Flexible Load Participation in Peaking Shaving and Valley Filling Based on Dynamic Price Incentives

Considering the widening of the peak-valley difference in the power grid and the difficulty of the existing fixed time-of-use electricity price mechanism in meeting the energy demand of heterogeneous users at various moments or motivating users,the design of a reasonable dynamic pricing mechanism to actively engage users in demand response becomes imperative for power grid companies.For this purpose,a power grid-flexible load bilevel model is constructed based on dynamic pricing,where the leader is the dispatching center and the lower-level flexible load acts as the follower.Initially,an upper-level day-ahead dispatching model for the power grid is established,considering the lowest power grid dispatching cost as the objective function and incorporating the power grid-side constraints.Then,the lower level comprehensively considers the load characteristics of industrial load,energy storage,and data centers,and then establishes a lower-level flexible load operation model with the lowest user power-consuming cost as the objective function.Finally,the proposed method is validated using the IEEE-118 system,and the findings indicate that the dynamic pricing mechanism for peaking shaving and valley filling can effectively guide users to respond actively,thereby reducing the peak-valley difference and decreasing users’purchasing costs.

Articulated Lifting System Modeling Based on Dynamics of Flexible Multi-Body Systems

In lifting sub-system of deep-sea mining system, spherical joint is used to connect lifting pipes to replace fixed joint. Based on Dynamics of Flexible Multi-body systems, the mechanics model of articulated lifting system is established. Under the four-grade and six-grade oceanic condition, dynamic responses of lifting system are simulated and experiment verified. The simulation results are consistent with experimental ones. The maximum moment of flexion is 322 kN-m on the first pipe under six-grade sea condition. It is seen that the articulated connection can reduce the moment of flexion. The bending deformation of pipe center is researched, and the maximum is 0. 000479 m on the first pipe. Deformation has a little effect on the motion of system. It is feasible to analyze articulated lifting system by applying the theory of flexible multi-body dynamics. The articulated lifting system is obviously better than the fixed one.

STUDY ON DYNAMICS, STABILITY AND CONTROL OF MULTI-BODY FLEXIBLE STRUCTURE SYSTEM IN FUNCTIONAL SPACE

The dynamics, stability and control problem of a kind of infinite dimensional system are studied in the functional space with the method of modern Mathematics. First, the dynamical control model of the distributed parameter system with multi-body flexible and multi-topological structure was established which has damping, gyroscopic parts and constrained damping. Secondly, the necessary and sufficient condition of controllability and observability, the stability theory and asymptotic property of the system were obtained. These results expand the theory of the field about the dynamics and control of the system with multi-body flexible structure, and have important engineering significance.

A New Flexible Multibody Dynamics Analysis Methodology of Deployable Structures with Scissor-Like Elements

There are vast constraint equations in conventional dynamics analysis of deployable structures,which lead to differential-algebraic equations(DAEs)solved hard.To reduce the difficulty of solving and the amount of equations,a new flexible multibody dynamics analysis methodology of deployable structures with scissor-like elements(SLEs)is presented.Firstly,a precise model of a flexible bar of SLE is established by the higher order shear deformable beam element based on the absolute nodal coordinate formulation(ANCF),and the master/slave freedom method is used to obtain the dynamics equations of SLEs without constraint equations.Secondly,according to features of deployable structures,the specification matrix method(SMM)is proposed to eliminate the constraint equations among SLEs in the frame of ANCF.With this method,the inner and the boundary nodal coordinates of element characteristic matrices can be separated simply and efficiently,especially on condition that there are vast nodal coordinates.So the element characteristic matrices can be added end to end circularly.Thus,the dynamic model of deployable structure reduces dimension and can be assembled without any constraint equation.Next,a new iteration procedure for the generalized-a algorithm is presented to solve the ordinary differential equations(ODEs)of deployable structure.Finally,the proposed methodology is used to analyze the flexible multi-body dynamics of a planar linear array deployable structure based on three scissor-like elements.The simulation results show that flexibility has a significant influence on the deployment motion of the deployable structure.The proposed methodology indeed reduce the difficulty of solving and the amount of equations by eliminating redundant degrees of freedom and the constraint equations in scissor-like elements and among scissor-like elements.

