Time-varying Load Research Articles

Analysis of layered soil under general time-varying loadings by fractional-order viscoelastic model

Time-varying loading is a frequently encountered loading type in geotechnical engineering. As the deformation of viscoelastic soil is related to its loading history, studying the viscoelastic problems under time-varying loads has important practical engineering significance. In this paper, the stress and displacement of a layered soil with fractional-order viscoelastic model under time-varying loads were solved using the complex variable method and the corresponding principle. Under the assumption of quasi-static and linear elasticity, this paper derives the quasi-static elastic solutions of a layered soil under time-varying strip loads. By introducing the fractional-order viscoelastic model and using the corresponding principle, the Laplace-domain analytical solutions are obtained. Finally, numerical methods are utilized to perform the Laplace inverse transform and obtain the solutions in the physical domain. The correctness of this paper is validated by comparing the numerical results with the ANSYS software, as well as by comparison with previous literature. Based on the experimental data, the material parameters of frozen soil at two temperatures are fitted. The settlement patterns of soil under two engineering loads were analyzed through case studies. By controlling variables, the influence of parameters of the fractional viscoelastic model on elastic aftereffect was investigated.

Power Quality Impacts of Grid-Tied PV Inverters on Low Voltage Distribution Networks a Smart OpenDSS Model to Find Power Quality Threshold Limits

As a renewable initiative, risen attention can be seen in solar photovoltaic (PV) installations in the world. Since tropical countries and even many other countries during summer experience higher irradiance levels, there is great potential for PV generation in solar panels. However, power quality can be impacted when the number of PV modules is increased in a network due to the emergence of harmonics, unbalanced voltages, voltage flicker, neutral voltage variations, etc. Therefore, it is essential to empirically analyse power quality parameters, i.e., total harmonic distortion (THD), voltage unbalance, etc., and find threshold margins of PV capacities in a network. Based on a case study conducted in Negombo, Sri Lanka, this work determines power quality impacts with reference to the number of PV interconnections in a distributed network. For the task, a low-voltage distribution network was chosen which was fed by a 250kVA, 11/0.4kV transformer with domestic loads and grid-tied PV inverters. A simulation model was developed in Open Distribution System Simulator (OpenDSS) with time-varying load patterns and PV generation. Consequently, a smart efficient method was introduced to model domestic loads with unique time-varying demand patterns. A determination criterion was established to derive snapshot load flow instants using time-varying load flow results to analyse voltage profiles along distribution feeders. Then, the model was enhanced to quantify the power quality parameters such as individual harmonic content, THD of voltage as well as current and neutral voltage variation. The results reveal that node voltage has improved with PV interception without violating the upper limit. The THD of voltage and current have slightly increased with the addition of PV inverters.

Repetitive process based indirect-type iterative learning control for batch processes with model uncertainty and input delay

This paper develops an indirect iterative learning control scheme for batch processes with time-varying uncertainties, input delay, and disturbances. In this paper, a predictor based on a state observer is designed to estimate the future state and to compensate for the input delay. Then a feedback controller based on the estimated state and the set-point error is used to track the specified reference trajectory, where, of the options available, a robust H∞ controller is designed in the presence of time-varying uncertainties and load disturbances. Then a proportional plus derivative type iterative learning control law is designed. An injection molding process model demonstrates the new method’s effectiveness, and a comparison with a direct-type design is given.

Dynamic misalignment effects on performance of dynamically loaded journal bearings

