Improving the Fuel Economy and Battery Lifespan in Fuel Cell / Renewable Hybrid Power Systems Using the Power-Following Control of the Fueling Regulators

: In this study, the performance and safe operation of the fuel cell (FC) system and battery-based energy storage system (ESS) included in an FC / ESS / renewable hybrid power system (HPS) is fully analyzed under dynamic load and variable power from renewable sources. Power-following control (PFC) is used for either the air regulator or the fuel regulator of the FC system, or it is switched to the inputs of the air and hydrogen regulators based on a threshold of load demand; these strategies are referred to as air-PFC, fuel-PFC, and air / fuel-PFC, respectively. The performance and safe operation of the FC system and battery-based ESS under these strategies is compared to the static feed-forward (sFF) control used by most commercial strategies implemented in FC systems, FC / renewable HPSs, and FC vehicles. This study highlights the beneﬁts of using a PFC-based strategy to establish FC-system fueling ﬂows, in addition to an optimal control of the boost power converter to maximize fuel economy. For example, the fuel economy for a 6 kW FC system using the air / fuel-PFC strategy compared to the strategies air-PFC, fuel-PFC, and the sFF benchmark is 6.60%, 7.53%, and 12.60% of the total hydrogen consumed by these strategies under a load proﬁle of up and down the stairs using 1 kW / 2 s per step. For an FC / ESS / renewable system, the fuel economy of an air / fuel-PFC strategy compared to same strategies is 7.28%, 8.23%, and 13.43%, which is better by about 0.7% because an FC system operates at lower power due to the renewable energy available in this case study.


Introduction
A report by the Intergovernmental Panel on Climate Change (IPCC) noted that so far the global temperature has risen by 1 • C due to warming by 0.2 • C per decade and may reach a critical value of 2 • C by the 2060s if the proposed environmental policies will not be implemented urgently worldwide [1].
through several means, such as reducing the fuel [24] and/or energy consumption [25] and maximizing energy efficiency [26].
An EMS aims at finding an optimal solution [27] for the specific system by considering several or all the mentioned aspects [19,20,[28][29][30]. Especially in the last decade, more attention has been paid to different topologies of multisource hybrid electric power systems used in mobility energy supply [31] and in stationary and portable power generation [32]. The major challenges faced by the ongoing research involve the integration of multiple and often conflicting objectives of power management strategy optimization in a real-time control system [33]. The EMS of a fuel cell hybrid power systems should aim at improving the system design (topology, dimensions, weight etc.), performances (fuel consumption, energy efficiency, lifespan, resilience, etc.) and cost, and at finding an optimal solution for the specific system by considering aforementioned objectives.
The main objective of this paper is to carry out a systematic evaluation of four fuel economy EMSs, three of which involves power-following control (PFC). These EMSs are referred to as air/fuel-PFC, air-PFC, fuel-PFC, and static feed-forward (sFF) strategies, and they are assessed in order to identify the best and safest strategy compared to the commercial standard based on the static feed-forward (sFF) control. For this, indicators such as fuel economy and oxygen excess ratio (OER) are used to evaluate the efficient and safe operation of an FC system and battery using power-following control (PFC) for the air regulator or the fuel regulator of the FC system, either separately or switched. The innovative switched mode proposed for the air/fuel-PFC strategy is comparatively analyzed with PFC-based strategies that control separately the air regulator or the fuel regulator of the FC system in order to highlight the fuel economy obtained for FC systems and FC/renewable hybrid power systems (HPSs). Net FC power is generated by PFC-based strategies for battery operation in sustained charging mode, with increased battery lifespan and cost less maintenance of the HPS.
Following this objective, the structure of the paper is as follows. The first section details the model of an FC/renewable HPS, a PFC-based fuel economy EMS, and the involved control and optimization loops. The second section presents and comments on the results obtained under dynamic load and variable power from renewable energy sources (RESs). The last two sections discuss the results and conclude the paper respectively.

