**Recurrent Neural Network-Based Adaptive Energy Management Control Strategy of Plug-In Hybrid Electric Vehicles Considering Battery Aging**

#### **Lu Han, Xiaohong Jiao \* and Zhao Zhang**

Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China; hanlu@stumail.ysu.edu.cn (L.H.); 201831030018@stumail.ysu.edu.cn (Z.Z.) **\*** Correspondence: jiaoxh@ysu.edu.cn

Received: 21 November 2019; Accepted: 27 December 2019; Published: 1 January 2020

**Abstract:** A hybrid electric vehicle (HEV) is a product that can greatly alleviate problems related to the energy crisis and environmental pollution. However, replacing such a battery will increase the cost of usage before the end of the life of a HEV. Thus, research on the multi-objective energy management control problem, which aims to not only minimize the gasoline consumption and consumed electricity but also prolong battery life, is necessary and challenging for HEV. This paper presents an adaptive equivalent consumption minimization strategy based on a recurrent neural network (RNN-A-ECMS) to solve the multi-objective optimal control problem for a plug-in HEV (PHEV). The two objectives of energy consumption and battery loss are balanced in the cost function by a weighting factor that changes in real time with the operating mode and current state of the vehicle. The near-global optimality of the energy management control is guaranteed by the equivalent factor (EF) in the designed A-ECMS. As the determined EF is dependent on the optimal co-state of the Pontryagin's minimum principle (PMP), which results in the online ECMS being regarded as a realization of PMP-based global optimization during the whole driving cycle. The time-varying weight factor and the co-state of the PMP are map tables on the state of charge (SOC) of the battery and power demand, which are established offline by the particle swarm optimization (PSO) algorithm and real historical traffic data. In addition to the mappings of the weight factor and the major component of the EF linked to the optimal co-state of the PMP, the real-time performance of the energy management control is also guaranteed by the tuning component of the EF of A-ECMS resulting from the Proportional plus Integral (PI) control on the deviation between the battery SOC and the optimal trajectory of the SOC obtained by the Recurrent Neural Network (RNN). The RNN is trained offline by the SOC trajectory optimized by dynamic programming (DP) utilizing the historical traffic data. Finally, the effectiveness and the adaptability of the proposed RNN-A-ECMS are demonstrated on the test platform of plug-in hybrid electric vehicles based on GT-SUITE (a professional integrated simulation platform for engine/vehicle systems developed by Gamma Technologies of US company) compared with the existing strategy.

**Keywords:** hybrid electric vehicles (HEVs); battery life; multi-objective energy management; adaptive equivalent consumption minimization strategy (A-ECMS); pontryagin's minimum principle (PMP); particle swarm optimization (PSO); recurrent-neural-network (RNN)

#### **1. Introduction**

Nowadays, the growing energy dilemma and environmental problem are initiating a revolution and innovation within the automobile industry. Hybrid electric vehicles (HEVs) have more of a degree of freedom for vehicle power distribution thanks to invertible energy storage devices and electric machines [1]. To ensure that all hybrid components work cooperatively, a lot of energy management strategies have been proposed. Generally speaking, an energy management control strategy can be categorized as a rule-based (RB) control strategy [2] and an optimization control strategy. The former is realized easily but the fine control performance is not guaranteed. The latter usually is categorized as instantaneous optimization, such as the equivalent consumption minimization strategy (ECMS) [3], model predictive control (MPC) [4], and global optimization including dynamic programming (DP) [5,6] and pontryagin's minimum principle (PMP) [7–9]. DP can obtain a globally optimal solution in theory, but has a serve computational burden and cannot be used in real-time due to the requirement of knowing the global driving cycles in advance. PMP converts energy management to a minimizing Hamilton function, thus greatly reducing the computational burden and making it easier to implement. Despite this, it is still difficult to solve the numerical solution because the dynamic of the co-state is a function of the battery's state of charge (SOC), which is nonlinear. In order to overcome the unknown driving information in advance, MPC is used to solve the energy management optimal control problem [10], which can predict driving information in the fixed prediction horizon. With the development of artificial intelligence, many intelligence algorithms have been applied to predict the driving information in MPC in order to obtain a closer to global optimum solution. For example, the neural network is used in [11] to predict demand power, which makes full preparation for the design of the energy management strategy. The radial basis function neural network (RBF-NN) is trained in [12] using engine working points that is optimized offline utilizing a distributed genetic algorithm. ECMS is applied to search the instantaneous minimum cost function and can be applied in real-time, which is evolved in PMP. Thus, ECMS can obtain more closely to a globally optimal solution by appropriately choosing the equivalent factor. [13] employed the shooting method of PMP to gain the initial co-state and then used the proportional integral (PI) controller to adjust the equivalent factor to guarantee that the SOC has a better trajectory in real time.

Most of the literature only regard minimizing fuel consumption as the optimization objective of energy management problem. In reality, the fading of a battery capcity and the shortening of its life due to the frequenct charge and discharge of a battery when the HEV is running, is inevitable. Furthermore, changing a battery before the HEV is scrapped will significantly increase the usage cost of a HEV. Many studies also have shown that battery life is responsible for the fuel economy of HEVs [14]. Thus it is necessary to consider battery life when designing an energy management control strategy. There are many factors that impact the battery life, such as a battery's thermal management, driving conditions, environment temperature, regional climate, and so on [15]. For this, many ways have been proposed to prolong the battery life for HEVs. In [16], in order to extend the service life of the battery, ultra-capacitors are also equipped to protect the battery by optimizing the distribution of current and using ultra-capacitors to buffer the excessive charge and discharge flow of the battery. [17,18] took fuel consumption and battery capacity loss together into the cost function and solved this multi-objective optimization problem for HEV using PMP and DP, respectively. [19] derived a causal energy management strategy under consideration of battery life for HEV, which effectively reduces battery wear with a reasonable penalty on fuel economy by using ECMS. The distinguishing features of plug-in HEVs (PHEV) over the conventional HEVs are a large variation range of SOC and the repeated charge and discharge of the battery. Moreover, it has been shown that a large depth of discharge (DOD) and frequent use can accelerate the decay of battery life [20]. Consequently, research on the energy management control problem for PHEV considering the battery life is more attractive. [21] established an electrochemical mechanism model for the battery capacity attenuation of PHEV, and formulated a multi-objective optimal energy allocation problem that can be solved by shortest-path stochastic dynamic programming (SP-SDP) while achieving satisfactory vehicle fuel economy and extending battery life. [22] used a genetic algorithm to optimize the energy management strategy aimed at minimum fuel consumption and battery capacity degradation. [23] presented a model predictive control (MPC) strategy and analyzed the Pareto optimal front of the cost function comprised by the equivalent fuel consumption and battery capacity fade during the charge sustaining mode of the battery. [24] further provided the impact of the estimated SOC by the battery management

system on the performance of MPC. [25] studied the nonlinear model predictive control for the energy management of a power-split hybrid electric vehicle (HEV) to improve battery aging while maintaining the fuel economy at a reasonable level. [26] employed the shooting method of PMP to obtain the optimal depth of discharge (DOD) and constructed a reference SOC with the optimal DOD, and then, a model predictive controller was used to optimize the conflict between the energy consumption cost and the equivalent battery life loss cost in a moving horizon. [27] used SDP and particle swarm optimization (PSO) to numerically solve the multi-objective optimal control problem under the consideration of the tradeoff between energy consumption and battery loss. The dynamic loop nest optimization of PSO and SDP was used to obtain offline an optimal solution according to the statistical characteristic of the real historical traffic data. The optimal solution was constructed as look-up mappings on different road segments and battery SOC so that in the online implementation of the management control strategy the power demand assignment can be obtained by these mappings without computational burden according to the current driving mode, system states, and road information.

It should be noted that it is necessary to keep a balance between fuel consumption and battery capacity loss in the design of the energy management control strategy for the economy of PHEV, while the designed management strategy should be integrated to global near optimization and the real-time performance. For this, both a globally sub-optimal and implementable energy management strategy, so-called recurrent neural network-based adaptive equivalent consumption minimization strategy (RNN-A-ECMS), is proposed in this paper for a power-split PHEV considering the battery life. Three efforts have been made. Firstly, RNN with long short term memory (LSTM) is trained utilizing the historical global optimal SOC trajectory that can be obtained by DP and real historical traffic data. Secondly, the maps of the weighting factor and main component of the ECMS' equivalent factor (EF) depending on power demand and battery SOC are obtained by PMP and PSO utilizing the real historical traffic data. The PSO is employed to search the weight factor and co-state of PMP, ensuring the vehicle's optimal economic performance, and the map of the PMP's co-state is converted into the main component's map of the ECMS's EF. Thirdly, the maps of weight factor and the main component of the EF and the model of the well-trained offline RNN are inserted into the core structure of A-ECMS to carry out the energy management control strategy responsibilities for online implementation.

The remainder of this paper is organized as follows. The PHEV mathematical model is given in Section 2. The optimal control problem is formulated in Section 3. Then, RNN-A-ECMS is designed in Section 4. The simulation result and the comparison with SDP-PSO are given to demonstrate the effectiveness of this approach in Section 5. Finally, the conclusion is summarized in Section 6.

#### **2. PHEV Model Description**

The power-split PHEV with a planetary gear set (PGS), shown in Figure 1, is analyzed in this paper. The powertrain of the PHEV mainly consists of the engine, the battery, motor, and generator.

**Figure 1.** Plug-in hybrid electric vehicle (PHEV) powertrain system architecture.

*Energies* **2020**, *13*, 202

Considering the aerodynamic drag and rolling friction force, the longitudinal dynamic equation of the vehiclecan be written as [28]:

$$M\dot{v} = \frac{\eta\_f T\_{\text{trac}} - T\_{\text{br}}}{R\_{\text{tire}}} - Mg\left(\mu\_r \cos \alpha + \sin \alpha\right) - \frac{1}{2}\rho A C\_d v^2,\tag{1}$$

where *M* is the PHEV mass. *v* denotes the velocity of the PHEV. *η<sup>f</sup>* is the transmission efficiency of the differential gear. *Ttrac* and *Tbr* are the traction torque and brake torque, respectively. *g* is the gravity acceleration. *μ<sup>r</sup>* is the coefficient of rolling resistance. *α* is the grade of the road. *ρ* is the air density. *A* is the frontal area of vehicle. *Cd* is the drag coefficient.

The PGS containing the sun gear, carrier gear, and ring gear respectively connecting to the generator, engine, and motor is a core component of PHEV, which allows the PHEV to run not only the series mode in which the engine provide power to generator to charge the battery or to motor through an inverter to drive the vehicle but also the parallel mode in which the engine directly propels the vehicle together with the motor. Under the assumption of rigid connections in the powertrain and without friction loss, the PGS speed and torque relationships are described as:

$$T\_r = \frac{R\_r}{R\_r + R\_s} T\_{c\_r} \quad T\_s = \frac{R\_s}{R\_r + R\_s} T\_{c\_r} \tag{2}$$

$$\left(\left(R\_r + R\_s\right)\omega\_\mathcal{L} = R\_r\omega\_r + R\_s\omega\_{s\star}\tag{3}$$

where *Tr*, *Tc*, and *Ts* are the torques of ring gear, carrier gear, and sun gear, and *ωr*, *ωc*, and *ω<sup>s</sup>* are the speeds of ring gear, carrier gear, and sun gear, respectively. *Rs* and *Rr* are the teeth number of sun gears and ring gears, respectively. With the assumption that the connecting shafts are rigid, the speed relationship between planetary gear set and powertrain is described as follows:

$$
\omega\_{\mathbb{C}} = \omega\_{\mathbb{C}'} \omega\_{\mathbb{T}} = \omega\_{\mathfrak{m}'} \omega\_{\mathbb{S}} = \omega\_{\mathbb{S}'} \tag{4}
$$

where *ωe*, *ωm*, and *ω<sup>g</sup>* are the speeds of engine, motor, and generator, respectively. In addition, the motor speed can be computed by the following equation:

$$
\omega\_m = \frac{\mathcal{S}\_f}{R\_{time}} v\_\prime \tag{5}
$$

where *Rtire* and *gf* are the tire radius of PHEV and the ratio of differential shaft.

Energy consumption chosen as one part of optimization objective contains fuel consumption *m*˙ *<sup>f</sup>* and electricity consumption *m*˙ *elec* which are defined as follows.

$$
\dot{m}\_{fuel} = \text{BSFC}(\omega\_{\varepsilon}, T\_{\varepsilon}) \cdot T\_{\varepsilon} \cdot \omega\_{\varepsilon} \cdot 10^{-5} / 36,\tag{6}
$$

$$
\dot{m}\_{\text{clcc}} = \mathbf{s} \cdot P\_{\text{clcc}} / \mathcal{H}\_{l\prime} \tag{7}
$$

where *Te* is the torque of engine. BSFC is brake specific fuel consumption. *Hl* is the lower heating value of the fuel. *s* is EF. *Pelec* is the total battery power, which can be expressed as follows:

$$P\_{\text{ellec}} = P\_b + P\_l = P\_b + I\_b^2 \cdot R\_{b\text{\textquotedblleft}} \tag{8}$$

where *Pl* is the internal loss power of the battery, *Ib* and *Rb* are the current and equivalent internal resistance, respectively. *Pb* is the electrical load at the terminals, which can be written as follows:

$$P\_b = \eta\_m^{k\_m} T\_m \omega\_m + \eta\_{\mathcal{S}}^{k\_{\mathcal{S}}} T\_{\mathcal{S}} \omega\_{\mathcal{S}'} \tag{9}$$

where *η<sup>m</sup>* and *η<sup>g</sup>* are the efficiency of the motor and generator, respectively. *Tm* and *Tg* are the motor torque and generator torque, respectively. *km*/*kg* = 1 when the motor/generator is in a discharging state, otherwise *km*/*kg* = −1.

Moreover, it has been shown the battery performance is affected by both storage time and usage, often categorized as Calendar life and Cycle life. Calendar life is the ability of the battery to withstand degradation over time, which may be independent of how much or how hard the battery is used. While, cycle life includes deep cycle life and shallow cycles. Deep cycle life is the number of discharge-recharge cycles the battery can perform in the charge-depleting (CD) mode. For example, one complete deep discharge with starting at 90% SOC, ending at 30% SOC, and recharging back to 90% SOC would complete one full cycle. Shallow cycles refer to SOC variations of only a few percent. These smaller variations occur throughout CD and charge-sustaining (CS) mode because the battery frequently takes in electric energy from the engine via a generator and from regenerative braking, and passes energy to the electric motor to power the vehicle. These frequent shallow cycles cause less degradation than deep cycles, but still affect battery life. Therefore, the management to the battery shallow cycle in operating modes should also be considered in order to minimize the battery life degradation in the discharge/charge cycles together with the minimization of energy consumption. There are many factors affecting battery life, such as temperature, Ah-throughput, and depth of discharge. With usage, battery performance in power and energy capacity can degrade. To get the depletion degree of battery capacity, the effective Ah-throughput (*Aheff*) is defined as [14,20]:

$$A h\_{eff}(t) = \int\_0^t \sigma(I\_{b\prime} T\_{bttt\prime} \text{SOC}) \cdot |I\_b(t)| \, dt,\tag{10}$$

where *Tbatt* is the battery temperature. *σ*(·) is called as severity factor, which describes the aging effect of any cycle the battery undergoes with respect to the nominal cycle, which is described as follows.

$$\sigma(I\_{b\prime}, T\_{batt\prime}, \text{SOC}) = \frac{\gamma(I\_{b\prime}, T\_{batt\prime}, \text{SOC})}{\Gamma} = \frac{\int\_0^{EOL} |I\_b(t)| \, dt}{\int\_0^{EOL} |I\_{nom}(t)| \, dt},\tag{11}$$

where *γ*(·) is the battery duration (Ah-throughput) corresponding to a given sequence of current, temperature, and SOC. Γ is the total Ah-throughput corresponding to the nominal cycle, called as the nominal battery life, which is expressed as:

$$
\Gamma = \int\_0^{EOL} |I\_{nom}(t)| \, dt,\tag{12}
$$

where *Inom* is the current profile under nominal conditions and *EOL* denotes the battery end of life. The battery life is regarded as the end when *Aheff* = Γ. Then, it may be regarded that the capacity loss is as *Qloss*% = *Aheff* /Γ. Thus, prolonging the battery life is equivalent to decreasing the depletion degree of battery capacity, which is also equivalent to minimizing the effective Ah-throughput. It should be worth mentioning that the severity factor *σ*(·) in this paper is obtained by the same approach as in [27], the fitting based on the experimental data.

Moreover, SOC dynamics in the energy management problem can be described as follows:

$$\text{SOC} = -\frac{I\_b}{Q\_b} = -\frac{P\_b}{Q\_b \cdot \mathcal{U}\_{\text{OC}}} \, \tag{13}$$

where *UOC* is open circuit voltage, and *Qb* is the battery capacity.

#### **3. Optimization Problem Formulation**

The energy management control for PHEVs is actually an optimization problem, which in this paper is to distribute power among the engine, motor, and generator meeting the power demand of the driver while minimizing energy consumption and prolonging battery life. To this end, the whole objective function can be written as follows:

$$J = \int\_0^{t\_f} \left\{ (1 - \theta(t)) \frac{\dot{m}\_f(t) + \dot{m}\_{\text{elxc}}(t)}{\Omega} + \theta(t) \frac{\sigma(t) \cdot |I\_b(t)|}{\Lambda} \right\} dt,\tag{14}$$

where *θ*(*t*)∈[0, 1] is a weight factor balancing two contradict objectives. Ω and Λ are introduced to make normalization, which are the optimal energy consumption with no consideration of battery loss, and the target effective Ah-throughput only the considering battery loss, respectively. The optimization is to calculate the control input *u* of the motor torque and the generator speed:

$$\mu^\* = \left[ T\_{m'}^\* \omega\_{\overline{\mathbb{g}}}^\* \right] = \arg\min\_{\mu \in \mathcal{U}} f \tag{15}$$

subject to the dynamic constraint in Equation (13) and the physical conditions:

$$\begin{cases} \text{SOC}\_{\text{min}} \le \text{SOC} \le \text{SOC}\_{\text{max}} \\ \omega\_{\varepsilon,\text{min}} \le \omega\_{\varepsilon} \le \omega\_{\varepsilon,\text{max}} \\ \omega\_{m,\text{min}} \le \omega\_{m} \le \omega\_{m,\text{max}} \\ \omega\_{\mathcal{S},\text{min}} \le \omega\_{\mathcal{S}} \le \omega\_{\mathcal{S},\text{max}} \\ T\_{\varepsilon,\text{min}}(\omega\_{\varepsilon}) \le T\_{\mathcal{E}} \le T\_{\varepsilon,\text{max}}(\omega\_{\varepsilon}) \\ T\_{m,\text{min}}(\omega\_{m}) \le T\_{m} \le T\_{m,\text{max}}(\omega\_{m}) \\ T\_{\mathcal{S},\text{min}}(\omega\_{\mathcal{S}}) \le T\_{\mathcal{S}} \le T\_{\mathcal{S},\text{max}}(\omega\_{\mathcal{S}}) \end{cases} \tag{16}$$

It should be noted from Equations (7) and (14) that the determinations of two factors *θ*,*s* play an important role in satisfying the objective and seeking the optimal solution in the actual operation of PHEV.

The weight factor *θ*(*t*) should balance the energy consumption and the battery aging in real time according to the operating mode and current state of the vehicle, which yields a Pareto front. Consequently, the determination of *θ*(*t*) is also an optimization problem. For this, in this paper, *θ*(*t*) will be offline optimized by PSO and PMP utilizing historical traffic data, and then established as a map table about the battery SOC and power demand.

The EF *s*(*t*) should be chosen to be linked to the optimal co-state of the PMP for guaranteeing more closely the global optimal solution of the energy management control problem. For this, in this paper, the major component of the *s*(*t*) is determined by the optimal co-state of the PMP that is optimized offline by PSO, and the tuned component will then be obtained by the PI controller of the deviation between the actual SOC and the reference trajectory of he SOC from a well-trained RNN by historical traffic data.

#### **4. RNN-Based Adaptive Energy Management Strategy**

In order to ensure that the designed management strategy is integrated, for global near optimization and real-time performance, in this paper, ECMS is used as the core algorithm of energy management. Considering the uncertainty of the driving condition, a RNN-based adaptive ECMS (RNN-A-ECMS) energy management strategy is designed. The design process of RNN-A-ECMS can be divided into the offline design part and the online implementation part.

The offline design includes two parts. One is the offline training of the recurrent neural network (RNN), in which the base set of the reference SOC is first generated by the DP algorithm using historical speed profile data, and then the RNN is trained by the reference SOC from the base set, as well as road and vehicle speed information extracted from historical traffic information. The other is offline optimizing the weight factor *θ*(*t*) and the co-state of the PMP corresponding to the major component of EF *s*(*t*) using PSO, and then to establish the maps of the weight factor and the major component of the EF of A-ECMS.

In the online part, the implemented energy management control strategy includes three parts: The core ECMS with the weight factor *θ*(*t*), mapping table considering the battery life, the adaptive mechanism of EF *s*(*t*) combining the main component mapping table and a PI controller, and a well-trained RNN generating the SOC reference according to current traffic information and vehicle states. The sketch of the design process is shown in Figure 2.

**Figure 2.** The sketch of the design process of the recurrent neural network- (RNN) based adaptive equivalent consumption minimization strategy (A-ECMS).

It is worth mentioning that in the actual operation of PHEV the energy management control is not complicated and has no computing burden, but the near-global optimality can be guaranteed because of the existence of RNN and the adaptability of the equivalent factor and weighted factor.

The details of the offline design for RNN predicting the SOC reference and maps of the weight factor and the major component of EF are as follows.

#### *4.1. Prediction Model of SOC Reference of RNN*

PHEV is different from HEV with the distinguishing feature of a larger battery capacity and being recharged from the power grid. Thus, it is favorable for fuel consumption and battery health to plan ahead a reasonable reference SOC trajectory, which is obtained based on the historical data and current traffic information. More specifically, the average speed *v*¯ of current driving information, distance *D*, and the SOC of the previous step are chosen as the input of RNN. The average speed (*v*¯) is equal to the distance traveled every ten seconds of PHEV divided by the time. The SOC of the previous step is obtained by the DP optimization and historical traffic data. DP is the global optimization algorithm that can convert the continuous optimization control problem into finding an optimal decision problem for *n* segments under the known driving cycles. Therefore, by using the historical driving cycles of traffic data, the optimal SOC trajectory obtained from the optimal control sequence of DP optimization can be served as the required SOC of the previous step. At this point, the detail is as follows:

Optimization is regarded as the search for a control decision variable so as to minimize the cost function in Equation (17) while satisfying the constraint condition of Equation (16):

$$J = \sum\_{k=0}^{n-1} L\left[\mathbf{x}(k), \boldsymbol{\mu}(k), k\right] = \sum\_{k=0}^{n-1} \dot{m}\_{fucl}(k) \cdot \Delta t\_{\prime} \tag{17}$$

where *n* and *L* represent the duration of the driving cycle and instantaneous fuel consumption, respectively. Δ*t* is the increment of time step and chosen as 1s in order to alleviate the computational burden. According to the Behrman's optimal principle, the optimal control problem described as Equation (17) can be decomposed into a series of single level decision problems. The specific steps are as follows:

$$Step\ \ n - 1: J^\*\left[\mathbf{x}(n-1)\right] = \min\_{u(n-1)} \left\{ L\left[\mathbf{x}(n-1), u(n-1), n-1\right] + G\left[\mathbf{x}(n)\right] \right\},\tag{18}$$

$$\text{Step } k(0 \le k \le n-2):\\
\text{J\*}\left[\mathbf{x}(k)\right] = \min\_{\mathbf{u}(k)} \left\{ L\left[\mathbf{x}(k), \mathbf{u}(k), k\right] + J^\*\left[\mathbf{x}(k+1)\right] \right\},\tag{19}$$

where *J*∗ [*x*(*k*)] is the optimal cost of the step *k*. *x*(*k*) is the state variable SOC. *G* [*x*(*n*)] is the cost of the step *n*. The solution of DP algorithm can be divided into the backward and forward process. In the backward process, optimal control *u* of each step is solved reversely according to the Equations (18) and (19). In the forward process, the optimal control sequence solved by the backward process is substituted into the system state equation to calculate the optimal SOC trajectory, which is regarded as the base sets of training RNN prediction model.

