Sizing of Lithium-Ion Battery/Supercapacitor Hybrid Energy Storage System for Forklift Vehicle "2279

Nowadays, electric vehicles are one of the main topics in the new industrial revolution, called Industry 4.0. The transport and logistic solutions based on E-mobility, such as handling machines, are increasing in factories. Thus, electric forklifts are mostly used because no greenhouse gas is emitted when operating. However, they are usually equipped with lead-acid batteries which present bad performances and long charging time. Therefore, combining high-energy density lithium-ion batteries and high-power density supercapacitors as a hybrid energy storage system results in almost optimal performances and improves battery lifespan. The suggested solution is well suited for forklifts which continuously start, stop, lift up and lower down heavy loads. This paper presents the sizing of a lithium-ion battery/supercapacitor hybrid energy storage system for a forklift vehicle, using the normalized Verein Deutscher Ingenieure (VDI) drive cycle. To evaluate the performance of the lithium-ion battery/supercapacitor hybrid energy storage system, different sizing simulations are carried out. The suggested solution allows us to successfully optimize the system in terms of efficiency, volume and mass, in regard to the battery, supercapacitors technology and the energy management strategy chosen.


Introduction
Industry 4.0 is part of the fourth industrial revolution [1]. With the rise of numerical technologies, sensors have become cheaper, smaller, more connected and have an increased memory storage capacity. Implemented on machines, a large amount of data can be provided and can be used to improve production lines [2]. Internet of Things (IoT), 3D printing, virtual reality, big data, artificial intelligence and collaborative robots are the main topics used to optimize the performance of "smart factories" [3][4][5]. Industry 4.0 is carried out by one main goal: more environmentally sustainable manufacturing, which leads to more optimal use of resources. Thereby, the use of fossil energy in factories tends to be restricted and even prohibited. One area of improvement is the use of electrical sources [1] to supply handling machines, such as forklift trucks.
Forklifts are part of the industrial environment and are useful in daily tasks when moving heavy loads from one place to another [6,7]. They have been used since the end of the 1800 s, where company braking and constant speed phases which are not representative of a driver real behavior. NEDC drive cycle is an example of modal driving used for car consumption in Europe until 2017. On the contrary, transient driving constitutes speed variation typical of real driving conditions and driver behavior. Thus, driving cycles are built according to vehicle, environment and road conditions in order to assess the performance of an internal combustion engine (ICE) vehicle or to define the range of an electric vehicle [40]. Common driving cycles for electric vehicles from the United States (FTP-75) and Europe (ARTEMIS, NEDC) can be found in [37], as well as the Worldwide Harmonized Light Vehicles Test Procedure (WLTP.) The driving cycles previously mentioned cannot be used in this study. In fact, to assess the performance of an industrial forklift, the "Verein Deutscher Ingenieure" (VDI 60) drive cycle is used [9,12,41]. It consists of a cycle repeated 45 times within 60 min with a load of about 70% of the rated capacity. Details can be found in the NF ISO 16769-2 norm and are summarized as follows (Figure 1a contrary, transient driving constitutes speed variation typical of real driving conditions and driver behavior. Thus, driving cycles are built according to vehicle, environment and road conditions in order to assess the performance of an internal combustion engine (ICE) vehicle or to define the range of an electric vehicle [40]. Common driving cycles for electric vehicles from the United States (FTP-75) and Europe (ARTEMIS, NEDC) can be found in [37], as well as the Worldwide Harmonized Light Vehicles Test Procedure (WLTP.) The driving cycles previously mentioned cannot be used in this study. In fact, to assess the performance of an industrial forklift, the "Verein Deutscher Ingenieure" (VDI 60) drive cycle is used [9,12,41]. It consists of a cycle repeated 45 times within 60 min with a load of about 70% of the rated capacity. Details can be found in the NF ISO 16769-2 norm and are summarized as follows ( Figure  1a As mentioned previously, the forklift is holding a load from the beginning until the end of the cycle without dropping it. Moreover, this protocol is only suitable for electric forklifts with a rated capacity lower than or equal to 5 t and a rated battery voltage lower than or equal to 36 V. Therefore only 45 cycles should be performed within 60 min with an adapted speed both for travelling and lifting operations. Thanks to specifications from forklift manufacturers, a first approach of the cycle can be deducted and built using information such as travelling speed, load lifting and lowering speed (see Figure 1b and Table 1).  As mentioned previously, the forklift is holding a load from the beginning until the end of the cycle without dropping it. Moreover, this protocol is only suitable for electric forklifts with a rated capacity lower than or equal to 5 t and a rated battery voltage lower than or equal to 36 V. Therefore only 45 cycles should be performed within 60 min with an adapted speed both for travelling and lifting operations. Thanks to specifications from forklift manufacturers, a first approach of the cycle can be deducted and built using information such as travelling speed, load lifting and lowering speed (see Figure 1b and Table 1).

