Real-time optimization strategies of Fuel Cell Hybrid Power Systems based on Load-following control: A new strategy, and a comparative study of topologies and fuel economy obtained

Applied Energy 241 (2019) 444–460

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Real-time optimization strategies of Fuel Cell Hybrid Power Systems based on Load-following control: A new strategy, and a comparative study of topologies and fuel economy obtained

T

Nicu Bizon

⁎

University of Pitesti, Faculty of Electronics, Communications and Computers Science, 1 Targu din Vale, Arges, 110040 Pitesti, Romania University Politehnica of Bucharest, Doctoral School, Bucharest, Romania

HIGHLIGHTS

assessment of currently real-time optimization strategies. • Critical of seven Fuel Cell Hybrid Power Systems. • Evaluation of the fuel consumption under unknown load demand. • Optimization of the optimization function improves the fuel economy. • Choosing • Switching for control and optimization loops is proposed. ARTICLE INFO

ABSTRACT

Keywords: Proton exchange membrane fuel cell Hydrogen savings Variable load Optimization strategy Load-following Battery charge-sustaining mode

An evaluation of currently optimization energy management strategies is done in this study. The load-following – based strategy for Proton Exchange Membrane Fuel Cell (FC) Hybrid Power Systems ensure the DC power flow balance using the FC system as main energy source. Thus, the battery will operate in charge-sustaining mode. So, the battery state-of-charge will vary in imposed window without need of monitoring the battery. Furthermore, the size and maintenance of the battery stack will decrease compared with rule-based strategies. So for the first time, the classification and evaluation of seven FC Hybrid Power Systems and their possible energy management strategies (including a new one) are performed using the performance indicators related to fuel economy and FC electrical efficiency of the FC system. Consequently, the optimization of the FC Hybrid Power Systems under variable load will mix these performance indicators through the weighting coefficients knet and kfuel into a new optimization function. A new switching strategy for the load-following control and real-time optimization loops is proposed to further increase the fuel economy based on the results obtained in this study. The objective of this study is to highlight how optimization function and switching strategy through choosing the weighting coefficients and the control references could improve the fuel economy. Thus, the design of the switching strategy based on available information about the current load demand and the distance to fuel stations is presented in this paper as well. This switching strategy will push hydrogen to become an energy carrier feasible for FC vehicles.

1. Introduction The challenge objective for the Fuel Cell Hybrid Power Systems (FCHPS) [1–4] and other hybrid energy systems [5–7] is to efficiently operate these systems. The energy harvesting is approached in [1] for FC systems and photovoltaic (PV) system based on FC modeling and control algorithms proposed in [2,3] and [5,6]. The advantages of optimal control are highlighted in [7] and applied in [4] for a battery/ ⁎

ultracapacitors FC/PV HPS. Thus, hundreds of rule-based and optimization-based strategies have been proposed in the last decade [8,9]. The strategies based on deterministic rules are simple to be implemented, but cannot find the optimum solution [10]. So, the research interest was focused to strategies based on optimization functions, even if the complexity of implementation in Real-Time Optimization (RTO) applications is increased [1,11]. It is worth to mention that

Address: University of Pitesti, Faculty of Electronics, Communications and Computers Science, 1 Targu din Vale, Arges, 110040 Pitesti, Romania. E-mail address: [email protected].

https://doi.org/10.1016/j.apenergy.2019.03.026 Received 24 August 2018; Received in revised form 11 February 2019; Accepted 5 March 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature AirFr aPESC AV BPF DP fd ECMS EMS EMU ES ESS FES FuelFr FC LPM LHV PFC PFcnet Pcm ηsys FCHPS FuelT Fueleff FFT GMPP

GES HILS HPF HPS kNp kNy LC LFW MEP MPC PMP MPP MRAC MV PEMFC PLoad pLoad PI PID PV RTO RES PESCs sFF SMES SOC WT

Air Flow rate Asymptotic Perturbed Extremum Seeking Control Average value Band-Pass Filter Dynamic Programming dither frequency Equivalent Consumption Minimization Strategy Energy Management Strategy Energy Management Unit Extremum Seeking Energy Storage System Flywheel energy storage Fuel Flow rate Fuel cell Liter per Minute Lower Heating Value FC stack power FC net power Air compressor power FC electrical efficiency Fuel Cell Hybrid Power Systems Total Fuel Consumption Fuel Consumption Efficiency Fast Fourier Transform Global Maximum Power Point

optimization-based strategies can track in real-time the optimal or suboptimal solution [7,12]. The used RTO algorithms can be as follows: Extremum Seeking (ES) algorithms [13,14], Equivalent Consumption Minimization Strategy (ECMS) [15,16], algorithms based on intelligent concepts [17–19], Model Predictive Control (MPC) methods [20,21], the sliding control [22,23], optimal adaptation of the ECMS [24], and the multi-scheme energy management strategy [25]. Note that the ECMSs based on Dynamic Programming (DP) [26,27] or are still the most used [10]. Due to their performance, different ES-based RTO strategies using classical [28,29], modified [30,31], and advanced [13,14,32,33] ES algorithms have been proposed. The modified ES algorithm proposed in [30] to improve the tracking robustness is different from the conventional ES algorithm due to use of a Band-Pass Filter (BPF) to process at least the first three power harmonics into the seeking signal. Thus, the tracking robustness can be improved and this approach was applied to FCHPS in [31]. The advanced ES algorithm proposed in [32] to improve the tracking accuracy is different from the modified ES algorithm due to amplitude modulation of the dither with first harmonic of the FC power. Thus, the FC power ripple will decrease once the Maximum Efficiency Point (MEP) is found, but this happens with faster tracking speed and same guaranteed robustness like as in classical ES algorithm. An analysis of performance of the ES-based RTO strategies is performed in [33,34]. The PV system efficiency is improved if the global Maximum Power Point (MPP) is tracked using the global ES (GES) algorithms proposed in [35–37]. The GES algorithm based on two BPFs [35] instead of one BPF [36] has more flexibility in design to improve the dither persistence by choosing the cut-off frequencies of the BPFs. The specific design for GES methods to find local or global MPP is shown in [37]. If the load demand in PV systems is sustained by PV panels and battery stack, the variations in load demand in FCHPS could be compensated on DC bus by controlling the power generated by the FC system via the FC boost converter and its Load-Following (LFW) control [38]. In this case, due to LFW control of the FC boost converter, the battery will operate in charge sustaining mode (with battery State-Of-

Global Extremum Seeking Hardware-in-Loop System High-Pass Filter Hybrid Power System Output normalization gain Input normalization gain Load Cycle Load-Following Maximum Efficiency Point Model Predictive Control Pontryagin's Minimum Principle Maximum Power Point Model Reference Adaptive Control Mean Value Proton Exchange Membrane Fuel Constant load power Variable load power Proportional-Integral Proportional-Integral-Derivative Photovoltaic Real-Time Optimization Renewable Energies Source Scalar Perturbed Extremum Seeking Control Static Feed-Forward Superconducting Magnetic Energy Storage State-Of-Charge Wind Turbines

