Mapping Fuzzy Energy Management Strategy for PEM Fuel Cell–Battery–Supercapacitor Hybrid Excavator

Abstract

By replacing conventional supplies such as fossil fuels or internal combustion engines (ICEs), this paper presents a new configuration of hybrid power sources (HPS) based on the integration of a proton-exchange membrane fuel cell (PEMFC) with batteries (BATs) and supercapacitors (SCs) for hydraulic excavators (HEs). In contrast to conventional architectures, the PEMFC in this study functions as the main power supply, whereas the integrated BAT–SC is considered as an auxiliary buffer. Regarding shortcomings existing in the previous approaches, an innovative energy management strategy (EMS) was designed using a new mapping fuzzy logic control (MFLC) for appropriate power distribution. Comparisons between the proposed strategy with available approaches are conducted to satisfy several driving cycles with different load demands and verify the strategy’s effectiveness. Based on the simulation results, the efficiency of the PEMFC when using the MFLS algorithm increased up to 47% in comparison with the conventional proposed EMS and other approaches. With the proposed strategy, the HPS can be guaranteed to not only sufficiently support power to the system even when the endurance process or high peak power is required, but also extend the lifespan of the devices and achieves high efficiency.

1. Introduction

Hydraulic excavators (HEs) are essential to construction and agriculture [1,2,3,4,5,6,7,8,9,10,11], however, existing issues such as low energy efficiency and carbon emissions in HEs using an internal combustion engine (ICE) have urgently imposed alternative energy requirements with the aim of reducing environmental and economic problems. In the trend of exploring and developing alternative power sources to take the place of fossil fuels, the proton-exchange membrane fuel cell (PEMFC) has become a potential candidate due to its high performance in high energy conversion efficiency, low chemical pollution, quiet operation, low weight, and low volume, especially in producing zero-emissions. However, low power density and slow power response are drawbacks of the PEMFC. Moreover, transient change in the load demand due to complicated requirements or working terrains is difficult to adequately satisfy using the standalone PEMFC. Furthermore, when the HEs are in regeneration modes or when the PEMFC releases more power than the demand, the PEMFC itself is not able to store the excess energy. A power deficiency when increasing the operating load and the waste power in the case of regeneration mode require at least one auxiliary device to enhance and optimize performance.

The first integrated configuration was reported by Yi et al. [12]. In his study, the integration of a fuel cell (FC) with batteries (BATs) was proposed as a power source for the HEs based on workload. The BAT is expected to be remarkably ideal and supportive storage in HEs. Nevertheless, the required hydraulic power in this paper indicates an abrupt and un-cyclical power demand under workloads of placing soil and putting it down after the HE has completed a slewing motion. In practice, HEs have to complete many combinations of motion (e.g., lifting, moving, rotating, braking, and auxiliary systems), which also generates transient power loads. Consequently, the BATs cannot sufficiently adapt in the case of rapidly changing power. Gong et al. [13] proposed the integration of the FC with an ultra-capacitor and derived a strategy to minimize an equivalent fuel consumption. Li et al. [14] proposed a suggested configuration comprising the PEMFC integrated with supercapacitors (SCs) for construction machines and developed an algorithm for an energy management system (ems) strategy that relies on model predictive control (MPC) [15]. The results indicated that this configuration could effectively adapt to the system operation and the state of charge (SoC) of the SCs could be maintained in good condition. Based on these approaches, Li et al. improved his algorithm and applied it to an excavator with the same configuration as the integrated power source [16]. Although the above works revealed that good results can be achieved, the SC cannot sufficiently supply energy when a high load power requires endurance missions regarded the SC characteristics, as presented in [17]. Accordingly, the SC is suitable when a large amount of power is required to support and absorb the transient peak power, whereas the BAT is capable of storing large amounts of energy and is useful for sustaining energy in the long term. Therefore, the use of the BAT–SC is more efficient than using segregated equipment, thus increasing workability and system reliability. The integration of BAT–SC with the PEMFC can achieve a higher performance, reduce system size, and minimize the fuel economy cost. Nevertheless, another issue arising from integrating the three devices is how to effectively manage the complex HPS. Thus, the design of an energy management strategy (EMS) is required to split the energy from the powertrain and appropriately distribute it to other components.

The literature on lightweight hybrid electric vehicles [18,19,20,21,22,23] provide helpful references for effectively delivering power between the components of the integrated system using the EMS. In [18], Vanessa et al. formulated a strategy in which the FC functioned as a primary source, whereas the BAT and SC functioned as buffer supplies. The order of using each component was explained by a flowchart in which the state of charge of each device was considered critically. In [19], Aya et al. expressed two configurations for vehicles: the hydrogen fuel-saving control strategy (HFS-CS) and the life cycle saving control strategy (LCS-CS). However, according to the two flowcharts, instability due to overcharging in each device or a lack of power in both SC and BAT can occur because the order of use is not appropriate. Zhang et al. suggested a strategy for the hybrid FC–BAT–SC power-sharing on a tram [20]. As obtained from the literature, most of those studies have focused on sketching the EMS in flowchart form without considering the change phase between the different modes. This implies that all components can be operated by switching modes (simply ON/OFF) to satisfy specific conditions. This may cause a delay to the system and cause instability due to sudden change, thereafter degrading the performance of the devices over time. Based on the fact that the status change of devices (especially for the FC and BAT, which have slow dynamics responses) requires a certain time to meet the demanded tasks, this is not feasible when simply embedding these flowcharts into real test benches. Consequently, many studies have been implemented to overcome this drawback.

