Advanced Methodology for the Optimal Sizing of the Energy Storage System in a Hybrid Electric Refuse Collector Vehicle Using Real Routes

Abstract

This paper presents a new methodology for optimal sizing of the energy storage system ($ESS$), with the aim of being used in the design process of a hybrid electric (HE) refuse collector vehicle ($RCV$). This methodology has, as the main element, to model a multi-objective optimisation problem that considers the specific energy of a basic cell of lithium polymer ($Li$–$Po$) battery and the cost of manufacture. Furthermore, optimal space solutions are determined from a multi-objective genetic algorithm that considers linear inequalities and limits in the decision variables. Subsequently, it is proposed to employ optimal space solutions for sizing the energy storage system, based on the energy required by the drive cycle of a conventional refuse collector vehicle. In addition, it is proposed to discard elements of optimal space solutions for sizing the energy storage system so as to achieve the highest fuel economy in the hybrid electric refuse collector vehicle design phase.

1. Introduction

In cities with high density of population, refuse collector vehicles ($RCV$s) are of vital importance due to the need to maintain a healthy city. However, the overuse of these trucks leads to a negative impact on the environment because high quantities of fuel are required and contribute to the pollution, aggravated by the automotive industry [1,2].

Accordingly, hybrid electric vehicles (HEVs) and electric vehicles (EVs) offer a solution for the environmental trade-off in terms of pollution problems. However, although HEVs and EVs have great advantages, the HEV is a mature technology in comparison to EV [3,4].

In addition, the HEVs are more feasible for RCV because a larger autonomy is required. Among the HEVs, the RCV is a specific application where the total weight variation, repetitive and aggressive drive cycles are important parameters for its design due to the fact that, although HEVs can cover large distances, a high fuel consumption is required [5]. Then, taking the last consideration on the RCV design, the energy storage system in relation to fuel consumption can be addressed.

Different energy storage elements, such as batteries, supercapacitors or fuel cells, for the energy storage system may be used. For instance, in [6], a hybrid heavy-duty trucks with battery is used, in order to perform a life cycle analysis. In addition, in [7], an energy management strategy for plug-in hybrid electric vehicles based on batteries is proposed.

On the other hand, the supercapacitors may also be used for applications of energy storage. For instance, in [8], a balancing circuit for a hybrid energy storage system with supercapacitor is proposed. In addition, in [9], a current-source converter for a hybrid energy storage system is performed to interface a supercapacitor (SC) module and a battery stack. Due to the supercapacitor advantages, an increase in the charge/discharge rate and cycling life is achieved [10,11].

Essentially, there are three types of methodologies: sequential, simultaneous and nested, wherein the main purpose is to achieve a $HEV$ design optimisation [12]. The structure for each methodology is based on levels such as topology, component sizing and control strategy. Although several layers are defined, the components sizing and the control strategy can fulfil the requirements to achieve the HEV optimal design, either for series, parallel or hybrid topology. In addition, taking previous consideration, in several works, the nested methodology is more suitable to obtain a better HEV design due to its advantage of low computational times [13,14]. However, for HEV design, if the methodologies consider limited parameters to develop a high-performance HEV, then an optimal design cannot be achieved.

Accordingly, interest in using more efficient optimisation methods has been increased because the optimal solutions can be delimited through well-defined restrictions. Thereby, the number of evaluations of the objective function decrease and the computational time is reduced [15].

Many optimisation methods have been presented based on a single objective [16,17,18]. For instance, in [19], the optimal component sizing based on the weight sum method is achieved for a hybrid refuse collector vehicle. In addition, in [20], the energy management of a serial hybrid electric bus with the convex optimisation is performed. Furthermore, in [21], the component sizing of a parallel hybrid electric powertrain by the genetic algorithm is proposed. In addition, the multi-objective optimisation has been presented, wherein the multi-objective optimisation methods are more robust because the space solutions can be delimited. It should be noted that, in the HEV design, multi-objective optimisation is required due to the nature of the system, i.e., energy storage system and control strategy.

In accordance with the above, the sizing procedure is considered as a multi-objective problem in [22,23]. For instance, in [24], the component sizing of hybrid hydraulic powertrain by non-dominated sorting genetic algorithm II is performed. In addition, in [25,26], the optimal powertrain component sizing with a multi-objective genetic algorithm is achieved. Nevertheless, real drive cycles are not considered in the optimal sizing methodologies.

