PSI - Issue 8

Francesco Mocera et al. / Procedia Structural Integrity 8 (2018) 126–136 Mocera, Vergori/ Structural Integrity Procedia 00 (2017) 000 – 000

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generator and a series resistor. The voltage generator represents the Open Circuit Voltage (V OC ) of the battery, which mainly depends on the State Of Charge (SOC). The V OC is a characteristic of each different battery chemistry. The series resistance represents the internal ohmic resistance of the battery. The Rint model can be expressed by Eq. 2, where V t is the terminal voltage, I is the current flowing through the battery and R 0 is the ohmic resistance. = − 0 ∗ (2) By convention, discharging current is defined positive and charging current is defined negative. In this model, the parameters to be determined are V OC and R 0 . Because V OC shows a marked dependency by SOC, in the present paper it is modelled as a function of this quantity according to a simplified electrochemical battery model. In these models, coefficients have no physical meaning and are just used to fit the battery response. Among the simplified electrochemical battery models, the Combined model (Eq. 3) was selected due to the best fitting performance of the battery response. = 0 − 1 − 2 ∗ + 3 ∗ ln( ) + 4 ∗ ln(1 − ) (3) It describes the open circuit voltage as a function of the SOC (indicated by z) using five different coefficients to be able to describe the trend of the whole curve. The data acquired with the testing equipment were used to identify the model parameters. The sampling period is very short with respect to the duration of the test so the problem is over-determined. To carry out the model parameters identification, the Least Squares procedure (LS) was adopted. To solve the LS, the QR factorization procedure, explained by Lawson et al. (1974), was implemented due to its good performance also with not well conditioned coefficients matrices. The identified parameters can be used to reproduce the battery terminal voltage starting from an input current. Among the various discharging profiles generated with the built equipment, the data set obtained with the DST profile was chosen to identify the model parameters. In fact, the DST profile was the one that guaranteed the lowest conditioning number for the coefficients matrix, and so the best regression possible. The dynamic stress test profile was designed by the USABC (US Advanced Battery Consortium) to represent the dynamic EV discharging profile and it consists in a series of positive and negative impulses of different duration. The amplitude and the duration of these impulses is defined by standards in USABC (1996). The total duration of the cycle is 360 seconds. The positive power is the discharging power and the negative one is the charging power. The cycle is iterated in time until the imposed discharging threshold voltage is reached. The data sets collected during the DST tests were used for the model parameters identification. During the tests, the current and the voltage on the battery terminals were measured. The tests were conducted in air so the main heat transfer mechanism acting was natural convection. The battery was not able to dissipate the whole amount of heat produced so the temperature was growing with current flowing. The external temperature was 27 °C. At first a discharge test with a constant low current was conducted to detect the rated capacity of the battery (capacity test described in PNVG (2001)). Thus, the rated capacity was determined and it was used to compute the state of charge of the battery, according to the Coulomb Counting formulation (Eq. 4). ( ) = (0) − 1 ∗3600 ∗ ∫ ( ) 0 (4) where Q rated is the rated capacity and SOC(0) is the initial state of charge. The SOC during the whole test was computed. The Combined model shows some singularities in SOC=0 and SOC=1, so the corresponding values were not considered. The set of points to be used for the identification process was selected and it was made of time, current, voltage and SOC. 5. Battery parameters identification 5.1. Parameters identification procedure