Dynamic Equivalent Model Research Articles

An Investigation into the Modeling Methodology of the Coil Spring

The coil spring is an important element in the suspension system of railway vehicles, and its structural vibration caused by the mass distribution can deteriorate the dynamic performance of the vehicle. However, the coil spring is usually modelled as a simple linear force element without considering the dynamic characteristics in multibody dynamic simulations of railway vehicles. To integrate the dynamic characteristics of the coil spring into the simulation, three equivalent dynamic models of the coil spring are established by treating the coil spring as multimass spring series, Timoshenko beam, and flexible spring, respectively. The frequency-sweep method is applied to obtain the dynamic response of the proposed models of coil spring, and the accuracy of the models’ results has been compared and verified by the laboratory test. Results show that all of these three equivalent models can reflect the influence of the spring mass distribution on its dynamic responses. Compared with the mass-spring series and beam element equivalent models, the flexible spring model can better reflect the dynamic stiffness and stress of the coil spring changing with the exciting frequency. Thus, the flexible spring model proposed in this paper is more applicable to railway vehicle system dynamics and the fatigue analysis.

An Accurate Numerical Method and Algorithm for Constructing Solutions of Chaotic Systems

In various fields of natural science, the chaotic systems of differential equations are considered more than 50 years. The correct prediction of the behaviour of solutions of dynamical model equations is important in understanding of evolution process and reduce uncertainty. However, often used numerical methods are unable to do it on large time segments. In this article, the author considers the modern numerical method and algorithm for constructing solutions of chaotic systems on the example of tumor growth model. Also a modification of Benettin's algorithm presents for calculation of Lyapunov exponents.

Research of ASW-FCM-Based Algorithm for Clustered Wind Turbine Group Equivalent Modeling

A new dynamic equivalent modeling method for a wind farm composed of direct-drive wind turbines is proposed. Firstly, the effective input wind speed is calculated considering the wake effect and wind direction change between wind turbines, the operating characteristics is analyzed, the effective wind speed, rotor speed, pitch angle and output power that reflect the wind turbine operating characteristics are selected as the multi-grouping indicators. Secondly, an adaptive sample weighting fuzzy C-means clustering algorithm (ASW-FCM) considering the differences and correlations among turbines operating conditions is designed to cluster the wind farm optimally. Then the equivalent model of the clustered wind turbine group is established based on the principle that the output characteristics before and after the equivalence are equal. Finally, an actual wind farm system is used as an example for modeling and simulation to verify the rationality and accuracy of the equivalent modeling method.

Analysis of dynamic battery characteristics based on dynamic synthesis equivalent circuit model

Analysis of dynamic battery characteristics based on dynamic synthesis equivalent circuit model

Thermal Efficiency for Passive Solar Chimney with and Without Heat Storage material

In this study, a different design of passive air Solar Chimney(SC)was tested by installing it in the south wall of insulated test room in Baghdad city. The SC was designed from vertical and inclined parts connected serially together, the vertical SC (first part) has a single pass and Thermal Energy Storage Box Collector (TESB (refined paraffin wax as Phase Change Material(PCM)-Copper Foam Matrix(CFM))), while the inclined SC was designed in single pass, double passes and double pass with TESB (semi refined paraffin wax with copper foam matrix) with selective working angle ((30o, 45o and 60o). A computational model was employed and solved by Finite Volume Method (FVM) to simulate the air induced through the test room by SC effect. The governing equation of Computational Fluid Dynamic (CFD) model was developed by the effective heat capacity method equation to describe the heat storage and release from PCM-CFM. Practical and computational Results referred to increase in thermal conductivity of the paraffin wax that supported by CFM than 10 times, while the ventilation effect is still active for hours after sun set amount. The maximum ventilation mass flow rate with TESB collector was 36.651 kg/hr., when the overall discharge coefficient equals 0.371. Also, the experimental results referred to the best working angle range 45~60o, while the highest approaching temperature (between air and collector) was appeared for the double passes flat plate collector. Results gave higher heat storage efficiency 47% when the maximum solar radiation 780 W/m2 at 12.00 pm, and the energy summation through duration of charging time was 18460 kJ. Double passes SC at 60o angle presented the highest efficiency with value approaching to 73%, while TESB collector efficiency depicted highest efficiency value 70% at 12:00 pm.