Charge (SOC) varying in the imposed window) and the battery size can be minimized. Thus, the cost of the batteries stack and its maintenance costs decreases. In addition, an increased lifetime for the batteries is obtained. Furthermore, this LFW control is simpler to be implemented for the air flow rate (AirFr) of the FC system instead of implementing an ES-based RTO routine to rescale it [39]. But it is true that recently some RTO-strategies have been proposed for FCHPS to improve the free air breathing of the Proton Exchange Membrane FC (PEMFC) system using the MEP [40] or MPP [41] tracking-based methods, or other control methods [42,43]. The improved MPP tracking method as tracking accuracy is proposed for a photovoltaic/FCHPS, where the operation of both PV and FC systems are simultaneously optimized [44]. The renewable HPS usually needs a FC system, an electrolyzer, and a fuel storage tank to compensate the DC power flow balance due to variable profile of the renewable power [45,46]. Besides the ES-based optimization algorithm [38], other algorithms are proposed to optimize the FC system as follows: algorithms based on intelligent concepts [47] such as neural networks [48], genetic algorithms [49], or data fusion method [50]; algorithms based on combinatorial techniques [51], Model Reference Adaptive Control (MRAC) [52], metaheuristic approaches [53], load prediction [54], and ECMSs [15]. Firstly, the Static Feed-Forward (sFF) control of the FC system has been implemented in practice [55], but then different other control methods for the air compressor system have been developed and most of them were tested using Hardware-in-Loop System (HILS) techniques [52,55–65]. HILS using the sub-optimal second order sliding mode controller for a commercial twin screw air compressor is proposed in [56]. HILS based on a load governor method prevents the oxygen starvation using constrained extremum technique [57]. HILS using a second order sliding mode controller can optimally control the AirFr of the PEMFC system [58]. The load variations effect on PEMFC operation was better mitigated using a disturbance rejection [59] or a differential flatness control [60] instead of Proportional-Integral (PI) control [55]. Also, the lifetime of the PEMFC system can be increased by control system of the cathode developed in [61]. The oxygen stoichiometry in 445

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PEMFC systems is better maintained in preset range using a LQR/LQG control [62]. Optimal control of the AirFr based on fuzzy ProportionalIntegral-Derivative (PID) control [63], ES algorithm scheme [32], optimal fuzzy PID control [64], time delay methods [65], and adaptive strategies [52] are other techniques proposed in the literature as potential control solutions for the air system. Besides control solutions for air system, many control solutions for fuel system such as global optimization using fuzzy logic [66] and genetic algorithms [49] were proposed to improve the fuel economy [43], but most of them are not RTO strategies due to restriction for a prior knowledge of the route. Other adaptive strategies based on fuzzy control [67] and EMS [68] improve the fuel economy, but these algorithms are not suitable for RTO algorithms due to the high signal processing level, even for the new DSP processors. Thus, the research to design advanced RTO strategies for FCHPS remains challenging. In this paper, six FCHPS topologies and one new are compared as performance. These topologies use the LFW control to attenuate the variability of the load and renewable power on battery SOC, and one or two optimization loops. The sFF strategy is used as reference to highlight the gaps in the performance indicators such as: (1) FC net power, (2) fuel consumption efficiency, (3) FC electrical efficiency, and (4) total fuel consumption. The proposed optimization function will improve the fuel economy of the FCHPS under variable profile of the Load Cycle (LC) by changing the values for the weighting coefficient kfuel. The optimum will be tracked in real-time by using the GES method proposed in [35]. The objective is to probe how optimization function through choosing the weighting coefficients knet and kfuel could be a crucial help when planning the fuel consumption of a FC vehicle driving on an unknown route. The research methodology used is as follows. Firstly, the RTO strategies for the FCHPS are classified in three classes after the place where the LFW control is applied: to controller of the FC boost converter, to AirFr regulator, or to Fuel Flow rate (FuelFr) regulator. Secondly, a comparative research is performed for all seven FCHPS topologies using same constant level for the load demand. Thus, the best topology in each class was identified. Thirdly, the selected strategies are further analyzed for different kfuel and variable load to validate the conclusions related to performance of selected strategies operating the FCHPS under constant load. So, based on the results obtained using the above research methodology, the novelty of this study can be highlighted as follows: (1) considering all three possible ways to control the FC power via the FuelFr regulator, the AirFr regulator, and the controller of the FC boost converter, seven RTO strategy have been identified for a FCHPS and then classified in three classes; (2) one of them is a new strategy proposed to be analyzed in this paper; (3) the best strategy in each class has been selected after a analysis performed using different performance indicators for the FCHPS under constant and variable load; (4) the selected strategies (including the new one proposed) have been further analyzed to see how the kfuel parameter improves the fuel economy in order to gives some guiding conclusions related to choosing the optimal switching strategy of the best RTO strategies depending on the load level; (5) finally, some rules to choose the appropriate optimization function considering the load profile and actual distance to fuel stations are given. Thus, the structure of the paper is as follows. Optimization objectives and algorithms are briefly presented in Section 2, with focus on optimization of FCHPSs and extremum seeking algorithm. The RTO strategy with load-following control and optimization loops is designed in Section 3 based on modeling of the FC system using the power flow balance on DC bus under assumption of charge-sustained mode for the battery. The results for all seven RTO strategies presented in Section 4 highlight the set of selected RTO strategies, which are the best in each class. The selected RTO strategies are further analyzed on constant and variable load to find the design rules for the

RTO switching strategy. Section 5 concludes the paper. 2. Optimization strategies and algorithms The RTO strategies proposed in this study will be designed using the optimization theory, which are usually used optimization applications. 2.1. Optimization algorithms The FCHPS operation will be optimized in real-time by trying to find a set of values to inputs variables of the optimization function that produce an extreme value of it, called the optimal value (or optimum) of the optimization function. This optimum was found for an input vector in the searching range and must be a global extreme in the searching range. So, the optimization algorithm used to find the optimum must to be an algorithm with global search feature and 100% hit count [5,6,69]. The challenging goal of any global optimization algorithm is to find the optimal or near-optimal solutions. So, the global optimization algorithm used to track the optimum must to be an algorithm with high tracking accuracy [35,36]. Furthermore, the dynamic of the FCHPS and perturbation into the system request a realtime and robust tracking of the next optimum [70]. The input variable must to quickly track the new optimum in the searching range. So, the global optimization algorithm used to track the optimum must to be an algorithm with high tracking speed. This feature will increase the tracking efficiency [71]. The ripple during stationary phase must be minimum [35,36,72] to increase the tracking efficiency as well. Also, it is known that the optimization function PFCnet = f(AirFf, FuelFr) has many peaks on the surface close to MEP [1]. Some of local peaks could be very close to MEP, so the used algorithm must have high searching accuracy to discern the MEP from them. From tens of algorithms that can comply these performance features, the ES algorithm proposed in [37] was used in this study due to its features reported. Note that the software-based tracking methods operate in two stages with a tracking time higher than 10 dither’s periods needed by GES algorithm [37] to track the optimum. So, the GES tracking time is less than 0.01 s for a 1000 Hz sinusoidal dither. Also, the tracking accuracy (Tacc) and searching resolution (SR) is higher than 99.9% and less than 1%, considering the following definitions [37]:

