A High Frequency Battery Model for Current Ripple Analysis

Transcription

1 A High Frequeny Battery Model for Current Ripple Analysis Jin Wang* Ke Zou Departent of Eletrial and Coputer Engineering The Ohio State University Colubus, OH, USA Chinghi Chen* Lihua Chen Ford Motor Copany Dearborn, MI, USA Abstrat In appliations where eries work together with power eletroni iruits, the urrent ripple generated by the power eletronis will be shared by both the ery and passive oponents in the iruit. The aount of ripple absorbed by the ery depends on its ipedane at the swithing frequeny of power eletronis. This paper presents an ipedane based high frequeny ery odel derived fro test results of a Ni- MH ery using a novel ery ipedane tester. The possible reasons for the ery ipedane harateristis in high frequeny region, inluding skin effet and proxiity effet, are also disussed. This ery odel an be diretly used in urrent ripple analysis, passive oponents design and ontrol strategy optiization of power eletroni iruits. The effet of the passive oponent values on the ery urrent ripple is analyzed using the a equivalent iruit of the test setup. I. INTRODUCTION In hybrid eletri vehiles (HEV) and other appliations, eries usually work together with power eletronis iruits suh as d/d onverters and d/a inverters, whih generate signifiant aount of swithing frequeny related urrent ripple. The urrent ripple absorbed by the ery is deterined by the ipedane of the ery itself as well as other passive oponents suh as its paralleled apaitor. Sine the ery ipedane hanges with its operation frequeny and urrent [], the knowledge of the ery ipedane at swithing related frequenies and high urrent ripple onditions is the key in designing the passive oponents and optiizing the ontrol strategy of the power eletroni iruits. Most ery ipedane testing ethods available today use sall signal testers, suh as the eletroheial ipedane spetrosopy (EIS) [2], [3]. This ay not be the best approah for power eletronis related appliations where high aplitude d and a are both present. This paper eploys a novel ipedane tester whih uses a d/d onverter to reate a d offset and a ripple to produe an environent that iis the operation of real power eletronis. For the ery odeling, equivalent iruit based ery odels have been extensively studied [4], [5]. However, ost of the are not suitable for power eletronis iruit analysis sine they are derived fro test frequenies lower than 5 khz and a urrent ripples whose aplitude is uh less than 5 A. The ery odel developed in this paper fouses on the noral swithing frequeny range (5 khz ~ 20 khz) of power eletronis in HEV operations and is developed fro high AC urrent ripple tests (larger than 0 A peak to peak). In setion IV, the odel is briefly analyzed. Possible reasons for the ery ipedane behavior in swithing frequeny regions, inluding skin effet and proxiity effet are investigated in the analysis. The effet of stray indutane in the auray of the odel is also disussed. Based on this odel, the ery urrent ripple is analyzed using the a equivalent iruit ethod with different passive oponent values. This analysis will help the passive oponents design and syste stability analysis of power eletronis iruits. II. TEST SETUP AND TEST METHOD The test setup diagra is shown in Fig., whih onsists of a boost d/d onverter, a high-auray fil apaitor and the ery under test. In this test setup, the boost onverters are realized using an integrated power odule (IPM) rated at 200V/200A. It is ontrolled by a TI TMS320F282 DSP and funtions as an a ripple generator to produe triangular ripple on the indutor. The high auray fil apaitor works as an ipedane referene. Under the assuption that the apaitane does not hange with frequeny, the ipedane of the ery an be alulated fro the urrent sharing relationship between the ery urrent and apaitor urrent. The apaitor urrent and ery urrent are easured aording to the diretion notation in Fig.. Then the ery ipedane Z an be alulated using (), i Z =, Z = i ib i 2πfC b + 90 () /0/$ IEEE 676