The lubrication characteristics of dynamically loaded journal bearings are significantly affected by misalignments. However, existing research on misalignment primarily focuses on fixed misalignment models, and studies on the nonlinear dynamic response of dynamically loaded bearings under dynamic misalignment are yet to be reported. To address this research gap, this study proposed a dynamic misalignment model coupled with rotor dynamics and transient mixed elastohydrodynamic lubrication. The model comprehensively considers factors such as journal eccentric translation, surface topography, oil film cavitation, and bearing elastic deformation. Upon model validation, numerical simulations are conducted to reveal the single-cycle nonlinear tribological characteristics of dynamically loaded bearings subjected to transient time-varying dynamic loads and time-varying misalignment moments. Based on the dynamic misalignment model, a series of parameter studies were conducted to explore the influence of operating conditions such as load magnitude and rotational speed on lubrication characteristics. The research also evaluated the impact of various structural parameters, including surface roughness, bearing bush thickness, and radial clearance, on the performance of dynamically loaded bearings. The numerical results indicate that the impact of fixed-value misalignment on the performance is highly dependent on the manually set deflection angles. Under light-load and high-speed nonstationary operating conditions, the effect of dynamic misalignment on the lubrication characteristics of dynamically loaded journal bearings was significantly amplified. Furthermore, a smoother surface, thicker bearing bush, and smaller radial clearance intensify dynamic misalignment's influence, compared to fixed-value misalignment, on the transient rough contact behavior at the interface. The findings of this study provide valuable guidance and references for the theoretical analysis and optimization design of dynamically loaded journal bearings.

Tribodynamic analysis of spur gear drives with uncertain time-variant loads: An interval process approach

Gear drives are inherently subjected to time-variant loads, which always create an uncertainty and may degrade the vibration performance and system reliability. However, due to their complicated statistical properties, it is impractical to employ probability-based dynamic analysis methods. Additionally, most studies neglect the elastohydrodynamic lubrication behaviors between tooth surfaces under time-variant load conditions. A novel tribodynamic analysis method is proposed to evaluate system responses efficiently, in which the uncertain time-variant loads are described using interval processes. Firstly, a deterministic tribodynamic model coupling the system dynamics and elastohydrodynamic lubrication is established. To reduce the computational cost, the interval Karhunen-Loeve expansion is employed to simplify the interval processes using a small number of uncorrelated interval variables, while the Chebyshev subinterval decomposition is carried out to approximate actual responses using one-variable functions. The proposed method shares a comparable accuracy with the time-consuming Monte Carlo simulation and experiments. Parametric studies show that the uncertain time-variant loads significantly affect the uncertainty of vibration and induce a more hazardous lubricating condition. Additionally, the variation trend of uncertain tribodynamic responses is highly correlated with the rotating speed.

3D viscoelastic solutions for bending creep of layered rectangular plates under time-varying load

Creep behavior is an inevitable problem for viscoelastic layered structures and needs to be predicted for long-term service situations. In this study, a new technique to obtain analytical solutions for three-dimensional (3D) viscoelastic equations for layered rectangular plates under time-varying loads is developed to predict bending creep behavior. In the analytical model, all the constituent materials of the plate, including the laminar layers and interlayers, exhibit viscoelastic properties, which are simulated by the Burgers model. The slip effect between neighboring laminar layers due to a relatively soft interlayer is considered. The stresses and displacements of each laminar layer in the layered plates are described by 3D elasticity theory combined with the Boltzmann superposition principle. The viscoelastic analytical solutions are obtained by means of series expansions and the Laplace transformation method. The present solution has good accuracy and agrees with the finite element (FE) solution. The influence of various parameters, such as the modulus degradation pattern, modulus ratio and viscoelastic constants, on the creep of the plate are studied.

Emission-Aware Sustainable Energy Provision for 5G and B5G Mobile Networks

A massive number of small cell base stations are expected to be deployed in the 5G and beyond 5G mobile communication networks due to the exponential increase in mobile traffic. This will directly lead to not only a significant increase in energy consumption but also the overall operational cost and carbon footprint. An energy provision based on renewable energy generation to power these small cell base stations is considered a sustainable and promising solution to address this challenge. This paper exploits the cost-effective and low-carbon energy provision solution for individual small-cell mobile networks and presents two different potential frameworks, i.e. centralized and distributed energy provision, respectively. The former supplies nearby small cell base stations through a centralized renewable energy source with energy storage facilities. For the latter, small cell base stations can be supplied by utilizing local renewable energy and storage facilities. These two frameworks are assessed and compared in terms of renewable energy utilization and carbon emission reduction in the presence of time-varying traffic loads, small cell locations and renewable energy availabilities. In addition, we devise energy management for these configurations by incorporating a resource-on-demand strategy in the proposed framework. The numerical simulation results demonstrate that the proposed centralized renewable energy generation strategy for nearby small cells maximizes the cost and energy efficiencies of the network.