Partition method for impact dynamics of flexible multibody systems based on contact constraint

The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are connected by specific boundary conditions, and the system after partition is equivalent to the original system. According to the rigid-flexible coupling dynamic theory of multibody system, system＇s rigid-flexible coupling dynamic equations without impact are derived. A local impulse method for establishing the initial impact conditions is proposed. It satisfies the compatibility con- ditions for contact constraints and the actual physical situation of the impact process of flexible bodies. Based on the contact constraint method, system＇s impact dynamic equa- tions are derived in a differential-algebraic form. The contact/separation criterion and the algorithm are given. An impact dynamic simulation is given. The results show that system＇s dynamic behaviors including the energy, the deformations, the displacements, and the impact force during the impact process change dramatically. The impact makes great effects on the global dynamics of the system during and after impact.

Nonlinear dynamics of flexible tethered satellite system subject to space environment

The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital eccentricity. The flexible tether is modeled as a series of lumped masses and viscoelastic dampers so that a finite multi- degree-of-freedom nonlinear system is obtained. The stability of equilibrium positions of the nonlinear system is then analyzed via a simplified two-degree-freedom model in an orbital reference frame. In-plane motions of the tethered satellite system are studied numerically, taking the space environments into account. A large number of numerical simulations show that the flexible tethered satellite system displays nonlinear dynamic characteristics, such as bifurcations, quasi-periodic oscillations, and chaotic motions.

Numerical and experimental studies on impact dynamics of a planar flexible multibody system

In this paper a computational methodology on impact dynamics of the flexible multibody system is presented. First, the floating frame of reference approach and nodal coordinates on the basis of finite element formulation are used to describe the kinematics of planar deformable bodies. According to the kinematic description of contact conditions, the contact constraint equations of planar flexible bodies are derived. Based on the varying topology technique the impact dynamic equations for a planar multibody system are established. Then the initial conditions of the equations in each contact stage are determined according to the discontinuity theory in continuum mechanics. The experiments between the aluminum rods are performed to check the correctness of the proposed method. Through the comparison between the numerical and experimental results the proposed method is validated. Experimental results also show that the impulse momentum method cannot accurately predict the complex impact dynamic phenomena and the continuous model may lead to a serious error when used to simulate the impact problems with significant wave propagation effects.

Complete geometric nonlinear formulation for rigid-flexible coupling dynamics

A complete geometric nonlinear formulation for rigid-flexible coupling dynamics of a flexible beam undergoing large overall motion was proposed based on virtual work principle, in which all the high-order terms related to coupling deformation were included in dynamic equations. Simulation examples of the flexible beam with prescribed rotation and free rotation were investigated. Numerical results show that the use of the first-order approximation coupling (FOAC) model may lead to a significant error when the flexible beam experiences large deformation or large deformation velocity. However, the correct solutions can always be obtained by using the present complete model. The difference in essence between this model and the FOAC model is revealed. These coupling high-order terms, which are ignored in FOAC model, have a remarkable effect on the dynamic behavior of the flexible body. Therefore, these terms should be included for the rigid-flexible dynamic modeling and analysis of flexible body undergoing motions with high speed.

Simulating Coupled Longitudinal, Pitch and Bounce Dynamics of Trucks with Flexible Frames

Simulating the dynamic response of trucks requires that a model be constructed and subjected to road inputs. Inclusion or omission of flexible frame effects is often based on intuition or assumption. If frame vibration is assumed to be significant, it is typically incorporated in one of two ways. Either a complex finite element model of the frame is used, or a simplified linear modal expansion model (which assumes small motions) is employed. The typical low-order modal expansion model, while computationally efficient and easier to use, is limited by the fact that 1) large rigid body motions and road grade changes are not supported, and 2) longitudinal dynamics are not coupled to vertical and bounce dynamics. In this paper, a bond graph model is presented which includes coupled pitch and bounce motions, longitudinal dynamics, and transverse frame vibration. Large rigid body motions are allowed, onto which small flexible vibrations are superimposed. Frame flexibility is incorporated using modal expansion of a free-free beam. The model allows for a complete pitch-plane representation in which motive forces can propel the truck forward over varying terrain, including hills. The effect of frame flexibility on vehicle dynamics can then be studied. This is an extension of the typical half-car model in which suspension motion is assumed vertical, pitch angles are small, and longitudinal dynamics are completely decoupled or omitted. Model output shows the effect of frame flexibility on vehicle responses such as forward velocity, pitch angle, and payload acceleration. Participation of individual modes can be seen to increase as road input approaches their natural frequency. The bond graph formalism allows for any or all flexible frame modes to be easily removed from the model if their effects are negligible, and for inclusion of more complex submodels for components such as suspension and engine if desired.

