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Virtual synchronous generators (VSGs) incorporate virtual resistance (VR) in inverter control as a damping mechanism for oscillations that appear around the synchronous frequency due to interactions between the inverter impedance and the line impedance while operating in low inertia grids. Damping is critical for synchronization stability in the small-signal and large-signal disturbance scenarios to suppress oscillations that threaten system stability. While VR enhances stability in the steady state, it is shown that its conventional application affects the transient stability of VSGs by reducing the angle overshoot range in the dynamic behaviour of the power angle δ, illustrated using the power-angle (P − δ) and frequency-angle (δ̇− δ) curves. In this article, a novel damping mechanism to improve the transient stability of VSGs using VR to enhance the power angle dynamics is proposed. By using the concept of virtual point of common coupling, the virtual power of the internal VSG is introduced in the active power feedback during a voltage sag, providing an equivalent damping effect proportional to the VR applied. In this way, the negative effects of VR on transient stability are averted while VR is used to improve the power angle dynamics of conventional VSG. Simulations of different transient stability scenarios are carried out in MATLAB/Simulink to verify the proposed method. [ABSTRACT FROM AUTHOR]

Aiming at the power coupling problem caused by the high impedance ratio between the distributed energy(DG)controlled by the virtual synchronous generator(VSG)and the power grid. In this paper,the power coupling mechanism is analyzed,and the coupling relationship between power and impedance ratio and power angle is established by relative static gain coefficient. A virtual power control technology based on virtual negative impedance is proposed. The virtual impedance is used to calculate the virtual voltage,and the obtained virtual voltage is fed back to the power calculation part to form the virtual power to realize power decoupling. Based on the constraint condition of coupling degree,the specific solution method of virtual resistance and inductance is given. Finally,the simulation model is built by using MATLAB/ Simulink simulation software. By comparing with the traditional virtual impedance technology,it is verified that the proposed virtual power control strategy has a significant effect on weakening the coupling between the active and reactive power loops. [ABSTRACT FROM AUTHOR]

An analytical efficiency expression for the 2K-V gearbox, which includes both rotational and revolutional power, is derived using virtual power analysis. The presence of a constant-speed ratio mechanism in the 2K-V gearbox results in certain components rotating revolution without self-rotation. New concept, the revolutional power, is introduced to address this aspect. The efficiency formula and power flow have been verified through several data sets and velocity iconography. Further analysis investigates the impact of specific design parameters on efficiency and power losses. Moreover, sensitivity weights for design parameters affecting total efficiency are identified using machine learning and an optimal parameter range for their optimization is established. Design recommendations aimed at enhancing efficiency are provided. The results show that the losses at the meshes are significantly lower when the ratio of the first stage gearing is set to speed-up rather than speed-down. The smaller the difference in the number of teeth in the second stage gearing, the greater the power losses at the meshes. In the majority of speed ratio scenarios, the second-stage gear pair will experience significant meshing losses as virtual power flows through it. The design parameters related to the second-stage gearing have a significant effect on the overall system efficiency. [ABSTRACT FROM AUTHOR]

This contribution presents a comprehensive, in-depth analysis of the solution of the mechanical equilibrium problem for a generic solid with microstructure. The exact solution to this problem, referred to here as the reference solution, corresponds to the full-scale model of the problem that takes into account the kinematics and constitutive behavior of its entire microstructure. The analysis is carried out based on the Principle of Multiscale Virtual Power (PMVP) previously proposed by the authors. The PMVP provides a robust theoretical setting whereby the strong links between the reference solution and solutions of the mechanical equilibrium obtained using coarser scale models are brought to light. In this context, some fundamental properties of coarser scale solutions are identified by means of variational arguments. These findings unveil a new homogenization landscape for Representative Volume Element (RVE) multiscale theories, leading to the construction of new Minimal Kinematical Restriction (MKR)-based models where either displacements or tractions may be prescribed on the RVE boundary. A careful observation of the aforementioned landscape leads naturally to the proposal of a new, multicontinuum strategy (a generalized continuum counterpart of multigrid strategies) to approximate the reference solution at low computational cost. In the proposed strategy, the mechanical interactions among neighboring microcells are accounted for in an iterative fashion by means of suitably chosen boundary conditions enforced alternately on the new MKR-based models. The proposed developments are presented assuming a classical continuum at all scales, but the results are equally valid when different kinematical and constitutive assumptions are made at different scales. [ABSTRACT FROM AUTHOR]

