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Register a new userModeling flywheel energy storage system charge and discharge dynamics
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Energy storage technologies are of great practical importance in electrical grids where renewable energy sources are becoming a significant component in the energy generation mix. Here, we focus on some of the basic properties of flywheel energy storage systems, a technology that becomes competitive due to recent progress in material and electrical design. While the description of the rotation of rigid bodies about a fixed axis is classical mechanics textbook material, all its basic aspects pertinent to flywheels, like, e.g., the evaluation of stress caused by centripetal forces at high rotation speeds, are either not covered or scattered over different sources of information; so it is worthwhile to look closer at the specific mechanical problems for flywheels, and to derive and clearly analyse the equations and their solutions. The connection of flywheels to electrical systems impose particular boundary conditions due to the coupling of mechanical and electrical characteristics of the system. Our report thus deal with the mechanical design in terms of stresses in flywheels, particularly during acceleration and deceleration, considering both solid and hollow disks geometries, in light of which we give a detailed electrical design of the flywheel system considering the discharge-stage dynamics of the flywheel. We include a discussion on the applicability of this mathematical model of the electrical properties of the flywheel for actual settings. Finally, we briefly discuss the relative advantages of flywheels in electrical grids over other energy storage technologies.
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In order to explore the complexity and diversity of the flywheels dynamics, we have developed the real-physics computer model of a universal mechanical rotor. Due to an arbitrary external force concept, the model can be adjusted to operate identical to the real experimental prototype. Taking the high-speed magnetic rotor on superconducting bearings as the prototype, the law for the energy loss in real high temperature superconducting bearings has been derived. Varying the laws of damping and elasticity in the system, we have found a way to effectively damp the parasitic resonances and minimize the loss of energy storage.
Conventional active magnetic bearing (AMB) systems use several separate radial and thrust bearings to provide a 5 degree of freedom (DOF) levitation control. This paper presents a novel combination 5-DOF active magnetic bearing (C5AMB) designed for a shaft-less, hub-less, high-strength steel energy storage flywheel (SHFES), which achieves doubled energy density compared to prior technologies. As a single device, the C5AMB provides radial, axial, and tilting levitations simultaneously. In addition, it utilizes low-cost and more available materials to replace silicon steels and laminations, which results in reduced costs and more convenient assemblies. Apart from the unique structure and the use of low magnetic grade material, other design challenges include shared flux paths, large dimensions, and relatively small air gaps. The finite element method (FEM) is too computationally intensive for early-stage analysis. An equivalent magnetic circuit method (EMCM) is developed for modeling and analysis. Nonlinear FEM is then used for detailed simulations. Both permanent magnets (PM) and electromagnetic control currents provide the weight-balancing lifting force. During the full-scale prototype testing, the C5AMB successfully levitates a 5440 kg and 2 m diameter flywheel at an air gap of 1.14 mm. Its current and position stiffnesses are verified experimentally.
Thanks to the unique advantages such as long life cycles, high power density, minimal environmental impact, and high power quality such as fast response and voltage stability, the flywheel/kinetic energy storage system (FESS) is gaining attention recently. There is noticeable progress made in FESS, especially in utility, large-scale deployment for the electrical grid, and renewable energy applications. This paper gives a review of the recent developments in FESS technologies. Due to the highly interdisciplinary nature of FESSs, we survey different design approaches, choices of subsystems, and the effects on performance, cost, and applications. This review focuses on the state of the art of FESS technologies, especially for those who have been commissioned or prototyped. We also highlighted the opportunities and potential directions for the future development of FESS technologies.
In this paper, we generalize Huygens principle (HP), extinction theorem (ET), and Franz-Harrington formulation (FHF). In our previous works, the traditional HP, ET, and FHF in homogeneous isotropic environment are generalized to inhomogeneous anisotropic lossy environment; the traditional FHF of homogeneous isotropic material system is generalized to inhomogeneous anisotropic lossy material system and then to piecewise inhomogeneous anisotropic lossy material system; the traditional HP, ET, and FHF of simply connected material system are generalized to multiply connected system and then to non-connected system; the traditional FHF of external scattering field and internal total field are generalized to internal scattering field and internal incident field. In previous work, it is proved that the generalized HP (GHP) and generalized ET (GET) are equivalent to each other; the GHP, GET, and generalized FHF (GFHF) satisfy so-called topological additivity, i.e., the GHP/GET/GFHF of whole electromagnetic (EM) system equals to the superposition of the GHP/GET/GFHF corresponding to all sub-systems. In this paper, the above results obtained in our previous works, which focuses on the EM system constructed by material bodies, are further generalized to the metal-material combined EM system in inhomogeneous anisotropic lossy environment, and traditional surface equivalence principle is generalized to line-surface equivalence principle.
The ongoing rapid urbanization phenomena make the understanding of the evolution of urban environments of utmost importance to improve the well-being and steer societies towards better futures. Many studies have focused on the emerging properties of cities, leading to the discovery of scaling laws mirroring, for instance, the dependence of socio-economic indicators on city sizes. Though scaling laws allow for the definition of city-size independent socio-economic indicators, only a few efforts have been devoted to the modeling of the dynamical evolution of cities as mirrored through socio-economic variables and their mutual influence. In this work, we propose a Maximum Entropy (ME), non-linear, generative model of cities. We write in particular a Hamiltonian function in terms of a few macro-economic variables, whose coupling parameters we infer from real data corresponding to French towns. We first discover that non-linear dependencies among different indicators are needed for a complete statistical description of the non-Gaussian correlations among them. Furthermore, though the dynamics of individual cities are far from being stationary, we show that the coupling parameters corresponding to different years turn out to be quite robust. The quasi time-invariance of the Hamiltonian model allows proposing an analytic model for the evolution in time of the macro-economic variables, based on the Langevin equation. Despite no temporal information about the evolution of cities has been used to derive this model, its forecast accuracy of the temporal evolution of the system is compatible to that of a model inferred using explicitly such information.
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