Multi-Direction Vibration Isolator for Momentum Wheel Assemblies

Abstract Momentum wheel assemblies (MWAs) play an important role in the attitude adjustment of the satellite by momentum exchange. The micro-vibration induced by the MWAs affects attitude adjustment and leads to unclear imaging and imprecise position. Considering the isolation of multi-directional vibration and transmission of the torque, a novel isolator inspired by rigid-flexible coupling characteristics of folded structure is proposed for the MWAs in this paper. Through the orthogonal arrangement of two Z-folded beams, the isolator has low stiffness in the translational directions and high stiffness in the direction of rotation. An equivalent dynamic model is developed to characterize the isolator. The experimental results verify that the developed model accurately predicts the response of the isolator under different excitations. The results also demonstrate that the prototype can effectively isolate vibration in low-frequency and a wide-frequency range under three excitation directions. Moreover, the isolator has been tested to verify that it has enough stiffness for torque transmission. The design is compact and can be applied to the MWAs of the satellite for multi-direction vibration isolation without influence on the attitude adjustment of the MWAs to the satellite.

Robustness Improvement on PMU Based Dynamic Equivalent Modeling of Distributed Small Hydropower Generator Stacks

Due to the geographic features and fruitful water resources, the distributed generation of Small Hydropower Generator Stack (SHGS) are vigorously developed in southwest China. As the more concerns about security and stability of power grids with the large amount of SHGS feed into the grid, the accurate models are critical to analyze those potential impacts. With the development of online monitoring technologies in smart grid, PMU based dynamic equivalent modeling for SHGS drawn many attentions. However, field applications reveal that traditional SHGS equivalent model may not be robustness enough to adapt the different disturbances. To overcome this deficiency, method to improve the robustness of SHGS dynamic equivalent modeling is proposed. In the paper, a coherency identification based multi-machine modeling method is introduced to enhance the accuracy of equivalent model. Sensitivity and correlation analysis based key parameters selection scheme is implemented to select the critical parameters, meanwhile avoiding the multiple solutions problem. Moreover, multi-objective optimization algorithm is designed for key parameters identification of the equivalent model. Additionally, hybrid dynamic simulation has adopted into the equivalent process to improve the computational efficiency. The effectiveness of the proposed method has been validated with an actual case from China Southwest grids.

Lubrication and Wear Characteristics of Mechanical Face Seals under Random Vibration Loading.

The service life of mechanical face seals is related to the lubrication and wear characteristics. The stable analytical methods are commonly used, but they cannot address effects of random vibration loading, which, according to experimental studies, are important factors for lubrication and wear of mechanical face seals used in air and space vehicles. Hence, a dynamic model for mechanical face seals is proposed, with a focus on the effects of random vibration loading. The mechanical face seal in the axial direction is described as a mass-spring-damping system. Spectrum analysis specified for random vibration is then performed numerically to obtain the response power spectral density (PSD) of the mechanical face seal and calculate the root mean square (RMS) values under random vibration conditions. A lumped parameter model is then developed to examine how dynamic parameters such as stiffness and damping affect the lubrication regimes of mechanical face seals. Based on the dynamic model and Archard wear equation, a numerical wear simulation method is proposed. The results elucidated that the increase of input acceleration PSDs, the decrease of axial damping, and the increase of axial stiffness lead to the probability of the mechanical face seal operating under full film lubrication regime increase and finally the decrease of wear. This research provides a guideline for improving the adaptability of mechanical face seals under random vibration environments.