SR =

Tacc =

min |yGMPP i

yLMPPi |

yGMPP yGMPP yGMPP

·100[%]

·100[%]

(1) (2)

where yGMPP , and yLMPP < yGMPP are the global and local extreme, and y GMPP < yGMPP is the tracked value using a Global Maximum Power Point (GMPP) tracking algorithm. In addition, the GES algorithm [37] is simple to be designed [73] and does not require complex tuning procedures [74]. Anyway, the performance of any optimization algorithm depends by the optimization objectives and constraints defined for the FCHPS. 2.2. Optimization objectives Even if the optimization is strictly followed, it will be very difficult to solve FCHPS optimization problems using one optimization criteria. So, it is recommended to adapt the optimization function to load demand and other constraints [75] by using penalty function [76] or a FC controller switched by the battery State-Of-Charge (SOC) level [77], or the RTO switching strategy for the control and optimization loops proposed in this study. The mathematical formulation for the FCHPS optimization is defined as below: 446

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Maximize: f (x , AirFr , FuelFr , Pload) = knet PFCnet + kfuel Fueleff

Subject to FCHPS dynamics: x = g (x , AirFr , FuelFr , Pload ), x

and constraints, but the priority is to reduce the number of sensors by using adaptive algorithms [83]. Constraints usually used to design a FCHPS based on Renewable Energy Systems (RES) are the number of available energy sources, renewable potential (considering the irradiance and wind speed estimated based on forecasting methods), technical characteristics of the RESs, battery (SOCmin , SOCmax ), used power storage devices to compensate the DC power flow balance, fuel tank, etc. [1,4]. In addition, for design a HPS for FC vehicle, more constraints can be considered as follows: limited space and weight for the FC HPS, and safety, lifetime and maintenance of both FC and battery stacks [81]. Thus, clearly there is no single optimization function to efficiently solve all such optimization objectives and constraints. Normally, the optimization function must be a linear combination of the conflicting indicators related to technical, economic, and environmental issues [1,45]. Besides the hydrogen consumption (or total fuel consumption: FuelT = FuelFr (t ) dt , measured in liter [L]) as performance indicator for the fuel economy, new indicators must be incorporated in the optimization function considering the type of application [84] and the profile of the load demand [85]. For example, the optimization function

(3a)

X (3b)

and battery SOC constraints: SOCmin < SOC < SOCmax

(3c)

where PLoad is the disturbance input, and knet and kfuel are weighting coefficients selected to be switched appropriately to objectives imposed in different stages of the LC [78]. For example, if the FCHPS is designed to be used by a FC vehicle, then the optimization functions will be automatically selected by the Energy Management Unit (EMU) considering on-line information about the route and driver commands [79,80]: so, if the FC vehicle goes up a hill, then the FC net power must be maximized, the fuel economy must be maximized, but if the FC vehicle is on highway, then the fuel economy is important; also, the fuel economy is important if the signaling sensors and communication units announce less fuel in the tank, so that a fuel station must be found near to actual position. It is obvious that improving fuel economy for plug-in FC vehicle [81] or FCHPS grid-connected [82] involves many decision variables

Fig. 1. aPESC, modified aPESC and Global aPESC schemes. 447

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used in [86] and [87] use the indicators related to fuel consumption, battery size and powertrain system durability, and, respectively, related to fuel consumption and electrical efficiency. Fuel consumption effiPFCnet ciency (Fueleff = FuelFr , measured in W/LPM because the FuelFr is measured in Liters per Minute [LPM]), FC electrical efficiency P ( sys = FCnet ), and hydrogen consumption efficiency P

Control (aPESC) scheme was proposed in [91] with an exponential modulation of the dither compared to Scalar PESC (PESCs) scheme [90], where the dither amplitude is constant (see Fig. 1a). The tuning parameters k1 and k2 are the gains in the adaptive tracking loop of the tracking signal ( p1) and the control loop of the sweeping signal ( p2 ). The value of the tuning parameter k2 in PESCs scheme cannot be increased in aPESC scheme to scan entire searching range because of the stability of the tracking loop. So, the sweeping signal p2 is the dither modulated with the dither gain Gd in the aPESC scheme (see Fig. 1a). Gain Gd sets the sweeping range based on function q. This decreases exponentially from a0 to 0. So, three parameters affect the tracking convergence: the position of the starting point, a0, and function q. The optimum will be tracked from any position of the starting point in the searching range only if the assumptions presented in [90] are respected. The Lyapunovbased aPESC scheme (aPESCLy) is presented in Fig. 1b. The aPESCLy scheme proposes to maintain the dither gain at a0 value until the optimum is found and then this evolves exponentially to zero, increasing the tracking speed without losing the tracking accuracy. But the aPESCLy scheme uses a complex Lyapunov function (depending by three signals and a switching threshold), which is difficult to be designed, besides the parameters a0 and ρ [92]. A simple approach is proposed in aPESCH1 scheme (see Fig. 1b) based on the first harmonic (H1) of the signal y: Gd = k2· H1, where the tuning parameter k2 sets the initial amplitude of the dither. The sweeping signal p2 decreases asymptotically to zero once the optimum is found [30]. It is worth to mention that the aPESCH1 scheme can find the global extreme in the searching range, so it is a Global aPESC (GaPESC) scheme (called GaPESCH1 scheme in Fig. 1c) [35]. This is compared as performance in [36] with the basic GaPESC scheme (using only one BPF centered on the dither frequency fd), the GaPESCbpf scheme (using two BPFs in series to improve the dither persistence), and the derivative GaPESC (GaPESCd) scheme (see Fig. 1c). All GaPESC schemes use different signal processing method approximate the derivate of the signal y [37]. The GaPESCbpf scheme (called below as GES scheme) compared to GaPESC scheme has an higher tracking speed due to improved persistence of the dither obtained using two BPF instead of one [37]. It is obvious that derivation of signals is not recommended in practice, so GaPESCd scheme is used only as reference in studies analyzing the performance of the GaPESC schemes. The Fractional-Order ES scheme has performance comparable with the GES scheme used in this paper [93]. The GES scheme presented in Fig. 2 implements (7) [37]:

FC 100·P

, where LHV is the lower heating value for hydrogen fuel ) (effH 2 = LHV ·FCnet are FuelT examples of performance indicators that can be also used. Note that sys is from 85% (at rated load) to 90% (at light load) and effH 2 is up to 60% [88]. It is known that the power consumed by air compressor (Pcm) is 8–12% from the FC power (PFC), reducing the FC net power to PFCnet PFC Pcm , where Pcm = Icm Vcm = (a2 AirFr 2 + a1 AirFr + a0 )(b1 IFC + b0) , and a0 = 0.6, a1 = 0.04 , a2 = 0.00003231, b0 = 0.9987 , and b1 = 46.02 [29]. Also, a 2nd order system with 0.1 s time constant and 0.7 damping ratio is used to model the dynamics of the air compressor [29]. This study was justified by the high complexity level to put in practice most of proposed strategies. In this paper, seven FCHPSs topologies are analyzed using the GES-based optimization strategy (1), and the same load and dynamics constraints. For example, the dynamics constraints used in this study are as follows: 0.2 s time constant for the FC system, 100 A/s slope for the FC current [89], 0.1 s time constant for the 2nd order system that models the air compressor [29], and the rest of dynamics parameters from the model of the FC system are set to default values. In next section, a brief survey on ES control algorithms will be presented to highlight the real-time searching behavior of the ES control used in this study.

