Equivalent Inertia Research Articles

Online Evaluation for the POI-Level Inertial Support to the Grid via Ambient Measurements

As renewable energy sources like wind and solar power increasingly replace traditional energy sources and are integrated into the power grid, the issue of insufficient system inertia is becoming more apparent. This paper presents an online adaptive time window inertia constant identification method based on ambient measurements to identify the equivalent inertia constant of the time-varying inertia at Point of Interface (POI) level. The proposed method takes advantage of the online inertia estimation and the data-driven equivalent inertia constant identification techniques to simultaneously achieve online tracking and accuracy. With this regard, this paper first describes the inertia providers in modern system. Then, based on the frequency and power data measured by the Phasor Measurement Unit (PMU), this paper provides an improved data-driven equivalent inertia constant identification method. Subsequently, the paper proposes an ambient data smoothing method to cope with the numerical errors and provides, as a byproduct, an adaptive time window inertia constant identification. The adaptive time window is designed to enhance the accuracy of the method. Finally, the feasibility and accuracy of the proposed method of tracking synthetic inertia are validated by the simulation tests based on a grid in northwest China with high renewable energy penetration and a Virtual Power Plant (VPP). The experimental results show that the accuracy of this method is within 5%.

Modeling and numerical analysis of Kangaroo lower body based on constrained dynamics of hybrid serial–parallel floating-base systems

This paper presents the modeling and numerical analysis of the Kangaroo lower body prototype, a novel bipedal humanoid robot developed and manufactured by PAL Robotics. Kangaroo features high-power linear electric actuators combined with unique serial–parallel hybrid chains, which allow for the positioning of all the leg actuators near the base of the robot to improve the overall mass distribution. To model and analyze such complex nonlinear mechanisms, we employ a constrained formulation that is extended to account for floating-base systems in contact with the environment. A comparison is made to demonstrate the significant improvements achieved with TALOS, another humanoid bipedal robot designed by PAL Robotics, in terms of equivalent Cartesian inertia at the feet and centroidal angular momentum. Finally, the paper includes numerical experiments conducted through simulation and preliminary tests performed on the actual Kangaroo platform.

Voltage stability control strategy for DC microgrid based on adaptive virtual DC motor

The large-scale integration of distributed energy sources and power electronic devices results in the DC microgrid exhibiting significant low inertia and weak damping characteristics. This, in turn, leads to inevitable fluctuations in the DC bus voltage, which endanger the stable operation of the DC system. Energy storage devices can provide equivalent inertia. To enhance the inertia and response speed of the DC bus interface converter, this paper proposes a power allocation parameter adaptive virtual DC motor control strategy based on a hybrid energy storage unit. The strategy introduces power allocation control to regulate the energy storage converter on the basis of virtual inertia parameter adaptive control, thereby enabling the energy storage converter to simulate the inertia and damping characteristics of a DC generator. The small-signal stability of the system is analyzed by establishing a small-signal model of the photovoltaic energy storage system and utilizing the impedance ratio criterion. Finally, the proposed control strategy is validated through simulation. The results demonstrate that the strategy effectively mitigates the fluctuations in bus voltage under varying photovoltaic power and sudden load changes, ensures the power distribution in the hybrid energy storage system, and enhances the dynamic response of the system.

Coordinated frequency control strategy for modern power system considering engagement willingness

The large scale integration of renewable energy sources (RES) is posing unprecedented challenges to the frequency stability of modern power systems, with system inertia being the primary concern. Under such a landscape, this paper introduces a coordinated control strategy aiming at enhancing frequency stability by swiftly adjusting the power output of flexible resources to mitigate power imbalances and further dampen frequency fluctuations. Firstly, a communication-free center of inertia (COI) frequency estimation method is proposed. An equivalent inertia estimation method tailored for modern power systems is then developed by exploiting the correlation between synchronous inertia and active power fluctuations. By integrating the COI frequency variation rate with the estimated equivalent inertia, the imbalance power is calculated and compensated through the proposed coordinated control strategy. In this work, two typical flexible resources including photovoltaic (PV) generation and electric vehicles (EVs) are modeled and integrated into the testing system in PSCAD/EMTDC. Considering the contradiction between maximizing generation profit and reducing power output to mitigate frequency variation, the Corporate Social Responsibility (CSR) of renewable Generation Companies (GENCOs) is modeled to sketch their willingness of engaging into frequency support. Moreover, the frequency modulation potential of EVs in both commercial and residential areas are quantified for practical implementation. The simulations results successfully validate the effectiveness of the proposed control strategy.