Various studies for the industrial vehicles (such as refuse collector vehicle, heavy duty vehicle) have been developed [27,28,29,30]. For instance, in [31], the optimal sizing and control of a hybrid tracked vehicle are performed. In addition, in [32], the optimisation problem for the sizing and control of a heavy-duty vehicle is formulated, the solution through several methods (brute force, DIviding RECTangles (DIRECT), sequential quadratic programming (SQP), genetic algorithms (GA) and particle swarm optimisation (PSO)) is achieved. However, the industry demands new methodologies for optimal powertrain sizing.

In this work, a new methodology is developed for optimal sizing of the energy storage system. The manufacturing cost and the volume of a basic cell of lithium polymer ($Li$–$Po$) battery are considered in the optimisation problem. A multi-objective genetic algorithm is used, with the purpose of obtaining a space of local optimal solutions. Each item from the optimal set allows for sizing the energy storage system, based on the real drive cycle of a conventional refuse collector vehicle. The validation of the proposed methodology is performed through a quasi-static model of an $HE$–$RCV$, which considers the real behaviour of a $Li$–$Po$ cell. The fuel consumption is calculated, in order to select the energy storage system with the lowest fuel consumption.

In Section 2, a hybrid electric refuse collector vehicle model is presented, taking into account a control strategy. In Section 3, an electrochemical model for the energy storage system is presented. In Section 4, an optimisation problem for sizing of the energy storage system is described. In Section 5, the validation of the methodology is presented. Finally, Section 6 provides the main conclusions of the paper.

2. Hybrid Electric Refuse Collector Vehicle

The powertrain of the proposed $HE$–$RCV$ is of the series type configuration, as shown in Figure 1. It consists of one internal combustion engine, two electrical machines and the energy storage system.

In this paper, a new methodology is proposed for the optimal sizing of the energy storage system in order to reduce the consumption of the $ICE$, as shown in Figure 2. It is based on the application of a multi-objective genetic algorithm with experimental data of real routes.

To apply this methodology, it is necessary to estimate the fuel consumption of the $HE$–$RCV$ taking into account a control strategy.

The well-known quasi-static model of the $HE$–$RCV$ powertrain includes the longitudinal dynamics [30,33]:

$$m_{RCV}·\frac{d}{dt}v\left(t\right)=F_t\left(t\right)-(F_a\left(t\right)+F_r\left(t\right)+F_g\left(t\right)),$$

(1)

where $m_{RCV}$ is the mass of the vehicle, taking into account the dynamic load (2) as a characteristic of an RCV, $F_a$ is the aerodynamic resistance (3), $F_r$ is the rolling resistance (4), and $F_g$ is the force caused by gravity during a route on a non-horizontal road (5):

$$m_{RCV}=m_{Vehicle}+m_d\left(t\right)+m_{EM}+m_{ESS},$$

(2)

$$F_a=\frac{1}{2}·{\rho }_a·v^2·A_f·C_d,$$

(3)

$$F_r=m_{RCV}·g·C_r·cos\left(\alpha \right),$$

(4)

$$F_g\left(\alpha \right)=m_{RCV}·g·sin\left(\alpha \right).$$

(5)

Based on the longitudinal dynamics, the power (6) and the energy (7) for the powertrain can be determined:

$$\begin{array}{c}\hfill P_{HE-RCV}=F_t\left(t\right)·v\left(t\right)=m_{RCV}·\frac{d}{dt}v\left(t\right)+(F_a\left(t\right)+F_r\left(t\right)+F_g\left(t\right))·v\left(t\right)\end{array},$$

(6)

$$\begin{array}{c}\hfill E_{HE-RCV}={\int }_0^t{P}_{HE-RCV}\end{array}.$$

(7)

The transmission plays an important role in the powertrain because there is a linear relationship between torque (${\tau }_{in}$) and angular speed (${\omega }_{in}$):

$$P_{out}=\frac{{\tau }_{in}·{\omega }_{in}}{\gamma }.$$

(8)

In order to simplify the estimation of the ICE consumption, the efficiency of the electrical machines is considered constant:

$$P_{out}={\eta }_{EM}·P_{in}.$$

(9)

The weight of the electrical machines is approximated with a linear dependency with the input power:

$$m_{ME}=1.685·\begin{array}{c}\hfill P_{in}\end{array}.$$

(10)

The minimum $SOC$ of 20% and a maximum of 100% for the energy storage system is considered [34,35], in order to formulate a rule-based control strategy (11):

$$P_{source}=\left\{\begin{array}{ccc}ESS,& \mathrm{if}& (P_{in}<=P_{ESS})or(P_{body}<=P_{ESS}),\\ ICE,& \mathrm{if}& (P_{in}>P_{ESS})or(P_{body}>P_{ESS}).\end{array}\right.$$

(11)

In order to protect the $ESS$ front aggressive energy demands, the following condition is imposed:

$$\frac{P_{in}}{V_{ESS}·C_{nom}}\le C_{discharge},$$

(12)

where $C_{nom}$ is the rated capacity and $C_{discharge}$ is the maximum discharge rate.