A fuzzy logic control (FLC) has been highlighted as a powerful tool to work out the complex issues concerning system logic. The use of the FLC was first suggested by Agustín et al. [24]. In his study, FLC was employed to split power for each device. The inputs of the FLC included the power required, SC state of charge (SoC_SC), and BAT state of charge (SoC_BAT), and the output was the demanded power for the PEMFC and BAT. The rules specified in the FLC were designed by following specific criteria. In [25], Li et al. proposed using FLC for energy and battery management in a series of hybrid electric vehicles. The study indicated that using FLC could constrain the system so that it operated within the fuel economic region and avoided the over-discharge of the BAT. In [26], Li et al. employed the FLC to manage power-sharing between three different sources and guarantee their performance. The simulations were implemented in four standard driving cycles and the results proved that the suggested algorithm could satisfy the power demanded in comparison with other methods. Using the advantages of FLC, Issam et al. applied this technique for the EMS used in stand-alone applications [27]. Another application was introduced by Fei et al. when a master–slave EMS-based fuzzy logic hysteresis state machine was exploited for power split management applied to a PEMFC–lithium battery–supercapacitor (PEMFC–LIB–SC) hybrid tramway powertrain system [28]. Saman et al. [29] utilized fuzzy rules combined with a genetic algorithm (GA) to improve the vehicle’s dynamic performance of the hybrid FC–BAT–SC system and fuel economy. As the author claimed, the study contributed to related research from different aspects. Summarizing from previous approaches, Yakup et al. realized an analysis and comparison of several control methodologies for fuel-saving in hydrogen fuel cell vehicles integrated with BAT and SC [30]. In [31], Zhang et al. conducted an investigation on unplugged electric vehicles (UEVs) by employing an online fuzzy for the power management of the HPS composed of the PEMFC and BAT, and presented the procedure for power split management. The power required from the FC was produced after being processed in the FLC. The pulsed-power profile was used to verify its effectiveness and stability to the rapid change of the instantaneous high-power demand. With a similar rule-based approach used in previous works, Cong et al. established a new on–off power following a strategy-based fuzzy algorithm for FC extended-range vehicles in which the BAT was employed as the main source while the FC was considered as an extender for the system [32]. The simulation demonstrated that good results and improvement could be accomplished in both system dynamics and economy. Eckert et al. [33] utilized GA to optimize the lower and upper values of the membership function to maximize system performance. In [34], Ameur et al. proposed a master–slave fuzzy algorithm to design the EMS to effectively manage a hybrid power system and prolong all component lifespans.

Based on the literature, the FLC that mimics human knowledge [35,36,37] is an appropriate tool for establishing the EMS and applying it to the complicated hybrid system. Despite achieving good performance, few studies have reported on an application of these accomplishments for HEs. Furthermore, due to mimicking designer knowledge, it is challenging to achieve a good performance without setting an appropriate value and condition for the fuzzy system. Optimization methods have been successfully applied for the experimental system; nevertheless, most configurations have been conducted in two-device configurations such as FC–BAT, FC–SC, and BAT–SC. When configurations of three devices are considered, the power-sharing strategies are more complicated. Although the FLC, known to mimic designer knowledge, is difficult to design, it is still a suitable solution for a power-sharing design of a hybrid FC–BAT–SC. This technique can cover all scenarios of the working operation and mutual influences of charging–discharging mode in BAT–SC to maintain the high performance of all components. Considering the advantages of the integration of FC–BAT–SC and a lack of algorithms when designing the EMS for HEs, this study proposed a novel algorithm in which the FLC is exploited as the EMS to appropriately distribute power to each component. Building on our previous work in [38], we focused on how to operate all components in an optimal condition as the prior criterion to increase efficiency, thus prolonging lifespan and reducing costs. In order to handle these problems, an optimal mapping FLC (MFLC) was systematically designed based on a self-tuning methodology to generate the optimized parameters of all devices, thus adjusting power-sharing. The contributions of this research are as follows:

(1)

With our experience in fluid power and construction HEs, we proposed a novel configuration for the integration of FC–BAT–SC and attempted to apply it to HEs. In contrast to the conventional configuration in which the BATs are considered as the main supply, in this configuration, the FC functions as the main power source, and the BAT–SC is attached as supplements.

(2)

A novel EMS strategy was introduced in which the MFLC was designed to match the optimal condition during operation. While FLC was employed to distribute sufficient power to each component under different scenarios, the mapping condition was first introduced to calculate a suitable fuel cell power. This control scheme is the key point to addressing problems associated with HE power distribution, which are considered as constrained multi-objective problems. The effectiveness of the proposed algorithm was validated by the standard driving cycle in which all working operations of the HE were investigated.

(3)

The regenerative mode of the HEs is mentioned and the difficulty in designing power-saving transmission for regeneration is explained.

(4)

The dynamic model of the entire system comprising the HE and integrated power sources were derived in detail. This model was simulated in a co-simulation AMESim-MATLAB/Simulink environment. The HE model was simulated in the AMESim software, whereas the models of FC, BAT, and SC were derived and performed in a MATLAB/Simulink software. The goal of this study was how to establish a real-time EMS, achieve the demand of the powertrain, and stabilize the entire platform when highly-fluctuating power occurred.

(5)

Finally, comparisons between the proposed algorithm with other conventional approaches are discussed to verify the effectiveness of the new configuration compared to previous conventional approaches.

The rest of this paper is organized as follows: Section 2 expresses the modeling of all components. Based on the characteristics of each device, the new configuration and the proposed EMS with regeneration mode are introduced in Section 3. Section 4 describes the MFLC based on the proposed EMS to achieve high efficiency and performance. To verify its advantages, comparative simulations between the proposed and conventional EMSs are discussed in Section 5. Finally, Section 6 summarizes and presents potential future applications.

