Fuel saving strategy using real-time switching of the fueling regulators in the proton exchange membrane fuel cell system

Applied Energy 252 (2019) 113449

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Fuel saving strategy using real-time switching of the fueling regulators in the proton exchange membrane fuel cell system Nicu Bizon

T

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Faculty of Electronics, Communication and Computers, University of Pitesti, 1 Targu din Vale, 110040 Pitesti, Romania Polytehnic University of Bucharest, 313 Splaiul Independentei, 060042 Bucharest, Romania

H I GH L IG H T S

fuel economy strategy switches the load-following to fueling regulators. • New combines Fuel Cell net power with fuel consumption efficiency. • Optimization fuel economy is the best compared to other load-following strategies. • The consumption is reduced with 14–29% compared to commercial strategies. • Fuel • Battery lifetime is improved by using charge-sustaining mode under variable load.

A R T I C LE I N FO

A B S T R A C T

Keywords: Fuel cell vehicle Fuel cell system Fuel saving Load-following control 2D optimization Switching strategy

A new strategy based on a real-time switching of the fueling regulators’ inputs is proposed in this paper to achieve better fuel saving for the fuel cell systems. The performance of the proposed strategy is compared with two basic strategies that operate in full loading range. In fact, by splitting the operating range in two ranges, where each basic strategy operates best, the proposed strategy mixes the benefits of these two strategies. The switching threshold between the loading ranges is optimally set using the sensitivity analysis. The fuel savings for all strategies analyzed in this study are compared to those obtained using the static feed-forward strategy for fueling regulators. The load-following mode for fueling regulators is implemented based on switching rule of the basic strategies, comparing the load demand with the aforementioned switching threshold. The load-based control provides huge advantages regarding battery size and operation in charge-sustained mode (which increases its lifetime). The best fuel saving can be obtained in real-time based on search flexibility on the optimization surface (with two variables). Compared with the best basic strategy, the fuel saving is 1.63 and 2.07 – times higher for a pulsed load and stair load, respectively. Also, compared with the total fuel consumption of the static feed-forward strategy, the fuel saving is 25.87% and 13.72% for the aforementioned load profiles. The obtained results are good and can motivate the further research in order to test and validate this strategy for fuel cell vehicles.

1. Introduction The energy power systems must be sustainably designed and developed using renewable energy sources and other green (non-polluting) energy sources, such as the proton exchange membrane fuel cell (PEMFC) system, to meet new energy and environment challenges [1,2]. The PEMFC system is frequently used as a backup green energy source for mobile [3,4] and stationary applications [5,6], such as FC vehicles and Hybrid Power Systems (HPS), including space applications [7,8]. The load profile for FC vehicles is unknown and highly dynamic,

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so advanced strategies must be developed for the FC system to safely compensate the load demand [9,10]. The DC power flow balance of HPSs based on rule strategies is sustained by the power exchanged with the batteries’ stack [11]. The large variability of the renewable power flows may raise some difficulty in monitoring the state-of-charge (SOC) of the battery [12]. So, new strategies that use the PEMFC systems as backup energy source have been proposed [13,14] to safely compensate the power flow balance of the renewable HPSs based on load-following control of the fueling regulators [14,15]. Precise and dynamic models for the PEMFC system are necessary

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

https://doi.org/10.1016/j.apenergy.2019.113449 Received 11 April 2019; Received in revised form 25 May 2019; Accepted 6 June 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

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fueling flow rates to avoid the fuel starvation [63] under dynamics load cycles [10,34,64]. Thus, beside the classical control techniques such as feed-forward, PID, and feed-forward PID control methods [64], due to nonlinear processes that must be also handled at the anode of the FC system [65,66], the nonlinear control methods are intensively tested based on multi-inputmultioutput (MIMO) nonlinear model [67] or a combination of linear and nonlinear models [68,69] for the hydrogenfeeding subsystem. Among the aforementioned control methods for airfeeding subsystem, the nonlinear MPC [70,71] and sliding control [72,73] techniques keep best the stoichiometric ratio for gases (hydrogen, nitrogen, and oxygen) in different conditions regarding nitrogen concentrations [74], fuel recirculation [69,75], and purge scheduling [76–82]. The purge interval can be optimally scheduled using optimal [76,77], adaptive [78,79], bleeding [80,81], or intelligent [82] strategies. The bleeding strategies seem to have the best performance due to permanent handling of nitrogen diffusing and gases leaking by advanced purge techniques that have been experimentally tested in [83,84]. The thermal [85,86], pressure [87], and humidification [88,89] conditions have been analyzed for the FC system in dead-end operating mode to avoid carbon monoxide poisoning [67] and improve the FC’s lifetime [90,91]. The best improvement in FC’s lifetime can be obtained using a management strategy that optimally integrates control of both thermal and water subsystems [92,93]. Due to the clear interdependence between the FC subsystems [94], the optimization strategies using this systematic approach based on the state diagram [11,95], fuzzy logic [96,97], and data fusion [98] approaches have been proposed for the FC system [99], the FC vehicles [33,100], and the FC Hybrid Power Systems [101]. Of course, the best results have been obtained with optimization strategies based on nonlinear control [102], MPC [12,103], and droop control [104], but these strategies offer a suboptimal solution to the optimization problem. The optimal solution is offered using global optimization strategies based on the Extremum Seeking (GES) algorithm [105], dynamic programming [106] or Pontryagin's minimum principle [107,108]. The optimization problem can be focused on the fuel economy [109,110], lifetime [96] and the safety [111] of FC systems, or a mix of them. So, for best fuel saving, a new strategy (called as the SW strategy) is proposed here based on an innovative switching of the load-following mode to the fueling regulators. The fuel saving using the SW strategy is compared with that obtained with the basic strategies [28] and [29], which use the load-following mode for the Air and Fuel regulator, respectively. So, all three strategies operate the battery in in chargesustained mode and the load demand is sustained by the FC system. Anyway, small differences in the power balance will be compensated by the battery, but the battery capacity is smaller compared to the rulebased strategies. In addition, the battery’s lifetime increases and the battery state-of-charge (SOC) is not necessary to be monitored. The proposed SW-strategy offers the best fuel economy by switching the basic strategies which operate best in low and high loading range, respectively, but not in the entire range. So, the threshold between the loading ranges must be found using the sensitivity analysis for best fuel economy. Consequently, the optimization problem is oriented to fuel economy by using a weighting factor of the fuel consumption efficiency, which is added to the FC net power. Thus, the novelty of this study and main advantages of the proposed strategy can be highlighted as follows: (1) a new real-time strategy (called SW-strategy) is proposed to improve the fuel saving for the FC systems; (2) the best fuel savings are obtained by switching the loadfollowing mode to the air and fuel regulators; (3) thus, the battery will be operated in charge-sustained mode due to the implementation of the load-following mode, with clear advantages (compared to the chargedischarge modes used in other rule-based strategies) such as: increased battery lifetime, reduced size, and without constraint for the energy strategy to monitor battery charge; (4) the sensitivity analysis has been

