Equivalent Load Model Research Articles

Equivalent load model for the numerical simulation of integrated induction heating and mechanical rolling forming of curved hull plates

Equivalent load model for the numerical simulation of integrated induction heating and mechanical rolling forming of curved hull plates

A composite load model aggregation method and its equivalent error analysis

Although load modeling techniques have been widely applied in practical power system studies, the equivalence of aggregate load models needs to be further illustrated since equivalent load models are commonly adopted to describe the overall characteristics of distributed multi-level power loads in practical scenarios. Driven by two basic aggregation steps, a general composite load model aggregation method is proposed for the first time with load network topology well considered. On this basis, detailed equivalent error analysis of load model aggregation is conducted in order to explain the possible error factors and their influence mechanisms on the equivalent accuracy. Case study results for the modified IEEE 39-bus system have validated the overall feasibility of the proposed model aggregation method and the influence of each error factor under different scenarios. Finally, practical effectiveness of the derived aggregate model is further proved with field measurements in a real-world load system. In this way, the equivalence of adopting aggregate load models can be clearly demonstrated, thus providing necessary foundation for the practical applications of composite load modeling.

A Robust Data-Driven Approach for Adaptive Dynamic Load Modeling

With the power system operating close to its stability margin, the increased penetration of renewable resources and loads with diverse characteristics, appropriate stability studies, and control decisions have become crucial. Due to the importance of accurate representation of aggregate loads in such studies, research interests for load modeling have increased. This paper puts forward a novel measurement-based load modeling approach that adapts itself based on the complex dynamics exhibited by the installed aggregate loads. The proposed approach primarily utilizes the collected measurements to gain insight regarding the dynamic trend in the measurements and subsequently determines the optimal order of an equivalent system or load model capable of effectively representing the aggregate load dynamics. An advanced signal pre-processing technique is employed, which effectively suppresses the noise and also preserves the transients present in the measurements. Afterward, an adaptive dynamic load model (ADLM) accurately represents the installed aggregate load. Lastly, the Refined Instrumental Variable (RIV) approach estimates the equivalent dynamic load model parameters. The results on a 2 bus and the IEEE 118 bus networks in DIgSILENT Powerfactory and a 7 bus network in Real-Time Digital Simulator (RTDS) reveal the efficacy of the proposed approach.

Fast average prediction method based on the upper -lower limit theory for ship’s mechanical noise

The equipment loads include acoustic excitation and mechanical excitation which is characterized by acceleration, and a reliable prediction method of mechanical noise is important to control the hull vibration noise and improve the accuracy of hydroacoustic detection. To address the issue, an accurately and efficiently predicting method is proposed and verified by the hydroacoustic experiments which included the three different diesel engine working conditions. In the method, for the acceleration loads with complete information, an equivalent load model and a gradient meshing model are used to identify the generalized forces, and the mechanical noise is predicted by the identified load and acoustic BEM. For the acceleration loads with missing partly information, the interval theory and the energy superposition method are introduced to calculate the mechanical noise, and the upper-lower limit theory and the average method are proposed to determine the range of mechanical noise and average value. The effect of acoustic excitation generated by diesel engines on mechanical noise is also discussed in detail. The results of hydroacoustic experiments show that the identified forces and mechanical noise can be obtained by the present method, with an error nearby 1 dB, under the accelerations with complete information. For the average acceleration, the range of mechanical noise is obtained and the average sound power is used to represent the ship's mechanical noise, with an error of less than 3 dB. The experimental results also reveal that the effect of acoustic cavity resonance should be included in low frequencies.

Rigid–flexible coupling dynamics analysis with joint clearance for a 5-DOF hybrid polishing robot

SUMMARYConsidering the polishing requirements for high-precision aspherical optical mirrors, a hybrid polishing robot composed of a serial–parallel manipulator and a dual rotor grinding system is proposed. Firstly, based on the kinematics of serial components, the equivalent load model for the parallel manipulator is established. Then, the elastodynamic model of kinematic branched-chains of the parallel manipulator is established by using the spatial beam element, and the rigid–flexible coupling dynamic model of the polishing robot is obtained with Kineto-elasto dynamics theory. Further, considering the dynamic properties of the joint clearance, the rigid–flexible coupling dynamic model with the joint clearance for the polishing robot is established. Finally, the equivalent load distribution of the parallel manipulator is analyzed, and the effect of the branched-chain elasticity and joint clearance on the motion error of the polishing robot is studied. This article provides a theoretical basis for improving the motion accuracy and dynamic performance of the hybrid polishing robot.

