Showing papers on "Inertia published in 2021"

The role of inertia for grid flexibility under high penetration of variable renewables - A review of challenges and solutions

Abstract: Several studies show that grid-integrated renewable energy (RE) sources have the potential to replace conventional synchronous generators in the network. This means the grid will experience low conventional inertia that is currently provided by synchronous generators. Low, unpredictable and time-changing inertia in the power system, as a result of high penetration of non-synchronous RE sources, can cause rapid frequency oscillations. The rapid and unpredictable frequency oscillations are the major source of stability challenges in the power system. Therefore, this research presents a comprehensive literature survey on the role of inertia for grid flexibility under high penetration of non-synchronous RE sources to the power system. As inertia is becoming a time-changing quantity, inertia estimation techniques have been gaining popularity as solutions to stability challenges faced by the power system. Related to time-changing inertia, the following are discussed in this survey research. First, synthetic inertia provision in the network and the need for inertia estimation are intensively discussed. Second, the importance of prior knowledge of the system inertia, which will help operators to apply suitable control strategies to mitigate stability challenges, is also addressed. Third, the significance of co-existence, coordination and optimization of both conventional synchronous generator's inertia and synthetic inertia, as a key feature towards reliable and flexible grid in low inertia environment, are also emphasized. Finally, technical challenges, key issues, and further research needs are highlighted.

On-Line Inertia Estimation for Synchronous and Non-Synchronous Devices

Abstract: This paper proposes an on-line estimation method able to track the inertia of synchronous machines as well as the equivalent, possibly time-varying inertia from the converter-interfaced generators. For power electronics devices, the droop gain of the Fast Frequency Response (FFR) is also determined as a byproduct of the inertia estimation. The proposed method is shown to be robust against noise and to track accurately the inertia of synchronous generators, virtual synchronous generators with constant and adaptive inertia, and wind power plants with inclusion of energy storage-based frequency control.

Inertial self-propelled particles.

Abstract: We study how inertia affects the behavior of self-propelled particles moving through a viscous solvent by employing the underdamped version of the active Ornstein–Uhlenbeck model. We consider both potential-free and harmonically confined underdamped active particles and investigate how the single-particle trajectories change as the drag coefficient is varied. In both cases, we obtain the matrix of correlations between the position, velocity, and self-propulsion and the explicit form of the steady-state probability distribution function. Our results reveal the existence of marked equal-time correlations between velocity and active force in the non-equilibrium steady state. Inertia also affects the time-dependent properties of the active particles and leads to non-monotonic decay of the two-time correlation functions of particle positions and velocities. We also study how the virial pressure of particles confined to harmonic traps changes as one goes from the overdamped to the underdamped regime. Finally, the study of the correlations in the underdamped regime is extended to the case of a chain of active particles interacting via harmonic springs.

Two-Stage Chance-Constrained Stochastic Thermal Unit Commitment for Optimal Provision of Virtual Inertia in Wind-Storage Systems

Abstract: The frequency security problem becomes a critical concern in power systems when the system inertia is lowered due to the high penetration of renewable energy sources (RESs). A wind-storage system (WSS) controlled by power electronics can provide the virtual inertia to guarantee the fast frequency response after a disturbance. However, the provision of virtual inertia might be affected by the variability of wind power generation. To address this concern, we propose a two-stage chance-constrained stochastic optimization (TSCCSO) model to find the optimal thermal unit commitment (i.e., economic operation) and the optimal placement of virtual inertia (i.e., frequency stability) in a power grid using representative power system operation scenarios. An enhanced bilinear Benders decomposition method is employed with strong valid cuts to effectively solve the proposed optimization model. Numerical results on a practical power system show the effectiveness of the proposed model and solution method.

Adaptive nonsingular predefined-time control for attitude stabilization of rigid spacecrafts

Abstract: This article proposes a novel adaptive nonsingular predefined-time control strategy for rigid spacecrafts with inertia uncertainties. Following the backstepping recursive design procedures, an adaptive attitude controller is systematically presented to ensure that the spacecraft attitude can converge into a small region around the origin within a predefined time, which can be explicitly determined in advance by assigning a simple parameter. Moreover, by designing quadratic functions in the controllers, the singularity can be avoided directly without using any filters or piecewise continuous functions, such that the stability analysis becomes more concise and straightforward. Simulations are conducted to show the effectiveness of the presented method.