2. System Configuration and Devices Modeling

2.1. Hydraulic Excavator Configuration

The power demand for running the HE is simply based on the total power needed for moving each element as requirements, driving crawlers, and running the hydraulic circuit. In the entire hydraulic system as depicted in Figure 1, the total power is a product of the outlet pressure and the flow rate of the hydraulic pump [39]:

$$P_p=\frac{p(t)\times D\times n(t)}{600\times \eta (t)}$$

(1)

$$P_M=\frac{P_p}{{\eta }_M}$$

(2)

where p, D, n, and η are the pressure (bar), displacement (l/rev), rotational speed (rev/min), and volumetric efficiency of the hydraulic pump, respectively. $P_M$ is the computed motor power to drive the hydraulic pump (kW); ${\eta }_M$ is an efficiency dropped when converting electric power to mechanical power.

The hydraulic circuit of the HE is inherited from the AMESim library and described in Figure 1 [40].

2.2. Fuel Cell Modeling

The PEMFC model is referred to in [41,42,43,44,45]. The dynamics of a single fuel cell is calculated as follows:

$$V_{cell}=E_{Nernst}-V_{act}-V_{conc}-V_{ohmic}$$

(3)

$$E_{Nernst}=1.229-8.5\times {10}^{-4}(T-298.15)+\frac{RT}{2F}\ln \left[p_{H_2}^{\prime }{(p_{O_2}^{\prime })}^{0.5}\right]$$

(4)

$$V_{ohmic}=i{R}_{int}$$

(5)

$$V_{act}={\xi }_1+{\xi }_{2}T+{\xi }_{3}T\ln \left({c^{\prime }}_{O2}\right)+{\xi }_{4}T\ln \left(i\right)$$

(6)

$$V_{conc}=\frac{RT}{nF}\ln \left(\frac{{\left(i/A\right)}_L}{{\left(i/A\right)}_L-\left(i/A\right)}\right)$$

(7)

where $E_{Nernst}$, $V_{act}$, $V_{conc}$, and $V_{ohmic}$ are voltage losses of the thermodynamic potential, activation process, concentration, and ohmic voltage loss, respectively. $p_{H_2}^{\prime },p_{O_2}^{\prime }$, T, R, and F represent the hydrogen and oxygen partial pressure, cell temperature, universal gas constant, and Faraday constant, respectively. $R_{\mathrm{int}}$ is the internal resistance of the electrolyte membrane; ${c^{\prime }}_{O2}$ is the oxygen concentration at the cathode/membrane interface; ${\xi }_1\dots {\xi }_4$ are parametric coefficients; and i is the cell current [38].

Due to the double capacitor layer effect at the electrode–electrolyte interface, the voltage drop can be computed as [46]

$$\frac{d{V}_d}{dt}=\frac{i}{C_{dl}}-\frac{V_d}{R_d{C}_{dl}}$$

(8)

$$R_d=\frac{V_{act}+V_{conc}}{i}$$

(9)

where R_d is the activation resistance and concentration resistance, and V_d is the voltage drop.

The voltage of a single cell and total voltage when combining the number of cells N can be computed as

$$V_{cell}=E_{Nernst}-V_d-V_{ohmic}$$

(10)

$$V_{stack}=N{V}_{cell}$$

(11)

On the anode-side, the reactant flow model is given by the following:

$$\frac{V_a}{RT}\frac{d{p}_{H_2}^{\prime }}{dt}={\dot{m}}_{H_2,in}-{\dot{m}}_{H_2,out}-\frac{Ni}{2F}$$

(12)

$${\dot{m}}_{H_2,out}=k_a\left(p_{H_2}^{\prime }-p_{\tan \mathrm{k}}\right)$$

(13)

$$\frac{V_c}{RT}\frac{d{p}_{O_2}^{\prime }}{dt}={\dot{m}}_{O_2,in}-{\dot{m}}_{O_2,out}-\frac{Ni}{4F}$$

(14)

$${\dot{m}}_{O_2,out}=k_c\left(p_{O_2}^{\prime }-p_{BPR}\right)$$

(15)

$$P_{tot}={\dot{m}}_{H_2,used}\mathsf{\Delta }H=\frac{Ni}{2F}\mathsf{\Delta }H$$

(16)

where $V_a,{\dot{m}}_{H_2,in},{\dot{m}}_{H_2,out}$ are the anode volume, hydrogen inlet, and outlet flow rates through the fuel cell (FC) stack, respectively. k_a is a flow constant for the anode, and $p_{\tan \mathrm{k}}$ is the pressure of the hydrogen tank. $V_c,{\dot{m}}_{O_2,in},{\dot{m}}_{O_2,out}$ are the cathode volume, oxygen inlet, and oxygen outlet flow rate through the FC stack, respectively. k_c and $p_{BPR}$ are the flow constant in the cathode and oxygen pressure at the outlet, respectively. $P_{tot}$ denotes a total power input of the system, which changes linearly with hydrogen consumed, and $\mathsf{\Delta }H$ is the hydrogen enthalpy of combustion.

Finally, the electrical output power can be obtained as

$$P_{elec}=V_{stack}i$$

(17)

2.3. Supercapacitor Modeling

The SC was selected as the first support unit to supply different power between the demand and power generated from the FC and BATs in the case of sudden change due to its advantages such as high power density, fast charge, and high release power. Without using a SC, the FC and BATs have to manage the entire required workload even when high peak power happens, thus degrading lifespan, or increasing the size and costs in a trade-off [47]. Moreover, as Phatiphat stated in [48], when the time constant is less than 0.1 s, energy cannot be obtained from the same sized BAT, but the SC can totally provide energy at a very high rate. This is the highlighted advantage of the SC. Many different models have been suggested using the RC circuit. The equivalent SC model can be referred to in [48,49,50]. Naturally, the SC consists of capacitors and resistors that represent the charging and discharging units, and an equivalent parallel resistor is the self-discharging loss [51]. The unit cell of the SC was constructed with two RC branches in a parallel manner, as presented in Figure 2 [52].

