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2010, 12th International Conference on Optimization of Electrical and Electronic Equipment, OPTIM 2010 Particle Swarm Optimization for Optimal Powertrain Component Sizing and Design of Fuel Cell Hybrid Electric Vehicle Omar Hegazy, Student Member, IEEE, and Joeri Van Mierlo Department of Electrical Engineering and Energy Technology (ETEC), Vrije Universiteit Brussel Omar.Hegazy@vub.ac.be RP ESR Emax Nscs Nscp Vscmax Vscmin SOCsc SOCsc0 VSC-Bus C2 Abstract -- In this paper, an optimal design to minimize the cost, mass and volume of the fuel cell (FC) and supercapacitor (SC) in a fuel cell hybrid electric vehicle is presented. Because of the hybrid powertrain, component sizing significantly affects vehicle performance, cost and fuel economy. Hence, during sizing, various design and control constraints should also be satisfied simultaneously. In this research, there are two optimization techniques have tested to achieve optimal design of the powertrain. These are Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The proposed schemes have been simulated by MATLAB/ SIMULINK. Simulation results have demonstrated that the optimal sizing of the powertrain components has been improved when the PSO is applied, which means highperformance operation for FCHEV. Optimization and Control strategy PSO Particle swarm optimization GA Genetic Algorithm PFC Power of fuel cell PReq The required electric power demand KFC Ratio of PFC to PReq PSC Power of SuperCapacitor LUT Look-Up Table PFC-Effmax Power of fuel cell at maximum efficiency PFCmax Maximum Power of fuel cell PFCmin Minimum Power of fuel cell SOCmin Minimum SOC of SC SOCmax Maximum SOC of SC Index Terms—Fuel cell Hybrid Electric Vehicle (FCHEV), Powertrain Modeling, Intelligent Optimization, Power Management System NOMENCLATURE Fuel Cell System (FCS) B, C Constants to simulate the activation over voltage in the PEMFC system Vfc-Bus Dc output voltage of FC system E Nernst instantaneous voltage ηact Activation over voltage ηohmi Ohmic over voltage E0 Standard no load voltage F Faraday’s constant IFC FC system current q Amount of hydrogen flow to meet load change Nfcs Number of series fuel cells in stack Nfcp Number of parallel stacks Rgas Universal gas constant Rint FC internal resistance T Absolute temperature (K) U Utilization rate C1 Cost per cell I. INTRODUCTION F UEL CELL (FC) technologies are expected to become a viable solution for vehicular applications because they use alternative fuel converters and are environment friendly. Although there are various FC technologies available for use in vehicular systems, the proton exchange membrane FC (PEMFC) has been found to be a prime candidate, since PEMFC has higher power density and lower operating temperatures when compared to the other types of FC systems [1], [2]. A stand-alone FC system integrated into an automotive powertrain is not always sufficient to satisfy the load demands of a vehicle. Although FC systems exhibit good power capability during steady-state operation, the response of fuel cells during transient and instantaneous peak power demands is relatively poor. Thus, the FC system can be hybridized with an ultracapacitor (UC) bank to meet the total power demand of a hybrid electric vehicle (HEV). In recent req H2 SuperCapacitor (SC) C Capacitance [F] Ceq Equivalent capacitance [F] 978-1-4244-7020-4/10/$26.00 '2010 IEEE Parallel resistance [Ω] Equivalent series internal resistance [Ω] Maximum amount of energy [W.s] Number of series capacitors Number of parallel strings Maximum voltage of SC Minimum voltage of SC State of charge of SC Initial State of charge of SC Dc output voltage of SC Cost per cell 1 601 years, many research works in the power distribution strategy of hybrid vehicles and sizing have been done. Some control algorithms for global optimization, based on a priori knowledge of a scheduled driving cycle, have been proposed to achieve fairly fuel economy with minimum cost [3, 4, 5]. In [6], the optimal design and sizing of fuel cell and supercapacitor in FCHEV were obtained by using trial and error method. In [7], a control method was proposed for energy control of supercapacitor/fuel cell hybrid power source. II. SYSTEM DESCRIPTION The hybrid power train consists of two power sources: the FC system (main source) and the SC bank (Energy Storage System). These components are connected to the dc-link via the Buck DC/DC converter (ηB=0.95) and Buck/Boost converter (ηB/B=0.95), respectively. The desired value of the DC-Bus voltage is chosen to be 400 V with variations of ± 10% are permissible. The power supplied by the power train has to be obtaining from the power demand predicted by the dynamics of the vehicle. The efficiency of each component in the hybrid power train is taken into account. A detailed model of the power train is built in MATLAB /SIMULINK. Figure 1 illustrates block diagrams of the hybrid power train. In this paper, for a given driving cycle, the size and the cost of fuel cell and supercapacitor are minimized by identifying the best number of units of each, respectively. Hence, a novel approach, PSO, is applied to evaluate the optimal number of units of fuel cell and supercapacitor. By analyzing and comparing the results, it is shown that PSO is more efficient than GA to minimize the objective function. (a) (b) Fig.1 Block Diagram of Fuel Cell/SuperCapacitor Hybrid Electric Vehicle (a) One DC/DC Converter (b) Two DC/DC Converters 2 602 A. Modeling of the vehicle power demand The load force of the vehicle consists of gravitational force, rolling resistance, aerodynamic drag force, and acceleration force. Hereby, the load power required for vehicle acceleration can be written as [2, 3]: (F + F +F +F ) *V g roll AD acc P = (1) load η GB Where: F g F F = M . g . sin( α ) roll AD (2) = M . g . f . cos( α ) r = 0 .5 ρ a dV F = M . acc dt V = ω . r w w .C D .A F .V (a) (3) 2 (4) (5) (6) The total electric power required from sources can be expressed as: P = req η P load .η .η m Inv Conv (7) Fig.2 Vehicle speed and Total Electric Power demand (a) NEDC Driving Cycle. (b) FTP75 Driving Cycle. The assumed parameters of the vehicle are given in Table I. In this paper, the analysis of FCHEV is performed with two standard driving cycles: B. Dynamic Modeling of a PEMFC 1) the Federal Test Procedure (FTP75) Urban; 2) the New European Driving Cycle (NEDC) The model of the PEMFC system predicts the output voltage and the partial pressures of hydrogen and oxygen in the FC stack for a certain electric current. The voltage signal is fed to a control voltage source in the simulation environment. The FC system consists of a FC stack with Nfcs cells in a series and Nfcp in parallel configuration. The output voltage of the stack can be calculated as follows [2, 8,9]: V FC − BUS = E + η act + η ohmic (8) These driving cycles are represented by vehicle speeds versus operating time. Figure 2 shows the vehicle speed and the total electric power demand from sources. Suppose that the efficiencies of the motor (ηm), inverter (ηInv), and DC/DC converter (ηConv= ηB= η B/B) are 0.90, 0.94 and 0.95, respectively. TABLE I ASSUMED PARAMETERS FOR THE VEHICLE [6] M Vehicle mass (kg) 1450 fr Rolling Resistance Coefficient 0.013 CD Aerodynamic Drag Coefficient (CD) 0.29 Af Front Area (m2) 2.13 rω Radius of the wheel (m) 0.28 ρa Air density (kg/m3) 1.202 η act = − B ln (C . I FC ) (9) η ohmic = − R int I FC (10) The Nerst’s instantaneous voltage may be expressed as [10] pH 2 po 2 RT E = N fcs E 0 + log (11) 2F PH 2 O The amount of hydrogen available from the hydrogen tank is given by q Hreq = 2 N fcs .N fcp 2 FU . I FC (12) The MATLAB/SIMULINK-based FC system is modeled in this paper using the aforementioned equations. Table II shows the specifications of PEM fuel cell system. 