RBF Neural Network Based Virtual Synchronous Generator Control With Improved Frequency Stability

Abstract: The virtual synchronous generator (VSG) based on the energy storage system is proposed to compensate the loss of inertia and damping of the power grid. Due to the introduction of inertia, VSG is more prone to power oscillation. In this article, the nonlinear relationship between inertia and angular velocity is analyzed, and adaptive neural network (NN) control is first applied to VSG. Based on this concept, an adaptive control strategy is proposed in this article. First, the radial basis function NN that enjoys a simple algorithm, strong ability of learning, and fast learning rate is used to adjust virtual inertia adaptively. This strategy not only improves response but also reduces frequency overshoot in tracking the steady-state frequency. And then, based on the fixed damping ratio, the damping coefficient is tuned adaptively with the change of the inertia to further suppress power oscillation. The proposed strategy is supported by simulation results, which show that the strategy has good performance in damping of oscillation.

Time-dependent inertia of self-propelled particles: The Langevin rocket.

Abstract: Many self-propelled objects are large enough to exhibit inertial effects but still suffer from environmental fluctuations. The corresponding basic equations of motion are governed by active Langevin dynamics, which involve inertia, friction, and stochastic noise for both the translational and orientational degrees of freedom coupled via the self-propulsion along the particle orientation. In this paper, we generalize the active Langevin model to time-dependent parameters and explicitly discuss the effect of time-dependent inertia for achiral and chiral particles. Realizations of this situation are manifold, ranging from minirockets (which are self-propelled by burning their own mass), to dust particles in plasma (which lose mass by evaporating material), to walkers with expiring activity. Here we present analytical solutions for several dynamical correlation functions, such as mean-square displacement and orientational and velocity autocorrelation functions. If the parameters exhibit a slow power law in time, we obtain anomalous superdiffusion with a nontrivial dynamical exponent. Finally, we constitute the ``Langevin rocket'' model by including orientational fluctuations in the traditional Tsiolkovsky rocket equation. We calculate the mean reach of the Langevin rocket and discuss different mass ejection strategies to maximize it. Our results can be tested in experiments on macroscopic robotic or living particles or in self-propelled mesoscopic objects moving in media of low viscosity, such as complex plasma.

Spatial velocity correlations in inertial systems of active Brownian particles

Abstract: Recently, it has been discovered that systems of active Brownian particles (APB) at high density organise their velocities into coherent domains showing large spatial structures in the velocity field. This collective behavior occurs spontaneously, i.e. is not caused by any specific interparticle force favoring the alignment of the velocities. This phenomenon was investigated in the absence of thermal noise and in the overdamped regime where inertial forces could be neglected. In this work, we demonstrate through numerical simulations and theoretical analysis that velocity alignment is a robust property of ABP and persists even in the presence of inertial forces and thermal fluctuations. We also show that a single dimensionless parameter, such as the Peclet number customarily employed in the description of self-propelled particles, is not sufficient to fully characterize this phenomenon either in the regimes of large viscosity or small mass. Indeed, the size of the velocity domains, measured through the correlation length of the spatial velocity correlation, remains constant when the swim velocity increases and decreases as the rotational diffusion becomes larger. We find that, contrary to the common belief, the spatial velocity correlation not only depends on inertia but is also non-symmetrically affected by mass and inverse viscosity variations. We conclude that in self-propelled systems, at variance with passive systems, variations in the inertial time (mass over solvent viscosity) and mass act as independent control parameters. Finally, we highlight the non-thermal nature of the spatial velocity correlations that are fairly insensitive both to solvent and active temperatures.

Data-Driven Estimation of Inertia for Multiarea Interconnected Power Systems Using Dynamic Mode Decomposition

Abstract: The refined estimation of inertia can provide a reliable basis for power system operation and control. In this article, a data-driven approach for the estimation of inertia is proposed, and it can estimate the effective inertia of different areas in the interconnected power systems. Based on eigenstructure analysis, the intrinsic relationships between inertia and the eigenvalue and eigenvector are analyzed using a linearized dynamic equation. Furthermore, detailed mathematical expressions between inertia and the eigenvalue and eigenvector are established. In addition, dynamic mode decomposition is introduced to extract eigenvalues and eigenvectors from the synchronized measurements to ensure that the scheme proposed in this article can estimate the effective inertia by using only the outputs measured by the phase measurement unit. The effectiveness of the proposed approach is demonstrated through numerical simulations on the IEEE 16-machine 5-area test system and the real measurements of an actual power system.

