Forecasting Li-ion battery State of Charge using Long-Short-Term-Memory network

Abstract

Estimating the state of charge (SOC) for lithium-ion batteries (LIB) has become a highly desirable task, but also critical, especially as electrified vehicles become more common. However, due to the non-linear behaviour of these batteries, accurately estimating SOC remains a challenge. As a result, traditional theory-based methods are often being replaced by data-driven approaches, thanks to the greater availability of battery data and advances in artificial intelligence. Recurrent neural networks (RNNs), in particular, are promising methods to be exploited, because they can capture temporal dependencies and predict SOC without a battery model. Long short term memory (LSTM), a specific type of RNN, can accurately predict SOC values in real-time and forecast future SOC values within diferent time horizons.

Keywords

• eol>State of Charge
• Long short term memory
• battery
• neural network
• estimation
• electric vehicle
• time horizons

1. Introduction

(ECM) that requires extensive battery test models and parameters [ 1 ].

Lithium-ion batteries have gained immense popularity In recent times, data-driven techniques have gained in various industries, particularly in electric vehicles, significant popularity owing to advancements in artifiand have become increasingly prevalent in recent years. cial intelligence and machine learning, coupled with the LIBs are highly eficient, delivering a greater amount wider availability of battery data. of energy for the same volume and mass compared to The most commonly used algorithms are: conventional batteries like lead-acid batteries. Accurately estimating the state of charge of a battery is crucial for • Artificial Neural Networks (ANN), which have making informed decisions at all stages of its life. SOC the ability to function under non-linear condiestimation also helps in enhancing vehicle performance, tions, and utilize inputs such as battery terminal safety, and passenger comfort, reducing costs associated voltage, discharge or charge current, and temperwith battery over-sizing, and improving overall vehicle ature. Unfortunately, they require large amounts eficiency. However, direct measurement of SOC is not of training data to derive accurate data-driven possible and must be estimated. models, thus high computational power and large

The key technologies for estimating the state of charge memory storage are needed to perform the learnof lithium-ion batteries for electric vehicles can be di- ing phase [ 5 ] eficiently; vided into three main groups: (1) model-based methods • Support Vector Machine (SVM), which can deal such as simplified electrochemical models and equivalent with noisy data and incorporate knowledge from circuit models [ 1 ][ 2 ][ 3 ][ 4 ], (2) machine learning methods other indicators such as energy, power, etc., but , including neural networks [ 5 ][ 6 ] [ 7 ][ 8 ][ 9 ][ 10 ]; and (3) on the other hand, training can be very timehybrid methods composed of two or more of the previ- consuming [ 6 ]; ously mentioned algorithms [ 2 ][ 1 ]. The most common • some other data-driven algorithms, e.g., fuzzy model-based methods for SOC estimation are Coulomb logic and genetic algorithms (see [ 5 ] for further counting and open-circuit voltage, which require many details). parameter measurements, usually afected by noise. More sophisticated models have been developed to deal with these uncertainties, including an equivalent circuit model

Hybrid techniques are utilized to enhance the precision

and efectiveness of battery models while circumventing the limitations of a single algorithm. The primary disadvantage of these techniques is their reliance on significant memory and computational power to execute complex mathematical calculations.

Battery modeling is a crucial step in developing a prelimitations in accurately assessing the battery’s aging By mathematically describing the internal processes process and updating the models continuously. Further based on electrochemical mechanisms, SEMs are caparesearch is required to enhance the precision of battery ble of reflecting the battery characteristics: for example, modeling. The process of modeling the behavior of bat- Coulomb Counting is an ampere-hour (Ah) counting estiteries and their adaptive control technology involves the mation method that integrates the discharging or chargutilization of expert system theories and artificial intel- ing current to determine the remaining charge in the ligence. With the huge amounts of data generated by battery; another method is open-circuit voltage (OCV), energy storage systems, it is natural to utilize machine which employs the battery’s stable electromotive force learning algorithms for state and parameter estimation, while in the open-circuit state, and uses the correlation although the accuracy of these approaches is low, which between the OCV and SOC to approximate the SOC value may become a problem in the optimal monitoring of the [ 1 ]. The ECMs are created by combining resistors, capacLIB state. itors, and voltage sources to generate a circuit network,