Discrete time transfer matrix method for dynamics of multibody system with flexible beams moving in space

In this paper, by defining new state vectors and developing new transfer matrices of various elements mov- ing in space, the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of multibody system with flexible beams moving in space. Formulations and numerical example of a rigid- flexible-body three pendulums system moving in space are given to validate the method. Using the new method to study the dynamics of multi-rigid-flexible-body system mov- ing in space, the global dynamics equations of system are not needed, the orders of involved matrices of the system are very low and the computational speed is high, irrespec- tive of the size of the system. The new method is simple, straightforward, practical, and provides a powerful tool for multi-rigid-flexible-body system dynamics.

Research on Rigid-flexible Coupling Dynamics of Flexible Cone-probe Docking Mechanism

In this paper,a new kind of flexible cone composed of the thin-walled plates based on space probecone docking mechanism for small-sized spacecraft is presented.The theoretical model of docking impact dynamics,which takes into account the additional stiffness terms,is derived based on Lagrange Analytical Mechanics theory and Hertz contact theory.Finite element method is employed for the discretization of the thin-walled plate.The results show that the traditional dynamic model without considering the additional stiffness terms will be difficult to reach steady state.The method proposed in this paper can correctly predict the dynamic behavior of the system.

Controller design based on viscoelasticity dynamics model and experiment for flexible drive unit

In order to ensure that the system has the advantage of light weight and vibration absorption, the steel rope is used as a flexible transmission part. A flexible drive unit(FDU) is developed, whose features are guided by steel rope, increasing force by the movable pulley group, modular, convenient and flexible. Dynamics model for controller is deduced based on the constitutive equation of viscoelasticity. Controller is designed for position control and is based on the viscoelasticity dynamics model compensation control strategy proposed. The control system is based on the TURBO PMAC multi-axis motion control card.Prototype loading experiments and velocity experiments results show that the FDU can reach 2 Hz with no load and the max speed of 30(°)/s. The FDU has the capability of the load torque 11.2 N·m and the speed of 24(°)/s simultaneously, and the frequency response is 1.3 Hz. The FDU can be used to be the pitch joint of hip for biped robot whose walking speed is 0.144 km/h theoretically.

DYNAMICS OF A ROTATING FLEXIBLE MANIPULATOR WITH TIP LOAD

The dynamics of a flexible manipulator is investigated in this paper. From the point of view of dynamic balance, the motion equations of a rotating beam with tip load are established by us ing Hamilton' s principle. By taking into account the effects of dynamic stiffening and dynamic softening, the stability of the system is proved by employing Lyapunov' s approach. Furthermore, the method of power series is proposed to find the exact solution of the eigenvalue problem The effects of rotating speed and tip load on the vibration behavior of the flexible manipulator are shown in numerical results.

Dynamic Bending of Bionic Flexible Body Driven by Pneumatic Artificial Muscles(PAMs) for Spinning Gait of Quadruped Robot

The body of quadruped robot is generally developed with the rigid structure. The mobility of quadruped robot depcnds on the mechanical properties of the body mechanism, It is difficult for quadruped robot with rigid structure to achieve better mobility walking or running in the unstructured environment. A kind of bionic flexible body mechanism for quadruped robot is proposed, which is composed of one bionic spine and four pneumatic artificial muscles（PAMs）. This kind of body imitates the four-legged creatures＇ kinematical structure and physical properties, which has the characteristic of changeable stiff＇hess, lightweight, flexible and better bionics. The kinematics of body bending is derived, and the coordinated movement between the flexible body and legs is analyzed. The relationship between the body bending angle and the PAM length is obtained. The dynamics of the body bending is derived by the floating coordinate method and Lagrangian method, and the driving tbrce of PAM is determined. The experiment of body bending is conductcd, and the dynamic bending characteristic of bionic flexible body is evaluated. Experimental results show that the bending angle of the bionic flexible body can reach 18. An innovation body mechanism for quadruped robot is proposed, which has the characteristic of flexibility and achieve bending by changing gas pressure of PAMs. The coordinated movement of the body and legs can achieve spinning gait in order to improve the mobility of quadruped robot.