Coordinated Control Strategy of Virtual Synchronous Generator Based on Adaptive Moment of Inertia and Virtual Impedance

Abstract: The application of virtual synchronous generators in the power system eases the pressure on the grid caused by penetration of lots of power electronic devices, but worsens the dynamic frequency stability of the grid Meanwhile, in order to solve the problem of power coupling in low-voltage micro-grid systems, most measures introduced virtual impedance technology to adjust the equivalent output impedance of the system Therefore, most studies have adopted the adaptive control strategy of the moment of inertia, to improve the dynamic frequency adjustment of the grid However, it will cause the frequency response speed reduction problem In order to deal with the contradiction between the moment of inertia and frequency response speed, the voltage phasor relationship of the micro-source - grid system under signal disturbance in the introduction of virtual impedance is analyzed Then an adaptive virtual impedance control strategy is proposed to accelerate the active power adjustment process of the virtual synchronous generator system, which helps to complete the first frequency modulation and improve the inertia adjustment ability Finally, combining these two control strategies, a coordinated adaptive moment of inertia and virtual impedance control strategy is proposed From the perspective of the moment of inertia and virtual impedance, the proposed method fully exploits the control advantages of the virtual synchronous generator system and achieves the purpose of adjusting the inertia of the virtual synchronous generator system while considering the acceleration of the frequency response speed The comprehensive simulation results verify the feasibility and effectiveness of the proposed method

Challenges and opportunities of inertia estimation and forecasting in low-inertia power systems

Abstract: Accurate inertia estimates and forecasts are crucial to support the system operation in future low-inertia power systems. A large literature on inertia estimation methods is available. This paper aims to provide an overview and classification of inertia estimation methods. The classification considers the time horizon the methods are applicable to, i.e., offline post mortem, online real time and forecasting methods, and the scope of the inertia estimation, e.g., system-wide, regional, generation, demand, individual resource. The framework presented in this paper facilitates objective comparisons of the performance of newly developed or improved inertia estimation methods with the state-of-the-art methods in their respective time horizon and with their respective scope. Moreover, shortcomings of the existing inertia estimation methods have been identified and suggestions for future work have been made.

A Virtual Inertia and Damping Control to Suppress Voltage Oscillation in Islanded DC Microgrid

Abstract: In this paper, a virtual inertia and damping control (VIDC) strategy is proposed to enable bidirectional DC (bi-DC) converter to dampen the voltage oscillation, using the energy stored in energy storage system (ESS) to emulate the inertia of DC microgrid (DC-MG) without modifications of system hardware. Both inertia part and damping part are modelled in the VIDC regulator, by analogizing with DC machine. Droop control is introduced to achieve multi-parallel operation of ESS. Further, its small signal model is established and the dynamic characteristic of the DC bus voltage during power fluctuation is analyzed. A 2nd-order equivalent model is introduced to simplify the parameters design. By analyzing the control performance indices, the VIDC parameters are optimized. At last, based on the principle of equivalent machine, an inertia matching method of the multi-parallel bi-DC converters is proposed. The simulation results verify that ESS, by acting as a synthetic inertia, can improve the voltage dynamic characteristics and stability in islanded DC-MG. Compared with other control methods, it has better control effect.

Maximum Virtual Inertia From DC-Link Capacitors Considering System Stability at Voltage Control Timescale

Abstract: In power electronics-dominant systems (PEDSs), the declining-inertia issue is one of the most significant challenges to tackle. The inertia emulation from DC-link capacitors is one cost-effective and application-friendly solution to enhance the system inertia. Although the virtual inertia control of the DC-link capacitor supports the grid frequency with a relatively long-term effect, it affects the dynamic of the power converter at multiple timescales. In turn, the maximum effective virtual inertia from the DC-link capacitor is limited by the operation condition of the converter. Thus, to properly design the virtual inertia control, the dynamics of the faster timescale than the inertia emulation should be addressed. With the above, this article analyzes the maximum virtual inertia of DC-link capacitors based on a multi-timescale model of power converters. First, the system stability considering virtual inertia control of DC-link capacitors is analyzed in the submodel at the voltage control timescale (VCT), where the virtual inertia control parameters are accordingly tuned on a pre-designed converter. Then, the maximum effective virtual inertia is identified in the submodel at the rotor motion timescale (RMT). The exploration and findings in this article are beneficial to the power converter design and future inertia placement optimization in PEDSs. Case studies on a hardware-in-the-loop platform are conducted to validate the proposed model and the analysis method.