Equivalent inertia prediction for power systems with virtual inertia based on PSO-SVM

Equivalent inertia prediction for power systems with virtual inertia based on PSO-SVM

VSG-LFC on multi-area power system under unsecured communication channel using hybrid trigger mechanism

This paper studies the frequency fluctuation problems of a multi-area power system with renewable energy sources (RESs) under denial-of-service (DoS) attacks. (i) Due to the decoupling of the RESs from power system using electronic devices, the RESs have no natural frequency response capability, which result in decreasing of entire power system equivalent inertia with large penetration of RESs. (ii) DoS attacks cause the insecurity of network communication, which can vanish data transmission and yield data packet dropout. To address the above issues, a virtual synchronous generator (VSG) incorporated with load frequency control (LFC) method (VSG-LFC) is proposed by introducing a hybrid-triggered mechanism (HTM) to (i) reduce the system sensitivity to the penetration level of RESs; (ii) compromise between frequency regulation performance and the reasonable usage of network resource under unsecured communication environments. Then, a switched system model is constructed considering non-identical DoS attack situations. Furthermore, theoretical analyses using Lyapunov functional related methods are carry out for asymptotical mean-square stability with H∞ performance on frequency regulation. Simulation evaluations of power system verify the effectiveness of this development. It shows that in a two-area power system frequency derivation performance indicators (IAE, ITAT, ISE) in Area1 are reduced by (82.996%, 86.273%, 85.823%) and in Area2 are reduces by (77.996%, 83.613%, 82.315%).

Capacitor virtual inertia control and equivalent inertia analysis for a grid-forming wind generation system

A grid-forming wind generation system exhibits exceptional grid frequency support abilities. The DC capacitor of the grid-forming wind generation system, which is characterized by rapid response and high sensitivity to minor disturbances, can provide short-term inertia support for the power system. This paper proposes the capacitor virtual inertia control for the grid-forming wind generation system, coupling the DC capacitor voltage with the power system frequency, which enables the DC capacitor to participate in the system frequency response process and reduces the rate of change of the system frequency during the disturbance. To analyze the inertia of the wind power generation system, this paper establishes an equivalent Philips–Heffron model for the grid-forming wind generation system and uses the equivalent inertia constant to quantify the inertia of the wind power generation system. The effectiveness of the proposed control strategy and the reasonableness of the inertia assessment method are verified through simulations in the single-turbine system and the IEEE four-machine two-area system.

Multi-objective configuration and evaluation of dynamic virtual inertia from DFIG based wind farm for frequency regulation

Modern power systems are gradually evolving into low-inertia systems due to the integration of high penetration of renewable energy and power electronic equipment. For the natural inertia on the rotor, doubly-fed induction generator (DFIG) based wind farms are expected to provide inertia support for systems. The paper proposed an analytical model of DFIG with df/dt inertia control for studying frequency dynamics, and investigates the optimal design of virtual inertia from wind farms, as well as its equivalent inertia contribution to system. The inertia response differences between DFIG and synchronous generator (SG) are discussed and analyzed for the first time, and then to accurately describe the frequency response with low cost, an analytical model of DFIG with inertia control is developed considering wind turbine aerodynamic characteristics. The explicit expression of virtual inertia provided by DFIG is derived according to the kinetic energy equilibrium, and the key factors that dominate the magnitude of virtual inertia are illustrated. Based on the system frequency response model including wind farms, taking the system frequency nadir (SFN) and the time of reaching nadir (ToN) as targets, a multi-objective optimal configuration model of virtual inertia is constructed and solved through MOPSO. The time domain simulations of a generic two machine four bus system and modified IEEE 9-bus test system are both performed in MATLAB/Simulink, the accuracy and efficiency of our proposed DFIG model on system frequency dynamics research are demonstrated, the pareto frontiers of virtual inertia configuration under different working conditions are optimized and analyzed as well as the impacts of different parameters on inertia evaluation.

