An optimal configuration for a battery and PEM fuel cell-based hybrid energy system using developed Krill herd optimization algorithm for locomotive application

Guo, Yingying; Dai, Xiangdong; Kittisak Jermsittiparsert; Razmjooy, Navid Article An optimal configuration for a battery and PEM fuel cell-based hybrid energy system using developed Krill herd optimization algorithm for locomotive application Energy Reports Provided in Cooperation with: Elsevier Suggested Citation: Guo, Yingying; Dai, Xiangdong; Kittisak Jermsittiparsert; Razmjooy, Navid (2020) : An optimal configuration for a battery and PEM fuel cell-based hybrid energy system using developed Krill herd optimization algorithm for locomotive application, Energy Reports, ISSN 2352-4847, Elsevier, Amsterdam, Vol. 6, pp. 885-894, https://doi.org/10.1016/j.egyr.2020.04.012 This Version is available at: https://hdl.handle.net/10419/244086 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ Energy Reports 6 (2020) 885–894 Contents lists available at ScienceDirect Energy Reports journal homepage: www.elsevier.com/locate/egyr Research paper An optimal configuration for a battery and PEM fuel cell-based hybrid energy system using developed Krill herd optimization algorithm for locomotive application Yingying Guo a,b, Xiangdong Dai a, Kittisak Jermsittiparsert c,∗, Navid Razmjooy d aSchool of Materials Science and Engineering, Central South University of Forestry and Technology, Changsha 410004, China bSchool of Architecture and Civil Engineering, Huanghuai University, Zhumadian 463000, China cSocial Research Institute, Chulalongkorn University, Bangkok 10330, Thailand dDepartment of Engineering, Tafresh University, Tafresh, Iran article info Article history: Received 1 January 2020 Received in revised form 13 March 2020 Accepted 4 April 2020 Available online xxxx Keywords: Hybrid energy system Lithium-ion battery Energy management optimization Locomotive Converged Krill herd optimization algorithm PEM fuel cell abstract A new methodology has been proposed for optimal size selection of a hybrid energy system (HES) including lithium-ion battery and polymer electrolyte membrane (PEM) fuel cell to supply the driving force of a locomotive. The main purpose is to minimize the total cost of HES with different constraints including the capacity constraint of the battery and the fuel cell state-of-charge limit The optimization problem has been solved based on a new improved model of the Krill Herd (KH) algorithm, converged krill herd optimization algorithm (CKH). Simulation results are analyzed based on the average power demand, speed demand of the locomotive, and the locomotive slope. The results of the presented CKH algorithm have been compared with the standard KH and PSO algorithm and the results declared that the total cost for HES based on CKH has the minimum value such that the value for the CKH for 0%, 1%, and 2% slope are 3.15 ×106, 3.56 ×106, and 3.93 ×106toward KH with 3.47 ×106, 4.01 ×106, and 4.56 ×106and PSO with 3.74 ×106, 4.27 ×106, and 4.72 ×106HES, respectively. ©2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). 1. Introduction The development of vehicles based on internal combustion engines, especially automobiles, is one of the great achievements of human science and technology (Ghadimi,2015;Haixiong et al., 2020;Firouz and Ghadimi,2015). This has led to serious problems for the environment and human life (Hosseini et al.,2012,2011). Air pollution, global warming and limited fossil fuel resources are the major problems (Hosseini et al.,2013). In recent decades, extensive research has been done on clean and efficient fuelefficient vehicles, including electric vehicles, electric hybrids, and fuel cells. These vehicles can be a good alternative to today’s vehicles in the future (Dongmin et al.,2019;Shamel and Ghadimi, 2016;Dongmin et al.,2020;Seyed-Shenava and Khezri,2014). A fuel cell (FC) stack is an energy converter to convert the fuel and oxidizer energy directly into electrical energy. High efficiency, low operating temperature (used as a driving force) and lack of pollutions such as sulfur (SOx) and nitrogen oxides (NOx), low vibration and noise, low efficiency depending on the size of the system, and a variety of fuel sources (renewable and non-renewable) are some of characteristics that turn Fuel cell ∗Corresponding author. E-mail address: [email protected] (K. Jermsittiparsert). as one of the popular options for replacing internal combustion engines and consequently a viable solution to reduce energy and environmental problems caused by direct fossil fuel consumption in the future (Aghajani and Ghadimi,2018;Liu et al.,2017). Currently, this energy converter is widely studied around the world in order to be competitive with combustion engines in various aspects, including price, fuel supply, stability, and safety. One of the problems of the fuel cell-based system is that due to their new technology, the cost of preparing them is a little high. Therefore, this paper focus on resolving the mentioned problems. The main innovation of the present work is highlighted below: 1. Optimal configuration of a Hybrid Energy System for Locomotive Applications. 