[16] to design and test their operation under high power ripple or pulses [7,17] in order to evaluate the FC lifetime [18]. The lifetime and durability of the FC systems are drastically reduced by gas starvation phenomena [19], cold start [20], and frequent start-stop operations [21]. These issues are analyzed in many experimental studies [3,22] and different ways to mitigate them are proposed in the literature [6,7], including, e.g., health-conscious energy management strategies [9] and the fault tolerant strategies [23]. Beside the safe operation of the FC systems, a hot research subject is to optimize their operation under different operating conditions, such as a variable load in the FC vehicle or an unpredictable variation of the renewable power that may be available in the FC/renewable HPS. An innovative strategy based on safe switching of the load-following mode to the fueling regulators has been proposed in this paper to obtain the best fuel saving. The load-following control was proposed to deal with dynamics compensation of the power flow balance under the different load cycles with less energy support from the battery [15] due to its operation in the charge sustaining mode [24,25]. The efficient and safe operation of the PEMFC system using different load cycles has been analyzed in [26,27]. It is know that the FC power can track the load based on the loadfollowing mode [15], controlling in the entire loading range the air regulator [28] or the fuel regulator [29] with improved fuel saving by using 2D searching [28,29] instead of 1D searching [25] on the optimization surface. The advantage of 2D searching of the best fuel saving obtained by using the aforementioned strategies is adopted here by innovative switching of the optimization and load-following loops. In general, the air regulator is controlled depending on the load demand (by using the control mode called load-following) to provide a suitable oxygen flow and pressure in the FC stack’s cathode [15,28,30] and improve the fuel savings [31]. The air compressor must to cope with load pulses, avoiding the oxygen starvation by ensuring an oxygen excess ratio around 2 [32,33], but mandatory higher than 1 [34]. Thus, many control methods have been proposed to regulate the oxygen excess ratio based on classical feed-forward [34], proportional–integral–derivative (PID) [35], and feed-forward PID [36] techniques, and its improved variants using fuzzy [37] and robust approach [38]. The intelligent control techniques have been extensively applied using fuzzy logic [39,40], neural networks [41], and genetic operators [42]. Due to the response delay of the air-feeding subsystem, the model predictive control (MPC) using linearized [43,44], constrained [45], or multivariable nonlinear [46,47] models have been proposed to mitigate this issue. The recommended method to control a highly nonlinear and dynamic process is to use the sliding control in the following operating modes: Lyapunov-based adaptive mode [48], high-order mode [49,50], nonlinear multivariable mode [51], and cascade adaptive mode [52]. Better performance is reported by combining the abovementioned sliding modes with flatness [53] and super-twisting [54,55] control techniques. Lastly but not least, the Model Reference Adaptive Control (MRAC) [56] can better supply the requested power by the air compressor, preventing the surges apparition. Also, compared to aforementioned MPC techniques, MRAC can better mitigate the delay effect as response to load variation. MRAC robustness was highlighted compared to other robust control techniques in [38,57,58]. But the shortest time obtained in handling the nonlinearities makes the sliding control to be a powerful control method in reducing the dynamics and power consumed by the air compressor [50]. It worth mentioning that intelligent control requests the highest computation time and the feedforward control has the simplest implementation [34]. To reduce the response time of the air compressor and the power consumed by the air-feeding subsystem (to less than 10% of FC power), new models and design procedures for air compressors have been proposed [59,60]. Even if the hydrogen-feeding subsystem is faster than the airfeeding subsystem [61,62], both get same attention in controlling the 2

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performed to find the best switching threshold between the operating modes of the basic strategies; (5) the best fuel saving is obtained by real-time searching the optimum of the fuel economy optimization function; (6) the optimization function may be oriented to improve the FC net power, the fuel consumption efficiency, or both, by using an appropriate weighting factor; (7) the flexibility in searching the optimum using two search variables for the basic strategies is preserved for the SW-strategy by safely switching of the control and optimization references, with smooth changes in the fueling flow rates due to the load-based control of fueling regulators that also include slope limiters; (8) using the sFF control-based strategy as reference, the fuel savings is compared with two advanced load-following optimization strategies based on air (S1) and fuel regulators (S2), respectively. The SW-strategy gives the best fuel saving under variable load as follows: (1) 1.63 – times and 3.67 – times higher compared to strategies S1 and S2 for a pulsed load; (2) 2.07 – times and 2.54 – times higher compared to strategies S1 and S2 for a symmetrical stair load. The fuel saving using the SW-strategy for the aforementioned load profiles is 25.9% and 13.7% from the total fuel consumption of the s-FF strategy. So, this SW-strategy could be of interest for researchers working to improve the fuel economy of the Fuel Cell vehicles. The paper is structured as follows. Modeling the Hybrid Power System is presented in Section 2 using the library of Matlab-Simulink®2013, and the Fuel Optimization Strategy proposed in this paper is detailed in Section 3. The fuel economy for constant and variable load is presented in the results section. The last section concludes the paper presenting the main findings and next research.