Materials and Methods
The fuel cell (FC) system, battery/ultracapacitor (UC) hybrid ESS, and FC/ESS/renewable hybrid power system (HPS) represented in Figure 1 are analyzed under dynamic load and variable power from renewable energy sources (RESs) respectively, with the preliminary results under dynamic load presented in [34]. The load profile that was chosen was up and down the stairs with levels changed at every 2 ms using a step of 1 kW (see P Load at the top of Figure 2). The renewable energy profile (see P RES in the 2nd plot of Figure 2) was generated by adding the power from two renewable sources, such as the power generated by a photovoltaic park and a wind turbine farm (see P RES1 and P RES2 in the 3rd plot of Figure 2), and the random profile with 1 kW peak (P RES3 in the 4th plot of Figure 2): (1) Figure 1. Fuel cell/energy storage system (FC/ESS) renewable hybrid power system (HPS) [34]. Figure 1. Fuel cell/energy storage system (FC/ESS) renewable hybrid power system (HPS) [34].
where boost η is the efficiency of the DC-DC converter; FC P and ( ) FC net P is the FC-generated power and FC net power, respectively; and cm P represents the power losses of the air compressor that is modeled using (6) and a 2nd order dynamic system with a 100 Hz natural frequency and 0.7 damping ratio [39,40]: A PFC-based strategy of FC net power can be implemented through the boost controller, the air regulator, and the fuel regulator, using the strategy settings block to set an , respectively (see the EMS unit in Figure 1). The fuel economy-based strategy can be implemented through optimal control based on the global extremum seeking (GES) controller [41][42][43] (see Figure 1) that generates the  A 6 kW FC system (with the slope limits of 100 A/s for the fueling regulators and a 0.2 s time constant) was used as the backup energy source to mitigate the variability of the power flow p RES from the renewable energy sources (RESs) under power-following control (PFC) implemented in the energy management strategy (EMS) unit. This PFC-based strategy operates the battery stack in the charge-sustained mode, avoiding frequent charge-discharge cycles, as is shown below, which will obviously lead to an increase in battery lifespan.
The power flow balance (2) is sustained by a 100 Ah battery with a 100 F ultracapacitor energy storage system (ESS) using a semi-active ESS topology, having the battery on a 200 V DC bus and the ultracapacitors via a bidirectional DC-DC buck-boost converter (see Figure 1): where C DC is the capacitor connected on the DC bus. The power difference on the DC bus, p Load − p RES , will be mainly generated by the FC system due to the PFC-based strategy implemented for the fueling regulators. Consequently, the mean value (MV) of the battery's power exchanged with the DC bus is almost zero, except the abrupt transition on load (as it is the case of the load profile chosen in this study):

