This paper deals with the thermal modeling of a large prismatic Li-ion battery (LiFePO 4 /graphite). A lumped model representing the main thermal phenomena in the cell, in and outside the casing, is hereby proposed. Most of the parameters are determined analytically using physical and geometrical properties. The heat capacity, the internal and the interfacial thermal resistances between the battery and its cooling system are experimentally identified. On the other hand, the heat sources modeling is considered to be one of the most difficult task. In order to overcome this problem, a heat generation model is included. More specifically, the electrical losses are computed thanks to an electrical model which is represented by an equivalent electric circuit. A method is also proposed for parameter determination which is based on a quasi-steady state assumption. It also takes into account the battery heating during characterization which is the temperature variation due to heat generation during current pulses. This temperature variation is estimated thanks to the coupled thermal and heat generation models. The electrical parameters are determined as function of state of charge (SoC), temperature and current. Finally, the proposed coupled models are experimentally validated with a precision of 1°C.
Purpose -The purpose of this paper is to apply a fast analytical model of the acoustic behaviour of pulse-width modulation (PWM) controlled induction machines to a fractional-slot winding machine, and to analytically clarify the interaction between space harmonics and time harmonics in audible electromagnetic noise spectrum. Design/methodology/approach -A multilayer single-phase equivalent circuit calculates the stator and rotor currents. Air-gap radial flux density, which is supposed to be the only source of acoustic noise, is then computed with winding functions formalism. Mechanical and acoustic models are based on a 2D ring stator model. A method to analytically derive the orders and frequencies of most important vibration lines is detailed. The results are totally independent of the supply strategy and winding type of the machine. Some variable-speed simulations and tests are run on a 700 W fractional-slot induction machine in sinusoidal case as a first validation of theoretical results. Findings -The influence of both winding space harmonics and PWM time harmonics on noise spectrum is exposed. Most dangerous orders and frequencies expressions are demonstrated in sinusoidal and PWM cases. For traditional integral windings, it is shown that vibration orders are necessarily even. When the stator slot number is not even, which is the case for fractional windings, some odd order deflections appear: the radial electromagnetic power can therefore dissipate as vibrations through all stator deformation modes, leading to a potentially lower noise level at resonance.Research limitations/implications -The analytical research does not consider saturation and eccentricity harmonics which can play a significant role in noise radiation. Practical implications -The analytical model and theoretical results presented help in designing low-noise induction machines, and diagnosing noise or vibration problems. Originality/value -The paper details a fully analytical acoustic and electromagnetic model of a PWM fed induction machine, and demonstrate the theoretical expression of main noise spectrum lines combining both time and space harmonics. For the first time, a direct comparison between simulated and experimental vibration spectra is made. NomenclatureElectrical notations f s ¼ fundamental stator supply frequency f r mn ¼ rotor current harmonic frequency linked to the n-th stator current time harmonic and m-th stator mmf space harmonic f s n ¼ stator current n-th time harmonic f mm ¼ magnetomotive force f R ¼ mechanical rotation frequency ð f R ¼ ð1 2 sÞf s =pÞ F r , F s ¼ rotor and stator mmf waves g ¼ air-gap width h r , h s ¼ integers involved in rotor and stator mmf space harmonics expression i r b ¼ b-th rotor bar current i s q ¼ q-th stator phase current k r , k s ¼ integers involved in rotor and stator slotting terms in permeance Fourier series l sd ¼ stator tooth width l se ¼ stator slot opening width l rd ¼ rotor tooth width l re ¼ rotor slot opening width L n ¼ force line number n m ¼ m-th space harmonic due to stato...
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