PBat (MV ) ≅ 0

(1)

The ultracapacitors’ stack energy will compensate the power pulses by charging-discharging the power needed on the DC bus by using, e.g., the control proposed in [7,17]. The mean value (MV) of the power exchanged by the ultracapacitors’ stack during a load pulse is zero. So, the mean value of the power exchanged by the hybrid Energy Storage System (ESS) during a load cycle, pESS , is close to zero.

PESS (MV ) ≅ 0

(2)

So, if the load-following control is implemented for the FC system, the load demand ( pload ) is mainly ensured by the FC system via the DCDC boost converter ( pDC ):

PDC = ηboost PFCnet ≅ Pload

(3)

where ηboost is the energy efficiency of the DC-DC boost converter and PFCnet is the FC net power:

PFCnet ≅ PFC − − Pcm

(4)

The power loss due to the air compressor (Pcm) is given by (5) [60]:

Pcm = Icm·Vcm = (a2 ·AirFr 2 + a1·AirFr + a0)·(b1·IFC + b0)

(5)

using a0 = 0.6a1 = 0.04a2 = −0.00003231b0 = 0.9987 , and b1 = 46. 02 . The dynamics part of the air compressor is usually modeled by a 2nd order system with a 100 Hz natural frequency and 0.7 damping ratio [34,60,111]. Note that (3) is obtained using (2) and the mean value of the power flow balance (6):

CDC udc dudc / dt = pDC + pESS − pload

2. Modeling the hybrid power system

(6)

where a 100 mF capacitor (CDC) will filter the DC voltage, which is stabilized at the reference value of 200 V (uDC ≅ VDC(ref) = 200 V). The CDC capacitance may be chosen in range 100–1,000,000 μF to observe on the DC voltage (200 V) the filtering effect of the low frequency noise and pulsed added on the load (in range 1–10% of rated load) [7,17]. The design is presented in [7,17] for capacitor CDC, ESS, and appropriate control (which is used to mitigate the load pulses via the DC-DC bidirectional power converter of the power device, such as the ultracapacitors stack in this study or a Superconducting Magnetic Energy Storage (SMES) device in [7,17]). As it will be observed in the results section, in addition to the ESS power pulses due to changes in load, the high frequency noise appears on DC voltage due to switching mode control of the DC-DC bidirectional power converter. For a 100 mF capacitance and 5% low frequency noise at load that are used in this

The Hybrid Power System (see Fig. 1) uses a 6 kW/45 V Fuel Cell system as the main energy source, having a nominal power of 6 kW obtained for an Air Flow rate (AirFr) and Fuel Flow rate (FuelFr) of 300 and 50 L per minute [lpm], and 8.3 kW maximum power obtained for an AirFr and FuelFr of 506 lpm and 84 lpm. The FC system will operate in standby-mode for light load in order to avoid complex start-stop procedure and reduce the fuel consumption during these phases. However, the load range considered in this study (from 2 kW to 8 kW) will operate the FC system in normal conditions. The both constant and variable loads are modeled by a current controlled source. If the loadfollowing control is implemented for the FC system to ensure the abovementioned advantages for the battery, a charge-sustained mode will be imposed for the batteries stack:

Fig. 1. Fuel cell hybrid power system. 3

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regulators, and the switching command (SW-command) for the DC-DC boost converter based on the FC system’s inputs (IFC, VFC, Pref(Air), AirFr, and FuelFr) and the load power (Pload), as it will be detailed in next section.

study, the obtained results highlight that the noise on the ESS power and the DC voltage is less than 100 W and 0.1 V, which are acceptable values to analyze fuel economy under the same normal operating conditions. The DC voltage regulation is better to be implemented on the side of the semi-active ESS topology, not on the FC system side, due to the large response time of the FC system to disturbance (load variation) on the DC bus. The 100 Ah/200 V battery (with 10 s constant time) is connected directly on the DC bus. The battery will compensate the minor energy difference given by (3) due to small changing of the FC current compared to the Iref (LFW ) reference given by the load-following control as (7)

IFC ≅ Iref (LFW ) = Pload (MV )/(ηboost VFC )

3. Fuel optimization strategy The subsystems of the Energy Management and Optimization Unit are as follows (see Fig. 2, where the relationships implemented by each subsystem are also mentioned): (1) the optimization subsystem, which will generate the references Iref (GES1) and Iref (GES 2) based on the optimization function (9) and two GES controllers (10); (2) the load-following (LFW) subsystem, which will generate the references Iref (LFW ) based on the LFW controller (7); (3) the boost control subsystem, which will generate the SW-command for the DC-DC boost converter based on 0.1 A hysteresis controller (the classical schemes were used for the DCDC boost converter and its hysteresis controller); (4) the strategy setting block, which is detailed in Fig. 3 and below using (12)–(15). The Energy Management and Optimization Unit will generate the references Iref (Air ) , Iref (Fuel) , and Iref (Boost ) based on the new optimization strategy proposed in this study using the optimization function (9):

(7)

