Sysem Idenfcaon of onlnear Sae-Space Space Baery odels WH We He wehe@calce.umd.edu Advsor: Dr. Chaochao Chen Deparmen of echancal Engneerng Unversy of aryland, College Par 1 Unversy of aryland
Bacground Lhum-on baeres are power sources for elecrc vehcles (EVs). Sae of charge (SOC) esmaon of baeres s mporan for he opmal energy conrol and resdual range predcon of EVs. SOC s he rao beween he remanng charge (Q reman ) and he maxmum capacy of a baery (Q max ) SOC Q reman Q max Full: SOC = 100% Empy: SOC=0% 2 Unversy of aryland
Equvalen Crcu odel of Baeres Equvalen crcu models have been used o model he relaonshp beween SOC and he measurable baery parameers: curren I L and volage U [1-3]. V I V L p p Cp CpRp V OCVSOCVp ILR0 where OCV s he open crcu volage as a funcon of SOC, whch can be deermned by baery ess. OCV 3.8 3.6 3.4 3.2 3 2.8 2.6 2.4 OCV-SOC ( Couresy: Ref. [1]) Cell #1 Cell #2 Cell #3 Cell #4 Cell #5 3 2.2 0 0.2 0.4 0.6 0.8 1 SOC Unversy of aryland
Sae-Space Represenaon Process funcon: SOC SOC 1 I L, Q max I L p V V exp V R 1exp I p p, 1, p p L, CR p p CR Cp CpRp p p V OCVSOCVp ILR0 easuremen funcon: V V OCV( SOC ) R I V, 0 L, p, easured Sgnals: I L IL I V V 2 I V (0, ) (0, ) I V Rp, Cp, R0, Qmax, I, v The model parameers wll change wh loadng condons and baery agng. Updang of he model parameers s necessary o ensure he accurae SOC esmaon 4 Unversy of aryland
Problem Formulaon Esmae he unnown parameers n x 1 f x, u,, y h x, u, e, based on he nformaon n he measured npu-oupu responses,...,,, y,...,, y U u u Y y y 1 1 usng a maxmum lelhood framewor ˆ arg max p Y arg max L Y 5 Unversy of aryland
Expecaon axmzaon (E) Expecaon sep (E sep): calculae he expeced value of he log lelhood funcon, wh respec o he condonal dsrbuon of X gven Y under he curren esmae of he parameers [4],,, p Q E L X Y Y L X Y p X Y dx axmzaon sep ( sep): fnd he parameer ha maxmzes hs quany: 1 arg max Q, If no converged, updae ->+1 and reurn o sep 2 I has been approved n Ref. [4] ha L,, Y 1 L Y Q 1 Q 6 Unversy of aryland
Expecaon axmzaon (E),,, Q E L X Y Y L X Y p X Y dx Tae E Y where, log, log log L X Y p Y X p Y X p X 1 log p x log p x x log p y x 1 1 1 1, 1 2 3 Q I I I I log p x log p x Y dx 1 1 1 1 1 I log p x x p x, x Y dxdx 2 1 1 1 1 I 3 log p y x p x Y dx 1 The parcle smooher provdes approxmaons for I 1 and I 3 : 1 p x Y x x 7 Unversy of aryland
Expecaon axmzaon (E) 1 I log p x x p x, x Y dx dx 2 1 1 1 1 usng Bayesan and arov propery 1, Y 1, Y 1 Y 1 p x 1 Y p x 1 x p x Y p x x p x Y dx p x x Y p x x Y p x Y p x x p x Y p x Y 1 1 p x Y 1 Sae equaon Parcle fler p x Y x x 1 Parcle Smooher 1 1 1 1 p x Y x x 1 8 Unversy of aryland
Expecaon axmzaon (E) Parcle smoohng approxmaons, 1 2 3 Q I I I 1 1 1 1 I I w log p x 1 j j I 2 I2 log w p x1 x 1 1 j1 1 3 3 1 1 I I w log p y x 1 9 Unversy of aryland
