外文翻譯--基于考慮擴散電阻的電池狀態(tài)估計器的功率預(yù)測（英文）

1、Power prediction from a battery state estimator that incorporates diffusion resistanceShuoqin Wang a,*, Mark Verbrugge b, John S. Wang a, Ping Liu aa HRL Laboratories, LLC, Malibu 90265, CA, USA b General Motors Research

2、 and Development, Warren, MI, USAh i g h l i g h t s< A new algorithm improves the prediction accuracy of state of power (SOP) of a Li-ion battery.< It incorporates a nonlinear diffusion resistance into the formula

3、s for the SOP prediction.< The results appear very promising in testing Hitachi cells in a simulated HEV environment.< It provides much more accurate power prediction than the original BSE.a r t i c l e i n f oArti

4、cle history:Received 5 January 2012Received in revised form22 April 2012Accepted 25 April 2012Available online 30 April 2012Keywords:Battery state estimatorBSE algorithmSOC (state of charge) estimationSOP (state of power

5、) estimationEquivalent circuit modela b s t r a c tWe present a new algorithm that improves the prediction accuracy of the maximum charge anddischarge power capabilities, i.e. state of power (SOP), of a battery state est

6、imator (BSE) using anequivalent-circuit representation of a battery. For short time (high frequency) operation, lithium iontraction batteries are often dominated by ohmic and interfacial kinetic resistance, and conventio

7、nalequivalent circuits employing resistors and capacitors (RC circuits) work well to characterize thesystem. However, for longer times, diffusion resistance becomes important and conventional BSEsbased on RC elements fai

8、l to provide useful power predictions. In order to take into account diffusionin the SOP prediction, we propose to incorporate a nonlinear resistance into the power predictionformulas that are otherwise based on an RC ci

9、rcuit formulation; The diffusion effect is addressed withthis nonlinear resistance whose value is proportional to the square root of time. The new approach isimplemented in a vehicle-simulation environment (a hardware-in

10、-the-loop setup) to predict the SOPof a lithium-ion battery. Simulation results demonstrate that this revised estimator provides muchmore accurate power prediction without compromising the regression performance of the o

11、riginalBSE.? 2012 Elsevier B.V. All rights reserved.1. IntroductionIn many battery-powered systems such as electric vehicles (EV) and hybrid electric vehicles (HEV), the efficiency of traction batteries can be greatly en

12、hanced by intelligent management of the electrochemical energy storage system [1]. These applications require a battery state estimator (BSE) to ensure accurate and timely estimation of the state of charge (SOC), the cha

13、rge and the discharge power capabilities (SOP), and the state of health (SOH). In this work, we focus on the SOP predictions of HEV lithium ion batteries.Various battery models have been studied within the framework of a

14、 BSE [2e17]. A physics-based electrochemical model may be able to capture the temporally evolved and spatially distributed behavior of the essential states of a battery [2,3,16,17]. Such analyses are built upon fundament

15、al laws of transport, kinetics and thermodynamics, and require inputs of many physical parameters. Because of their complexity, longer simulation times are needed, and there is no assurance of convergence in terms of sta

16、te estimation. Thus, while these more complex models are suitable for battery design and analysis, they have not been used in commercial BSEs. Due to limited memory storage and computing speed of embedded controllers emp

17、loyed in many applications and the need for fast regression in terms of parameter extraction, a (zero dimensional) lumped parameter approach based on an equivalent circuit model has been found to be most practical for BS

18、E formulation. A circuit employing* Corresponding author. Tel.: þ1 310 317 5183; fax: þ1 310 317 5840.E-mail address: swang@hrl.com (S. Wang).Contents lists available at SciVerse ScienceDirectJournal of Power S

19、ourcesjournal homepage: www.elsevier.com/locate/jpowsour0378-7753/$ e see front matter ? 2012 Elsevier B.V. All rights reserved.doi:10.1016/j.jpowsour.2012.04.070Journal of Power Sources 214 (2012) 399e406with Fig. 2(a)

20、for the discharge power test and 2(b) for the charge power test. The predicted values are close to the measured values at short times but deviate from the measured values for longer times. It may be explained that in the

21、 beginning, the power is mainly determined by electron-transfer kinetics; therefore the faradaic impedance can be approximated with a linear charge-transfer resistance [25]. In the longer term, the battery current is lik

22、ely influenced by diffusion resistance. Fig. 2 also demonstrates that the SOP deviation is more severe for discharge than charge, indicating the diffusion effect may be more dominant in discharge cases, which is consiste

23、nt with the experiment results published in the Ref. [24]. Diffusion resistance is revealed more clearly in Fig. 3, which is based on several SOP measurements at different values of Voc. We choose It1/2 for the ordinate

24、of the figure because the diffusion- limited current may be approximated by the Cottrell equation [25] and therefore the diffusion region would be manifest as a plateau in the figure. As it is shown in Fig. 3(a), the dis

25、charge currents appear to transition from kinetic control initially to diffusion control (plateaus) in the longer term. We can also deduce from the figure that as the Voc increases, diffusion control takesplace earlier.

26、Fig. 3(b), which corresponds to the charge power tests, shows no obvious plateaus during the 10-s period, verifying that the diffusion effect is smaller during charge, and therefore the R-RC circuit model can predict cha

27、rge power with small error without addressing diffusion for the conditions investigated [24]. Electrochemical impedance spectroscopy (EIS) analysis was also conducted on the cell as shown in Fig. 4. The battery impedance

28、 Z(u) ¼ Z0(u)?iZ00(u) was measured from 0.01 Hz to 10 Hz. The measurements were performed at four different values of Voc. Two different regimes are depicted in Fig. 3: the semicircles capture ohmic and interfacial

29、kinetics losses at higher frequencies, and diffusion (e.g., Warburg) impedance is seen at lower frequencies. We can roughly estimate that for frequencies lower than 3 Hz, the diffusion starts to impact the kinetic behavi

30、or. We may therefore expect that in the time-domain, for power predictions of durations longer than a third of a second, diffusion resistance will play an important role. It should be noted that EIS is normally conducted

31、 with small-signal (current or voltage) perturbations and therefore the cell is around equilibrium during the experiment, which may be somewhat different from the maximum power test experiment, wherein the cell is driven

32、 far away from equilibrium.3. Theory of the R-RC circuit model including diffusion resistanceFig. 1 illustrates the one RC circuit model, based on which the regression algorithm (BSE) and the power equations are derived.

33、 As we mentioned in the first section, the diffusion resistance Rdiffusion is only used in the power calculation, but not in the parameter regression. The governing equation for the regression is derived as following wit

34、h the application of Kirchhoff’s circuit lawsV ¼ ðR þ RctÞ I þ RRctCddIdt ? RctCddVdt þ Voc (1)In Eq. (1), V and I are measured inputs (their time derivatives being derived directly from mea

35、surements) and R, Rct, Cd, and Voc are model parameters needed to be regressed at each time step. Therefore, the formalism corresponds to a parameter identificationFig. 3. The plots of It1/2 vs. t. I is the measured curr

36、ent. Each curve results from a powertest with the battery is set at its corresponding Voc. (a) Corresponds to the dischargecases and (b) to the charge cases.Fig. 4. Impedance spectra of a Li-ion cell measured at four dif

37、ferent open circuitpotential Voc. Z0 and Z00 are the real and imaginary impedance response of the battery.The frequencies were swept from 0.01 Hz to 60 Hz with 10 logarithmically interval.S. Wang et al. / Journal of Powe