Inertia Model Research Articles

A novel four parameter formula for the rotational spectra of even-even nuclei

In this article, the authors presents a novel four parameter formula based on developing an expression for the moment of inertia in terms of Bohr-Mottelson Geometric Collective Model (GCM). The formula provides an excellent agreement with the experimental data for all nuclei under consideration. Some key quantities will also be derived such as the rotational frequency, the kinematic and dynamical moment of inertia, and their variation with spin will be investigated. A comparison between our proposed four parameter model with both the variable moment of inertia model, and the recently proposed β-stretching model is also presented. Various ΔI=1 and ΔI=2 energy staggering indices will be presented and compared to the experimental counterpart in the paper.

Two-Stage Optimal Configuration Strategy of Distributed Synchronous Condensers at the Sending End of Large-Scale Wind Power Generation Bases

The transmission end of large-scale wind power generation bases faces challenges such as high AC-DC coupling strength, low system inertia, and weak voltage support capabilities. Deploying distributed synchronous condensers (SCs) within and around wind farms can effectively provide transient reactive power support, enhance grid system inertia at the transmission end, and improve dynamic frequency support capabilities. However, the high investment and maintenance costs of SCs hinder their large-scale deployment, necessitating the investigation of optimal SC configuration strategies at critical nodes in the transmission grid. Initially, a node inertia model was developed to identify weaknesses in dynamic frequency support, and a critical inertia constraint based on node frequency stability was proposed. Subsequently, a multi-timescale reactive power response model was formulated to quantify the impact on short-circuit ratio improvement and transient overvoltage suppression. Finally, a two-stage optimal configuration strategy for distributed SCs at the transmission end was proposed, considering dynamic frequency support and transient voltage stability. In the first stage, the optimal SC configuration aimed to maximize system inertia improvement per unit investment to meet dynamic frequency support requirements. In the second stage, the configuration results from the first stage were adjusted by incorporating constraints for enhancing the multiple renewable short-circuit ratio (MRSCR) and suppressing transient overvoltage. The proposed model was validated using the feeder grid of a large energy base in western China. The results demonstrate that the optimal configuration scheme effectively suppressed transient overvoltage at the generator end and significantly enhanced the system’s dynamic frequency support strength.

Thermal Inertia Performance via TRNSYS Software of Recycled Wastewater Treatment Plant Sludge as a Construction Material Additive to Ecological Lightweight Earth Bricks

This research investigates the thermal performance of earth bricks made with different percentages of wastewater sludge additive (0%, 1%, 3%, 7%, 15%, 20%) in terms of cooling and heating loads, time lag and decrement factor. The simulation of a reference house (2.5m,10m,6m) using TRNSYS software allows for the evaluation of these parameters, external wall thicknesses, bulk density, thermal conductivity, and specific heat capacity are employed as inputs in dynamic thermal inertia model. The results showed that the use of bricks with higher sludge additive percentages resulted in a drop in cooling and heating loads, the lowest cooling and heating loads of 1720 KWH and 1534 KWH respectively were recorded with the highest percentage of wastewater sludge additive of 20% and the biggest wall thickness of 30cm, it was also noted that the use of higher wastewater sludge additive percentages and bigger wall thicknesses led to higher time lags and lower decrement factor, the highest time lag of 15 hours and the lowest decrement factor of 0.019 were as well recorded with the highest wastewater sludge additive of 20%, and the biggest wall thickness of 30cm. These results were attributed to the higher specific heat capacity, and lower thermal conductivity of the bricks with higher wastewater sludge additive percentages.

ASTERIA — Thermal inertia evaluation of asteroid Didymos

Asteroid Didymos, recently targeted by the NASA DART mission, is also planned to be visited by the ESA Hera mission. The main goal of the DART mission was to impact Dimorphos, the small satellite of Didymos, which was accomplished in September 2022. This collision altered the Didymos–Dimorphos system, generating a notable quantity of ejecta that turned Dimorphos into an active asteroid, with some ejecta potentially settling on the surfaces of both components. This prompts the investigation into the extent of post-impact surface alterations on these bodies, compared to their original states. The purpose of this study is to independently evaluate the pre-impact thermal inertia of Didymos. We employed ASTERIA, an alternative to conventional thermophysical modeling, to estimate the surface thermal inertia of Didymos. The approach is based on a model-to-measurement comparison of the Yarkovsky effect-induced drift on the orbital semi-major axis. These results, alongside existing literature, enable an evaluation of the impact-induced alterations in Didymos’s thermal inertia. Our nominal estimate with a constant thermal inertia model stands at Γ=211−55+81 J m−2 K−1 s−1/2, while assuming it varies with the heliocentric distance with an exponent of −0.75 thermal inertia of Didymos is found to be 258−63+94 J m−2 K−1 s−1/2. Subsequent verification confirmed that this result is robust against variations in unknown physical parameters. The thermal inertia estimates for Didymos align statistically with values reported in the literature, derived from both pre- and post-impact data. The forthcoming Hera mission will provide an opportunity to further corroborate these findings. Additionally, our results support the hypothesis that the thermal inertia of near-Earth asteroids is generally lower than previously expected.