Methodology for Sizing Lithium-Ion Battery/Supercapacitor Hybrid Energy Storage System
There are many different architectures from passive to fully active lithium-ion battery/supercapacitor HESS [20]. The chosen topology here is a semi-active hybrid one, with a DC/DC bi-directional converter in the side of supercapacitors ( Figure 2). The advantages of this configuration are mainly the reliability, better use of SC energy and a lighter overall weight compared to architectures with two DC/DC converters [15,20,29]. Moreover, the converter used allows the charge and discharge of supercapacitors and assures a lighter weight thanks to its simplicity.

Methodology for Sizing Lithium-Ion Battery/Supercapacitor Hybrid Energy Storage System
There are many different architectures from passive to fully active lithium-ion battery/supercapacitor HESS [20]. The chosen topology here is a semi-active hybrid one, with a DC/DC bi-directional converter in the side of supercapacitors ( Figure 2). The advantages of this configuration are mainly the reliability, better use of SC energy and a lighter overall weight compared to architectures with two DC/DC converters [15,20,29]. Moreover, the converter used allows the charge and discharge of supercapacitors and assures a lighter weight thanks to its simplicity.

Conversion from a Driving Cycle to a Power Cycle
In order to get the power requested, dynamic equations of the forklift were established (see (1)(2)(3)), where is the vehicle speed. The VDI cycle will define the vehicle power requirement for vehicle traction. However, handling maneuvers can be also added to the dynamic equation. In fact, some forklifts have different energy sources for travelling and lifting operation (e.g., hydraulic equipment or hybrid forklift) [8]. In our study, the electric HESS also provides power for lifting operation. Equations are detailed in (4-7). The EFG 110 forklift from Jungheinrich ( Figure 3) will be used as an example, and its parameters are tabulated in Table 1.

Conversion from a Driving Cycle to a Power Cycle
In order to get the power requested, dynamic equations of the forklift were established (see (1)-(3)), where V VEH is the vehicle speed. The VDI cycle will define the vehicle power requirement for vehicle traction. However, handling maneuvers can be also added to the dynamic equation. In fact, some forklifts have different energy sources for travelling and lifting operation (e.g., hydraulic equipment or hybrid forklift) [8]. In our study, the electric HESS also provides power for lifting operation. Equations are detailed in ((4)- (7)). The EFG 110 forklift from Jungheinrich ( Figure 3) will be used as an example, and its parameters are tabulated in Table 1.

Methodology for Sizing Lithium-Ion Battery/Supercapacitor Hybrid Energy Storage System
There are many different architectures from passive to fully active lithium-ion battery/supercapacitor HESS [20]. The chosen topology here is a semi-active hybrid one, with a DC/DC bi-directional converter in the side of supercapacitors ( Figure 2). The advantages of this configuration are mainly the reliability, better use of SC energy and a lighter overall weight compared to architectures with two DC/DC converters [15,20,29]. Moreover, the converter used allows the charge and discharge of supercapacitors and assures a lighter weight thanks to its simplicity.