New Method for Predicting the Motion Responses of A Flexible Joint Multi-Body Floating System to Irregular Waves

A new hybrid method of frequency domain and time domain is developed in this paper to predict the motion responses of a flexibly joint multi-body floating system to irregular waves. The main idea of the method is that the three-dimensional frequency method is used to obtain the hydrodynamic coefficients and the response equations are solved in time domain step by step. All the forces can be obtained at the same time. The motions and nonlinear mooring forces of a box type six-body floating system are predicted. A comparison of the theoretical method-based Solutions with experimental results has shown good agreement.

Analysis for the Deployment of Single-Point Mooring Buoy System Based on Multi-Body Dynamics Method

Deployment of buoy systems is one of the most important procedures for the operation of buoy system. In the present study, a single-point mooring buoy system which contains surface buoy, cable segments with components, anchor and so on is modeled by applying multi-body dynamics method. The motion equations are developed in discrete node description and fully Cartesian coordinates. Then numerical method is used to solve the ordinary differential equations and dynamics simulations are achieved while anchor is casting from board. The trajectories and velocities of different nodes without current and with current in buoy system are obtained. The transient tension force of each part of the cable is analyzed in the process of deployment. Numerical results indicate that the transient payload increases to a peak value when the anchor is touching the seabed and the maximum tension force will vary with different floating configuration. This work is helpful for design and deployment planning of buoy system.

Dynamic analysis of spatial parallel manipulator with rigid and flexible couplings

The dynamics of spatial parallel manipulator with rigid and flexible links is explored. Firstly, a spatial beam element model for finite element analysis is established. Then, the differential equation of motion of beam element is derived based on finite element method. The kinematic constraints of parallel manipulator with rigid and flexible links are obtained by analyzing the motive parameters of moving platform and the relationships of movements of kinematic chains, and the overall kinetic equation of the parallel mechanism with rigid and flexible links is derived by assembling the differential equations of motion of components. On the basis of abovementioned analyses, the dynamic mechanical analysis of the spatial parallel manipulator with rigid and flexible links is conducted. After obtaining the method for force analysis and expressions for the calculation of dynamic stress of flexible components, the dynamic analysis and simulation of spatial parallel manipulator with rigid and flexible links is performed. The result shows that because of the elastic deformation of flexible components in the parallel mechanism with rigid and flexible links, the force on each component in the mechanism fluctuates sharply, and the change of normal stress at the root of drive components is also remarkable. This study provides references for further studies on the dynamic characteristics of parallel mechanisms with rigid and flexible links and for the optimization of the design of the mechanism.

ON THE DYNAMIC MODELING AND CONTROL OF 2-DOF PLANAR PARALLEL MECHANISM WITH FLEXIBLE LINKS

The object of study is about dynamic modeling and control for a 2degree-of-freedom (DOF) planar parallel mechanism (PM) with flexible links. The kinematic anddynamic equations are established according to the characteristics of mixed rigid and flexiblestructure. By using the singular perturbation approach (SPA), the model of the mechanism can beseparated into slow and fast subsystems. Based on the feedback linearization theory and inputshaping technique, the large scale rigid motion controller and the flexible link vibrationcontroller can be designed separately to achieve fast and accurate positioning of the PM.

Nonlinear Dynamic Analysis of Flexible Marine-Risers

A nonlinear dynamic analysis model is estabilished on the basis of 'lumped mass' approach, which takes the influence of the fluid flow within the pipe into consideration. Numerical results are compared with the published works, and the effects of internal fluid flow, internal pressure, dyanmics as well as the nonlinear characteristics on the behavior of flexible risers are discussed. From this work, some useful conclusions are drawn.

Discrete Element with Flexible Connector for Dynamic Analysis of 3-D Beam Structures

Combined multi-body dynamics with structural dynamics, a new discrete element with flexible connector, which is applicable for 3-D beam structures, is developed in this paper. Both the generalized elastic coefficient matrix of the flexible connector and the mass matrix of discrete element may be off-diagonal in a general case. The zero-length rigid element is introduced to simulate the node at which multiple elements are jointed together. It may also be effective when the axes of adjacent elements are not in the same line. The examples for eigenvalue calculation show that the model is successful. It can be extended to the geometric nonlinear response analysis.