2. Using an optimal configuration for Battery and PEM fuel cells in the Hybrid Energy System. 3. Optimal Size selection of the Battery and PEM fuel cell in the Hybrid Energy System. 4. Using Chinese locomotive class HXD3Gas a practical case study. 5. Proposing a new version of the Krill Herd optimization algorithm for optimization of the sizes of the HES components. https://doi.org/10.1016/j.egyr.2020.04.012 2352-4847/©2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). 886 Y. Guo, X. Dai, K. Jermsittiparsert et al. / Energy Reports 6 (2020) 885–894 Fig. 1. Model cost of FC system ($/kWnet ) over the time (year). Fig. 2. Fuel consumption chart for transportation and other sectors (Mirzapour et al.,2019). 2. Literature review In recent years, research funded by DOE Hydrogen and Fuel Cell organization claimed that they succeed to reduce the cost of transportation fuel cells by 60% since 2006. They also proofed that Fuel cell reliability has improved by a factor of 4 since 2006 (Gollou and Ghadimi,2017) (see Fig. 1). Fuel cells do not also produce negligible pollutants such as SOxand NOx, particulate matter and organic compounds, but also produce significantly less CO and CO2pollutants than combustion engines (CO and CO2production in the fuel cell are 0.25% and 46% of the combustion engine). The transportation industry, followed by automobiles, is a major contributor to fossil fuel consumption; Fig. 2 shows the fuel consumption chart for transportation and other sectors (Mirzapour et al.,2019). As shown in Figure, on average, 49% of the world’s fuel is spent on industrial and developing countries for transportation. It is projected that fuel consumption in the transport sector is projected to increase by about 11.4 million barrels per day from the year 1997 to the year 2020 in industrialized countries. The same trend is also seen in developing countries, with almost 50% devoted to this sector in the year. On this basis, there is high interesting today in the automobile industry for the use of more efficient vehicles than the internal combustion engines and the use of clean fuels. Recently, several research works have been developed about the hybrid energy system (HES) based on PEMFC-battery in transportation applications. The literature has been principally divided into two research directions. The first direction is to use different control techniques for handling the energy management strategy (EMS) and the second direction is the works that have been focused on the optimization techniques. The optimization techniques have usually two types including energy management optimization (EMO) method to optimize EMS and design optimization (DO) method for optimizing the HES component sizing. The method of optimization can be done by classical methods and like dynamic programming (Firouz et al.,2016), non-linear programming (Hamian et al.,2018), and meta-heuristics like genetic algorithm and particle swarm optimization (Leng et al., 2018). Different works have been worked about the application of energy management strategy on electric vehicles (Akbary et al., 2019). For example, Ahmadi et al. (Homayoun et al.,2018) developed a hybrid FC-based electric vehicle with ultra-capacitor (FCHEV) and battery in terms of performance and fuel economy based on optimized EMS. An optimized fuzzy-based strategy was presented for controlling the FCHEV system. Final results were assessed for showing the system efficiency and showed less than 2% for the battery charge level variations. Zhou et al. (Khodaei et al.,2018) proposed an online EMS based on a fractional-order extremum seeking (ES) approach. The presented technique was an improved version of the traditional integer-order ES method along with fractional-order Oustaloup approximation evaluation to improve the speed of method convergence with higher reliability. For analyzing the system’s reliability and speed, an experimental test was done. The final results declared that using the proposed technique for controlling the PEMFC based system is completely efficient (Eslami et al.,2019; Gao et al.,2019;Saeedi et al.,2019). Hong et al. (2018) introduced a dynamic power factor-based EMS for a locomotive using hybrid fuel cell and battery. The method had a self-adaption function for obtaining less H2con- sumption and higher performance in different driving cycles. The efficiency of the system was finally analyzed to determine each part’s capability. Bendjedia et al. (2018) presented an optimized sizing technique for an ESS including a lithium-ion battery and a fuel cell for providing the power to a lightweight vehicle for 700 km. At last, for showing the effect of the ESS design driving cycles, it was analyzed based on New European Driving Cycle )NEDC( and then the system durability