Operational Challenges in Continuous Crystallization: A Study of the Polymorphs of L-Glutamic Acid.

The crystallization of the two polymorphs of l-glutamic acid (LGA) is carried out in a continuous crystallization process, and its performance according to different criteria is evaluated. The study aims at identifying suitable operating conditions for producing either αLGA or βLGA with a high polymorphic purity. To this end, we investigate the process both from a theoretical perspective and through experiments using either a single stirred-tank crystallizer or a cascade of two stirred-tank crystallizers in series. In terms of theory, we extend the MSMPR-based steady-state stability analysis of Farmer et al. (Farmer, T. C. et al. AIChE J.2016, 62, 3505-3514) by accounting for the possibility of a nonrepresentative withdrawal of the solid phase from the crystallizer. Additionally, the process is simulated using population balance equations, thereby investigating the effect of operating conditions on polymorphic purity, yield, and productivity. Guided by the model-based conclusions, we identified suitable operating conditions and experimentally tested them. The experimental campaign has demonstrated that βLGA could be successfully and continuously produced in both process configurations according to the theory with performance as expected, whereas that was not possible for αLGA. The difference between the two stems from different operational challenges, whose consequence is that steady-state operation is attained in the case of βLGA but not in that of αLGA. In the former case, the needle-like βLGA crystals, which exhibit no agglomeration, tend to be only slightly oversampled; in the latter case, the prismatic αLGA crystals undergo major agglomeration and hence are very difficult to suspend and effectively withdraw from the crystallizer.

A reinforcement learning approach to Automatic Voltage Regulator system

An Automatic Voltage Regulator (AVR) system utilized to keep the terminal voltage of a synchronous generator at the desired level has received much attention among researchers. Designing an efficient and robust control scheme for the AVR system to maintain a specified voltage level is an important research area. From the control area perspective, reinforcement learning, an adaptive optimal control method, has received increasing attention in reference tracking problems. This article discusses a reinforcement learning approach to an AVR system and its experimental validation. A deep deterministic policy gradient (DDPG) agent working in continuous-time is designed offline to improve dynamic system characteristics of the AVR system besides its robustness against load disturbance, parameter uncertainties, and reference change. In the DDPG agent design process, the limits of the produced control signal are taken into account to perform a feasible simulation similar to a real-time application. The performance of the proposed learning-based controller is analyzed in three categories: transient and steady-state responses, stability analysis, and robustness analysis against parameter uncertainties, reference change, and load disturbance. A comparison with recently published papers employing Fuzzy-PID, PID-F, PIλDND2N2, PIDD2 ,and PID controllers in which various heuristic optimization algorithms were employed to optimally tune the controller parameters is made. Furthermore, to demonstrate that the behavior of the learning-based approach provides a stable and satisfactory performance, it is analyzed for a real synchronous generator connected to a 230 kV network using Matlab/Simulink environment. The results presented in this paper indicate that the proposed learning-based controller ensures the stability of the AVR system, significantly improves the regulating performance, and most impressively, is robust against parameter uncertainties, reference change, and load disturbance.

Modeling and analysis of a piezoelectric transducer embedded in a nonlinear damped dynamical system

This paper focuses on the dynamical analysis of the motion of a new three-degree-of-freedom (DOF) system consisting of two segments that are attached together. External harmonic forces energize this system. The equations of motion (EOM) are derived utilizing Lagrangian equations, and the approximate solutions up to the third order are investigated using the methodology of multiple scales. A comparison between these solutions and numerical ones is constructed to confirm the validity of the analytic solutions. The modulation equations (ME) are acquired from the investigation of the resonance cases and the solvability conditions. The bifurcation diagrams and spectrums of Lyapunov exponent are presented to reveal the different types of the system’s motion and to represent Poincaré maps. The piezoelectric transducer is connected to the dynamical system to convert the vibrational motion into electricity; it is one of the energy harvesting devices which have various applications in our practical life like environmental and structural monitoring, medical remote sensing, military applications, and aerospace. The influences of excitation amplitude, natural frequency, coupling coefficient, damping coefficient, capacitance, and load resistance on the output voltage and power are performed graphically. The steady-state solutions and stability analysis are discussed through the resonance curves.