Power System Inertia Estimation Using HVDC Power Perturbations

Abstract: This paper describes a power system inertia estimation method that utilizes power perturbations caused by the flow switch on an HVDC interconnector. The analysis is performed using real power system measurements from Ireland's all-island power system. The method employs an energy based estimation technique which permits a non-step power change to be used for inertia calculation and encapsulates the challenges associated with the use of real data. While it is shown that synchronous generators account for most of the power system inertia, other contributors are also investigated, namely power station auxiliary load, distributed generation and power system demand. Time-of-day and wind related effects on Ireland's power system inertia are explored. Recommendations are made for the practical implementation of the method.

Achieving Smooth Motion for Piezoelectric Stick Slip Actuator with the Inertial Block Structure

Abstract: A piezoelectric stick slip actuator with the inertial block structure is presented in an attempt to achieve smooth motion. Under asymmetric excitation, the inertial block produces different inertia, which can dynamically change the normal pressure between the stator and rotor to adjust the friction. During the slip stage, the driving arm produces a deflection away from the rotor, the normal pressure between the stator and rotor can be eliminated, and the angular impulse of the moment of friction force on the rotor can be almost reduced to zero. To verify the feasibility of the prototype, finite element method (FEM) simulation is performed. On the basis of the experimental system, the output characteristics of the prototype are systematically studied. The experimental results indicate that the prototype can achieve smooth motion under large pre-tightening displacement. The displacement curve under the load of 2.0 kg still shows good smoothness, and the resolution is 1.56 rad. This work proposes a new design concept of dynamic control of the normal pressure to achieve smooth motion for piezoelectric stick slip actuators, even under heavy-load conditions, using the inertial block structure.

Inertia-Enhanced Distributed Voltage and Frequency Control of Low-Inertia Microgrids

Abstract: This paper proposes a novel inertia-enhanced distributed control method to complement the inertia of microgrids. The rate of change of frequency (RoCoF) and the rate of change of voltage (RoCoV) are employed in this paper to quantify the frequency inertia and voltage inertia, respectively. Then, a fully distributed algorithm with constrained changing rates is proposed. By bounding the changing rates of frequency and voltage during the consensus control, the algorithm can address the consensus problem while enhancing the inertia of microgrids. Compared with most inertia control methods, the proposed method can utilize the reserve power of scattered DGs to supply inertia. Besides, it performs better under disturbances and delays than conventional distributed control methods. The effectiveness of the proposed method is validated by several cases in MATLAB/Simulation and a hardware experiment.

Experimental observation of the origin and structure of elastoinertial turbulence.

Abstract: Turbulence generally arises in shear flows if velocities and hence, inertial forces are sufficiently large. In striking contrast, viscoelastic fluids can exhibit disordered motion even at vanishing inertia. Intermediate between these cases, a state of chaotic motion, “elastoinertial turbulence” (EIT), has been observed in a narrow Reynolds number interval. We here determine the origin of EIT in experiments and show that characteristic EIT structures can be detected across an unexpectedly wide range of parameters. Close to onset, a pattern of chevron-shaped streaks emerges in qualitative agreement with linear and weakly nonlinear theory. However, in experiments, the dynamics remain weakly chaotic, and the instability can be traced to far lower Reynolds numbers than permitted by theory. For increasing inertia, the flow undergoes a transformation to a wall mode composed of inclined near-wall streaks and shear layers. This mode persists to what is known as the “maximum drag reduction limit,” and overall EIT is found to dominate viscoelastic flows across more than three orders of magnitude in Reynolds number.