Equivalent mechanical load model methodology to simulate lightning strike impact on protected and painted composite structure

Lightning strike damage on aircraft composite structure is very difficult to predict. The main source of this damage is the mechanical constraint generated by the lightning in interaction with the structure made of composite, protected with a metallic mesh and painted. The purpose of this paper is to propose a numerical model able to reproduce the surface overpressure generated by the explosion of the lightning strike protection (LSP) and its confinement with the paint. Comparisons of numerical displacements with lightning experimental ones are presented in order to analyse the predictability of the model. This is a first step in order to assess the damage in the composite structure depending on the design configurations (CFRP, LSP and Paint) when combined with a damage model.

Numerical Modeling Method and Experimental Verification of Prestressed Lining with Unbonded Annular Anchors

Prestressed lining with unbonded annular anchors is a new type of lining used in hydraulic pressure tunnels. First, the key points of numerical modeling are analyzed based on the stress characteristics of the lining. Thus, the corresponding modeling methods are proposed: the contact relationship is set to simulate the different constraint effects of surrounding rock on the lining, the equivalent load and solid model are superposed to simulate the changing prestress state of anchors, and the nonlinear distribution of prestress loss is simulated by applying the gradient load in sections. Finally, based on the finite-difference software FLAC3D, the modeling analysis of Xiaolangdi pressure silt-releasing tunnel in an engineering case is conducted to verify the correctness of the modeling method presented in this study. The research shows that the new modeling method has a clear principle, fast modeling, and reliable results, which is of guiding significance to structure design.

Benchmark study on slamming response of flat-stiffened plates considering fluid-structure interaction

This paper presents a benchmark study on the slamming responses of offshore structures’ flat-stiffened plates. The objective was to compare the fluid-structure interaction (FSI) simulation methodologies, modeling techniques, and established researchers' experiences in predicting slamming pressure. Three research groups employing the most common commercial software packages for numerical FSI simulations (i.e. LS-Dyna ALE, LS-Dyna ICFD, ANSYS CFX, and Star-CCM+/ABAQUS) participated in this study. Wet drop test data on flat-stiffened aluminum plates of light-ship-like bottom structures available in the open literature was utilized for validation of the FSI modeling. A summary of the experimental conditions including the geometry model and material properties, was distributed to the participants prior to their simulations. A parametric study on flat-stiffened steel plates having actual scantlings used in marine installations was performed to investigate the effect of impact velocity and plate rigidity on slamming response. The FE simulation results for the total vertical forces acting on the stiffened plates and their structural responses to those forces, as obtained from the participants, were analyzed and compared. The reliable and accurate predictions of slamming loads using the aforementioned commercial FSI software packages were evaluated. Additionally, equivalent static slamming pressures resulting in the same permanent deflections, as observed from the FSI simulations, were reported and compared with analytical models proposed by the Classification Standards DNV and existing experimental data for calculation of the slamming pressure. The study results showed that the equivalent load model depends on the water impact velocity and plate rigidity; that is, the equivalent static pressure coefficient decreases with an increase in impact velocity, and increases when impacting structures become stiffer.

A Statistical-Based Approach to Load Model Parameter Identification

In the last few years, a great number of methods for identifying the load model parameters have been proposed. This article discusses the use of statistical approach to estimate the substation equivalent load model parameters for supplying to oil-producing industrial region. The disadvantages of existing statistical approach are the low accuracy obtained for the parameter estimates, especially when using samples size is small. To eliminate this deficiency, the current measurement data archive from SCADA system of electrical parameters for 15 months was collected. For the purpose of verifying the obtained results of statistical processing of SCADA data, a full-scale experiment was carried out in relation to the studied substation. The article describes the statistical method used to process the current SCADA measurement data, the results of archived statistical processing and experimental SCADA data. The electrical load models’ parameters received from the experimental studies results are of practical importance.