2 i l ib i C in Figure. The general diagra of test setup. where i, ib are the swithing frequeny oponents of apaitor urrent and ery urrent, f is the swithing frequeny and C is the apaitane of the apaitor. Experients were onduted within a swithing frequeny range of 5 khz to 20 khz. A 6.5V Ni-MH ery fro a urrent ass prodution hybrid vehile was disharged to a resistive load through the boost onverter. In the experients, the ery is harged to 50% SOC and the disharging tie for eah test is liited to less than 3 seonds to ensure that in the whole experient the SOC variation is less than 3%. The onnetion able between the ery and the apaitor is intentionally twisted to redue its stray indutane. Fig.2 shows the test setup on the ery side. Fig. 3 shows the urrent test result under the ondition of 0 khz swithing frequeny and 00A d offset. The ery urrent is alost in phase with the apaitor urrent. Aording to the notation of Fig., this iplies the ery ipedane is indutive. Fig. 4 shows the ery ipedane aplitudes and angles at different frequenies and 5A d offset. The detailed test results an be found in [6]. Figure 4. Ipedane vs. swithing frequeny at 5A d offset. Current easureents were ade with Tektronix TCP050 urrent probes whih have a typial d error less than %. The easured urrent signal was reorded by a Tektronix 4054 digital osillosope operating in high resolution (Hi-res) ode. The digitizer of the osillosope is bit at this ode. In the easureent the wavefors are adjusted to posses at least 4 vertial divisions (one half of the sreen) so the digitization error is less than 0.%. The reorded urrent data ontains at least 500 points per yle whih is proessed by the oputer using DFT to find out the swithing frequeny oponent. The overall easureent error ould be ontrolled to be less than 3%. Sine this syste eploys a urrent easureent ethod, it an test a ery ell or a string of eries with the sae level of auray. Other types of eries and other energy storage devies suh as fuel ells ould also be tested using this tester. III. DERIVATION OF HIGH FREQUENCY, HIGH CURRENT BATTERY MODEL The ipedane based ery odel an be derived using an approxiation of the frequeny response urve shown in Fig. 5 and Fig. 6. This paper eploys an advaned vetor fitting ethod introdued by Gustavsen [7]-[9]. This ethod approxiates a frequeny response f(s) with a rational funtion, expressed in the for of a su of partial frations: N f + d + se (2) s a = where ters d and e are optional. and and poles, respetively. a are the residuals Figure 2. The test setup on the ery side. Figure 3. Current wavefors at 0 khz, 00 A d offset. Figure 5. Measured and approxiated ipedane aplitude. 677

3 Figure 6. Measured and approxiated ipedane angle. As shown in Fig. 6, in the frequeny range fro 5 khz to 20 khz, the ery ipedane is indutive so d and e ould not be oitted. Sine the frequeny response (both aplitude and angle) is quite linear, this iplies one pole is enough to desribe the ery ipedane harateristi at this frequeny range, so =. Using the vetor fitting ode provided by Gustavsen [0] and the above restritions, paraeters in (2) are found to be: 7 4 d = , e = , a = , = 3.5. Then the ery urrent-voltage transfer funtion an be written as (3) Z s (3) s The approxiated and easured urve of ery ipedane aplitude and angle are opared in Fig. 5 and Fig. 6, respetively. Sine (3) is a seond order transfer funtion, the ipedane based ery odel is proposed as shown in Fig. 7, whih onsists of two indutors and two resistors. Fro Fig.7, the ery ipedane an be expressed as (4): L R s L L s + ( L R + L R ) s + R R Z = Ls + R + = (4) L2s + R2 L2s R2 Coparing (3) and (4), eah oponent in Fig. 7 an be alulated as shown in Table I. Figure 7. The proposed high frequeny ery odel. TABLE I. PASSIVE COMPONENTS PARAMETERS IN THE PROPSED BATTERY MODEL Coponent Value L µh R Ω L µh R Ω IV. MODEL ANALYSIS The odel presented in Fig.7 is a siple one aiing to help with the design and ontrol of power eletroni iruits. The obvious differenes of this odel fro noral lowfrequeny odels are the addition of indutive oponents and the eliination of apaitive oponents. These reflet the ery s indutive behavior at noral swithing frequeny range. The paralleled L-R branh represents the fat that the equivalent indutane dereases as the frequeny inreases. It should be noted that extra apaitive oponents, suh as the traditional R-C branhes, an be added in the odel to ake it ore aurate. However, this odel akes the proess easier for ripple analysis and power eletronis design. The ery s indutive behavior at high frequeny is due to its intrinsi indutane whih is usually been negleted in the low frequeny region. Previous studies on ery s ipedane at high frequeny also inlude indutive oponents in the odel. For exaple, in [], an indutor is added to the iruit odel. However, those works were not foused on the power eletronis swithing