2.3. Extremum Seeking control algorithm The nonlinear system is defined by (4) [90]:

x =

dy = f (x (t ), u (t )), y = h (x (t )) dx

(4)

where f (x , u) , h (x ) , and u = g (x (t ), p) define the dynamics, nonlinear function, and the control law of the system, x ∈ Rn is the state vector, u ∈ Rm is the inputs vector, and y ∈ R is the output vector, and p is the parameter vector. The system using the ES control evolves based on the seeking vector p to the optimum set by xe, xe:Rl → Rn:

f (x , g (x , p)) = 0

x = x e (p )

(5)

y = h (x ) = h (x e (p)) = h (p)

(7a)

y = f (v1, v2), yN = kNy· y

on the surface:

yf =

(6)

h ·yf

+

yDM = yBPF ·sd,

The basic ES control loop is presented in the top of Fig. 1. Different ways to modulate the dither’s amplitude (using the signal Gd) are presented in Fig. 1a–c. The Asymptotic Perturbed Extremum Seeking

yInt = yDM

Fig. 2. The GES scheme. 448

h · yN ,

yHPF = yN

sd = sin( t )

yf , yBPF =

l · yBPF

+

l · yHPF

(7b) (7c) (7d)

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Gd = |yMV |, yMV =

1 · Td

yBPF dt

(7f)

yM = Gd p1 = k1· yInt , k1 =

normalization gain of input signal y is kNy = 1/ YMax , where YMax is the maximum estimated for the optimization function [94]. The other parameters are designed considering [73]: k1 = 1, k2 = 2, fd1 = 100 Hz and fd2 = 200 Hz, bh1 = 0.1 and bl1 = 3.5 for the cut-off frequencies (bh1 fd and bl1 fd) of the BPF1 (to increase the dither persistence), and bh2 = 0.1 and bl2 = 1.5 for the cut-off frequencies (bh2 fd and bl2 fd) of the BPF2 (which approximate the first harmonic H1). The shapes of the signal Gd for the GaPESC, GaPESCH1 and GaPESCbpf schemes are presented in Fig. 1d, considering the above mentioned values for the parameters. It is worth to mention the realtime searching behavior of all GaPESC schemes, including the GES scheme considered in this study. The optimum (GMPP) will be tracked in less than 10 periods of the dither [73], which means less than 200 ms (see Fig. 1d). Thus, the tracking time is less that the FC time constant

(7e)

sd·

(7g)

p2 = k2·yM ·sd

(7h)

p3 = Am ·sd

(7i)

IrefGES = kNp·(p1 + p2 + p3 ),

(7j)

The components of the searching signal (p) for starting of searching ( p3 ), and then for sweeping ( p2 ) and tracking ( p1) of the optimum, will set signal IrefGES using the normalization gain kNp = IFC (rated) /2 The

Fig. 3. The FC HPS and EMU. 449

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(which is set at 200 ms in this study), but other limitations of the searching speed will be imposed by constrains for the safe operation of the FC system, such as the limited slope of FC current (which is recommended to be less than 100 W/s), as will be explained in Section of results. The Energy Management Unit (EMU) will use as control variable of the FCHPS the signals Iref(GES1), Iref(GES2), and Iref(LFW) (the output of the LFW controller) as will be presented in next section.

position. For example (see the RTO strategy setting block in Fig. 4 and Table 1), besides Iref (LFW ) = Iref (boost ) , the selecting strategy ensures the following connections in case of the strategies from class C1: Iref (Fuel) = IrefGES 2 + IFC and Iref (Air ) = IFC for the RTO1 strategy, Iref (Fuel) = IrefGES 2 and Iref (Air ) = IrefGES1 + IFC for the RTO2 strategy, and Iref (Fuel) = IrefGES 2 + IFC and Iref (Air ) = IrefGES1 + IFC for the RTO7 strategy. The connections in case of the strategies from class C2 are as follows: Iref (Air ) = Iref (LFW ) , Iref (Fuel) = IFC , and Iref (boost ) = IrefGES1 for the RTO 3 strategy, and Iref (Air ) = Iref (LFW ) , Iref (Fuel) = IrefGES 2 + IFC and Iref (boost ) = IrefGES1 for the RTO 5 strategy (see Fig. 4). So, the FC net power generated will be that given by (15) due to LFW control of the air regulator. Also, the FC net power generated will be that given by (15) due to LFW control of the fuel regulator in case of the strategies from class C3, where the connections are as follows: Iref (Fuel) = Iref (LFW ) , Iref (Air ) = IFC and Iref (boost ) = IrefGES1 for the RTO 4 strategy, and Iref (Fuel) = Iref (LFW ) , Iref (Air ) = IrefGES 2 + IFC and Iref (boost ) = IrefGES1 for the RTO 6 strategy (see Fig. 4). The signals Iref (Fuel) and Iref (Air ) will set FuelFr and AirFr based on (18) [55]:

3. Energy management strategy of hybrid power system The FCHPS is shown in Fig. 3 (top) and the EMU is detailed in bottom of the Fig. 3. The signal Iref(LFW) can be obtained based on DC power flow balance (8):

CDC uDC

duDC = p + pESS dt DC

pDCreq

(8)

where pDC and pESS are the output power of the boost converter and Energy Storage System (ESS), and pDCreq if the FC power requested on DC. Capacitor CDC filters the voltage on DC bus (udc). Considering ηboost ≅ 95%, the FC power on DC bus is:

pDC =

(9)

boost pFCnet

FuelFr =

DC power flow balance (8) in average value (AV) is:

0=

boost PFCnet (AV )

+PESS (AV )

PDCreq (AV )

(10)

AirFr =

If the battery will operate in charge-sustaining mode:

PESS (AV )

(11)

0

IFC (AV ) =

PDCreq (AV ) (12)

boost VFCnet (AV )

where:

pDC

pDCreq = pLoad

PDCreq (AV )

PLoad (AV )

(13)

Based on RTO strategy setting, the reference signal generated by LFW controller (Iref(LFW)) can be the input of the boost controller (Iref(boost)), air regulator (Iref(Air)), or fuel regulator (Iref(Fuel)) (see Fig. 1). Thus, three classes can be defined (see Table 1): class C1 if Iref(LFW) = Iref(boost) (the RTO1, RTO2, and RTO7 proposed in [95,96], and [78], class C2 if Iref(LFW) = Iref(Air) (the RTO3 and RTO5 proposed in [97;82], and class C1 if Iref(LFW) = Iref(Fuel) (the RTO4 and RTO6 proposed in [87] and in this paper. For example, because of hysteretic control of the boost converter, the FC current will follow Iref(LFW) if Iref(LFW) = Iref(boost) (the strategies RTO1, RTO2, and RTO7 from class C1), so:

IFC (AV )

PDCreq (AV ) / (

boost VFCnet (AV ) )

sys

boost VFCnet (AV ) )

(14)

(15)

sysk

(19a)

sys0

(19b)

Fueleff 0

(19c)

FuelT 0

Table 1 RTO strategies setting.