Conversion from a Driving Cycle to a Power Cycle
In order to get the power requested, dynamic equations of the forklift were established (see (1)(2)(3)), where is the vehicle speed. The VDI cycle will define the vehicle power requirement for vehicle traction. However, handling maneuvers can be also added to the dynamic equation. In fact, some forklifts have different energy sources for travelling and lifting operation (e.g., hydraulic equipment or hybrid forklift) [8]. In our study, the electric HESS also provides power for lifting operation. Equations are detailed in (4-7). The EFG 110 forklift from Jungheinrich ( Figure 3) will be used as an example, and its parameters are tabulated in Table 1.  Equations for travelling operations [38]: Equations for lifting operations: The angle of inclination (working surface slope) is equal to zero as forklifts operate mostly on a plane surface. The load weight is equal to 70% of the maximum load, as specified in the VDI driving cycle. Friction forces were neglected in lifting operations.

Sizing of the Battery
When integrating the power cycle, the energy needed to assure the range of the vehicle is given. In our case, one VDI drive cycle corresponds to 1 h of operating time. There are three hypotheses which can lead to the battery sizing [37]: • Ensure the maximal consuming power (using maximal power requested) • Ensure the maximal braking power (using minimal power requested) • Ensure only the vehicle range (using final value of the energy) The last hypothesis will be used in order to use the battery as the main source because of its high specific energy and supercapacitors as a secondary source in regard to its high specific power. The bus voltage is set as Ubus = 24 V ( Figure 2) according to the EFG-110 specifications. The number of serial battery cells can be determined as Nsb = Ubus/U elb and the number of parallel battery cells, Npb, thanks to Equation (15), Ev cons with being the energy required by the forklift for several repeated VDI drive cycles, E elB representing the energy, M elB the weight, R 0elb the internal resistance, and U elb the nominal voltage for one battery cell. The depth of discharge (DOD) is the percentage of battery energy used and is limited to 80% in order to minimize the battery ageing [42], and ∂Ev cons is the variation of total energy according to the battery weight added to the vehicle [43]. This last variable takes into account the weight added by the battery to the vehicle. The battery is then sized in order to respect (8): with E bat , the battery energy: ∆E V , the energy variation due to the added weight: Energies 2020, 13, 4518 6 of 18 and E_Loss B , the energetic battery loss: which leads to the following equation:

Energy Management Strategy
Once the battery is sized, its weight is added to the forklift and a new power requirement is calculated. This power needs to be shared into the battery (Pbat) and the supercapacitor (Psc). Different energy managements can be used from rule-based to optimal and artificial intelligence-based algorithms [44][45][46][47][48][49]. In this study, a simple rule-based battery power limitation is used [24,50] combined with a supercapacitor energy supervision, with PbatD and PbatC being the power battery limitation block in Figure 4, respectively, the power battery limitation in discharge and in charge, as imposed by the manufacturer.

Energy Management Strategy
Once the battery is sized, its weight is added to the forklift and a new power requirement is calculated. This power needs to be shared into the battery ( ) and the supercapacitor ( ). Different energy managements can be used from rule-based to optimal and artificial intelligencebased algorithms [44][45][46][47][48][49]. In this study, a simple rule-based battery power limitation is used [24,50] combined with a supercapacitor energy supervision, with and being the power battery limitation block in Figure 4, respectively, the power battery limitation in discharge and in charge, as imposed by the manufacturer. From Figure 4, is split into _0, and _0, through the saturation block. In fact, power between and is sent to the battery, while power outside those limitations is sent to supercapacitors. However, supercapacitors should act like buffers that charge or discharge themselves when needed but must also be charged at a reference level at all times to provide or store energy. This means that no energy drift is allowed in the supercapacitors. To prevent this phenomenon, a supercapacitor energy supervision is implemented and redistributes the power between the battery and supercapacitor to charge or discharge the SC through the battery or the load [43]. Simulation results are given in Section 4.4.