Symmetry-breaking bifurcations for compartmental reaction kinetics coupled by two bulk diffusing species with comparable diffusivities in 2-D

For a 2-D coupled PDE-ODE bulk-cell model, we investigate symmetry-breaking bifurcations that can emerge when two bulk diffusing species are coupled to two-component nonlinear intracellular reactions that are restricted to occur only within a disjoint collection of small circular compartments, or “cells,” of a common small radius that are confined in a bounded 2-D domain. Outside of the union of these cells, the two bulk species with comparable diffusivities and bulk degradation rates diffuse and globally couple the spatially segregated intracellular reactions through Robin boundary conditions across the cell boundaries, which depend on certain membrane reaction rates. In the singular limit of a small common cell radius, we construct steady-state solutions for the bulk-cell model and formulate a nonlinear matrix eigenvalue problem that determines the linear stability properties of the steady-states. For a certain spatial arrangement of cells for which the steady-state and linear stability analysis become highly tractable, we construct a symmetric steady-state solution where the steady-states of the intracellular species are the same for each cell. As regulated by the ratio of the membrane reaction rates on the cell boundaries, we show for various specific prototypical intracellular reactions, and for a specific two-cell arrangement, that our 2-D coupled PDE-ODE model admits symmetry-breaking bifurcations from this symmetric steady-state, leading to linearly stable asymmetric patterns, even when the bulk diffusing species have comparable or possibly equal diffusivities. Overall, our analysis shows that symmetry-breaking bifurcations can occur without the large diffusivity ratio requirement for the bulk diffusing species as is well-known from a Turing stability analysis applied to a spatially uniform steady-state for typical two-component activator-inhibitor systems. Instead, for our theoretical compartmental-reaction diffusion bulk-cell model, our analysis shows that the emergence of stable asymmetric steady-states can be controlled by the ratio of the membrane reaction rates for the two species. Bifurcation theoretic results for symmetric and asymmetric steady-state patterns obtained from our asymptotic theory are confirmed with full numerical PDE simulations.

Enskog kinetic theory of binary granular suspensions: Heat flux and stability analysis of the homogeneous steady state.

The Enskog kinetic theory of multicomponent granular suspensions employed previously [Gómez González, Khalil, and Garzó, Phys. Rev. E 101, 012904 (2020)2470-004510.1103/PhysRevE.101.012904] is considered further to determine the four transport coefficients associated with the heat flux. These transport coefficients are obtained by solving the Enskog equationby means of the application of the Chapman-Enskog method around the local version of the homogeneous state. Explicit forms of the heat flux transport coefficients are provided in steady-state conditions by considering the so-called second Sonine approximation to the distribution function of each species. Their quantitative variation on the control parameters of the mixture (masses and diameters, coefficients of restitution, concentration, volume fraction, and the background temperature) is demonstrated and the results show that in general the dependence of the heat flux transport coefficients on inelasticity is clearly different from that found in the absence of the gas phase (dry granular mixtures). As an application of the general results, the stability of the homogeneous steady state is analyzed by solving the linearized Navier-Stokes hydrodynamic equations. The linear stability analysis (which holds for wavelengths long compared with the mean free path) shows that the transversal and longitudinal modes are always stable with respect to long-enough wavelength excitations. This conclusion agrees with previous results derived for monocomponent and (dilute) bidisperse granular suspensions but contrasts with the instabilities found in previous works in dry (no gas phase) granular mixtures.