In this paper, we present a data-driven methodology which results in their high level of accuracy, robustness, based on LSTM cells to estimate SOC accurately. The and insensitivity to external disruptions [ 4 ]: the Kalman proposed approach maps battery measurement signals iflter is one such example of an ECM that employs mathesuch as voltage, current, and temperature to the battery matical equations to recursively compute a linear optimal SOC. Specifically, the novel contribution of this paper is ifltering solution for SOC estimation [ 3 ]. twofold: Machine learning methods for estimating SOC, which • the application of the LSTM network to predict includes neural network methods, are summarized in SOC at diferent time horizons. SOC works like a [ 5 ]. The Support Vector Machine (SVM) is one of them: fuel gauge in a car, so an accurate prediction of it has an excellent generalization capability compared SOC at a given time horizon can be critical for to neural networks that may have local minimization users to know how long they can drive their car problems. A regression SVM is applied by [ 6 ] to prebefore the battery dies or stops working. On the dict SOC of a LIB. For estimating SOC, neural network other hand, from car manufacturers perspective, algorithms can generally be divided into recurrent and SOC real-time estimation and prediction at dif- non-recurrent. Recurrent algorithms have a memory ferent future horizons can help monitor battery for the past, while non-recurrent algorithms depend on status and plan future maintenance and repair the data input at the current time step. At McMaster work. In addition, it is crucial when the battery University, Carlos Vidal and his team have shown that reaches the end of its first life, and manufactur- training a feed-forward neural network is faster than ers must decide whether it can be used for other training a recurrent network and that the error is smaller purposes or disassemble it. [ 7 ]. Creating a suficiently large battery dataset to train • With the proposed method, we show how power- a deep neural network (DNN) for SOC estimation can ful the LSTM is in predicting SOC: the key point be challenging. To reduce the required test data, a Canais that data collected at diferent frequencies can dian university [ 9 ] proposes to use a specific DNN, the lead to diferent results in predicting future val- LSTM, which can estimate the SOC of diferent types of ues of SOC. This means that the granularity of lithium-ion batteries. In [ 8 ], the authors propose a LSTM the input data used to train an LSTM must be network to estimate SOC of a Panasonic 18650 battery determined concerning the time horizon we want cell, and show that it provides competitive estimation to use to estimate the battery SOC. performance compared to other algorithms reported in the literature. In contrast to unidirectional RNNs, Yang’s

The remainder of this paper is organized as follows. team at Beihang University proposed a model using a Section 2 contains a literature review, highlighting the bidirectional LSTM and the study demonstrated the netnew contribution of this work. Section 3 introduces the work’s ability to comprehend the temporal information data set and describes the data preprocessing and model- present in sequential sensor data obtained from LIBs. building steps. Section 4 presents the experimental re- This includes variables such as voltage, current, and temsults, and Section 5 provides some concluding remarks. perature measurements captured in both forward and backward directions. Additionally, the network efec2. Related work tively summarizes temporal dependencies from past and future contexts. [ 10 ].

SOC estimation methods can be divided into the fol

lowing three categories: the simplified electrochemical models (SEM)[ 1 ][ 2 ], the equivalent circuit models (ECM) [ 4 ][ 3 ][ 2 ] and the machine learning models [ 5 ][ 6 ] which includes neural network models [ 7 ][ 8 ][ 9 ][ 10 ].

3. Methodology

In this section, we provide a detailed description of the

steps we took to obtain a SOC estimate: as shown in Figure 1, the first step is data collection of battery’s parameters thanks to measurement sensors; the second step is to preprocess and prepare the data to obtain a training set and a test set to be fed into the network; the last step is LSTM training and performance evaluation.

3.1. Data collection

Data plays a crucial role in driving innovative advancements in battery development, modeling, and management. For instance, the development of a battery management system (BMS) to regulate battery operations necessitates the usage of data both for its creation, as well as for the training and calibration of the models employed to estimate battery states, such as State of Health (SOH), SOC, and Remaining Useful Life (RUL). The authors in [ 11 ] presented an overview of publicly available battery datasets: electric vehicle (EV) battery requirements difer from those for laptops, cell phones, stationary energy storage, and other devices. Thus, application-specific data are needed for: • cycle aging data: typically, input data include in-cycle measurements of current, voltage, and temperature and per-cycle measurements of capacity and internal resistance or impedance; • drive cycle data: input data are collected by cycling batteries according to the drive schedules; • chemistry cell modeling: is mainly based on the short-term responses of current and voltage and focuses on the impedance variance at diferent battery SOC levels and temperatures; • calendar aging: data include information related to battery cycler such as voltage, current, capacity, and energy from periodic characterization tests.