frequeny so the frequeny range is usually fro 0.0 Hz to several khz and the a ripple is uh less than 0 A. So their results either did not over the swithing frequeny region, or had different ipedane response, in both aplitude as well as phase, fro the one desribed in this paper. The stray indutane of the onnetion ables between the ery and the apaitor also ontributes to part of the total indutane in the odel. The aount of stray indutane is deided by the able-ery loop area and the width of the ables. Using twisted able or speially designed busbar ould eliinate ost of the stray indutane. For exaple, if the ables in Fig. 2 are not twisted together, the stray indutane ould be as large as several hundreds of nanohenry. However, if they are twisted together, the stray indutane ould be redued to several tens of nanohenry whih will signifiantly inrease the auray of the ery ipedane easureent in the test. The test results also show that, together with the derease or equivalent indutane, the ery resistane atually inreases with the frequeny. These fats provide us lues as to the possible reasons for this ery ipedane harateristi in swithing frequeny region: A. Skin Effet Skin effet is the unequal distribution of a urrent within a ondutor. The surfae of the ondutor tends to have ore urrent density than in the iddle. This leads to an inrease of resistane and derease of indutane of the ondutor in a onditions opared to d. For the ery, sine its diaeter is uh larger than the skin depth, the resistane is approxiately proportional to the square root of swithing frequeny. A frequeny sweeping test is perfored to find out the possible relationship between the skin effet and ery ipedane harateristi at swithing frequeny region. In this test, the ery is plae far fro any ondutors and the test frequeny ranges fro 4 khz to 20 khz with a step of khz. The ery resistane is alulated and noralized with 678

4 respet to the resistane at 4 khz, i.e. if the resistane at 4 khz is r 0, the noralized resistane r n for a easured resistane r is r n = r / r0. The square root of swithing frequeny is also noralized with respet to the square root of 4000 Hz and plotted together with the noralized resistane in Fig.8. It an be seen in Fig.8 that the hange of resistane of the ery in the tested frequeny region generally follows the square root of swithing frequeny. This indiates that the skin effet ould be a possible soure for the high frequeny behavior of ery. B. Proxiity Effet The proxiity effet aounts for the fat that the urrent distribution within one a-arrying ondutor is affeted by other ondutors lose to it. The proxiity effet will also inrease the equivalent resistane of the ondutor. A frequeny sweeping test is perfored in whih the ery is bounded together with a able that is arrying sae aount of urrent as the ery but in the opposite diretion. Fig. 9 shows the test results. It an be seen that at lower frequenies (less than 5 khz), the resistane follows the urve of square root of frequeny. Then at the region above 5 khz, the resistane soars, whih possibly iplies the influene of the proxiity effet. Figure 8. The noralized R and noralized square root of swithing frequeny without nearby ondutors. The proxiity effet inreases the inauray of ery ipedane testing. So in the tests, the ery should be plaed away fro other ondutors to redue their influene. V. AC EQUVALENT CIRCUIT ANALYSIS The purpose of the derived ery odel is to help with ery ripple analysis. In [], an a sall signal iruit is introdued to analyze the voltage ripple on photovoltai ells. Siilarly, here the a equivalent iruit of the test setup is used to analyze the a ripple on the ery. For the ery disharge ode, the boost onverter is replaed by a square voltage soure V operating at swithing frequeny to sq generate a ripple, as shown in Fig. 0 (a). The boost onverter indutor L, the apaitor C and equivalent ery indutane work together as a LCL filter. So the square wave voltage soure V sq an be replaed by its fundaental V, as shown in Fig. 0(b). The aplitude of V an be alulated using (5): 2 V = sin(( D) π ) V (5) out π where V out is the aplitude of boost onverter output voltage. This replaeent will ause error sine V does not inlude ery urrent haronis, whih depends on the duty ratio D. For ases with large THD, V sq ould be siulated by several sinusoidal soures inluding V and low order haronis. In real HEV appliations, a 285V ery, onsisting of a string of 44 eries, is used. So all of the paraeters in Table I are ultiplied by 44 in the siulation. For the oponent values speified here, the THD of I is 0.8% when D=0.5 and is 2.6% when D=0.2. The ipedanes of C, L and the whole iruit are Z =, Z = Ls, Z = Z Z // Z, L total L + Cs respetively. Thus, the aplitude of ery urrent ripple an be expressed as (6): I V = Z Z total ZC + Z C (6) Figure 9. The noralized R and noralized square root of swithing frequeny with nearby ondutors. (a) (b) Figure 0. The a equivalent iruit (a) square wavefor soure (b) sinusoidal wavefor soure. 679