3. Energy Storage System

Although a generic $ESS$ [36,37,38] may include several elements, such as batteries, supercapacitors [39,40], fuel cells [41], etc., in this paper, only an $ESS$ based on batteries is considered due to its specific energy, energy density and discharge rate.

Several models have been proposed with the intention of reproducing the real electrical behaviour of a battery-based $ESS$ [42]. The proposed $ESS$ is composed of a number of cells connected in series and parallel, in order to provide the required voltage and current. Each cell may be approximated with a first order electrical model, as shown in Figure 3 [43,44,45].

$V_L$ is the output voltage of the cell:

$$V_L=V_{OC}-R_0{I}_L-\int \left(\frac{I_L}{C_1}-\frac{V_{R_1{C}_1}}{R_1{C}_1}\right)dt,$$

(13)

where $V_{OC}$ is the open circuit voltage of the cell. This voltage may be estimated by using the state of charge ($SOC$) of the cell:

$$SOC=100-\frac{1}{3600·C}\int I_L\left(t\right)dt.$$

(14)

The behaviour of the cell can be estimated by experimental measuring of the $SOC$ based on 1C discharge rate beginning at 100 % of $SOC$. A 1C rate means that the discharge current will discharge the entire battery in one hour. As shown in Figure 4, $V_L$ is the voltage of the cell when the load is connected with the constant current $I_L$ and $V_L^{{}^{\prime }}$ is the voltage when the load is disconnected.

It is possible to estimate the value of $R_0$ (15), $R_1$ (16) and $C_1$ (17) for the considered model of the cell (Figure 3) [42,46]:

$$R_0=\frac{V_{OC}-V_L}{I_L},SOC=100,90,\dots ,$$

(15)

$$R_1=\frac{V_{OC}-V_L^{{}^{\prime }}}{I_L},SOC=100,90,\dots ,$$

(16)

$$C_1=\frac{{\tau }_{SOC-V_L^{{}^{\prime }}}}{R_1},SOC=100,90,\dots$$

(17)

Once a cell is experimentally characterised, the parameters of the electric model of the ESS considering $N_s$ in series are:

$$\begin{array}{c}\hfill \begin{array}{cc}\hfill V_{OC}& =N_s·V_{{OC}_{cell}},\hfill \\ \hfill R_1& =N_s·R_{1_{cell}},\hfill \\ \hfill C_1& =\frac{1}{N_s}·C_{1_{cell}}.\hfill \end{array}\end{array}$$

(18)

4. Optimal Sizing of the ESS

In the design of an $HE$–$RCV$, one of the most important points is the cost. However, other magnitudes, such as weight, volume, autonomy and efficiency, may be taken into account in order to design a more efficient vehicle. In this work, reduction of cost and volume of the $ESS$ are considered in the design of the powertrain.

For these objectives, it is possible to formulate a nonlinear multi-objective optimisation problem under several restrictions, which allows for finding optimal space solutions with a trade-off between the objectives (19):

$$\begin{array}{c}\hfill \begin{array}{cc}\hfill minF\left(x\right)& =(f_1\left(x\right),f_1\left(x\right),\dots ,f_n\left(x\right)),\hfill \\ \hfill s.t.\\ \hfill g_i& \le 0,i=1,\dots ,m,\hfill \\ \hfill h_i& =0,i=1,\dots ,m.\hfill \end{array}\end{array}$$

(19)

Since it is not possible to correlate the manufacturing cost and the volume of a cell, in this work, it is proposed to use the maximisation of the energy density as an objective in the optimisation problem. Given this cost and density, a continuous nonlinear multi-objective optimisation problem with several constraints is defined:

$$\begin{array}{c}\begin{array}{cc}\hfill F\left(x\right)=& \left\{\begin{array}{cc}min& cost\left(eD\right),\\ max& eD(C_{nom},& V_{nom},L),\end{array}\right.\hfill \\ \hfill s.t.& \hfill \\ \hfill & \begin{array}{ccccc}l{b}_{cost}& \le & cost& \le & u{b}_{cost},\\ l{b}_{eD}& \le & eD& \le & u{b}_{eD},\\ l{b}_{C_{nom}}& \le & C_{nom}& \le & u{b}_{C_{nom}},\\ l{b}_L& \le & L& \le & u{b}_L,\end{array}\hfill \end{array}\end{array}$$

(20)

where the energy density is computed as:

$$eD=\frac{C_{nom}·V_{nom}}{L},$$

(21)

where $C_{nom}$ is the rate capacity, $V_{nom}$ is the rate voltage and L the volume in a cell.