Sizing of the Supercapacitor
Now that power sent to supercapacitors ( ) is defined, the number of serials ( ) and parallel ( ) supercapacitor cells can be found thanks to (19) and (20), with representing the capacity, the nominal voltage and the weight of one supercapacitor cell. Supercapacitor energy ( ) can be obtained by integrating its power. Thus, Δ represents the maximal variation of , and and represent extrema of as a function of the weight [43,51] for charge and discharge of the supercapacitor, respectively. Here, SC losses are neglected because of their small internal resistance compared to batteries. However, although SC Columbic efficiency is high (85% to 98%), an 85% yield can be applied to calculate the worst-case energy used in a SC [52]. Then, the following equation must be respected: From Figure 4, Pv is split into Psc_0, and Pbat_0, through the saturation block. In fact, power between PbatD and PbatC is sent to the battery, while power outside those limitations is sent to supercapacitors. However, supercapacitors should act like buffers that charge or discharge themselves when needed but must also be charged at a reference level at all times to provide or store energy. This means that no energy drift is allowed in the supercapacitors. To prevent this phenomenon, a supercapacitor energy supervision is implemented and redistributes the power between the battery and supercapacitor to charge or discharge the SC through the battery or the load [43]. Simulation results are given in Section 4.4.

Sizing of the Supercapacitor
Now that power sent to supercapacitors (P sc ) is defined, the number of serials (Ns sc ) and parallel (Np sc ) supercapacitor cells can be found thanks to (19) and (20), with C elsc representing the capacity, Uel sc the nominal voltage and M elsc the weight of one supercapacitor cell. Supercapacitor energy (Esc) can be obtained by integrating its power. Thus, ∆E sc represents the maximal variation of Esc and γ C sc and γ D sc Energies 2020, 13, 4518 7 of 18 represent extrema of Esc as a function of the weight [43,51] for charge and discharge of the supercapacitor, respectively. Here, SC losses are neglected because of their small internal resistance compared to batteries. However, although SC Columbic efficiency is high (85% to 98%), an 85% yield can be applied to calculate the worst-case energy used in a SC [52]. Then, the following equation must be respected: with ∆Esc W , which represents the variation of ∆E sc according to the weight: Esc is the energy provided by the battery pack. Only 3 4 of the energy is used in one supercapacitor cell, which represents a voltage variation between nominal voltage and half the nominal voltage.
These equations lead to the following final equations: For battery and supercapacitor weight estimation, an additional 40% ratio [53] is added to take into account the weight of the packaging and associated electronics. See Equations (10) and (17).

DC/DC Converter Sizing
The weight of the converter can be estimated. In principle, the latter is mainly due to the weight of the self and the heat sink. In this paper, only the weight of the self is taken into account. Thus, the Ae * Sb product of the self must be found and multiplied by k 1 and k 2 , respectively, for estimating the weight and the volume of the self [39], with Isc_max representing the maximal current requested by the SC, I sc_rms the root mean square (RMS) current, L the value of the self, B max the maximal induction, J the current density, and K B the winding ratio. The current requested by the supercapacitors is given by I sc_rms = P sc /U bus (see Table 2 and Equations (21)-(24)).

Adjusting the Number of Cells
The final step consists of adding converter and supercapacitor weights to the dynamic model. The new power and energy requested must be calculated and should respect the following conditions:

•
The energy of the battery, taking into account the DOD, is higher than the total energy requested by the vehicle range: • The supercapacitor energy, taking into account a yield of 85%, is higher than the difference between the two extrema of supercapacitor energy after energy management Esc ≥ ∆Esc.
If one of the two conditions is not respected, a parallel battery or supercapacitor branch is added respectively for the first or second condition. Then dynamics of the vehicle will be checked again until the two conditions are fulfilled. Figure 5 summarizes the algorithm described from steps 3.1 to 3.6.
Energies 2020, 13, x FOR PEER REVIEW 8 of 18 If one of the two conditions is not respected, a parallel battery or supercapacitor branch is added respectively for the first or second condition. Then dynamics of the vehicle will be checked again until the two conditions are fulfilled. Figure 5 summarizes the algorithm described from steps 3.1 to 3.6.