As depicted in Figure 2, the main cell, R₁C₁, specifies the immediate response during the charge or discharge process within a short time duration [53]. All charged energy is in the capacitor C₁ of the immediate branch at the end of the charging mode. Then, the charge re-splits itself to the second slow cell, R₂C₂. The resistor R_f denotes a leakage behavior based on the fact that there always exists a leakage current flow of the SC during a self-discharge phenomenon [54]. This current leakage is approximately several milliamps in a large SC. The model of SC is derived as

$$U_{sc}=N_{s\_sc}\left(v_1+R_1\frac{I_{sc}}{N_{p\_sc}}\right)$$

(18)

$$i_1=C_1\frac{d{v}_1}{dt}=\frac{d{Q}_1}{dt}=\left(C_0+C_v{v}_1\right)\frac{d{v}_1}{dt}$$

(19)

$$Q_1=C_0{v}_1+\frac{1}{2}{C}_v{v}_1^2$$

(20)

$$i_1=i_{sc}-i_2$$

(21)

$$v_2=\frac{1}{C_2}{\displaystyle \int \frac{1}{R_2}\left(v_1-v_2\right)dt}$$

(22)

$$Q_2={\displaystyle \int i_{2}dt}$$

(23)

where U_sc and I_sc are the voltage and current of the pack SCs; and v_sc and i_sc are the voltage and current of an elementary SC. $N_{s\_sc}$ and $N_{p\_sc}$ denote the number of SCs in a serial connection and the number of parallel branches, respectively. i₁ and i₂ are the current through the main cell and the slow cell. Q₁ and C₁ are the instantaneous charge state of the main cell. v₁, v₂ is the voltage of the first and secondary branches. Q₂ and C₂ are the instantaneous charge states of the slow cell.

Finally, the SoC_SC is an important parameter to evaluate the state of the SC bank for designing the EMS. The change rate of the SoC_SC is proportional with the charging current i_sc [55]:

$$\frac{d}{dt}So{C}_{SC}=\frac{i_{SC}}{Q_{SC\max }}$$

(24)

where Q_SCmax denotes the maximum capacity of the SC.

2.4. Battery Modeling

The BAT is the second buffer supply for the system when the FC and/or the SC cannot maintain the workload demand during the endurance process. The BAT model is constructed with specific invoked parameters to evaluate its working status, thereby establishing criteria for effectively initializing the EMS. The BAT model used in this study follows the circuit proposed in [56].

$$E=E_0-K_{BAT}\frac{Q_{BAT\max }}{Q_{BAT}}+A_{BAT}{e}^{B\left(Q_{BAT}-Q_{BAT\max }\right)}$$

(25)

$$\begin{array}{l}{V}_{bat}=E-R_{BAT}{i}_{BAT}\\ P_{BAT}=V_{BAT}{i}_{BAT}\end{array}$$

(26)

$$Q_{BAT}=Q_{BAT}\left(t_0\right)-{\displaystyle \underset{t_0}{\overset{t}{\int }}{i}_{BAT}d\tau }$$

(27)

where E is the controlled voltage source; V_BAT and P_BAT are the BAT voltage and output power, respectively; Q_BAT and Q_BATmax denote the instant and maximum BAT capacity, respectively; i_BAT is the load current; and t is time parameterized. A_BAT is an exponential zone amplitude (V).

The SoC_BAT can be derived from the current charge and the maximum charge of it.

$$So{C}_{BAT}=\frac{Q_{BAT}}{Q_{BAT\max }}$$

(28)

The SoC_BAT is another important parameter, along with the SoC_SC, that reveals the device status and is invoked to assess the available energy remaining. The direction of the current determines the charge or discharge mode of the BAT. Compared with the BAT model in [47,57,58], this model gives the shortened form and can be used in both charge and discharge mode without losing its characteristics.

2.5. DC/DC Converter Modeling

For the studied hybrid electric excavator system, the BAT and SC were interfaced with the DC bus by using a bidirectional DC/DC converter, which can allow energy flow in both directions. The PEMFC system was linked with the DC bus via a buck DC/DC converter, which can adapt the voltage level of the DC bus. These DC/DC converters are the crucial execution devices of the energy management process, which can regulate an output voltage and current using a local controller. The energy management process is at a higher level than a local controller of the DC/DC converters and it is assumed that the time constant of the inductors in the DC/DC converters are much greater than the switching period [59]. Therefore, once the inner-loop subsystem is well controlled, it can respond immediately to the reference. Thus, it is reasonable to reduce the fast dynamics of the DC/DC converter using the following equivalent static model [60,61].

$$V_I-V_h=L\frac{d{i}_L}{dt}+i_L{R}_L$$

(29)

$$V_h={\kappa }_{DC}{V}_O$$

(30)

$$i_O={\kappa }_{DC}{i}_L{\eta }_{DC}^{\epsilon }$$

(31)

where V_I, V_O are the DC/DC converter input and output voltage, respectively; R_L is the resistor of the inductor and L is its inductance; κ_DC is the ratio of converter output and input voltage; i_L and i_O are currents through the inductor and the output current of the converter, respectively; η_DC is the converter efficient; ε = 1 for boost mode or the bidirectional mode with $i_O{V}_O\ge 0$ and ε = –1 for bidirectional mode when $i_O{V}_O<0$.