Performance analysis of a novel single-flywheel resettable-inertia damper with eddy-current damping

The clutching inertia model presents an ideal Bang-Bang control approach, but it is challenging to realize practically through passive means. In this paper, a single-flywheel resettable-inertia damper (SRID) is proposed on the basis of the clutching inertia model. This device is implemented with a rack-and-pinion system, a right-angle gearbox system, and a flywheel-mounted eddy-current damping system. Initially, a mechanical analysis model of this device is established according to its working mechanism. Subsequently, comparative analyses are performed on the performance of SRID in a single degree-of-freedom (SDOF) structure compared to viscous dampers (VDs) subjected to harmonic and seismic excitations. The results show that the SRID can achieve a comparable control effect as VDs with a much smaller need for the damping coefficient, reflecting a damping amplification effect over 100 times. The SRID is effective in controlling peak displacement and absolute acceleration responses, especially for long-period structures. Moreover, the control performance is significantly improved with increasing magnetic induction intensity.

Integration of a Europe-wide public building database with retrofit strategies and a thermal inertia model into an open-source optimization framework

Integration of a Europe-wide public building database with retrofit strategies and a thermal inertia model into an open-source optimization framework

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.

Nuclear softness in the variable moment of inertia model and its application to superdeformed bands in the mass region A ≈ 60 - 90

For superdeformed (SD) bands 58Ni (b1), 58Cu, 59Cu (b1), 61Zn, 62Zn, 65Zn, 68Zn, 84Zr, 86Zr (b1), 88Mo (b1, b2, b3) and 89Tc in the A ≈ 60 - 90 mass region, the nuclear softness (NS) parameter, σ, has been calculated using the VMINS3 model. The SD bands 58Ni (b1), 58Cu, 59Cu (b1), 62Zn, 65Zn, and 88Mo (b2, b3) have NS parameter values that are greater than those of the normal deformed bands, indicating smaller rigidity. The fluctuation of the NS parameter versus the gamma energy ratio, R, of SD bands in the A ≈ 60 - 90 mass region is one of the study's findings. The ratio of transition energies was used to calculate the band head spin, I0, by the Descartes method (the greatest technique to solve the quartic equation based on an auxiliary cubic equation) which was then confirmed by root mean square deviations. The estimated and observed transition energies are in good agreement.

Simulation model of a flat plate air solar collector

Simulation model of a flat plate air solar collector

Feedback linearization control method for hydraulic flight simulation turntable based on variable inertia model compensation

Feedback linearization control method for hydraulic flight simulation turntable based on variable inertia model compensation

Internal Modal Resonance Analysis for Full Converter-Based Wind Generation Using Analytical Inertia Model

Full converter-based wind generation (FCWG) has become a prevailing choice in new wind farms. It is usually regarded that low short circuit ratio (SCR) or weak grid is a key condition to induce oscillations associated with wind farms. However, we have recently discovered a rare phenomenon that even in a strong grid with a large SCR, the internal modal resonance of FCWG can still lead to oscillations and threaten the converter-driven stability. To determine the internal modal resonance in FCWG, a novel analytical inertia model (AIM) is derived to elaborate all oscillation modes of FCWG (FOMs) for the first time. The derived model reviews the complex relations of all FOMs in a formulaic manner, which not only provides guidance on parameter resetting, but also illuminates how FOMs interact with each other. On this basis, an equivalent transfer function is integrated into the state space equation to characterize the interaction effect, and a universal torque model is proposed to yield insights into the mechanism of internal modal resonance owing to the variation of operating conditions. Furthermore, the effectiveness of AIM is substantiated as well as the analysis method, and the unusual event of internal modal resonance is also demonstrated.