As SOC, distance, and vehicle speed are a sequence about time, RNN is chosen as the predictive model. Although it might be difficult to learn long-term dependence due to the vanishing gradient problem resulting from the gradient propagation of the recurrent network over many layers, Long Short Term Memory (LSTM) can overcome the gradient disappearance in the basic RNN when it introduces a forgetting mechanism. Thus, LSTM can more accurately predict the SOC reference than the basic RNN.

The structure of RNN with LSTM is shown in Figure 3, where *xi* represents the input of LSTM including the average speed *v*¯*i*, distance *Di*, and the SOC of the previous step. SOC*<sup>i</sup>* is the output of LSTM representing the current SOC reference. The bottom of Figure 3 is the relationship among hidden layers which are named long and short term memory units.

The memory cell *ct* that retains data of the time step (*t* − 1) plays a important role in the LSTM model. Keeping the value or resetting the value of the cell *ct* is managed by several gates. Specially, forgetting, reading, and outputting the new cell value are decided by the forget gate (*ft*), input gate (*it*), input modulation gate (*gt*), and output gate (*ot*), which are defined as follows:

$$f\_t = \mathcal{F}\left( \left( \begin{array}{cc} w\_{hf} & w\_{xf} \end{array} \right) \cdot \left( \begin{array}{cc} h[t-1,:] \\ x[t,:] \end{array} \right) + b\_f \right),\tag{20}$$

$$\dot{\mathbf{w}}\_t = \mathcal{F}\left( \left( \begin{array}{cc} w\_{hi} & w\_{xi} \end{array} \right) \cdot \left( \begin{array}{cc} h[t-1,:] \\ x[t,:] \end{array} \right) + b\_i \right), \tag{21}$$

$$\log\_t = \tanh\left(\begin{pmatrix} w\_{\text{hy}} & w\_{\text{xg}} \end{pmatrix} \cdot \begin{pmatrix} h[t-1,:] \\ x[t,:] \end{pmatrix} + b\_{\text{jl}}\right),\tag{22}$$

$$\rho\_t = \mathcal{F}\left( \left( \begin{array}{cc} w\_{\text{ho}} & w\_{\text{xo}} \end{array} \right) \cdot \left( \begin{array}{c} h[t-1,:] \\ x[t,:] \end{array} \right) + b\_o \right). \tag{23}$$

Moreover, the calculations on the cell update and output are defined as follows:

$$\mathfrak{c}\_{t} = f\_{t} \odot \mathfrak{c}\_{t-1} + i\_{t} \odot \mathfrak{g}\_{t} \tag{24}$$

$$h\_t = o\_t \odot \tanh(c\_t),\tag{25}$$

where denotes the multiplying each element and the *w* matrices are the network important parameters. *ht* is the hidden state and employed to compute the current output and the next step hidden state. The LSTM can perfect to solve the vanishing gradients. The activation function F and tanh are the nonlinearity functions of logistic sigmoid and hyperbolic tangent, respectively.

**Figure 3.** Structure of Long Short Term Memory (LSTM).

#### *4.2. Control Parameters Optimization Based on PSO-PMP*

To improve adaptability to the changes in driving conditions, a kind of adaptive EF *s*(*t*) is selected, which can be updated by a PI controller in real-time. The specific formulation is as follows:

$$s(t) = s\_0 + \delta s = s\_0 + \left[K\_p(\text{SOC}\_{ref} - \text{SOC}) + K\_i \int\_0^t (\text{SOC}\_{ref} - \text{SOC})dt\right],\tag{26}$$

where *s*<sup>0</sup> is the initial value of equivalent factor *s*(*t*) (major component of EF) and *δs* is the tuning component of EF. SOC, SOC*ref* represent the actual SOC and the reference SOC trajectory from the RNN, respectively. *Kp*, *Ki* are proportional and integral coefficients, respectively, which are determined using the estimation method for the upper and lower bounds of the EF presented in [29] and calibration with trials similar to [13].

In order to more closely obtain the global optimal solution of the energy management control problem, the *s*<sup>0</sup> is determined by the co-state *λ*(*t*) of the PMP optimized offline by PSO. In the PMP, minimizing the objective function is converted to minimizing the Hamiltonian function:

$$H(\text{SOC}(t), u(t), \lambda(t), \theta(t)) = (1 - \theta(t)) \frac{\dot{m}\_f(t)}{\Omega} + \theta(t) \frac{\sigma(t) \cdot |I\_b(t)|}{\Lambda} + \lambda(t) \cdot \text{SOC},\tag{27}$$

where *λ*(*t*) is the co-state, and its dynamics can be described as:

$$\dot{\lambda}(t) = -\frac{\partial H(\text{SOC}(t), u(t), \lambda(t), \theta(t))}{\partial \text{SOC}}.\tag{28}$$

The optimal control trajectory is given by:

$$\mu^\* = \left[ T\_{m\prime}^\* \omega\_{\mathcal{S}}^\* \right] = \arg\min\_{u \in \mathcal{U}} H(\text{SOC}(t), u(t), \lambda(t), \theta(t)), \tag{29}$$

where the weighting factor *θ*(*t*) and the co-state *λ*(*t*) are obtained offline by PSO.

The flowchart of PSO is shown in Figure 4.

**Figure 4.** Particle swarm optimization (PSO) flowchart.

In PSO, considering the optimization time and convergence efficiency, the number of swarm *N* and the maximum iteration *km* is set as 5, 15, respectively. In order to facilitate online looking-up table, SOC is discretized as [0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9]. As the range of power demand of the studied PHEV is 0 kW to 50 kW and usually locates in 0 kW to 30 kW, power demand is discretized as [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 35, 40, 45, 50]. Thus, in the PSO algorithm, the swarm is defined as *X*<sup>1</sup> = *θswarm*, *X*<sup>2</sup> = *λswarm*, and the initialization swarm *θ*<sup>0</sup> *swarm* and *λ*<sup>0</sup> *swarm* are denoted as two [20 × 13 × *N*]-dimensional tensors. The velocities of *θswarm*, *λswarm* are *V*<sup>1</sup> and *V*<sup>2</sup> which are also two [20 × 13 × *N*]-dimensional tensors. The update principles of the velocities *V*1, *V*<sup>2</sup> and positions *X*1, *X*<sup>2</sup> during the iterations are described as follows:

$$\boldsymbol{V}\_{1i}^{k+1} = \boldsymbol{w} \boldsymbol{V}\_{1i}^{k} + \boldsymbol{c}\_{1} \boldsymbol{r}\_{1} \left(\boldsymbol{P}\_{1i}^{k} - \theta\_{\text{sum}m}^{k}\right) + \boldsymbol{c}\_{2} \boldsymbol{r}\_{2} \left(\boldsymbol{G}\_{1i}^{k} - \theta\_{\text{sum}m}^{k}\right),\tag{30}$$

$$V\_{2i}^{k+1} = wV\_{2i}^{k} + c\_1 r\_1 \left(P\_{2i}^{k} - \lambda\_{\text{swarm}}^{k}\right) + c\_2 r\_2 \left(G\_{1i}^{k} - \lambda\_{\text{swarm}}^{k}\right),\tag{31}$$
 
$$\dots \quad k \cdot 1 \qquad \dots \quad k \cdot 1 \qquad \dots \tag{31}$$

$$X\_{1i}^{k+1} = X\_{1i}^k + V\_{1i}^{k+1} \, \prime \tag{32}$$

$$X\_{2i}^{k+1} = X\_{2i}^k + V\_{2i}^{k+1},\tag{33}$$

where *i* = 1, 2, ..., *N* is the current number of swarm and *k* = 1, 2, ..., *km* is the current iteration step. *w*, *c*1, and *c*<sup>2</sup> are particle inertia and acceleration constants, respectively. *r*1,*r*<sup>2</sup> ∈ [0, 1] are uniformly distributed random values. *P*1/*P*<sup>2</sup> is the individual extremum and *G*1/*G*<sup>2</sup> is global extremum.

Figure 5 shows the optimization result of the fitness function, which can converge to a constant. The maps of *θ* and *λ* according to the battery SOC and the power demand are shown as Figure 6.

**Figure 6.** Maps of weighting factor and co-state.

From Figure 6, it can be seen that both weighting factor *θ* and co-state *λ* have a complex functional relationship with SOC and power demand. However, some qualitative conclusions can be drawn, for example, when the power demand is higher than 30 kW and SOC is less than 0.5, the weight factor has larger value. Meanwhile, when the power demand is lower than 10 kW and SOC is larger than 0.7, the co-state has a smaller value. According to the objective function defined in Equations (14) and (7), the evaluation of battery aging is more important than that of energy consumption in optimization than if the *θ* had a larger value, and then the engine would be used more. Similarly, if the co-state had a smaller value, namely, the corresponding EF was smaller, it means that the evaluation of fuel consumption would be more important than that of electrical consumption in the optimization of energy consumption, which would lead to more use of the battery-powered motor.

#### **5. Simulation Verification on GT-SUITE Test Platform**

The effectiveness of the proposed energy management strategy in this paper is demonstrated on the GT-SUITE test platform. The detail of the PHEV system with the proposed energy management control strategy in the simulation is shown in Figure 7. Where the PHEV model is established in GT-SUITE environment so as to more realistically simulate the real PHEV powertrain. The proposed energy management control strategy is constructed in MATLAB/Simulink (MathWorks, Natick, MA, USA) which computes the required torque of motor *T*∗ *<sup>m</sup>* and the required speed of generator *ω*<sup>∗</sup> *<sup>g</sup>*. Then, it can send the two control variable to PHEV in real-time. In Figure 7, the module of cost function consists of energy consumption and battery life characterized as effective Ah-throughput, which are balanced by the weight factor *θ*.

**Figure 7.** Simulation environment.

In simulation, the parameters and specifications of model components are listed in Table 1.


**Table 1.** PHEV model parameters.

Moreover, the historical traffic data used in training RNN and offline optimization of DP and PSO is from the real driving cycles provided by [30]. Then, the driving cycles, used in testing RNN and verifying the effectiveness of the online implementation of the designed energy management control strategy, are also from the historical traffic data provided by [30]. Additionally, the Urban Dynamometer Driving Schedule (UDDS) and New European Driving Cycle (NEDC) were chosen as the test driving cycles. However, it is worth pointing out that the actual traffic routes of the HEV [30] is 28 km from home to office and back from office. In research, it is assumed that the PHEV is charged once after a day's commute, namely, SOC is the maximum of 0.9 before going to work in the morning and SOC is about 0.4 after 28 km, close to the minimum 0.3. Accordingly, the distances of both UDDS and NEDC are too short to fully verify the effectiveness and practicability of the proposed control strategy, because the SOC change is too small for such a short distance. For this regard, both UDDS and NEDC are repeated up to 28 km.

Firstly, because the precision of the RNN model has a significant impact on the adaptability of the energy management strategy, the constructed RNN is verified by a comparison between the basic RNN and LSTM. The third week of traffic data not used in training is chosen as the testing set. Figure 8 shows the comparison between the two in three evaluation indexes, mean absolute error (MAE), mean radial error (MRE), and root mean square error (RMSE), which are defined as follows:

$$\text{MAE} = \frac{\sum\_{i=1}^{I} |F\_i - T\_i|}{I},\tag{34}$$

$$\text{MRE} = \frac{\sum\_{i=1}^{I} |F\_i - T\_i| / T\_i}{I},\tag{35}$$

$$\text{RMSE} = \sqrt{\frac{\sum\_{i=1}^{I} |F\_i - T\_i|^2}{I}},\tag{36}$$

where *I* is the total number of prediction point, *Fi* is the prediction value of the battery SOC, and *Ti* is the true value of the battery SOC.

**Figure 8.** Comparison of basic RNN and LSTM.

It is obvious from Figure 8 that the LSTM has better precision than the basic RNN. That is because LSTM introduces the forgetting mechanism based on the basic RNN, which can capture long-term dependencies.

To verify the applicability of the proposed strategy on a real driving cycle on the third Monday week dating from [30], Urban Dynamometer Driving Schedule (UDDS) and New European Driving Cycle (NEDC) were chosen as the test driving cycles. Meanwhile, to demonstrate the advantage of the proposed energy management control strategy in performance improvement, the comparison results among the proposed strategy (RNN-A-ECMS), the SDP-PSO energy management strategy proposed in [27], and the conventional charge depleting-charge sustaining (CD-CS) strategy are given based on the same simulation environment. In the CD-CS mode strategy, the threshold SOC switching from charge depleting (CD) to charge sustaining (CS) mode was set as 0.35 instead of the lowest value 0.3 so as to avoid excessive discharging of the battery.

Figures 9–11 show the simulation results and comparisons among the three strategies under the three driving cycles, respectively. Figure 9a–d are the operating results of the PHEV with the proposed RNN-A-ECMS strategy, where it can be seen that the actual vehicle speed profile could greatly track the reference speed profile, see Figure 9a, which guarantees the drivability due to low power demand (Figure 9b), the engine not working long (Figure 9c), and the torque and speed of engine, motor, and generator matching with the power demand of the driver and the PHEV working in pure electric mode most of the time (Figure 9d). Figure 9e–h are the comparisons on SOC trajectory, fuel consumption, effective Ah-throughput, and equivalent fuel consumption including electricity consumption. It indicates that the proposed energy management strategy had a better control performance: The actual SOC curve was closest to the reference SOC predicted by RNN (Figure 9e). Fuel consumption, effective Ah-throughput, and equivalent fuel consumption all were much lower than that of CD-CS although the effective Ah-throughput of the proposed RNN-A-ECMS was a little more than that of the

SDP-PSO, the fuel consumption of RNN-A-ECMS was much lower than that of the SDP-PSO, so that the equivalent fuel consumption of the RNN-A-ECMS was the lowest.

**Figure 9.** Simulation and comparison results under a real driving cycle.

Similar simulation results can be seen from Figures 10 and 11. Although UDDS and NEDC are not in the database used by RNN, the driveability and control performance are also satisfied in these two conditions.

**Figure 10.** Simulation and comparison results under Urban Dynamometer Driving Schedule (UDDS).

It shows that RNN with LSTM have a stronger generalization ability than the basic RNN. Moreover, the weight factor and the initial value of equivalent factor are converted into a 2-dimension

table, which can obtain the different *θ* and *s*<sup>0</sup> according to the real-time traffic information to adapt the different driving conditions and get the optimal solution and better control performance.

To further demonstrate the advantage of the proposed energy management control strategy in the performance improvement, the comparison results among the RNN-A-ECMS, the SDP-PSO [27], and the CD-CS strategy are given under multiple driving cycles.

Firstly, the simulation result in another driving cycle on the second Monday week dating from [30] is shown in Figure 12. Table 2 shows the simulation comparison results of the three strategies in the driving cycles of the workdays in the second week, which include the fuel consumption per hundred kilometers FC [L/100 km], battery *Qloss*, and final SOC SOC*fin*.

From Figure 12, it can be seen that the final SOC of the RNN-A-ECMS was 0.42 which is lower than the final SOC of the SDP-PSO strategy, which was 0.49, and the final SOC of the CD-CS strategy was always 0.35. The lower average final SOC could reflect that RNN-A-ECMS was more dependent on battery for driving than the SDP-PSO. It may lead to that the battery *Qloss* of RNN-A-ECMS was slightly higher than that of the SDP-PSO. However, the fuel consumption of the RNN-A-ECMS is greatly lower than that of the SDP-PSO because the battery is frequently involved in driving in RNN-A-ECMS. It indicates that RNN-A-ECMS sacrifices small battery loss to greatly increase fuel consumption. Without the optimization management for either fuel consumption or the battery aging in the CD-CS strategy, no matter what driving conditions the electrical power is first used to propel the vehicle until the CD-CS switching threshold value of the SOC and then engine works while retaining the threshold level of SOC, as a result, both the battery *Qloss* and the fuel consumption are the highest.


**Table 2.** Simulation comparison results.

According to the average of the second week in Table 2, it can be calculated that the fuel consumptions of the RNN-A-ECMS and the SDP-PSO were reduced by 18.1% and 14.4% compared with that of the CD-CS strategy, respectively. The battery losses of the two strategies were also reduced by 3.3% and 4.3%, respectively. Meanwhile, the fuel consumption was reduced by 4.3%, however, battery loss only sacrificed 1.03% between the two strategies. It means that the RNN-A-ECMS calculating different weight values for different SOC and power demand could be a better solution to the multi-objective optimization problem than the SDP-PSO.

**Figure 11.** Simulation and comparison results under the New European Driving Cycle (NEDC).

**Figure 12.** Comparison result between the proposed RNN-A-ECMS and the stochastic dynamic programming (SDP)-PSO strategy.

#### **6. Conclusions**

This paper proposed a novel sub-optimal and real-time energy management control strategy RNN-A-ECMS to distribute power demand between the engine and electric machines while considering the fuel consumption and battery aging. Prolonging the battery life and decreasing the fuel consumption were contradictory. Thus, the energy management strategy including battery aging should be regarded as a multi-objective optimization problem. In order to gain the Pareto optimal set, PMP and PSO were used in this paper to solve the multi-objective optimal problem offline, and the time-varying weight factor and the major component the ECMS's EF were obtained as two maps depending on power demand and SOC. In order to enhance adaptation to uncertain driving conditions, RNN with LSTM was trained offline using historically optimal SOC trajectory resulting from DP, and a PI controller was used to form the adaptive mechanism of the adaptive EF. In the implementation of the control strategy, the values of weighting factor and the major component of equivalent factor were generated online by looking up the two maps according to the current SOC of the battery and power without computational burden. Meanwhile, the equivalent factor was adjusted by the PI controller in order to make the actual SOC trajectory close to the optimal SOC trajectory, which could ensure that the real-time energy management strategy was closer to the optimal energy management strategy. The simulation verification and comparison with the existing strategy, which were implemented on GT-SUITE test platform, showed that the proposed energy management strategy in this paper possessed the effectiveness and adaptability to various driving cycles and had the advantage in compromising multi-objective of decreasing the fuel consumption and prolonging battery life.

**Author Contributions:** L.H. and X.J. conceived of and designed the framework of control methods. L.H. wrote the initial draft, drew the figures, and performed the simulations. X.J. was responsible for supervising this research and involved in exchanging ideas and reviewing the article draft. Z.Z. provided assistance with the architecture of RNN. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (Grant No. 61573304 and No. 61973265) and the Natural Science Foundation of Hebei Province (Grant No. F2017203210).

**Acknowledgments:** The authors would like to express their thanks to Yuji Yasui and Masakazu Sasaki for the vehicle speeds and battery degradation data support for this research, respectively.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature**



#### **References**


c 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Analysis of the Electric Bus Autonomy Depending on the Atmospheric Conditions**

#### **Călin Iclodean \*, Nicolae Cordos, \* and Adrian Todorut,**

Department of Automotive Engineering and Transports, Technical University of Cluj-Napoca, Cluj-Napoca 400001, Romania; adrian.todorut@auto.utcluj.ro

**\*** Correspondence: calin.iclodean@auto.utcluj.ro (C.I.); nicolae.cordos@auto.utcluj.ro (N.C.); Tel.: +40-743-600-321 (C.I.)

Received: 4 November 2019; Accepted: 27 November 2019; Published: 28 November 2019

**Abstract:** The public-transport sector represents, on a global level, a major ecological and economic concern. Improving air quality and reducing greenhouse gas (GHG) production in the urban environment can be achieved by using electric buses instead of those operating with internal combustion engines (ICE). In this paper, the energy consumption for a fleet of electric buses Solaris Urbino 12e type is analyzed, based on the experimental data taken from a number of 22 buses, which operate on a number of eight urban lines, on a route of approximately 100 km from the city of Cluj-Napoca, Romania; consumption was monitored for 12 consecutive months (July 2018–June 2019). The energy efficiency of the model for the studied electric buses depends largely on the management of the energy stored on the electric bus battery system, in relation to the characteristics of the route traveled, respectively to the atmospheric conditions during the monitored period. Based on the collected experimental data and on the technical characteristics of the electric buses, the influence of the atmospheric conditions on their energy balance was highlighted, considering the interdependence relations between the considered atmospheric conditions.

**Keywords:** electric bus; battery; energy efficiency; environmental conditions

#### **1. Introduction**

Urban public transport plays a very important role in society, as it is the current means of transport serving a significant number of people every day. The sustainable tendency of urban mobility is to transport as many people daily as possible, with ecological, nonpolluting means of transport, which will have a direct effect not only on the reduction of the greenhouse gases (GHG), but also on the reduction of the environmental noise, traffic congestion, and the infrastructure vibration due to the vehicles equipped with internal combustion engines (ICE).

Most electric vehicles adopt AC motors due to their higher reliability and longer service life. Various electric motors and batteries used in electric vehicles are still subject to research, and innovative strategies are explored to compete with thermal-engine technology [1].

Due to the tendency of the big cities agglomeration, there is a need to increase the number of buses in the public transport fleets, and if the bus fleet is not renewed with environmentally friendly, nonpolluting means of public transport, it will result an increase of the environmental pollution (chemical and acoustic) that would affect the health of the population. Also, by renewing the bus fleet park of the public transport companies, the aim is to encourage the use of the environmentally friendly, nonpolluting means of transport, to the detriment of using personal cars in urban traffic.

In [2], Grijalva et al. noted that a bus used at the nominal occupancy level could replace up to 40 personal cars from urban traffic.

Regarding the problems mentioned above, the main solution for eliminating them is to replace the classic buses equipped with ICE with silent and nonpolluting electric buses.

However, this solution has two major drawbacks: the high purchase price of an electric bus (which can be double compared to a classic bus with the same capacity [3], but which can be compensated by accessing European non-reimbursable funds [4]), respectively the autonomy of the electric bus, which depends on the capacity of the batteries that equip this bus and on the charging strategy (fast charging between buses route, respectively slow charging overnight) [5]. Because the batteries are the most expensive elements of an electric bus [6,7] and also have a considerable mass (between 1500 and 3000 kg) [8,9], the energy store in them must to be used to the maximum. The energy consumption for the electric bus varies according to a large number of parameters (the technology used in the construction of the electric bus, the experience of the driver, the traffic conditions, atmospheric conditions, the altitude profile of the route, the degree of the boarded passengers, etc.) between 1.0 and 3.5 kWh/km [10–14].

The batteries of the electric buses are recyclable, and their major advantage is the operational costs with electricity that is much cheaper than conventional fuels [3], respectively the maintenance costs that practically do not exist for a period of up to 10 years [15]. The most important feature of a battery pack is to store a maximum amount of energy in a volume and at a minimum mass, in order to ensure the maximum autonomy [16].

In [17], Demircali et al. studied a virtual model for a battery of an electric vehicle, directly dependent on the ambient temperature, showing that, with the increase or decrease of this temperature, the energy stored in the battery is changed.

The energy consumption for the electric vehicles is influenced by the atmospheric conditions, not only from the point of view of the direct influence on the storage capacity of the batteries, but also from the point of view of the increase of the energy consumption due to the supply of the auxiliary systems (heating, ventilation, and air-conditioning in the vehicle), as demonstrated by Iora et al., in [18].

In [5], Vepsäläinen et al. showed that the optimal energy consumption of an electric bus takes place at an ambient temperature of 20 ◦C. However, the studies of Qian et al. [19] showed that ambient temperature plays an important role in the battery life of an electric vehicle and, therefore, implicitly on the energy storage capacity. Thus, the increase or decrease in ambient temperature above certain thresholds lead to the more frequent use of cooling or heating, resulting in premature aging of the battery and the reduction of its storage capacity.