A multi-objective genetic algorithm is used, as shown in Figure 5, with the purpose to find a finite space of local optimal solutions (S) in a limited interval of time. Each element in the optimal solution space defines the characteristics of a cell (22), taking into account the constraints (18):

$$\begin{array}{cc}\hfill \{C_{nom},V_{nom},L\}=S(cos{t}_i,e{D}_i),i& =1,2,\dots ,n\hfill \\ \hfill C_{nom}& \in [l{b}_{C_{nom}},u{b}_{C_{nom}}]\hfill \\ \hfill L& \in [l{b}_L,u{b}_L].\hfill \end{array}$$

(22)

Considering the present Li-Po battery technology, the parameters for the multi-objective genetic algorithm are displayed in

Table 1. Multi-objective genetic algorithm parameters.

Parameters	Value
Manufacturing cost	125–1300 US/kWh
Energy density (eD)	295–305 Wh/L
Objectives	2 ($Cost,dE$)
Variables	3 ($C_{nom}$, $V_{nom}$, L)
Population	10
Crossover	0.8
Tolerance	1 × 10${}^{-9}$

.

The number of cells is determined by each element of the optimal solution space:

$$N_s=\frac{C_{ESS}}{C_{nom}·V_{nom}},$$

(23)

where $C_{ESS}$ (24) is the energy consumed by the powertrain taking into account a real drive cycle:

$$C_{ESS}=\lambda ·E_{HE-RCV}.$$

(24)

The ESS model is defined by (18) using $N_s$ cells in series.

Then, the final characteristic of $ESS$ is determined through the optimal solution space, taking into account the minimal consumption of the $ICE$:

$$IC{E}_{consumption}=\int \frac{{\tau }_{in}·{\omega }_{in}}{LHV},$$

(25)

where $LHV$ is the lower heating value of the fuel.

5. Validation

To validate the proposed methodology, in this work, a real drive cycle from an $RCV$ Iveco Stralis GNC 270 (The vehicle is driven from Tarrega to La Faneca, both in the NE of Spain) is used, as shown in Figure 6. To obtain a real drive cycle, a datalogger CANalyzer CANCase XL (Vector Informatik GmbH, Stuttgart, Germany) with two CAN ports (SN 007130-011289) is used, allowing the storage of torque and rpms of the $ICE$. These parameters are obtained from the $ECM$, through the communication bus (CAN J1939) of an $RCV$ during an 8-hour workday. The parameters of this $RCV$ are displayed in

Table 2. $RCV$ Characteristics.

Combustion engine	200 kW
Gears	6
Gear ratios ($\gamma$)	1 (4.59), 2 (2.25), 3 (1.54)
	4 (1.000), 5 (0.75), 6 (0.65)
Weight ($m_{Vehicle}$)
(Empty/Full loaded)	15,000/25,000 kg
Frontal area ($A_f$)	7.5 m${}^2$
Drag coefficient ($C_d$)	0.6210
Rolling resistance ($C_r$)	0.009
Tire (Radius)	315/80/R22.5 (0.5455 m)

. Based on the maximum collection weight, a dynamic weight profile is proposed, as shown in Figure 7, which distributes the maximum weight during traction moments of drive cycle.

Using the quasi-static model described in Section 2, the power and the energy of RCV in a real route is determined, as shown in Figure 8.

A Li-Po 3.7 V cell is characterised experimentally in order to set the parameters of the model described in Section 3. The state of charge is determined as shown in Figure 9.

The parameters $R_0$, $R_1$ and $C_1$ are determined by using the $V_{OC}$, $V_L$ and $V_L^{{}^{\prime }}$ for an hour according to 1C discharge rate, as shown in Figure 10, Figure 11 and Figure 12, respectively.

The open circuit voltage $V_{oc}$ is approximated through the $SOC$ using a lookup table, as shown in Figure 13.