Two-stage stochastic robust optimization scheduling of electric–thermal microgrid with solid electric thermal storage

During the periods of high heat load (HL) demand in winter, the increased heat output of combined heat and power units (CHPs) can significantly compress the electric power regulation range, thereby posing a threat to the safety of the power system. The solid electric thermal storage (SETS) can be employed as the regulating resource for both electric and thermal systems, expanding the dispatch space of microgrids to promote renewable energy consumption. In this paper, a two-stage stochastic robust optimization scheduling model of an electric–thermal microgrid with SETS is proposed, and the electric–thermal bi-directional regulation characteristics of SETS are considered. First, a SETS operation model based on the heat transfer characteristics of the homogeneous material-type thermal storage unit is established. Second, a regional thermal inertia model under a constant-flow variable-temperature system is established, which integrates HL at different locations to the heat source, avoiding the calculation of variation in water temperature, thus reducing the calculation difficulty. Finally, the two-stage stochastic robust optimization scheduling model of an electric–thermal microgrid with SETS is established. The model decouples the power and heat generation of CHP through the bi-directional regulation function of SETS. Case studies demonstrate the validity and effectiveness of the proposed scheduling model.

Importation of band head spin for superdeformed bands in mass region A ∼ 60 - 90 using the variable moment of inertia model

We are currently applying the variable moment of inertia model to nuclei in mass region A ∼ 60 - 90 in order to improve spectroscopic analysis of its rotational bands in the superdeformed region, which in turn is helpful in the band head spin prediction and other spins for superdeformed bands. The moment of inertia of the ground state, ϑ0 and restoring force constant, C, were calculated by fitting the observed transition energies. The band head spin, I0 was determined in terms of the ratio of transition energies, verified by root mean square deviations. We verified that the observed high spin superdeformed bands display a near-rigid rotor behavior by studying transition energies over twice the angular momentum (RTEOS). The calculated and observed transition energies agree well.

Optimal Allocation Strategy of Virtual Inertia and Damping for Improving the Small-signal Stability

The application of the virtual synchronous generator (VSG) control technology to engage the inertia response of renewable energy generation systems is an effective means of coping with the problem of weak inertia in power systems. To deal with the problem of small-signal stability in the weak inertia power system, this paper studies how the strength of virtual inertia and damping affect the small-signal stability, and proposes an optimal allocation strategy of virtual inertia and damping for improving the small-signal stability. The optimal allocation model of virtual inertia is constructed to minimize the energy imbalance of the system under small-signal by selecting the virtual inertia and damping as optimization variables. Regarding the aforementioned model, the evolutionary algorithm is used to obtain the optimal allocation of virtual inertia and damping. Simulations on a virtual synchronized microgrid system show the effectiveness of the proposed strategy in improving small-signal stability.

Search for Super-Deformed Identical Bands in the A = 190 Mass Region on the Basis of Level Spin

The systematic study of Super-Deformed (SD) bands in the A=190 mass region has been performed. We observed a large number of pairs of SD bands, with different mass numbers, having transition energies nearly equal (within 3 keV) and having identical dynamic moments of inertia. The bands having nearly equal transitions energies and other parameters are called identical bands. We have performed detailed analysis and found 16 pairs of Super-Deformed Identical Bands (SDIBs) whose Eγ energies and moment of inertia are in good agreement with each other. The modified Variable Moment of Inertia (VMI) model is applied to 16 pairs of SDIBs to estimate the band spins by fitting the two parameters J0 and C. We found that out of 16 pairs, the band-head spin is consistent with moment of inertia and transition energies for four pairs. For another seven pairs, the transition energies and moment of inertia are identical, but originate from levels with different spins. The remaining five pairs have the identical energy but spins are either increasing or decreasing by one unit in the pair. Secondly, the NpNn scheme is applied to verify the existence of SDIBs. The parameters deduced from the NpNn scheme are also in good agreement for the mentioned case. The study indicates that each pair of conjugate nuclei have nearly identical spin, moment of inertia (dynamic) and gamma transition energy.

A novel assembly method of aero-engine rotors with minimized spindle inertia

Assembly is an essential part of aero-engine manufacturing, and the assembly quality will affect the engine’s stability and service life. Spindle inertia is an essential factor affecting aero-engine dynamic performance. Assembly can affect the spindle inertia of the aircraft engine, which in turn affects the dynamic performance of the engine. This paper proposes a transfer model of spindle inertia based on machining error transmission, studying the variation law of spindle inertia of multi-stage rotors under the influence of assembly, providing an optimized assembly method with minimized spindle inertia. The influence law of machining errors on spindle inertia is analyzed through the simulation and probability density method. The assembly results of the designed rotors verify the effectiveness of the inertia transfer and assembly model. The results show that the spindle inertia of multi-stage rotors is affected by machining errors, and the spindle inertia can be adjusted by changing the assembly methods. This paper provides a new idea for the transmission and adjustment of spindle inertia of assembly rotors.