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This charging mode is very useful in operating a battery stack, increasing the battery lifespan, reducing its size (capacity) and maintenance costs [35,36]. Due to the 20 s time constant of the battery used in simulation, the dynamic compensation of the power balance (2) will be ensured by capacitor C DC of 0.01 F and by 100 F ultracapacitors via the bidirectional DC-DC buck-boost converter controlled by DC voltage regulation loop [37,38].
Thus, considering (3), the MV of the power balance (2) can be written as (4): The FC power (P FCgen ) that is generated on the DC bus is the FC net power (P FCnet ): where η boost is the efficiency of the DC-DC converter; P FC and P FC(net) is the FC-generated power and FC net power, respectively; and P cm represents the power losses of the air compressor that is modeled using (6) and a 2nd order dynamic system with a 100 Hz natural frequency and 0.7 damping ratio [39,40]: where a 0 = 0.6, a 1 = 0.04, a 2 = −0.00003231, b 0 = 0.9987, and b 1 = 46.02. Considering (4) and (5), the PFC reference (I re f (PFC) ) is given by (7): A PFC-based strategy of FC net power can be implemented through the boost controller, the air regulator, and the fuel regulator, using the strategy settings block to set an I re f (PFC) reference to one of their references, I re f (Boost) , I re f (Air) , or I re f (Fuel) , respectively (see the EMS unit in Figure 1). The fuel economy-based strategy can be implemented through optimal control based on the global extremum seeking (GES) controller [41][42][43] (see Figure 1) that generates the I re f (GES) reference by maximizing the multicriteria optimization function (8) that mixes the FC net power (P FCnet ) and the fuel consumption efficiency (Fuel eff = P FCnet /FuelFr): where vector x represents the FC state variables [44,45]; and GES variables v 1 = AirFr and v 2 = FuelFr are the air flow rate (AirFr) and the fuel flow rate (FuelFr), respectively, given by (9) [46]: [47]. P Load and P RES act as a perturbation during the GES-based search of the optimal point, depending on the weighting parameter k fuel , which can be set at zero to maximize P FCnet [48] or at 25 (lpm/W) to reduce the fuel consumption, i.e., Fuel T = FuelFr(t)dt [49,50].
In this study, the DC-DC boost converter was optimally controlled to improve fuel economy, and the PFC-based strategy of the FC net power was implemented through the air regulator or the fuel regulator using the strategies air-PFC or fuel-PFC, respectively, or by both fueling regulators in the switching (SW) strategy (called air/fuel-PFC) that switches the I re f (PFC) reference to the air regulator or the fuel regulator using a power threshold of 5.5 kW for the power requested on the DC bus (P DCreq = P Load − P RES > 0). Thus, the strategies air-PFC, fuel-PFC, and air/fuel-PFC are set by (10a), (10b), and (10c) respectively: The diagram of FC/ESS renewable HPS using the strategies air-PFC, fuel-PFC, and air/fuel-PFC is presented in Figure 3, and k RES sets the level of RES power on the DC bus. If k RES is zero (P RES = 0), then the case of the FC system will be analyzed. If k RES is different to zero, then the case of the FC/renewable HPS will be analyzed. In the last case, if P RES > P Load , then the excess of power (P RES − P Load > 0) will supply an electrolyzer to produce hydrogen.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 23 The command of the DC-DC boost converter (the signal SW command in Figure 1) is obtained using a 0.1 A hysteresis controller with inputs FC I and The GES controller shown in Figure 1 has the following operational relationships [41][42][43]: The performance and safe operation of FC/renewable HPS using the strategies air-PFC, fuel-PFC, and air/fuel-PFC is highlighted and compared to the static feed-forward (sFF) control sets by (11) [43]: where I FC is the FC current.
Appl. Sci. 2020, 10, 8310 8 of 23 The command of the DC-DC boost converter (the signal SW command in Figure 1) is obtained using a 0.1 A hysteresis controller with inputs I FC and I re f (boost) .
The GES controller shown in Figure 1 has the following operational relationships [41][42][43]: where the first harmonic of the FC power (y BPF ) is approximated using a band-pass filter with the cut-off frequencies ω l = b l ω and ω h = b h ω, where β l = 1.5 and β h = 0.1. This is demodulated with a sinusoidal dither, s d = sin(ωt), and integrated to obtain the search gradient (y Gradient ), where ω = 2π f d and f d = 100 Hz. The search and location signals (p 1 and p 2 ) are tuned using k 1 and k 2 to speed up tracking of the optimum. In this study, k 1 = 1 and k 2 = 2, and the input and output are normalized using k Ny = 1/1000 and k Np = 20.
It is worth mentioning that after the transitory regime, the stationary values are almost zero [40], resulting in a negligible ripple of FC power and a 99.9% tracking accuracy [43].
OER (λ O 2 ) is used as an indicator of safe operation of FC/renewable HPS [51]: where c 0 = 402.6, c 1 = 8. 38. The fuel consumption measured in liters [l] is the performance indicator. This is estimated during 20 s from one minute using (14): Because FuelFr is measured in liters per minute (Lpm), a gain of 1/3 (= 20 s/60 s) is requested to compute the fuel consumption (Gain Fuel_T in Figure 3).

Results
The performances of the strategies air-PFC, fuel-PFC, and air/fuel-PFC are compared to the sFF benchmark, starting with the FC system and then with the FC/renewable HPS.