5 Fig. shows the ery urrent ripple agnitude as a funtion of L and C at a swithing frequeny of 0 khz and 0.5 duty ratio. This result gives a diret indiation on C and L seletion. For exaple, if the axiu ery urrent ripple allowed is 0.5 A, the C ould be seleted as 260 μf and L is 260 μ H. To verify the urrent ripple alulated here, PSIM was used to siulate the iruit in Fig.0 (a) under the following ondition: C=260 μ F and L=260 μ H. The siulation result is shown in Fig. 2 and the urrent ripple aplitude is about 0.49A, whih is onsistent with the result of the previous alulation. VI. CONCLUSIONS This paper presents a high frequeny, high urrent ery odel based on the test results on a Ni-MH ery. This odel only onsists of two resistors and two indutors so it an be easily used in ery ripple analysis and the ontrol strategy design for power eletronis systes. The possible reasons for the ery ipedane under high frequeny, high a urrent onditions, inluding the skin effet and the proxiity effet are also investigated. Using the a equivalent iruit of the ery ipedane test apparatus, the influene of passive oponent values on ery urrent ripples is studied. This paper is the first in a series of papers to investigate the ipedane based ery odel for high urrent and high frequeny onditions. Fig. 3 shows the ain iruit of the autoati tester whih will be built in the next step. A grid- Figure. Battery urrent ripple vs. C and L. Figure 2. Siulated ery urrent ripple (C=260 μ F, L=260 μ H ). i b V b Contator i C L i l S S 2 Figure 3. The ain iruit for the autoati ery tester. -tied H-bridge inverter is added into the autoati tester. In this shee, during the ery disharge ode, the ery works as a d soure by providing power to the utility grid and during the harge ode it absorbs power fro the utility grid. A dspace ontroller is eployed to ontrol the ery urrent and realizing SOC traking. Effort will also be ade on detailed analysis of high frequeny ery harateristis, power eletronis syste stability analysis and ontrol strategy optiization. REFERENCES [] S. Buller, M, Donker and E. Karden, Ipedane-based siulation odels of superapaitors and Li-Ion eries for power eletroni appliations, IEEE Trans. Industry Appliations, vol. 4, no. 3, MAY/JUNE 2005, pp [2] P. Mauraher and E. Karden, Dynai odelling of lead/aid eries using ipedane spetrosopy for paraeter identifiation, J. Power Soures, vol.67, Aug. 997,pp [3] X.Feng and Z. Sun, A ery odel inluding hysteresis for State-of- Charge estiation in Ni-MH ery, in IEEE 2008 Vehile Power and Propulsion Conferene,Sept. 2008, pp. 5. [4] M.Chen, G.Rinon-Mora, Aurate Eletrial Battery Model Capable of Prediting Runtie and I V Perforane, IEEE Trans. Energy Conversion, vol.2, no.2, June 2006, pp [5] R. Kroeze and P. Krein, Eletrial Battery Model for Use in Dynai Eletri Vehile Siulations, in IEEE 2008 Power Eletronis Speialists Conferene, June 2008, pp [6] Stephen Nawroki, Renxiang Wang, Ke Zou and Jin Wang, High Current Battery Ipedane Testing for Power Eletronis Ciruit Design Optiization, in IEEE 2009 Vehile Power and Propulsion Conferene, Sept [7] B. Gustavsen and A. Selyen, "Rational approxiation of frequeny doain responses by Vetor Fitting," IEEE Trans. Power Delivery, vol. 4, no. 3, pp , July 999. [8] B.Gustavsen, Iproving the pole reloating properties of vetor fitting, IEEE Trans. Power Delivery, vol. 2, no. 3, pp , July [9] D. Deshrijver, M. Mrozowski, T. Dhaene, and D. De Zutter, Maroodeling of ultiport systes using a fast ipleentation of the vetor fitting ethod, IEEE Mirowave and Wireless Coponents Letters, vol. 8, no. 6, pp ,June [0] B. Gustavsen, User s guide for vetfit3.. SINTEF Energy Researh, N-7465 Trondhei, Norway. [Online]. Available: : VFIT3.zip [] N.Benavides. P. Chapan, Modeling the effet of voltage ripple on the power output of photovoltai odules, IEEE Trans. Industrial Eletronis, vol 55, Issue 7,July 2008 pp V d S 3 S 4 S 5 S 6 680