was assessed. The main purpose of the present work is to use HES based on PEM fuel cells in transportation. From the literature, it can be observed that there are a few types of research about the application of the PEM fuel cell in locomotives. The literature review shows that there is no (or maybe little) research about mathematical modeling of EMO and DO for the PEMFC-battery HES in the locomotive application. This reason has been a big motivation to work on it. Generally, the primary objective of the presented study is to improve a hybrid battery-PEM fuel cell HES model for supplying the tractive effort of a locomotive. For improving the system efficiency, the sizes of the HES components have been obtained by a new improved version of the krill herd optimization algorithm. The aim of the optimization here is to minimize the overall cost of the HES components by considering different constraints such as instantaneous power demand, battery SOC, and PEMFC capacity. The final results have been compared with some different methods from the literature. In the following, Section 2describes the mathematical model of the system. Section 3declares the methodology for EMS. Section 4introduced a detailed explanation for the optimization of the studied HES. Section 5determines the method of solving the problem. Simulation results are illustrated in Section 4and the work has been concluded in Section 5. 3. Mathematical model of the system The modeled HES system contains PEM fuel cell and a pack of lithium-ion batteries as the main energy source and the backup Y. Guo, X. Dai, K. Jermsittiparsert et al. / Energy Reports 6 (2020) 885–894 887 Fig. 3. Diagram of the hybrid PEMFC/battery system. Fig. 4. A general schematic of the PEMFC stack. energy source, respectively thanks to its several benefits such as high energy and power density and longer lifetime. Here, a 100 Wh/kg lithium manganese oxide (Li2MnO2The) battery is utilized for simulation (Geng et al.,2014). Fig. 3 shows the diagram of the Hybrid PEMFC/battery system based on HES. Indeed, the HES system is introduced to replace the diesel engine of the Chinese locomotive class HXD3Gthat is utilized in china railways since 2015. Due to several numbers of intermediate stops in the intercity passenger trains between the terminal stations, the speed of the trains has been changed continuously which provides floating power demand for the train. The minimum size of the PEMFC has been selected to be higher than the power demand of the locomotive due to the PEM fuel cell slow dynamic response. The battery stack is utilized for absorbing the generated power during the regenerative braking. In the following, the mathematical model of the hybrid locomotive parts has been given. 3.1. The model of PEMFC stack Fuel cell stacks are some kinds of energy resources that convert chemical energy directly into electricity with no combustion. Thanks to their clean energy production and high efficiency, Fuel cells have been turned into one of the most popular energy conversion systems (Luo et al.,2015;Razmjooy et al.,2018). One of the most used fuel cells is the proton-exchange membrane fuel cells (PEM fuel cell). A PEM fuel cell includes three principal parts: an anode, a cathode, and an electrolyte membrane. Fig. 4 shows the general schematic of a PEMFC stack. In a PEM fuel cell, H2has been ionized by anode to generate protons and electrons. Afterward, the electrons have been transmitted into an external circuit for the current generation and H2 protons transmitted into the membrane by remising molecules to each other. In the cathode side, O2has been synthesized by the protons from the anode and the electrons from the external circuit by generating water and heat. The total output voltage of a PEMFC has been illustrated in the following (Corrêa et al.,2004; Aouali et al.,2017): Vo=Nnc ×(EN−Eop −EO−Eops)(1) where, Nnc defines the number of connected cells, Eop describes the activation over-potential of the cells, EOrepresents the Ohmic voltage drop of the cells, Eops determines the over-potential saturation in the cells, and ENis the Nernst equation which declares the cell reversible voltage per cell and is achieved as follows (Kandidayeni et al.,2019): EN=1.23 −8.5×10−4×(TFC −298.15) +4.31 ×10−5×TFC ×[ln (PH2)+0.5×ln (PO2)] (2) here, PH2=Rha ×PH2O 2⎡ ⎢ ⎣ 1 Rha×PH2O Pa×e 1.635IFC/A T1.334IFC −1⎤ ⎥ ⎦(3) PO2=Rhc ×PH2O⎡ ⎢ ⎣ 1 Rhc×PH2O Pc×e 1.635IFC/A T1.334IFC −1⎤ ⎥ ⎦(4) here, Arepresents the membrane active area, IFC describes the fuel cell operating current, Rhc and Rha determine the vapor relative humidity in electrodes, Paand Pcdescribe the anode and the cathode inlet partial pressures, respectively. For the PEMFC operating temperature, the saturation vapor pressure is formulated as follows: log 10 (PH2O)=0.0295 ×(TFC −273.15)−9.18 ×10−5T2 c +1.4×10−7T3 c−2.18 (5) The value for the reference temperature is considered 25 ◦C. The Ohmic voltage drop for all the cells is modeled by the following