Fuel Consumption
The behavior of the FC system using the strategies sFF, air-PFC, fuel-PFC, and air/fuel-PFC is presented in Figures 4-7 under the same load profile (see the 1st plot).      OER varies under the recommended limits for all strategies (see the 2nd plot), but minor The plots of Figures 4-7 represent the same waveforms as follows: the 1st plot shows the DC load profile; the 2nd plot, OER; the 3rd plot, ESS power; the 4th and 5th plots, AirFr and FuelFr, respectively; the 6th plot, Fuel T ; the 7th plot, Fuel e f f ; and the 8th plot, η sys = P FCnet /P FC .
OER varies under the recommended limits for all strategies (see the 2nd plot), but minor differences appear due to the specific operation under each strategy (see the next sections). P ESS is almost zero (see the 3rd plot), except the load transitions, validating the charge-sustaining mode of the battery.
The load profile is followed by the both AirFr and FuelFr in the sFF strategy, then by AirFr and FuelFr in the strategies air-PFC and fuel-PFC respectively, and by FuelFr and then by AirFr in the air/fuel-PFC switching strategy (see plots 4 and 5).
The fuel consumption of the FC system using the strategies sFF, air-PFC, fuel-PFC, and air/fuel-PFC is mentioned in Table 1 (see the 6th plot). The last two plots show the variations of the performance indicators Fuel e f f and η sys . It should be noted that the ranges of variation for Fuel e f f and η sys using the air/fuel-PFC strategy are the same as those using the strategy air-PFC for P Load > P re f and the strategy fuel-PFC for P Load ≤ P re f , respectively. Table 1. Fuel consumption of the FC system using the strategies sFF, air-PFC, fuel-PFC, and air/fuel-PFC [34]. The fuel economy of the strategy air/fuel-PFC compared to the strategies sFF, air-PFC, and fuel-PFC is estimated in Table 2 Table 2. Fuel economy of the FC system using strategy air/fuel-PFC compared to the strategies sFF, air-PFC, and fuel-PFC.

FC Net Power and Electrical Efficiency
FC electrical efficiency, η sys = P FCnet /P FC , varied in the range of 82% to 92% for all used strategies analyzed in this paper (Figure 8). The low and high values were obtained for large and light loads, respectively. Higher values can be obtained using k fuel = 0 in the optimization function (9) because the objective is the maximization of P FCnet . The air/fuel-PFC strategy uses the power threshold P re f to switch between the strategies air-PFC and fuel-PFC.
FC electrical efficiency, sys FCnet FC P P η = , varied in the range of 82% to 92% for all used strategies analyzed in this paper (Figure 8). The low and high values were obtained for large and light loads, respectively. Higher values can be obtained using kfuel = 0 in the optimization function (9) because the objective is the maximization of FCnet P . The air/fuel-PFC strategy uses the power threshold ref P to switch between the strategies air-PFC and fuel-PFC.  Thus, P FCnet levels using the air/fuel-PFC strategy for P Load ≤ P re f are close to those of the fuel-PFC strategy and different than those of the air-PFC strategy, especially at light load (see Figure 8). However, the P FCnet levels using the air/fuel-PFC strategy for P Load > P re f and the air-PFC strategy are slightly different due to different initial conditions for the FC system operated under the strategies air/fuel-PFC and air-PFC. The P FCnet levels using the sFF strategy are very close to those using the air/fuel-PFC strategy.

Oxygen Excess Ratio
The OER of the FC system using the strategies sFF, air-PFC, fuel-PFC, and air/fuel-PFC is shown in Figure 9.

Oxygen Excess Ratio
The OER of the FC system using the strategies sFF, air-PFC, fuel-PFC, and air/fuel-PFC is shown in Figure 9. to those of the strategies fuel-PFC and sFF, but different than those of the air-PFC strategy (see Figure  9). For all the strategies analyzed, the OER levels for the FC system operated near the maximum Figure 9. Oxygen excess ratio [34].
The air/fuel-PFC strategy uses the power threshold P re f to switch between the strategies air-PFC and fuel-PFC. In this way, the OER levels using the air/fuel-PFC strategy for P Load ≤ P re f are close to those of the strategies fuel-PFC and sFF, but different than those of the air-PFC strategy (see Figure 9). For all the strategies analyzed, the OER levels for the FC system operated near the maximum power were close to each other. In any case, for any level and transition in the load profile, the OER varies within the safe limits (from 2.3 to 4), ensuring a safe operation of the FC power system [43,45,50].
The results obtained for the FC system and battery stack are validated in next section for FC/renewable HPS.