In different climatic zones, the ambient temperature can directly influence the efficiency of an electric vehicle, having the effect of increasing the energy consumption due to the use of air-conditioning systems for cooling or heating [10,20–25]. In [24], Yuksel et al. showed, by analyzing the energy consumption according to the ambient temperature during more than 7000 trips in six regions of the US, that the energy consumption for extreme values of the ambient temperature can be doubled (–30 ◦C to +40 ◦C), but it is kept at optimum values for a thermal regime between +17 and +27 ◦C.

Zhu et al. [26] showed that, under extreme temperature conditions (–30 ◦C to +40 ◦C), the energy efficiency of the electric bus batteries is low and, at the same time, the degradation of the battery characteristics is accelerated. These authors demonstrate the importance of the thermal management of the batteries which, regardless of the atmospheric conditions, must ensure an optimum temperature on the surface of the batteries around +30 ◦C.

The studies conducted by Jardin et al. in [27] showed that the optimum operating temperature for an electric bus based on energy consumption (kWh/km) is in the range between +20 and +25 ◦C, the maximum consumption being at low ambient temperatures.

The main objective of this work is to highlight the energy consumption and, respectively, the energy recovered for a fleet of 22 electric buses, Solaris Urbino 12e type, which operate on eight urban lines, on a route about 100 km from the city Cluj-Napoca, Romania. The consumption was monitored for 12 consecutive months (July 2018–June 2019). The temperate climate that characterizes most of the cities located in the continental area of Europe implies the existence of four seasons with extreme differences of environment temperatures (from –30 ◦C in the winter months and up to +40 ◦C in the summer months) [28–30], differences that can have a significant impact on the electric buses autonomy.

#### **2. Materials and Methods**

#### *2.1. Electric Bus Model*

#### 2.1.1. Electric Bus Model Data

Electric buses use electric propulsion based on an electric motor powered by rechargeable batteries via a voltage inverter. The battery-charging strategy involves the use of slow-charging stations (overnight), with a power of 40 kW and a full battery life between 4 and 6 hours, respectively, fast-charging stations (between races) with a power of 230 kW, and a charging time to ensure the autonomy required for a 10 to 20 minute ride [13].

The values for the main technical characteristics of the electric buses Solaris Urbino 12e model (Figure 1) that were used to carry out the study presented in this paper are listed in Table 1 [9,31].

**Figure 1.** Solaris Urbino 12e electric bus fleet (author photo).


**Table 1.** Technical characteristics of the electric buses.

#### 2.1.2. Battery Pack Data

The battery pack acts as a chemical storage unit for the electricity required to operate the motors that provide the bus propulsion. At the same time, the energy from the batteries must supply the auxiliary systems (cooling, heating, ventilation, lights, multimedia, telematics, etc.) under extreme ambient temperature values, ranging from –30 ◦C to +40 ◦C.

The basic unit of the battery pack is the cell. A number of "n" cells arranged in a series-parallel grouping form a module [32,33]. In the present case, for the studied Solaris Urbino 12e buses, the standard battery pack consists of eight modules interconnected in parallel that provide the nominal voltage of 690 Vcc at the terminals of the battery pack and which is applied as the input voltage to the system of the voltage inverter. The inverter converts the direct current (DC) voltage into a three-phase alternating current (AC) voltage (3 × 380 Vac) which supplies the electric propulsion motors. To increase the autonomy, the electric buses are powered by a system of 3 to 6 battery packs, connected in parallel, to increase the value of the current and thus of the stored energy [34].

The Li4Ti5O12 (LTO) batteries that equip the electric buses (Figure 2) are batteries with superior thermal stability, high energy storage capacity in cells, and a high lifespan (expressed through charge–discharge cycles) [9,35]. LTO batteries have the following advantages: operating safety, longevity, performance, and power density, but have a low energy density and are expensive [36].

**Figure 2.** LTO batteries that equip the Solaris Urbino 12e electric buses (author photo).

The virtual model for the basic cell of the battery pack is shown in Figure 3, and, based on this model, the electrical equations that describe the characteristics of cells, modules, and of the battery packs were formulated [34,37–42].

**Figure 3.** Equivalent circuit models (ECM) of the battery cell.

The voltage at the terminals of a cell (Ucell) is calculated with the following equation [38]:

$$\mathcal{U}\_{\rm cell} = \mathcal{U}\_{\rm occ} - I\_{\rm cell} \cdot R\_{\rm domain} - \sum\_{i=1}^{n} \frac{Q\_i}{\mathcal{C}\_i} \tag{1}$$

where Uocv (V) is the voltage of the open circuit of the open-circuit voltage cell (OCV), Icell (A) is the current at the cell terminals, Rohmic (Ω) is the internal resistance of the cell, Qi (W) is the load capacity of the cell, and Ci (F) is the capacity of the cell capacitor.

The load capacity of the cell is expressed by the following equation [38]:

$$Q\_i = \int I\_{\mathcal{C}\_i} \cdot dt = \int \left( I\_{\text{cell}} - \frac{Q\_i}{R\_i \cdot \mathcal{C}\_i} \right) \cdot dt\_\prime \tag{2}$$

where *ICi* (A) is the current through the cell capacitor, and *Ri* (Ω) is the resistance of each resistor–capacitor (RC) element of the cell.

The electrical voltage at the terminals of a battery module (Umodule) is calculated according to the number of cells connected in series (nseries), using the following relation:

$$
\mathcal{U}\_{module} = \mathcal{U}\_{\text{cell}} \cdot n\_{\text{series}}.\tag{3}
$$

The electric current at the terminals of a battery module (Imodule) is calculated according to the number of cells connected in parallel (nparallel), using the following relation:

$$I\_{module} = I\_{cell} \cdot n\_{parallel} \cdot \tag{4}$$

The state of charge (SOC) of a battery module Qmodule (%) is calculated based on the number of cells and on the charge level of each cell Qcell (%), respectively, on the number of cells connected in parallel (nparallel), using the following relation [38]:

$$Q\_{\text{module}} = Q\_{\text{cell}} \cdot \eta\_{\text{parallel}} = Q\_{\text{max}} \cdot \text{SOC} \cdot \eta\_{\text{parallel}} \tag{5}$$

where *Qmax* (%) is the maximum loading degree of each RC element of the cell.

The power of a battery module Pmodule (W) is calculated according to the number of cells and to the power of each cell Pcell (W), respectively, according to the number of cells connected in series (nseries), using the following relationship:

$$P\_{\text{module}} = P\_{\text{cell}} \cdot \mathfrak{n}\_{\text{series}} = \mathcal{U}\_{\text{cell}} \cdot I\_{\text{cell}} \cdot \mathfrak{n}\_{\text{series}}.\tag{6}$$

The lost power of a battery module (Ploss, module (W)) is calculated using the following relation:

$$P\_{\text{loss,module}} = \left(I\_{\text{cell}}^2 \cdot R\_{\text{olmicic}} + \sum\_{i=1}^{n} I\_{R\_i}^2 \cdot R\_i\right) \cdot n\_{\text{series}}.\tag{7}$$

Instant charge of the battery is given by the following relation, based on the *Coulomb-Counting* algorithm [43]:

$$Q(t) = Q\_0 - \int\_0^t I\_{batt}(t)dt,\tag{8}$$

where Q0 is the initial battery charging status, and Ibatt (A) is the current at the battery.

The SOC of the battery is expressed as a percentage of the maximum charge capacity, Qmax [43,44]:

$$SOC(t) = 100\% \cdot \frac{Q(t)}{Q\_{\text{max}}}.\tag{9}$$

*Energies* **2019**, *12*, 4535

Similarly, depth of discharge (DOD) of the battery is expressed as a percentage of total capacity consumed [43]:

$$DOD(t) = 100\% \cdot \frac{Q\_{\text{max}} - Q(t)}{Q\_{\text{max}}}.\tag{10}$$

The functional characteristic of the battery cell is shown in Figure 4, and the values of the main characteristic parameters of the battery pack that equip the electric buses are shown in Table 2 [39,45].



**Table 2.** Technical characteristics of the electric batteries.

#### 2.1.3. Electric Machine

Electric buses are powered by an electric motor, asynchronous motor (ASM) type, which operates in electric-motor mode, consuming battery power, or in generator mode, recovering the energy when descending slopes or in particular braking situations. The operating characteristic of the electric propulsion system is described by the motor torque diagram vs. speed, for all the possible traction regimes (Figure 5) [38,46,47].

**Figure 5.** Motor speed-torque diagram (traction modes).

The torque of the electric motor is maximum from the start and remains constant until it reaches a constant speed corresponding to the cruise speed. The power of the electric motor increases linearly until maximum, and then it descends simultaneously with the decrease of the motor torque (Figure 6) [48,49].

Regenerative braking involves the partial recovery of the kinetic energy and the storage of this energy in the battery to increase the range of the electric buses. During the regenerative braking, the electric motor turns into a generator and charges the batteries. The kinetic energy of the electric buses depends on their mass and speed, but only half of this energy, at most, can be recovered, and this depends on the generator's ability to produce electricity, respectively, on the battery's charging capacity [50,51].

**Figure 6.** Motor speed-torque/power characteristic.

#### *2.2. Environment Model*

#### 2.2.1. Ambient Temperature

The meteorological data regarding the temperature history for Cluj-Napoca, related to the monitored period (July 2018–June 2019), were taken from the archive of the weather station rp5.ru [52]. The average daily values for temperature were calculated as the average values for the electric buses operating at hourly intervals, from the beginning of the program (5:00 a.m.) to the end of the program (11:00 p.m.), based on daily records of variations in temperature values, obtaining the results that are presented in Figure 7.

**Figure 7.** The average daily temperature values recorded for the monitored period.

#### 2.2.2. Ambient Humidity

Similar to the temperature history (See Section 2.2.1), compared to the monitored period (July 2018–June 2019), data were taken regarding the values for the atmospheric humidity [52]. The average values for the atmospheric humidity were calculated as the average values for the electric buses operating at hourly intervals, based on daily records of the variations for the atmospheric humidity values, obtaining the results that are presented in Figure 8.

**Figure 8.** The average daily atmospheric humidity values recorded for the monitored period.

#### 2.2.3. Pressure and Air Density

Similar to the temperature history (see Section 2.2.1), compared to the monitored period (July 2018–June 2019), data were taken regarding the atmospheric pressure values [52]. The average values for the atmospheric pressure were calculated as the average values for the electric buses operating at hourly intervals, based on the daily records of the atmospheric pressure values' variations, obtaining the results that are presented in Figure 9.

**Figure 9.** The average daily atmospheric pressure values recorded for the monitored period.

The average daily air-density value (Figure 10) was calculated based on the average daily recordings of the thermal values, using the following relation [53]:

$$
\rho\_{air} = \frac{p - 0.378 \cdot \mu \cdot p\_s}{287.05 \cdot T},
\tag{11}
$$

where ρ*air* is the average daily air density (kg/m3), *p* is the average daily atmospheric pressure (Pa), u is the average daily relative humidity (-), ps is the saturation pressure (Pa), and T is the absolute temperature (K) relative to the average daily ambient temperature (T (K) = t (◦C) + 273.15).

The saturation pressure was calculated using the following relation [54]:

$$p\_{\mathfrak{s}} = \frac{e^{(77.3450 + 0.0057 \cdot T - \frac{72.35}{T})}}{T^{8.2}}.\tag{12}$$

**Figure 10.** The calculated average daily air density values for the monitored period.

#### *2.3. Energy Balance*

#### 2.3.1. Energy Consumption

The energy consumption of the electric buses is influenced by a number of factors, such as: increasing the total mass of buses by loading the passengers, the consumption generated by the auxiliary systems that cause a significant increase in the amount of energy consumed by the batteries (air conditioner equipment, multimedia equipment, lighting equipment, telematics equipment, auxiliary equipment), some of these factors being not dependent on the distance traveled by the electric buses [55–57]. At the same time, the altitude profile of the route can influence the energy consumption. This increases during periods of acceleration or ascent of the ramps and decreases when descending the slopes or when the bus decelerates, reaching negative values (the energy is transferred from the electric motor that works in generator mode, to the battery). The data collected for the monitored period (July 2018–June 2019) showed an average daily distance traveled between 100 km (one driver/electric bus) and 200 km (two drivers/one electric bus).

In addition to these factors, there are climatic parameters (ambient temperature, atmospheric humidity, air pressure, and density) that have a major influence on the energy consumption of the electric buses. The experimental data recorded during the monitored period include the atmospheric conditions characteristic for all seasons with extreme values during a calendar year (ambient temperatures between –15 ◦C in January 2019 and +32 ◦C in August 2018, respectively humidity values between 14% in November 2018 and 100% in most months of the year).

Yuan et al. in [58], consider that it is difficult to obtain real traffic data on the energy consumption for electric buses, and standards for defining this consumption and registration procedures are used to evaluate the energy consumption (ISO 8714-2002 Electric road vehicles—Reference energy consumption and range—Test procedures for passenger cars and light commercial vehicles [59], respectively, GB 18386-2017 Electric vehicles—Energy consumption and range—Test procedures [60]).

In this paper, the data on the energy consumption were recorded by real-time monitoring of bus operation in the city of Cluj-Napoca, which is achieved through the system of tracking and monitoring the traffic Thoreb [61], a system that allows the observation of buses in real-time by monitoring on a digital map based on the signals generated by the Global Positioning System (GPS) modules installed on the buses and transmitted to the dispatchers using the General Packet Radio Service (GPRS) technology. At the same time, from the bus controller area network (CAN), data regarding the technical status of the buses, the distance traveled, the energy consumption, the number of passengers transported, etc. are collected and sent to the dispatchers [13].

The evaluation of the energy consumption data on the electric buses for the monitored period (July 2018–June 2019) was performed with a Boxplot graph (Figure 11 and Table 3) which, based on the initial data, generates a statistical model for each monitored month.

**Figure 11.** Boxplot analysis of energy consumption (kWh/km).


**Table 3.** Boxplot analysis of energy consumption (kWh/km).

#### 2.3.2. Regenerative Braking Energy

Similar to the energy consumption of the electric buses, the energy recovered through the regenerative braking was recorded for the monitored period (July 2018–June 2019).

The evaluation of the data regarding the energy recovered by the regenerative braking of the electric buses for the monitored period was performed with a Boxplot graph (Figure 12 and Table 4) which, based on the initial data, generates a statistical model for each monitored month.

**Figure 12.** Amount of the energy recovered by regenerative braking (kWh/km).


**Table 4.** Amount of the energy recovered by regenerative braking (kWh/km).

#### 2.3.3. Total Energy Balance

The energy balance recorded during the monitored period (July 2018–June 2019) for the Solaris Urbino 12e electric buses, depending on the atmospheric conditions (ambient temperature, atmospheric humidity, air pressure, and density) is shown in Table 5 and Figure 13.



**Figure 13.** The energy balance of the Solaris Urbino 12e electric bus.

#### **3. Results**

As the costs associated with the integration into the urban transport system of the electric buses are high, it is necessary to carry out studies and research in order to provide the best solution in relation to their optimal use, taking into account the particularities imposed by the zoning characteristics (length and the gradient of routes, the flow of the transported passengers, the loading infrastructure, the volume of traffic, the characteristics of the environment, etc.).

The study of the energy performances for the 22 electric buses during the monitored period (July 2018–June 2019) highlighted their behavior at different values of the climatic parameters (temperature, humidity, atmospheric pressure, and air density).

The climatic parameters were monitored during a calendar year and give a clear picture regarding the atmospheric conditions and their influence on the energy consumption, respectively, on the energy recovery during the operation of the electric buses.

The parameters resulting from the behavior of the driver are invariable, difficult to estimate and impossible to generalize because they are psychological factors specific to each individual. However, taking into account the data on variations in atmospheric pressure and air density, there is the possibility to correlate human behavior with these variations, so that in the situation of increasing these values, the behavior of drivers becomes more active, and in the situation of decreasing these values, behavior becomes more passive.

From the results captured in Table 5 and in Figure 13, the average annual values of the climatic parameters can be obtained, as follows: the average annual temperature, 11.6916 ◦C; the average annual humidity, 75.3083%; the average annual atmospheric pressure, 726.6333 Torr; average annual energy consumption of 1.3716 kWh/km; average annual energy recovery, of 0.4016 kWh/km. Taking these into account, in Figures 14–18 the variations of the respective parameters are presented, as monthly average values obtained, compared with their annual average values.

**Figure 14.** Monthly average temperature variation vs. average annual temperature.

**Figure 15.** Monthly average humidity variation vs. average annual humidity.

**Figure 16.** Monthly average atmospheric pressure variation vs. average annual atmospheric pressure.

**Figure 17.** Variation of average monthly energy consumption vs. average annual energy consumption.

**Figure 18.** Variation of average monthly energy recovery vs. annual average energy recovery.

A summary of the obtained results, as the interdependence between them and the influence parameters on them, is captured in Figure 19. Thus, for each considered month from the monitored period (July 2018–June 2019), the influence of the atmospheric conditions on the energy efficiency of the studied electric buses was highlighted. Also, for each considered month, the reciprocal link between temperature, humidity, atmospheric pressure, and air density is captured in Figure 19. Thus, it was found that with the increase of the temperature, there is a reduction in air density, a slight decrease in atmospheric pressure, and the recorded humidity showed a reduce tendency. The recorded values of the humidity show that, with its increase, the air density increases, and the atmospheric pressure is reduced. It also notes that the increase in pressure indicates an increase in air density.

Regarding the energy consumption of the electric buses, it can be seen that it increases with decreasing the temperature and the atmospheric pressure, but the same tendency exists in the situation of increasing the air humidity and the air density (Table 6 and Figure 19). The energy recovered by the regenerative braking of the electric buses increases with the increase of the temperature and decreases with the increase of the air humidity, air density, and atmospheric pressure. Also, it can be seen that energy recovery largely compensates for the energy consumption of the electric buses.


**Table 6.** Data for energy consumption and energy recovery vs. atmospheric conditions.

**Figure 19.** Matrix scatter plot.

#### **4. Discussion**

In the summer months (July 2018, August 2018, and June 2019), it resulted in high energy consumption compared to the average monthly values, due to the use of the air-conditioning system, when the ambient temperature exceeded 30 ◦C. This temperature threshold was imposed from the construction of the electric buses and results in the automatic operation of the air-conditioning until the ambient temperature in the passenger compartment drops below 25 ◦C. Regarding the recovered energy, an increase of it with the increase of the ambient temperature was noticed, under the conditions of maintaining low values of the atmospheric humidity, which facilitates the braking capacities of the electric buses on a dry road, respectively the increase of the electrical resistance of the braking system, preventing the energy losses through braking rheostats. In the summer months, characterized by the average monthly temperature values (see Table 5) higher than the annual average, with 79.61% in July 2018, 79.61% in August 2018, and 98.43% in June 2019 (see Figure 14), the atmospheric humidity is higher than the annual average by 0.25% in July 2018, lower by 9.57% in August 2018, and with 9.31% in June 2019 (see Figure 15), and the atmospheric pressure is lower than the annual average by 0.39% in July 2018, higher by 0.09% in August 2018, and with 0.04% in June 2019 (see Figure 16), resulting in lower energy consumption compared to the average annual consumption, by 17.62% in July 2018, 15.43% in August 2018, and 3.04% in June 2019 (see Figure 17), and a higher amount of energy recovered compared to its annual average, with 7.05% in July 2018, 21.99% in June 2019, and lower by 0.41% in August 2018 (see Figure 18).

From the recorded results, it can be seen that the autumn months (September 2018 and October 2018) are the months with low energy consumption, mainly due to the thermal conditions, with values of temperature of approx. 20 ◦C, but also with low values of the atmospheric humidity, being generally dry weather, which facilitates the movement of the electric buses with a minimum of energy consumed and a maximum recovered energy. During these months, the monthly average temperatures (see

Table 5) were higher than the annual average, with 59.09% in September 2018 and with 14.61% in October 2018 (see Figure 14), with lower atmospheric humidity compared to that annual average with 11.69% in September 2018 and with 7.58% in October 2018 (see Figure 15), and the atmospheric pressure higher than the annual average, with 0.28% in September 2018 and with 0.33% in October 2018 (see Figure 16), resulted in a lower energy consumption than the average annual consumption, with 21.99% in September 2018 and with 5.43% in October 2018 (see Figure 17), and a higher amount of energy recovered compared to its annual average, with 4.56% in September 2018 and with 7.05% in October 2018 (see Figure 18).

Since November 2018, the cold season has started, which, due to the decrease of the ambient temperature, especially in the time periods from the beginning of the work program (from 5:00 a.m. to 8:00 a.m.), respectively in the periods after the end of the work program (from 8:00 p.m. to 11:00 p.m.), resulted in an accelerated increase of the average energy consumption. Due to the increase of the atmospheric humidity and the reduction of the grip due to the wet road, the value of the recovered energy decreased. November 2018 was characterized by monthly average values of the temperature lower than the annual average value with 57.23% (see Figure 14), the atmospheric humidity higher than the annual average with 12.47% (see Figure 15), and the atmospheric pressure compared to the annual average by 0.50% higher (see Figure 16), resulted a higher energy consumption than the average annual consumption, by 5.71% (see Figure 17), and a lower amount of recovered energy compared to its annual average, with 5.39% (see Figure 18).

The winter months (December 2018 and January 2019) were the months with the lowest temperatures in the entire monitored period. In addition to the negative temperatures of the day, the start of the working program for the electric buses took place below the freezing threshold. Electric buses, which are connected overnight to the external slow-charging stations, and the batteries are heated by the thermal management system, consume, on the cold winter days (with temperatures below −10 ◦C) up to 10% of the energy from the batteries, for heating the interior passenger compartment, only in the interval of preparation for the buses' departure on the route. Thus, combined with the increased of the daily consumption and the wet road conditions, it is reached that, during the cold season, the consumption increase by 2 to 2.5 times compared to the periods with the lowest values of consumption, and the energy values recovered will near zero. During these months, the monthly average temperatures (see Table 5) were lower than the annual average by 101.71% in December 2018 and by 106.84% in January 2019 (see Figure 14), the humidity was higher than the annual average with 27.34% in December 2018 and with 25.75% in January 2019 (see Figure 15), and the atmospheric pressure was higher than the annual average, with 0.28% in December 2018 and lower, with 0.71% in January 2019 (see Figure 16). The result was a higher energy consumption than the average annual consumption, with 29.77% in December 2018 and 38.52% in January 2019 (see Figure 17), and a reduced amount of energy recovery compared to its annual average, by 27.80% in December 2018 and by 25.31% in January 2019 (see Figure 18).

The transition from extremely low winter temperatures to thermal relaxation took place in February 2019, which started with low temperatures, especially in the early morning, but also with a slight increase in temperatures in the second half of the day, which have to lead to a reduction in energy consumption. Due to low values of the atmospheric humidity and the lack of precipitation, respectively, on a dry road, the amount of energy recovered during this period also increased. February 2019 was characterized by monthly average values of the temperature lower than the annual average value by 81.18% (see Figure 14), the atmospheric humidity higher than the annual average by 6.76% (see Figure 15), and the atmospheric pressure compared to the annual average higher with 0.44% (see Figure 16). In February it resulted in higher energy consumption than the average annual consumption, with 16.65% (see Figure 17), and a reduced of the energy recovery compared to its annual average, with 25.31% (see Figure 18).

The spring months (March 2019 and April 2019) began with accelerated warming of the weather, with the reduction of the atmospheric humidity, environmental aspects that led to the gradual reduction

of the energy consumption to normal values and to the increased of the energy recovery. Even though, during the two months, the mornings were colder, with temperatures around 0 ◦C, the thermal regime did not influence the electric bus batteries when the buses started on the route. During these months, the monthly average temperatures (see Table 5) were lower than the annual average by 29.86% in March 2019 and higher by 0.93% in April 2019 (see Figure 14), with lower atmospheric humidity compared to the annual average, with 17.41% in March 2019 and with 20.99% in April 2019 (see Figure 15), and the atmospheric pressure was lower than the annual average, with 0.06% in March 2019 and with 0.20% in April 2019 (see Figure 16), and it resulted in lower energy consumption compared to the average annual consumption, with 5.22% in each of the two months (see Figure 17), and a reduced amount of energy compared to its annual average by 0.41% in March 2019 and by 19.50% higher in April 2019 (see Figure 18).