Optimal placement of time-varying distributed generators by using crow search and black widow - Hybrid optimization

This paper focuses on the optimal reorganization of radial distribution system (RDS) and the superlative location of time-varying power generation distributed generators, considering time-varying loads. The electric generators, utilizing non-conventional energy sources, are directly connected to the distribution grids with lower ratings compared to conventional source-driven generators. In this study, a combination of optimization techniques, such as the black widow and crow search techniques, is employed to enhance performance in terms of optimal reorganization and superlative location of distribution generation. The reorganization problem is examined and analyzed by considering various scenarios in a standard 69-bus grid, as well as in larger-scale 119-bus and 135-bus systems, with and without the presence of distributed generation resources. The analysis of the proposed optimization techniques with the obtained results is well discussed in this paper.

Hierarchical optimal intelligent battery thermal management strategy for an electric vehicle based on ant colony sliding mode control

Excessive temperature of battery pack causes the performance degradation, affecting the normal operation and safety of the electric vehicles (EVs). This paper proposes an ant colony optimization-fuzzy sliding mode control (ACO-FSMC) hierarchical strategy for the battery thermal management system (BTMS) of EVs. Ignoring the dynamic process of the pump and compressor leads to the deviation of the cooling efficiency of EVs. Therefore, a control-oriented BTMS model is established to describe the temperature dynamics of battery pack and coolant, considering driving current effect on the speed of pump and compressor. Then, a hierarchical optimization strategy is designed to realize the control of the battery cooling rate as well as the speed of the pump and compressor. The upper layer of controller use an ant colony optimization (ACO) to solve the reference speed of the pump and compressor while satisfying constraints of physical characteristics of actuators, aiming at reducing battery temperature deviation and saving energy of BTMS. Considering the nonlinearity of lower layer of BTMS caused by the disturbance of time-varying load torque, fuzzy sliding mode control (FSMC) is applied to control the speed of pump and compressor, in which an integral sliding surface is designed to reduce the influence of disturbance. In order to weaken the chattering of sliding mode control and reduce energy consumption, fuzzy controller is used to adjust the reaching law parameters of sliding mode surface. The simulation results show that compared with PID, the maximum temperature deviation of ACO-FSMC is reduced by 43%, and the energy consumption is reduced by 23%.

Dynamic reliability analysis of the existing bridges based on probability density evolution method

Existing bridges have experienced time-varying load effects and resistance degradation during the service periods. The complex dynamic loads and diverse failure modes make the existing bridges face high service risks, therefore, it is urgent to make time-dependent reliability assessment for the service bridges. The classical time-varying reliability analysis method is increasingly complex and challenging with the increase of the number about random variables. In this paper, probability density evolution theory is introduced as a more advantageous approach to solve the above problem, which is more advantageous for solving the reliability of complex structures with multiple random variables. The dynamic reliability of the existing bridge in serviceability limit state and ultimate limit state is analyzed by considering the bridge resistance degradation and the increase of load effects, as well as the time-varying factors such as shrinkage and creep effect of concrete bridges. The accuracy and computational efficiency for this method are compared with the Monte Carlo method, and the effectiveness of the proposed method is verified, which has the advantages of higher computational efficiency and better accuracy and can be applied to complex nonlinear structures under various loads.