3. Configuration and Proposed Energy Management Strategy (EMS) for the Hydraulic Excavator

3.1. Hybrid Power Hydraulic Excavators Configuration

The hybrid power HE (HP–HE) was constructed as depicted in Figure 3a, in which the ICEs were alternatively replaced by the hybrid FC–BAT–SC power source and electric motor. The entire system can be considered as the HPS associated with the hydraulic actuators (HAs) through the DC bus. The HPS comprises the PEMFC functioning as the primary supply and the BAT–SC functioning as auxiliary buffers. The goal of the HPS is to supply power as the load power required and store energy in the case of regeneration. The power induced from the HPS provides power to the electric motor through DC/DC converters, and the electric motor drives the practical hydraulic system. The HAs consisted of three hydraulic cylinders for the driving boom, arm, and bucket, and one swing hydraulic motor for driving the HE body. The movement of the three cylinders was distinguished by using a main control valve block to control the flow rate to each actuator. Furthermore, the HAs were extended by the regeneration part to recover the energy-saving when the boom automatically moves down due to gravity, as shown in Figure 3b.

3.2. Proposed Energy Management Strategy (EMS)

Based on the fact that HEs perform various functions such as digging, lifting soil, spinning, ground leveling, and so on, an EMS was proposed to productively achieve the requirements. Improving the system performance and considering regeneration mode for saving energy were taken into consideration. From the requested motions of the excavator, the power required (P_red) was determined as a reference for running the power from the HPS. The SoC_BAT and the SoC_SC were used to evaluate the state of the components. Furthermore, the minimum SoC signed by SoC_{BAT_min} and SoC_{SC_min} was used to monitor when the two devices needed to be charged. The flowchart of the proposed EMS is depicted in Figure 4.

As depicted in Figure 4, in the beginning, the power required was examined to determine if its value was negative. In this case, the HE is moving downhill, when the swing is braking after spinning the entire body, or when the boom is moving down, whereas other elements do not operate. When these events happen, the BAT–SC is not required to release power. Instead, depending on the level of the power-saving, the FC is switched OFF or runs in an optimal value in which the highest efficiency can be achieved to charge the BAT–SC.

Otherwise, when P_req is positive, the following circumstances should be considered. If the power demand is less than the nominal power of the FC (P_{fc_n}), the FC primarily supplies power to the system and charges the auxiliary supplements for later use. The charging is stopped if the SoC_BAT/SoC_SC reaches the maximum value (SoC_BAT/SoC_SC = SoC_Max). If the load demand exceeds the FC nominal power, the combination between the FC and BAT or SC is considered, if their power can sufficiently satisfy the load demand. This scenario is highlighted in light blue and light green in Figure 4. The combination of FC–SC is considered in the case when the BAT cannot satisfy the sudden change in power required, as explained in the SC modeling part. Otherwise, the prior combination of FC–BAT is used. During this process, if the SoC_BAT (or SoC_SC) drops to the minimum level, the SC (or BAT) is alternatively used, and the other device is alarmed and switched to charge mode. If the P_req exceeds the combination of FC–BAT (or FC–SC), all devices enter together and provide power to the system. During these processes, the SoC_BAT and SoC_SC should be monitored and the SC is always charged first.

3.3. Regeneration Mode

In electric vehicles (EVs), the charge mode occurs when the cars are moving downhill or braking, while the FC is still supplying power to the system. One important point to clarify is that the charge and discharge mode cannot simultaneously occur as analyses in conventional algorithms. Since the BAT–SC is connected with only one engine and the engine is directly coupled with two-back-wheels, by using bi-directional DC/DC converters in the hybrid source, the state of the devices can be easily switched to capture or release power, depending on the state of the system and can be used in the same transmission line.

In contrast to the EVs, the powertrain of the HEs consists of various links (boom, arm, bucket, swing, and crawlers). Therefore, designing the regeneration mode in the HEs is more complicated than that of the EVs. We need to consider a case when one link is in a power-saving procedure (for instance, the boom is moving down automatically due to gravity), while the others continuously operate as usual. This implies that the power sources supplying progress for the system and power-saving progress from one or more elements occur at the same time. Hence, we cannot apply the same design as that of the EVs. For general hydraulic circuits, one sub-system should be connected as the second line for saving energy. Consequently, in this design, the circuit diagram for hybrid sources is separated into two distinguished transmission lines: one for supply and one for regeneration. The power captured from the generation is transmitted through the second transmission line.

4. Fuzzy EMS for the Integrated System

According to the working principle presented by the above flow chart, the power obtained from the driving cycle can be separated into four cases: high power, medium power, low power, and regenerative mode. The conventional EMS can simply be considered as an on–off switch between devices. However, this method may generate a delay to the system, as explained in the Introduction. In practice, the change in the status of devices requires a certain time to achieve and adapt to the required tasks. This problem can be handled by employing a FLC, which is known to be a useful tool to split and distribute power. This method was previously suggested by [18]. In this approach, the prior SoC_SC is retained so that the stability of the SoC_SC is maintained in an acceptable condition. However, in practice, maintaining the SoC_SC in an acceptable condition is not as important as that of BAT due to its specification. In large systems that always work under high power for an extended period, the BAT operation and its status should be regulated so that its SoC exhibits variation or is prevented from dropping down to a very low value as a solution to prolong life-time. The efficiency curve of the PEMFC is shown in Figure 5.

As shown in Figure 5, efficiency does not increase as power increases. High power achievement requires more energy from the auxiliary devices (cooling or heating system), thus reducing the overall efficiency of the system. Therefore, designing an algorithm to maintain high efficiency when operating the FC is practically prioritized as the main criterion. Thereby, we can reduce hydrogen consumption and limit the on/off cycles of the system to extend lifespan. The FLS was set up with the following criteria to satisfy the above analysis:

• Increase the FC efficiency and minimize hydrogen consumption.
• The SoC_BAT should be frequently maintained within the range of 0.5~0.9 as a solution to prolong lifespan.
• The SoC_SC should be maintained at a high level to boost the power in the case of an emergency.