Requested Power and Energy
Following Section 3, a sizing algorithm was implemented on the Matlab/Simulink software environment. Figure 6 shows the power profile of 80 s of VDI drive cycle detailed in Section 2. A 90% yield was applied on traction and lifting powers to take into account loss from the inverter and the

Requested Power and Energy
Following Section 3, a sizing algorithm was implemented on the Matlab/Simulink software environment. Figure 6 shows the power profile of 80 s of VDI drive cycle detailed in Section 2. A 90% yield was applied on traction and lifting powers to take into account loss from the inverter and the electric motor. According to the forklift datasheet, the motor for lifting operation is sized for a nominal power of 6 kW which matches the power in lowering phases. Equations (4)-(7) are basics and do not take into account all the forces such as resistive forces. In addition, the acceleration time was set arbitrarily short (not given in the datasheet). Moreover, during the VDI drive cycle, the forklift is only handling 70% of the maximum load.

Comparison of Single Source Sizing
Simulations were made to size the forklift for 1, 5, 7, 10 and 12 h of VDI drive cycle for a single energy source. High-power (HP) lithium-ion batteries (Kokam 3.7 V/40 Ah SLPB100216216H, Kokam 3.7 V/75 Ah SLPB125255255H, Winston 3.2 V/40 Ah LFP040AHA) and high-energy lithium-ion batteries (Kokam 3.7 V/40 Ah SLPB90216216, Kokam 3.7 V/75 Ah SLPB120255255, European Battery 3.2 V/45 Ah EB45AH) were used in this study. The results can be found in Figure 7 and Table 3.  A 4 kW motor is announced for traction operations, whereas simulations show power peaks of up to 12 kW ( Figure 6). In fact, assumptions were made, when the VDI drive cycle was built, as the forklift is travelling at maximal speed with a 70% load, which is not always realistic. Therefore, this hypothesis oversizes the power requested from the forklift and will be taken into account in the final discussion.

Comparison of Single Source Sizing
Simulations were made to size the forklift for 1, 5, 7, 10 and 12 h of VDI drive cycle for a single energy source. High-power (HP) lithium-ion batteries (Kokam 3.7 V/40 Ah SLPB100216216H, Kokam 3.7 V/75 Ah SLPB125255255H, Winston 3.2 V/40 Ah LFP040AHA) and high-energy lithium-ion batteries (Kokam 3.7 V/40 Ah SLPB90216216, Kokam 3.7 V/75 Ah SLPB120255255, European Battery 3.2 V/45 Ah EB45AH) were used in this study. The results can be found in Figure 7 and Table 3.
Simulations were made to size the forklift for 1, 5, 7, 10 and 12 h of VDI drive cycle for a single energy source. High-power (HP) lithium-ion batteries (Kokam 3.7 V/40 Ah SLPB100216216H, Kokam 3.7 V/75 Ah SLPB125255255H, Winston 3.2 V/40 Ah LFP040AHA) and high-energy lithium-ion batteries (Kokam 3.7 V/40 Ah SLPB90216216, Kokam 3.7 V/75 Ah SLPB120255255, European Battery 3.2 V/45 Ah EB45AH) were used in this study. The results can be found in Figure 7 and Table 3.   The typical EFG 110 Jungheinrich energy storage system is a 24 V/500 Ah lead-acid battery composed of 12 cells of 2 V/500 Ah connected in series. This information is deduced from the datasheet and the DIN 43,535 A norm. For each lithium-ion battery technology and each operating hour, the total battery weight is always lower than 300 kg, except for LFP040AHA cells, whereas initial lead-acid battery weight is equal to 380 kg (see Figure 7). In addition to the small weight, lithium-ion battery offers better capacity, which is explained by its higher specific energy (Table 2) [24]. One comment can be given on high-power and high-energy battery. Single source sizing was made to provide maximal power traction, maximal power in recovery phase and maximal range for a given operating time [31]. Thus, for lower range (1 h), maximal power is the main criterion to be fulfilled, but high energy is more constraining when the range becomes higher (12 h). Therefore, Figure 7 and Table 2 show that HP batteries are more suitable for a lower range, with fewer cells than HE batteries, which are oversized. However, a 12 h range is already a very high range for forklift application and Figure 7 shows that for different technologies, high power and high energy battery can have the same weight for a specific range. However, for forklift applications, high power batteries are more suitable because of power peaks that must be provided to assure good dynamics.