3 603 TABLE II PEM FUEL CELL SYSTEM MODEL PARAMETERS [4, 6] Activation Voltage constant (B) 0.04777(A-1) Activation Voltage constant (C) 0.0136 [V] Faraday’s constant (F) 96484600[C/kmol] FC internal resistance (Rint) 0.177 (Ώ) No load voltage (E0) 1V Nominal voltage (V) 0.81 Nominal power per cell (w) 3.4 FC absolute temperature (T) 343 [K] Fig.3 SuperCapacitor equivalent circuit [2] Utilization factor (U) 0.85 Universal gas constant (R) TABLE III SUPERCAPACITOR SPECIFICATIONS [6, 8] 8314.47 [J/ kmol K] Weight (M1) (g) 16.28 Capacitance (F) 2500 Volume (V1) (L) 0.0142 Internal Resistance (Rs) 65mΏ Cost (C1) ($) The parallel Resistance (for Leakage Current) (Rp) 1.23 C. Modeling of a Supercapacitor The natural structure of SC is appropriate to meet the transient and instantaneous peak power demands. The simulated super-capacitor is a Maxwell PC2500 whose characteristics are reported in Table III [6]. The reason for considering a supercapacitor in the vehicle setup is its high specific power rate and its ability to accept a full recharge in a very short time, which leads to an improvement in the vehicle efficiency and energy economy. Figure 3 illustrates a simple electrical equivalent circuit of a supercapacitor unit [2-3]. The output voltage of the supercapacitor can be expressed as follows: Vsc _ cell = icell Rs +ν c νc = − 1 C i c = i cell SOCsc ∫ = ( ν c R p V V cup ( t = 0 ) = ( cell C Rated current (A) 625 Cost (C2) ($) Initial State Of Charge (SOCSC0) 725 0.6 20 80% III. OPTIMIZATION PROBLEM FORMULATION This section describes the formulation of optimization problem and their constraints. A. The Objective Function (14) ) 2 * 100 The first goal of optimization problem is to minimize the cost of the fuel cell (FC) and supercapacitor (SC) in the fuel cell hybrid vehicle. It is assumed that, the cost of the fuel cell and supercapacitor is a function of the number of units of each, respectively [6]. The layout of the fuel-cell stack and that of the supercapacitor bank are shown in Fig. 4(a) and (b), respectively. As shown in Fig.4, fuel-cell and supercapacitor units are connected in series to form branches. The objective function chosen for the study, F(x), is given as follows [6]: (16) _ max SOCsc 0 )V max 100 2.5 Volume (V2) (L) (15) ν Max_ Cell Voltage [Vmaxcell](V) Weight (M2) (g) (13) ic (t ) dt + V cup ( t = 0 ) + 1kΏ -3kΏ cell (17) The MATLAB/SIMULINK-based SC is modeled using the aforementioned equations. F ( x ) = C 1 . Nfcs . Nfcp + C 2 . Nscs . Nscp 4 604 (18) P FC min ≤ Pfc ( t ) ≤ P FC max (21) 4. Constraints of State Of Charge The level of SOCmin and SOCmax are chosen to 25% and 90%, respectively. SOC min ≤ SOCsc ( t ) ≤ SOC max (22) IV. INTELLIGENT OPTIMIZATION [IO] A. Genetic Algorithm (GA) (a) (b) Fig.4. (a) Layout of the FC; (b) Layout of the SC Genetic algorithms (GA) are stochastic global search techniques, which mimic the process of natural biological evaluation (Survival of fitness). They have been shown to be an effective strategy to solve complex engineering optimization problems characterized by non-linear, multimodal, non-convex objective functions. The structure of a GA is composed by an iterative procedure through the following five main steps [10, 11]: 1. Creating an initial population P0, 2. Evaluation of the performance of each individual Pi of the population, by means of a fitness function, 3. Selection of individuals and reproduction of a new population, 4. Application of genetic operators: crossover and mutation, 5. Iteration of steps 2–4 until a termination criterion is fulfilled B. Constraints 1. Constraints of Nfcs and Nscs It is considered that the desired value of the DC-link voltage (VSC-Bus, and VFC-Bus) is chosen to be 270 V with variations of ± 10% are permissible. These constraints are presented in Table IV. 2. Constraints of Nscp The supercapacitor is supposed to cover the power fluctuation above the average power. The magnitude of energy above Pav is calculated by: t2 E = ∫ ( Pinst − Pav ) dt t1 (19) The GA search was performed in MATLAB environment. To apply GA to the optimization of FCHEV, a fitness function is required in order to evaluate the status of each solution. This function can be