Research on Active Disturbance Rejection Algorithm for Loading Control of 3-DOF Parallel Robot

A three-dimensional (3D) loading device based on a pneumatic 3-universal-prismatic-universal (UPU) parallel manipulator (three chains with UPU joint each) is designed to apply time-varying multi-dimensional loads to a target. First, according to the principle of vector superposition and Newton–Raphson method, the inverse and forward kinematics of the loading device are analyzed. Second, based on the screw theory, the static mapping between the dynamic platform and actuations is derived. Third, a second-order mathematical model is established for pneumatic 3-UPU parallel mechanism based on proportional flow valve and a metal seal pneumatic cylinder. A referential inaccurate model is provided for the control algorithm during modeling. Fourth, based on active disturbance rejection control (ADRC) technique, a 3D loading control algorithm is proposed and dynamic loading control is realized. Experimental results show that the ADRC algorithm has good robustness against disturbances, the steady-state control accuracy is less than 2 N, and the mean square error in dynamic tracking (sinusoidal tracking at 0.2 Hz) is less than 10.5 N.

Probabilistic optimal planning of multiple photovoltaics and battery energy storage systems in distribution networks: A boosted equilibrium optimizer with time-variant load models

In recent years, there has been a rapid increase in distributed generation (DG) technologies incorporated into distribution networks (DNs) to meet the challenge of load growth. However, the stochastic nature of renewable energy, such as photovoltaic (PV), makes the amount of energy produced uncertain. This uncertainty, along with changes in generation and load demand, can increase energy losses and voltage instability. To address this issue, energy storage systems can be integrated to decrease the effects of the intermittency associated with renewable technologies. This paper proposes a new variant of an equilibrium optimizer (EO) based on reinforced learning, named RLEO, for optimal incorporation of multiple battery energy storage (BES) units integrated synchronously with solar PVs into distribution systems while minimizing energy loss. The RLEO algorithm employs reinforced learning mechanisms to prevent premature convergence of the EO and improve its exploration and exploitation capabilities. The performance of the RLEO algorithm is assessed using standard CEC 2017 benchmark functions and compared with the original EO and other popular algorithms using various statistical criteria. The RLEO algorithm is also applied to determine the optimal size and position of multiple PV units in IEEE 69-bus and 118-bus DNs with single and multi-objective optimization problems. Using the developed algorithm, the optimal arrangement of three non-dispatchable PVs results in a slight increase in the percentage reduction of energy loss across various load profiles: 53.0035 % for commercial, 19.6372 % for industrial, and 28.1783 % for residential. In contrast, by employing the optimal configuration of three PV + BES units, the reduction in energy loss percentage experiences a remarkable surge to 68.3466 % for commercial, 68.0917 % for industrial, and 68.1779 % for residential load scenarios using the proposed algorithm. This clearly indicates that the proposed RLEO algorithm significantly surpasses recent optimization methods documented in the literature when it comes to addressing the challenge of optimal allocation for multiple DGs. Furthermore, its applicability extends to more intricate optimization problems.

Carbon Nano-Onions as Nanofillers for Enhancing the Damping Capacity of Titanium and Fiber-Reinforced Titanium: A Numerical Investigation

Improving the damping capacity of metal matrix composites is crucial, especially for applications in the aerospace industry where reliable performance against vibrations and shocks is mandatory. The main objective of the present study is the numerical prediction of the damping behavior of alpha titanium matrix nanocomposites reinforced with hollow carbon nano-onions at various volume fractions. According to the proposed numerical scheme, a structural transient analysis is implemented using the implicit finite element method (FEM). The metal matrix nanocomposites are modeled via the utilization of appropriate representative volume elements. To estimate the mechanical and damping behavior of the nanocomposite representative volume elements, axial sinusoidally time-varying loads are applied to them. The damping capacity of the metal matrix nanocomposites is then estimated by the arisen loss factor, or equivalently the tan delta, which is computed by the time delay between the input stress and output strain. The analysis shows that the loss factor of alpha titanium may be improved up to 60% at 100 Hz by adding 5 wt% carbon nano-onions. The numerical outcome regarding the dynamic properties of the carbon nano-onions/alpha titanium nanocomposites is used in a second-level analysis to numerically predict their damping performance when they are additionally reinforced with unidirectional carbon fibers, using corresponding representative volume elements and time-varying loadings along the effective direction. Good agreement between the proposed computational and other experimental predictions are observed regarding the stiffness behavior of the investigated metal matrix nanocomposites with respect to the mass fraction of the carbon-onion nanofillers in the titanium matrix.