Experimental and numerical analysis on serviceability of cantilevered floor based on human-structure interaction

To evaluate the vibration serviceability of structure under human-induced excitation, experimental and numerical analysis were conducted on a cantilevered floor of a gymnasium, which was assumed as a case study. A series of field tests were performed using the ambient excitation and the human excitation approaches on the floor to obtain the fundamental vibration characteristics and human-induced response, respectively. Finite element models (FEMs) of the cantilevered floor were established, modified and validated according to the field test results and the weak constraint effect of glass curtain walls was proposed in this paper. The numerical analysis of human-induced vibration was conducted by considering the pedestrian load as the combination of the Fourier series load model and the mass-spring-damper (MSD) human dynamic model. To better simulate the human-structure interaction (HSI), both the main-harmonics and sub-harmonics load spectra were considered for the equivalent load model due to the characteristics of narrow bands. The results showed that both structural vibration modes and human-induced acceleration responses were in good agreement compared with experimental results. The weak constraint effect of glass curtain walls was then validated. The numerical results were more accurate when considering the influence of HSI on the structural vibration serviceability in practical engineering applications.

System level design of wireless sensor node powered by piezoelectric vibration energy harvesting

This paper proposes a design of wireless sensor node powered by piezoelectric vibration energy harvesting system. A complete system level coupling circuit model is established to predict the performance characteristics. The piezoelectric vibration energy harvester (PVEH) is based on a PZT bimorph cantilever, in which a big proof mass is introduced to decrease resonant frequency and a shell served as a stopper to avoid overload. Lumped parameters of the model are identified by experiments and calculations. Electromechanical analogy model of PVEH is simulated in LTspice software. The power consumption of a temperature WSN is tested and the equivalent load model is simulated. A power management circuit (PMC) with LTC3588-1 is designed for rectifying and regulating output of PVEH. Electrical energy is stored in a capacitor. Finally, a system level coupling model is established. Time domain circuit simulation can provide the detailed parameters about the WSN powered by PVEH such as full charge time and sustainable time of the system. Test curves of capacitor charging and WSN power supply in prototype testification show good consistency with the simulation results in LTspice. An application for temperature WSN powered by PVEH is testified as an example. The method and model proposed in this paper can set up a reference to optimize system parameters for WSN powered by PVEH.

Model and control method of a downhole electromagnetic transmitter for EM-MWD system

Downhole electromagnetic transmitter is an important part of EM-MWD system, which can send low-frequency EM waves data from a downhole tool to surface in real time for oil and gas exploration. In order to reduce the volume and weight of the downhole electromagnetic transmitter and improve the depth and accuracy of petroleum exploration, a novel downhole electromagnetic transmitter topology for electromagnetic MWD system is designed. Aiming at the complex and changeable characteristics of load impedance of transmitter, an equivalent load model for downhole electromagnetic transmitter is established with drill string, casing, drill-bit, drilling fluid and formation being taken into account. Because the attenuation characteristic of electromagnetic signal in the wellbore is similar to that of capacitor discharge, the characteristic of electromagnetic channel can be equivalent to the combination of capacitance and resistance. Then, in order to ensure that the downhole electromagnetic transmitter will produce the nominal load voltage, irrespective of disturbances such as variations in the lithium batteries voltage, perturbations in the switching times, and the load, a dual-loop real-time feedback control scheme with an outer voltage loop and an inner current loop is proposed. Simulation and experimental results with laboratory prototype demonstrate the effectiveness of the control method for downhole electromagnetic transmitter. It also ensures the downhole electromagnetic transmitter's excellent stability and the accuracy of the established equivalent load model as well as its ability to meet the requirements of practical field deep exploration. The findings of our work can help for better understanding of approximate load model of downhole electromagnetic transmitter. Furthermore, it will be of great significance for designing control algorithm of downhole electromagnetic transmitter for different areas or boreholes, achieving the purpose of increasing transmission depth. The research results can be used to improve the design and optimization of electromagnetic MWD measurement system in the aspects of improving the control accuracy of the transmitter, saving energy and increasing the transmission depth.