Comparison of Hybrid Source
For reasons mentioned in Section 3.2, a HE battery can be used in forklift applications if it is used with a high specific power storage component. Thereby, supercapacitors are able to provide high power peaks in a short amount of time. For this simulation, Maxwell BCAP0350 350 F/2.7 V (sc1), Maxwell BCAP0450 P270 S18 450 F/2.7 V (sc2) and Maxwell BCAP3400 P300 K04/05 3400 F/3.0 V (sc3) supercapacitors were used. Each supercapacitor technology was tested with each of the HE batteries for a 7 h operating time with the VDI drive cycle (Figure 8 and Table 4).
For reasons mentioned in Section 3.2, a HE battery can be used in forklift applications if it is used with a high specific power storage component. Thereby, supercapacitors are able to provide high power peaks in a short amount of time. For this simulation, Maxwell BCAP0350 350 F/2.7 V (sc1), Maxwell BCAP0450 P270 S18 450 F/2.7 V (sc2) and Maxwell BCAP3400 P300 K04/05 3400 F/3.0 V (sc3) supercapacitors were used. Each supercapacitor technology was tested with each of the HE batteries for a 7 h operating time with the VDI drive cycle (Figure 8 and Table 4).  In regard to Figure 8 and Table 3, batteries are sized according to the energy requested, which explains why batteries have approximatively the same energy (kWh). Only 0.1 kWh of supercapacitor must be added to take into account the dynamics of the forklift. If the right set of  In regard to Figure 8 and Table 3, batteries are sized according to the energy requested, which explains why batteries have approximatively the same energy (kWh). Only 0.1 kWh of supercapacitor must be added to take into account the dynamics of the forklift. If the right set of battery/supercapacitor is found, the weight of the hybrid storage system can be equal to a single source solution (for example, Ko75HE and BCAP3400 (sc3)). Maxwell BCAP3400 SC significantly decreases the weight of the supercapacitor banks because of the nominal voltage of 3 V, which is not common in typical supercapacitors (usually around 2.7 V).

Energy Management Influence
As the weight is not an issue in forklift application, using lithium-ion batteries enable increasing the vehicle range from 7 h to half a day without reaching the battery weight recommended by the manufacturer. In regard to battery and supercapacitor technologies, the total weight can become lower or higher than a single source solution [39]. In either way, adding a supercapacitor limits battery stresses and improves battery lifetime. It is then critical that SCs act like buffers. The goal of the energy management is to ensure supercapacitor energy to track a reference value in order to be ready to provide or store energy from any operational phases. The power battery limitation detailed in Section 3.3 is then illustrated in Figures 9 and 10. Power battery limitations PbatD and PbatC were set at 6 and −6 kW. Without violating those limitations, battery or load power is used to recharge supercapacitors to prevent them from any energy drift (Figure 9b). the energy management is to ensure supercapacitor energy to track a reference value in order to be ready to provide or store energy from any operational phases. The power battery limitation detailed in Section 3.3 is then illustrated in Figures 9 and 10. Power battery limitations and were set at 6 and −6 kW. Without violating those limitations, battery or load power is used to recharge supercapacitors to prevent them from any energy drift (Figure 9b). Simulations were made to emphasize the importance of energy management. Figure 11 shows weight results for a hybrid sizing with the EB45AH and BCAP0350 and a 7 h operation. The power split algorithm is ruled by the power limitation chosen. Usually, they are chosen according to the manufacturer specifications. For previous simulations, they were chosen arbitrarily as 8 to −8 kW ( Figure 8 and Table 3). Different values of power battery limitations were set. The results show that, for this energy management strategy, the smaller the battery power limits are, the higher the supercapacitor weight is and therefore higher the overall HESS weight is ( Figure 11 and Table 5).   Simulations were made to emphasize the importance of energy management. Figure 11 shows weight results for a hybrid sizing with the EB45AH and BCAP0350 and a 7 h operation. The power split algorithm is ruled by the power limitation chosen. Usually, they are chosen according to the manufacturer specifications. For previous simulations, they were chosen arbitrarily as 8 to −8 kW (Figure 8 and Table 3). Different values of power battery limitations were set. The results show that, for Energies 2020, 13, 4518 13 of 18 this energy management strategy, the smaller the battery power limits are, the higher the supercapacitor weight is and therefore higher the overall HESS weight is ( Figure 11 and Table 5).