Various countries and organizations create driving cycles, which are employed to evaluate vehicles’ performance in terms of factors like fuel consumption, pollutant emissions, and trafic impact. Cycling batteries can gather a lot of data based on these driving schedules, which can then be utilized for SOC estimation algorithms under realistic conditions. The universally recognized driving cycle tables can be classified into European, American, and Asian driving cycles [ 11 ].

Most used in literature are the following American (US) driving cycles: • highway fuel economy test (HWFET) is a chassis dynamometer driving schedule representing highway driving conditions under 60 mph, for the determination of fuel economy of light-duty vehicles over highway driving cycle; • federal test procedure (FTP-75) has been created by US EPA (Environmental Protection Agency) to represent a commuting cycle with a part of urban driving including frequent stops, and a part of highway driving; • US06 is a supplemental federal test procedure cycle that represents aggressive, high speed and/or high acceleration driving behaviour; • LA92 unified dynamometer driving schedule was developed as an emission inventory improvement tool, and is for Class 3 heavy-duty vehicles (power-to-mass ratio is greater than 34); • urban dynamometer driving schedule (UDDS) is also known as "the city test" and represents city driving conditions. It is used for light-duty vehicle testing.

3.2. Data preprocessing

3.2.1. Data gathering

In this paper, the dataset used for training, testing and val

idation of the network was released by the Department of Electrical and Computer Engineering, McMaster University, Hamilton, Ontario, and is freely available online [ 12 ].

All tests were performed in a thermal chamber with cell test equipment showed in Figure 2: the control computer contains the databases with the driving schedules and then, after the termal chamber is set to the desired ambient temperature and the cell is fully charged, the system starts to record the current drive cycle. The 3Ah LG 18650HG2 battery cell was subjected to four drive cycles, UDDS, HWFET, LA92, US06, and eight drive cycles (mix 1-8) consisting of a random mix of UDDS, HWFET, LA92, and US06. Following every test, the battery was charged at a rate of 1C with 50mA until it reached a voltage of 4.2V, after which it was turned of. It was ensured that the battery temperature remained at or above 22°C throughout this process. The cycler collects the following measurements:

The training data set consists of the eight mixed driv

ing cycles and their corresponding charges, while the test consists of the UDDS, LA92, and US06 driving cycles and their corresponding charges. All the measurements refers to tests performed only in a 25°C thermal chamber since analyzing how diferent temperatures can afect the SOC estimation is out of our work’s scope.

• Time (time in seconds) • TimeStamp (timestamp in MM/DD/YYYY

HH:MM:SS AM format) • Voltage (measured cell terminal voltage, sense strongly correlated with SOC. Unfortunately, as menleads welded directly to battery terminal) tioned earlier, capacity was used to evaluate SOC, so • Current (measure current in amps) both capacity and energy must be excluded as predictors. • Capacity (measured amp-hours (Ah), with Ah So the variables used as inputs are voltage (V), current counter, typically reset after each charge, test, or (A) and temperature (°C).

drive cycle) • Energy (measured watt-hours (Wh), with Wh 3.2.3. Sampling counter, reset after each charge, test, or drive cycle) The collected data from battery cyclers may have dif• Battery_Temp_degC (battery case temperature, ferent frequencies: in our dataset [ 12 ], data related to at the middle of battery, in degrees Celsius) driving cycles and mix have a time step of 0.1 seconds, while data related to the charging phase have a slower dynamic and were considered less important, so they were stored at a lower data rate of 1 minute.

As mentioned in Section 3.2.1, both the training and test data contains drive cycles and charges, so both must be up-sampled to obtain the same frequency. 3.2.4. Normalization 3.2.2. Feature selection: correlation

The features relating to the battery are voltage, current,

capacity, energy, and temperature. The response variable, the state of charge of the battery, is obtained from the capacity (Ah) of the battery calculated by the battery cycler (detailed procedure is explained in Section 3.2.5).

To measure how much the relationship between dataset features and target variable (SOC) is close to a linear function, the Pearson correlation coeficient is used: the more the absolute value of the correlation coeficient is higher, the more the correlation is stronger [ 13 ].