The transition to the hot season at summer temperatures began in May 2019, a month characterized by positive thermal values throughout the operating range of the electric buses, respectively by the average values of the atmospheric humidity. These climatic factors allowed us to achieve average energy consumption within the normal limits specified by the manufacturer, cumulating with maximum energy recovery for the entire monitored interval. May 2019 was characterized by monthly average values of the temperature higher than the annual average value, with 29.15% (see Figure 14), the atmospheric humidity higher than the annual average by 3.97% (see Figure 15), and the atmospheric pressure lower than the annual average by 0.61% (see Figure 16). In May, it resulted in lower energy consumption than the average annual consumption, by 6.68% (see Figure 17), and an amount of recovered energy higher than its annual average, with 24.48% (see Figure 18).

#### **5. Conclusions**

The energy efficiency of the electric buses was evaluated for 12 consecutive months (July 2018–June 2019), based on the weather conditions in Cluj-Napoca city, Romania, conditions that are specific to the vast majority of continental Europe, taking into account other area features, such as the loading infrastructure, traffic conditions, altitude profile of the traveled routes, the degree of loading with passengers, and the traffic management.

Based on our findings, the following conclusions can be drawn:


The authors intend to develop various models to describe other influences on the energy balance of the electric buses, to use them in their modeling, simulation, and exploitation. In addition, based on the collected experimental data and on the technical characteristics of the real model of the electric buses, the authors have already highlighted, with promising results, the influence of the atmospheric conditions on their energy balance, taking into account the interdependence of the climatic parameters (ambient temperature, atmospheric humidity, air pressure, and air density).

**Author Contributions:** The authors have contributed equally to this article.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors wish to thank CTP Cluj-Napoca SA for providing the data from the Opportunity Studies.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Lithium-Ion Polymer Battery for 12-Voltage Applications: Experiment, Modelling, and Validation**

#### **Yiqun Liu, Y. Gene Liao \* and Ming-Chia Lai**

Mechanical Engineering, Electric-drive Vehicle Engineering, Wayne State University, Detroit, MI 48202, USA; yiqun.liu@wayne.edu (Y.L.); mclai@wayne.edu (M.-C.L.)

**\*** Correspondence: geneliao@wayne.edu

Received: 12 January 2020; Accepted: 27 January 2020; Published: 3 February 2020

**Abstract:** Modelling, simulation, and validation of the 12-volt battery pack using a 20 Ah lithium–nickel–manganese–cobalt–oxide cell is presented in this paper. The cell characteristics influenced by thermal effects are also considered in the modelling. The parameters normalized directly from a single cell experiment are foundations of the model. This approach provides a systematic integration of actual cell monitoring with a module model that contains four cells connected in series. The validated battery module model then is utilized to form a high fidelity 80 Ah 12-volt battery pack with 14.4 V nominal voltage. The battery cell thermal effectiveness and battery module management system functions are constructed in the MATLAB/Simulink platform. The experimental tests are carried out in an industry-scale setup with cycler unit, temperature control chamber, and computer-controlled software for battery testing. As the 12-volt lithium-ion battery packs might be ready for mainstream adoption in automotive starting–lighting–ignition (SLI), stop–start engine idling elimination, and stationary energy storage applications, this paper investigates the influence of ambient temperature and charging/discharging currents on the battery performance in terms of discharging voltage and usable capacity. The proposed simulation model provides design guidelines for lithium-ion polymer batteries in electrified vehicles and stationary electric energy storage applications.

**Keywords:** battery modelling and simulation; battery testing cycler; battery thermal model; lithium-ion polymer battery; SLI battery

#### **1. Introduction**

Lead–acid-based batteries have a long-term historical usage in the automotive and stationary standby power market, ranging from 12-volt high-power such as automotive starting–lighting–ignition (SLI) applications, low-power applications such as emergency lighting or uninterruptible power supplies (UPSs) for individual computers, to high-power, high-voltage electric energy storage in renewable energy systems or UPSs telecommunications facilities. Typical lead–acid batteries have several problems including high self-discharge rate, relatively heavy and large, and shallow depth of discharge (DOD). For the past decades, lithium-ion batteries have been widely used in portable electronics due to their features of high energy density, high discharge power, and long cycle life. The emerging applications of the lithium-ion batteries to electric-drive vehicles and large-scale energy storage systems for renewable energy make them a promising solution for challenges of environmental preservation and resource conservation [1,2]. The lithium-ion battery is also a suitable replacement for the conventional 12-volt SLI lead–acid battery; for example, Porsche offers an option of a lithium-ion SLI battery [3], and some medium-duty truck manufacturers use a lithium-ion battery for 12/24 V electrical systems [4,5]. The lithium-ion polymer battery uses a high conductivity semisolid (gel) polymer electrolyte instead of a liquid electrolyte. The battery cell voltage depends on the electrode material

chemistries. The lithium–metal–oxide-based (such as LiCoO2) cell has 2.5–2.8 V fully discharged voltage and 4.2 V fully charged voltage, while the lithium–iron–phosphate-based (such as LiFePO4) cell has 1.8–2.0 V fully discharged voltage and 3.6–3.8 V fully charged [6,7]. The lithium polymer battery has higher specific energy than do other lithium-based batteries [6]. The polymer electrolyte gives the lithium polymer battery more stable performance under vibration conditions. These two features have led to the promotion of lithium polymer batteries in electric-drive vehicle applications.

The lithium-ion batteries, however, still encounter some roadblocks that complicate their applications. One of the major roadblocks is temperature influence on the operation of lithium-ion batteries. The operating temperature of a battery is the result of ambient temperature augmented by the heat generated by an electrochemical reaction. Operating temperatures from −20 ◦C to 60 ◦C is a typically acceptable range for lithium-ion batteries [8]. Pesaran et al. [9] presented that the optimal temperature range for lithium-ion batteries is from 15 ◦C to 35 ◦C, which is similarly comfortable for humans. To avoid a severe temperature gradient that might lead to different degradation rates and unbalanced cells, 5 ◦C should be set as the maximum temperature difference from cell to cell within a module [9,10]. The impacts of temperature can generally be considered as low and high temperature effects [11]. At low operating temperatures, the lithium-ion batteries experience slow chemical reaction and charged transfer-rate, which decrease ionic conductivity and diffusivity [12,13]. Therefore, the battery energy capacity and power are reduced at low temperatures. At high temperatures, the energy capacity and power are degraded, respectively, due to loss of the reduction of active materials and increase of internal resistance [14]. Self-ignition and even explosion caused by thermal runaway may happen if the temperature is too high. The effects caused by low battery temperature mostly occur during low ambient temperatures, while the effects induced by high battery temperature could occur either in low or high ambient temperatures. For an example, the battery temperature could highly increase at a large discharging current even in a low ambient temperature environment. The ambient temperature dominates in low temperature effects, and the battery internal temperature during operations plays a more important (than ambient temperature) role in high temperature effects.

The battery cell characteristics are determined by the electrode materials, electrolyte materials, cell size and shape, as well as the operating conditions including temperature, charging, discharging current, etc. The cell characteristics are essential parameters in battery pack design, thermal management system design, and battery management control. The battery cell characteristics typically are acquired through a series of charging and discharging experimental tests, which are time-consuming and require several pieces of equipment, such as a cycler, temperature chamber, and device for data acquisition. Analytical approach uses certain numbers of cell parameters gathered from less experimental tests to form a mathematical model. The battery model is also helpful for predicting parameters that cannot be directly measured by any sensors, such as state of charge (SOC), state of health (SOH), and state of life (SOL). Model-based estimation algorithms are usually used to compute or estimate theses parameters [15,16]. Nevertheless, a high-fidelity battery model is required to obtain accurate simulation results. Many battery models have been developed ranging from simple models with a few parameters to complex models having a large number of parameters [17–27]. The common battery modelling approaches are electrochemical, mathematical or analytical, and electric circuit-based model [28,29].

This paper describes the development and validation of an electric circuit-based Simulink model of the lithium–nickel–manganese–cobalt–oxide (LiNiMnCoO2)-based cell with 3.6 V nominal voltage and 20 Ah capacity. The thermal effects on cell characteristics are also considered in the model. The experiments apply several charging and discharging currents to the battery cell and module that are enclosed in a chamber with controlled temperatures of −20 ◦C, −10 ◦C, 0 ◦C, 20 ◦C, and 50 ◦C as the ambient temperatures. The experimental data are used to calibrate the model parameters. A 12-volt battery pack (14.4 V, 80 Ah) model is built based on validated simulation models of a battery cell and module. This SLI-type pack has four parallel-connected modules where each module (14.4 V, 20 Ah) consists of four cells connected in series. As the 12-volt lithium-ion battery packs might be ready for mainstream adoption in automotive SLI, micro-hybrid (or stop–start engine idling elimination), and

UPS applications, this paper investigates the ambient temperature effect on the battery performance in terms of discharging voltage and usable capacity. The proposed simulation model provides design guidelines for lithium-ion polymer batteries in electric-drive vehicle and stationary UPS applications.

#### **2. Battery Modelling from Cell to Pack**

A high-fidelity single cell model is a foundation to form a reliable battery module and pack with statistical confidence. The equivalent circuit technique is commonly used for electrochemical impedance characterizations in a cell model. This study uses parameters normalized directly from single cell experiments, which provide a systematic integration of actual cell monitoring with a module model. The approach begins with single cell model development and validation. A module with four cells connected in series is also validated. A high fidelity SLI battery pack model is then achieved.

#### *2.1. An Enhanced Equivalent Electric Circuit Cell Model*

The equivalent electric circuit approach has been adopted by many researchers to model battery cells ranging from lead–acid to lithium-ion batteries. The most commonly used equivalent electric circuit models are the Thevenin-based model [17–19], impedance-based model [20–22], and the runtime-based model [23,24]. The Thevenin-based model can predict battery response to the transient load at a certain SOC due to a series resistor and resistor–capacitor parallel network in the model. An impedance-based model is formed by an AC-equivalent impedance model in the frequency domain and the electrochemical impedance spectroscopy method. The runtime-based model utilizes a capacitor and controllable current source to predict battery capacity, SOC, runtime, and open circuit voltage (OCV). The battery operation time and DC voltage response under a constant discharge C-rate also can be simulated by the runtime-based model. The advantages of the runtime-based model and Thevenin-based model are combined in a model presented by [26], as shown in Figure 1. Based on [27], an equivalent electric circuit model with improved features is presented in this paper. In the developed Simulink model shown in Figure 2, three inputs (discharging current, initial SOC ranging from 0 to 1, and battery capacity) replace the battery runtime model. Since the initial SOC is an input variable, the developed model can simulate batteries that are not fully-charged. The OCV is calculated according to real-time SOC, which is predicted from three inputs to the model. Subtracting both voltages of the resistor-capacitor (RC) parallel networks and series resistor (*RS*) from the OCV gives the cell terminal voltage (Vt), which is an output of the developed model. The real-time SOC, OCV, RC value, RC parallel network voltages, and series resistor voltage are calculated by five developed submodels.

**Figure 1.** Thevenin with runtime-based model.

**Figure 2.** Developed cell model with three inputs.

Equation (1) calculates the real-time SOC, in which SOC0 denotes the initial SOC, *I* denotes the discharging current, and *UC* denotes the usable capacity. A submodel calculating SOC is presented in Figure 3a, in which three inputs are *SOC0*, *I*, and *UC* and output is real time SOC. Equation (2) is derived from numbers of experimental discharging curves using the method presented in [26] that provides relationship between the SOC and OCV. The interpolation–extrapolation lookup method is applied to calculate and determine the most suitable RC values, as a submodel presented in Figure 3b. The transient response of the battery cell voltage in the developed model is computed by the voltages of RC parallel networks. Equation (3) calculates the voltages of RC parallel networks in the s-domain, as a submodel shown in Figure 3c. For a typical lithium–metal–oxide polymer cell, the series resistor is 0–0.01 ohms in the 20%–100% SOC range, and 0.01–0.06 ohms within the 0%–20% SOC range [26]. Therefore, the developed model uses 0.001 ohms for 20%–100% SOC and 0.03 ohms for 0%–20% SOC in all discharging currents. The voltage on the series resistor (*VS*) is calculated by Equation (4) where *RS* is the series resistor resistance, and a submodel is presented in the Figure 3d. Equation (5) calculates the terminal voltage (*Vt*) of the battery cell. A more detail description of the submodels and their paraments is presented in [30].

$$\text{SOC} = \text{SOC}\_0 - \int \frac{\text{I}}{\text{UC} \times 3600} \text{dt} \tag{1}$$

$$\text{OCV} = -1.031 \text{e}^{-25 \times \text{SOC}} + 3.685 + 0.2156 \times \text{SOC} - 0.1178 \times \text{SOC}^2 + 0.3201 \times \text{SOC}^3 \tag{2}$$

$$\mathbf{V} = \left(\frac{1}{\mathbf{s}}\right) \left[\frac{\mathbf{I}}{\mathbf{C}} - \frac{\mathbf{V}}{\mathbf{R}\mathbf{C}}\right] \tag{3}$$

$$\mathbf{V\_{S}} = \mathbf{I} \times \mathbf{R\_{S}} \tag{4}$$

$$\mathbf{V\_{t}} = \mathbf{OCV} - \mathbf{V\_{1}} - \mathbf{V\_{2}} - \mathbf{V\_{S}} \tag{5}$$

**Figure 3.** Simulink submodels for developed cell model: (**a**) Calculation of R and C value; (**b**) Calculation of SOG; (**c**) Calculation of RC parallel voltage; (**d**) Calculation of *VS*.

#### *2.2. Cell Thermal Model*

The lithium-ion polymer cell thermal model was built in the Simulink battery block platform, which implemented similar equations as those discussed in Section 2.1 with thermal effects. In the discharge model (i∗ > 0), Equations (6)–(11) are implemented to represent the temperature effect on the battery model parameters [31]. The temperature tab requires several parameters, which are determined by battery discharging test under 20 ◦C ambient temperature. The initial cell temperature is set to the ambient temperature because each cell is cooled down or warmed up to the ambient temperature before starting the discharging test. The "nominal ambient temperature T1 (◦C)" parameter is the ambient temperature during nominal operations. It is assumed that all parameters in the parameters tab are obtained at 20 ◦C ambient temperature. The procedures of establishing the cell thermal model in the Simulink platform are presented in [32]. Figure 4 shows the Simulink battery cell discharging model considering ambient temperature effects.

$$\text{rf}\_1(\text{it}, \text{i}\*, \text{i}\_\text{,} \text{T}, \text{T}\_\text{a}) = \text{E}\_0(\text{T}) - \text{K}(\text{T}) \cdot \frac{\text{Q}(\text{T}\_\text{a})}{\text{Q}(\text{T}\_\text{a}) - \text{it}} \cdot (\text{i}\* + \text{it}) + \text{A} \cdot \exp(-\text{B} \cdot \text{it}) - \text{C} \cdot \text{it} \tag{6}$$

$$\mathbf{V\_{batt}(T) = f\_1(\text{it}, \ \mathbf{i} \ast \ \mathbf{i} \text{, } \ \mathbf{T} \ \ \ \ \ \mathbf{T\_a}) - \mathbf{R(T)} \cdot \mathbf{i} \tag{7}$$

$$\mathrm{E}\_{\mathrm{0}}(\mathrm{T}) = \mathrm{E}\_{\mathrm{0}} \Big|\_{\mathrm{T}\_{\mathrm{ref}}} + \frac{\partial \mathrm{E}}{\partial \mathrm{T}} (\mathrm{T} - \mathrm{T}\_{\mathrm{ref}}) \tag{8}$$

$$\mathbf{K}(\mathbf{T}) = \mathbf{K} \Big|\_{\mathbf{T}\_{\text{ref}}} \cdot \exp\left[\alpha \left(\frac{1}{\mathbf{T}} - \frac{1}{\mathbf{T}\_{\text{ref}}}\right)\right] \tag{9}$$

$$\mathbf{Q(T\_a)} = \mathbf{Q} \Big|\_{\mathbf{T\_a}} + \frac{\Delta \mathbf{Q}}{\Delta \mathbf{T}} \cdot (\mathbf{T\_a} - \mathbf{T\_{ref}}) \tag{10}$$

$$\mathcal{R}(\mathbf{T}) = \mathcal{R}\Big|\_{\mathbf{T}\_{\rm ref}} \cdot \exp\left[\beta\left(\frac{1}{\mathbf{T}} - \frac{1}{T\_{\rm ref}}\right)\right] \tag{11}$$

where: Tref (K) nominal ambient temperature, T (K) cell or internal temperature, Ta (K) ambient temperature, E/T (V/K) reversible voltage temperature coefficient, α Arrhenius rate constant for the polarization resistance, β Arrhenius rate constant for the internal resistance, (Ah/K) maximum capacity temperature coefficient, CΔQ/ΔT (V/Ah) nominal discharge curve slope.

**Figure 4.** Battery cell thermal model in Simulink.

#### *2.3. Battery Module and Pack Model*

A battery module model containing four cells connected in series was created in the Simulink platform, as shown in Figure 5. The controlled current source, four battery cells, breakers with control algorithms to perform the battery management system (BMS) function, and voltage measurement with scopes are the four submodels in the module model. The charging and discharging current to each cell model are generated by the controlled current source sub-model, which has two parameters, namely DC source type and zero initial amplitude (A). The controlled current source block is connected to a constant block for generating a continuously constant charging or discharging current. A value in the constant block is the constant charging/discharging current. The pulse generator block is applied to generate a pulse charging/discharging current. Cell breaker, bypass breaker, cell voltage tag, and cell control tag form a BMS submodel for each cell. When the cell is charged to a voltage higher than 4.3 V or discharged to a voltage lower than 2.3 V, the control tag opens the cell breaker and closes the bypass breaker to prevent the cell from becoming over-charged or over-discharged. Each submodel contains one pair of tags for the breakers. Figure 5 shows only one pair of tags for a better display. Each cell voltage curve is shown in its scope and a terminal voltage is displayed in total voltage scope. All the parameters in this model are determined from the continuous and pulse discharge tests. A more detail description of the submodels and their paraments is presented in [33].

**Figure 5.** A Simulink battery module model consisting of four series-connected cells.

#### **3. Experiment and Model Validation**

The lithium-ion polymer cells used in this study were EiG ePLB C020 lithium–nickel–manganese–cobalt–oxide-based cathode and graphite-based anode with 3.6 V nominal voltage and 20 Ah capacity. Figure 6 shows the test equipment using in this study, namely a Digatron charge/discharge cycler, a computer with Digatron Battery Manager 4 (BM4) software (Battery Manager 4.0, Digatron Power Electronics Inc., Shelton, CT, USA) [34], and an Envirotronics temperature chamber. A fixture was designed to restrain the battery cells and cycler output cables inside the chamber. Three experimental procedures included calibration of battery cell model parameters, validation of the four series-connected battery module, and validation of the battery cell thermal model.

**Figure 6.** Battery experimental test setup: (**a**) Cycler and chamber; (**b**) cell testing; (**c**) module testing.

#### *3.1. Battery Cell Model Calibration and Validation*

An initial battery performance evaluation test was conducted on 27 cells disassembled from a hybrid electric vehicle battery pack. Each cell was charged to 4.17 V and then fully discharged to 2.46 V using 1 C rate in the initial evaluation test. The cell model parameter determination, correlation, and validation utilized six cells with best performance in the initial evaluation test. Figure 7a shows an experimental curve generated by averaging curve data for each testing case (1/3, 1/2, 1, 1.5, and 2 C discharging current). These tests were used to calibrate the cell model parameters. The determination of cell model parameters is presented in [30]. Examples of simulated and experimental discharging curves are shown in Figure 7b. A 7% or less discrepancy between simulations and experiments existed in the 0% to 80% DOD range during constant current discharge.

**Figure 7.** Examples of simulated and experimental discharging curves: (**a**) Averaged constant current discharging curves from tests; (**b**) simulated and test constant current discharging curves; (**c**) simulated and test constant current discharging curves; (**d**) simulated and test pulse discharging.

#### *3.2. Cell Thermal Experiment and Validation*

To ensure the battery cell completely cooled down or warmed up to a specific ambient temperature, the battery cell was kept charging by a small current to sustain its voltage in the neighbor of 4.17 V. The temperature chamber was then set to a specific temperature for 15 minutes before applying the discharging current. The validation process consisted of 12 discharging tests, which were 10 A, 20 A, and 40 A constant discharging currents, and each discharging test was conducted under 4 different ambient temperatures (−20, −10, 0, 20, and 50◦C). The simulated discharging curves from each discharging current with specified ambient temperature were compared to corresponding experimental discharging curves. Examples of comparisons between simulated and experimental discharging curves using constant currents, 10 A, 20 A, and 40 A, under four different ambient temperatures are shown in Figure 8. A full comparison results is shown in [32]. In each discharging test, the experimental and the simulated discharging curves matched well in the range from 0% to 80% DOD (assuming 100% DOD at 2.5 V). The discrepancy between each comparison was under 7%. From the range of 80% to 100% DOD, the discrepancy became much larger. This large discrepancy might be due to the fact that battery model parameters were acquired in the nominal voltage of 3.6 V. The accuracy of the model was acceptable because most of the batteries only used up to 80% DOD. The experimental and simulated discharging time to reach 2.5 V were correlated in most test cases. Under higher ambient temperature (50 ◦C), the battery usable capacity increased so the total discharging time was longer than 1 hour for the one C-rate (20 A) discharging test. A similar phenomenon occurred in the one-half C-rate (10 A) test, which showed more than two hours discharging time. However, the Simulink model could not simulate the increase of battery usable capacity under high ambient temperature. Table 1 summarizes two

correlated data under different ambient temperatures and discharging currents; discharging voltage at 50% DOD (assuming 100% DOD at 2.5 V) and total discharging time to reach 2.5 V are compared.

**Figure 8.** Examples of comparisons between simulated and experimental 20A discharging curves in battery module: (**a**) 0 ◦C; (**b**) 50 ◦C.


**Table 1.** Summary of comparisons between experimental and simulation results.

#### *3.3. Battery Module Experiment and Validation*

For the module testing, four series-connected cells formed a battery module, where the four cells were numbered from #1 to #4. This section was abstracted from [33]. The inconsistency of the cells was taken into account in the experiments and analytical models. All tests were conducted at a constant temperature of 25 ◦C in the chamber. Figure 6c shows the assembled-module experimental setup in the cycler. The four cells selected for the experiments had slightly different aging, internal resistance, and voltage, although they performed very similarly to each other (voltage variation between four cells was smaller than 0.08 V) under loads, as the example shows in Figure 9a. At any specific time, the difference between the highest and lowest voltage among the four cells was always no larger than 0.08 V. Figure 9b indicates that the module terminal voltage measured by the cycler was higher than the summation value of each cell terminal voltage (measured by individual voltmeter) during continuous charging. This phenonium might be due to internal resistances existing in the connecting wires between cells. The difference between cycler measurement and summation voltage became larger as the charging current increased (0.04 V for 10 A, 0.1 V for 20 A, 0.25 V for 30 A, and 0.5 V for 40 A). In continuously constant current discharge tests, each cell had very similar 10 A and 20 A discharging voltage curves. At any timeframe, the difference between the highest and lowest voltage among the four cells was always no larger than 0.15 V, as the example shows in Figure 9c. The internal resistances in the connecting wires between cells resulted in that module voltage measured by the cycler always being lower than the summation value of each cell terminal voltage measured by each individual voltmeter. As the discharging current increased, the voltage difference between the cycler measurement and summation became larger (0.05 V for 10 A, 0.2 V for 20 A, 0.3 V for 30 A, and 0.5 V for 40 A). This discrepancy was clearly observed during the 40 A discharging test shown in Figure 9d.