Therefore, the fuzzy control rules can serve to map the input linguistic variables P_req, SoC_BAT, and SoC_SC to the output linguistic variables P_fc, P_BAT, and P_SC, respectively. The input linguistic P_req is characterized by four membership functions as four levels of operation. The input linguistics SoC_BAT and SoC_SC are characterized by five membership functions (L (Low), ML (Medium–low), M (Medium), MH (Medium–high), H (High)). The output linguistics of the FC-P_{FC_ref} are characterized by four membership functions (O (Off), L (Low), M (Medium), H (high)), whereas the output P_BAT is a gain distributed within [−1,1] interval and characterized by nine membership functions (NVB (Negative Very Big), NB (Negative Big), NM (Negative Medium), NS (Negative Small), Z (Zero), PS (Positive Small), PM (Positive Medium), PB (Positive Big), PVB (Positive Very Big)). The matrix rules in the four cases are expressed in

Table 1. High power required.

Phigh		SoCSC (0.2~0.9)
	Pfc_ref |PBAT	L		ML		M		MH		H
SoCBAT (0.5~0.9)	L	H	PS	H	PS	H	PS	H	PS	H	PS
	ML	H	PB	H	PB	H	PB	H	PM	H	PM
	M	H	PB	H	PB	H	PB	H	PM	H	PM
	MH	H	PVB	H	PVB	H	PVB	H	PVB	H	PVB
	H	H	PVB	H	PVB	H	PVB	H	PVB	H	PVB

,

Table 2. Medium power required.

Pmed		SoCSC (0.2~0.9)
	Pfc_ref |PBAT	L		ML		M		MH-H		H
SoCBAT (0.5~0.9)	L	H	Z	H	NS	H	NM	H	NB	M	NB
	ML	H	PS	H	Z	H	NS	M	NM	M	NM
	M	H	PM	H	PS	M	Z	M	NS	M	NS
	MH	H	PB	M	PM	M	PS	M	Z	M	NS
	H	M	PVB	M	PB	M	PM	M	PS	M	Z

,

Table 3. Low power required.

Plow		SoCSC (0.2~0.9)
	Pfc_ref |PBAT	L		ML		M		MH		H
SoCBAT (0.5~0.9)	L	H	Z	H	NS	H	NM	H	NB	M	NB
	ML	H	PS	H	Z	H	NS	M	NM	L	NM
	M	H	PM	H	PS	M	Z	L	NS	L	NS
	MH	H	PB	M	PM	L	PS	L	Z	L	NS
	H	M	PVB	L	PB	L	PM	L	PS	L	Z

and

Table 4. Regeneration mode.

PFC_ref|PBAT|Psc		SoCSC (0.2~0.9)
		L			ML			M			MH			H
SoCBAT (0.5 ~ 0.9)	L	Opt. value	NS	NVB	Optimal value	NS	NVB	Optimal value	NM	NVB	Optimal value	NB	NM	Opt. value	NVB	NS
	ML		NS	NVB		NS	NVB		NS	NVB		NM	NM		NB	NS
	M		Z	NVB		Z	NVB		NS	NVB		NS	NM	O	NM	Z
	M		PS	NVB		PS	NVB		Z	NVB	O	NS	NM	O	NS	Z
	H		PM	NVB		PM	NVB	O	PS	NVB	O	Z	NM	O	NS	Z

. The membership function of the inputs and outputs are described in Figure 6.

For the regeneration mode, because the excavator does not require any power from the power supply, the power of the FC is adjusted to operate at maximum efficiency in the case of charging auxiliary devices when the SoC drops down to a low value and off when the SoC level is high. Furthermore, the power of BAT and SC power are assigned as outputs of the FLC. The fuzzy rule of the regenerative mode is presented in Table 4.

In this study, triangular membership functions are exploited as depicted in Figure 6. The left side illustrates the inputs of the FLS in which the power required P_req, SoC_BAT, and SoC_SC are considered; the right side is the product including the FC power and gains of the BAT for charging or discharging mode. Additionally, to match the aforementioned criteria, the four following requirements should be satisfied:

• In the case of low devices SoC (SoC_BAT and SoC_SC are low), the FC power can be set up to a high value for quick charging, even when the system is operating with medium or low power required.
• For medium and low power required, if the SoC_BAT is greater than medium level, the BAT charges the SC instead of using FC; therefore, the FC does not need to run at a high value, and the efficiency can be increased consequently.
• In the case of charging, the SC is always charged so that a good condition of the SoC_SC can be maintained for later use.
• The final goal is to force the FC power to the highest efficiency point, as shown in Figure 5.

The completed control schematic diagram is depicted in Figure 7.

Since the power of the system in some cases can be referred to as the mixture between two cases, (for instance, if the required power is 85 kW, then this value can belong to both high power and medium power), then the scheduling gains is used to calculate the exact output power of the FLC. Let us define the vector $K={\left(\begin{array}{cccc}\alpha & \beta & \gamma & \sigma \end{array}\right)}^T$ as the gains of the high power, medium power, low power, and regenerative power, respectively. Then, the output power is calculated as:

$$P_{FC}^{*}=K^T{P}_{FC}^{*}=\alpha P_{FC1}^{*}+\beta P_{FC2}^{*}+\gamma P_{FC3}^{*}+\sigma P_{FC4}^{*}$$