equivalent: EO=IFC ×(Rm+Rc) (6) here, Rm=ρm×l×S−1(7) ρm= 181.6×[0.062 ×(TFC 303 )2 ×(IFC S)2.5 +0.03 (IFC S)+1] [λ−0.063 −3(IFC S)]×e TFC−303 TFC (8) The over-potential activation loss is formulated as follows: Eop = − [γ1+γ2TFC +γ3TFC ln (CO2)+γ4TFC ln (IFC)](9) here, CO2represents the saturation value of the O2in the catalytic interface of the cathode (mol/cm3) and are achieved as follows: CO2=PO2 5.1×106×e 498 TFC (10) and, γ2=29 ×10−4+21 ×10−5ln (A)+43 ×10−6ln(CH2) (11) here, CH2represents the saturation value of the H2in the catalytic interface of the cathode (mol/cm3) and are achieved as follows: CH2=PH2 1.1×106×e −77 TFC (12) 888 Y. Guo, X. Dai, K. Jermsittiparsert et al. / Energy Reports 6 (2020) 885–894 Table 1 The optimal parameter estimation extracted from Aghajani and Ghadimi (2018). Parameter Value Parameter Value β1−1.03 β4×10−5−9.48 β2×10−33.48 β0.01 β3×10−57.79 Rc×10−41.63 And the over-potential saturation (Eops ) in each cell is as follows: Eops = −β×ln (J2 max −J×Jmax Jmax )(13) here, Sdescribes the membrane surface (cm2), IFC represents the fuel cell operating current, Idescribes the thickness of the membrane, βidescribes the empirical coefficients, TFC determines the operating cell temperature (◦), λrepresents a controllable parameter, βdetermines a parametric coefficient, PH,PO2, and PH2Orepresents the partial pressure of the H2, O2,and H2O, respectively, Jand Jmax are the standards and the maximum current densities, respectively, Rha and Rhc represent the vapor relative humidity at anode and cathode, respectively, Pcand Padescribe the inlet pressure for the cathode and the anode, CH2and CO2are the hydrogen and oxygen (mol/cm3) saturation, Rcand Rmdescribe the connections resistance and the membrane resistance. In this paper, for the unknown parameters, the optimum values from Aghajani and Ghadimi (2018) have been extracted which is illustrated in Table 1. In the following, the efficiency of a PEMFC system is formulated as follows: ηFC =ηfc (1−Paux fc Pfc )(14) here, ηfc =Pfc PH2 (15) Pfc =Vo×Io(16) here, Iodescribes the fuel cell stack current. The total fuel consumption of the PEM fuel cell (mH2) is formulated as follows: CFC =∫PFC LHV ×ηFC(PLR)dt (17) here, LHV describes the hydrogen lower heating value and ηFC(PLR) is the PEM fuel cell efficiency map as a function of the part-load ratio (PLR) (Maleki and Rosen,2017). The corresponding heat generated, Qheat , during the driving period is as follows: Qheat =CFC ×LHV (18) Although, it should be considered that the existence of the auxiliary elements in the fuel cell system makes a restriction on the fuel cell net power output ratio which is because of the slow dynamic response of the auxiliary elements. In the present study, the limitation value, A is achieved as follows: A=0.9of Prated FC T(19) here, T=30 s. Finally, PFC (t)=A×t+P0 FC (20) here, P0 FC describes the beginning of the deceleration/acceleration period. 3.2. Lithium-ion battery The lithium-ion battery is a family of high-density rechargeable batteries. Unlike the disposable lithium battery, the lithiumion battery uses a lithium-ion compound instead of metal lithium as the electrode (Bagal et al.,2018). Usually, lithium-ion batteries are considerably lighter than other kinds of rechargeable batteries of the same size. Lithium-ion batteries have been widely utilized in portable electronics. The utilized lithium-ion battery here is employed in the presented HES for assisting the output power of the PEMFC in the transient conditions. The instantaneous output power of the lithium-ion battery is achieved as follows: Pb(t)=PLo (t)−PFC(t) (21) where, PLo (t)describes the total instantaneous power demand for the locomotive. The positive value for Pb(t)shows the discharging state, the negative value for the Pb(t)implies to charging state of the operation and the zero value implies that the battery remains idle. The SOC of the battery at any moment belongs to the SOC of the battery at the prior moment (t−∆t) and is obtained as follows: SOC (t)=SOC (t−∆t)−ηb×Pb(t) Qbc ∆t(22) here, ηbrepresents the charging/discharging efficiency of the battery and is achieved by the following equation: ηb={1 ηcharge for Pb(t)≤0,Charging 1 ηdischarge for Pb(t)>0,Discharging (23) here, ηcharge and ηdischarge describe the charging and discharging battery efficiencies, ∆tdescribes the small increment in time, and Qbc represents the capacity of the battery. 