(16)

The optimization strategy will be implemented selecting the reference currents for fueling regulators as below:

Iref (Air ) = IrefGES1 + IFC Iref (Fuel) = IrefGES 2 + IFC

=

The 6 kW/45 V PEMFC model from the library of Matlab-Simulink® [101] (with 0.2 s FC time constant given by the electrical capacitance, 100 A/s slope for the FC current, and the other parameters are set to default values) is used in this study. The variable FC voltage (VFC) is boosted to VDC ≅ VDC(ref) = 200 V via a boost converter. The boost controller is of hysteretic type with 0.1 A hysteresis band in order to obtain a high switching frequency for the boost converter. So, this will be able to optimize in real-time the FC system. 100 Ah/100 V lithium-ion batteries’ stack and 100 F ultracapacitors’ stack are chosen for the ESS semi-active topology used to stabilize the DC voltage and mitigate the pulses on DC bus [102]. The

So, the load-following control will be implemented using (12) because PESS(AV) ≅ 0 based on (10). The AV-based filtering technique is used in this study for the safe operation of the FC system due to simple implementation [98,99]. Thus, considering (13), the LFW control is implemented using (16):

Iref (LFW ) = PLoad (AV ) / (

(18b)

4F ·(101325·Pf (O2) )·(Uf (O2)/100)·(yO2 /100)

FuelT = FuelTk

PDCreq (AV ) boost

60000· R·(273 + )· NC ·Iref (Air )

Fueleff = Fueleffk

and:

PFC (AV ) = IFC (AV ) VFCnet (AV )

(18a)

where 100 A/s slope is used for the signals Iref(Fuel) and Iref(Air), and the rest of parameters are set as default [100]. The load-following control is applied via the boost controller (class C1), the air regulator (class C2), and the fuel regulator (class C3), so the battery charge sustaining mode will be obtained in all cases (with advantages related to size, lifetime and maintenance cost). In addition, constraint (3c) for the battery SOC is obviously fulfilled. For a fair comparison of each strategy RTOk, k = 1 ÷ 7, compared to the sFF strategy [55], the LFW control must be implemented in the same way. The differences (19) will be estimated:

then the reference signal generated by LFW controller will be:

Iref (LFW )

60000·R·(273+ )·NC · Iref (Fuel) 2F ·(101325· Pf (H 2) )·(Uf (H 2)/100)·(xH 2 /100)

(17)

RTO strategy will be implemented if both switches are on GES 450

No.

Iref(Boost)

Iref(Air)

Iref(Fuel)

RTO strategy

Reference

Class

0 1 2 3 4 5 6 7

ILFW ILFW ILFW IGES1 IGES1 IGES1 IGES1 ILFW

IFC IFC IGES1 + IFC ILFW IFC ILFW IGES2 + IFC IGES1 + IFC

IFC IGES1 + IFC IFC IFC ILFW IGES2 + IFC ILFW IGES2 + IFC

sFF RTO1 RTO2 RTO3 RTO4 RTO5 RTO6 RTO7

[54] [97] [98] [99] [89] [84] [–] [80]

C1 C1 C2 C3 C2 C3 C1

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Fig. 4. RTO strategy setting block.

Furthermore, 100 μF capacitor CDC on DC bus (with the initial value of VDC = 200 V) is used to filter the DC voltage.

Table 2 sFF strategy applied to FC HPS at different Pload. Pload [kW]

PFCnet0 [W]

ηsys0 [%]

Fueleff0 [W/LPM]

FuelT0 [L]

2 3 4 5 6 7 8

1942 2884 3786 4650 5467 6229 6912

93.26 91.85 90.43 88.75 86.89 84.78 82.3

137.3 129.5 121.6 113.4 104.7 95.16 83.75

34.02 56.3 74.88 98.6 125.58 158.34 176

4. Results The optimum of the optimization function (3a) will be tracked by the GES-based RTOk strategy in case of three sets of the weighting coefficients knet and kfuel:

case A (knet = 0.5, kfuel=0),case B (knet = 0.5, kfuel = 25), and case C (knet = 0.5, kfuel = 50) This analysis was performed for different scenarios for the power flow on DC bus (variable or constant load demand).

ultracapacitors’ stack has the initial voltage, the equivalent series resistor (ESR) and parallel resistor (EPR) of 100 V, 0.1 Ω and 10 kΩ. The bidirectional DC-DC converter used to connect the ultracapacitors’ stack to the DC bus is controlled to stabilize the DC voltage, ensuring the dynamic compensation of the power flow balance (8) as well. During the lack of power from the FC system (because of delayed response in the output power at changes in fueling flow rates due to mainly of 0.2 s FC time constant and maximum 100 A/s for the inputs of the fueling regulators (the signals Iref(Fuel) and Iref(Air)); note that the thermal effects are minor at level of hundreds of seconds). The batteries’ stack is connected directly on DC bus, and initially has 80% SOC and the default values for the other model parameters. Both stacks use models from Matlab & Simulink® toolboxes [100].

4.1. HPS under constant load demand and kfuel = 0 The value of the performance indicators ηsys0, Fueleff0, and FuelT0 using the sFF strategy are presented in Table 2. 4.1.1. FC electrical efficiency The gaps in FC electrical efficiency are presented in Table 3 for each RTOk strategy, k = 1 ÷ 7, compared to sFF strategy. Figs. 5–7 shows the gaps in FC electric efficiency for the RTO strategies from class C1, C2, and C3. The gaps in FC electric efficiency for the best RTO strategies in each 451

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Table 3 Gaps in FC electric efficiency. Pload [kW]

Δηsys1 [%]

Δηsys2 [%]

Δηsys3 [%]

Δηsys4 [%]

Δηsys5 [%]

Δηsys6 [%]

Δηsys7 [%]

2 3 4 5 6 7 8

0.27 0.42 0.53 0.61 0.69 0.91 2.65

−0.62 −0.51 −0.48 −0.31 −0.15 0.18 1.61

−0.35 −0.01 0.06 0.13 0.27 0.63 1.61

0.14 0.14 0.3 0.43 0.94 2.4 2.65

0.09 0.23 0.28 0.67 0.94 1.52 2.13

−3.26 −2.06 −1.46 −0.79 0.24 1.09 1.88

0 0.1 0.29 0.38 0.47 0.57 0.84

Fig. 8. Gaps in FC electric efficiency for the best RTO strategy in each class and the new RTO6 strategy.

Fig. 5.

sys for

class (RTO1, RTO5, and RTO4) are positive in full range of the load demand and have almost the same values (see Fig. 8, where the gap in FC electric efficiency for the strategy RTO6 proposed in this paper is presented as well). Note that the gap in FC electric efficiency for the RTO6 strategy is positive only for high load demand. So, the FC net power could be maximized if the FC vehicle ascends up a hill (with power demand greater than the rated power of 6 kW) using any of the RTO strategies outlined in Fig. 8 (RTO1, RTO4, RTO5 and even RTO6). The better performance of RTO4 strategy compared to other strategies must be validated in different scenarios below.

class C1.

