The main focus of LIB degradation has been capacity fade so far. On the other hands, efficiency degradation was pointed out in recent years. Battery aggregation, that is expected to absorb the surplus of variable renewable energies like photovoltaic energy, would be affected in terms of economic gain decrease by efficiency degradation. Reuse LIB would be used as a component of aggregation in the future, naturally, the variety of charge-discharge efficiency might be more complex. To improve an operation efficiency of aggregation including reuse LIB, we proposed the quasiunsupervised learning of open circuit voltage profiles. This method showed good accuracy of the estimation of charge-discharge energy. From this, it is expected that this diagnosis could be contribute to an economic improvement of battery aggregation.
* Created this document Transmission and Distribution Co., 2021). Naturally, it would be resulted in the loss of economic and environmental benefits despite of renewable energy capital investment.
One of its expected solutions is aggregated rechargeable batteries supported by IoT(Isono et al.,
2013). That is, the surplus renewable energy could be charged, and discharged later in the time of
demand dominance. Lithium-ion battery (LIB) is an important candidate and has been adopted as the
components of electric vehicles and stable energy storage systems. For lower resource demands,
lower prices and more commercially widespread of LIB, many considerations of reuse
LIB has an important characteristic of performance decline depending on cycle times and storing
period (Ramadass et al., 2002)
An efficiency degradation diagnosis has three essential parameters. That is, a value of full charge
capacity, and profiles of open circuit voltage and internal impedance
Moreover, it is desirable that the training data of efficiency degradation diagnosis is few. In this case, the measurement data of charge–discharge cycle test for establishing LIB’s degradation models is applicable. A large amount of training data would improve the accuracy of these models however it would be necessary to spend many times and works of measurements. Furthermore, there would be many models and manufacturers of aggregated LIB, therefore there would be a lot of test samples to be measured.
In consequence, the estimation of open circuit voltage profiles with few teacher data, that is, quasi-unsupervised learning, is required. In addition, it should be carried out using data measured by a battery management system mounted on LIB for reducing its cost. 1.3
There are many reports of open circuit voltage profile measurements, and these could be roughly divided into two groups. One group is ‘pseudo open circuit voltage (pOCV)’ (Pastor-Fernández et al., 2019). pOCV is the method of charge–discharge in the range of full-discharge to full-charge with lower than 10 hours rate constant current (C/10). Other is called ‘Galvanostatic intermittent titration technique (GITT)’ (Birkl et al., 2015). GITT is the method of square waved current charge or discharge with long time relaxation between waves. The conditions of pOCV and GITT are quite different from battery aggregation. We propose the unsupervised learning of open circuit voltage profiles using data of a battery management system. The contribution of this study is the adaption to real LIB operation of profile information acquisition. 2
The unsupervised learning of open circuit voltage profiles that we proposed is described as below. 2.1
This method adopts the additive processing of gaussian function profiles estimated by the value of open circuit voltage at that time. The equation of it is defined as follows.
− = + = = ⎜ − , ⎛ , ⎞
⋮ ⎝ , ⎠
⎟ + − − ,
⋮
≤ ≤
, ∈ + , can be defined as follows.
charge,
is the deformation amount and are the sample values of estimated open circuit voltage profile and , are the sample values of Where − denotes the estimated open circuit voltage profile after transformation,
is the calculated estimation error of open circuit voltage, is the learning rate, is a standard deviation of gaussian function namely the index of deformation width, ,0 is the deformation center on the axis of state of charge . The image of one deformation process is described in Fig.1. was calculated from chronological data of charge–discharge cycles. Charge–discharge voltage for each 0.01 state of for each 0.01 state of charge, , = + + + , (2) Where denotes the estimated internal resistance and is the estimation error of it, , is the charge–discharge current and it defined charge as positive value and discharge as negative. In this study, it was assumed that is given as the correct values from calculation of chronological data, and the contributions of errors of open circuit voltage and internal resistance are equal, that can be given as follows.
(1) is the pre , − , = = , (3) noted that the first learning. was calculated by comparing measured charge–discharge voltage with and contributions of errors according to equation (2) and (3). Thereafter, − was calculated based on the additive gaussian sample values adjusted by learning rate . would be corrected without training data by repeating a series of learning calculation periodically during charge–discharge cycles. It should be values must be given artificially. Namely, it can be said as quasi-unsupervised In this equation, the profile was denoted as a function of . ( ) was fitted by the estimated sample values − based on the deformative learning of equation (1)-(3). That is, can be denoted as the sample values based on equation (4) as follows.