**Figure 9.** Examples of cell and module charging/discharging curves from tests: (**a**) Individual cell voltage in 20 A charging; (**b**) module voltage in 20 A charging; (**c**) individual cell voltage in 40 A discharging; (**d**) module voltage in 40 A discharging.

Comparing the simulated module voltage curves with experimental voltage curves generated by the summation of four individual cells was conducted for module model validation. The module voltage curve measured by the cycler was not used for comparison because it was affected by the resistance of the connecting wires. Figure 10a–d shows that all the simulated curves matched well with the experimental ones during continuous charging and discharging. An up to 9% discrepancy occurred at the end of each charging and discharging cycle. Figure 10e and f indicate that simulated pulse charging and discharging curves matched with the experimental ones, particularly in the beginning of the cycle. The largest discrepancy was 7.8%, which occurred at the end of the 30 A pulse discharge curve. The validation of the developed battery module model presented an acceptable discrepancy.

The BMS function was simulated in the battery module model with predefined initial conditions. In one example of 25 A continuous charge current to the model, Cell #4 reached 4.3 V earlier than other cells because Cell #4 had a higher initial voltage. Therefore, the BMS opened the cell breaker and closed the bypass breaker to prevent Cell #4 from being overcharged. The voltage of Cell #4 then dropped to 4.08 V, as shown in Figure 11a. In the other example of 35 A continuous discharge current, Cell #4 reached 2.3 V first because it had a lower initial voltage. The BMS opened the cell breaker and closed the bypass breaker to prevent Cell #4 from being overdischarged. The Cell #4 voltage then increased back to 2.8 V.

**Figure 10.** Comparisons of module simulated and experimental charging/discharging curves: (**a**) Simulated and test of 20 A charging in module; (**b**) simulated and test of 20 A discharging in module; (**c**) simulated and test of 40 A charging in module; (**d**) simulated and test of 40 A discharging in module; (**e**) simulated and test of 20A pulse charge in module; (**f**) simulated and test of 30A pulse discharge in module.

**Figure 11.** Demonstration of BMS functions: (**a**) 25 A continuous charging; (**b**) 35 A continuous discharging.

#### **4. Twelve-Volt Battery Pack Model**

The new designed or future vehicle needs an SLI battery with a higher capacity to support increasing vehicle accessory or auxiliary loads [35,36]. Additionally, the 12-volt battery pack could become a building module to form a high-voltage battery pack (such as 48-volts or higher) used in electrified vehicle and stationary electric energy storage for renewable energy. An 80 Ah SLT-type battery pack with 14.4 V nominal voltage is proposed in this study. This battery pack contains four modules connected in parallel where each module (14.4 V, 20 Ah) has four ePLB-C020 cells connected in series. A Simulink model of the proposed battery pack is shown in Figure 12.

**Figure 12.** Simulink model of an 80 Ah SLI-type battery pack.

The model scope displays the battery pack voltage, which is a summation of each module voltage. Both simulated battery pack and module have the same shapes of constant current charging/discharging voltage curves. Obviously, the pack has four times charging/discharging durations of the module. The pack voltage curves have large fluctuations in each pulse during 20 A pulse charge simulation (180 seconds charge, 120 seconds pause, and repeat) and 30 A pulse discharge simulation (180 seconds discharge, 120 seconds pause, and repeat), as indicated in Figure 13. Figure 14 shows the simulated discharging curves of a 14.4 V 80 Ah SLI battery with one C-rate (20 A) and two C-rate (40 A) under five ambient temperatures.

**Figure 13.** Voltage curves of the 80 Ah SLI battery pack during pulse charging and discharging simulations: (**a**) Charging; (**b**) discharging.

**Figure 14.** Simulated discharging curves of a 14.4 V 80 Ah SLI battery under five ambient temperatures: (**a**) One C-rate (20 A); (**b**) two C-rate (40 A).

#### **5. Conclusions**

Modelling, simulation, and validation of SLT-type 12-volt lithium-ion polymer battery are presented in this paper. The MATLAB/Simulink-based modelling starts from using parameters deduced directly from single cell experiments, which provide convenient integration with actual cell monitoring, to a module containing four cells connected in series. A validated module model is utilized to model a high fidelity 80 Ah SLI-type battery pack with 14.4 V nominal voltage. The battery cell thermal effectiveness and battery management system functions are also considered. The experimental tests are carried out in an industry-scale setup with a charge/discharge cycler, temperature chamber, and computer-controlled software for battery testing.

In the cell-level model validation, either with or without thermal effectiveness, the experimental and the simulated discharging curves match well in the range from 0% to 80% DOD (assuming 100% DOD at 2.5 V). The discrepancy between each comparison is under 7%. From the range of 80% to 100% DOD, the discrepancy becomes much larger. The module model validation indicates a 9% or less discrepancy in all continuous and pulse charge/discharge simulation results. An 80 Ah SLI-type battery pack model with 14.4 V nominal voltage then can be achieved with statistical confidence.

The 12-volt lithium-ion battery packs might be ready for mainstream adoption in automotive SLI, stop–start engine idling elimination, and UPS applications. Additionally, the 12-volt battery pack could become a building module to form a high-voltage battery pack (such as 48-volts or higher) used in electrified vehicle and stationary electric energy storage for renewable energy. The proposed simulation model provides design guidelines for lithium-ion polymer batteries in electric-drive vehicle and stationary energy storage applications.

**Author Contributions:** Experiment, Software Simulation, Y.L.; Paper Writing, Y.L., Y.G.L.; Paper Review and Editing, Y.G.L., M.-C.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported in part by the National Science Foundation, ATE: Centers, under grant number DUE-1801150.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

#### *Article*

### **Real Time Design and Implementation of State of Charge Estimators for a Rechargeable Lithium-Ion Cobalt Battery with Applicability in HEVs**/**EVs—A Comparative Study**

#### **Nicolae Tudoroiu 1,\*, Mohammed Zaheeruddin <sup>2</sup> and Roxana-Elena Tudoroiu <sup>3</sup>**


Received: 26 March 2020; Accepted: 27 May 2020; Published: 31 May 2020

**Abstract:** Estimating the state of charge (SOC) of Li-ion batteries is an essential task of battery management systems for hybrid and electric vehicles. Encouraged by some preliminary results from the control systems field, the goal of this work is to design and implement in a friendly real-time MATLAB simulation environment two Li-ion battery SOC estimators, using as a case study a rechargeable battery of 5.4 Ah cobalt lithium-ion type. The choice of cobalt Li-ion battery model is motivated by its promising potential for future developments in the HEV/EVs applications. The model validation is performed using the software package ADVISOR 3.2, widely spread in the automotive industry. Rigorous performance analysis of both SOC estimators is done in terms of speed convergence, estimation accuracy and robustness, based on the MATLAB simulation results. The particularity of this research work is given by the results of its comprehensive and exciting comparative study that successfully achieves all the goals proposed by the research objectives. In this scientific research study, a practical MATLAB/Simscape battery model is adopted and validated based on the results obtained from three different driving cycles tests and is in accordance with the required specifications. In the new modelling version, it is a simple and accurate model, easy to implement in real-time and offers beneficial support for the design and MATLAB implementation of both SOC estimators. Also, the adaptive extended Kalman filter SOC estimation performance is excellent and comparable to those presented in the state-of-the-art SOC estimation methods analysis.

**Keywords:** lithium-ion cobalt battery; state of charge; state of energy; adaptive EKF SOC estimation; linear observer SOC estimation; MATLAB; Simscape

#### **1. Introduction**

Currently, hybrid and electric vehicles (EVs) represent a means of transport with low CO2 emissions. Also, soon, the energy required for these vehicles is expected to be provided by clean, renewable energy sources, such as solar panels. An essential feature of EVs is the recovery of energy they would lose during braking. Of various energy storage systems (ESS), "electrochemical batteries are devices that store chemical energy converted then into electricity to power the electric vehicles; they are preferred over capacitors and flywheels, due to their higher energy density" [1]. Based on a wide range of powers, three main categories are mentioned in [1], namely "EVs light electric vehicles with a power demand of less than several kilowatts, sedan vehicles, including electric sedan hybrid vehicles (HEVs) with a power up to 100 kW and heavy vehicles, used for public transport, with a

power exceeding 100 kW". For electric powertrains, the "lithium-ion (Li-ion) battery represents a good choice for EVs/HEVs" [1]. Today, it is already becoming a reality that, "among the batteries with low memory effects", the Li-ion outperforms the most popular nickel-based technologies. They excel by "lighter weight, high density of energy, long life and low self-discharge rate" [1]. However, HEVs/EVs continue to be powered for a long time by both nickel-metal hydride (Ni-MH) batteries and lithium-ion [1–12]. The strengths and weaknesses in "terms of cost, specific energy and power, safety, life span performance for the main different chemistries" are analyzed in [1]. Hard research work is being carried out in the field of lithium-ion batteries to increase their energy density, and to take advantage of the advancement of anode and cathode material technologies. The "common materials used for the positive electrode are cobalt oxide, manganese oxide, iron phosphate, nickel manganese cobalt oxide and nickel cobalt aluminum oxide" [1]. Among them, lithium nickel-manganese-cobalt oxide battery is a suitable choice for EVs since it offers "an excellent trade-off between safety, capacity and performance" [1]. The most popular cobalt Li-ion (Li-ion Co) battery "used in consumer products was believed to be not robust enough"; nevertheless, due to its "high energy density", this "computer battery" power nowadays "the Tesla Roadster and Smart Fortwo ED small cars". The behaviour of the battery changes during deep cycles when "its capacity decreases rapidly" and, it is also sensitive to "high mechanical, thermal or electrical stresses" [6,10]. Specifically, the power of the battery "decreases drastically in cold weather", and "when operating at high temperatures, its performance and life cycle visibly deteriorate" [10]. To avoid these situations and to extend the battery life, a "cooling and heating" system is usually installed. [6,10]. Additionally, the lithium-ion battery is "vulnerable to short-circuiting and overcharging" which could lead to a "combustion reaction, explosion and fire" as is mentioned in [6,10]. Thus, to "prevent overcharging of batteries in hazardous situations", the battery management system (BMS) monitors the battery cells through a "precise voltage control system" [10]. Particular progress is being made today in "lithium-air" and in "nanotechnologies" batteries, as they "have a higher energy density due to oxygen being a lighter cathode and a freely available resource", as mentioned in [13]. Of course, new technology also means high costs, but battery prices are gradually declining over time, as the manufacturing capacity of batteries becomes expanding as well. The Li-ion Co battery is an essential component of BMS which has as its primary function "improving battery performance, extending its life and operating safely" [3,10–12]. Therefore, it must continuously monitor, through the sensors, the internal parameters of the battery, such as the SOC, temperature, cells' currents balance and voltage [3,10].

SOC as an internal battery state, is a priority task for BMS to monitor, as it severely affects battery health and battery life [2,3,5–7,10–12]. In references [2,3,6–12] is defined as an "available battery capacity", which cannot be measured directly; therefore, an estimation technique is needed to prevent hazardous situations and to improve battery performance [3,10,11]. Mostly, the battery SOC estimation techniques are model-based, as is well documented in [7–24].

In conclusion, motivated by some preliminary results of our research, published in [10–12], this article focuses on the selection of the Li-ion Co battery model, the design and implementation of two real-time SOC estimators on a MATLAB simulation platform. The other chapters of this paper are structured as follows. In Section 2 are described the BMS, the selection criteria, the parameters of the battery and identifies the main disturbances that affect the functionality and the battery life. Also, is made a detailed analysis of state of the art on SOC measurement and estimation methods reported in the literature, and at the end of the same section are presented some modelling aspects and validation of Li-ion Co battery. In Section 3 are designed and implemented in MATLAB an adaptive extended Kalman filter (AEKF) and a linear observer (LOE) SOC estimators. The MATLAB simulations result, and rigorous performance analysis are presented at the end of the section. Section 4 is assigned for discussions, and Section 5 concludes the research paper contributions.

#### **2. Lithium-Ion Battery-Cell Modelling and Validation**

In this section, we focus our attention on the following topics regarding the Li-Ion batteries cells and packs:


#### *2.1. Battery Management System; Definition, Multitask and Safety Functions, Hardware and Software Components*

A most comprehensive and mature Battery Management System (BMS) is an analogue-digital multitasking safety functions device integrated into the battery control system structure. The main task is to perform "a variety of safety functions to prevent the voltage, temperature and current in the battery cells from exceeding the specified limits", as stated in [16]. The hardware components include those regarding "the safety circuitry, sensors, data acquisition, charging and discharging, control, communications and thermal management" [12]. In most automotive applications, the BMS performs tasks regarding "the safe operation and reliability of the battery, protecting battery cells and battery systems against damage, as well as battery efficiency and service life" [16]. Besides, it achieves interfacing, protection, control voltage, fault detection diagnosis and isolation (FDDI) and performance management functions, as is revealed in [16]. In a centralized configuration, it combines "into a single printed circuit board (PCB)" up to three module levels into hierarchical architecture, such as at the first level is located "the battery cell monitoring unit" ("data acquisition"), at the second one is the "module management unit" ("cell supervisor circuit" and at the highest level is the "package management unit" ("central management unit") [16]. Thus, the required tasks can be managed and distributed among different subcomponents through PCB connected to the battery cells. Moreover, its advanced modular topology, known as "the master-slave-topology" is an exciting feature [16].

The advantage of this configuration consists of reducing to a minimum "the functions and the elements of the slaves" such that the "master" to implement only the functions related to the battery system [16]. One of the most critical parameters controlled by the BMS is the temperature inside the battery. As it was mentioned in the Introduction section, temperature significantly affects battery performance and, for most cases, when it exceeds the maximum limits, it leads to "fire and explosion", known as "thermal runaway" process; it is an "irreversible process" with a significant heat "dissipated from the battery cells casing" [16]. In a battery pack, the battery's cells can be connected in series, parallel or as mixt combinations to "adapt the voltage level and the battery capacity" to meet the requirements of an HEV/EV or stationary storage applications. Moreover, the primary constraint of the functionality of any BMS, regardless of its chemistry, is the maximum cell voltage measured on the cell monitoring unit. Of the Li-ion batteries, "lithium-iron-phosphate cells are one of the lowest voltage batteries with a maximum of 3.65 V, while for the widespread nickel-manganese-cobalt cells the maximum voltage is 4.2 V" [16]. At least one "communication interface" uses a "CAN-bus communication line for easy interfacing with other controllers in the car environment" [16]. Moreover, currently, the "wireless" devices "operating via wireless networks have promising potential to significantly reduce wiring, connectors and cable effort during assembly" [16].

However, it is possible to disturb the wireless network by "electromagnetic noise inside the car and outside entities, which can create safety and security issues" [16].

For each safety issue, it is necessary to prevent "the deep discharge and the overcharge" of the battery's cell. Thus, the SOC of the battery pack is one of the most critical parameters estimated that keeps the "track" of the energy flow and reacts anytime when it is not operating within the specified range [16]. If SOC exceeds the limits, an alarm signal shall be sent as soon as possible to the "vehicle systems" concerned to prevent possible damage. Also, the battery cells need protection from possible damage generated during a "deep discharge", such as dangerous "internal short circuits" [16].

Like, in the case of an overload, the information is sent to "propulsion controller" that decides to "stop charging the battery" anytime if the "maximum limit value is reached" [16]. Among the main software components of the BMS are highlighted the following [12]:


These components control the hardware operations, receive signals from sensors and "implement in real-time the estimation of SOC, SOH algorithms and of possible faults using FDDI techniques" [10]. Also, the BMS fulfil the task of estimation and monitoring the battery internal and insulation resistances [10,11].

Soft battery failures are detected using FDDI estimation techniques and identify defective components and "abnormal" functionality. In [10] are mentioned the sensor voltage faults (gain and drift) in measured terminal battery voltage, sensor current faults, sensor temperature faults, and fan motor faults. The estimation of sensor faults is particularly useful for improving the "reliability" of BMS [10]. Well, "several faults" have their roots in defective components, "safety component failures or human errors" [10]. Usually, the fault can be persistent, intermittent, unique or overlap with other faults, for which its root cause may be a faulty cable connection, a sensor bias (voltage, current) or a temperature drift [10]. A faulty fan is detected only when a complete dc motor failure occurs.

#### *2.2. Battery Selection Criteria*

The main battery selection criteria in all HEV/EVs applications can be found in [10], including "energy and power density, capacity, weight, size, lifespan, cost and memory effect" features that make the difference for selecting any battery. Of these, power and capacity are necessary to optimize the design of the battery, selecting the most suitable cells and package size, able to be adapted to a custom application [10]. Furthermore, given that most HEVs/EVs operate for different climatic conditions of harsh operation and stress caused by abuse and vibration, the size of the battery needs to be adequate to provide a certain amount of energy [10]. Additionally, some constraints can be imposed on the capacity of the battery in terms of "depth of discharge (DOD), SOC, discharging rate and generative braking charge", as is stated in [10].

#### *2.3. Battery Parameters Test*

Mainly, the Li-ion battery life span depends significantly on SOC real-time estimation, aging effects, temperature operating conditions and frequency "of the changes in operating cycles" [10].

Also, internal DC resistance and insulation resistance are among the most critical parameters of the battery that have a significant impact on battery life. Related to first battery parameter, in reference [10] the life cycle is defined as "the number of the cycles performed by the battery before its internal resistance increases 1.3 times or double than its initial value when was new". The main factors that affect the internal resistance are revealed in reference [11], including "the conductor and electrolyte resistances, ionic mobility, temperature effects and changes in SOC".

Related to the second battery parameter, in reference [10] is stated that the "high voltages components, electrical motor, battery charger and its auxiliary device deal with a large current and insulation"; thus, the "insulation issues" are under investigation during the" battery design stage" [10]. The harsh "working conditions" detailed in [11], have a significant impact on "fast aging of the power cable and insulation materials", decreasing drastically "the insulation strength" and "endanger the personnel". Thus, it needs to ensure safe operating conditions for personnel are required to evaluate the insulation conditions for entire HEV's BMS. Many details about the insulation standards can you

can find in [11]. In conclusion, to ensure the insulation security of on-board BMS, it is necessary to "detect the insulation resistance and raise the alarm in time" as is mentioned in [10].

#### *2.4. Disturbances that A*ff*ect the Battery Operation and the Life Span*

In "real life", the primary disturbances affecting battery operation and life are well-identified in [10], and include:

Chemical changes—leading to damage to the battery cells.

Active chemicals depletion—take place under different operating conditions, as was mentioned in the Introduction section.

Temperature—battery operation significantly depends on the temperature, which also affects the performance of the battery.

Pressure—is affected by the temperature that increases the internal pressure inside the battery cell. DOD—is related to SOC and depends on operating temperature conditions and discharge rate, becoming "proportional to the amount of active chemicals" [10].

Charging level limits—the full charge of the battery must be prevented to keep the battery safe.

Charging rate—to keep the battery safe, discharging the battery at high rates should be avoided. Voltage—to counteract "undesirable chemical reactions" inside the battery cells the values of the battery terminal voltage must be within a specified range [10].

Cell aging—cell aging is mainly affected by the current flow through the battery cells, as well as by the heating and cooling processes of the cells.

Coulombic efficiency (CE)—is an important performance indicator of the charging efficiency of the battery through which the electrons are transferred inside the battery. The CE rating of Li-ion batteries exceeds 99% and is among the highest values of any rechargeable battery.

Electrolyte loss—it has a significant impact on the capacity of the cells whenever there is a reduction in the active chemicals inside the battery.

Internal and insulation resistances—their impact was described in the previous subsection.

#### *2.5. Li-Ion Battery SOC—State of the Art of Measurement and Estimation Methods Reported in the Literature*

Basically, "the battery model, estimation algorithm selection, and cells balancing" have a high impact on SOC accuracy and robustness, as is stated in [17]. Also, in [17] the authors investigate several existing SOC estimation techniques reported in the literature field and analyze their "issues and challenges". In reference [17] are well summarized the main Li-ion battery SOC estimation techniques related to HEVs/EVs field, including:


Our investigations are motivated by the lack of a sensor capable of measuring the battery SOC and therefore it is necessary to estimate it. Several measurement methods and estimation techniques are well documented and summarized in [12,16–18].

#### 2.5.1. Conventional Direct Measurement Methods

	- A laboratory method for determining SOC—even if it is not suitable for the field of HEV applications, it is still one of "the most accurate SOC measurement" methods [10].

This method consists of completely discharging the battery, recording the "discharged ampere-hours" and then determining the "remaining cell capacity available".


accurate compared to other SOC calculation methods [10,17]. The most significant advantage of the Ampere-hour counting method is its low power computation cost, and it is secure and reliable when the sensor current measurements are accurate, and a re-calibration point is accessible [10,17].

(6) Model-based method. Since the "previous mentioned methods are not appropriate for online SOC estimation and to achieve an accurate online SOC estimate value, suitable battery models need to be developed" [17]. Among the most suitable models for online SOC estimation are the electrochemical and equivalent circuit models (ECMs) [10,11,17]. More details about ECMs models you can find in [3,4,7–12,17]. In closing, "an ideal ECM should be able to simulate the actual battery terminal voltage to any charging or discharging battery input current", as is stated in [17].

#### 2.5.2. Adaptive Filter Estimators

The adaptive filter estimators improve the "accuracy and the robustness of the battery SOC estimation significantly and reduce" drastically the impact of measurement and process noises on the battery model [17], such those developed in [7–12,14,18]. Among the Kalman filtering estimation techniques in the field literature the Kalman filter [KF], extended Kalman filter (EKF) [4,7–9,11,17,18], adaptive Kalman filter (AEKF) [17], fading Kalman filter (FKF) [17], unscented Kalman filter (UKF) [12,14,18], sigma-point Kalman filter (SPKF) [17] and particle filter (PF) are reported [17].

The KF was developed by Rudolph Kalman in 1960 and currently has become the most popular estimation algorithm. It is an "optimum state estimator and intelligent tool" for linear systems [17]. Its EKF version is also a KF applied to the linearized dynamics of a non-linear system by using the first-order Taylor's series expansion around the current value of the state estimate in each step of the algorithm, as developed in the next section and in [7–9,17]. A combination of KF state estimator and Ah Coulomb counting method can be used to "compensate for the non-ideal factors that can prolong the operation of the battery" [17]. The KF SOC estimator is the most used since it can estimate the battery SOC more accurately even if when the battery is affected by external disturbances mentioned in previous subsections.

Although, if the dynamics of Li-ion battery model are "highly nonlinear", "linearization error may occur due to the lack of accuracy in the first-order Taylor series expansion under a highly non-linear conditions" [17]. The simplicity of the SOC EKF estimator design and implementation motivates researchers to apply this estimation technique for different Li-ion battery models, as in [4,7–9,11,16–24]. In [16] an exciting research project that performs a detailed and rigorous analysis of state of the art on Li-ion BMSs, including also a detailed presentation of the main SOC estimation techniques, among them the adaptive Kalman filtering techniques, is presented. Similarly, [17] presents an intense study of state of the art on Li-ion battery SOC estimation for electric vehicles that completely reviews of all the existing SOC direct measurement and estimation techniques reported in the field literature. Similarly, in [18] a brief review describing the SOC estimating methods for the same Li-based batteries is provided. In [19], the authors proposed a dual EKF for state and parameter estimation for a first-order EMC RC Li-ion battery model. The SOC simulation results reveal an excellent accuracy of the SOC estimate, but the robustness algorithm robustness is not investigated. Comparing the SOC simulation results obtained in current research work and in [19], one can observe an excellent accuracy, and the robustness of the algorithm developed in our research for several scenarios. In [20], the authors use an improved non-linear second-order RC EMC battery model and based on this model have developed an EKF algorithm to estimate the Li-ion battery SOC. The simulations are conducted on the MATLAB platform using two different driving cycles current profiles, namely Urban Dynamometer Driving Schedule (UDDS) and HWFET. The results are compared to those obtained by a Coulomb counting method and reveal an excellent SOC accuracy, but degradation is visible in the robustness performance to changes of battery model parameters values provided by two datasets, compared to the SOC estimator robustness performance designed in our research, for many scenarios introduced in Section 3. In [21] is developed a new application "model-based fault diagnosis scheme to detect and isolate the faults

(FDDI) of the current and voltage sensors applied in the series battery pack based on an adaptive extended Kalman filter (AEKF)". The AEKF algorithm is designed to estimate the magnitude of the faults. The FDDI scheme is validated in the MATLAB/Simulink platform, and the result of the simulations demonstrates the "effectiveness" of the proposed FDDI for "various fault scenarios using the "real-world driving cycles".