The mean-value based filtering technique is used in this study to smoothen the load power, but other low-pass filtering techniques can be used as well [112]. The small change of the FC current due to the optimization loops proposed for the switching strategy will be explained in next section based on the references Iref(Air) and Iref(Fuel) used for the fueling regulators using (8) [64]:

AirFr =

FuelFr =

60, 000·R·(273+θ)·NC ·Iref (Air ) 4F ·(101,325·Pf (O2) )·(Uf (O2)/100)·(yO2 /100)

f (x , AirFr , FuelFr , PLoad ) = 0.5·PFCnet + kfuel·Fueleff (8a)

where x is the state vector, of the 9th order [34,64] or 6th order [55]. The optimization function (9) combines the FC net power (PFCnet) and the fuel consumption efficiency (Fueleff ≅ PFCnet/FuelFr) using the weighting parameter kfuel [lpm/W] to further improve the fuel economy based on the sensitivity analysis performed in range 0–50 lpm/W. The references Iref (GES1) and Iref (GES 2) used for searching the optimum on the optimization surface f are generated by two GES controllers using the frequency fd = 100 Hz and 2fd = 200 Hz for the dithers in order to improve the dither persistency (by new harmonics obtained as response to the dithers on the nonlinear power characteristic of the FC system) [114]. The GES algorithm operates based on relationships (10):

60, 000·R·(273+θ)·NC ·Iref (Fuel) 2F ·(101,325·Pf (H 2) )·(Uf (H 2)/100)·(xH 2 /100)

(9)

(8b)

where the FC parameters (NC,θ,Uf(H2),Uf(O2),Pf(H2),Pf(O2),xH2,YO2) are set to default values [113], the FC time constant is set to 0.2 s, R = 8.3145 J/(mol K), and F = 96485 As/mol. The optimum searching speed is limited to 100 A/s by the slope limiters included in the fueling regulators for safe operation of the FC system. Thus, the aforementioned response delay of the FC system (which will be given mainly by the 100 A/s slope limiters, 0.2 s FC time constant, and 0.1 s air compressor time constant) causes the FC system’s power to follow with delay the smooth part of the variable load profile (Pload (MV ) ). So, during a pulsed load, the power difference (3) must be dynamically compensated by the 100 F ultracapacitors’ stack from the hybrid ESS. For this, the bidirectional DC-DC buck-boost converter is appropriately controlled by the DC voltage regulator implemented on the stack side of ultracapacitors. The Energy Management and Optimization Unit (see Fig. 2) will generate the control references Iref(Air) and Iref(Fuel) for fueling

y = f (v1, v2), yN = kNy·y

(10a)

̇ yḟ = −ωh ·yf + ωh ·yN , yHPF = yN − yf , yBPF = −ωl ·yBPF + ωl ·yHPF

(10b)

ωh = bh ω,

ω = 2πfd

(10c)

p1 = k1·yGradient

(10d)

ωl = bl ω,

yDM = yBPF ·sd,

̇ yGradient = yDM ,

Fig. 2. Energy management and optimization unit. 4

sd = sin(ωt ),

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Fig. 3. Strategy setting block. Table 1 Fuel savings for keff = 0.

yM =

Pload [kW]

FuelT(sFF) [l]

FuelT(SW) [l]

ΔFuelT(SW) [l]

ΔFuelT(S1) [l]

ΔFuelT(S2) [l]

2 3 4 5 6 7 8

34.02 56.3 74.88 98.6 125.58 158.34 176

33.6 54.6 71.78 93.42 114.02 133.86 132.66

−0.42 −1.7 −3.1 −5.18 −11.56 −24.48 −43.34

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

FuelT(sFF) [l]

FuelT(SW) [l]

ΔFuelT(SW) [l]

ΔFuelT(S1) [l]

ΔFuelT(S2) [l]

2 3 4 5 6 7 8

34.02 56.3 74.88 98.6 125.58 158.34 176

33.46 54.3 71.12 87.18 107.76 128.1 128.28

−0.56 −2 −3.76 −11.42 −17.82 −30.24 −47.72

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

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

FuelT(sFF) [l]

FuelT(SW) [l]

ΔFuelT(SW) [l]

ΔFuelT(S1) [l]

ΔFuelT(S2) [l]

2 3 4 5 6 7 8

34.02 56.3 74.88 98.6 125.58 158.34 176

33.6 54.3 71.22 92.26 112.58 134.44 130.48

−0.42 −2 −3.66 −6.34 −13 −23.9 −45.52

8.56 4 1.1 −6.34 −13 −23.9 −45.52

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

p2 = k2·yM ·sd

(10e) (10f)

The optimization function f uses two searching variables, v1 = AirFr and v2 = FuelFr, based on a sinusoidal dither frequency, sd = sin(ωt ) . The normalization (10a) of the optimization function f is needed in order to use this algorithm for different FC systems as power levels. The band-pass filter (BPF) is implemented using (10b) and the cut-off frequencies ωl = bl ω and ωh = bh ω are defined related to dither frequency fd using the parameters bl and βh (10c). The BPF output is demodulated and the resulted signal ( yDM ) is integrated to obtain the gradient signal ( yGradient ). The search signal ( p1) is proportional with the gradient signal (10d) through the tuning parameter k1. The dither amplitude is modulated with the signal yM for fast locating of the maximum. The location signal ( p2 ) is proportional with the modulated dither ( yM ·sd ) (10e) through the tuning parameter k2 . The output of the GES controller is proportional with the sum of search and location signals through the normalization parameter kNp . The design of the both GES controllers using [115] gives the values of the parameters as follows: the same tuning parameters, k1 = 1 and k2 = 2, are used because the stability of the optimization system is ensured for both frequencies (fd = 100 Hz and 2fd = 200 Hz) of the sinusoidal dithers; using these dithers’ frequencies, the cut-off frequencies of the low-pass filters (LPF) are given by bh = 0.1 and the cutoff frequencies of the high-pass filter (HPF) by bl = 1.5; the normalization gains are kNp = 20 , and kNy = 1/1000 . Considering the performance reported in [114,115], the searching of the optimum can be done in less than 10 periods of 100 Hz dither, which means less than 0.1 s. Thus, compared with the aforementioned delay in response of the FC system (which is much higher than 0.1 s), the searching of the optimum is performed in real-time by the GES controllers. The response delay of the FC system will be given by the dynamic model of the FC system based on smooth function g [34,64]:

Table 3 Fuel savings for kfuel = 50 lpm/W. Pload [kW]

∫ yBPF dt ,

Iref (GES ) = kNp·(p1 + p2 )

Table 2 Fuel savings for kfuel = 25 lpm/W. Pload [kW]

1 · Td

x ̇ = g (x , AirFr , FuelFr , PLoad ), x ∈ X

(11)

The new strategy proposed in this study (called SW-strategy) will be compared with the basic strategies (called as S1-strategy and S2strategy) and the reference strategy based on Static Feed-Forward (sFF) 5

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Fig. 5. Fuel savings in Case 1: variable load with different Pload(AV) values.

control [64] (called sFF-strategy). The sFF-strategy (which is commercially available) uses the settings (12) [64]:

Iref (Fuel) = IFC , Iref (Air ) = IFC , and Iref (boost ) = Iref (LFW )

(12)

The S1 strategy (based on the air regulator) uses the settings (13) (see also Fig. 3):

Iref (Fuel) = IFC + Iref (GES 2), Iref (Air ) = Iref (LFW ), and Iref (boost ) = Iref (GES1) (13) The S2 strategy (based on the fuel regulator) uses the settings (14) (see also Fig. 3):

Iref (Air ) = IFC + Iref (GES 2), Iref (Fuel) = Iref (LFW ), and Iref (boost ) = Iref (GES1) (14) The SW-strategy uses the settings (15) (see also Fig. 3):

Iref (LFW ), if Pload ⩽ Pref Iref (Fuel) = ⎧ IFC + Iref (GES 2), if Pload > Pref ⎨ ⎩

(15a)

IFC + Iref (GES 2), if Pload ⩽ Pref Iref (Air ) = ⎧ I , if Pload > Pref ⎨ ⎩ ref (LFW )

(15b)

Iref (boost ) = Iref (GES1)

(15c)

So, the setting block for the strategies S1 and S2 establishes the references for the fueling regulators (Iref (Air ) and Iref (Fuel) ) and the boost controller (Iref (boost ) ) based on the following inputs: Iref (LFW ) , Iref (GES1) , and Iref (GES 2) . In addition, the SW-strategy supplementary uses the level of the load power (Pload) to implement the switching of strategies S1 and S2 based on the threshold Pref . The value of the threshold Pref will be optimally established for the best fuel economy based on a sensitivity analysis performed for variable load. It is worth mentioning that all strategies implement the load-following for a fair comparison of the total fuel consumption (FuelT = ∫ FuelFr (t ) dt ) during a variable profile of the load demand. The reference Iref (LFW ) (7) will set the FC current close to the value requested by the load demand:

Fig. 4. Fuel savings in case of constant load. (a) keff = 0. (b) keff = 25. (c) keff = 50. Table 4 Fuel savings in Case 1: variable load with different Pload(AV) values.

IFC ≅ Pload (MV )/(ηboost ·VFC )

Pload(AV) [kW]

FuelT(sFF) [l]

FuelT(SW) [l]

ΔFuelT(SW) [l]

ΔFuelT(S1) [l]

ΔFuelT(S2) [l]

2 3 4 5 6

34.14 53.92 75.8 100.62 130.2

34.04 52.88 72.7 89.22 87.66

−0.1 −1.04 −3.1 −11.4 −42.54

10.8 8.74 −0.26 −12.96 −42.54

−0.1 −1.04 −3.84 −9.3 −18.56

(16)

Thus, the fueling regulators in the sFF-strategy will follow the load demand as well. The optimum on the optimization surface is close to the operating point under the sFF-strategy [31], so the searching range for the reference Iref (GES 2) may be limited to ± 10% from the FC current. Thus:

Iref (Fuel) = IFC + Iref (GES 2) ≅ IFC ≅ Iref (LFW )

(17)

Iref (Air ) = IFC + Iref (GES 2) ≅ IFC ≅ Iref (LFW )

(18)

Consequently, the switching between close levels IFC + Iref (GES 2) and 6

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Fig. 6. FCHPS behavior in Case 2: pulsed load. (a) Using the S1-strategy. (b) Using the S2-strategy. (c) Using the SW-strategy.

Iref (LFW ) can be done quickly and safely (due to the slope limiters from the fueling regulators). The 0.1 A hysteresis controller of the DC-DC boost converter has as inputs the FC current (IFC ) and the reference Iref (Boost ) . The strategies S1, S2, and SW use the same setting for the boost reference, Iref (boost ) = Iref (GES1) , so the FC current will follow the searching reference Iref (GES1) : IFC ≅ Iref (boost ) = Iref (GES1)

(20b)

ΔFuelT (SW ) = FuelT (SW ) − FuelT (sFF )

(20c)