(32)

where $P_{FC}^{*}={\left(\begin{array}{cccc}{P}_{FC1}^{*}& P_{FC2}^{*}& P_{FC3}^{*}& P_{FC4}^{*}\end{array}\right)}^T$ is an output of the four FLC, respectively, $K={\left(\begin{array}{cccc}\alpha & \beta & \gamma & \sigma \end{array}\right)}^T$ is calculated as:

$$\{\begin{array}{l}K={\left(\begin{array}{cccc}\alpha & \beta & \gamma & \sigma \end{array}\right)}^T={\left(\begin{array}{cccc}0& 0& 0& 1\end{array}\right)}^{T}if{P}_{req}\le x_{reg}\\ K={\left(\begin{array}{cccc}\alpha & \beta & \gamma & \sigma \end{array}\right)}^T={\left(\begin{array}{cccc}0& 0& 1& 0\end{array}\right)}^{T}if{x}_{L,1}\le P_{req}\le x_{L,2}\\ \{\begin{array}{l}\alpha =1-sat\left(\frac{\left|x_H-P_{req}\right|}{x_H-x_{M,2}}\right)\\ \beta =1-sat\left(\frac{\left|x_{M,1}-P_{req}\right|}{x_{M,1}-x_{L,2}}\right)\times \frac{\left|sign\left(x_{M,1}-P_{req}\right)-sign\left(x_{L,2}-P_{req}\right)\right|}{\left|sign\left(x_{M,1}-P_{req}\right)\right|+\left|sign\left(x_{L,2}-P_{req}\right)\right|}\\ -sat\left(\frac{\left|x_{M,2}-P_{req}\right|}{x_H-x_{M,2}}\right)\times \frac{\left|sign\left(x_{M,2}-P_{req}\right)-sign\left(x_H-P_{req}\right)\right|}{\left|sign\left(x_{M,2}-P_{req}\right)\right|+\left|sign\left(x_H-P_{req}\right)\right|}\\ \gamma =1-sat\left(\frac{\left|X_{L,2}-P_{req}\right|}{x_{M,1}-x_{L,2}}\right)\end{array}\mathrm{Otherwise}\\ K={\left(\begin{array}{cccc}\alpha & \beta & \gamma & \sigma \end{array}\right)}^T={\left(\begin{array}{cccc}0& 1& 0& 0\end{array}\right)}^{T}if{x}_{M,1}\le P_{req}\le x_{M,2}\\ K={\left(\begin{array}{cccc}\alpha & \beta & \gamma & \sigma \end{array}\right)}^T={\left(\begin{array}{cccc}1& 0& 0& 0\end{array}\right)}^{T}if{P}_{req}\ge x_H\end{array}$$

(33)

Consequently, the FC power used for the net is computed as

$$P_{FC\_net}={\eta }_{FC}{P}_{FC}^{*}$$

(34)

5. Numerical Simulation and Discussion

5.1. Parameters Setup for Simulation

In this section, the simulations and comparisons between the proposed control strategy with previous approaches are examined to evaluate the effectiveness of the proposed HPS under different working conditions. The simulations were conducted in a co-simulation between LMS AMESim 15.2 software and MATLAB/Simulink 2019a as depicted in Figure 8.

The LMS AMESim, known as specialized software for dynamic simulation with various applications, was employed to express the HE configuration. The parameters for simulating the HE are described in

Table 5. Parameters for the excavator model.

Component	Value	Unit
Boom cylinder (Piston diameter × Rod diameter × Stroke length)	0.35 × 0.22 × 1.8	m
Arm cylinder	0.18 × 0.125 × 1.7	m
Bucket cylinder	0.21 × 0.13 × 1.33	m

. The modeling of the HPS was deployed in MATLAB/Simulink, in which all mathematical equations were embedded, and the results were displayed with a sampling time of 10 ms. The component sizes of the HPS were reasonably chosen to satisfy the demand and verify the proposed methodology as listed in

Table 6. Fuel cell system parameters [38,41].

Parameter		Value	Unit
Number of cells	N	35	-
Number of stacks	-	18	-
Rated power	-	3.6	kW
Membrane thickness	-	178	μm
Anode pressure	$p_{H2}$	3	atm
Cathode pressure	$p_{O2}$	3	atm
Cell area	A	232	cm2
Coefficients	ξ1	−0.948	-
	ξ2	0.00286 + 2 x10–4 × ln(A) + 4.3×10–5 × ln(cH2)	-
	ξ3	7.6 × 10–5	-
	ξ4	–1.93 × 10–4	-
Membrane resistivity parameter	-	12.5	-
Fuel cell capacitance	Cdl	0.035 × 232	F
Flow constant for the anode	ka	0.065	mol s–1 atm–1
Flow constant for the cathode	Kc	0.065	mol s–1 atm–1
Anode volume	Va	0.005	m3
Cathode volume	Vc	0.01	m3
Hydrogen enthalpy of combustion	ΔH	285.5 × 103	kJ mol–1
Thermal resistance	-	0.115	C.W–1
Total energy (for 6 h)	-	302.522	kWh

,

Table 7. Supercapacitor parameters [52].

Parameter		Value	Unit
Model	-	BCAP3000	-
Number of supercapacitors	NS_SC	80	-
Rated voltage	-	2.7	V
Absolute maximum voltage	-	2.85	V
Absolute maximum current	-	1900	A
Rated capacitance	-	3000	F
Capacitance in the main cell	C0	2100	F
-	C1	623	F
Capacitance in the slow cell	C2	172	F
Resistance in the main cell	R1	0.36 × 10–3	Ω
Resistance in the slow cell	R2	1.92	Ω

and

Table 8. Battery parameters [38].

Parameter		Value	Unit
Capacity	QBATmax	6.5	Ah
Rated voltage	-	1.2	V
Battery constant voltage	E0	1.2848	V
Internal resistance	RBAT	0.0046	Ω
Number of batteries	-	360	-
Exponential zone amplitude	ABAT	0.144	V
exponential zone time constant inverse	B	2.3077	(Ah)–1
Polarization resistance constant	KBAT	0.01875	Ω

. The testing trajectories of the boom, arm, and bucket of the excavator are described in Figure 9, and the required power from those motions is performed in Figure 10.