4.1.2. Fuel efficiency The gaps in fuel efficiency are presented in Table 4 for each RTOk strategy, k = 1 ÷ 7, compared to sFF strategy. The gaps in fuel efficiency for the RTO strategies from class C1, C2, and C3 are presented in Figs. 9–11. The gaps in fuel efficiency for the same RTO strategies (RTO1, RTO5, RTO4 and RTO6) are presented in Fig. 12. Only the strategy RTO4 ensures positive values in full range of the load. Almost the same values are obtained for the strategies RTO5, RTO4 and RTO6 in the upper range of the load demand. So, any of these strategies (RTO5, RTO4, RTO6, and even RTO1) can be used for a FC vehicle climbing up a hill with power demand greater than the rated power of 6 kW, when improved performance in both fuel efficiency and FC electric efficiency indicators are obtained. Fig. 6.

Fig. 7.

sys for

class C2.

sys for

4.1.3. Fuel economy The fuel economy (as gaps in Fuel Total consumption) is presented in Table 5 for each RTOk strategy, k = 1 ÷ 7, compared to sFF strategy. Also, the fuel economy is shown in Figs. 13–15 for the RTO strategies from class C1, C2, and C3. Only the strategies RTO4, RTO6, and RTO7 ensure fuel economy in full range of the load. The fuel economy for the same RTO strategies (RTO1, RTO5, RTO4 and RTO6) is presented in Fig. 16. Almost the same values are obtained for the strategies RTO4 and RTO6, and the strategy RTO5 ensures a fuel economy only in the upper range of the load demand. So, the fuel economy can be maximized if the FC vehicle runs with reduced power on a smooth route by using the strategies RTO4 or RTO6. If the FC vehicle ramps a hill, then the recommended strategy is the RTO5 strategy. The fuel consumption efficiency must be maximized to obtain the best fuel economy if the signaling sensors and communication units announce that the fuel tank is almost empty but a fuel station is nearby to current position of the FC vehicle. The best fuel economy will be analyzed for different kfuel in next section considering all seven RTO strategies.

C3.

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Table 4 Gaps in Fuel efficiency. Pload [kW]

ΔFueleff1 [W/LPM]

ΔFueleff2 [W/LPM]

ΔFueleff3 [W/LPM]

ΔFueleff4 [W/LPM]

ΔFueleff5 [W/LPM]

ΔFueleff6 [W/LPM]

ΔFueleff7 [W/LPM]

2 3 4 5 6 7 8

−1 −0.7 0.7 1.8 3.5 6.21 10.35

−1.8 −1.5 −0.7 −0.5 −0.4 0.62 11.2

−15.3 −3 −0.7 0.4 1.4 3.31 11.2

1.2 1.8 2.4 3 4.7 7.6 10.35

−15.3 −9 −3.4 3.4 4.9 8.84 11.47

−2.3 −0.2 1.5 3.1 5.3 8.14 11.26

−0.1 1.4 2.3 2.8 3.1 3.52 4.28

Fig. 9. Gaps in fuel efficiency for the RTO strategies from class C1.

Fig. 12. Gaps in fuel efficiency for selected RTO strategies in each class. Table 5 Fuel economy. Pload [kW]

ΔFuelT1 [L]

ΔFuelT2 [L]

ΔFuelT3 [L]

ΔFuelT4 [L]

ΔFuelT5 [L]

ΔFuelT6 [L]

ΔFuelT7 [L]

2 3 4 5 6 7 8

1.22 0.13 −0.13 −0.38 −1.38 −4.34 −11.8

1.2 0.79 0.77 0.55 0.42 −0.14 −4

11.26 4.14 2.08 −0.08 −2.28 −12.16 −28.48

−0.46 −1.22 −2.28 −5.6 −7.66 −13.56 −22.92

8 6.16 1.94 −5.18 −11.56 −24.48 −43.34

−0.42 −1.7 −3.1 −5.24 −8.48 −14.04 −27.36

−0.22 −0.38 −0.54 −0.72 −0.9 −1.08 −1.38

Fig. 10. Gaps in fuel efficiency for the RTO strategies from class C2.

Fig. 13. ΔFuel for class C1.

4.2. Fuel economy for the HPS under constant load demand and different kfuel

Fig. 11. Gaps in fuel efficiency for the RTO strategies from class C3.

The fuel economy is presented in Table 6–9 for selected RTO strategy (RTO1, RTO5, RTO4 and RTO6) compared to sFF strategy, 453

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Table 7 ΔFuel for RTO4 strategy. Pload [kW]

ΔFuelT4A [L]

ΔFuelT4B [L]

ΔFuelT4C [L]

2 3 4 5 6 7 8

−0.46 −1.22 −2.28 −5.6 −7.66 −13.56 −22.92

−0.644 −3.876 −5.176 −8.76 −12.54 −24.26 −26

−0.1 −3.7 −5.264 −8.76 −13.98 −20.74 −25

Table 8 ΔFuel for RTO5 strategy. Fig. 14. ΔFuel for class C2.

Pload [kW]

ΔFuelT5A [L]

ΔFuelT5B [L]

ΔFuelT5C [L]

2 3 4 5 6 7 8

8 6.16 1.94 −5.18 −11.56 −24.48 −43.34

6.78 1.76 −3.72 −11.42 −17.82 −30.24 −47.72

8.56 4 1.1 −6.34 −13 −23.9 −45.52

Table 9 ΔFuel for RTO6 strategy.

Fig. 15. ΔFuel for class C3.

Pload [kW]

ΔFuelT6A [L]

ΔFuelT6B [L]

ΔFuelT6C [L]

2 3 4 5 6 7 8

−0.42 −1.7 −3.1 −5.24 −8.48 −14.04 −27.36

−0.56 −2 −3.76 −6.52 −11.28 −20.76 −37.98

−0.42 −2 −3.66 −6.28 −9.42 −14.48 −23.44

considering the case A (knet = 0.5, kfuel=0),case B (knet = 0.5, kfuel = 25), . and case C (knet = 0.5, kfuel = 50)

The fuel economy for selected RTO strategies in case A (knet = 0.5, kfuel=0) is presented in Fig. 16, and fuel economy for case B (knet = 0.5, kfuel = 25) and case C (knet = 0.5, kfuel = 50) is shown in Figs. 17 and 18. Note that the performance in fuel economy and even the order of the selected RTO strategies (RTO1, RTO4, RTO5, and RTO6) remain the same for all cases A, B, and C (see Figs. 16–18) if the FCHPS operates under high load demand (greater than the rated power of 6 kW).