3.3. The model of the instantaneous power demand for the locomotive This research considers HES based on battery and fuel cell to drive intercity passenger locomotives. Therefore, the mathematical modeling of the instantaneous power demand is significant. The locomotive model contains the force of friction between the railway track (Ffr) and the wheels, the aerodynamic drag (Fd), the force of acceleration (Fa), and force to overcome a slope (Fsg) as given below. Ffr =Met ×dν(t) dt (24) Fsg =Met ×g×sin β(25) Fd(t)=0.5×D×ρ×σ×ν(t)2(26) Ffr =Met ×g×CRr ×cos β(27) here, ρ=1.293 kg/m3describes the air density, σis the cross-sectional area (m2), Drepresents the drag coefficient, CRr describes the coefficient of rolling resistance, νrepresents the locomotive velocity, and βis the gradient. In the above equations, Met describes the locomotive mass and is mathematically modeled as follows: Met =nch ×mch +Mlcm (28) here, nch describes the number of non-air-conditioned coaches, mch represents the mass of a non-air-conditioned coach, and Mlcm describes the mass of locomotive. Table 2 illustrates the parameters information for the studied HXD3Glocomotive that is taken from Li-xin (2010). Y. Guo, X. Dai, K. Jermsittiparsert et al. / Energy Reports 6 (2020) 885–894 889 Table 2 The parameters information for the studied Chinese locomotive class HXD3G. Parameter Value Unit Parameter Value Unit Starting traction 584 kN Axle load 25 t Max. speed 120 Km/h Power 9600 kW Fig. 5. Drive cycle for intercity passenger locomotive running in China. Due to the fact that all the elements are non-air-conditioned coaches, this research considers only the mass of the non-air- conditioned coach. The instantaneous power demand for the locomotive is achieved as follows: Pd=((Ffr (t)+Fsg (t)+Fd(t)+Ffr (t))×ν(t))/ηs(29) here, ηsdescribes the transmission system performance that is considered 85%. The total instantaneous power demand is as follows: PT d(t)=Paux +Pd(t)(30) here, Paux summed up with the instantaneous power demand. 3.4. Drive cycles The drive cycle is basically showing the speed variations of the locomotive during the time. The drive cycle is an important effective parameter on the instantaneous power demand of the locomotive. The studied drive cycle is based on the data from Jaafar et al. (2013). This data is provided using the mean value of the driving patterns followed by the locomotives. Fig. 5 shows the plot of the drive cycle and Table 3 illustrates the parameter values for the studied drive cycle. 4. Materials and methods 4.1. The method of energy management strategy The main purpose of Energy Management Strategy (EMS) in the locomotive is to collect the instantaneous output power of the energy sources to provide the instantaneous power demand of the locomotive. Therefore, the EMS here is to make an instantaneous power trade-off between the locomotive power demand and HES output. The studied EMS includes the following considerations: - The output power of the fuel cell is set to enhance at the acceleration time until it obtains the rated capacity of the fuel cell. - The output power is then employed to operate at the obtained ratio until the locomotive decelerates. - However, the rate of change of the fuel cell output power is limited by the rate constraint, the output power of the fuel cell has been decreased during braking and deceleration. - The battery operates in both charging/discharging modes in the entire driving period based on the instantaneous power demand and the output power of the fuel cell. - If the fuel cell output power is less than the instantaneous power demand, the battery has been discharged and if the fuel cell output power has a bigger value than the battery, the battery has been charged. 4.2. Design optimization model for the studied HES The objective of this research is to optimal determining the battery and PEMFC sizes to develop the presented HES capability for supplying the time-dependent power demand of an intercity locomotive in China. The optimization purpose is to minimize the total cost of the components of the hybrid energy system. Since this optimization model should consider the cost of the battery, electric motor and also fuel cell, the cost function is considered as follows: min F(x)=fb+fm+fFC +fr b+fr FC (31) here, fb,fm, and fFC describe the cost of Li-Ion battery, the electric motor, and the fuel cell, respectively and fr FC and fr bdescribe the replacement costs of the battery and the fuel cell, respectively. By considering the operational constraints such as output power variation of the PEM fuel cell and the battery SOC (x= [Pr FC,Qr FC]T): SOCmin ≤SOC (t)≤SOCmax (32) PT dem (t)=PFC (t)+Pb(t)(33) Pr FC ≥Pavg dem (34) 0≤PFC (t)≤Pr FC (35) here, Pr FC and Qr FC describe the fuel cell power rating and battery capacity, respectively, Cmin =0.25 and Cmax =0.9 describe the minimum and the maximum constraints of the SOC, respectively, PT dem (t)describes the average power demand of the locomotive, Pb(t)and PFC (t)describe the instantaneous power output of the battery and fuel cell, respectively, PT dem (t)represents the total locomotive instantaneous power demand. The reason for considering only the replacement cost of the fuel cell is that the only critical component of it is the part that contains the platinum catalyst, the polymer membrane, and the electrodes (Barbir and Gomez,1997). The equations for the components have been given below: fb=fub ×Qr FC +Cb(36) fm=fum ×Pr b+Cm(37) fFC =fuFC ×Pr FC (38) fr b=Vfu b×Mb r (1+Ri)M(39) fr FC =Vfu FC ×NFC r (1+Ri)N(40) here, Ridescribes the interest rate (here Ri=7% (Wu et al., 2011)), M(N) determine the life-time for the battery (PEM fuel cell) in years, Mb r(NFC r) describe the number of replacements of the battery (PEM fuel cell), fub =652($/kWh), fum =22($/kWh), and fuFC =48($/kWh), represent the cost of the battery, the electric motor, and the PEM fuel cell per unit rating respectively, Cb=679($) and Cm=420($) are the constant cost for the battery and the motor, respectively, Vfu band Vfu FC describe the future value of the battery and the PEM fuel cell, respectively (U. S. d. o. e. report). 