Efficient structure crash topology optimization strategy using a model order reduction method combined with equivalent static loads

In this study, an efficient topology optimization method under crash loads is proposed by combining the equivalent static loads with a model order reduction method, which is referred as the reduced model–based equivalent static loads method for nonlinear dynamic response topology optimization method. Considering that some parts of the vehicle experience large nonlinear deformations, whereas others exhibit only small linear deformations in a vehicle crash scenario, the linear and nonlinear behavior parts are identified and the whole model of the complete structure is divided into nonlinear and linear sub-models. At each cycle, the model order reduction method is used in the linear sub-model during crash analysis to solve the low-density-elements-induced mesh distortion problem and accelerate this process. In the linear static topology optimization, the nonlinear sub-model that was initially used to describe the nonlinear behavior part is linearized by the equivalent static loads method and then reduced by the Guyan reduction method. Then, the reduced equivalent static load model is assembled into the linear sub-model that is defined as the design space to formulate a reduced topology optimization model of the complete structure and the reduced equivalent static loads that only act on master degrees of freedom are calculated. Finally, the linear static topology optimization is performed based on the reduced topology optimization model with the reduced equivalent static loads to enhance the efficiency and improve the numerical stability. The process is repeated until the convergence criterion is satisfied. The effectiveness of the proposed method is demonstrated by investing a numerical example. The results show that the proposed method provides a feasible strategy for the topology optimization under crash loads, which can effectively improve the numerical stability and convergence.

Harmonic Transfer-Function-Based Impedance Modeling of a Three-Phase VSC for Asymmetric AC Grid Stability Analysis

Impedance modeling and stability analysis of a grid-voltage source converters (VSC) system under symmetric ac grids have been extensively discussed in the literature, where the dq domain impedances are usually adopted. As for asymmetric ac grids, impedance modeling is no longer straightforward in the dq domain due to the presence of negative sequence components, where the linearization will result in a linear-time-periodically-varying system, making the frequency-domain analysis intractable. One way to address this issue would be the harmonic-transfer-function (HTF) approach. Although this method is conceptually clear, its application to the stability analysis of an unbalanced grid-VSC system is still challenging and an effective model is missing here, therefore this paper aims to bridge this gap. First, the sequence impedances of an unbalanced grid-VSC system is modeled in the HTF framework. Then the HTFs are truncated into four-by-four matrices by exploiting the property of frequency couplings. Based on this, the equivalent source and load model for Nyquist-based analysis are established, and they are thoroughly verified by impedance measurements as well as the accuracy on stability analysis. Finally, several stability concerns of the unbalanced grid-VSC system, as well as the feasibility of symmetric models for asymmetric ac grid stability analysis are discussed and clarified.

Aggregated dynamic model of active distribution networks for large voltage disturbances

This paper proposes a “grey-box” aggregated dynamic model for active distribution networks, taking into account a heterogeneous fleet of generation technologies alongside their expected behavior when taking into account the latest European grid codes requirements in terms of voltage support services. The main goal of the proposed model and underlying methodology for its identification is to represent the transient behavior of the active distribution system following large voltage disturbances occurring at the transmission side. The proposed aggregated model is composed by three main components: an equivalent power converter for generation and battery energy storage systems portfolio representation; an equivalent synchronous generation unit; and an equivalent composite load model. The model’s parameters are estimated by an evolutionary particle swarm optimization algorithm, by comparing a fully-detailed model of a distribution network with the aggregated model’s frequency domain’s responses of active and reactive power flows, at the boundary of transmission-distribution interface substation.

Equivalent constant-amplitude fatigue load method based on the energy equivalence principle

An equivalent constant-amplitude cyclic loading method for random vehicle load is proposed based on the concept of energy equivalence. The filtered compound Poisson process is adopted to describe random vehicle load, through which the vehicle load spectrum is gained. The total dissipated energy due to fatigue loads subjected to concrete structures is deduced by introducing a multi-scale model, in which the energy dissipation induced by the nano-cracks level is presented, and the energy transition from nano to macro scales is derived. By assuming that the total energy dissipation under random loading equals that under equivalent constant-amplitude loading, the equivalent load ratio and amplitude as well as the number of equivalent cycles for random vehicle load are obtained. To validate the effectiveness of the proposed method, a set of numerical simulations is presented. The fatigue damage accumulations for concrete structures under both the random load and the equivalent loads converted by the proposed method and the classic root mean square method are calculated. By comparing with the root mean square method, the accuracy and advantage of the proposed equivalent load model are verified.