Approach to Enhance the Robustness on PMU-Based Power System Dynamic Equivalent Modeling

Due to the maturity of wide area measurement technology, phasor measurement unit (PMU)-based dynamic equivalent modeling method (PDM) has been wildly used in large-scale power system modeling. However, traditional “event-based” PDM equivalent model may face serious robustness issues, such as although derived equivalent models show the good ability on reproduction of the system behaviors under recorded events where they derived from, they may not work well for other possible disturbances. In this article, to improve the robustness of equivalent model, a novel method on dynamic equivalent modeling of power system is proposed. Based on the result of coherency identification, generators inside the equivalent system can be aggregated into different coherent subgroups and represented by multimachine equivalent model. Key parameter selection, which can shrink the scale of identified parameters, is designed to avoid multiple solutions of the equivalent model. Moreover, a multiobjective parameter identification algorithm is developed to fully consider the PMU measurements in different system events. In addition, hybrid dynamic simulation is performed so that each equivalent submodel can be identified separately. Finally, the effectiveness of the proposed method is verified in an actual power grids in China.

Beta Observation-Driven Models With Exogenous Regressors: A Joint Analysis of Realized Correlation and Leverage Effects

We consider a general class of observation-driven models with exogenous regressors for double bounded data that are based on the beta distribution. We obtain a stationary and ergodic beta observation-driven process subject to a contraction condition on the stochastic dynamic model equation. We derive conditions for strong consistency and asymptotic normality of the maximum likelihood estimator. The general results are used to study the properties of a beta autoregressive process with threshold effects and to establish the asymptotic properties of the maximum likelihood estimator. We employ the threshold autoregressive model with leverage effects to analyze realized correlations for several sets of stock returns. We find that the impact of past values of realized correlation on future values is at least 10% higher when stock returns are negative rather than positive. This finding supports the conjecture that correlation between stock returns tends to be higher when stock prices are falling, and lower when there is a surge in stock prices. Finally, we conduct an out-of-sample study that shows that our model with leverage effects can enhance the accuracy of point and density forecasts of realized correlations.

Wind Farm Dynamic Equivalent Modeling Method for Power System Probabilistic Stability Assessment

The uncertainty of power system is intensified by the integration of large-scale renewable energy resources such as wind farm (WF). Considering the impact of system uncertainties, the probabilistic stability analysis methods have been used in the stability assessments of power system with the WF integration. However, in traditional probabilistic analysis methods, WF is normally considered as PQ bus or aggregated as one single-machine equivalent model regardless of wake effect, which might reduce the accuracy of probabilistic stability studies. In this article, a dynamic equivalent modeling method of WF for probabilistic stability assessments is proposed. The wake effect is considered in the modeling process and a practical four-machine clustering method is used in wind turbines clustering. Besides, the fisher discriminant analysis (FDA) is adopt to combine the similar WTs clustering results reasonably. Then, the WF is aggregated to a multi-machine equivalent model by capacity weighted method. Also, the established WF probabilistic model can be directly used in time-domain simulation based on Monte Carlo simulation and FDA. Finally, the efficiency of the proposed method is verified in an actual WF in China.

A Mixed Stress/Displacement Approach Model of Homogeneous Shells for Elastodynamic Problems