UNIFIED POWER FLOW CONTROLLER CONTROL STRATEGIES for POWER FLOW

In order to address power flow control issues, this study introduces the use of Unified Power Flow Controller (UPFC) models. These models are based on regulating the variables influencing the transmission line’s power flow, and they are capable of controlling the bus voltage, the line’s actual and reactive power, all at once and independently. The idea behind the UPFC technique proposed in this paper is to provide the unique functional capability of independently controlling both the real and reactive power flow in the line. The in-phase component of the series injected voltage dominates the reactive power while the quadrature component affects the real power. A conventional controlling steady-state analysis and dynamic stability analysis of the power system is developed based on the UPFC model. UPFC provides real-time controlling of all or any combination of the power system parameters which determine the transmittable power. UPFC can force and maintain strategically chosen values of the active power and the reactive power at a given point of the line by PI control.

Kinetic theory of granular particles immersed in a molecular gas

The transport coefficients of a dilute gas of inelastic hard spheres immersed in a gas of elastic hard spheres (molecular gas) are determined. We assume that the number density of the granular gas is much smaller than that of the surrounding molecular gas, so that the latter is not affected by the presence of the granular particles. In this situation, the molecular gas may be treated as a thermostat (or bath) of elastic hard spheres at a fixed temperature. The Boltzmann kinetic equation is the starting point of the present work. The first step is to characterise the reference state in the perturbation scheme, namely the homogeneous state. Theoretical results for the granular temperature and kurtosis obtained in the homogeneous steady state are compared against Monte Carlo simulations showing a good agreement. Then, the Chapman–Enskog method is employed to solve the Boltzmann equation to first order in spatial gradients. In dimensionless form, the Navier–Stokes–Fourier transport coefficients of the granular gas are given in terms of the mass ratio$m/m_g$($m$and$m_g$being the masses of a granular and a gas particle, respectively), the (reduced) bath temperature and the coefficient of restitution. Interestingly, previous results derived from a suspension model based on an effective fluid–solid interaction force are recovered in the Brownian limit ($m/m_g \to \infty$). Finally, as an application of the theory, a linear stability analysis of the homogeneous steady state is performed showing that this state is always linearly stable.

A linear hybrid active disturbance rejection controller design to extenuate powerline bushfires in resonant grounded distribution power systems

This paper proposes a robust linear hybrid controller by combining the active disturbance rejection and proportional–integral controllers (ADRC+PI) for inverter-based arc suppression coils (ASCs) in resonant grounded distribution power systems (RGDPSs). Resonant grounding techniques are used in real power distribution networks for reducing the fault current in order to reduce the severity of powerline bushfires in the presence of single line-to-ground (SLG) faults. The severity of bushfire hazards due to these SLG faults depends on environmental conditions (e.g., wet or dry grounds) that define the behavior of the system. With respect to these conditions, the fault resistance will be lower for wet grounds for which the system model comprises one dominant pole while dry grounds force the system to have one dominant zero with two dominant poles. By considering the circumstances of such groundings, the behavior of power distribution systems changes when there are SLG faults. This paper investigates a detailed analysis in frequency- and time-domains to design a robust arc mitigator based on the hybrid ADRC+PI controller. Furthermore, the robustness of the proposed hybrid controller against the input disturbances is explored in terms of transient and steady-state stability analysis and the results are compared with the ADRC and PI controllers. In addition, the performance of the proposed hybrid ADRC+PI controller is justified by utilizing virtual- and real-time implementations in a digital signal processor (DSP) through MATLAB/SIMULINK platform on a 22 kV (line-to-line) RGDPS under distinctive grounding conditions.

Wrinkling and multiplicity in the dynamics of deformable sheets in uniaxial extensional flow