formulated as follows: Hence, the size of supercapacitor is calculated according to the maximum value of the energy is found among various intervals (t1, t2). Therefore, the equivalent of capacitance of the SC is written as follows: Ceq = C * Nscp 2 . E max ≥ Nscs (Vsc max 2 − Vsc min 2 ) Minimize F(x) (Nscp, Nfcp) (20) B. Particle Swarm Optimization [PSO] Particle Swarm Optimization (PSO) is an evolutionary computation technique (a search method based on a nature system). PSO is a population based stochastic optimization technique developed by Kennedy and Eberhart. PSO method is a member of the wide category of Swarm Intelligence methods (SI). It can be used to solve a wide range of optimization problems. Most of the problems that can be solved using Genetic Algorithms could be solved by PSO. For example, neural network training and nonlinear optimization problems with continuous variables can be easily achieved by PSO. It can be easily expanded to treat problems with discrete variables [12]. PSO shares many similarities with evolutionary computation techniques such as Genetic Algorithms (GA). The system is initialized with a population of random solutions and searches for optima by 3. Constraints of power and Acceleration The initial-acceleration performance for the vehicle is defined as accelerating the vehicle from standstill to 60 mi/h in 10 s. The level of PFCmin and PFCmax are chosen to 1kW and 50 kW, respectively. This range is satisfied to power demand during acceleration and gradeability at maximum speed. The power balance of the system is shown in (19). TABLE IV CONSTRANITS OF Nfcs & Nscs Reference DC-Link Voltage Variation [V] Nmin Nmax = Nselected FC 243 < Vdc < 297 243 297 SC 243 < Vdc < 297 97 119 5 605 updating generations. However, unlike GA, PSO has no evolution operators such as crossover and mutation [13]. PSO can be represented by the concept of velocity and position. The Velocity of each agent can be modified by the following equations: (23 & 25): v k +1 k X2 Agent X3 k = w v i + c 1 r1 * ( pbest 1 − s i ) + (23) k X1 c 2 r2 * ( gbest − s i ) Where: νk ν i k+1 Xn : Current velocity of agent i at iteration. : Modified velocity of agent i r1 , r2 : random number distributed [0,1], Ski : current position of agent i. pbest : p best of agent gbest : g best of the group. ω : weight function for velocity of agent i, Fig.6. Searching concept with agents in a solution space by PSO In this research, PSO is applied to evaluate the optimal number of units of each source that minimize the cost of the fuel cell (FC) and supercapacitor (SC). In addition, PSO is applied to determine the best degree of hybridization between sources to minimize the energy consumption in (24). The problems can be formulated as follows: c1, c2 : positive constants; [c1+ c2< 4]. The following weighting function is usually utilized in (23). ω = ω max − ω max − ω min iter max * iter (24) Minimize F(x) (Nscp, Nfcp) Where: ωmax : Initial weight, ϖ min : Final weight, V. CONTROL STRATEGY BASED ON EFFICIENCY MAP itermax : Maximum iteration number, iter : Current iteration number. Using the above equation, a certain velocity can be calculated that gradually gets close to (pbests) and (gbest). The current position (searching point in the solution space) can be modified by the following equation: ski+1 This control strategy is applied to improve the hydrogen consumption. A simulation is performed for each driving cycle in such a way that the FCS works alternately in two operating points, namely “On” and “Off”, according to the actual SOSsc (k): (i) when SOSsc (k) < SOSsc0, the FCS is operated at its point of maximum efficiency (the “On” point) and, (ii) when SOSsc (k) > SOSsc0, the FCS is turned off (the “Off” point). Figure 7 illustrates the efficiency map of FC. Figure 8 shows a scheme with the FC operation to perform the analysis previously described. = ski + vki+1 (25) Figure 4 shows the concept of modifying the searching point by PSO. Figure 6 shows the searching concept