From the correlation matrix in Figure 3, the strongest correlation is between capacity and energy and both are Since machine learning algorithms generally do not work well with numerical attributes with diferent scales, the dataset must be rescaled. To ensure that input features are within a bounded range of 0 to 1, a technique called minmax scaling, or normalization, is employed. While there are several other methods available, min-max scaling is preferred specifically for neural networks as unbounded input features may pose dificulties [ 14 ]. 3.2.5. Data Labelling Prediction algorithms require apriori knowledge about the values to be predicted (i.e., SOC in our research). Unfortunately, SOC cannot be measured directly but can be easily estimated. Following the SOC definition, it is time of the network, and each of these batches is then defined as the battery percentage remaining charge and fed into the LSTM network [ 14 ]. A forward pass begins is obtained by dividing its remaining capacity (Ah), by when the training data (all batches) are fed into the netits nominal capacity. Each label (SOC) is associated with work, and ends when the SOC estimates are generated the corresponding features for the real-time prediction of at each time step . Each forward pass is followed by a SOC. On the other hand, when predicting SOC for difer- backward pass where the network weights and biases are ent future time horizons, each label is shifted with respect updated: this cycle is referred to as epoch, and is denoted to its initial position by the number of rows needed to by . reach that time horizon: for example, if we try to predict Training a very large neural network can be very slow. SOC within 10 minutes and the data is sampled at 610 Hz, Beyond the mini-batches, one way to speed up training each label will be shifted by 10 rows. is to use a faster optimizer than gradient descent [ 14 ]. The most commonly used one [ 8 ][ 9 ][ 7 ][ 10 ] is adaptive 3.3. Data modelling moment estimation (Adam): it keeps track of an exponentially decaying average of past gradients and also an Long Short Term Memory is a type of recurrent neural exponentially decaying average of past quadratic gradinetwork. RNNs have an internal unit that can form a ents of the loss function, when weights and biases are cycle to show the state history of the previous input. A updated. Once the network has computed all the hidden general LSTM unit consists of: states ℎ of the last epoch, the estimated SOC is obtained by a fully (dense) connected layer: • input gate = (ΨΨ + ℎℎ− 1 + ) which controls which value of the input should be used to modify the memory. The sigmoid function decides which values to let through 0 or 1; • memory where is the weights matrix and is the bias corresponding to the last fully connected layer. A loss function cell = − 1 + is needed to measure the prediction’s accuracy at each tanh (ΨΨ + ℎℎ− 1 + ) where time step. Mean absolute error (MAE) is chosen because tanh function gives weights to the values which of its simple structure and easy calculations [ 14 ]: are passed, deciding their level of importance ranging from -1 to 1; = ℎ + • forget gate = (Ψ Ψ + ℎ ℎ− 1 + ) that regulates the details to be discarded from the block using the sigmoid function ; • output gate = (ΨΨ + ℎℎ− 1 + ) that is the result of the input and the memory cell gate. Again here, the sigmoid function can be zero-valued, so it can inhibit the flow of information to the next computational node; • state of the cell ℎ = tanh where tanh function gives weights to the values which are passed, deciding their level of importance ranging from -1 to 1.

Each gate has its set of network weights denoted by and a bias is added at each matrix multiplication to increase the flexibility of the network to the data. Ψ denotes the vector of inputs to the network, which are the voltage, current, and temperature of the battery measured at time step . 3.3.1. Training The training dataset consists of Ψ = [ (), (), ()] as input and SOC as the response variable to be predicted. Since neural networks require large amounts of data to be trained, they are collected in smaller fixed-size mini-batches to shorten the training =

1 ∑︁| − * | =0 where is the length of the sequence and and * are the estimated and true values of the battery’s state of charge. 3.3.2. Evaluation The validation of the algorithm is done using the test set consisting of the three previously mentioned driving cycles and their respective charges. Only one forward run is required here since all parameters have already been learned during training. The measures used to validate the results obtained are again MAE and the root mean squared error [ 14 ]:

=0 ⎯⎸ = ⎷⎸∑︁ 1 ( − * )2.

3.3.3. Prediction

SOC prediction is performed again with the test set. We do not show prediction results here because the built-in model is not properly optimized, and this task is outside the scope of our work.

4. Preliminary experimental results

As mentioned above, the vector of collected inputs

is defined as Ψ = [ (), (), ()], where (), (), () are the voltage, current, and temperature measurements of the battery at time step , respectively. The train set consists of the eight mix and the corresponding charges, and the test set consists of the UDDS, LA92, and US06 drive cycles and the corresponding charges. After performing all the preprocessing steps explained in Section 3.2, both the training and test set are split into batches to better feed the network.