890 Y. Guo, X. Dai, K. Jermsittiparsert et al. / Energy Reports 6 (2020) 885–894 Table 3 The parameters information for the studied Drive cycle. Parameter Value Unit Parameter Value Unit Total driving time 15980 s Average acceleration 0.5 m/s2 Distance 220 km Maximum deceleration −0.7 m/s2 Max. Speed 45 kmh Average deceleration −0.5 m/s2 Average Speed 37.33 kmh Max. acceleration 0.7 m/s2 According to (U. S. d. o. e. report), the projected and the ultimately projected life-time of the PEM fuel cell for transportation in 2020 are 5000 and 8000 h. Therefore, by considering the operation of the passenger locomotive 9 h a day and the projected PEMFC life-time of 8000 operating hours, the value of Ncan be estimated as 3 years. In addition, based on U. S. d. o. e. report, the lifetime of a lithium-ion battery for replacement is ten years (M=10). Therefore, by considering 20 years working period, the number for replacement of the PEM fuel cell and the battery are achieved one and three, respectively. 4.3. Basic Krill Herd algorithm The Krill Herd (KH) algorithm was first introduced by Gandemi and Alavi to solve the optimization problems (Wang et al., 2014a,b;Wang and Yi,2018;Wang et al.,2016a). The Krill Herd algorithm is categorized as one of the crowded intelligence algorithms, and it examines the mass movement of the krill to find food (Wang et al.,2014d,2016b,2019). Using this algorithm, we can solve NP-Hard class problems that do not have a precise solution in a reasonable time and find a sub-optimal solution for them. This algorithm is based on simulating the movements and behavior of a bunch of creatures to find food. In the Krill Herd algorithm, the minimum distance between each krill to food and the distance to the central population of the krill batch is assumed to be the cost function for the krill movement. The timedependent location for each krill in the Krill Herd algorithm is formulated by three factors. The KH algorithm is inspired based on three main behaviors including explore to find food, random moving, and motivated motion based on the herd that can be modeled by a Lagrangian model for the ith krill as follows: dXi dt =Fi+Di+Ni(41) here, Fidescribes the exploring to find food, Diis the random moving behavior, and Nirepresents the krill motivated motion based on the herd. −Exploring to find food This term contains two parts including food position and its previous experience. For the ith krill, it can be mathematically modeled as follows: Fi+1=Fi×ωf+Vf×βi(42) βi=βfood i+βb i(43) here, ωf∈ [0,1]represents the inertia weight, Vfdescribes the speed of exploring, Fidescribes the last exploring motion, βfood i represents the food attractive and βb irepresents the effect of the best cost of the ith krill so far. −Random moving Random moving is mainly a random process that is be formulated as follows: Di=Dmax ×δ(44) here, Dmax describes the maximum random speed, and δdescribes the random vector in the range 0 and 1. −Krill motivated motion based on the herd. Based on the research, each of the krills attempts to keep itself close to the herd and move along with the mutual effects (Hofmann et al.,2004). The direction of motion αiis divided into three parts including the local effect, the repulsive effect and the target effect. This can be mathematically modeled as follows: Ni+1=Ni×ωn+Nmax ×αi(45) here, αi=αle i+αT i(46) here, Nidescribes the last motivated motion, ωn∈ [0,1]represents the inertia weight, Nmax determines the maximum motivated speed, αle idescribes the local effect, and αT irepresents the target direction effect. In the above equation, the local effect and the target direction effect are achieved by the following equations: αle i= l ∑ j=1 ˆ Ki,j׈ Xi,j(47) ˆ Ki,j=ki−kj kw−kb(48) ˆ Xi,j=Xj−Xi  Xj−Xi +ϵ(49) αT i=Cb׈ Ki,b׈ Xi,b(50) here, Xdetermines the related positions, ldescribes the number of the neighbors, kiand kjdescribe the fitness of the ith and jth krill (j=1,2,..., l), respectively, kband kware best and the worst fitness of the krill, respectively and Cbdescribes the effective coefficient of each krill with the best fitness to the ith krill individual. The algorithm also uses genetic reproduction mechanisms including mutation and crossover operators. More details can be achieved by Gandomi and Alavi (2012). 