For the pre-synchronization method of the virtual synchronous generator (VSG), only the case of a single VSG pre-synchronization and grid connection has been studied and analyzed. If the phase synchronization of multiparallel VSGs in a decentralized microgrid is realized by controlling a VSG, power circulation exists in the pre-synchronization process. Firstly, the structure and control mode of the microgrid are introduced. For the decentralized structure, a control mode switching mechanism under distributed communication is designed, and a pre-synchronization method of parallel VSGs based on control mode switching is proposed. Secondly, a theoretical analysis of the active power circulation problem is performed by an equivalent frequency model for parallel VSGs in the pre-synchronization process. Finally, the simulation results show that the proposed pre-synchronization method can reduce the dynamic power circulation of parallel VSGs by 83%, and improve the pre-synchronization speed by 75%. [ABSTRACT FROM AUTHOR]

To improve the connection efficiency to grid of distributed power sources, and solve the problems of insufficient damping and inertia in inverter grid connection, an inverter control method was investigated to realize traditional synchronous generator's function, which was named as virtual synchronous generator (VSG) technology. Based on the role of phase locked loop (PLL) in virtual synchronous generator, the pre-synchronization control method was proposed based on virtual power. The secondary frequency modulation and the secondary voltage regulation functions were simulated in the power loop. The output value compensated the loss of active power and reactive power through inertia link, and the control parameters were flexibly adjusted according to power levels. Regarding the voltage and current on the VSG generator side, the PR control method was used to increase the constraint on the electrical value for preventing grid connection failure. The topology structure and the mathematical model of VSG were analyzed, and the improved control method of VSG was given. A corresponding simulation model was established to verify VSG control effect from two aspects of pre-synchronous grid-connection and grid connection stability under mutation load. The results show that the improved VSG control can reduce the complexity of grid-connected inverter and the oscillation frequency of output power and suppress the current impact on the grid side, which makes the inverter follow the dynamic change process of power grid at all time. [ABSTRACT FROM AUTHOR]

This paper researched on the pre-synchronization grid connection method of a virtual synchronous generator (VSG), and proposed a fast pre-synchronization method based on the virtual power loop. According to the self-synchronization characteristics of the VSG power loop, the double power loop design was adopted in this paper. The two power loops had the same structure, which the power loop 1 was used to implement the basic VSG function, and the power loop 2 was used to achieve rapid pre-synchronous control. Therefore, the mathematical model of the VSG was similar to the synchronous generator in the pre-synchronization control. This method did not require a phase-locked loop and VSG has a good inertia and Damping performance. Moreover, this method was suitable for the networking of multiple VSGs.

RV reducer is the core component of industrial robot. It is of great significance to raise the transmission efficiency of RV reducer for improving the transmission performance of industrial robot. RV reducer belongs to the 2K-V type planetary gear train and consists of an equal speed ratio mechanism. Therefore, according to the structural characteristics of RV reducer, the virtual power theory and split power theory are adopted, and a calculation method of transmission efficiency for RV reducer is proposed. Firstly, the structure of a common RV reducer is introduced. Related structural analysis, kinematic analysis, and loaded analysis are given. Secondly, RV reducer is represented by the method of graph theory. By the virtual power theory and split power theory, the power flow direction is determined, and the values of split powers are calculated. Finally, according to the graph representation for RV reducer and the calculation principle of meshing power loss of planetary gear, the power losses of meshing gear pairs are calculated, respectively. According to the input and output values described in graph representation of RV reducer, the formula of transmission efficiency for RV reducer is derived. The calculation of transmission efficiency for RV-40E reducer is considered as an example. The result is compared with previous work on the subject, and the relations between design parameters and transmission efficiency of RV reducer are discussed. [ABSTRACT FROM AUTHOR]

Based on the objective physical fact that the supporting surface would make the supporting point move slightly, the micro variable degrees of freedom independent of the macro constraints were introduced to describe the gap function at the support points, and the virtual elastic stiffness of the support surfaces was introduced to describe the resistance of the support surfaces. In order to overcome the difficulty of numerical solution caused by the "switch effect" of virtual elastic stiffness, the transition function was introduced to smooth that. According to the macroscopic force condition, the equilibrium equation was established, and the support reaction of the support points was obtained by solving the nonlinear equations. A variety of support reactions were calculated and compared with the experimental data to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The behavior of third gradient materials is analyzed. They possess stress tensor fields of second, third and fourth order. Starting from the principle of virtual power, we derive the admissible boundary conditions. Those on free surfaces can only be obtained by the application of the divergence theorem of surfaces. On the other hand, such an application to fictitious internal cuts makes no sense although it is usually practiced. We prove that some of the boundary conditions on a free surface may be interpreted as the equilibrium conditions of a shell. So a crust shell exists on such a surface and a beam exists where patches of the surface meet. On the other hand, no such shells or beams can be found with fictitious surfaces in the interior of a continuum. Our finding does not depend on any specific constitutive assumption. [ABSTRACT FROM AUTHOR]