Compensation function observer-based model-compensation backstepping control and application in anti-inference of quadrotor UAV

This study has considered the dynamical equations of a quadrotor unmanned aerial vehicle (UAV) with model uncertainties, time-varying loads and wind disturbances during actual flight. Then, a model-compensated control idea is innovatively proposed for quadrotor UAV attitude and position tracking control, and a compensation function observer-based model-compensated backstepping controller (CFO-based MC-BC) is designed on this basis. The benefits of this approach arc that the proposed controller not only retains the backstepping control strategy in terms of globally asymptotic stability based on Lyapunov criterion. As well as, a compensation function observer (CFO) with high estimation accuracy is used, which can make excellent use of the system state information to accurately estimate the modeling deviations, parameter variations with time, and external unknown disturbances of the system. And it is incorporated into the controller to dynamically offset this negative impact adaptively. This approach effectively addresses the issue of traditional backstepping control performance relying on modeling accuracy. In addition, this paper introduces a high-order differentiator (HOD) that extracts up to the derivatives of the signal with higher accuracy, effectively solving the issue of “differential explosion”. Finally, a large number of simulation results and experimental validation are presented. The results show that the proposed CFO-based MC-BC is superior than the other four schemes in accurate tracking performance, system transient performance, anti-interference ability, anti-time-varying-load, and unknown information estimation ability.

Discontinuous Control Algorithm for Buck Converter under Time-Varying Load and Input Voltage

In this paper, the problem of the output voltage regulation of buck converters is considered. The novelty of the problem statement is that the external electric load and the input voltage of the converter are unknown bounded functions of a certain class. In particular, the external load equivalent scheme is similar to the successive connection of the inductive and resistive elements. In this case, the behavior of the load current is described by the differential equation with time-varying coefficients. In this equation, the equivalent inductance and resistance are described by unknown arbitrary bounded functions with several bounded derivatives. Under known bounds for these functions and their derivatives, the initial system can be transformed into the special form with smooth bounded perturbation. This disturbance is an unknown function, and its action channel differs from the input channel. Therefore, the influence on the unknown external load can not be compensated for directly by the control input. Due to this reason, the new control strategy is developed in the paper with the help of a “vortex” algorithm, which provides asymptotic convergence of the regulation error to zero in time. How to choose the converter parameters and the bounds for the input voltage to operate the closed-loop system properly are shown. The convergence proof is organized with the help of the Lyapunov function approach, and the transient rate is also estimated. The simulation results show the efficiency of the designed control law for the wide class of input voltage and electrical parameter functions. The proposed control scheme may be further used in electric drive systems.

A Gershgorin Circle Theorem Inspired Controller for Renewable Energy Source Integrated Power Systems and Multimicrogrids

Increasing load demands, variations in the operating conditions, continuous integration of the renewable energy sources constitute a multifarious challenge for the researchers to maintain the quality in performances of a load frequency controller. To contemplate such issues, a Gershgorin circle theorem inspired controller assimilated with the particle swarm optimization is proposed for multiarea power systems. The proposed method ensures system stability while abating the frequency variations in the operational areas and the power deviations in the interconnected tie-lines. The present analysis is substantiated through an interconnected photovoltaic (PV) integrated thermal power systems. Furthermore, the competence of the proposed method against increasing complexities is validated by considering an interconnected multimicrogrid systems consisting of renewable and nonrenewable energy sources. The performances of the proposed controller are demonstrated considering fixed and time-varying load disturbances, and fluctuations in renewable energy sources. Results corroborate that the proposed method is successful in maintaining the system stability while mitigating the frequency and the power deviations in all such operating conditions. A comparative analysis of the proposed method with prevalent control techniques (e.g., PI and PID-based controllers, tilt–integral–derivative, integral–tilt–derivative) and optimization algorithms (e.g., genetic algorithm, gravitational search algorithm, imperialist competitive algorithm) is presented to highlight the substantial performance improvements in the considered systems.