The AEKF is an EKF with an adaptive feature, i.e., in the new design the EKF algorithm updates at each step the process and measurement noise covariance matrices to increase the accuracy of EKF SOC estimation. The same feature is also added to the EKF algorithm developed in our research that is very useful to increase the accuracy and the robustness of the SOC EKF estimator. In fact, by updating the noise covariance matrices, a new retuning procedure of the EKF parameters is not more required unlike the time consuming "trial and error" strategy. In the reference [21] you can see the effectiveness of the AEKF algorithm that estimates accurately four injected faults, the first is a fault assigned to a sensor current, and the other three faults are assigned to three different voltage sensors. The robustness of the FDDI technique is demonstrated for a 20% change in the SOC initial value and a current profile corresponding to a UDDS driving cycle. Unfortunately, the MATLAB simulations results don't show the SOC estimated values, very useful to analyze the impact of each fault on the SOC estimation performance. In the reference [22] "an experimental approach is proposed for directly determining battery parameters as a function of physical quantities". The battery model's parameters are dependent on SOC and of the discharge C-rate. This approach is exciting since the battery model's parameters "can be expressed by regression equations in the model" to derive "a continuous-discrete dual EKF SOC state and parameters estimates" [22]. A "standard correction step" of the EKF algorithm is applied to "increase the accuracy of the estimated battery's parameters" [22]. The EKF simulation results with the experimental results for several operating scenarios reveal a high accuracy and the robustness of the estimator for correct identification of the battery parameters. In the reference [23] an adaptive fading EKF (AFEKF) is proposed for Li-ion battery SOC estimation accuracy and convergence speed. The AFEKF SOC estimator combines both structures AEKF and a fading EKF (FEKF). A FEKF "adopts a variable forgetting factor least square (VVFFLS)" to identify the Li-ion battery parameters [23]. The AFEKF estimator can reduce the SOC estimation error of less than 2%. Also, in our research, we add the same feature to the proposed AEKF SOC estimator, and the MATLAB simulation results reveal a high SOC estimation accuracy and robustness for many scenarios including three driving cycles tests UDDS, FTP and EPA-UDDS. Comparing the MATLAB simulation results obtained in [23] to those obtained in our research work, for same UDDS cycle, you can notify that the SOC estimator designed in [23] performs better in terms of accuracy. Instead, the proposed estimator in the current research performs better in terms of robustness and convergence speed. The speed convergence and robustness performance are revealed for a 20% decrease in SOC initial value in [23] and 30% in our case study.

In [24] an exciting online EKF SOC Li-ion internal resistance parameter estimator to "overcome defects from simplistic battery models" is developed. The battery is a first-order ECM RC model for which the internal resistance is dependent on SOC, temperature and aging effects.

For an accurate real-time internal resistance, the EKF estimated values "can be distinguished well" and also "improve the accuracy of SOC and SOH estimation" [24]. The internal resistance test device consists of a dc power supply source, a dc voltmeter, a pulse control switch and a microcontroller unit that controls the testing procedure, the dc power source, the switching time and voltage measurement. The EKF estimator is conceived as parameter estimator. Hence, its model is like for EKF state estimator. Still, in this case, the internal resistance dynamic is given by a slow varying first-order differential equation that has injected a Gaussian process noise. The EKF estimator can also estimate at the same time the SOC of Li-ion battery; thus, it is designed as a dual state-parameter EKF algorithm. The simulation results indicate an excellent accuracy of SOC estimate, for "a repeated current constant-constant voltage of 3200 mA discharge current and 1600 mA charging current, and the estimation error is smaller than 3%" [24]. Unfortunately, a new estimation result from a performance comparison is not possible since

the input current profiles used in current research work (UDDS, FTP and EPA-UDDS) are entirely different than the current profile used in [24].

A viable alternative to EKF SOC estimator can be the unscented Kalman filter (UKF) and sigma point Kalman filter (SPKF) that avoid the linearization of nonlinear dynamics of the battery model; thus, they are more accurate and robust than EKF [10,11,14,17]. Also, a particle filter (FP) method is used to estimate the states, estimating the "probability density function" of a nonlinear dynamics of the Li-ion battery model, using a Monte-Carlo simulation technique, such as developed in [12,17].

#### 2.5.3. Learning Methods

In this category the artificial neural networks (ANN), support vector machine (SVM), extreme machine learning (ELM), genetic algorithm (GA) and fuzzy logic (FL), well documented in [17], can be highlighted.

#### 2.5.4. Linear and Nonlinear Observers

The nonlinear observers (NLO), sliding mode observer (SMO) and proportional-integral observer (PIO) are proposed to estimate the SOC of Li-ion batteries, and a detailed description can be found in [17].

#### 2.5.5. Hybrid Methods

The hybrid method is a combination of two or more algorithms' structures, such as an EKF-Ah algorithm, an adaptive EKF (AEKF) and a support vector machine (SVM), like the one developed in [17].

#### *2.6. Li-Ion Battery Cell—Model Selection, Validation and Case Study*

In this section, we are focused on the generic Li-ion Co cell model description in a bidimensional continuous and discrete-time state-space representation. Since "the new technologies heavily depend on battery packs, it is therefore important to develop accurate battery cell models that can conveniently be used with simulators of power systems and on-board power electronic systems", such is mentioned in [25]. The Li-ion Co battery model adopted in this research paper is a generic MATLAB/Simscape nonlinear model suggested in [25] and depicted in Figure 1.

**Figure 1.** The non-linear Li-ion Co battery generic model (see [25]). (it is common picture met in the literature, it is not copyright issues!).

In this schematic the battery is modeled by a controlled voltage source E, which is a no-load voltage (open circuit voltage (OCV)) [25], given by:

$$\mathbf{E} = \mathbf{OCV} = \mathbf{f}(\mathbf{E}\_0, \mathbf{K}, \mathbf{Q}\_{\text{max}}, \mathbf{t}) = \mathbf{E}\_0 - \mathbf{K} \frac{\mathbf{Q}\_{\text{max}} \int \text{id}\mathbf{t}}{\mathbf{Q}\_{\text{max}} - \int \text{id}\mathbf{t}} + \mathbf{A}\_{\text{exp}} \mathbf{e}^{(-\mathbf{B}\_{\text{exp}} \int \text{id}\mathbf{t})} \tag{1}$$

*Energies* **2020**, *13*, 2749

On the internal resistance is dissipated the power losses Ploss, useful to design the thermal model in the next section to simulate the temperature effects on the battery, given by:

$$P\_{\rm loss}(\mathbf{t}) = \mathcal{R}\_{\rm int} \mathbf{i}^2(\mathbf{t}) \tag{2}$$

The battery terminal voltage Vbatt is related to OCV according to following highly non-linear dynamic relationship:

$$\mathbf{V\_{batt}(t) = E - R\_{\rm int}i(t) = E\_0 - K \frac{\mathbf{Q\_{max}} \int \mathrm{idt} \mathbf{t}}{\mathbf{Q\_{max} - \int \mathrm{idt}}} + A\_{\rm exp} \mathbf{e^{(-R\_{\rm sup} \int \mathrm{idt})} - R\_{\rm int}i(t)},\tag{3}$$

where the meaning of all the variables and coefficients can be found in Table 1. Additionally, we attach the Coulomb counting equation to define the SOC of the battery, which is an important battery internal state supervised by BMS. It delivers a valuable "feedback about the state of health of the battery (SOH) and its safe operation", as is mentioned in [10]. The battery SOC is defined in [10] as:

$$\text{SOC} = \frac{\text{Remaining capacity}}{\text{Rated capacity}}\tag{4}$$

**Table 1.** Description of Li-ion cobalt voltage model variables.


The battery SOC is 100% for a battery fully charged and, 0% for a battery fully empty. Typically, the battery SOC can be defined for a positive current discharging cycle as:

$$\text{SOC}(t) = 100(1 - \frac{\eta\_{\text{disch}}}{Q\_{\text{rated}}} \int\_0^t i(\tau)d\tau) \quad (\%), \quad i(\tau) \ge 0 \tag{5}$$

where η*disch* is the Coulombic efficiency of the discharging cycle, while *Q*max represents the maximum capacity of the battery capacity, typically 1.05*Qrated*, close to those provided in the battery manufacturer's specs. The relation (5) can be written as a first order differential equation that, together with Equations (1) and (3), will be particularly useful for SOC state estimation in the next section of this research paper, i.e.:

$$\frac{d}{dt}(SOC(t)) = -100 \frac{\eta\_{\text{discharge}} \times i(t)}{Q\_{\text{rated}}}, \ i(t) \ge 0 \tag{6}$$

It is worth mentioning that for a discharging cycle, the battery current in (6) is positive and for a charging cycle it is negative.

#### 2.6.1. Li-Ion Cobalt MATLAB Simscape Model

A full representation of the generic battery model, dependent on the temperature and aging effects, is developed in MathWorks (Natick, MA, USA; www.mathworks.com) in the MATLAB R2019b/Simulink/Simscape/Power Systems/Extra Sources Library-Documentation. The MATLAB Simscape Li-ion cobalt battery cell specifications are shown in Table 2.


**Table 2.** Li-ion Cobalt cell specifications.

The MATLAB Simscape model of a generic battery is beneficial to set up a particular choice of battery chemistry and operation conditions that take into consideration the thermal model of the battery (internal and environmental temperatures) and also its aging effects. The battery terminal voltage, current and SOC can be visualized to monitor and control the battery SOH condition. The nominal current discharge characteristic according to a choice of the Li-ion Co battery having a nominal capacity of 5.4 Ah and a nominal voltage of 7.4 V is shown in Figure 2.

**Figure 2.** Nominal discharge characteristic of Li-ion Co at 0.2037C-rate (1.1 A)-MATLAB generic model. (**a**) In hours (minutes) (**b**) In Ampere-hours (Ah).

This characteristic corresponds to a constant discharge current of 0, 2037C-rate (0.2037 × 5.4 Ah = 1.1 A). The first battery characteristic from the top side of Figure 2 provides useful information about the estimated coefficients of the open-circuit voltage (OCV) included in Table 1, i.e., E0 = 8.0259 V, Rint = 0.01333 Ω, K = 0.001834 V, Aexp = 0.35904 V, and Bexp = 3 (Ah)-1. To show the evolution of the battery terminal voltage for different input current profiles, at the bottom of same Figure 2 other three nominal current discharge characteristics for three constant discharging currents (6.5, 13 and 32.5 A) are shown. These characteristics reveal that for the highest constant discharging current of 32.5 A, the discharging time of the battery decreases drastically to 10 min compared to 54 min corresponding to the smallest discharging current of 6.5 A. The same trend can be seen in Figure 3, where for a nominal discharging constant current of 1.08 A the Li-ion Co battery needs almost six hours to be fully discharged. The Simscape model of a generic battery set up for a Li-ion Co battery is shown in Figure 4.

**Figure 3.** Nominal characteristic for a constant current discharge of 1.08 A—details.

**Figure 4.** The Simscape model of the generic 5.4 Ah and 7.4 V Li-ion Co battery (without temperature and aging effects).

2.6.2. Li-Ion Cobalt Model in Continuous Time State Space Representation

The purpose of this section is to select and design the most suitable Li-ion Co battery model, which excels in simplicity, accuracy and is easy to implement in the MATLAB real-time simulation environment. Specifically, an accurate battery model is useful to develop in the following section the proposed real-time SOC estimators, which must also be of high precision and robustness. Related to SOC is the DOD, defined in [10] as:

$$DOD(t) = 100(1 - SOC(t)) \quad (\%) \tag{7}$$

The SOH is another internal battery derived parameter defined in [10] "as the ratio of the maximum charge capacity of an aged battery to the maximum charge capacity when this battery was new", as is also mentioned in [2,26]. The "actual operating life of the battery is affected by the charging and discharging rates, DOD, and by the temperature effects" [10]. Also, in [10] is stated that "the higher the DOD is, the shorter is the life cycle", and to attain "a higher life cycle, a larger battery is required to be used for a lower DOD during normal operating conditions", as is stated in [2,11,12]. Another important parameter for BMS in HEVs/EVs is the state of energy (SOE). From "engineering perspective, the SOE is more useful since it takes battery terminal voltage into account, which can predict the available energy for HEVs/EVs" [26].

While SOC indicates "the remaining capacity of the battery, the SOE indicates the remaining energy stored in the battery", as is defined in [26]:

$$SOC(t) = 100(1 - \frac{\eta\_{\text{solid}}}{E\_a} \int\_0^t V\_{\text{batt}}(\tau) i\_L(\tau) d\tau) \quad (\%), \quad i\_L(\tau) \ge 0 \tag{8}$$

or equivalent to:

$$\frac{d}{dt}(SOC(t)) = -100 \frac{\eta\_{\text{slickch}} V\_{\text{batt}}(t) \times i\_L(t)}{E\_a}, \ i\_L(t) \ge 0 \tag{9}$$

where *Ea*, *iL*(*t*), η*sdisch* represent the available battery energy, the load current and the "battery energy efficiency" respectively [26]. The input-output battery model Equation (1) is a simplified version of the original Shepherd's combined model that follows the development from [25] and [27–29] replacing:

$$\mathbf{E}(\mathbf{t}) = \mathbf{E}\_0 - \mathbf{K} \frac{\mathbf{Q}\_{\text{max}} \int \text{idt}}{\mathbf{Q}\_{\text{max}} - \int \text{idt}} + \mathbf{A} \mathbf{e}^{(-\mathbf{B}\_{\text{max}} \frac{1}{\mathbf{Q}\_{\text{max}}} \int \text{idt})} \tag{10}$$

by:

$$\mathbf{E(t)} = \mathbf{E\_0} - \frac{\mathbf{K}f \text{ idt}}{\text{SOC(t)}} + \mathbf{A}e^{(-\mathbf{B}(1-\mathbf{SOC(t)}))} \tag{11}$$

where A and B are two empirical parameters that are determined by a curve fitting procedure. The advantage of new version is to get a simplified OCV nonlinear model dependent only on SOC, as is developed in [26].

In the case study, we follow the development from [25] corrected by making small changes to increase the model accuracy, as is suggested in [26]. The development from [25] has the advantage to determine the battery model parameters by extracting the values based on simple algebraic manipulations, directly from the battery type OCV curve specifications provided by manufactures [7,10–12,25]. According to (11), the input-output battery generic model Equation (3) in continuous time becomes:

$$\mathbf{V}\_{\rm bart}(\mathbf{t}) = \mathbf{E} - \mathbf{R}\_{\rm int} \mathbf{i}(\mathbf{t}) = \mathbf{E}\_0 - \frac{\mathbf{K} \int \mathbf{i}(\mathbf{t}) \mathbf{d}\mathbf{t}}{\mathbf{SOC}(\mathbf{t})} + \mathbf{A}\_{\rm exp} \mathbf{e}^{(-\mathbf{R}\_{\rm rep} \mathbf{Q}\_{\rm max} (1 - \mathbf{SOC}(\mathbf{t})))} - \mathbf{R}\_{\rm int} \mathbf{i}(\mathbf{t}), \tag{12}$$

Let's now assign two state variables to the description (12):

$$\begin{array}{l} \mathbf{x}\_1(\mathbf{t}) = \text{SOC}, \mathbf{x}\_2(\mathbf{t}) = \mathbf{A}\_{\text{exp}} \mathbf{e}^{((-\text{B}\_{\text{exp}} \text{Q}\_{\text{rad}} / \eta\_{\text{SOC}}) \times (1 - \mathbf{x}\_1(\mathbf{t}))})\\ \mathbf{u}(\mathbf{t}) = \text{I}\_{\text{bat}}(\mathbf{t}) \text{ is the input current profile} \\ \mathbf{y}(\mathbf{t}) = \text{V}\_{\text{bat}}(\mathbf{t}), \text{is the battery terminal voltage} \end{array} \tag{13}$$

Therefore, a new modelling version is developed for designing and implementing the Li-ion Co battery model. In the new version, the model is described in continuous time in a two-dimensional representation of the state space as:

$$\begin{cases} \frac{d\mathbf{x}\_1(\mathbf{t})}{d\mathbf{t}} = -\left(\frac{\eta\_{\rm BOC}}{Q\_{\rm rated}}\right) \times \mathbf{u}(\mathbf{t})\\ \frac{d\mathbf{x}\_2(\mathbf{t})}{d\mathbf{t}} = -\mathbf{B}\_{\rm exp}\mathbf{x}\_2(\mathbf{t}) \times \mathbf{u}(\mathbf{t})\\ \frac{d\mathbf{x}\_3(\mathbf{t})}{d\mathbf{t}} = -\left(\frac{\eta\_{\rm BOC}}{\mathbf{E}\_s}\right) \times \mathbf{V}\_{\rm bath}(\mathbf{t}) \times \mathbf{u}(\mathbf{t})\\ \mathbf{y}(\mathbf{t}) = \mathbf{E}\_0 - \frac{\mathbf{K}\int \mathbf{i}(\mathbf{t})d\mathbf{t}}{\mathbf{x}\_1(\mathbf{t})} + \mathbf{x}\_2(\mathbf{t}) - \mathbf{R}\_{\rm int}\mathbf{u}(\mathbf{t}) \end{cases} \tag{14}$$

and it is implemented in Simulink in the next subsection. The advantage of this representation is the model simplicity, its accuracy and easy to implement in real time.

#### 2.6.3. Li-Ion Model in Discrete Time State Space Representation

To design both SOC estimators based on the adopted generic Li-ion Co battery model, the state space Equation (13) will be converted in discrete time representation. For SOC estimation purpose, a full Li-ion Co model in discrete time space representation is given in (15) and (16):

$$\begin{aligned} \mathbf{x}\_1(\mathbf{k}+1) &= \mathbf{x}\_1(\mathbf{k}) - \mathbf{T}\_\mathbf{s}(\frac{\text{Distance}}{\text{Q}\_\text{rated}}) \times \mathbf{u}(\mathbf{k})\\ \mathbf{x}\_2(\mathbf{k}+1) &= \mathbf{x}\_2(\mathbf{k}) - \mathbf{T}\_\mathbf{s} \mathbf{B}\_\text{exp} \mathbf{x}\_2(\mathbf{k}) \times \mathbf{u}(\mathbf{k}) \end{aligned} \tag{15}$$

$$\mathbf{y}(\mathbf{k}) = \mathbf{E}\_0 - \frac{\mathbf{K}\mathbf{u}(\mathbf{k})\Delta\mathbf{t}}{\mathbf{x}\_1(\mathbf{k})} + \mathbf{x}\_2(\mathbf{k}) - \mathbf{R}\_{\text{int}}\mathbf{u}(\mathbf{k})\tag{16}$$

$$\begin{array}{l} \mathsf{x}\_{1}(\mathsf{k}) \triangleq \mathsf{x}\_{1}(\mathsf{k}\mathsf{T}\_{\mathsf{s}}) \; , \mathsf{x}\_{2}(\mathsf{k}) \triangleq \mathsf{x}\_{2}(\mathsf{k}\mathsf{T}\_{\mathsf{s}}) \; , \mathsf{u}(\mathsf{k}) \triangleq \mathsf{u}(\mathsf{k}\mathsf{T}\_{\mathsf{s}}) ,\\ \mathsf{y}(\mathsf{k}) \triangleq \mathsf{y}(\mathsf{k}\mathsf{T}\_{\mathsf{s}}) \; , \mathsf{k} \in \mathbb{Z}^{+} \end{array}$$

where <sup>k</sup> <sup>∈</sup> <sup>Z</sup>+, is a positive integer number, <sup>Δ</sup><sup>t</sup> <sup>=</sup> Ts is the sampling time, set to 1 s in all MATLAB simulations.

#### 2.6.4. Model Validation on ADVISOR MATLAB Integrated Platform

The validation of the Li-ion Co battery model is tested by using one or more driving cycles under different realistic driving conditions required for battery simulation tests. A collection of such of driving cycles profiles is stored in a large database of the US National Renewable Energy Laboratory (NREL) Advanced Simulator (ADVISOR) integrated into a MATLAB simulation environment [10]. The ADVISOR simulator is recommended by the excellent results obtained in [10] and by the fact that so far it has been one of the most used software design tools in the HEV/EV automotive industry, as mentioned in [11,29–32]. More details about this integrated ADVISOR MATLAB platform can be found in [10]. Among the three options of ADVISOR input battery models we choose a NREL Rint internal resistance installed on a hypothetical car model selected from the ADVISOR database, necessary for the validation of the Li-ion Co battery proposed in the case study, such in [10]. The proposed Li-ion Co battery model given by the Equation (14) and integrated into an HEV BMS structure is validated by using three of the most common driving cycles tests provided by Simulink and ADVISOR database, such as an Urban Dynamometer Driving Schedule (UDDS), Environmental Protection Agency (EPA) UDDS, and FTP/FTP-75 [10]. The Li-ion Co battery SOC tests result compared to those obtained by an NREL's internal resistance Rint lithium-ion battery model SOC installed on a midsize hypothetical car, for the same driving cycles tests and in the same initial conditions, like in [10] for a UDDS driving cycle test. Like [10], the hypothetical midsize car has almost the same characteristics. The "midsize town car is selected as an input vehicle on the integrated platform under same standard initial conditions SOCini = 70%, modelled in Simulink" in Figure A1 (Appendix A), and shown as an "ADVISOR page setup" in Figure 5 [10]. An Urban Dynamometer Driving Schedule (UDDS) test is used to validate the battery model in this section and the other two driving cycles tests, FTP (FTP-75), and UDDS-EPA are used in Section 3 for validation of the MATLAB SOC simulations results for both proposed estimators. The UDDS driving cycle profile in (mph) and the discharging battery current (A) are represented on the top and the bottom graphs from the same Figure 6 [10].

For performance comparison purposes, Figure 7 shows the corresponding SOC curves for the proposed Li-ion Co battery model design (red colour) and the ADVISOR SOC estimator (blue colour) on the same graph. The SOC simulations are performed for the same initial conditions (SOCini = 70%) and reveal an excellent SOC accuracy and an estimation error less than 2% between the battery model selection and NREL ADVISOR Rint battery model. The result confirmed by the second source from the first line of Table 3 (battery model vs. ADVISOR Rint model), for which the mean absolute error (MAE) is 0.0658. Other two sources can confirm the model validation by performing same comparisons for UDDS-EPA driving cycle test that will be developed in Section 3.3.2 with the statistical results shown in Table A1 from Appendix A. The third FTP driving cycle test will be developed in Section 3.3.3 and statistical results are shown in Table A2 from the same Appendix A.

The results reveal an estimate value less than 2%, MAE = 0.0235 (Table A1) and MAE = 0.0285 (Table A2) respectively. The MATLAB simulation results of all three tests for UDDS, UDDS-EPA and FTP driving cycles, for same initial conditions show an excellent accuracy for adopted battery model versus ADVISOR Rint and an estimation error less than 2%, confirmed by the results from Table 3, Tables A1 and A2 from Appendix A. Since from three different sources, the simulation results converge to an average error of less than 2% and show an accurate estimate value, we can conclude that these results validate the Li-ion Co battery. This outstanding result is encouraging to use the validated proposed battery model as a support for building "robust, accurate and reliable real-time battery estimators", both developed in Section 3. Further, in Figure A2a,b shown in Appendix A, you can see the statistics obtained for the SOC generated by the proposed Li-ion Co battery model and for SOC

estimated by the generic ADVISOR Rint Li-battery model. Figure 8 shows the Simulink model of the adopted generic model that implements the set of Equation (13).