Regarding the working cycles in Figure 9, the characteristic line sloped down when the element moved down (i.e., the cylinder retraces and increases when the element moves up, i.e., the cylinder is extending. With the driving cycles shown in Figure 9, changes in the characteristic lines result in changes in the power required, as depicted in Figure 10, for instance, referring to the driving cycle (a) at the time of the 5th to 10th second when all three elements are moving, the power required in Figure 10 increases. Through the power curve, the power needed to run the boom was the highest compared with that of the other two; in particular, the power curve increased significantly when the boom moved up. After that, at the time of the 25th second, all elements were kept in a fixed position and the power decreased. Therefore, the buffer supplements were charged at these times as in this scenario.

5.2. Simulation Results and Discussion

In this section, the two simulations comprising the proposed EMS in [38] and the proposed fuzzy EMS (F–EMS), as expressed in Section 3, were conducted and compared with the three other strategies: (1) conventional EMS (C–EMS) [62], (2) HFS–CS, and (3) LCS–CS in [16].

The responses of the total power supply, FC, BAT, and SC are described in Figure 11, Figure 12, Figure 13 and Figure 14, respectively. In each figure, the responses when embedding the proposed EMS, proposed F–EMS, C–EMS, HFS–CS, and LCS–CS are depicted in sub-figures (a), (b), (c), (d), and (e), respectively. The total power supplied from the proposed algorithm is depicted in Figure 11a and proposed F–EMS is depicted in Figure 11b. The other results when embedding the C–EMS, HFS–CS, and LCS–CS into the system are depicted in Figure 11c–e, respectively. These results reveal that the proposed strategies can provide sufficient power to the system and maintain stable levels during an endurance process; consequently, good performance can be achieved.

In contrast, the other EMS strategies were not capable of maintaining sufficient energy. For this reason, the C–EMS did not consider the charging process for auxiliary devices when their SoC_BAT/SoC_SC dropped to a low level. When the SoC_BAT/SoC_SC reached the minimum level as shown in Figure 15, the supplements were out of power and could not support the system.

As a result, the system can not complete the requirement due to the shortage of power, starting at the time of the 140th second. For the two HFS–CS and LCS–CS strategies, charging procedures were considered in which the positive power of the auxiliary devices indicates that they are in discharge mode, whereas the negative value indicates that they are in charge mode. However, instability occurs due to the inappropriate order of using devices. Starting at the time of the 210th second, when the SoC_BAT/SoC_SC dropped down to the minimum level, the chattering phenomenon took place because the devices immediately switched from releasing to charging mode when the SoC_BAT/SoC_SC hit the minimum level. Subsequently, when the SoC_BAT/SoC_SC is greater than the minimum level, the states of the devices instantly shift from charging to releasing the power, despite low remaining power. These processes repeatedly occur and generate high-frequency fluctuations. Therefore, these paradigms need to be noticeably improved based on the fact that either the system has to stop for charging like in conventional algorithms, or employ another strategy to maintain performance.

Compared with the three previous strategies, the proposed algorithm, which considers all circumstances for stable power-sharing, has greater endurance and the supplements are considerably maintained in good condition to extend the duration for the requirements. As expressed in Figure 15, the SoC_BAT varied negligibly from 0.769 at the start to 0.7685 at the end of the process. The SoC_SC had a periodic oscillation around the value of 0.6 with a high magnitude due to the high power required. Moreover, for the proposed EMS, the P_fc was maintained at constant power and was only switched off in the case that no power was required. Consequently, the BAT and SC are charged every time when high power is not required. However, this is not an optimal solution for the EMS since overcharge happened in the SC at the time of the 50th second, as shown in Figure 15. Moreover, the SoC_BAT increased from the beginning to the end of the process because when the SC reached the maximum level, no additional power could be captured and the excess power from the FC was transferred to the BAT. Due to maintaining the constant level, the FC required more hydrogen consumption and the FC efficiency was low as a result. This issue was resolved by using the F–EMS employing the MFLC as explained in Section 4. Based on the comparison between the two proposed EMSs, the FC in the F–EMS consumes less fuel than that of the proposed EMS and is forced to the rated power to increase efficiency. The BAT takes the place of the FC in charging energy for the SC and maintaining it in good condition, instead of using the FC all the time.

Referring to the FC model in Section 2, the efficiency of the FC can be calculated as [63]

$$Eff=\frac{P_{elec}}{P_{tot}}\times \max \left(0,1-\frac{P_{aux}}{P_{elec}}\right)$$

(35)

The comparison of the efficiency for the two proposed algorithms is depicted in Figure 16.

As revealed in Figure 16, the maximum efficiency that the FC can reach when applying the proposed EMS was approximately 37% due to maintaining the constant value of 65 kW. Conversely, the efficiency when embedding the F–EMS was higher than that of the proposed EMS due to reducing the hydrogen consumption. With the response of the FC shown in Figure 12a, the efficiency of the FC could reach up to 47%. The average efficiency of the FC increased from 32% when using the proposed EMS to 42% when applying the F–EMS under the same conditions. Furthermore, the number of ON/OFF switches decreases as a solution for extending the FC lifespan.

6. Conclusions

The new configuration for the hydraulic excavators equipped with a hybrid power source comprising the fuel cell, batteries, and supercapacitors with the proposed EMS is the merit of this paper. Instead of using one auxiliary supplement until it runs out of power and using the other as a compensation supply later, the EMS was exploited to distribute the energy from the powertrain to each device so that good performance is achieved and the lifespan of all components can be extended. The simulation results displayed that the proposed EMS can satisfy the requirements in comparison with other previous approaches under different working conditions. Moreover, the generation procedure was considered as the time for healing buffer supplements. In a going effect, the use of the proposed F–EMS confirmed its effectiveness when reducing the fuel consumption in the FC while maintaining the SC in a good condition for use in the event of an emergency. The achievements in this study can not only guarantee power supply performance and prolong the lifespan of all devices, but also reduce the fuel consumption and increase the efficiency of the system. Therefore, this study is a premise for developing a hybrid power source for construction machinery in the future.