Evaluating the Fast Frequency Support Ability of the Generation Units in Modern Power Systems

Modern power systems include synchronous generators (SGs) and inverter-based resources (IBRs) that provide fast frequency support (FFS) to the system. To evaluate the FFS ability of both SGs and IBRs under a unified framework, this paper proposes a method that evaluates the FFS ability of each generation unit via its dynamic trajectories of the active power output and the frequency following a contingency. The proposed method quantified FFS ability via two indexes, namely, the equivalent inertia constant and the equivalent droop, of each generation unit. The Tikhonov regularization algorithm is employed to estimate the FFS ability indexes. The New England 10-machine system serves to validate the feasibility and accuracy of the proposed method and illustrate the different FFS ability of the grid−forming and grid−following IBRs.

Power reserve control for utility-scale PV power plants under cloud conditions

The photovoltaic generation growth has posed challenges for the control and operation of contemporary power systems, degrading the system frequency response and stability margins. The decrease of the system equivalent inertia and the performance deterioration of the primary frequency control are the main causes of these problems. Such challenges can be overcome by the provision of ancillary services from photovoltaic power plants. However, the provision of ancillary services based on active power, such as inertial response, frequency regulation, and curtailment, requires the de-loaded operation of the photovoltaic power plants. In such context, this work proposes a de-loaded control approach (or, equivalently, power reserve control) for large photovoltaic power plants under shading conditions caused by cloud movements. This kind of shading condition poses a significant challenge for the de-loaded control, as it causes large and fast variations in the maximum power point of the multiple photovoltaic generation units that compose the photovoltaic power plant. A test system corresponding to a 100 MWac photovoltaic power plant with 25 photovoltaic generation units of 4 MWac is employed to evaluate and validate the proposed control approach. The stochastic distribution and movement of clouds, as well as the solar irradiance over the photovoltaic power plant are generated by an approach based on the fractal geometry. The proposed control was effective and presented a good performance under different cloud coverage levels.

Active Power Allocation Method of Doubly Fed Induction Generators Based on Rotor Speed

The integration of wind power into a grid on a large scale results in a reduction of the system’s inertia level, causing an impact on the stability of the system frequency. Doubly fed induction generators (DFIG) can optimize active output but lack inertia support under maximum power point tracking control. To make the wind turbine improve the inertia support ability of the system based on virtual inertia control, a method for active power allocation based on the rotor speed of DFIG is proposed. Firstly, the minimum system inertia requirement based on the frequency change rate of the system is established. Active power allocation assumes that the wind farm inertia meets the minimum system inertia requirement. Secondly, the objective is to enhance the inertia support capability and overall active power output of the wind farm, considering the constraint of the minimum system inertia requirement. Based on the rotor speed to establish the inertia allocation weight factor, the weight of the power command is assigned to a single machine to achieve the wind farm active power allocation. Finally, it is verified that the system’s equivalent inertia meets the minimum inertia requirement of the system. Simulations show that the proposed allocation method can adequately elevate the inertia support capability of DFIGs to the system and the rotor kinetic energy utilization.

Inertial Estimation in Power Grids Considering Load Contribution Based on FF-UKF

Abstract In modern power systems, the extensive integration of renewable energy sources leads to a reduction in system inertia, thereby affecting grid stability. This study proposes a novel method for estimating grid inertia, which, under quasi-steady state conditions, effectively incorporates load contribution by combining class noise signals collected by PMUs (Phasor Measurement Units) with the Forgetting Factor Unscented Kalman Filter algorithm (FF-UKF). The research initially analyzes the characteristics of various inertia sources in power systems dominated by renewable energy. Building on this, we propose a grid node equivalent inertia estimation model based on node equivalent frequency response, developing an FF-UKF-based algorithm that allows for the continuous dynamic estimation of inertia at various grid nodes. Simulation experiments conducted within the IEEE 39 bus system validate the method’s effectiveness and demonstrate the spatiotemporal distribution of grid inertia under varying levels of renewable energy penetration. This study is significant for understanding and enhancing frequency control and stability in power systems, providing key technical support for the modernization of the power system and the efficient integration of renewable energy.