Security constraint is a key component in unit commitment to guarantee reliable generator commitment. Large set of security constraints are notorious for making the problem difficult to solve. Constraint screening, i.e., filtering out non-dominating constraints, is regarded as a powerful tool to address this challenge. This work presents a security-constraint screening that can effectively integrate virtual transaction and capture changes online in real-time or look-ahead markets. The proposed approach takes advantage of both deterministic and statistical methods, which leverages mathematical modeling and historical data. Effectiveness are verified using Midcontinent Independent System Operator (MISO) data. [ABSTRACT FROM AUTHOR]

On the eve of Human-Robot-Interaction (HRI) becoming customary in our lives, the performance of HRI robotic devices remains strongly conditioned by their gearboxes. In most industrial robots, two relatively unconventional transmission technologies—Harmonic Drives© and Cycloid Drives—are usually found, which are not so broadly used in other industries. Understanding the origin of this singularity provides valuable insights in the search for suitable, future robotic transmission technologies. In this paper we propose an assessment framework strongly conditioned by HRI applications, and we use it to review the performance of conventional and emerging robotic gearbox technologies, for which the design criterion is strongly shifted toward aspects like weight and efficiency. The framework proposes to use virtual power as a suitable way to assess the inherent limitations of a gearbox technologies to achieve high efficiencies. This paper complements the existing research dealing with the complex interaction between gearbox technologies and the actuators, with a new gearbox-centered perspective particularly focused on HRI applications.

Due to their closed-loop structure and kinematic constraints, dynamic modelling of parallel manipulators presents an inherent complexity. In the present research, an approach to obtain the nonlinear dynamics equations of motion of a 3-RRcP spherical parallel manipulator is presented. The proposed approach is based on the principle of virtual power and the screw theory. To obtain the dynamics equations of motion, we propose an influence matrix which relates the passive joint rates to the actuated joint rates for each branch. The presented method allows a straightforward computation of torques of the actuated joints in terms of the resultant external forces and the desired trajectory. In order to represent correctness and accuracy of the obtained equations of motion, two case studies are considered that their solutions are compared by a commercial dynamics software package (CDSP). [ABSTRACT FROM AUTHOR]

There are some problems on multi-user downlink power allocation and beamforming in a cognitive radio network (CRN) which works in the underlay mode. They are the high complexity of the conventional SDR algorithm. the limited applicability and ignoring the interferences of the primary network (PN) to the secondary user(SU) , etc. Aiming at these problems, this paper firstly added the term of interference of the PN to the SU to the CRN model and formulated the optimization problem. Then based on the duality of uplink-downlink, it obtained the simple and fast iterative algorithm by introducing virtual power, transforming the optimization problem into the problem of uplink power allocation and beamforming. And it analyzed the convergence of the algorithm to obtain the convergent conditions. It also reckoned the algorithm complexity. The result demonstrates that iterative algorithm is superior to the SDR algorithm. Numerical simulation results show that the algorithm conveiges faster, and that the variation of transmitting power of the primary base station (PBS) could affect the feasibility region. They also show that the increasing of transmitting power of the PBS could lead to the downlink power increasing. The influences are notable. [ABSTRACT FROM AUTHOR]

Highlights • The theory of screws is undergoing a revival in machines and robotics. • The theory is significantly generalized and extended in various directions. • Use is made of exterior algebra of multi-vectors. • A formulation in terms of tensor densities is also provided. Abstract The theory of screws is generalized to yield a formulation of Statics in higher-dimensional spaces in the absence of any distinguished metric structure. This level of generality necessitates the use of the tools of the exterior algebra of multi-vectors. The minimal structure retained serves to bring into relief the essential difference between screws and counter-screws as well as a weak version of the notion of rigid-body velocity field. An essential feature of the theory is the introduction of higher-order forces and displacements, whose relevance in the context of structured media can be determined in specific potential applications. [ABSTRACT FROM AUTHOR]

In this work we develop a multi-scale model to characterise the large scale constitutive behaviour of a material featuring a small scale fibrous architecture. The Method of Multi-scale Virtual Power (MMVP) is employed to construct the model. At the macro-scale, a classical continuum mechanics problem is formulated in the finite strain regime. At the micro-scale, a network of fibres, modelled as one-dimensional continua, composes the representative volume element (RVE). The MMVP provides a full characterisation of the equilibrium problem at the RVE, with consistent boundary conditions, as well as the homogenisation formula which defines the first Piola–Kirchhoff stress tensor. Particular attention is given to the fact that the macro-scale continuum could be considered incompressible. Numerical experiments are presented and model consistency is verified against well-known phenomenological constitutive equations. Scenarios departing from the hypotheses of such phenomenological material models are discussed. [ABSTRACT FROM AUTHOR]