Fig. 16. Fuel economy for selected RTO strategies in case A (knet = 0.5, kfuel = 0). Table 6 ΔFuel for RTO1 strategy. Pload [kW]

ΔFuelT1A [L]

ΔFuelT1B [L]

ΔFuelT1C [L]

2 3 4 5 6 7 8

1.22 0.13 −0.13 −0.38 −1.38 −4.34 −11.8

1.22 −0.25 −0.71 −1.03 −2.08 −10.56 −22.92

1.28 0.1 −0.23 −0.48 −1.08 −3.56 −6.8

Fig. 17. Fuel economy for selected RTO strategies in case B (knet = 0.5, kfuel = 25). 454

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Table 10 Load cycles (LC) with different Pload(AV) and fuel economy FuelT0(LC) for the sFF strategy. LC stage

0–4 s

4–8 s

Pload(AV) [kW]

Levels of power [kW]

2 3 4 5 6 6.25

1.50 2.25 3.00 3.75 4.50 4.6875

2.50 3.75 5.00 6.25 7.50 7.8125

8–12 s

FuelT0(LC) [L]

2.00 3.00 4.00 5.00 6.00 6.25

34.14 53.92 75.8 100.62 130.2 138.86

kfuel = 25 is compared to that obtained for kfuel = 0 and kfuel = 50. The biggest increase of the fuel economy is obtained for RTO2 strategy, which are in class C1. Also, it is worth to mention that the strategies RTO1 and RTO4 use only one GES controller to maximize the fuel economy, and higher fuel economy is obtained by optimal control of the boost converter instead of the fuel regulator or the air regulator. Anyway, the strategies RTO5 and RTO6 still remain of interest to be analyzed for FCHPS under variable load demand in next section.

Fig. 18. Fuel economy for selected RTO strategies in case C (knet = 0.5, kfuel = 50).

Also, note that only the strategies RTO4 and RTO6 ensure fuel economy in full range of the load and in all cases A, B, and C. Thus, the conclusion obtained in previous section remains valid and can be summarized as follows: (i) if the FC vehicle runs with reduced power on a smooth route the recommended strategies are RTO4 or RTO6; (ii) if the FC vehicle ramps a hill, then the recommended strategy is the RTO5 strategy. Note that fuel economy increases if kfuel ≠ 0 and best fuel economy could be obtained for kfuel around value of 25 if the fuel economy for

4.3. Fuel economy for the HPS under variable load demand and different kfuel To exemplify, the behavior of the FCHPS is presented in Fig. 19 under LFW control and 6.25 kW load demand, using the strategies

a. The behavior of the FC HPS

b. Gaps in performance indicators

Fig. 19. FC HPS under variable load. a. The behavior of the FC HPS. b. Gaps in performance indicators.

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RTO1 (Iref (LFW ) = Iref (boost ) , Iref (Fuel) = IrefGES 2 + IFC ,and Iref (Air ) = IFC ) with kfuel = 25. The 6.25 kW LC (Pload (AV ) = 6.25 kW ) is shown in first graphic of Fig. 19a and defined in Table 10, where other load cycles with different Pload(AV) values are defined as well. The fuel economy FuelT0(LC) for the sFF strategy is presented as reference in last column of Table 10. The structure of the Fig. 19a is as follows: the profile of the load power (PLoad) is presented in the first plot; the FC net power profile (PFCnet) is presented in the second plot and note that this profile tries to follow the smooth profile of the load demand, highlighting that the LFW control is implemented for the FC system; the ESS power presented in the third plot also highlights the advantage of the LFW control: the battery will operate in charge-sustaining mode (PESS(AV) ≅ 0), sustaining to power flow balance on DC bus only during sharp variation of the load demand; the next two plots represent the fueling flow rates (AirFr and FuelFr); the fuel consumption (FuelT), the fuel efficiency (ΔFueleff), and the FC electric efficiency (ηsys) are represented in the last three plots. As it was mentioned, for sharp changes in the load demand, the FC system generates power with some delay due to 0.2 s FC time constant and slope constraints ( ± 100 A/s) for the safe operation of the FC system. For example, during the step-up in load demand, the step-up level of the FC current will be obtained after about 0.3 s due to a limited increase with 100 A/s. During this time, the lack of power on DC bus will be compensated by the ultracapacitors’ stack (see the power pulse on the 3rd plot in Fig. 19a). During the step-up in load demand, the step-down level of the FC current will be also obtained with delay, so an excess of power will be on DC bus due to FC power generated. This excess power will charge the ultracapacitors’ stack. So, the power flow balance (8) will be dynamically compensated by the ultracapacitors’ stack via the bidirectional DC-DC converter. The ultracapacitors’ stack was designed to ensure the requested power pulses. The differences in FC net power (ΔPFCnet = PFCnet1 − PFCnet0), FC energy efficiency (Δηsys), fuel efficiency (ΔFueleff), and fuel economy (ΔFuelT) are represented in Fig. 19b, where the real-time searching behavior is better highlighted. Note the improved performance in all performance indicators of the FCHPS under variable load. The fuel economy for selected RTO strategies compared to sFF strategy (see Table 11–14) will be used to evaluate the performance of these strategies. The fuel economy under variable load demand for selected RTO strategies in case A (knet = 0.5, kfuel = 0), case B (knet = 0.5, kfuel = 25), and case C (knet = 0.5, kfuel = 50) is shown in Figs. 20–22. Note that the performance in fuel economy and even the order of the selected RTO strategies (RTO1, RTO4, RTO5, and RTO6) remain the same in all cases analyzed for the FCHPS (under variable and constant load demand; see Figs. 20–22, compared to Figs. 16–18). Also, for the FCHPS under variable load demand, the fuel economy increases if kfuel ≠ 0 (the best fuel economy is obtained for kfuel around value of 25). The fuel economy is obtained in full range of the LCs used in this study for the RTO 6 strategy (see Table 14) and almost in full range for the RTO 4 strategy (see Table 12), which validate the results obtained for constant load demand (see Tables 7 and 9). Also, the recommended strategy remains the RTO5 strategy for variable load demand with Pload(AV) > 4.5 kW (see Fig. 21) or Pload(AV) > 5 kW (see Figs. 20 and 22). So, the possible rules for a switching strategy designed to obtain the best fuel economy can be as follows: (i) kfuel must be set around 25; (ii) the selected strategy must be RTO4 or RTO6 (from class C3) if the load demand is less than 5 kW; (iii) the selected strategy must be RTO3 or RTO5 (from class C2) if the load demand is higher than 5 kW. The fuel economy for the strategies RTO4 and RTO3 is represented in Fig. 23 for constant and variable load demand in order to be compared with the fuel economy represented in Fig. 24 for the strategies RTO6 and RTO5.

Note that the strategies RTO5 and RTO5 use two GES controllers instead of one GES controller for the strategies RTO3 and RTO4, so the last variant could be preferred due to simpler implementation. But this must be further analyzed in next work. 5. Conclusion In this paper, besides a critical assessment of currently real-time optimization strategies, the performance of six Fuel Cell Hybrid Power Systems topologies and one new has been analyzed. The Fuel Cell Hybrid Power Systems based on load-following control can mitigate the load demand variability to the battery state of charging. So, the battery will operate in charge-sustained mode, with clear benefits related to battery size, its lifetime and maintenance cost, and simple implementation of the Energy Management Strategy by eliminating monitoring condition of the battery state of charging. Also, the Fuel Cell Hybrid Power Systems use one or two RTO loops to reduce the fuel consumption. Three classes for the RTO strategies are defined and analyzed for the Fuel Cell Hybrid Power System under constant or variable load demand. The Static Feed-Forward strategy is used as reference to highlight the performance of the RTO strategies using the performance indicators such as the fuel consumption efficiency, the Fuel Cell electrical efficiency, and the total fuel consumption fuel for constant load demand, and fuel economy for variable load demand. The optimization function of the fuel economy is a weighted function of the Fuel Cell net power and the fuel consumption efficiency through the weighting coefficients knet and kfuel. The optimum of the optimization function will be found in real-time using the GES algorithm proposed in [35]. The objective was to probe how optimization function through choosing the weighting coefficients knet and kfuel could be a crucial help when planning the fuel consumption of a Fuel Cell vehicle under unknown route. The comparative research is performed for all seven Fuel Cell Hybrid Power Systems topologies using same profile for the load demand. The Fuel Cell Hybrid Power Systems topologies are classified in three classes after the place where the Load-Following control is applied: to controller of the Fuel Cell boost converter, to Air Flow rate regulator, or to Fuel Flow rate regulator. The obtained performance for the RTO strategies analyzed defines the best strategy from each class. The switching strategy of the best strategies is proposed to further increase the fuel economy for an unknown profile of the load cycle. The main findings of this study are as follows:

• The gaps in FC electric efficiency for the strategies RTO1, RTO5, and

•

RTO4 are positive and best in full range of the load demand (see Fig. 8). The set of best RTO strategy in each class is completed with the new strategy RTO6 proposed in this paper, due to almost same positive gap in FC electric efficiency for high load demand. Thus, any of best RTO strategy can maximize the FC net power if the FCC vehicle climbs a hill, usually with power demand greater than the rated power. The gaps in fuel efficiency presented in Fig. 12 for the same RTO strategies (RTO1, RTO5, RTO4 and RTO6) have shown that only the

Table 11 ΔFuel for RTO1 strategy under variable load.

456

Pload(AV) [kW]

ΔFuelT(LC)1A [L]

ΔFuelT(LC)1B [L]

ΔFuelT(LC)1C [L]

2 3 4 5 6 6.25

1.3 0.71 0.07 −1.6 −3.8 −4.56

0.5 −0.48 −1.8 −3 −5.3 −6.36

0.51 −0.47 −1.58 −2.99 −5.23 −6.21

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Table 12 ΔFuel for RTO4 strategy under variable load. Pload(AV) [kW]

ΔFuelT(LC)4A [L]

ΔFuelT(LC)4B [L]

ΔFuelT(LC)4C [L]

2 3 4 5 6 6.25

0.7 −0.56 −0.82 −4.72 −11.46 −14.54

1.92 0.82 −0.64 −4.16 −10.08 −12.86

3.4 2.9 −0.5 −3.98 −9.46 −12.06

Table 13 ΔFuel for RTO5 strategy under variable load. Pload(AV) [kW]

ΔFuelT(LC)5A [L]

ΔFuelT(LC)5B [L]

ΔFuelT(LC)5C [L]

2 3 4 5 6 6.25

8.26 6.7 2.84 −2.84 −29.08 −34.28

10.8 8.74 −0.26 −12.96 −42.54 −52.7

10.14 8.82 4.92 −9.66 −37.26 −42.4

Fig. 21. Fuel economy under variable load demand for selected RTO strategies in case B (knet = 0.5, kfuel = 25).

Table 14 ΔFuel for RTO6 strategy under variable load. Pload(AV) [kW]

ΔFuelT(LC)6A [L]

ΔFuelT(LC)6B [L]

ΔFuelT(LC)6C [L]

2 3 4 5 6 6.25

−0.18 −1.32 −2.84 −4.52 −8.22 −10.4

−0.1 −1.04 −3.84 −9.3 −18.56 −21.86

−0.38 −1.18 −2.88 −6.2 −16.38 −19.68

Fig. 22. Fuel economy under variable load demand for selected RTO strategies in case C (knet = 0.5, kfuel = 50).

• • • Fig. 20. Fuel economy under variable load demand for selected RTO strategies in case A (knet = 0.5, kfuel = 0).

•

•

strategy RTO4 ensures positive values in full range of the load, but almost the same values are obtained for all strategies in the upper range of the load demand. So, all strategies can maximize the both FC net power and fuel efficiency performance indicators if the Fuel Cell vehicle climbs a hill. The fuel economy obtained for the RTO strategies considered is different: the strategies RTO4 and RTO6 ensure fuel economy in full range of the load demand and twice compared to RTO1 strategy; the RTO5 strategy fuel economy only in the upper range of the load

demand, but twice compared to that obtained with the strategies RTO4 and RTO6. So, the fuel economy can be maximized using the RTO4 strategy and RTO5 strategy (or RTO6 strategy and RTO5 strategy) for the Fuel Cell vehicle which runs on a smooth route and, respectively, the Fuel Cell vehicle ramps a hill. The same performance in fuel economy is obtained for selected RTO strategies under variable load demand compared to constant load demand (see Figs. 20–22 compared to Figs. 16, 17, and 19). The fuel economy increases if kfuel ≠ 0 and best fuel economy for constant and variable load demand is obtained for kfuel lower than 50. The fuel economy can be maximized using the RTO4 strategy (or RTO6 strategy) for the Pload(AV) < 4.5 kW and RTO5 strategy for Pload(AV) > 4.5 kW. Best fuel economy can be obtained using the proposed RTO switching strategy with optimum value for weighting coefficient kfuel based on following switching rule: if the load demand is lower than 5 kW then the selected strategy must be the RTO4 strategy or the RTO6 strategy from class C3, otherwise the selected strategy must be the RTO3 strategy or the RTO5 strategy from class C2.

It is worth to mention that the strategies RTOk, k = 1 ÷ 4 use only one Global Extremum Seeking controller to maximize the fuel economy, so may be simple to implement the RTO switching strategy using the RTO4 strategy for Pload < 5 kW and RTO3 strategy for Pload > 5 kW, but this analysis will be performed in next work.

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a. Constant load demand

a. Constant load demand

b. Variable load demand Fig. 24. Fuel economy for strategies RTO6 and RTO5 with kfuel = 25.

b. Variable load demand

Appendix A. Supplementary material

Fig. 23. Fuel economy for strategies RTO4 and RTO3 with kfuel = 25.

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.apenergy.2019.03.026.

Also, it was important to know which the best strategy in each class is in order to focus the experiment only on these selected strategies. The experiment will use a Fuel Cell system in flow-through mode to avoid the fuel starvation during transitory regimes. Also, in this mode the 99.56% conversion of hydrogen is obtained. So, unreacted fuel is negligible and does not greatly affect the performance indicators considered in this study in order to compare the experimental and simulation results. As a final conclusion, this study clarifies how the next research in Fuel Cell Hybrid Power Systems could be conducted to obtain better results than those reported in the literature.

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Acknowledgements This work was supported by Research Center “Modeling and Simulation of the Systems and Processes” based on grants of the Ministry of National Education and Scientific Research, CNCS/CCCDIUEFISCDI within PNCDI III “Increasing the institutional capacity of bioeconomic research for the innovative exploitation of the indigenous vegetal resources in order to obtain horticultural products with high added value” PN-III P1-1.2-PCCDI2017-0332, and within RDI Program for Space Technology and Advanced Research - STAR, project number 167/2017: “Concept Development of an Energy Storage Unit Using High Temperature Superconducting Coil for Spacecraft Power Systems (SMESinSpace).

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