⋮
⊺ = × × ⋯ × ⎡ , ⎤ ⎢ , ⎥ = ⎢⎢ ⋮ ⎥⎥
⎣ , ⎦ × = ⎢ ⎡ ⎢
−
− ⎢ ( ⎣ ( − − ) ⎥ − )⎦ ⎤ ⎥ ⎥ ⋮ ⋮ = × × ⋯ ×
− × = ( ( ( − ) − ) ⋮ − ) (5) (6) as (7) (8) (9) function 1 including calculation of error with − as follows. 5×1 are coefficient vector of equation (4). Updated ( ) were fitted based on the evaluation = × × ⋯ × − − follows.
The estimated sampling data of internal resistance was fitted as 6th order polynomial of based on correct values calculated from chronological charge–discharge data as follows. ( ) = ∑= + 7×1 are coefficient vector of equation (7) and ( ) were fitted based on the evaluation function 2.
The values of full charge capacity were set as a measured and calculated values of charge– discharge of each cycle. Calculation of charge–discharge energy , was carried out as follows.
, = ∫ ( ) + , ( ) ( ) , ( ) is the function of operation current and it was defined by the charge–discharge operator. Calculation of equation (9) was practically carried out as sectional quadrature. The estimation of charge and discharge energy each would result in that of energy efficiency, namely, it could be said as efficiency degradation. 3
For the verification of this profile learning, offset and noise were added to some parameters. First, +10 % offset error was added to the overall profile of open circuit voltage which was set prior to all learning processes. This was the assumption of reuse LIB having unknown profiles that was introduced in a battery aggregation. Second, maximum ±25 % gaussian noise was added to an internal detailed learning conditions are shown in Table 1. resistance value of each learning opportunity. This was the assumption of estimation error by Kalman filter or another similar method. In this verification, the learning rate was set as 3 types of fast, medium, and slow. In addition, the index of deformation width was adjusted depending on .the
This verification was carried out based on the chronological data of 700 times charge–discharge cycle of LIB module. The detailed cycle conditions are shown in Table 2. The results were shown in Fig 2. Black lines are actual values of each cycle charge–discharge energy. And red, blue, and green lines are the estimated one based on the deformative learning of open circuit voltage. Solid lines are denoted as charge, and dot lines are denoted as discharge. In the case of condition A, the estimated values were fitted to the actual values within only dozens of cycles. On the other hands, about 150 cycles were necessary in condition B, and about 500 cycles in condition C. The errors of condition A in the range between 601 to 700 cycles were less than 0.3 % in charge, and 0.7 % in discharge. From this, we can conclude in the following way. This proposed method of quasi-unsupervised learning of open circuit voltage profiles could realize the efficiency degradation diagnosis of LIB in combination with capacity degradation diagnosis and internal resistance estimation. Together with this, it is important that the appropriate values of and are selected. We should note that it could be valid for reuse LIB having unknown profiles.
In this study, we pointed out the problem of upcoming reuse LIBs from the point of efficiency degradation. From this, we proposed the quasi-unsupervised learning of open circuit voltage profiles. Compared to pOCV or GITT, this method has a demerit that an open circuit voltage profile might not be obtained from only one charge–discharge process. On the other hands, the merit is a high practicality based on the adaptability of real LIB operation. Therefore, it could realize the efficiency degradation diagnosis in combination of capacity and internal resistance estimation. Moreover, wide variety of open circuit voltage profiles would be expressed by not only reuse but also the difference of active materials like iron phosphate cathode and titanium oxide anode, and the proposed method might be applicable these overall conditions. It is expected that this diagnosis could be contribute to an economic improvement of battery aggregation.
CAISO (2016) What the duck curve tells us about managing a green grid. Available at: https://www.caiso.com/documents/flexibleresourceshelprenewables_fastfacts.pdf (Accessed: 1 June 2021).
IRENA (2021) Renewable Capacity Statistics 2021. Available at: https://www.irena.org/publications/2021/March/Renewable-Capacity-Statistics-2021 (Accessed: 1 January 2021).
IEEE Grenoble Conference. IEEE, pp. 1–6. doi: 10.1109/PTC.2013.6652141.
Journal of Power Sources, 112(2), pp. 606–613. doi: 10.1016/S0378-7753(02)00474-3.
oxide-based batteries during calendar aging’, Journal of Power Sources, 353, pp. 183–194. doi: 10.1016/j.jpowsour.2017.03.090.