**Figure 5.** The setup ADVISOR page of the input HEV midsize car.

**Figure 6.** UDDS driving cycle input profile.

**Figure 7.** The UDDS test on the ADVISOR 3.2 integrated MATLAB platform. SOC battery model versus Li-ion ADVISOR battery SOC.

**Figure 8.** Simulink generic selected battery model.

The block from the top side of Simulink diagram calculates the SOC, OCV and battery terminal voltage Vbatt, shown in detail in Figure 9a,b. For a constant discharging current of 1C-rate (5.4 A), the battery terminal voltage, the OCV-SOC battery characteristic, and SOC are represented in Figure 10a–d. Furthermore, the adopted battery model generates the SOC that is shown in Figure 11a–c for three different driving conditions, namely for a UDDS, an FTP-75 and a constant 1C-rate (5.4 A) discharging current.

It is worth mentioning that a 100 Ah rated pack capacity Li-ion battery model is integrated in a MATLAB-Simulink SimPower Systems library, very helpful to be used for designing and implementation of different HEVs and EVs powertrains configurations, such is suggested in the EV application shown in Figure A3 from Appendix A.

**Figure 10.** *Cont*.

**Figure 10.** The battery model full discharging cycle at 1C-rate (5.4 A); (**a**) battery terminal voltage; (**b**) OCV vs. SOC characteristic; (**c**) terminal voltage vs. SOC; (**d**) battery SOC.

**Figure 11.** Battery SOC for three different current profiles; (**a**) For UDDS driving cycle current profile; (**b**) For a FTP-75 current profile; (**c**) for a 1C-rate (5.4 A) discharging current profile.

#### *2.7. Li-Ion Cobalt Battery Thermal Model*

The dynamics of thermal model block is described by the following equation:

$$\text{mc}\_{\text{p}} \frac{\text{dT}\_{\text{cell}}(\text{t})}{\text{dt}} = \text{hA} (\text{T}\_{\text{amb}} - \text{T}\_{\text{cell}}(\text{t})) + \text{R}\_{\text{int}} \text{I}^2(\text{t}) \tag{17}$$

where m—the mass of the battery cell [kg]; cp—the specific heat capacity [J/molK]; S—the surface area for heat exchange [m2]; Tcell(t)—the variable temperature of the battery cell [K]; Tamb—the ambient temperature [K]; Rint—the value of internal resistance of the battery cell [Ω]; I(t)—the input charging and discharging profile current [A].

For simulation purposes, the battery temperature profile and the robustness of the proposed SOC battery estimators, are tested for the following approximative values, closed to a commercial battery type ICP 18,650 series:

$$\begin{aligned} \text{S} &= 4.4 \text{E} - 3 \text{ [m}^2\text{]}, \text{m} = 0.043 \text{ [kg]}, \text{c}\_{\text{P}} = 925 \text{ [J/kgK]},\\ \text{h} &= 5 \text{ [w]}, \text{R}\_{\text{int}} = 0.01333 \text{ [ $\Omega$ ]}, \text{T}\_{\text{int}} = 293.15 \text{ [K]} \end{aligned}$$

An accurate simplified thermal model is given in MATLAB R2019b library, at MATLAB/Simulink/ Simscape/Specialized Power Systems/Electric Drives/Extra Sources/Battery, for a lithium-ion generic battery model, implemented in Simulink as is shown in Figure 12:

$$\text{T}\_{\text{cell}}(\text{s}) = \frac{\text{R}\_{\text{th}}\text{P}\_{\text{loss}} + \text{T}\_{\text{amb}}}{\text{T}\_{\text{Cs}}\text{s} + 1} \tag{18}$$

where Tcell(s)—the internal temperature of the cell [◦K] in complex s-domain (the Laplace transform). Rth—thermal resistance, cell to ambient (◦C/W). Tc—thermal time constant, cell to ambient (s). Ploss - RintI 2-the overall heat generated (W) during the charge or discharge process [w]. Tamb—the ambient temperature set up by the user [K].

**Figure 12.** The detailed Simulink diagram of the thermal model block.

The internal resistance and the polarization constant Rint(T) and K(T) respectively vary with respect to temperature according to Arrhenius relationships:

$$\begin{array}{l} \mathbf{K}(\mathbf{T}) = \mathbf{K}|\_{\sf T\_{\rm ref}} \exp(\boldsymbol{\alpha} \left( \frac{1}{\sf T\_{\rm coll}} - \frac{1}{\sf T\_{\rm ref}} \right)), \boldsymbol{\alpha} = \frac{\mathbf{E}}{\mathbf{RT}}\\ \mathbf{R}\_{\rm int}(\mathbf{T}) = \mathbf{R}\_{\rm int}|\_{\sf T\_{\rm ref}} \exp(\boldsymbol{\beta} \left( \frac{1}{\sf T\_{\rm coll}} - \frac{1}{\sf T\_{\rm ref}} \right)), \boldsymbol{\beta} = \frac{\mathbf{E}}{\mathbf{RT}} \end{array} \tag{19}$$

where Tref—the nominal ambient temperature, in K. α—the Arrhenius rate constant for the polarization resistance. β—the Arrhenius rate constant for the internal resistance.

For simulation purpose for implemented thermal block in Simulink, we use the following approximative values for the Li-ion battery thermal model parameters:

> Rth = 6 [ ◦C], Tc = 2000 [s], α = β = <sup>E</sup> <sup>R</sup>, E = 20 [kJ/mol] − activation energy R = 8.314 [J/molK] − Boltzman constant

The ambient temperature profile and the output temperature of the Simulink thermal model described by the Equations (18) and (19) are shown in Figure 13a,b, respectively. The evolution of the internal resistance of the battery cell Rint (T) and of polarization constant K(T), at room temperature Tref = 293.15 [K], is shown in Figure 14a,b.

**Figure 13.** (**a**) The ambient temperature profile; (**b**) The output temperature of the thermal model block.

**Figure 14.** (**a**) The internal battery Rint at ambient temperature (20 degC); (**b**) The polarization constant at ambient temperature (20 degC).

The output temperature of the thermal model for changes in ambient temperature is shown in Figure A4a, and the effects on internal battery resistance Rint and polarization constant K are presented in Figure A4b,c, shown in Appendix A.

#### **3. Li-Ion Co Battery State of Charge Estimation Algorithms**

Almost all BMS HEV/EV systems in the automotive industry have integrated emergency systems that indicate the available battery capacity. As the SOC is not directly measured, its estimation is required. For estimating SOC, several methods for estimating adaptive filtering are developed in the field literature, among which the Kalman filters are the most used. More details about battery modelling, linear and nonlinear Kalman filter estimators, especially for state and parameter estimation, can be found in [4,7–12,14,15,26–37]. For performance comparison purposes, in this actual study, we develop two well-suited real-time SOC estimators, namely an Adaptive Extended Kalman Filter (AEKF) with the process and measurement noises correction, and a linear observer estimator (LOE) with a constant Luenberger gain.

#### *3.1. Li-Ion Cobalt Battery-Adaptive Extended Kalman Filter SOC Estimator*

As we mentioned in the previous section, the most suitable method for estimating SOC in real-time is the Coulomb counting method. The main disadvantage of this estimation technique is the difficulty of "predicting" the most appropriate initial SOC value of the battery, which could lead to an increase in time of the SOC estimation error and to a new "SOC calibration" based on "OCV measurement" [5]. However, "it is tough to measure the battery OCV in real-time and, consequently, a small OCV error may lead to a significant battery SOC difference", as is stated in [5].

Thus, one is thinking of improving the Coulomb metering method, a viable alternative is using an EKF SOC real-time estimator, suitable for a wide range of HEV/EVs applications. Besides, the adopted version of an adaptive EKF (AEKF) real-time estimator combines the advantages of both the Coulomb counting method and battery OCV calibration [5]. More precisely, the AEKF SOC estimator is an EKF, as is developed in detail in [7,8,10] with the performance improved in [5,30].

Additionally, the AEKF algorithm makes a recursive correction of the Gaussian process and measurement noises that simplifies the tuning procedure significantly. In [17], the correction is beneficial to calculate the Kalman gain of the AEKF SOC estimator, which leads to optimal results for the SOC estimation, as is shown in [5]. Furthermore, AEKF algorithm can improve its estimation performance by using "a fading memory factor to increase the adaptiveness for the modelling errors and the uncertainty of Li-ion battery SOC estimation, as well as to give more credibility to the measurements", as is stated in [5,7].

As we mentioned in the previous section, the AEKF requires a dynamic state-space representation model of Li-ion Co battery, in order "to develop a simulation model for the emulation of a nonlinear battery" behaviour [17]. The AEKF algorithm is based on the linearized model of the battery, as is developed in [5,7–10,17,26]. In our research paper, for the case study, we adopt the AEKF algorithm developed in [17] and is presented briefly in Table 3. For more details, the reader can refer to the papers [7–9]. The discrete-time state-space representation of the generic Li-ion Co battery model, required to design and implement in real-time the AEKF SOC estimator, is given by the Equations (20) and (21), further simplified to a unidimensional SOC state-space discrete-time representation:

$$\mathbf{x}\_{1}(\mathbf{k}+1) = \mathbf{x}\_{1}(\mathbf{k}) - \mathbf{T}\_{\mathbf{s}}(\frac{\eta\_{\text{SOC}}}{\mathbf{Q}\_{\text{rated}}}) \times \mathbf{u}(\mathbf{k}) \tag{20}$$

$$\begin{cases} \mathbf{y}(\mathbf{k}) = \mathbf{E}\_{0} - \frac{\mathbf{K}\mathbf{u}(\mathbf{k})\mathbf{A}\mathbf{t}}{\mathbf{x}\_{1}(\mathbf{k})} + \mathbf{A}\mathbf{e}\mathbf{x}\mathbf{e}^{\mathbf{u}}((-\mathbf{B}\mathbf{u}\mathbf{p}\mathbf{Q}\mathbf{u}\mathbf{u}\mathbf{d}/\mathbf{p}\mathbf{s}\mathbf{C})\mathbf{x}(1-\mathbf{x}\_{1}(\mathbf{k}))) - \mathbf{R}\_{\mathrm{int}}\mathbf{u}(\mathbf{k})\\\mathbf{x}\_{1}(\mathbf{k}) \triangleq \mathbf{x}\_{1}(\mathbf{k}\mathbf{T}\_{\mathrm{s}}) \text{ } \text{SOC (k)} \triangleq \text{SOC (kTS)} \rightarrow \mathbf{x}\_{1}(\mathbf{k}) = \text{SOC (k)}\\\mathbf{u}(\mathbf{k}) \triangleq \mathbf{u}(\mathbf{k}\mathbf{T}\_{\mathrm{s}}), \mathbf{I}\_{\mathrm{bat}}(\mathbf{k}) \triangleq \mathbf{I}\_{\mathrm{bat}}(\mathbf{k}\mathbf{T}\_{\mathrm{s}}) \rightarrow \mathbf{u}(\mathbf{k}) = \mathbf{I}\_{\mathrm{bat}}(\mathbf{k})\\\mathbf{y}(\mathbf{k}) \triangleq \mathbf{y}(\mathbf{k}\mathbf{T}\_{\mathrm{s}}), \mathbf{V}\_{\mathrm{bat}}(\mathbf{k}) \triangleq \mathbf{V}\_{\mathrm{bat}}(\mathbf{k}\mathbf{T}\_{\mathrm{s}}) \rightarrow \mathbf{y}(\mathbf{k}) = \mathbf{V}\_{\mathrm{bat}}(\mathbf{k})\\\mathbf{k} \in \mathbf{Z}^{+} \end{cases} \tag{21}$$

where Ibat(k), Vbat(k) are the battery input current profile and terminal voltage at the discrete time k, Δt = Ts is the sampling time, set to 1 in MATLAB simulations. In this representation the state space Equation (17) and input-output Equation (18) depends only on SOC, the first equation is linear and the second one is highly nonlinear. The proposed algorithm AEKF follows the same steps such in [5,7–9] combined with the approach developed in [17], as is shown below:

AEKF SOC estimation algorithm steps:

[AEKF 1.1] Write Li-ion Co battery discrete-time nonlinear generic model equations:

$$\text{SOC}(\mathbf{k}+1) = \text{SOC}(\mathbf{k}) - \text{T}\_s(\frac{\eta\_{\text{SOC}}}{\text{Q}\_{\text{rated}}}) \times \mathbf{u}(\mathbf{k}) \tag{22}$$

*Energies* **2020**, *13*, 2749

$$\begin{array}{l} \text{y}(\mathbf{k}) = \mathbf{E}\_0 - \frac{\text{Ku}(\mathbf{k})\mathbf{A}\mathbf{t}}{\text{SOC}(\mathbf{k})} + \mathbf{A}\_{\text{exp}}\mathbf{e}^{\dagger} (\left(-\text{B}\_{\text{exp}}\mathbf{Q}\_{\text{trad}}/\eta\_{\text{SOC}}\right) \times \left(1 - \text{SOC}(\mathbf{k})\right) - \mathbf{R}\_{\text{int}}\mathbf{u}(\mathbf{k})\\ \text{u}(\mathbf{k}) = \mathbf{I}\_{\text{bat}}(\mathbf{k}) \text{ , } \mathbf{y}(\mathbf{k}) = \mathbf{V}\_{\text{bat}}(\mathbf{k}) \end{array} \tag{23}$$

[AEKF 1.2] Write the unidimensional Li-ion Co battery model in discrete-time state space representation:

$$\begin{cases} \mathbf{x}(\mathbf{k}+1) = \mathbf{x}(\mathbf{k}) - \mathbf{T}\_{\mathbf{s}}(\frac{\text{RSC}}{\text{Q}}) \times \mathbf{u}(\mathbf{k}) + \mathbf{w}(\mathbf{k}) = \mathbf{f}(\mathbf{x}(\mathbf{k}), \mathbf{u}(\mathbf{k})) + \mathbf{w}(\mathbf{k})\\ \mathbf{y}(\mathbf{k}) = \mathbf{E}\_{0} - \frac{\mathbf{K}\mathbf{A}}{\mathbf{x}(\mathbf{k})}\mathbf{u}(\mathbf{k}) + \mathbf{A}\_{\text{exp}}\mathbf{e}^{((-\mathbf{R\_{exp}}\mathbf{Q}/\eta\_{\text{K}\text{K}})\times(1-\mathbf{x}(\mathbf{k})) \\ \mathbf{u}(\mathbf{k}) = \mathbf{I}\_{\text{bat}}(\mathbf{k}), \mathbf{y}(\mathbf{k}) = \mathbf{V}\_{\text{bat}}(\mathbf{k}) \end{cases}$$

where the process *w*(*k*) and measurement output *v*(*k*) are white uncorrelated noises of zero mean and covariance matrices *Q*(*k*) and *R*(*k*) respectively, i.e.,

$$\begin{aligned} w(k) &\sim (0, Q(k)), v(k) \sim (0, R(k)) \\ E(w(k)w(j)^T) &= Q(k)\delta\_{kj}, E(v(k)v(j)^T) = R(k)\delta\_{kj} \\ \delta\_{kj} &= \begin{Bmatrix} 0, & k \neq j \\ 1, & k = j \end{Bmatrix} \end{aligned} \tag{25}$$

[AEKF 2] Initialization:

The initial value of SOC is estimated as a Gaussian random vector of the mean and covariance values given in (26).

For k ≥ 0 set

$$\begin{aligned} \hat{\mathbf{x}}\_{0} &= \mathbb{E}[\mathbf{x}\_{0}] - \text{the initial mean value} \\ \hat{\mathbf{P}}\_{\mathbf{x}\_{0}} &= \mathbb{E}[(\mathbf{x}\_{0} - \hat{\mathbf{x}}\_{0})(\mathbf{x}\_{0} - \hat{\mathbf{x}}\_{0})^{\mathsf{T}}] - \text{the initial state covariance matrix} \end{aligned} \tag{26}$$

[AEKF 3] Linearize the Li-ion Co nonlinear dynamics and calculate the Jacobian matrices:

The nonlinear dynamics of Li-ion Co battery is linearized around the most recent estimation state value *x*ˆ(*k*|*k*) and *x*ˆ(*k*|*k* − 1) respectively, considered as an operating point. The Jacobian matrices of the linearization are given by:

$$\begin{array}{l} A(k) = \frac{\partial f(k, \mathbf{x}(k), \boldsymbol{\mu}(k))}{\partial \mathbf{x}(k)} \vert\_{\hat{\mathbf{x}}(k|k)} = 1 \\ B(k) = -\frac{\eta\_{\text{SCC}}}{Q} \\ \mathbf{C}(k) = \frac{\partial g(k, \mathbf{x}(k), \boldsymbol{\mu}(k))}{\partial \mathbf{x}(k)} \vert\_{\hat{\mathbf{x}}(k|k-1)} = \frac{K}{\mathbf{x}^2(k)} \vert\_{\boldsymbol{\Omega}(k|k-1)} + \frac{A\_{\text{exp}} \mathbf{R}\_{\text{exp}} \mathbf{Q}}{\eta\_{\text{SOC}}} \exp\left(-\frac{\mathbf{R}\_{\text{exp}} \mathbf{Q}}{\eta\_{\text{SOC}}} (1 - \mathbf{x}(k))\right) \vert\_{\hat{\mathbf{x}}(k|k-1)} \end{array} \tag{27}$$

For k ∈ [1, +∞) do [AEKF 4] Prediction phase (forecast or time update from (k|k) to (k + 1)|k):

$$\begin{aligned} \hat{x}(k+1|k) &= A(k)\hat{x}(k|k) + B(k)u(k) \\ \hat{P}(k+1|k) &= A(k)\hat{P}(k|k)A(k)^T + a^{-2k}Q(k) \end{aligned} \tag{28}$$

**Remark:** In this phase, the predicted value of the state vector *x*ˆ(*k* + 1|*k*) is calculated based on the previous state estimate *<sup>x</sup>*ˆ(*k*|*k*) and the state covariance positive definite matrices *<sup>P</sup>*ˆ(*k*|*k*) and *<sup>P</sup>*ˆ(*<sup>k</sup>* + <sup>1</sup>|*k*) (unidimensional in the case study) are affected by a fading memory coefficient α.

[AEKF 5] Compute an updated value of Kalman filter gain:

$$K(k) = a^{2k} \mathcal{P}(k+1|k) H(k)^T (H(k) a^{2k} \mathcal{P}(k+1|k) H(k)^T + R(k))^{-1} \tag{29}$$

[AEKF 6] Correction phase (analysis or measurement update):

The Li-ion Co battery SOC estimated state is updated when an output measurement is available in two steps:

[AEKF 6.1] Update the SOC estimated state covariance matrix:

$$
\hat{P}(k+1|k+1) = \left(I - K(k)H(k)\right)\hat{P}(k+1|k)\left(I - K(k)H(k)\right)^T + a^{-2k}K(k)R(k)K(k)^T \tag{30}
$$

[AEKF 6.2] Update the SOC estimated state variable:

$$\pounds(k+1|k+1) = \pounds(k+1|k) + K(k)(\mathcal{y}(k) - \mathcal{g}(\pounds(k+1|k), u(k), k))\tag{31}$$

[AEKF 7] Adaptive process and measurement noise covariance matrices correction in two steps: For k >= L, the length of the window's samples, compute: [AEKF 7.1] Output variable error and the correction factor:

$$\begin{aligned} \mathbf{E\_{rr}(k)} &= \mathbf{y\_{rms}(k)} - \mathbf{g(\widehat{x}(k|k), u\_k)} \\ \mathbf{c(k)} &= \frac{\sum\_{i=k-L+1}^{k} \mathbf{E\_{rt}(k)E\_{rr}^{T}(k)}}{L} \end{aligned} \tag{32}$$

[AEKF 7.2] Measurement noise correction:

$$\mathbf{R(k)} = \mathbf{c(k)} + \mathbf{H(k)P(k|k)H(k)}^{\mathrm{T}} \tag{33}$$

[AEKF 7.3] Process noise correction:

$$\mathbf{Q(k)} = \mathbf{K(k)c(k)K(k)}^T \tag{34}$$

The AEKF estimator is easy to implement since its "recursive predictor-corrector structure that allows the time and measurement updates at each iteration" [5]. The tuning parameters of AEKF SOC estimator are the following: *Q*(0) and *R*(0), *P*ˆ*x*<sup>0</sup> , the fading factor α and the window length L, obtained by a "trial and error" procedure based "on designer's empirical experience" [5]. It is worth noting that step 7 of the estimation algorithm simplifies substantially the procedure of tuning parameters without to affect the AEKF algorithm convergence. Moreover, the covariance matrices *Q*(0) and *R*(0) are chosen as positive definite diagonal matrices, and then during MATLAB simulations, both matrices are adaptively updated using the correction Equations (33) and (34). For simulation purposes, to test the effectiveness of the AEKF SOC estimator we set up the Kalman filter estimator parameters for all three driving cycle profile tests to the same values, i.e., *<sup>Q</sup>*(0) = <sup>5</sup>*<sup>E</sup>* <sup>−</sup> 4, *<sup>R</sup>*(0) = 0.2*<sup>E</sup>* <sup>−</sup> 3, <sup>∝</sup>= 1.001, Pˆ x0 = 1*E* − 10, *L* = 10 samples.