Construction and failure analysis of ultra-light GFRP fluted-core sandwich protective structures

Pultruded glass fiber reinforced polymer (GFRP) fluted-core sandwich panel is easily made and is a lightweight construction for protective structures. Blast-resistant doors are designed and constructed through combining three pultruded fluted-core sandwich panels framed by steel beams. With weight of 98.34 kg, the composite door is much lighter compared with traditional steel and concrete protective doors. Blast resistances of the composite protective doors are investigated by explosion testing. In current research, when the scaled distance is not smaller than 1.494 m/kg1/3, the door panel exhibits excellent anti-blast ability without any damage. When the scaled distance is less than 1.357 m/kg1/3, the structure damage is firstly characterized by the fluted-core shear and finally featured by the flexural failure of the delaminated sandwich panel. Including the deflection induced by the shear deformation of the fluted-core, dynamic one-way sandwich slab theory is proposed to predict the dynamic responses. The predictions are in agreement with the experimental results with acceptable errors. The dynamic theory can predict the critical scaled distance for the composite door based on core-shear failure criterion and the prediction is well consistent with the experiments. An equivalent static load model is suggested. Through the research, it is concluded that constructing protective door through pultruded GFRP fluted-core sandwich panels is a convenient, weight-saving and cost-saving way.

Determination of equivalent blasting load considering millisecond delay effect

In the analysis of the effects of rock tunnel blasting vibration on adjacent existing buildings, the model of simplified equivalent load produces higher calculation result of vibration, due to the lack of consideration of the millisecond delay effect. This paper, based on the static force equivalence principle of blasting load, proposes a new determination method of equivalent load of blasting vibration. The proposed method, based on the elastic-static force equivalence principle of stress wave, equals the blasting loads of several single blastholes in the same section of millisecond blasting to the triangle blasting load curve of the exploded equivalent elastic boundary surface. According to the attenuation law of stress wave, the attenuated equivalent triangle blasting load curve of the equivalent elastic boundary is applied on the tunnel excavation contour surface, obtaining the final applied equivalent load. Taking the millisecond delay time of different sections into account, the time-history curve of equivalent load of the whole section applied on the tunnel excavation contour surface can be obtained. Based on Sailing Tunnel with small spacing on Sanmenxia-Xichuan Expressway, an analysis on the blasting vibration response of the later and early stages of the tunnel construction is carried out through numerical simulation using the proposed equivalent load model considering millisecond delay effect and the simplified equivalent triangle load curve model respectively. The analysis of the numerical results comparing with the field monitoring ones shows that the calculation results obtained from the proposed equivalent load model are closer to the measured ones and more feasible.

Experimental Study on the Long-Term Behaviour of RBPC T-Beams

This study compares the mechanical properties of the retard-bonded and conventionally bonded prestressed concrete (RBPC and BPC, respectively) under uniform loads. Results show that the prestressed strands and concrete of the RBPC T-beams are firmly bonded with harden of retard-bonded materials, thereby exhibiting the same mechanical properties as that of the BPC beams. The growth rate of the long-term deflections of the RBPC T-beam is slightly lower than that of the BPC T-beam. Given the effect of concrete shrinkage, creep and time variation of prestress loss, the regular patterns of deflection growth of the RBPC T-beam mid-spans are analysed based on the age-adjusted effective modulus method, method of equivalent prestress load and calculation model of prestress loss. Accordingly, the long-term deflection development curves of the RBPC T-beam mid-spans under self-weight, prestressing force and external loads are obtained. Calculation results are in good agreement with the test results. This method has immense applicability for the computation of the RBPC T-beams, and can be used to estimate the long-term deflection growth of regular patterns of the RBPC components.

Reduced-order models for vertical human-structure interaction

For slender and lightweight structures, the vibration serviceability under crowd- induced loading is often critical in design. Currently, designers rely on equivalent load models, upscaled from single-person force measurements. Furthermore, it is important to consider the mechanical interaction with the human body as this can significantly reduce the structural response. To account for these interaction effects, the contact force between the pedestrian and the structure can be modelled as the superposition of the force induced by the pedestrian on a rigid floor and the force resulting from the mechanical interaction between the structure and the human body. For the case of large crowds, however, this approach leads to models with a very high system order. In the present contribution, two equivalent reduced-order models are proposed to approximate the dynamic behaviour of the full-order coupled crowd-structure system. A numerical study is performed to evaluate the impact of the modelling assumptions on the structural response to pedestrian excitation. The results show that the full-order moving crowd model can be well approximated by a reduced-order model whereby the interaction with the pedestrians in the crowd is modelled using a single (equivalent) SDOF system.