with agents in the solution space. Each agent changes its current position using the integration of vector vk+1as shown in fig. 5. Y Sk+1 VK+1 Vgbest VK SK VPbest X Fig.7 The efficiency map of Fuel Cell Fig.5. Concept of modification of a searching point by PSO 6 606 TABLE V I GA ALGORITHM PARAMETERS Parameters Value Population size 40 Number of Generations 200 Crossover Probability 0.85 Mutation Probability 0.1 Figure 9 provides an example of the optimization algorithm output. PSO is applied to minimize the total cost of Fuel cell and supercapacitor during the FTP75 driving cycle. Figure 10 illustrates the comparison between design methods. Fig. 8 Scheme of Control Strategy Based on Efficiency Map VI. SIMULATION STUDY To verify that the optimal design based on intelligent optimization of the FCHEV can provide the required vehicle performance and the power of the powertrain corresponding to a standard driving cycles such as FTP75 and NEDC are simulated and presented. Simulation results are obtained using MATLAB/SIMULINK and SimPowerSystems by implementing the detailed mathematical and electrical models of the system described earlier in section II. In this section, there are three methods have been designed to achieve the optimal sizing. These are conventional method, trial and error, as was mentioned in [6], GA, and PSO. In addition, to minimize the fuel consumption of the FCHEV, the control strategy based on max-efficiency map described earlier in section V. The parameters used of PSO are shown in Table V. The parameters used of GA are shown in Table VI. Fig.9 Best value of total cost for FTP75 TABLE V PSO ALGORITHM PARAMETERS Parameters Population size Max. iter c1 c2 Max. weight Min. weight r1 r2 Lbnd [ Nscp Nfcp] Upbnd [ Nscp Nfcp] Lbnd [Kfc] Upbnd [kfc] Value 20 100 0.5 0.5 1.2 0.1 [ 0,1] [ 0,1] [1 2] [10 60] 0 1 (a) (b) 7 607 Fig.12 Power of fuel cell during the FTP75 driving cycle (c) Fig.13 DC-Bus voltage variation during the FTP75 In Fig.14, it is shown the comparative of the hydrogen consumption between the control strategy and pure fuel cell during the FTP75 and NEDC driving cycles. The results show the control strategy based on efficiency map achieving hydrogen improvement up to 9.22% during the NEDC driving cycle and 13.29% during the FTP75 with respect to the pure fuel. (d) Fig.10 Results of optimal design for FCHEV (a) Optimal numbers of cells of FC and SC (b) Driving cycles Comparison based optimal total cost (c) Driving cycles Comparison based optimal total mass (d) Driving cycles Comparison based optimal total volume The power of the fuel cell and the supercapacitor during the FTP75 driving cycle are shown in Fig.11 and Fig.12. Figure 13 demonstrates the DC-Bus voltage variation during the FTP75 driving cycle. Fig. 14 Comparative of between the hydrogen consumption between Pure FC and control strategy based on efficiency map Fig.11 Power of fuel cell during the FTP75 driving cycle 8 608 VII.CONCLUSION This paper deals with the applicability of the intelligent optimization to optimize both the vehicle design in order to minimize the total cost, volume and the mass of the fuel cell and supercapacitor components, and to minimize the fuel consumption of fuel cell during different driving cycles based on control strategy. As is clear from results, it is possible to significantly improve the hydrogen consumption in FCHV compared with the pure FC case without SC: 9.22% on NEDC and 13.29% on FTP75. In addition, the reduction of total cost of the fuel cell and supercapacitor components is around 13.40% on NEDC and 12.21% on FTP75. By analyzing and comparing the results, it is shown that PSO is more efficient than GA to achieve the optimal performance for FCHEV. [4] Diego Feroldi, Maria Serra, and Jordi Riera “Design and Analysis of Fuel-Cell Hybrid Systems Oriented to Automotive Applications”, IEEE Transactions On Vehicular Technology, Vol. 58, No. 9, November 2009 [5] Oliver Bohlen, Rik W. 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