4.4. Converged Krill Herd algorithm In the present study, two main improvements have been employed for the KH algorithm. First, a self-adaptive weight is proposed to control the tendency of approaching the best optimal solution. For updating the location of the krills, random changes have been applied to the food exploring and the repulsive effect terms. Although using high exploring in the search space is so promising for initial iterations, at the final iterations, it is better to use exploitation and local search which helps to develop the algorithm population quality. This feature is applied to the food exploring and the repulsive effect terms as follows: Fi,new={Fi+ϕ1×S(Fi)⊗Fi,rand >0.5 Fi−ϕ1×S(Fi)⊗Fi,rand ≤0.5(51) Ni,new={Ni+ϕ2×S(Ni)⊗Ni,rand >0.5 Ni−ϕ2×S(Ni)⊗Ni,rand ≤0.5(52) here, ϕ1={(f(Fbest) f(Fworst))2 ,if f (Fworst)= 0 1,if f (Fworst)=0 (53) ϕ2={(f(Nbest) f(Nworst))2 ,if f (Nworst)= 0 1,if f (Nworst)=0 (54) Y. Guo, X. Dai, K. Jermsittiparsert et al. / Energy Reports 6 (2020) 885–894 891 Table 4 The general information about the benchmarks employed for the validation. Type Function Equation Optimal Unimodal Rotated high conditioned elliptic F1(x)=f1(M(x−o1)) +F∗ 1100 Rotated bent cigar F2(x)=f2(M(x−o2)) +F∗ 2200 Rotated discuss F3(x)=f3(M(x−o3)) +F∗ 3300 Multimodal Shifted and rotated Rosenbrock F4(x)=f4(M(2.048(x−o4) 100 ))+F∗ 4400 Shifted and rotated Ackley F5(x)=f5(M(x−o1)) +F∗ 8500 Table 5 The benchmark functions utilized in the validation. Type ID Function f∗ Unimodal f1Rotated high conditioned elliptic function 100 f2Rotated bent cigar function 200 f3The function of Rotated discus function 300 Multimodal f4Shifted and rotated Rosenbrock function 400 f5Shifted and rotated Ackley’s function 500 here, f(Fworst),Nworst, and f(Fbest),Nbest describe the cost function values of the worst solution and best solution, respectively. In this technique, the value of the presented weight is increased gradually to reduce the difference between the worst and the best solutions. This technique also does not require any Another advantage of this technique is that there is no need for parameter adjusting. This study also uses a chaotic mechanism for improving system exploration. The best solution for each iteration is significant such that the other entire krill herd attempt to move based on the best solution experience to get better results. However, sometimes the best solution may be stuck in the local optimum. This problem makes a misleading solution to the other krill individuals to follow the best individual that finally leads to premature convergence. To resolve this problem, the random moving equation has been reformulated based on chaos theory. Chaotic mechanisms have ergodic and sequence random characteristics that are very helpful to improve the algorithm premature convergence (Yang et al.,2007;Rim et al.,2018). Here, the well known logistic map mechanism has been used for this purpose. Applying this improvement on the random moving gives the following formulation: Dnew i+1=Dnew i+σi×Dnew i(55) where, σi+1=4σi(1 −σi) (56) here, σidetermines the value for the ith chaotic iteration, and the initial value σ1∈ [0,1]describes a random value. 4.5. Algorithm validation For validating the performance of the presented algorithm, five benchmarks are employed and the results are compared with some different bio-inspired algorithms such as gravitational search algorithm (GSA) (Rashedi et al.,2009), emperor penguin optimization (EPO) (Dhiman and Kumar,2018), world cup optimization algorithm (WCO) (Razmjooy et al.,2016), and the original KH (Gandomi and Alavi,2012) to show the system efficiency. Table 4 illustrates the information about the utilized benchmarks for the algorithm validation Table 5 illustrates the benchmark functions utilized in the validation. The population size for all algorithms is considered 100, function evaluations are 100,000 for all functions, and the stopping criteria is based on a maximum number of function calculation (Khalilpuor et al.,2001;Namadchian et al.,2016;Razmjooy and Ramezani,2016). The dimension is 30 (n=30). The best efficiency is achieved by over 55 runs in Table 6 for all functions. Here, ‘‘std’’ describes the standard deviation, ‘‘Median" represents the median of the result fitness values, and ‘‘maximum’’ and ‘‘minimum’’ are the maximum and minimum fitness values for each algorithm, respectively. Table 6 illustrates that the presented algorithm has the best results than the other compared algorithms for the analyzed benchmarks. In order to judge whether the results of a proposed method are significant, a nonparametric statistical test called Wilcoxon’s rank-sum test has been carried out. Wilcoxon signed ranks test investigate if there are two samples from two unlike populations. In the Wilcoxon test, the dominance of the two algorithms is determined based on the hypothesis test that is described by the null hypothesis (H0) and the alternative hypothesis (H1). If there is an alteration between two algorithms, the hypothesis is alternative and if there is no alteration between two algorithms, the hypothesis is null. More explanation can be found in Wang et al. (2014c). In this study, the Wilcoxon signed-rank test is adopted for statistical validation of the superiority of the MEHO algorithm toward the analyzed algorithms. Table 7 indicates the p-values obtained by Wilcoxon signed-rank test. CKH vs GSA (Rashedi et al.,2009) EPO Dhiman and Kumar (2018) WCO (Razmjooy et al.,2016) KH (Gandomi and Alavi, 2012) 5.12e−4 8.27e−4 4.87e−4 0.0115 As can be seen, the P-values are very small that illustrate the important outperformance of CKH over all other compared algorithms except the KH algorithm. However, in this dimension, CKH outperforms KH, its p-value is not small enough. 