Multi-level coordinated control of islanded DC microgrid integrated with electric vehicle charging stations with fault ride-through capability

This paper presents an integrated control framework for islanded DC microgrid (MG) with electric vehicle (EV) charging stations, energy storage unit, and AC/DC loads. The proposed DC MG consists of two DC buses with different voltages, photovoltaic (PV) arrays as intermittent power generation sources, energy storage, three EV charging stations, and a three-phase inverter to power time-varying three-phase loads. Control strategies are proposed to select the charge-discharge mode of EVs that does not negatively affect the MG, as well as coordinate the production and demand management. A central control system enables the operation of MG under different working conditions by managing generation, consumption, and energy storage and also monitors the performance of the charging/discharging unit and the issues relevant to commands of different charging/discharging programs. A specific control strategy has also been implemented to provide fault ride-through (FRT). As a result, the MG feeds its loads in any operating condition. Nonlinear simulations are carried out in MATLAB/SIMULINK software to show that the proposed control methods easily and effectively achieve all objectives, including supplying DC/AC loads, managing battery/resources/charging stations, and detecting/dealing with AC faults.

Transient response of rectangular plate on viscoelastic foundation under time-variable load based on fractional-order differential model

Transient response of rectangular plate on viscoelastic foundation under time-variable load based on fractional-order differential model

Optimal dynamic multi-microgrid structuring for improving distribution system resiliency considering time-varying voltage-dependent load models

This paper presents an innovative approach for enhancing distribution network resiliency against severe weather-related faults. Given the importance of loads in the resiliency concept, an exact and realistic load model is developed along with the consumption pattern and voltage-dependency of each load type. By defining two technical and economic objective functions, a unique method is used to combine and optimize the objective functions through Imperialist Competitive Algorithm (ICA). Two main strategies, namely the dynamic arrangement of microgrid regions via hourly network reconfiguration as well as grid voltage control through Automatic Voltage Regulation (AVR) of distributed generation facilities, are utilized for increased load restoration. The effect of each of these strategies on grid resiliency is evaluated along with the overall approach efficiency based on simulations on a sample 33-bus network comprising renewable and non-renewable resources and commercial, residential and industrial loads. Using this approach, the strategy to encounter each particular type of failure is obtained.

Modelling the Quench Behavior of an NI HTS Applied-Field Module for a Magnetoplasmadynamic Thruster Undergoing a 1kW Discharge

Recent advances in commercial miniaturised cryocoolers and high-temperature superconductors (HTS) have revived the discussion of using HTS electromagnets to enhance the thrust and efficiency of electric thrusters for space applications. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">An HTS applied-field magnetoplasmadynamic (AF-MPD) thruster is currently being developed. While the thruster is operating, there will be a large time-variable heat load on the cryogenic environment. The operation of a low-power cryocooler and energised HTS coils (operating at 70 K) adjacent to streams of hot plasma and large electrical discharges (on the order of 1 kW) represents a significant thermal management problem. The electromagnetic and thermal behaviour of non-insulated (NI) coils under these conditions, and how resilient they are to quenching during thruster operation, is not well understood. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">In this paper, a model is formulated to study the transient electromagnetic and thermal behaviour of an HTS-AF-MPD thruster with NI coils. The thruster and a conduction cooled cryogenic design are coupled via surface-to-surface radiation heat transfer. The model predicts current flow within the HTS, copper stabiliser and between turns, with the contact resistivity being a key input variable. Critical current is determined locally using temperature, magnetic field, and field angle in combination with a measured data set for a specific conductor. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">This model reveals conditions where the cryocooler can passively compensate for large instantaneous heat loads on the coils, demonstrating quench resistance.