4. Results 4.1. Constant load

(19) The fuel consumption during a 12 s cycle of constant load is estimated for the strategies sFF, S1, S2, and SW (with kfuel = 0, 25, and 50 lpm/W, and Pref = 5 kW for SW-strategy) using the Fuel Cell Hybrid Power System (FCHPS) diagram from Fig. 1 with the aforementioned settings. The fuel consumption for different load demand levels (see the first column of Tables 1–3) are recorded (in the 2nd and 3rd column of Table 1–3) only for the strategies sFF and SW, because the same values are obtained for the S2-strategy and S1-strategy for 2 kW ⩽ Pload ⩽ Pref and 8 kW ⩾ Pload > Pref . This is highlighted in color for the fuel savings recorded in the 4th, 5th, and 6th columns of Tables 1–3 for the strategies S1, S2, and SW, respectively. The fuel savings for the SW-strategy are the best values obtained with strategies S1 and S2 using kfuel ≠ 0

Considering (17)–(19), the searching references Iref (Fuel) and Iref (Air ) will closely follow the FC current during the optimization cycle. But relative minor differences between the optimum points (tracked in realtime by the strategies S1, S2, and SW) and the operating point set by the sFF-strategy will mean enough fuel economy for the strategies S1, S2, and SW compared to the sFF-strategy, as it will be shown in next section. The fuel economy for the strategies S1, S2, and SW compared to the sFF-strategy will be estimated using (20):

ΔFuelT (S1) = FuelT (S1) − FuelT (sFF )

ΔFuelT (S 2) = FuelT (S 2) − FuelT (sFF )

(20a) 7

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Fig. 6. (continued)

the weighting parameter kfuel close to 25 [116], thus this value will be considered in next simulations.

and Pref = 5 kW (see Table 2 and 3 for kfuel = 25 lpm/W and kfuel = 50 lpm/W). This value of the threshold Pref is, in fact, on the middle of the considered load range (5 kW = (2 kW + 8 kW)/2). In case of kfuel = 0 (see Table 1), the values obtained for a 5 kW load using strategies S1 and S2 are quite close (5.18 L and 5.24 L, respectively). The fuel economy (ΔFuel ) for strategies S1, S2, and SW using kfuel = 0, 25, and 50 lpm/W is shown in Fig. 4a–c compared to the sFF strategy, highlighting the aforementioned aspect (the best fuel economy value is obtained with the SW-strategy in the entire range of load demand). It is worth mentioning that the best fuel economy is obtained in case kfuel = 25 due to optimal weighting of the terms involved in the optimization function. For example, if FC system operates in nominal condition under a 6 kW load, the FC net power (PFCnet ) is about 6600 W and the fuel consumption efficiency (Fueleff ) is of 140 W/lpm. So, the terms are 0.5PFCnet ≅ 3300 W and kfuel·Fueleff ≅ 3500 W, being close one to another. On the other hand, the best fuel economy is obtained in case kfuel = 0 when the optimization function remains to be the FC net power and the optimum is usually called as Maximum Efficiency Point (MEP). The sensitivity analysis highlighted the best fuel economy for a value of

4.2. Variable load demand 4.2.1. Case 1: Variable load with different Pload(AV) values The first case of variable load considers a 12 s cycle using the following levels of power on each 4 s: 0.75 ⋅ Pload(AV), 1.25 ⋅ Pload(AV), and 1.00 ⋅ Pload(AV). So, the average value (AV) of variable load is Pload(AV) and the used values are recorded in the first column of Table 4. The power levels are 4.5, 7.5, and 6 kW for Pload(AV) = 6 kW, so the maximum load value (7.5 kW) requires the maximum power from the FC system (≅8.3 kW) if ηboost = 90%. The power levels are 1.5, 2.5, and 2 kW for Pload(AV) = 2 kW, so the minimum load value (1.5 kW) requires about 1.7 kW from the FC system (1.5 kW/0.9 ≅ 1.7 kW), which is higher than the standby-mode threshold (usually set to 0.5 kW). Choosing the same rule as for constant load, the threshold Pref may be chosen in the middle of the load range as follows:

(0.5 + 7.5)/2 = 4 kW ⩽ Pref < 4.5 kW = (1.5 + 7.5)/2 8

(21)

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Fig. 6. (continued)

the following plots: the next two plots represent the FC net power (PFCnet ) and the ESS power (PESS ); the other next two represent the fueling flow rates (AirFr and FuelFr); FuelT is represented in the 6th plot; Fueleff and ηsys = PFCnet / PFC are represented in the last two plots. The following findings are noteworthy: (1) using the S1-strategy, the load-following control is applied to the AirFr regulator, so AirFr will follow the load’s pulsed profile (see the 4th plot in Fig. 6a); (2) using the S2-strategy, the load-following control is applied to the FuelFr regulator, so the FuelFr will follow the load’s pulsed profile (see the 5th plot in Fig. 6b); (3) using the SW-strategy, during the rising or falling edge of the load impulse, the load-following mode switches based on rules (15) and this can be seen in the 4th plot (AirFr) and 5th plot (FuelFr) of Fig. 6c; the switching between the close levels IFC + Iref (GES 2) and Iref (LFW ) can be done quickly and safely due to the slope limiters from the fueling regulators (see the minor spikes in AirFr and FuelFr); (4) the battery operates in charge-sustained mode due to the use of load-following control in all strategies (see the 3rd plot in Fig. 6); (5) the power flow balance is compensated by the ultracapacitors’ stack in all strategies (see the 3rd plot in Fig. 6); (6) the range for Fueleff and ηsys is from 96 to 145 W/lpm (see the 7th plot in Fig. 4) and from 86 to 95%

Table 5 Fuel savings in Case 2: pulsed load. Pload(pulse) [kW]

FuelT(sFF) [l]

FuelT(SW) [l]

ΔFuelT(SW) [l]

ΔFuelT(S1) [l]

ΔFuelT(S2) [l]