4.6. System solution based on CKH algorithm In this research, the proposed CKH algorithm is employed for determining the optimal sizes for the PEM fuel cell and the battery to provide the minimum total cost of the hybrid energy system. Here, the sizes information for both battery and PEM fuel cell have been encoded by the Krill in CKH algorithm. The CKH algorithm is then embedded by the proposed EMS (Section 3) as the support subroutine. Fig. 6 shows the general diagram of the proposed methodology. 5. Simulation results This section analyzes the results of the introduced hybrid energy system (HES) system. As aforementioned, the primary objective of this study is to achieve the minimum value for the total cost of the HES by determining the sizes of the battery and the PEM fuel cell based on an optimal solution. A definite drive 892 Y. Guo, X. Dai, K. Jermsittiparsert et al. / Energy Reports 6 (2020) 885–894 Table 6 Comparative results of the algorithms. GSA (Rashedi et al.,2009) EPO (Dhiman and Kumar, 2018) WCO (Razmjooy et al.,2016) KH (Gandomi and Alavi, 2012) CKH f1Maximum Minimum Median std 5.27E+07 4.73E+06 7.96E+06 2.26E+07 7.98E+07 6.14E+06 1.97E+07 2.53E+07 3.24E+06 3.27E+05 1.28E+06 6.13E+05 1.05E+06 1.16E+05 5.32E+05 3.47E+05 2.83E+05 2.45E+04 1.58E+05 1.01E+05 f2Maximum Minimum Median std 2.71E+04 2.98E+03 7.84E+03 3.15E+03 7.86E+06 1.45E+06 4.06E+06 1.73E+06 3.69E+04 5.78E+03 1.76E+04 9.20E+03 2.39E+03 2.64E+02 4.52E+02 2.41E+02 1.35E+03 1.95E+02 3.16E+02 2.01E+02 f3Maximum Minimum Median std 7.62E+04 1.98E+04 5.23E+04 9.14E+03 4.96E+04 6.37E+02 8.24E+03 1.69E+04 1.67E+04 3.62E+03 7.82E+03 3.48E+03 1.93E+03 4.81E+02 2.11E+02 3.48E+02 1.23E+03 3.36E+02 4.27E+02 2.30E+02 f4Maximum Minimum Median std 7.91E+02 6.17E+02 7.42E+02 4.81E+01 5.87E+02 3.80E+02 6.19E+02 4.01E+01 5.16E+02 3.52E+02 4.97E+02 3.14 E+01 2.20E+02 3.86E+02 4.53E+02 3.54E+01 5.16E+02 2.85E+02 4.01E+02 3.48E+01 f5Maximum Minimum Median std 5.20E+02 5.20E+02 5.20E+02 4.78E−03 5.20E+02 5.20E+02 5.20E+02 3.85E−04 5.20E+02 5.20E+02 5.20E+02 4.19E−03 5.14E+02 5.20E+02 5.20E+02 4.8E−04 20E+02 5.20E+02 5.20E+02 6.98E−05 Fig. 6. The flowchart diagram of the proposed solution strategy. Table 7 The selected parameters for the CKH algorithm. Parameter Value No. of Krill herd population 50 No. of iteration 500 explore to find food 0.05 motivated motion 0.005 cycle has been utilized here (Section 4.2) such that the average power demand (Pavg dem) of it corresponding to 0%, 1%, and 2% slope of the railway track (β) are considered 3.1 MW, 3.7 MW, and 3.9 MW, respectively. At the beginning of the drive cycle, the initial value for SOC, (SOCinitial) is assumed to be 0.7. Table 7 illustrates the selected parameters for the CKH algorithm after multiple trials and errors. Table 8 shows the optimum sizes of the PEM fuel cell and the battery for the considered drive cycle based on the proposed CKH algorithm and its comparison with the PSO algorithm and the typical KH algorithm. Here, three different values for the slope have been considered. Table 8 illustrates that by increasing the percentage of slope, the required power demand for both battery and fuel cell has been increased. Furthermore, it is clear that using the presented CKH algorithm gives a larger size for the PEM fuel cell in energy management. Totally, the difference among the three algorithms (EMS ) is that the required battery size for the system in PSO is larger than the KH algorithm and in the KH algorithm is larger than the CKH and due to the high cost of battery technology, the proposed CKH algorithm is better selection for this purpose, i.e. whatever the size of the fuel cell has been increased, we need a battery with smaller size. In the following, the dynamic behavior of the HES has been analyzed. Fig. 7 show the diagram of the output power of the battery and the fuel cell variations and SOC variation with time. The figure declares that the battery should be discharged when the locomotive power demand exceeds the output power of the PEM fuel cell. This happens when the locomotive has a speed higher than the average speed of the drive cycles that reduce the battery SOC at this time. In contrast, the battery has been charged when the locomotive has a lower speed than the average speed which increases the battery SOC.