This paper presents the development of a model of homogeneous, moderately thick shells for elastodynamic problems. The model is obtained by adapting and modifying SAM-H model (stress approach model of homogeneous shells) developed by Domínguez Alvarado and Díaz in (2018) for static problems. In the dynamic version of SAM-H presented herein, displacements and stresses are approximated by polynomials of the out-of-plane coordinate. The stress approximation coincides with the static version of SAM-H when dynamic effects are neglected. The generalized forces and displacements appearing in the approximations are the same as those involved in a classical, moderately thick shell model (CS model) but the stress approximation adopted herein is more complex: the 3D motion equations and the stress boundary conditions at the faces of the shell are verified. The generalized motion and constitutive equations of dynamic SAM-H model are obtained by applying a variant of Euler–Lagrange equation which includes pertinently Hellinger–Reissner functional. In the constitutive equations, Poisson’s effect of out-of-plane normal stresses on in-plane strains is not ignored; this is one important feature of SAM-H. To test the accuracy of dynamic SAM-H model, the following structures were considered: a hollow sphere and a catenoid. In each case, eigenfrequencies are first calculated and then a frequency analysis is performed applying a harmonic load. The results are compared to those of a CS model, MITC6 (mixed interpolation of tensorial components with 6 nodes per element) shell element calculations, and solid finite element computations. In the two problems, CS, MITC6, and dynamic SAM-H models yield accurate eigenfrequencies and eigenmodes. Nevertheless, the frequency analysis performed in each case showed that dynamic SAM-H provides much more accurate amplitudes of stresses and displacements than the CS model and the MITC6 shell finite element technique.

Dynamic equivalent model of a SMART control rod drive mechanism for a seismic analysis

The SMART (System-integrated Modular Advanced ReacTor) is an integral-type small modular reactor developed by KAERI (Korea Atomic Energy Research Institute). This paper discusses the development of a dynamic equivalent model of the SMART control rod drive mechanism that can be efficiently utilized for complicated analysis during the design of the SMART. A semi-empirical approach is used to develop the equivalent model; that is, the equivalent model is defined analytically and verified empirically. Two types of tests, dynamic characteristics tests and seismic loading tests, are conducted for the development and verification of the dynamic equivalent model, respectively. Acceleration response spectra from the seismic analysis based on the developed equivalent model show good agreement with those from the seismic loading tests.

Robust model‐free adaptive iterative learning formation for unknown heterogeneous non‐linear multi‐agent systems

The formation problem for a class of non-linear multi-agent systems (MASs) is considered under bounded disturbance and repetitive environment. The agent dynamics here is unknown and heterogeneous, and the disturbances are both time-varying and iteration-varying. Based on a novel disturbance-related dynamic linearisation technique, the agent dynamics is first transformed into an equivalent dynamic linearisation data model along the iteration axis. Then, distributed robust model-free adaptive iterative learning protocols are designed to drive the agents to the desired formation pattern. By theoretic analysis, the formation tracking error of the MASs is ultimately bounded and the result is further extended to an iteration-varying topology and pattern case. As a data-driven method, the protocol design has the feature that only the input and output data of neighbouring agents are used. Finally, numerical examples are presented to show the effectiveness and robustness of this method.

A novel energy management strategy for the ternary lithium batteries based on the dynamic equivalent circuit modeling and differential Kalman filtering under time-varying conditions

The dynamic model of the ternary lithium battery is a time-varying nonlinear system due to the polarization and diffusion effects inside the battery in its charge-discharge process. Based on the comprehensive analysis of the energy management methods, the state of charge is estimated by introducing the differential Kalman filtering method combined with the dynamic equivalent circuit model considering the nonlinear temperature coefficient. The model simulates the transient response with high precision which is suitable for its high current and complicated charging and discharging conditions. In order to better reflect the dynamic characteristics of the power ternary lithium battery in the step-type charging and discharging conditions, the polarization circuit of the model is differential and the improved iterate calculation model is obtained. As can be known from the experimental verifications, the maximize state of charge estimation error is only 0.022 under the time-varying complex working conditions and the output voltage is monitored simultaneously with the maximum error of 0.08 V and the average error of 0.04 V. The established model can describe the dynamic battery behavior effectively, which can estimate its state of charge value with considerably high precision, providing an effective energy management strategy for the ternary lithium batteries.