3/7 kW

105.9

78.5

−27.4

−16.79

−7.43

In this case, the SW-strategy will operate as the S2-strategy for light load cycles (of Pload(AV) = 2 kW and 3 kW) and as the S1-strategy for the maximum load cycle of Pload(AV) = 6 kW (see the values highlighted in Table 4). When the S2-strategy operates specifically by switching the load-following mode in concordance with the rules (15), the fuel economy is between the fuel economy obtained with strategies S1 and S2 for load cycles of Pload(AV) = 4 kW and 5 kW (see Fig. 5). The S2strategy operates specifically in case of pulsed load. 4.2.2. Case 2 of pulsed load The pulsed load switches at each 3 s between the levels of 3 kW and 7 kW (see the 1st plot in Fig. 6). The behavior of the FCHPS using the strategies S1 (Fig. 6a), S2 (Fig. 6b), and SW (Fig. 6c) is highlighted in 9

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Fig. 7. FCHPS behavior in Case 3: variable load using a symmetrical stair as profile. (a) Using the S1-strategy. (b) Using the S2-strategy. (c) Using the SW-strategy with Pref = 4.5 kW .

about 13.72% from FuelT (sFF ) (100⋅39.3 L/286.5 L ≅ 13.72%). Also, it is worth mentioning that the fuel economy for the SW-strategy is 2.07 – times and 2.54 – times higher compared to strategies S1 and S2. Fuel savings are shown in Fig. 8 for strategies SW, S1 and S2 compared to the sFF-strategy. The fuel economy using the SW-FLW strategy with Pref = 2.5 kW is very close to that obtained using the Air-FLW strategy; the minor difference in the fuel saving for SW-strategy with Pref = 2.5 kW compared to S1-strategy is done during starting phase by using the S2-strategy until Pload > Pref = 2.5 kW . The FCHPS behavior using the strategies S1, S2 and SW is shown in Fig. 7a–c, considering the same variables as in Fig. 6. Apart from the aforementioned findings in case of a pulsed load, it is worth mentioning the additional findings: (7) the optimum's search for Pload > Pref = 4.5 kW is done via the fuel regulator for both S1 and SW strategies (see the shape of FuelFr in the 5th plot of Fig. 7a and c, which is almost the same); (8) power flow imbalance on the DC bus will be compensated by the battery, which exchanges power (see the 3th plot in Fig. 7a and c), but SOC is the same at the end; (9) the optimum's search for Pload < Pref = 4.5 kW is done via the air regulator for both S2 and SW strategies (see the shape of AirFr in the 4th plot of Fig. 7b and c,

(see the 8th plot in Fig. 4); so, as it was mentioned before, the terms kfuel·Fueleff and 0.5·PFCnet have comparable values for kfuel = 25; furthermore, a new optimization function f = ηsys + kfuel·Fueleff could be defined and tested for best fuel economy. The fuel economy for the SW-LFW strategy compared to the sFF strategy is recorded in Table 5 and this represents about 25.87% from FuelT (sFF ) . Also, it is worth to mention that the fuel economy for the SWstrategy is 1.63 – times and 3.67 – times higher compared to strategies S1 and S2. Finally, it is obvious that using any threshold Pref between the pulsed load levels (3 kW < Pref < 7 kW ) the same results are obtained. But for a variable load in the entire range of load the optimal threshold Pref must be validated established based on a sensitivity analysis. So, in case 3, the variable load uses a symmetrical stair as profile. 4.2.3. Case 3: Variable load using a symmetrical stair as profile The symmetrical stair is presented in the 1st plot of Fig. 7. The threshold Pref will be selected between the stair levels (which are 3, 4, 5, 6, and 7 kW), as it is mentioned in the first column of Table 6. The fuel economy is recorded in Table 6 for strategies SW, S1 and S2. The threshold Pref = 5.5 kW gives the best fuel saving for the SW-strategy of 10

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Fig. 7. (continued)

this being highest for maximum load; (3) the best percentage (which means the best fuel economy) in the aforementioned ranges are obtained for keff = 25. The fuel savings (ΔFuelT(SW) j ) compared to the sFF-strategy in Case j = 1 (variable load with Pload(AV) = 2–6 kW), j = 2 (pulsed load), and j = 3 (symmetrical stair for the load and Pref = 5.5 kW) are recorded in Table 8 based on the data from the previous tables. The percentage increases are noted in the last three columns of Table 7. The nonlinear fuel economy increase with the load level is also observed for a variable load (j = 1). It is worth to mention that the fuel economy is almost double for a 3 kW/7 kW pulsed load compared to a load with symmetrical stair profile (which increases from 3 kW to 7 kW and then decreases to 3 kW, with same 1 kW step) due to the nonlinear increase of fuel economy with the load level:

which is almost the same during the starting phase or after the spike); (10) the batteries’ stack is strictly operated in charge-sustained mode using the S2-strategy (see the 3rd plot in Fig. 7b). Beside the strategies S1 and S2, the performance of the SW-strategy compared to the sFF strategy will be commented in next section. The sFF strategy is the most used as a reference strategy due to availability of the experimental or simulation results (this strategy has been applied to the FC systems that are commercially available or this strategy is easy to implement for a specific FC system using the settings (12) [64]).