The processing of thin-structured materials in a fluidic environment, from nearly inextensible but flexible graphene sheets to highly extensible polymer films, arises in many applications. So far, little is known about the dynamics of such thin sheets freely suspended in fluid. In this work, we study the dynamics of freely suspended soft sheets in uniaxial extensional flow. Elastic sheets are modeled with a continuum model that accounts for in-plane deformation and out-of-plane bending, and the fluid motion is computed using the method of regularized Stokeslets. We explore two types of sheets: "stiff" sheets that strongly resist bending deformations and always stay flat, and "flexible" sheets with both in-plane and out-of plane deformability that can wrinkle. For stiff sheets, we observe a coil-stretch-like transition, similar to what has been observed for long-chain linear polymers under extension as well as elastic sheets under planar extension: in a certain range of capillary number (flow strength relative to in-plane deformability), the sheets exhibit either a compact or a highly stretched conformation, depending on deformation history. For flexible sheets, sheets with sufficiently small bending stiffness wrinkle to form various conformations. Here, the compact-stretched bistability still occurs, but is strongly modified by the wrinkling instability: a highly-stretched planar state can become unstable and wrinkle, after which it may dramatically shrink in length due to hydrodynamic screening associated with wrinkling. Therefore, wrinkling renders a shift in the bistability regime. In addition, we can predict and understand the nonlinear long-term dynamics for some parameter regimes with linear stability analysis of the flat steady states.

On Steady-State Voltage Stability Analysis Performance in MATLAB Environment

Nowadays, electric power systems have been often operated close to their limits due to increased electric power consumptions, vast installments of renewable power sources and deliberated power market policies. This poses a serious threat to stable network operation and control. Therefore, voltage stability is currently one of key topics worldwide for preventing related black-out and islanding scenarios. In this paper, modelling and simulations of steady-state voltage stability problems in MATLAB environment are performed using author-developed computational tool implementing both conventional and more advanced numerical approaches. Their performance is compared with Simulink-based library Power System Analysis Toolbox (PSAT) in terms of solution accuracy, CPU time, and possible limitations. Their use for both real-time and off-line monitoring and assessment of system's voltage stability are also discussed.

Steady-state and nonlinear stability analysis for the feasibility of different fluids in a supercritical natural circulation loop

A numerical model for a supercritical natural circulation loop is developed to examine the flow instabilities by nonlinear stability analysis. The supercritical natural circulation loop is a loop geometry, which is driven by natural circulation with supercritical fluids as a coolant. A mathematical formulation is developed to study the steady-state and transient solution procedure for supercritical natural circulation loop. This mathematical model is then used to perform various parametric studies with different supercritical fluids (water, [Formula: see text], R134a, ammonia, R22, propane, and isobutane). The behavior of all the fluids is analyzed on identical geometrical and operating conditions. A comprehensive numerical study of the nonlinear stability analysis is presented with particular emphasis on the feasibility of various fluids in a natural circulation loop environment. The 50% increment in loop diameter and height increased the stable operating zones and shifted the marginal stability boundary upward respectively by approximately three times and 25–40% of the previous value. However, further increase in diameter and height reduces the increment of stable operating zones; hence the marginal stability boundary shifts upward marginally than the previous value. Furthermore, the marginal stability boundaries are generated to identify the stable and unstable zones for the available geometrical and operating conditions.

Influence of Aerodynamic Preloads and Clearance on the Dynamic Performance and Stability Characteristic of the Bump-Type Foil Air Bearing

The dry lubricated bump-type foil air bearing enables a carrying load capacity due to a pressure build up in a convergent air film. Since the air bearing provides low power dissipation above the lift-off speed and the flexible foil provides an adaptivity against high temperatures, manufacturing errors or rotor growth, the bump-type foil air bearing is in particular suitable for high speed rotating machineries. The corresponding dynamic behavior depends on the operational parameters, the behavior of the flexible foil structure, and in particular on the circumferential clearance. In order to avoid or suppress the critical subsynchronous motion at high rotational speeds, many researchers recommend adding an aerodynamic preload to the bore shape, representing a transition from a circular to a lobed bearing bore shape. In addition to positive effects on the stability, preliminary studies demonstrated degrading effects on the stiffness and damping due to increasing preload values. This observation leads to the assumption, that the preload value meets an optimum with respect to stability, load-capacity, and lift-off speed. With the aim of deriving an appropriate lobe configuration for the design of the bump-type foil air bearing, this work performs comprehensive numerical investigations on the dynamic performance and the stability characteristic as a function of preload and minimum clearance. To this end, this work uses steady-state and transient stability analysis methods to recommend optimal aeroydnamic preload values with respect to the corresponding minimum clearance.