The model is implemented in Python 3.10.6 version with Tensorflow 2.9.1 package: it is built sequentially, starting with the input layer, then an LSTM layer, and ifnally, a dense layer that computes the output. The parameters of the network, summarized in Figure 4, were kept constant in all experiments in order not to influence the results:

The following results are obtained by considering two diferent sampling frequencies: 1Hz (one observation per second) and 610 Hz (one observation per minute). Since we consider two diferent data granularities, aggregate mean and standard deviation of voltage and current were calculated to avoid information loss when down-sampling the data set: thus, the vector of inputs fed into the network is are quite low; on the other hand, when the time horizon is higher and we predict SOC within the next 30 minutes, the training errors doubled with respect to results obtained for real-time estimation (h = 0), and validation errors are quite high. This is why we need to up-sample: considering a dataset with observations every second is not optimal to predict with reasonable accuracy within a horizon of 30 minutes.

The results in Table (a) are also confirmed by evaluating the Pearson correlation coeficient between SOC values corresponding to diferent time intervals (Lags): • Lag is of 1 second: 0.9939 • Lag is of 10 minutes: 0.9263 • Lag is of 20 minutes: 0.7968 • Lag is of 30 minutes: 0.5404

When two values of SOC have a diference of half

an hour, the correlation coeficient drops significantly, confirming that this algorithm with fine-grained data cannot correctly predict SOC for 30 minutes or larger time horizons. 4.2. Sampling to 610 Hz To obtain train and test sampled to 1Hz, driving cycles are down-sampled from 10 to 610 Hz. The collected results are shown in Table (b). When predicting real-time SOC (h = 0), both train and validation errors are lower than the ones in Table (a). When the time horizon is of 10 minutes, the training error is bigger, but the validation error is lower. By looking at results with a time horizon of 20 minutes, there are no significant diferences between the prediction with the fine-grained and coarse-grained data set. The same happens when the time horizon considered is of 30 minutes.

By looking at the Pearson correlation coeficient between SOC values corresponding to diferent time intervals (Lags): • Lag is of 1 minute: 0.9965 • Lag is of 10 minutes: 0.9692 • Lag is of 20 minutes: 0.8991 • Lag is of 30 minutes: 0.7938 Ψ = [ (), (), (), (), (), The coeficients are more significant than the ones (), ()]. obtained when the frequency of input data is 1Hz, but for time horizons of 20 and 30 minutes, the coeficients 4.1. Sampling to 1Hz are too small, confirming that to predict SOC for those time horizons, a more coarse-grained data set is needed.

Recalling the diferent frequencies of stored data of drive The improvements obtained with real-time SOC escycles (and mix) and charges, to obtain train and test timation (h = 0) are due to the increasing information sampled to 1Hz we down-sample driving cycles from 10 about the past given by the aggregation measures comto 1Hz and up-sample charges from 610 Hz to 1Hz. The puted. When the time horizon is of 20 and 30 minutes results obtained are presented in Table (a): the training er- the algorithm overfits when trying to predict with a finerors with a time horizon of 0, 10 minutes and 20 minutes grained dataset: the training error is relatively low, but Training errors

Test errors

h 0min 10min 20min 30min 0min 10min 20min 30min the validation error is very high; moreover, when we try to up-sample, dataset size reduces a lot, and this aspect can influence the network performance negatively so that when we validate the network, we cannot see improvements, such as the ones with a time horizon of 10 minutes.

5. Discussion

In the final analysis, this work shows how the input data’s diferent granularity can afect the LSTM network’s performance in predicting SOC within diferent time horizons: the more distant the considered horizon, the more we need to aggregate the data and collect them in a coarsegrained dataset. The results are promising, especially for a time horizon of 10 minutes. A very important aspect that should be considered for improvements of this work and future developments is the reduction of the size of the considered dataset: this can afect the performance of the estimation, since neural network-based algorithms always require a significant amount of data to derive proper models. The more distant the horizon, the larger the period of the collected data needs to be.

Thanks to a promising estimation, some business developments can be defined: the integration of anomaly detection techniques in the battery management system (BMS) based on future predictions of SOC, a predictive maintenance plan for the battery, an appropriate target for the second life of the battery to make the most of its remaining useful life; the implementation of a user interface that makes it easier for the owner of an electric vehicle to monitor the battery parameters.

Even though LSTM can self-learn its own parameters, the results obtained in this paper are promising and can be improved thanks to the optimization of LSTM parameters, which will be addressed in future work. Furthermore, it is essential to have a kind of regulation that guarantees the uniformity of electric vehicle battery data, and accessibility for analysts to train the algorithms to improve SOC estimation easily: most innovative ideas have been developed in the laboratory environment, so further improvements are needed in the area of real-time vehicle monitoring.

Acknowledgments

This work was partially supported by

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