Once the cell model has been obtained, the proposed ESS optimisation methodology is applied to find the main parameters (energy density, volume, capacity) of the optimal solutions, taking into account the following constraints:

$$\begin{array}{c}\begin{array}{c}l{b}_{C_{nom}}=0.2A\le C{}_{nom}\le u{b}_{C_{nom}}=20A,\\ l{b}_L=0.01l\le L\le u{b}_L=0.5l.\end{array}\end{array}$$

(26)

The space of local optimal solution with the multi-objective genetic algorithm and the particle swarm optimisation (as shown in Figure 14) are compared in Figure 15. Some optimal solution in both optimisation methods are similar; however, based on the optimisation problem, the multi-objective genetic algorithm allows for finding the space of local optimal solutions with a trade-off between the objectives.

Then, the number of cells in series is calculated by using (24) for each element of the set of optimal space solutions, as shown in

Table 3. Optimal solution set.

#	$\mathit{Cost}$	$\mathit{eD}$ (Wh/L)	L (L)	${\mathit{C}}_{\mathit{nom}}$ (Ah)	${\mathit{N}}_{\mathit{s}}$
1	1.300812	−305.006906	0.144788	11.93545	440
2	0.123982	−294.991340	0.115369	9.198045	571
3	0.927891	−301.833114	0.142080	11.59035	453
4	1.300812	−305.006906	0.144788	11.93545	440
5	0.241222	−295.989126	0.115397	9.231446	569
6	0.677771	−299.704430	0.127566	10.33298	508
7	1.180479	−303.982803	0.137194	11.27155	466
8	1.019624	−302.613820	0.142736	11.67404	450
9	0.851227	−301.180651	0.131935	10.73951	489
10	0.123982	−294.991340	0.115369	9.198045	571

. From the total energy required by the powertrain (Figure 8), in order to validate the present methodology, it is proposed to cover 10% ($\lambda =0.1$) equivalent to a capacity of $C_{ESS}$ = 19.434 kWh.

A fuel consumption of 30.12 kg was obtained in the conventional vehicle configuration. On the other hand, the calculation was made of the fuel consumption of each element of the set of solutions, as shown in

Table 4. Fuel consumption of $HE$–$RCV$.

#	${\mathit{C}}_{\mathit{nom}}$ (Ah)	${\mathit{N}}_{\mathit{s}}$	Array Capacity (Wh)	Consumption (kg)
1	11.93545	440	19,430.92	19.64
2	9.198045	571	19,432.71	19.61
3	11.59035	453	19,426.60	19.61
4	11.93545	440	19,430.92	19.64
5	9.231446	569	19,434.96	19.03
6	10.33298	508	19,421.88	19.06
7	11.27155	466	19,434.42	20.00
8	11.67404	450	19,437.28	20.00
9	10.73951	489	19,431.00	19.47
10	9.198045	571	19,432.71	19.61

. The final choice consists of the solution that presents a lower fuel consumption.

To validate the found optimal solution, the charge/discharge of ESS is shown in Figure 16.

6. Conclusions

A new methodology is developed for the optimal design of the energy storage system for an $HE$–$RCV$, which has been validated using real routes from an Iveco Stralis GNC 270 $RCV$.

A model of a nonlinear multi-objective optimisation problem with constraints is achieved, which allows for defining the characteristics of the cell that makes up the $ESS$.

In addition, the cost and volume were set as objectives in the optimisation problem in order to obtain an optimal design of an $ESS$.

To solve the problem, a multi-objective genetic algorithm was used to determine the optimal solutions space and evaluated through an $HE$–$RCV$ with serial topology so as to finally determine the characteristics of the $ESS$ that offer the lowest fuel consumption of an $RCV$.

A $Li$–$Po$ cell characterisation is performed through experimental measuring in order to fit the parameters of the cell model.

Furthermore, it was possible to define a control strategy based on rules, which considers the discharge rate of the $ESS$. This allows for improving the design of an $ESS$ avoiding the physical damage by a peak discharge.

Finally, the proposed methodology results in an efficient optimal sizing of the $ESS$, achieving a $36.82\%$ reduction in fuel, through an optimal $ESS$ that contains an array of 569 cells in series with a capacity of 9.231446 Ah. The $ESS$ covers $10\%$ of the energy required by the $RCV$ during a real driving cycle. The energy required by the power train is defined as a parameter of the optimal sizing of the $ESS$ in the methodology.

The proposed methodology can be used to design an optimal $ESS$ considering any percentage of energy required by a hybrid electric vehicle. In addition, this methodology allows for finding the characteristics of an $ESS$ with the lowest possible cost and volume.