5. Discussion Fuel savings (ΔFuelT(SW) A / B / C ) of the SW-strategy compared to the sFF-strategy (FuelT(sFF)) are recorded in Table 7 under constant load for case A (keff = 0), B (keff = 25), and C (keff = 50) based on the data from the previous tables. The percentage increases are noted in the last three columns of Table 7. It is worth to mention the following: (1) the percentage increase depends on the load level, e.g., being of about 1.2–1.6%, 4–5%, 10–15%, and 25–27% for load levels of 2 kW (light load), 4 kW (average load), 6 kW (rated load), and 8 kW (maximum load); (2) the fuel economy increase with the load level is not linear,

ΔFuelT(SW)2 = 25. 87%, FuelT(sFF)

ΔFuelT(SW)3 = 13. 72% FuelT(sFF)

(22)

A percentage of 13.72% means a fuel economy of 39.3 L/ 20 s = 19.65 lpm, which represents about a quarter of the maximum value of the FuelFr (84.5 lpm) requested at maximum load. The recommended methodology to implement the SW-strategy may 11

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Fig. 7. (continued) Table 6 Fuel savings in Case 3: variable load using a symmetrical stair as profile. Pref [kW]

FuelT(sFF) [l]

FuelT(SW) [l]

Δ FuelT(SW) [l]

Δ FuelT(S1) [l]

Δ FuelT(S2) [l]

2.5 3.5 4.5 5.5 6.5

286.5 286.5 286.5 286.5 286.5

267.1 257.8 251.3 247.2 252.8

−19.4 −28.7 −35.2 −39.3 −33.7

−19 −19 −19 −19 −19

−15.5 −15.5 −15.5 −15.5 −15.5

be as follows: (1) Firstly, because the load demand can have very high dynamics, this must be filtered before being compared with the threshold Pref and a 300 W hysteresis controller is recommended instead of a simple comparison; (2) the preliminary validation of the fuel savings for strategies S1 and S2 must be performed using a Fuel Cell emulator and an easy to implement searching algorithm; (3) the fueling values will be considered for the look-up table-based SW-strategy to implement the load-following mode for the fueling regulators; (4) the fuel savings obtained using a Fuel Cell emulator will be compared with those using a Fuel Cell system; (5) the fuel savings could be improved changing the threshold Pref , using an advanced searching algorithm

Fig. 8. Fuel saving in Case 3: variable load using a symmetrical stair as profile

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Table 7 Fuel savings compared to the sFF-strategy under constant load and keff = 0, 25, and 50 lpm/W (case A, B, and C). Pload

FuelT(sFF)

ΔFuelT(SW) A

ΔFuelT(SW) B

ΔFuelT(SW) C

[kW]

[l]

[l]

[l]

[l]

[%]

[%]

[%]

2 3 4 5 6 7 8

34.02 56.3 74.88 98.6 125.58 158.34 176

−0.42 −1.7 −3.1 −5.18 −11.56 −24.48 −43.34

−0.56 −2 −3.76 −11.42 −17.82 −30.24 −47.72

−0.42 −2 −3.66 −6.34 −13 −23.9 −45.52

1.23 3.02 4.14 5.25 9.21 15.46 24.63

1.65 3.55 5.02 11.58 14.19 19.10 27.11

1.23 3.55 4.89 6.43 10.35 15.09 25.86

1 1 1 1 1 2 3

(Pload(AV) = 2) (Pload(AV) = 3) (Pload(AV) = 4) (Pload(AV) = 5) (Pload(AV) = 6) (pulsed load) (stair /\)

FuelT(sFF)

ΔFuelT(SW)j

[l]

[l]

[%]

34.14 53.92 75.8 100.62 130.2 105.9 286.5

−0.1 −1.04 −3.1 −11.4 −42.54 −27.4 −39.3

0.29 1.93 4.09 11.33 32.67 25.87 13.72

ΔFuelT(SW) B FuelT(sFF)

ΔFuelT(SW) C FuelT(sFF)

reference strategy on a load with pulse and stair profiles, respectively. The switching strategy proposed in this paper greatly improves the fuel saving of the Fuel Cell system and increases the battery’s lifetime, so it is of high interest for the Fuel Cell vehicles.

Table 8 Fuel savings compared to the sFF-strategy in Case j = 1 (variable load with Pload(AV) = 2–6 kW), 2 (pulsed load), and 3 (symmetrical stair for the load and Pref = 5.5 kW). Case

ΔFuelT(SW) A FuelT(sFF)

ΔFuelT(SW) j FuelT(sFF)

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 of Romania, CNCS/CCCDI-UEFISCDI 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. Appendix A. Supplementary material

(such as that proposed in this paper), implementing the switching strategy based on a hysteresis controller, and so on.

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.apenergy.2019.113449.

6. Conclusion

References

A fuel saving strategy using real-time switching of the fueling regulators in the Proton Exchange Membrane Fuel Cell System is compared with two basic load-following strategies, based on the air and fuel regulators, respectively, and the reference strategy based on static FeedForward control. The fuel economy for dynamic load in entire load range is obviously better for the switching strategy compared to basic strategies due to switching of the fueling regulators for the best fuel economy at a given load. The load-following strategy based on the air regulator gives the best fuel economy for high-load levels and the one based on the fuel regulator is better adjusted for low-load levels. Consequently, the optimal threshold has been found based on sensitivity analysis to be around the middle of the loading range. So, for a variable load across the entire range, the load-following mode is safely switched between the fueling regulators in order to continuously operate the battery in charge-sustained mode, thus maintaining the aforementioned basic strategies’ advantages for the switching strategy as well. The fueling regulator which does not operate in the load-following mode is optimally controlled in the fuel economy optimization loop. The second optimization loop controls the DC-DC boost converter. Thus, flexible real-time searching on the optimization surface is performed to find the fuel economy optimum. So, the principal findings of this paper are the following: (1) a new switching strategy is proposed to improve fuel savings compared to other strategies considered in this study; (2) the excellent advantages (increased lifetime and reduced size) due to the charge-sustained mode implemented for the battery by using the switching strategy of the loadfollowing mode for air and fuel regulators; (3) compared to basic strategies, the fuel saving is 1.63 – times and 3.67 – times higher for a pulsed load, and 2.07 – times and 2.54 – times higher for a load having a symmetrical stair profile over the entire loading range; (4) the fuel saving is 25.9% and 13.7% of the total fuel consumption by using the

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