Recovery time and strategy of DFIG speed based on a high-proportional hydropower grid

Large-scale wind power access reduces the equivalent inertia of a power system. The wind turbine has a considerable reserve of rotational inertia, which is important for reducing the risk of low-inertia operation in a grid and for improving frequency reliability. In this work, a doubly fed induction generator (DFIG) inertia frequency regulation strategy is studied. The secondary dip in frequency caused by speed recovery after the wind turbine participates in frequency regulation is an important factor that limits regulation capability on the DFIG. To address such problem, the power dip and recovery generated by the DFIG after active speed recovery is analyzed and modeled. Then, a linearized frequency response model of a hydropower single machine is established to investigate the secondary disturbance effect of wind turbine active speed recovery moment on the frequency of the high-ratio hydropower system.A conclusion is drawn that the moment that corresponds to the first recovery of system frequency to the quasi-steady-state frequency is the optimal recovery moment of the turbine in the linear SFR model. Combined with the frequency control characteristics of the frequency limit control(FLC)’s “large dead zone, ” an active speed recovery strategy of the turbine based on frequency deviation judgment is designed.

A Review of Recent Control Trchniques of Virtual Synchronous Machine for Renewable Energy

Abstract Increased distributed generation (DG) integration into power system via power electronic devices results in a reduction in the total equivalent inertia of power grid utility, which lead to serve frequency stability and performance degradation of the power system. To facilitate the penetration of DG into the power grid utility, improved control schemes of the power electronics converter based DG are required to improve the system stability when it is dominated by DG based inverter. A virtual synchronous generator (VSG ) approach is suggested, which consists in controlling the static power converter to mimic the essential dynamic behavior of the conventional synchronous generator. The main objective of this paper is to review the most recent topologies of virtual inertia control. Along this work, a detail description of each topology is presented. In addition, VSG control equations given voltage and frequency control is explained in detail. The VSG problems and future research on VSG control are discussed.

Analysis of equivalent inertia of induction motors and its influencing factors

Analysis of equivalent inertia of induction motors and its influencing factors

Mechanical Model and Damping Effect of a Particle-Inertial Damper

Particle dampers (PD) are safe, economical, and effective energy-dissipation devices for structures. However, the additional mass of PD must be sufficiently large to provide a better damping effect, and the initial movement condition of particles has a significant impact on the damping effect of PD. In this study, a particle-inertial damper (PID) is proposed to overcome these problems, and its mechanical model is established with and without considering particle collision. Subsequently, the influence of particle rolling friction and particle collision on the inertial amplification capacity as well as the dynamic response of a single degree of freedom (SDOF) structure with non-collision and collision PID (SDOF-PID) are systematically analysed. Finally, the control effects of a PID and a tuned mass damper (TMD) are compared based on two typical optimisation methods. The results indicate that particle rolling friction has little influence on the inertia amplification effect of a PID and the displacement response of a SDOF-PID. Under harmonic excitation, particle collision significantly affects the damping mechanism of a PID by its equivalent inertia coefficient, equivalent damping coefficient, and equivalent stiffness coefficient. The fixed-point theory and ‘performance-cost’ theory can be used to optimise the PID to a certain extent. The damping effect of a PID on the SDOF under the most severe seismic excitation is better than that of the PID under white noise excitation. With respect to the decreasing ratio of 40~50%, the additional mass of the PID is only one thousandth that of the TMD under the same damping capacity demand.

Small-Signal Synchronous Stability of a New-Generation Power System With 100% Renewable Energy

The traditional power system dominated by synchronous generators (SGs) is now evolving into a new-generation power system dominated by voltage source converter (VSC)-based renewable energy, causing substantial changes in the dynamical behavior. This paper investigates the small-signal synchronous stability of a new-generation power system composed solely of grid-following and/or grid-forming power electronics devices in the absence of an infinitely strong bus. The phase-lock-loop (PLL)-based VSC is taken as a representative of grid-following devices and treated as a controlled-current source whose phase is driven by the power factor angle. In sharp contrast, the virtual synchronous generator (VSG)-based VSC is taken as a representative of grid-forming devices and treated as a controlled-voltage source whose phase is driven by the active power. Small-signal synchronization stability models are established for multiconverter power systems within the framework of the classical Phillips–Heffron model for traditional power systems. Explicit expressions for equivalent inertia, damping, and synchronization coefficients are obtained. We find that both PLL-based and VSG-based VSCs show similar synchronization principles and contribute to the inertia and damping of the system. All these findings are well supported and verified by our modal analysis and time-domain simulations.