Price Constraint
As shown in previous results, the weight of the forklift energy storage system can be drastically decreased using a Li-ion battery instead of a lead-acid battery. In forklift applications, weight is not an issue and it is better if the battery is quite heavy. Therefore, a lot of battery cells can be added to increase the vehicle range (hours of operations) until meeting the forklift battery weight specification.

Price Constraint
As shown in previous results, the weight of the forklift energy storage system can be drastically decreased using a Li-ion battery instead of a lead-acid battery. In forklift applications, weight is not an issue and it is better if the battery is quite heavy. Therefore, a lot of battery cells can be added to increase the vehicle range (hours of operations) until meeting the forklift battery weight specification.
The only limit is then the price. Lithium-ion batteries display an average cost of 176 USD/kWh in 2018 [54] against 150 USD/kWh for lead-acid battery [55]. Nevertheless, Li-ion battery cost is still decreasing, and they request less maintenance and last much longer [54]. Therefore, it can be assumed that the total cost of ownership [19] of a lithium-ion forklift is better than a classical electric forklift. Moreover, by adding an extra USD/kWh of a supercapacitor and some more for the converter [39] the ageing of the battery is improved and allows the forklift to be more efficient and to last longer.

Ageing Analysis
In fact, our model does not take into account the ageing of the battery. However, RMS power provided by the battery can be analyzed. If the bus voltage is supposed to be almost constant during operation, therefore the power profile will be almost the same as the current profile. The higher the current, the higher the heat loss that will occur in the internal resistance of the battery. However, heat is one of the critical ageing factors [11,21,22,56,57]. Therefore, by decreasing the RMS battery power, battery lifetime can be improved. Simulations ( Figure 12) were made for a single source and for a hybrid source to fulfill a 7 h VDI cycle. Power battery limitations were also changed from [8, −8 kW] to [6, −6 kW]. The results show that HESS decreases RMS battery power from 3% to 10% following the case study. In fact, with additional supercapacitor, battery power stresses can be decreased even more (example of [6, −6 kW] battery power limitations in Figure 12). Therefore, with a HESS, battery ageing is reduced. The use of optimal energy management is crucial to limit battery stresses.

Conclusions
The sizing of a hybrid energy storage system using a lithium-ion battery and a supercapacitor for a forklift application has been presented in this study. Unlike automotive applications, where the weight of the battery is designed to be as light as possible, the weight of the overall forklift must be high enough to allow the counterbalance effect during lifting operations. Simulations show that even for a very high range of operation (12 h) and an oversized requested power, the HESS is still lighter than the lead-acid battery recommended by the manufacturer, in regard to battery and supercapacitor cells chosen. Despite a higher price compared to the lead-acid battery, lithium-ion technology has better power performance, energy efficiency, cycle life, charging time and needs less maintenance. Moreover, supercapacitors allow for a better yield in regard to recovery power during braking and lowering phases, and allow one to put less stress on the battery. In fact, thanks to the energy management presented, RMS battery power can be reduced down to 10%, compared to a single source solution, and therefore improve the battery ageing. An optimal energy management algorithm is absolutely critical to improve battery lifetime. Finally, with hybridization, the forklift battery total cost of ownership is also improved compared to the current solution with lead-acid batteries. Light weight issues can be solved by adding extra ballast to meet battery weight specifications.