Parcle E Algorhm [4] 1. Se = 0 and nalze 2. Expecaon (E) Sep: a) Run parcle fler and parcle smooher b) Cl Calculae l Q, I1I2 I3 3. axmzaon () Sep: Compue: 1 arg max Q, 4. Chec he non-ermnaon condon Q,, 1 Q If sasfed updae 1 and reurn o sep 2, oherwse ermnae. 10 Unversy of aryland
Parcle Fler Algorhm [4-5] 1. Inalze parcles, { x } ~ P ( x ) and se = 1. 0 1 0 2. Predc he parcles by drawng..d samples accordng o x ~ P x x, 1,..., 1 3. Compue he mporance weghs w 1 P y x w w x, 1,..., j P y x j1 4. For each j = 1,, draw a new parcle x x wh replacemen e (resample) e) accordng o j j ( Px x ) w, 1,..., 5. If < ncremen 1 and reurn o sep 2, oherwse ermnae. 11 Unversy of aryland
Parcle Smooher Algorhm [4-6] 1. Run he parcle fler and sore he predced parcles { x } 1 and her weghs, for = 1,,. w 1 w 2. Inalze he smoohed weghs o be he ermnal flered weghs a me =. w w, 1,..., and se = -1. w w 1 3. Compue he smoohed weghs usng he flered weghs and parcles 1 { x, x 1 } va 1 P 1 ( x x ) w w w1 where v wp ( x 1 x ) v 1 1 4. Updae 1. If > 0 reurn o sep 3, oherwse ermnae. 12 Unversy of aryland
Implemenaon Hardware Dell Lapop wh a 2.67G Hz Inel Core 7 CPU and 4 GB of RA Sofware alab 13 Unversy of aryland
Valdaon Smulaed daa wll be used o valdae each componen: he parcle fler, parcle smooher and he parcle E. Smulaed daa wll be generaed wh he assumed exac values for he model parameers and saes. Valdaon of parcle fler and smooher odel parameers are assumed o be nown Sae flerng and smoohng resuls wll be compared wh he rue sae values o verfy he algorhm. Valdaon of parcle E odel parameers and saes are assumed be unnown 14 Unversy of aryland
Projec Schedule and lesones Projec proposal: Ocober 5 2012 Algorhm Implemenaon: - Parcle fler and smooher: December 1 2012 - The full algorhm (parcle E): February 1 2012 Valdaon: arch 15 2012 Tesng: Aprl 15 2012 Fnal Repor: ay 1 2012 15 Unversy of aryland
Delverables Codes Smulaed daa ses Presenaons and repors 16 Unversy of aryland
References 1. H. He, R. Xong, and H. Guo, Onlne esmaon of model parameers and saeof-charge of LFePO4 baeres n elecrc vehcles. Appled Energy, 2012. 89(1): p. 413-420. 2. C. Hu, B.D. Youn, and J. Chung, A ulscale Framewor wh Exended Kalman Fler for Lhum-Ion Baery SOC and Capacy Esmaon. Appled Energy, 2012. 92: p. 694-704. 3. H.W. He, R. Xong, and J.X. Fan, Evaluaon of Lhum-Ion Baery Equvalen Crcu odels for Sae of Charge Esmaon by an Expermenal Approach. Energes, 2011. 4(4): p. 582-598. 598. 4. T.B. Schön, A. Wlls, and B. nness, Sysem denfcaon of nonlnear saespace models. Auomaca, 2011. 47(1): p. 39-49. 5..S. Arulampalam, S. asell,. Gordon, and T. Clapp, A uoral on parcle flers for onlne nonlnear/non-gaussan Bayesan racng. Sgnal Processng, IEEE Transacons on, 2002. 50(2): p. 174-188. 6. A. Douce and A.. Johansen, A uoral on parcle flerng and smoohng: ffeen f years laer. Handboo of onlnear Flerng, 2009: p. 656-704. 6 17 Unversy of aryland