A Control Technique Based on Distributed Virtual Inertia for High Penetration of Renewable Energies Under Weak Grid Conditions

Abstract: Distributed virtual inertia is an approach of providing synthetic inertia in small-scale modern grids dominated by converter-based generators. In this method, the inertial response of synchronous machines is emulated by the energy stored in the dc-link capacitors of grid-tied converters. Nonetheless, it results in instability of the interfaced converter in weak grids. To overcome this problem and get the most benefit out of the acceptable dc-link capacitor voltage deviations, a new compensation technique is proposed in this article. The grid-interactive converter in the presented framework is controlled in the current control mode, compositing of two conventional inner and outer control loops, distributed virtual inertia controller, and a novel compensator. The detailed small-signal representation of the whole control scheme in state-space form is derived. Then, it is revealed that the coupling between d- and q- axis controllers introduced by the distributed virtual inertia gain and its differential operator gives rise to the system instability in weak grids, which can be eliminated through the ancillary compensator. The time-domain simulation model is built to confirm the efficacy of the proposed control technique. The results depict that the ancillary active power provided by the proposed approach during frequency disturbance is 14% of the converter power rating of 20 kW, which yields the improvement of frequency rate of change by 18.82%.

Light-driven autonomous self-oscillation of a liquid-crystalline polymer bimorph actuator

Abstract: Oscillation, widely existing in nature, is of vital importance for human society (e.g., energy utilization, signal transmission and communication), but preparing soft self-oscillators with facile accessibility, fatigue resistance, precise and noncontact control in multi-way tunable approaches is still desirable and challenging. Here, we report the fabrication of a light-driven tunable self-oscillator based on bimorph films of commercial Kapton and photoactive liquid-crystalline polymers with physical crosslinking sites, which can be remotely powered under constant irradiation of UV/visible light. The photomechanical behaviors of the bimorph actuators are acquired from the photoinduced changes in the volume of the photoactive polymer, and both the cis-azobenzene content and the trans–cis dynamic isomerization process are determinant factors. By combining the self-shadowing effect and inertia effect of the actuator, self-sustained oscillation is obtained. In nature, only leaves with particular size and weight could sway as appropriate strong wind blows from a specific direction, which inspires us to tune the oscillating frequency and amplitude with multiple approaches, like light intensity/wavelength (from UV to visible light), irradiated position, and size/weight of the oscillator for regulating the inertia effect. Such autonomously light-fueled self-oscillators are found to have potential applications in detecting charges and signal transmission.

Enabling Dynamic Behaviors With Aerodynamic Drag in Lightweight Tails

Abstract: Many agile legged animals employ lightweight, furry tails to regulate orientation during running, leaping, and turning. Most robots attempting the same tasks either lack a tail or employ one with high inertia, which can induce impractical payload and energy costs. Inspired by nature's solution to this tradeoff, we explore the use of aerodynamic drag tails in reorientation tasks. In this article, we present a model of the aerodynamic drag and from this derive a metric that allows for direct comparison between aerodynamic and inertial tails. Motivated by this model, we construct a tail to maximize this effectiveness while minimizing inertia. We demonstrate the utility of this tail for two dynamic behaviors executed on a quadrupedal robot. First, in aerial reorientation the robot achieves a 90 $^{\circ }$ rotation within one body length of fall at the same performance as an inertial tail but with just 37% of the normalized inertia. Second, the forward acceleration of the robot is improved by 12% despite increasing the system mass by 10% over a tailless version. These results show that aerodynamic drag can provide significant control authority for a robot while decreasing the payload and energy cost.

Decoupling Scheme for Virtual Synchronous Generator Controlled Wind Farms Participating in Inertial Response

Abstract: In this paper, the dynamic coupling between the wind turbine rotor speed recovery (WTRSR) and inertial response of the conventional virtual synchronous generator (VSG) controlled wind farms (WFs) is analyzed. Three distinguishing features are revealed. Firstly, the inertial response characteristics of VSG controlled WFs (VSG-WFs) are impaired by the dynamic coupling. Secondly, when the influence of WTRSR is dominant, the inertial response characteristics of VSG-WFs are even worse than the condition under which WFs do not participate in the response of grid frequency. Thirdly, this phenomenon cannot be eliminated by only enlarging the inertia parameter of VSG-WFs, because the influence of WTRSR would also increase with the enhancement of inertial response. A decou-pling scheme to eliminate the negative influence is then proposed in this paper. By starting the WTRSR process after inertial response period, the dynamic coupling is eliminated and the inertial response characteristics of WFs are improved. Finally, the effectiveness of the analysis and the proposed scheme are verified by simulation results.

Static and seismic bearing capacity of shallow strip foundations on slopes

Abstract: In this paper the static and seismic values of bearing capacity factors for shallow strip foundations adjacent to slopes have been evaluated using the method of characteristics, accounting, through...