Fuel Consumption
The behavior of the FC/renewable HPS using the strategies sFF, air-PFC, fuel-PFC, and air/fuel-PFC are presented in Figures 10-13 under the same load profile (see the 1st plot), but using the profile of renewable energy presented in Figure 2 and is seen here in the 2nd plot.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 23 Figure 12. FC/renewable HPS behavior using the fuel-PFC strategy.   It can be seen that the structure of the plots in Figures 10-13 are the same as that of Figures 4-7, with the exception of adding RES power in the 2nd plot, being as follows: the 1st plot shows the DC load profile; the 2nd plot, RES power; the 3rd plot, OER; the 4th plot, ESS power; the 5th and 6th It can be seen that the structure of the plots in Figures 10-13 are the same as that of Figures 4-7, with the exception of adding RES power in the 2nd plot, being as follows: the 1st plot shows the DC load profile; the 2nd plot, RES power; the 3rd plot, OER; the 4th plot, ESS power; the 5th and 6th plots, AirFr and FuelFr, respectively; the 7th plot, Fuel T ; the 8th plot, Fuel e f f ; and the 9th plot, η sys = P FCnet /P FC . The OER of the FC/renewable HPS under all strategies varies in a large range (from 2.3 to 7) compared to the OER of the FC system (from 2.3 to 4), but it still is under recommended limits (see the 3rd plot).
It can be seen that P ESS still varies around zero but is noisy due to the random part added to renewable energy (see the 4th plot), thus validating the charge-sustaining mode of the battery in the case of FC/renewable HPS.
The power profile P Load − P RES > 0 is followed by the both AirFr and FuelFr in the sFF strategy, by AirFr and FuelFr in the strategies air-PFC and fuel-PFC respectively, and by FuelFr and then by AirFr in the air/fuel-PFC switching strategy (see plots 5 and 6). If P RES − P Load > 0, then the FC system operates in standby mode, and the excess of power (P RES − P Load ) will supply an electrolyzer to produce hydrogen.
The fuel consumption of the FC system using the strategies sFF, air-PFC, fuel-PFC and air/fuel-PFC is mentioned in Table 3 (see the 7th plot). The last two plots show the values of the performance indicators Fuel e f f and η sys . It should be noted that the values of Fuel e f f and η sys are lower due to the standby mode of the FC system operation in the case where RES power exceeds the load demand (P RES > P Load ). Table 3. Fuel consumption of FC/renewable HPS using the strategies sFF, air-PFC, fuel-PFC, and air/fuel-PFC. The fuel economy of the strategy air/fuel-PFC compared to the strategies sFF, air-PFC, and fuel-PFC is estimated in Table 4 using (16):

FC Net Power and Electrical Efficiency
The P FCnet levels using all strategies (see Figure 14) vary from about 0.1 kW (standby operating mode) to 6 kW (nominal operating mode). To avoid having many start-stop occurrences in the FC system, the standby operating mode was chosen, but an appropriate strategy to supply the electrolyzer during the stages when RES Load P P > must be used.

Oxygen Excess Ratio
Because FCnet P varies in the range of 0.1 to 6 kW for the FC system and from 2.8 to 6.5 kW for FC/renewable HPS, the OER will vary in a large range for FC/renewable HPS (from about 2.3 to 7) but is still within the safe limits (see Figure 15). To avoid having many start-stop occurrences in the FC system, the standby operating mode was chosen, but an appropriate strategy to supply the electrolyzer during the stages when P RES > P Load must be used.

Oxygen Excess Ratio
Because P FCnet varies in the range of 0.1 to 6 kW for the FC system and from 2.8 to 6.5 kW for FC/renewable HPS, the OER will vary in a large range for FC/renewable HPS (from about 2.3 to 7) but is still within the safe limits (see Figure 15). must be used.

Oxygen Excess Ratio
Because FCnet P varies in the range of 0.1 to 6 kW for the FC system and from 2.8 to 6.5 kW for FC/renewable HPS, the OER will vary in a large range for FC/renewable HPS (from about 2.3 to 7) but is still within the safe limits (see Figure 15).