Small-Signal Modeling and Stability Analysis of a Grid-Following Inverter with Inertia Emulation

Power-converter-based energy-harvesting and storage systems are becoming more prevalent in the electrical grid, replacing conventional synchronous generators. Consequently, grid inertia is diminishing, and to address this, inverter-based energy conversion systems are required by grid codes to provide frequency control support to the main grid. This is undertaken to increase the equivalent inertia of the system and reduce frequency variations. This type of control is necessary and designed for handling large system transients. However, it also impacts the small-signal stability of the grid-connected converters. To investigate this issue, this paper addresses the influence of synthetic inertia control on the output admittance of a grid-following inverter and its interaction with the grid equivalent impedance. A synchronous reference frame dynamic model of the grid-following inverter closed-loop system is obtained and linearized at an operating point to analyze the small-signal stability of the low-switching frequency inverter. The models are validated through numerical simulations. The analysis verifies the interactions of the internal control loops, such as the AC current control with voltage feedforward, DC-link voltage control with power-feedforward, phase-locked loop, and AC voltage control with inertial control. Additionally, the interactions between the output admittance of the inverter and the grid impedance are verified using the generalized Nyquist criterion. The stability regions are validated through simulations, and the results show that the system gain margin is reduced for increasing values of synthetic inertia gain and lower grid short-circuit ratios. Furthermore, there is a limit in the voltage and power-feedforward bandwidth to avoid degrading the system stability when utilizing the synthetic inertia control.

Unit Combination Scheduling Method Considering System Frequency Dynamic Constraints under High Wind Power Share

Power systems with a high wind power share are characterized by low rotational inertia and weak frequency regulation, which can easily lead to frequency safety problems. Providing virtual inertia for large-scale wind turbines to participate in frequency regulation is a solution, but virtual inertia is related to wind power output prediction. Due to wind power prediction errors, the system inertia is reduced and there is even a risk of instability. In this regard, this article proposes a unit commitment model that takes into account the constraints of sharp changes in frequency caused by wind power prediction errors. First, the expressions of the equivalent inertia, adjustment coefficient, and other frequency influence parameters of the frequency aggregation model for a high proportion wind power system are derived, revealing the mechanism of the influence of wind power prediction power and synchronous machine start stop status on the frequency modulation characteristics of the system. Second, the time domain expression of the system frequency after the disturbance is calculated by the segment linearization method, and the linear expressions of “frequency drop speed and frequency nadir” constraints are derived to meet the demand of frequency regulation in each stage of the system. Finally, a two-stage robust optimization model based on a wind power fuzzy set is constructed by combining the effects of wind power errors on power fluctuation and frequency regulation capability. The proposed model is solved through affine decision rules to reduce its complexity. The simulation results show that the proposed model and method can effectively improve the frequency response characteristics and increase the operational reliability of high-share wind power systems.

The effects of compliant support on the dynamics of a dielectric elastomer actuator: a parametric study

The resonant actuation of dielectric elastomer actuators (DEAs) can greatly amplify the power outputs and energy efficiencies and has facilitated numerous applications in soft robotics. In many circumstances, the DEAs are mounted on robotic bodies that are made of soft materials or compliant structures. Such compliant supports can demonstrate an equivalent stiffness and inertia comparable to the DEAs, thereby complicating the dynamics of the DEAs and threatening the performance and controllability of the soft robots by introducing additional degrees of freedom to the systems. Toward the goal of achieving reliable and controllable resonating actuation of the DEAs on soft robots, the effects of compliant supports on the dynamics of DEAs require dedicated investigations. By adopting a double cone DEA configuration, this work conducts a comprehensive study on the dynamics of a double cone DEA-compliant support system. A nonlinear dynamic model of the double cone DEA-compliant support system is developed. Together with experimental studies, the dynamics of the system in different support configurations are characterized and the influences of the key parameters in the system are clarified. The key findings of this work can potentially guide the designs of future high-performance DEA-driven soft robots.