Design of Two-Degree-of-Freedom Fractional-Order Internal Model Control Algorithm for Pneumatic Control Valves

In response to the problems of the inaccurate pneumatic control valve model, the slow valve position control, and the low precision in the industrial control process, some improvement methods are proposed. Firstly, the fractional-order concept is introduced based on the first-order inertia model and IBBO (improved biogeography-based optimization) is used for iteration to obtain a specific transfer function model. Secondly, a fractional-order and two-degree-of-freedom combined internal model control algorithm is proposed. Finally, semi-physical experiments are carried out on a semi-physical experimental platform. The results show that in the field of pneumatic regulating valves, the fractional-order model has good adaptability and effectiveness, and the two-degree-of-freedom fractional-order internal model control algorithm also effectively improves the accuracy, speed, and robustness of the valve position control.

Simulation and investigation into the pluvial effect on peri-urban unsewered drainage basin of Kolkata due to rapid urbanization

A pluvial effect is a geologic event caused by the action of water during excessive precipitation in a particular region, resulting in water logging, which affects the drainage system of that area, or it may be caused by the spill of a large amount of water beyond the normal limit from the water bodies. The pluvial effect is also referred to as a flood having highly devastating consequences when it affects a region's urban or peri-urban areas. It affects the day-to-day activities of people staying in those areas and causes various social and economic losses. This effect would even grow further if proper planning and management of land were not done in a given time. Therefore, through this paper, the authors try to address the issue of urban flooding along with its consequences and impacts. For this study, the peri-urban region of the Tollygunge-Panchannagram Basin in Kolkata, India, is considered. The zero inertia model, Triangular Irregular Network Flood (TINFLOOD), is employed for surface flow simulation, whereas the storm water management model (SWMM) is used to determine the lateral flow. The output of this study provides various hyetographic presentations, considering infiltration during advanced, intermediate, and delayed rainfall conditions. Here, the time of concentration is also examined for different rainfall intensities to observe the time for peak flow. The simulated data obtained from this model has been validated with the real-time data of a pumping station situated at Chowbhaga. Nevertheless, this study helps assess flood risk management upstream of a region's basin and peri-urban areas.

Inertia estimation of power system with new energy considering with high renewable penetrations

The emerging energy technologies, such as wind energy and photovoltaic (PV), will gradually replace the traditional synchronous generator in wide-area power system. As the wind, PV and energy storage equipment are all controlled by power electronic inverters, which are decoupled from the system and cannot provide effective inertial support to the power system with new energy (PS-NE), resulting in stability problems caused by the low inertia of the PS-NE. In particular, this paper investigates the inertia response of synchronous generator and PS-NE, and the inertia model of PS-NE considering with high renewable penetrations. Then the relation between inertia and frequency of PS-NE with high renewable penetrations are explored in this paper. Besides, the real-time inertia of the PS-NE is estimated by using the statistical algorithm based on the historical data of the PS-NE, and the range of the inertia and synchronous generator start-up capacity of the PS-NE can be estimated by using the statistical algorithm based on the renewable penetrations when we cannot obtain the historical data of the PS-NE. In addition, IEEE39 system of PS-NE is used to verify the relation between inertia and frequency of PS-NE with high renewable penetrations, and the inertia estimation of PS-NE with high renewable penetrations is analyzed in this paper.

Quantitative study on steam system thermal inertia based on a dynamic hydraulic analytical model

Integrated energy system (IES) in industrial parks is pivotal to China's carbon neutrality path, where steam plays a critical role as an energy carrier and raw materials in the production process. Utilization of the thermal inertia of steam systems may become a means to address challenges in industrial park IES dispatch. However, researchers have less discussed the dynamic modeling and inertia quantification of industrial steam systems compared to district heating. This work proposes a dynamic hydraulic analytical model (DHAM) of steam systems reflecting the spatial and temporal transportation of steam by introducing the reference temperature and momentum linearization assumptions. Further, a steam thermal inertia model (STIM) which comprises five storage key parameters and two indexes, is developed to quantify the thermal inertia based on DHAM. Validation results of DHAM in an industrial park demonstrate that the relative error is less than 3%, achieving high accuracy. Whilst the thermal inertia of a 163-node steam system in two operation conditions is quantified and compared. Results show that the net heat storage of the steam system could reach 7440.30 kg while the positive utilization rate in both scenarios never rises above 3%. It indicates that the thermal inertia as virtual storage can fully cover the dispatching demand while is not utilized and lacks the regulation strategy of active charging in operation. DHAM and STIM proposed in this study lay the quantitative basis for steam system analysis and operation optimization of industrial park IES.