Discussion
The results were comparatively analyzed in section of the results for the FC system and the FC/renewable HPS using the strategies sFF, air-PFC, fuel-PFC, and air/fuel-PFC; here, we summarize and discuss these further in the frame of the working hypotheses.

Discussion
The results were comparatively analyzed in section of the results for the FC system and the FC/renewable HPS using the strategies sFF, air-PFC, fuel-PFC, and air/fuel-PFC; here, we summarize and discuss these further in the frame of the working hypotheses.
The fuel consumption using the strategies sFF, air-PFC, fuel-PFC, and air/fuel-PFC for the FC system and the FC/renewable HPS is summarized in Table 5. It is worth mentioning that the lowest fuel consumption was obtained using the air/fuel-PFC strategy for both FC-based power systems and then by using the strategies air-PFC, fuel-PFC, and sFF (see the first two rows of Table 5).
In addition, it should be noted that the difference in the fuel consumption for the FC system and FC/renewable HPS, Fuel T(strategy) − Fuel Renewable T(strategy) , represents about 57% of the fuel consumption of the FC system using that strategy (see the last row of Table 5).
This difference results from operating the FC system from the FC/renewable HPS at low power due to contribution of RES power on the load demand. The profiles of the load demand and RES power shown in Figure 2 have a MV of 5 kW and about 2.5 kW, justifying the 57% reduction in the fuel consumption for the FC system and FC/renewable HPS.
The fuel economy strategies for the FC/renewable HPS compared to the FC system are better by about 0.7% (see last row of Table 6) due to the same reason (FC system operates at lower power due to available renewable energy on the DC bus).

Conclusions
This paper performed a systematic evaluation of the strategies referred to as air/fuel-PFC, air-PFC, fuel-PFC, and sFF, with the latter being a commercial benchmark used in the analysis of the obtained results. The following findings resulted for FC system (FC/ESS/RES HPS with P RES = 0):

•
The four strategies mentioned above were analyzed as the performance and safe operation of the FC system and battery pack using indicators such as fuel economy and OER.

•
Following the analysis, the fuel economy strategies for the FC system were ordered starting with the best strategy: air/fuel-PFC, air-PFC, fuel-PFC, and sFF.

•
The percentage of hydrogen economy for an air/fuel-PFC strategy compared to the strategies sFF, air-PFC, and fuel-PFC is 6.60%, 7.53%, and 12.60% of the total hydrogen consumption of these strategies (see Table 2). • FC net power is generated based on the power flow balance (2) and on a PFC-based strategy to operate the battery in charge-sustained mode (see the 3rd plot in Figures 4-8), increasing their lifespan. • OER varies within the safe limits (see Figure 9).
The results obtained for the FC system and battery pack were validated for an FC/ESS/RES HPS with P RES > 0, producing the following findings:

•
From point of view of the hydrogen economy, the same order of the strategies were obtained for an FC/renewable HPS: air/fuel-PFC, air-PFC, fuel-PFC, and sFF.

•
The integration of the FC system into a renewable HPS will increase with 0.7% of the fuel economy of the air/fuel-PFC strategy for the FC/renewable HPS compared to the FC system (see last row of Table 6) due to the FC system operating at lower power when the renewable energy is available. • PFC-based strategies still operate the battery pack in the charge-sustained mode (see the 4th plot in Figures 10-13) even under variable RES power, increasing battery lifespan. • OER still varies within the safe limits (see Figure 15).
Thus, the novelty and contribution of this paper can be summarized as follows: • The use of a PFC-based strategy will establish the FC-system fueling flows so that FC net power compensates the balance of power flows on the DC bus using a battery stack with lower capacity than in other strategies proposed in the literature due to the battery pack operating in charge-sustained mode. The next work will analyze whether only the ultracapacitors pack can dynamically compensate the power flow balance via a bidirectional DC-DC power converter.

•
The maximization of the fuel economy was obtained by using a real-time optimal control of the boost power converter.

•
The operation of FC system under a PFC-based strategy and optimal fuel economy control is done in safe operating conditions, maintaining OER within the safe limits.
However, before implementing the air/fuel-PFC strategy, these findings should be validated by several future studies using different profiles of charging demand and renewable energy.