Flexibility Hub's dynamic equivalent model: improving the representation of the distribution grid for system planning

Flexibility Hub's dynamic equivalent model: improving the representation of the distribution grid for system planning

Optimal Frequency Control for Inverter-Based Micro-Grids Using Distributed Finite-Time Consensus Algorithms

This paper addresses the distributed frequency control and economic dispatch problem of micro-grid systems. The optimal frequency control problem is formulated considering both frequency regulation and generation cost minimization, by establishing an equivalent nonlinear second-order dynamic model. A distributed finite-time consensus protocol is proposed to solve the optimal frequency regulation problem based on the equivalent model. Despite the nonlinear dynamics, the system frequency converges to the nominal value and the economic dispatch is achieved both in finite time. It is proved that the equilibrium point of the closed-loop system is the unique optimal solution to the associated economic dispatch problem. Simulation results verify the theoretical analysis and demonstrate the effectiveness of the proposed control method.

Hovering Control of Submersible Transformer Inspection Robot Based on ASMBC Method

Aiming at the difficulty in locating and identifying the faults of oil-immersed transformers, a new spherical submersible transformer inspection robot is designed. The robot has a spherical structure with a zero turn radius, which ensures its flexible motion. It is a difficult problem for the underactuated spherical robot to realize the hovering control for identifying transformer fault points. To address the problem, the dynamic model and kinematics equations of the robot are derived by the hydrodynamic theory at first. Then, an adaptive sliding mode backstepping control (ASMBC) is used to design the cascade control system. The cascade control system consists of the depth control and the yaw control. The performance of the controller is verified by both simulation and real experiments. The simulation experimental results demonstrate that ASMBC controller is superior to the single neuron PID. The tank trials results show that the movement of the robot is flexible, and the hover control can satisfy the requirement of fault observation tasks.

Unsupervised learning method for clustering dynamic behavior in the context of power systems

Abstract Aggregated dynamic equivalent models of active distribution networks (ADNs) are commonly derived using the measurement-based approach. This method exploits acquired data in order to estimate the model parameters using system identification techniques. However, most of the approaches assume that the system maintains the same dynamics for different operating conditions, even though the load mix and the distributed generation (DG) composition are constantly changing. To this end, this paper presents a novel method, which can be used as the first step of the system identification procedure, in order to take into account different system dynamics in ADN modeling. To do so, three unsupervised learning methods for clustering the various dynamic behaviors are introduced, yielding groups of measurements that represent different dynamics. In this context, the proposed methods leverage four clustering algorithms of different notion and complexity, namely k-means++, k-medoids, fuzzy c-means (FCM) and hierarchical clustering. To assess the validity of the proposed approach, real measurements acquired within a year in six real substations in Southern Germany are processed. The results highlight the remarkable difference in system dynamics justifying the necessity of an initial cluster analysis. Finally, the ratio of ”Within Cluster sum of squares” to ”Between Cluster Variation” (WCBCR) is deployed to compare the effectiveness of the clustering algorithms.

Dynamic Equivalent Modeling for Wind Farms With DFIGs Using the Artificial Bee Colony With K-Means Algorithm

With the increasing penetration of wind power, it is recognized that wind power will have a greater and greater impact on the planning and operation of the original power system. And the detailed modeling of wind farm with doubly-fed induction wind generator (DFIG) will require large storage and computation resources, which poses technical challenges for equivalent modeling of wind farm. In this paper, a multi-machine dynamic equivalent modeling method for wind farms with DFIGs is proposed. First, the artificial bee colony with k-means (ABC-KM) algorithm is proposed to improve the effectiveness of wind farm clustering. Second, the operating data composed of wind speed, pitch angle, rotor angular velocity, rotor current, real-time active and reactive power are selected as clustering indicators. A wind farm with DFIGs is divided into several groups and DFIGs in the same group are clustered as one DFIG through equivalent parameter aggregation. The proposed wind farm modeling method consisting of clustering method and clustering indicators is verified by comparing the simulation results of equivalent and detailed models at steady-state and dynamic-state cases.