#### *3.2. Li-Ion Cobalt Battery-Linear Observer SOC Estimator with Constant Gain*

Linear and non-linear observers can estimate the states of the control systems. A linear observer estimator can be used to estimate SOC, as it is easy to adapt to the Li-ion Co battery model. Compared to AEKF SOC estimator performance, the proposed linear observer (LOE) SOC estimator seems to have a fast convergence rate and high estimation accuracy, as mentioned in [18]. It is easy for design a MATLAB/Simulink implementation. Besides, it is robust to changes in the initial value of SOC, to changes in the battery internal resistance and polarization constant due to temperature effects. Furthermore, it has a high capability of compensating the effects of nonlinearity and uncertainty exhibited by Li-ion Co battery model. The main drawback of LOE SOC is its inability to filter the measurement noise, so it is not robust to the measurement noise level compared to AEKF that has this great feature. The proposed linear observer relies on the determination of the appropriate feedback that achieves better SOC estimation accuracy. The following equations describe the dynamics of the linear observer estimator (LOE):

$$\begin{aligned} \frac{\text{dSC}(\mathbf{t})}{\text{d}t} &= -(\frac{\eta\_{\text{SOC}}}{\text{Q}\_{\text{inload}}}) \times \mathbf{u}(\mathbf{t})\\ \text{V}\_{\text{batt}}(\mathbf{t}) &= \mathbf{E} - \mathbf{R}\_{\text{in1}} \mathbf{i}(\mathbf{t}) = \mathbf{E}\_{0} - \frac{\mathbf{K} \int \text{idt}}{\text{SOC}(\mathbf{t})} + \mathbf{A}\_{\text{exp}} \mathbf{e}^{\left(-\mathbf{B}\_{\text{exp}} \mathbf{Q}\_{\text{max}} (1 - \text{SOC}(\mathbf{t}))\right)} - \mathbf{R}\_{\text{int}} \mathbf{u}(\mathbf{t})\\ \mathbf{u}(\mathbf{t}) &= \mathbf{i}(\mathbf{t}) \end{aligned} \tag{35}$$

Thus, Equation (35) describes the dynamics of Li-ion Co battery generic model that is unidimensional and dependent only on battery SOC. In this development, the input-output battery terminal voltage equation is linearized around a SOCop battery operating point, retaining only the first order term of Taylor series:

$$\text{V}\_{\text{bat}}(\text{SOC}) = \text{V}\_{\text{bat}}(\text{SOC}\_{\text{op}}) + (\frac{\text{dV}\_{\text{bat}}}{\text{dSOC}})|\_{\text{SOC}\,\text{op}}(\text{SOC} - \text{SOC}\_{\text{op}}) \tag{36}$$

In discrete time, the LOE battery SOC is described by the following equations:

$$\begin{aligned} \text{SOC}(\text{k}+1) &= \text{SOC}(\text{k}) - \frac{\text{Tosot}\_{\text{KCC}}}{\text{Quam}} \mathbf{u}(\text{k}) = \mathbf{A} \times \text{SOC}(\text{k}) + \text{Bu}(\text{k})\\ \text{V}\_{\text{ball}}(\text{SOC}(\text{k})) &= a\_{\text{SOC}} \times \text{SOC}(\text{k}) + \text{k}\_{\text{SOC},\text{u}} \text{SOC}(\text{k}) \mathbf{u}(\text{k}) + \text{k}\_{\text{u}} \mathbf{u}(\text{k}) + \text{E}\_{\text{0,\text{op}}} = \text{C} \times \text{SOC}(\text{k}) + \text{g}(\text{SOC}(\text{k}), \mathbf{u}(\text{k})) \quad \text{(37)}\\ \text{A}=\text{I}, \text{C}=a\_{\text{SOC}}, \text{B}=-\frac{\text{Tosot}\_{\text{KCC}}}{\text{Quam}}, \text{g}(\text{SOC}(\text{k}), \mathbf{u}(\text{k})) = \text{k}\_{\text{SOC},\text{u}} \times \text{SOC}(\text{k}) \mathbf{u}(\text{k}) + \text{k}\_{\text{u}} \times \mathbf{u}(\text{k}) + \text{E}\_{\text{0,\text{op}}} \end{aligned}$$

where the values of the coefficients αSOC, kSOC,u, ku and E0,op depend on the linearization operating point SOCop. For example, if the operating point is SOCop = 60%, these coefficients get the following values: αSOC = 0.0019,kSOC,u = 0.000077,ku = −0.0133 and E0,op = 8.0146. The Equation (37) are showing that the current output battery terminal voltage Vbat(SOC(k)) and its future evolution are both determined solely by its current state SOC (k) and the battery current input u(k). If the battery generic model system Equation (37) is observable, then the output battery terminal voltage can be used to steer the SOC(k) state of the observer. After linearization, it is easy to see that the pair (A, C) = (1, αSOC) is observable, since αSOC 0, regardless of the battery operating point. The observer model of the physical system of the Li-ion Co battery is then typically derived from the Equation (37). Additional terms may be included in order to ensure that, on receiving successive measured values of the Li-ion Co battery u(k) = i(k) input and Vbat(SOC(k)) output, the model's state SOC ¯(k) converges to SOC(k) of the battery. In particular, the output of the observer V ¯bat(SOC(*k*)) may be subtracted from the battery output Vbat(SOC(k)) and then is multiplied by a constant gain L to produce a so-called Luenberger observer, defined by the following equations:

$$\begin{aligned} \overline{\text{SOC}}(\text{k}+1) &= \mathbf{A} \times \overline{\text{SOC}}(\text{k}) + \mathbf{L}(\text{V}\_{\text{bat}}(\text{k}) - \overline{\text{V}\_{\text{bat}}}(\text{k})) + \text{Du}(\text{k})\\ \widehat{\text{V}}\_{\text{bat}}(\text{k}) &= \mathbf{C} \times \widehat{\text{SOC}}(\text{k}) + \mathbf{g}(\widehat{\text{SOC}}(\text{k}), \text{u}(\text{k})) \end{aligned} \tag{38}$$

The linear observer SOC estimator is asymptotically stable if the SOC state error:

$$\mathbf{e}\_{\text{SOC}}(\mathbf{k}) = \bar{\mathbf{SOC}}(\mathbf{k}) - \mathbf{SOC}(\mathbf{k}) \to 0 \quad \text{when} \quad \mathbf{k} \to \infty \tag{39}$$

For a Luenberger observer, the SOC state estimation error satisfies the following relationship:

$$\mathbf{e}\_{\rm SOC}(\mathbf{k}+1) = (\mathbf{A} - \mathbf{L}\mathbf{C})\mathbf{e}\_{\rm SOC}(\mathbf{k})\tag{40}$$

The asymptotically condition (41) is satisfied only if (A-LC) is a Hurwitz matrix, so all the eigenvalues of this matrix are located in z-plane inside of the unit circle |z| = 1. For an unidimensional system, such in our case, A-LC must satisfies the relationship:

$$\begin{cases} -1 < \text{A} - \text{LC} < 1 \to -1 < 1 - \text{L} \ast \alpha\_{\text{SOC}} < 1\\ \text{L} \in \left(0, \frac{2}{a\_{\text{SOC}}}\right) \end{cases} \tag{41}$$

For MATLAB simulations L is set to 1, 10, and 100 to analyze the performance of the LOE estimator in terms of convergence speed, robustness and SOC estimation accuracy for same driving conditions tests, UDDS, UDDS-EPA and FTP-75, like the AEKF SOC estimator developed in the previous subsection. The Simulink models of the LOE SOC, Li-ion Co battery model, thermal model block and the input driving cycles current profiles are shown in Figure 15. The battery model and the LOE SOC estimator block is detailed in Figure 16, and the Simulink model of thermal block is shown in Figure 12.

**Figure 15.** The Simulink diagram of the combined Li-ion Cobalt battery model and LOE block located to the top side and, the Simulink diagram of thermal model block located in the bottom side.

**Figure 16.** The detailed Simulink diagram of the combined Li-ion Co battery and LOE models.

#### *3.3. Real-Time MATLAB Simulation Results*

In this section, an extensive number of simulations, conducted on MATLAB software platform, is performed to validate the battery model and to analyze the performance of both proposed AEKF and LOE SOC estimators. The performance of both, AEKF and LOE SOC estimators is analyzed in terms of accuracy, robustness, convergence speed and real-time implementation simplicity. Robustness is tested for changing driving conditions by performing tests based on each of the three most commonly used driving cycle profiles provided in the ADVISOR-MATLAB platform, namely UDDS, UDDS-EPA and FTP described in Section 2. Furthermore, for each driving cycle profile, the robustness of both SOC estimators are testing the following four scenarios:

	- -R11—for SOCini = 100%
	- -R12—for SOCini = 40%
	- -R21—for SOCini = 100%, noise measurement level σ = 0.01(increased from 0.001)
	- -R22—for SOCini = 40%, noise measrement level, σ = 0.01(increased from 0.001)
	- -R31—for SOCini = 100%, Qnom = 2.7 Ah (decresed from 5.4 Ah)
	- -R32—for SOCini = 40%, Qnom = 2.7 Ah (decresed from 5.4 Ah)
	- - R41—for SOCini = 100%, Rint = Rint(T) changes from Rint = 0.01333 [Ω], K = K(T) changes from K = 0.0099892 [V]
	- - R42—for SOCini = 40%, Rint = Rint(T) changes from Rint = 0.01333 [Ω], K = K(T) changes from K = 0.0099892 [V]

Also, the statistical errors in terms of standard deviation (MATLAB command std, σ), root mean squared error (RMSE), mean squared error (MSE) and mean absolute error (MAE) defined for each driving cycle test by the Equations (42)–(44), are summarized in one table.

$$\text{RMSE} = \sqrt{\frac{\sum\_{i=1}^{N} \left( \text{SO} \widehat{\text{C}} \text{ (i)} - \text{SOC}\_{\text{Battery\\_model}} \text{(i)} \right)^{2}}{N}} \tag{42}$$

$$\text{MSE} = \frac{\sum\_{i=1}^{N} \left( \text{SO} \widehat{\text{C}} \text{ (i)} - \text{SOC}\_{\text{Battery\\_model}} \text{(i)} \right)^{2}}{N} \tag{43}$$

$$\text{MAE} = \frac{\sum\_{i=1}^{N} |\text{SO}\widehat{\text{C}}\text{ (i)} - \text{SOC}\_{\text{Battery\\_model}}(\text{i)}|}{N} \tag{44}$$

N − number of samples.

#### 3.3.1. Test 1-UDDS Driving Cycle Profile

A. Li-ion Co generic model accuracy performance

In Figure 17 the following MATLAB simulation results are shown:


**Figure 17.** Li-ion Co battery model SOC accuracy performance (**a**) The UDDS current profile; (**b**) LOE SOC estimate vs. battery model SOC and ADVISOR SOC estimate; (**c**) AEKF estimate terminal voltage versus battery model terminal voltage; (**d**) AEKF SOC estimate versus battery model SOC and ADVISOR SOC estimate.

The simulation results reveal that the battery SOC is very accurate with respect to ADVISOR SOC estimate for same SOC initial value, like in Section 2.6.4. Also, the AEKF and LOE SOC estimators are very accurate compared to battery model SOC. Additionally, the Figure 17c reveals a strong ability of the AEKF SOC estimator to predict the battery terminal voltage.

B. Robustness of AEKF and LOE SOC Estimators

• R1-scenario

A great robustness of AEKF and LOE SOC estimators for this scenario is shown in Figure 18a,c, for R11, and in Figure 18b,d for R12.

**Figure 18.** SOC Estimators robustnsess-Scenario R1; (**a**) AEKF for R11; (**b**) AEKF for R12 (**c**) LOE for R11; (**d**) LOE for R12.

• R2-scenario

The MATLAB simulation results shown in Figure 19a–d indicate a great robustness of AEKF SOC estimator compared to LOE SOC.

**Figure 19.** *Cont*.

**Figure 19.** The robustness of AEKF and LOE SOC estimators-Scenarion R2 (**a**) AEKF for R21; (**b**) AEKF for R22; (**c**) LOE for R21 (**d**) LOE for R22.

The AEKF SOC estimator has a great ability to filter the measurement noise, thus AEKF SOC estimator outperforms the LOE SOC regarding the robustness performance to changes in noise level.

• R3-scenario

About the MATLAB simulations shown in Figure 20a–d it is worth highlighting the great robustness performance for both SOC estimators for this scenario.

**Figure 20.** The SOC estimators' behaviour for R3-scenario (**a**) AEKF for R31; (**b**) AEKF for R32; (**c**) LOE SOC for R31; (**d**) LOE SOC for R32.

#### • R4-scenario

The output temperature profile of thermal model and the effects of temperature changes on the internal resistance Rint and polarization constant are shown in Figure A4. For this scenario, the MATLAB simulation results depictured in Figure 21a–d show an excellent robustness performance for both SOC estimators.

**Figure 21.** AEKF and LOE SOC estimators robustness performance for R4-scenario; (**a**) AEKF for R41; (**b**) AEKF for R42; (**c**) LOE SOC for R41; (**d**) LOE for R42.

The statistical errors corresponding to all four scenarios developed for UDDS driving cycle test are summarized in Table 3.


The results of statistical errors performance analysis for all scenarios from Table 3, for UDDS driving cycle test, indicate that the AEKF SOC estimator surpasses the LOE SOC estimator in the competition for robustness performance.

3.3.2. Test 2: UDDS-EPA Charging Current Profile

A. Cobalt Li-ion generic model accuracy and validation

The MATLAB simulation results are shown in Figure 22:


**Figure 22.** Li-ion Co battery model SOC accuracy performance and validation; (**a**) UDDS-EPA driving cycle; (**b**) LOE SOC estimate vs. battery model SOC and ADVISOR SOC estimate; (**c**) AEKF battery terminal voltage estimate vs. battery model terminal voltage; (**d**)AEKF SOC estimate vs. battery model SOC vs. ADVISOR SOC.

Like UDDS driving cycle, the MATLAB simulation results presented in Figure 22b,d reveal that the Li-ion Co battery model fits very well, within a 2% SOC error, the experimental setup ADVISOR-MATLAB platform SOC estimate. So, once again these results certainly confirm the validity of the generic lithium-ion cobalt battery model.

#### B. Robustness of AEKF SOC Estimator

To keep the manuscript lenght reasonable, for the second driving cycle test, we show only the results for SOCini = 40%, i.e., for R12, R22, R32, and R42-scenarios.

#### • R1-scenario

The MATLAB simulation results shown in Figure 23a,b indicate an excellent robustness performance for both SOC estimators.

**Figure 23.** The robustness of AEKF and LOE SOC estimators for R1-scenario; (**a**) AEKF for R12 (**b**) LOE for R12.

• R2-scenario

A great robustness for both SOC estimators for this scenario and R22 case is also shown in Figure 24a,b.

**Figure 24.** The robustness of AEKF and LOE SOC estimators for R2-scenario; (**a**) AEKF SOC for R22 (**b**) LOE SOC for R22.

#### • R3-scenario

The MATLAB simulation results depicted in Figure 25a,b reveal a great robustness performance for the AEKF SOC estimator compared to the LOE SOC estimator that has small changes in SOC estimate accuracy.

**Figure 25.** Robustness performance of AEKF and LOE SOC estimators for R3-scenario; (**a**) AEKF SOC for R32; (**b**) LOE SOC for R32.

• R4-scenario:

For this scenario is considered the output temperature profile of thermal model and the effects of temperature changes on the internal resistance Rint and polarization constant K shown in Figure A4. The MATLAB simulation results of AEKF and LOE SOC estimation robustness performance are presented in Figure 26a,b.

**Figure 26.** Robustness of AEKF and LOE SOC estimators for R4-scenario (**a**) AEKF SOC for R42; (**b**) LOE SOC for R42.

For this scenario, the simulation results shown in Figure 26 indicate a great robustness performance for both SOC estimators. The statistical errors RMSE, MSE, MAE and standard deviation are summarized in Table A1 in Appendix A.

Like UDDS, the result of the performance analysis, for all the scenarios included in Table A1, indicates once again that the AEKF SOC estimator remains the most suitable SOC estimator as compared to LOE SOC estimator.

#### 3.3.3. Test 3: FTP-ADVISOR Driving Cycle Current Profile

A. Battery model SOC accuracy and model validation

The FTP driving cycle current profile for testing the battery is shown in Figure 27a. For generic battery model validation, the AEKF SOC estimate, the Li-ion Co battery model SOC and the ADVISOR-MATLAB Rint Li-battery SOC estimate are shown on the same graph in Figure 27b.

**Figure 27.** Li-ion Co battery model SOC accuracy performance and validation. (**a**) The FTP driving cycle current profile; (**b**) AEKF SOC estimate vs. battery model SOC; (**c**) AEKF terminal voltage estimate vs. battery terminal voltage; (**d**) LOE estimate vs. battery model SOC vs. ADVISOR SOC estimate.

Similarly, the same graphs related to LOE SOC estimator performance are shown in Figure 27d. Furthermore, the SOC accuracy of the battery Li-ion Co model revealed by MATLAB simulation results are supported by the experimental results shown in Figure 28 for same FTP driving cycle test performed on the ADVISOR-MATLAB platform.

**Figure 28.** FTP driving speed cycle of the input HEV midsize car; HEV car speed cycle; estimated Rint Li-ion battery SOC on NREL ADVISOR- MATLAB platform, and current profile (from the top to the bottom).


In Figure 29a,b are depicted the simulation results for both SOC estimators that reveal a great robustness performance for LOE SOC compared to AEKF SOC estimator.

**Figure 29.** Robustness performance of AEKF and LOE SOC estimators for R1-scenario; (**a**)AEKF SOC for R12; (**b**) LOE SOC for R12.

• R2-scenario

For this scenario, the simulation results shown in Figure 30a,b indicate a great robustness for AEKF SOC estimator compared to LOE SOC.

**Figure 30.** AEKF and LOE SOC estimators - robustness performance for R2-scenario (**a**) AEKF SOC for R22; (**b**) LOE SOC for R22.

• R3-scenario

For the third scenario, the results presented in Figure A5a,b in Appendix A show a slight superiority of the LOE SOC estimator compared to the AEKF SOC estimator.

• R4-scenario

The output temperature profile of thermal model and the effects of temperature changes on the internal resistance Rint and polarization constant are shown in Figure A4a–c, and the results of MATLAB simulations are presented in Figure A6a,b (both figures in Appendix A). From Figure A6, it seems that the LOE SOC estimator performs better than AEKF SOC estimator. Also, the statistical errors for FTP ADVISOR driving cycle are summarized in Table A2 form Appendix A. As in the first two driving cycles, for the FTP driving cycle test the result of the robustness performance analysis based on the statistical errors included in Table A2 confirms again that the AEKF SOC estimator performs better than its competitor LOE SOC estimator. Thus, based on the statistical results of the three tables, it can now decide that the most appropriate SOC estimator for this type of HEV application is the AEKF SOC estimator which shows an absolute superiority compared to the LOE SOC estimator, due to its ability to filtrate the measurement noise, as well as more robust to the aging effects on the Li-ion Co battery.

#### **4. Discussions**

During this research, we have substantially enriched our experience in designing, modelling, implementing and validating Li-ion batteries, developing and implementing real-time SOC estimation algorithms in a friendly and attractive MATLAB-Simulink environment. Now we try to summarize some of the most relevant aspects that have captured our attention during this research.

#### *4.1. SOC Estimators' Convergence Speed*

The analysis of the convergence speed performance of both SOC estimators can be done visually by examining the graphs strictly related to SOC. In almost all the graphs, the AEKF SOC estimate reaches the true value of Cobalt Li-ion battery model SOC after 40–190 s, when decreasing the SOC initial value from 80% to 40% or 16–150 s for an increase from 80% to 100%, as shown in Figure 31a,b by zooming at the beginning of the transient, which obviously is a rapid convergence speed.

Compared to AEKF SOC estimator, the convergence speed of LOE SOC estimator can be controlled by choosing the most appropriate value for the observer gain. For high gain values, the LOE SOC estimator becomes much faster as can be seen for the FTP driving cycle test, where the observer gain is 100. For the UDDS driving cycle, the observer gain is 10 and, for performance analysis purpose, the observer gain for UDDS-EPA driving cycle is intentionally set to 1. For this case, the LOE SOC estimator reaches the true value of the battery model SOC after 400 s, much higher as compared to AEKF SOC estimator.

**Figure 31.** AEKF SOC estimation convergence speed; (**a**) for a decrease SOC initial value; (**b**) for an increase initial value.

#### *4.2. SOC Estimation Accuracy*

The MATLAB simulation results shown in the previous section reveal, in most cases, an excellent SOC estimation accuracy of AEKF SOC estimator after the estimate reaches the battery model SOC true value. Still, in some cases, due to unsuitable values for the tuning parameters, the AEKF SOC estimate is biased compared to LOE SOC estimator. On the other hand, the LOE SOC estimator accumulates a significant estimation error during the transient. Regarding the EKF SOC estimator, we observed that the SOC accuracy depends on a "trial and error" empirical adjustment procedure of tuning parameter values. Unfortunately, this procedure takes a lot of time. Moreover, a new readjustment procedure is required when changing the driving conditions and SOC initial value, as well as when aging and temperature effects take place. The adopted version AEKF due to its adaptive features attenuates the tuning procedure of the parameters significantly.

#### *4.3. SOC Estimator-Measurement Noise Filtration*

An important aspect that we also observed in this research is the measurement noise filtration by both estimators. Only the AEKF has this ability to filtrate the measurement noise compared to LOE SOC estimator, as you can see, for example, in Figure 30b.

#### *4.4. SOC Estimators-Real Time Implementation*

As we mentioned in the previous section due to its "predictor-corrector structure", the AEKF SOC estimator becomes a recursive algorithm, "more simple to implement in real time and computationally efficient" [10]. Also, the LOE SOC structure is simple and easy to design and implement in real time, in particular due to its linearized structure and having a single parameter needed for adjustment. In addition, the proposed generic lithium-ion cobalt battery model is simple, easy to design and quickly to implement in real time, based directly on the manufacturer's battery specifications. MATLAB-Simulink software platform provides a valuable and practical Simscape SimPower Systems library, helpful to be used for designing and implementation of different HEVs and EVs powertrains configurations.

#### *4.5. SOC Estimators-Statistical Errors Analysis*

The results from the first line (RMSE, MSE, MAE) provide the accuracy of the battery model SOC and ADVISOR estimate, beneficial for Li-ion Co battery model validation performed in Section 2.6.4 for first UDDS driving cycle test and for third one FTP-75. The validation of the battery model for second UDDS-EPA driving cycle test is proved in Section 3.3 based on the MATLAB simulation results shown in Figure 22. The statistical errors from Table 3, Tables A1 and A2 are valuable to compare the results of both SOC estimators to those obtained in the field literature by similar algorithms SOC estimators, for same driving cycle tests, and same performance error indicators (RMSE, MSE, MAE). In Section 2.5.2 the state of the art analysis focused on adaptive filters SOC estimators reported in the literature is made. For this analysis, Table 3, Tables A1 and A2 provide valuable information to compare the results obtained by AEKF SOC estimator, in terms of accuracy and robustness performance, developed in actual research work to those obtained in [18–24] for similar conditions, especially for same input current cycle profiles. Unfortunately, it was possible to make only a partial analysis since many researchers use different input current profiles and different error indicators that do not match with those used in our research. But, for the cases that match with our current profile, the information collected in all three Table 3, Tables A1 and A2 corresponding to each input current cycle profile can be useful to analyse all similar situations. Thus, the present research work can be a valuable source of inspiration for readers and researchers.

#### **5. Conclusions**

In this research paper, among the most relevant contributions the following may be highlighted:


The case study is a 5.4 Ah Li-ion Cobalt battery, of high simplicity and accuracy, easy to be implemented in real-time and to provide beneficial support to build two real-time AEKF and LOE SOC estimators. For a good insight on the realistic battery life environment, the case of the battery internal resistance and polarization coefficient as parameters temperature-dependent is also investigated. Both parameters are updated dynamically through a simplified thermal model designed in Section 2.7. The robustness and accuracy of both SOC estimators is investigated in detail, for three most used driving cycles tests in the automotive industry (UDDS, UDDS-EPA and FTP) and changes in:



Based on the statistical errors calculated for each driving cycle test in terms of RMSE, MSE and MAE, it was possible to choose from both competitors the most suitable SOC estimator. The result of overall performance analysis indicates that the AEKF SOC estimator performs better than LOE SOC estimator.

In the future work, we continue our investigations on lithium batteries regarding an improved modelling approach by "integrating the effect of degradation, temperature and SOC effects" [10], and for possible extensions to more accurate adaptive neural fuzzy logic SOC estimation techniques.

**Author Contributions:** R.-E.T. has contributed for algorithms conceptualization, manuscript preparation and writing it. N.T. has contributed for battery model validation, performed the MATLAB simulations and analyzed the results. M.Z. has contributed for a formal analysis of the results, for the visualization, the project supervision and administration. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** Research funding (discovery grant) for this project from the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**


*Energies* **2020**, *13*, 2749

#### **Appendix A**

*Appendix A.1. Figures*

**Figure A1.** The Simulink block diagram of a hypothetical midsize town car-the diagram includes the following blocks: differential, clutch, gear, battery system, transmission and accessories


**Figure A2.** The UDDS test on the ADVISOR 3.2 integrated MATLAB platform; (**a**) The plot of statistic errors for Li-Ion CO2 battery model, (**b**)The plot of the statistic errors for Advisor Li battery Rint model.

**Figure A3.** (**a**) Electric Vehicle simulation model application. (**b**) motor speed in RPM; (**c**) battery SOC (%); (**d**), US fuel economy; (**e**) motor torque (Nm); (**f**) discharge battery current profile.

(**a**) **Figure A4.** *Cont*.

**Figure A4.** Temperature effects on Rint and K. (**a**) output temperature profile; (**b**) internal battery resistance Rint; (**c**) polarization constant K.

**Figure A5.** Robustness performance of AEKF and LOE SOC estimators for R3-scenario; (**a**) AEKF SOC for R32; (**b**) LOE SOC for R32.

**Figure A6.** Robustness of AEKF and LOE SOC estimators for R4-scenario; (**a**) AEKF SOC for R42; (**b**) LOE SOC for R42.

#### *Appendix A.2. Tables*





#### **References**


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